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MHT-CET 112020 II
General Instructions
■
■
■
■
■
■
■
This question booklet contains 150 Multiple Choice Questions (MCQs).
Section-A: Physics & Chemistry- 50 Questions each and
Section-B: Mathematics - 50 Questions.
Choice and sequence for attempting questions will be as per the convenience of the candidate.
Read each question carefully.
Determine the one correct answer out ofthe four available options given for each question.
Each question with correct response shall be awarded one (1) mark. There shall be no negative marking.
No mark shall be granted for marking two or more answers ofsame question, scratching or overwriting.
Duration ofpaper is 3 Hours.
SECTION-A
PHYSICS
1.
For the same cross-sectional area and for a given
load, the ratio of depressions for the beam of a
square cross-section and circular cross-section is
(a) 3: JC
2.
3.
4.
5.
(b) JC: 3
If three equal masses
(c)l:JC
(d)JC:1
are placed at the three
vertices of an equilateral triangle of side 1Im then
what force acts on a particle of mass 2m placed at
the centroid?
(a) Gm2
(b) 2Gm2 (c) Zero (d) -Gm2
m
6.
A stretched wire 60 cm long is vibrating with its
fundamental frequency of256 Hz. Ifthe length of
the wire is decreased to 15 cm and the tension
remains the same. Then the fundamental
freuqency of the vibration of the wire will be
(a) 1024
(b) 572
(c) 256
(d) 64
A soap film of surface tension 3 x 1o-2 formed in
a rectangular frame cam support a straw as shown
in Fig. If g = 10 ms- 12 , the mass of the straw is
In a reverse biased diode when the applied voltage
changes by 1 V, the current is found to change
by 0.5 µA. The reverse bias resistance of the
(a) 0.006g
diode is
(b) 0.06 g
(a) 2 x 105 w
(b) 2
(c) 200n
(d) 2Q
X
106 W
(c) 0.6g
7.
y 1 = 0.1 cos m.
The phase difference of the velocity ofparticle 1
with respect to the velocity of particle 2 is
JC
(a) 3
(b)
-JC
6
JC
(c) 6
(d)
-JC
3
---+1
Soap
film
\
Straw
(d) 6 g
Two simple harmonic motions are represented
by the equations y 1 = 0.1 sin ( lO0JCt + ; ) and
10cm
A circular disc ofradius R is removed from a bigger
circular disc of radius 2R such that the
circumferences of the discs coincide. The centre
of mass of the new disc is a/R form the centre of
the bigger disc. The value of a is
(a) 1/4
(b) 1/3
(c) 1/2
(d) 1/6
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2020-2
8.
Target MHT-CET
Two sources of equal emf are connected to an
external resistance R. The internal resistance of
the two sources are R 1 and Rz (Rz > R 1). If the
potential difference across the source having
internal resistance R2 is zero, then
(b) R= R 2 x (R 1 + R 2 ) /(R 2 -R 1 )
(c) R= R 1R 2 /(R 2 -R 1)
(d) R= R 1R 2 /(R 1 -R 2 )
9.
10.
A vessel contains oil (density= 0.8 gm/cm3) over
mercury (density = 13.6 gm/ cm 3). A
homogeneous sphere floats with half of its
volume immersed in mercury and the other half
in oil. The density of the material of the sphere in
gm/cm3 is
(a) 3.3
(c) 7.2
(d) 12.8
(b) 6.4
A current ofI ampere flows
in a wire forming a circular arc
ofradius r metres subtending
an angle 0 at the centre as
shown. The magnetic field at
the centre O in tesla is
~tol0
(a)
(c)
11.
12.
13.
4m
I
~LO
(b)
µo I0
Q\
I
I
/
15.
16.
µo 18
4r
2r
A broadcast radio transmitter radiates 12 kW
when percentage of modulation is 50%, then the
unmodulated carrier power is
(d) 12kW
X
(b) II,IV
II,III
(d) I,IV
A beam of electrons is moving with constant
velocity in a region having simultaneous
perpendicular electric and magnetic fields of
strength 20 vm- 1 and 0.5 T respectively at right
angles to the direction of motion of the electrons.
Then the velocity of electrons must be
(a) 8 mis
(b) 20 mis
(c) 40mls
1
(d) -m / s
A particle of mass Mis situated at the centre of a
sphe1ical shell of same mass and radius a . The
a
gravitational potential at a point situated at
2
40
The period ofoscillation of a magnet in a vibration
magnetometer is 2 sec. The period of oscillation
of a magnet whose magnetic moment is four times
that of the first magnet is
(a)
1 sec
(b) 5 sec
(c) 8 sec
17.
Two trains are moving towards each other with
speeds of20mls and 15 mis relative to the ground.
The first train sounds a whistle of frequency 600
Hz. The frequency of the whistle heard by a
passenger in the second train before the train
meets, is (the speed of sound in air is 340 mis)
(a) 600Hz
(b) 585Hz
(c) 645Hz
(d) 666Hz
distance from the centre, will be:
For a particle executing SHM the displacementx
is given by x = A cos rot. Identify the graph which
represents the variation ofpotential energy(P.E.)
as a function of time t and displacementx.
PE
Pc
(c)
(d)
(c) 9.6kW
a
\
2m
(b) 7.15kW
4GM
(d) - - a
(a) I, ill
J0
(a) 5.67kW
a
~b:x ,,
O\
\
(b) - - -
GM
(c)
14.
(a) R= R 2 -R 1
2GM
3GM
a
(a) - - -
(d) 0.5 sec
A cell having an emf i; and internal resistance
r is connected across a variable external
resistance R. As the resistance R is increased,
the plot of potential difference V across R is
given by
(a)
J:···-. ~) tc:.
R
"tI·······
········
(c) V
0
R
R
(d)
v~
0
R
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MHT-CET 2020
18.
2020-3
The transition from the state n = 4 to n = 3 in a
hydrogen like atom results in ultraviolet radiation.
Infrared radiation will be obtained in the transition
from
24.
A rod PQ of mass M and length L is hinged at
end P. The rod is kept horizontal by a massless
string tied to point Q as shown in figure. When
string is cut, the initial angular acceleration of
the rod is
(a) g /L
19.
(b) 2g/L
A light rod of length 2m suspended from the
ceiling horizontally by means of two vertical
wires of equal length. A weight Wis hung from a
light rod as shown in figure.
(c)
2g
3L
p _ _ _ _ _ _ __, Q
_
- - - - L -----,,
3g
2L
Let Q denote the charge on the plate of a
capacitor of capacitance C. The dimensional
(d)
Steel T1
25.
T2
Brass
2
The rod hung by means of a steel wire of crosssectional area A 1 = 0.1 cm2 and brass wire ofcrosssectional areaA 2 = 0.2 cm2 . To have equal stress in
both wires, T/T2 =
(a) 1/3
20.
21.
(b) 1/4
(c) 4/3
(a) 0=60°
(b) 0=120°
(c) 0 = 0°
(d) 0=90°
22.
(a) 6040 A
(b) 4026 A
(c) 5890 A
(d) 7248 A
The least coefficient of friction for an inclined plane
inclined at angle a with horizontal in order that a
solid cylinder will roll down without slipping is
2
(a) -tan a
3
5
(d) -tan a
7
Two balls are projected at an angle 0 and (90° 0) to the horizontal with the same speed. The
ratio of their maximum vertical heights is
23.
(a) 1:1
(b) tan0:l
(c) 1: tan0
(d) tan2 0: 1
(d) [L2M2 T 2 ]
27.
A glass flask is filled up to a mark with 50 cc of
mercury at l 8°C. If the flask and contents are
heated to 38°C, how much mercury will be above
the mark? (a for glass is 9 x 10---6/"Candcoefficient
of real expansion ofmercury is 180 x 1Q---0/ 0 C)
28.
(a) 0.85 cc
(b) 0.46 cc
(c) 0.153cc
(d) 0.05cc
With the increase in ten1perature, the angle ofcontact
decreases
mcreases
remains constant
sometimes increases and sometimes
decreases
A prism has a refracting angle of60°. When placed
in the position ofminimum deviation, it produces
a deviation of 30°. The angle of incidence is
(a) 300
(c) 15°
(d) 60°
(b) 45°
A planet in a distant solar system is 10 times
more massive than the earth and its radius is 10
times smaller. Given that the escape velocity from
the earth's surface is 11 km s- 1 , the escape
velocity from the surface of the planet would be
(a) 1.1 km s-1
(b) 11 km s-1
(c) 110km s-1
(d) O.llkms-1
(a)
(b)
( c)
(d)
29.
2
(b) -tan a
7
(c) tan a
(c) [L2 MT-2 ]
A common emitter amplifier has a voltage gain of
50, an input impedance of lOOQ and an output
impedance of 2000. The power gain of the
amplifier is
(a) 500
(c) 1250 (d) 50
(b) 1000
The width of a slit is 0.012 mm. Monochromatic
light is incident on it. The angular position of
first bright line is 5.2°. The wavelength ofincident
light is [sin 5.2° = 0.0906].
(b) [LMT2]
26.
(d) 1/2
For which angle between two equal vectors A and
B will the magnitude ofthe sum of two vectors be
equal to the magnitude of each vector?
formula for _g__ is
C
(a) [L2 M 2T]
30.
IWWW.JEEBOOKS.INI
2020-4
31.
32.
33.
34.
35.
36.
37.
Target MHT-CET
The fringe width in a Young's double slit
experiment can be increased if we decrease
(a) width of slits
(b) separation of slits
(c) wavelength oflight used
(d) distance between slits and screen
Two radiations of photons energies 1 eV and 2.5
eV, successively illuminate a photosensitive
metallic surface ofwork function 0 .5 eV The ratio
of the maximum speeds ofthe emitted electrons is
(b) 1: 2
(a) 1: 4
(c) 1: 1
(d) 1: 5
An electromagnetic wave going through vacuum
is described by E = E 0sin(kx- rot); B = B 0 sin (kx
- rot). Which of the following equations is true?
(a) E 0k = B 0ro
(b) E 0 ro = B 0k
(c) E 0B 0 = rok
(d) None of these
A galvanometer ofresistance 100 Q gives a full
scale deflection for a current of 10-5 A. To
convert it into a ammeter capable of measuring
upto 1 A, we should connect a resistance of
(b) 10-3 n in parallel
(a) 1 n in parallel
5
(d) 100 Qin series
(c) 10 Qin series
A spherical ball of iron of radius 2 mm is falling
through a column of glycerine. If densities of
glycerine and iron are respectively
1.3 x 103 kg/m3 and 8 x 103 kg/m3 . ri for glycerine
= 0.83 Nm-2 sec, then the terminal velocity is
(a) 0.7 mis
(b) 0.07 mis
(c) 0.007mls
(d) 0.0007mls
A Carnot engine whose low temperature reservoir
is at 7°C has an efficiency of 50%. It is desired to
increase the efficiency to 70%. By how many
degrees should the temperature of the high
temperature reservoir be increased?
(a) 840K (b) 280K (c) 560K (d) 380K
The two blocks, m = 10 kg andM= 50 kg are free
to move as shown. The coefficient of static
friction between the blocks is 0.5 and there is no
friction between Mand the ground. A minimum
horizontal force Fis applied to hold m againstM
that is equal to
F-:J, :J~:oth
77
(a) lO0N (b) 50N
(c) 240N (d) 180N
38.
The pressure on a square plate is measured by
measuring the force on the plate and length of
the sides of the plate by using the formula
P=
~ . Ifthe maximum errors in the measurement
f
of force and length are 6% and 3% respectively,
then the maximum error in the measurement of
pressure 1s
(a) 1%
39.
(b) 2%
(c) 12%
An electron of mass m and charge e initially at
rest gets accelerated by a constant electric field
E. The rate of change of de-Broglie wavelength
of this electron at time t ignoring relativistic
effects is
-h
-eht
(a)
(b)
2
eEt
E
-mh
(c)
40.
41.
-h
(d)
2
eE
eEt
A piano-convex lens is made of material of
refractive index 1.6. The radius of curvature of
the curved surface is 60 cm. The focal length of
the lens is
(a) 50cm
(b) 100cm
(c) 200cm
(d) 400cm
A mass m is revolving in a vertical circle at the
end of a string of length 20 cm. By how much
does the tension of the string at the lowest point
exceed the tension at the topmost point?
(a) 2mg
42.
(b) 4mg
44.
(c) 6mg
(d) 8 mg
Two conducting circular loops ofradii R 1 and R 2
are placed in the same plane with their centres
coinciding. IfR1>>R2 , the mutual inductance M
between them will be directly proportional to
(a) R/ R2
(b) RzlR 1
(c) R/ I R2
43.
(d) 10%
(d) R} ! R1
If x = at + bt2 , where x is the distance travelled
by the body in kilometers while tis the time in
seconds, then the unit of bis
(a) krn/s
(b) krns
(c) km/s 2
(d) kms2
An organ pipe P 1 closed at one end vibrating in
its first overtone and another pipe P 2 open at
both ends vibrating in third overtone are in
resonance with a given tuning fork. The ratio of
the length of P 1 to that of P2 is
(a) 8/3
(b) 3/8
(c) 1/2
(d) 1/3
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MHT-CET 2020
45.
2020-5
If one mole of monoatomic gas ( Y =
with one mole ofdiatomic gas ( Y =
46.
CHEMISTRY
¾) is mixed
f),
51.
the value of
y for the mixture is
(a) absorbs CO2 and increases 0 2 content
(b) 1.50
(a) 1.40
(c) 1.53
(d) 3.07
In a series resonant circuit, having L,C and Ras
its elements, the resonant current is i. The power
dissipated in circuit at resonance is
(b) eliminates moisture
(c) absorbs CO2
( d) produces ozone.
52.
(a) (roL-1 / roC)
(c)
(b) zero
53.
i2 roL
Whereas ro is angular resonant frequency
47.
A U-tube is of non uniform cross-section. The
area of cross-sections of two sides of tube are A
and 2A (see fig.). It contains non-viscous liquid
of mass m. The liquid is displaced slightly and
free to oscillate. Its time period of oscillations is
A
2A
U
m
(a) T=
m
2n✓3pgA
(c) T=2nH£
pgA
48.
(b) 4
54.
2A
···-·--+
[ l:=:j
Y.i · ......Y.g·
:
--
-- -
:-_-_-_-: :
-
(b) T=
2n✓ 2pgA
m
(c) 16
(d) 10- 15 cm
(c) N 2ABI
(b) NABI2
(d) NAB!
Which ofthe following is a bactericidal antibiotic?
(a) Ofloxacin
(b) Tetracycline
(c) Chloramphenicol
(d) Erythromycin
An ideal gas expands against a constant external
pressure of 2.0 atmosphere from 20 litre to 40
litre and absorbs 10 kJ of heat from surrounding.
What is the change in internal energy of the
system?
(given: latm-litre = 101.3 J)
(a) 4052J
(b) 5948J
(c) 14052J
(d) 9940J
In a solution of CuSO4 how much time will be
required to precipitate 2 g copper by 0.5 ampere
current ?
(a) 12157.48 sec
(b) 102 sec
(c) 510 sec
(d) 642 sec
Which of the following compounds will undergo
self aldol condensation in the presence of cold
dilute alkali?
(a) CH 2 =CH-CHO
56.
(b) CH=C-CHO
An element having an atomic radius of 0.14 nm
crystallizes in an fee unit cell. What is the length
(d) 32
A moving coil galvanometer has N number of
turns in a coil of effective area A, it carries a
current I. The magnetic field B is radial. The
torque acting on the coil is
(a) NA 2B 2I
55.
(d) None of these
An a-particle ofenergy 5 MeV is scattered through
180° by a fixed uranium nucleus. The distance of
closest approach is of the order of
(b) 10- 10 cm
(a) 10-12 cm
(c) 10-20 cm
50.
A
From a supply ofidentical capacitors rated 8 rnF,
250V, the minimum number ofcapacitors required
to form a composite 16 rnF, 1000V is
(a) 2
49.
KO2 (potassium super oxide) is used in oxygen
cylinders in space and submarines because it
of a side of the cell ?
57.
(a) 0.56nm
(b) 0.24nm
(c) 0.96nm
(d) 0.4nm
120 g of an ideal gas of molecular weight 40 g
mo1- 1 are confined to a volume of20 Lat 400 K.
Using
R=0.0821 L atm K- 1 mo1- 1, the pressure of the
gas 1s
(a) 4.90atm
(b) 4.92atm
(c) 5.02atm
(d) 4.%atm
IWWW.JEEBOOKS.INI
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58.
Target MHT-CET
Fluorobenzene (C6Hl) can be synthesized in the
laboratory
(a) by direct fluorination ofbenzene with F 2 gas
(b) by reacting bromobenzene with NaF solution
(c) by heating phenol with HF and KF
59.
60.
61.
(d) from aniline by diazotisation followed by
heating the diazonium salt with HBF4
Substance used for the preservation of coloured
fruit juices is
(a) benzene
(b) benzoic acid
(c) phenol
(d) sodium meta bisulphite
Which of the following compounds gives dye
test?
(a) Aniline
(b) Methylamine
(c) Diphenylamine
(d) Ethylamine
The correct statement with regard to H! and H 2
IS
66.
IS
(a) 1
67.
(c) (CH3) 3COH
(d) CH3C8i-O-C8iC~
68.
69.
63.
(c) 759.00torr
(d) 7.60torr
Mark the oxide which is amphoteric in character
64.
(a) CO2
(b) SiO2
(c) SnO2 (d) CaO
The standard EMF for the cell reaction,
O
Cl
I
I
(b) CH 3 -CH 2 -CH-CH 2Cl
I
I
(c) CH3CH2 -C-CH3
I
Cl
(d) CH 3 -CH-CH 2CH 2I
I
Cl
70.
Cinnamic acid, is
(b)
O
Predict the product C obtained in the following
reaction of butyne-1.
I
The reactant (X) in the reaction
(a)
(d) 0.4
~) CH3 -CH 2 -CH 2 -?-H
(d) --0.1 lOV
COOH
(c) 0.2
I
Zn+Cu 2+ ~Cu+Zn 2+ is 1.1 voltat25°C.
The EMF for the cell reaction, when 0.1 M Cu 2+
and 0.1 M Zn 2+ solutions are used, at 25°C is
(a) 1.10V
(b) 0.10V
CH3COONa
(CH3CO)iO
(b) 0.6
HI
18 g of glucose (C 6H 1p 6) is added to 178.2 g of
water. The vapour pressure of water for this
aqueous solution is
(a) 76.00torr
(b) 752.40 torr
(X)
Number of moles ofKMnO4 required to oxidize
one mole ofFe(Cp4) in acidic medium is
CH3CH2 -C = CH + H C l ~ B ~ C
(d) Both H! and tt:2are equally stable
65.
(d) 0
(b) CH3CHOHC8iCH3
(c) H! is more stable than H2
(c) -1.l0V
(c) 3
A substance C 4 H 10O yields on oxidation a
compound, C 4 H 8O which gives an oxime and a
positive iodoform test. The original substance
on treatment with cone. H 2SO4 gives C 4 H8 . The
structure of the compound is
(a) 0.167
(b) H 2 is more stable than H!
(b) 2
(a) CH3C8iC8iC8iOH
(a) Both H! and H 2 do not exist
62.
The brown ring complex is formulated as
[Fe(Hp) 5 NO]SO4 . The oxidation number ofiron
CH O
The vapour pressure of a solvent A is 0.80 atm.
When a non-volatile substance B is added to
this solvent its vapour pressure drops to 0.6 atm.
the mole fraction ofB in the solution is
(a) 0.25
(b) 0.50
(c) 0.75
(d) 0.90
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MHT-CET2020
71.
72.
73.
The electric cookers have a coating that protects
them against fire. The coating is made of
(a) heavy lead
(b) zinc oxide
(c) magnesium oxide
(d) sodium sulphate
Chlorine is liberated when we heat
(b) I<iCr 2O 7 + MnO2
(a) KMnO4 + NaCl
(c) Pb(NO:J2 +MnO2 (d) I<iCrp7 +HCI
Which of the following solutions will have the
maximum lowering ofvapour pressure at 300 K
(a) 1 MCaCl2
74.
75.
76.
(c) Na3 PO4
(d) MgC½
The element which has not yet been reacted with
F2 is
(a) Ar
(b) Xe
(c) Kr
(d) Rn
Which is the best oxidising agent among the
following?
77.
78.
(b) 0
80.
82.
83.
(d) Te
84.
85.
86.
(b) 50kJ 11101- 1
(d) 60 kJ 11101- 1
At anode in the electrolysis of fused NaCl
(b) cJ-isoxidized
(a) Na+isoxidized
(c) Cl is reduced
(d) Na is reduced
Molarity of liquid HCI will be, if density of
solution is 1.17 glee
(b) 32.05
(a) 36.5
(d) 42.10
(c) 18.25
Which of the following bicarbonates does not
exist as solid?
(a) KHCO 3
(b) NaHCO 3
(c) CsHCO3
(d) LiHCO3
P2 O5 is heated with water to give
(a) hypophosphorous acid
(b) phosphorous acid
(c) hypophosphoric acid
(d) orthophosphoric acid
What is the IUPAC name of the compound?
Which of the following is correct for a first order
reaction?
(a) t 112 oca
(b) t112 oc 1/a
(c) t 112 oc a O
( d)
t 112 ex: 1/ a 2
Standard enthalpy and s tandard entropy
changes for the oxidation of ammonia at 298 K
are - 382.64 kJ 11101- 1 and - 145.6 JK- 1 moJ- 1,
respectively. Standard Gibb's energy change for
the same reaction at 298 K is
(a) -22.lkJmoi- 1
79.
(c) Se
A ➔ B, AfI = - 10kJ moJ- 1, Ea(f) = 50 kJ 1110 1- 1, then
Ea ofB ➔ A will be
(a) 40 kJ 1110 1- 1
(c) - 50kJmoJ- 1
(b) 1 MNaCI
(d) 1 M sucrose
(c) 1 M Phenol
Which ofthe following electrolyte will be most
effective in coagulation of negative sol?
(b) K 4 [Fe(CN) 6]
(a) KN03
(a) S
81.
(a) 1, 1 - dimethyl - 1- cyclopentyl methane
(b) 2 - cyclopentyl propane
87.
(b) -339.3 kJ mol-l
(c) -439.3 kJ mol- 1 (d) -523.2 kJ moi- 1
Which of the following polymers do not involve
cross linkages?
(a) Melmac
(b) Bakelite
(d) Vulcanised rubber
(c) Polythene
(a) RCOOK
(d) Neither of them is needed
Electrolytic
oxidation
Br2
(b) RCOO - Ag+
(c) CH 3 CH 3
When a metal is to be extracted from its ore and
the gangue associated with the ore is silica, then
(a) an acidic flux is needed
(b) a basic flux is needed
(c) both acidic and basic fluxes are needed
(c) 1 - (1 - methyl) ethyl cyclopentane
(d) Cumene.
Which one of the following reactions is expected
to readily give a hydrocarbon product in good
yields?
(d) ( CH 3 ) 3 CCI
88.
Cl2
hu
C 2 H5OH
Among the trihalides of nitrogen which one is
most basic ?
(a) NF3
(c) N13
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89.
90.
91.
92.
93.
94.
Target MHT-CET
Omeoprazole and lansoprazole are used as (b) antiallergic
(a) antifertility
(c) antibiotic
(d) antacid
Hydrolysis of sucrose is called
(b) saponification
(a) hydration
(c) esterification
(d) inversion
van Arkel method of purification of metals
involves converting the metal to a
(a) volatile stable compound
(b) volatile unstable compound
(c) non volatile stable compound
(d) None of the above
When SO2 is passed through acidified solution
of potassium dichromate, then chromium
sulphate is formed. The change in valency of
chromium is
(a) +4to+2
(b) +5 to+3
(d) +7 to+2
(c) +6to+3
Which of the following polymer is used for
manufacturing of buckets, dustbins, pipes etc?
(a) Low density polythene
(b) High density polythene
(c) Teflon
(d) Polyacrylonitrile
What is X in the following reaction ?
+
(b) CH 3OH,CH 3O- Na
(c) H 2 O / H 2 SO 4 followed by CH 3 OH
(d) CH 3 MgBr I ether followed by H 3 0 +
95.
Zn(Hg)/HCI
(B)
In the above reaction, product (B) is:
CY
(b)v
C•l
(c)V
~OH
(d)
V
The compounds [PtClz(NH 3 ) 4 ]Br 2 and
[PtBr/NH3) 4]Cl2 constitutes a pair of
(a) coordination isomers
(b) linkage isomers
(c) ionization isomers
(d) optical isomers
97. Which of the following factors may be regarded
as the main cause oflanthanoid contraction?
(a) Greater shielding of 5d electrons by 4f
electrons
(b) Poorer shielding of 5d electrons by 4f
electrons
(c) Effective shielding of one of 4felectrons by
another in the subshell
(d) Poor shielding of one of 4/ electron by
another in the subshell
98. The polymer used in making synthetic hair wigs is
made up of
(a) CH2 =CHC1
(b) CH2 = CHCOOCH3
(c) C6H5CH=CH2
(d) C~=CH - CH=C~
99. Which of the following is called Wilkinson's
catalyst?
(b) TiC14 + (C2H5) 3 Al
(a) [(Phl)3 RhCl]
(c) (C2H5\ Pb
( d) [PtC12 (NH3) 2 ]
100. One mole of an ideal gas is allowed to expand
reversibly and adiabatically from a temperature
of27°C. If the work done during the process is
3 kJ, the final temperature will be equal to
(CV= 20 JK-1)
(a) 150K
(b) lOOK
(d) 295K
(c) 26.85K
96.
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MHT-CET 2020
2020-9
SECTION-B
MATHEMATICS
1.
2.
3.
4.
In an entrance test, there are multiple choice
questions. There are four possible answers to
each question, of which one is con-ect. The
probability that a student knows the answer to a
question is 90%. Ifhe gets the correct answer to
a question, then the probability that he was
guessmg 1s
2
1
1
1
(c) 37
(a) 40
(d) 43
(b) 39
Ifn / 2 <x< n, then
dx=
fx✓l+cos2x
2
10.
The value of --;::===-dx 1s equal to
✓1-sin 2x
(a) ✓sin 2x + c
12.
➔R
be a function defined by
f(x) = 4x -7. Then
(a) f is one-one -into (b) fis many-one - into
(c) f is many-one onto (d) f is bijective
3
5.
Three vertices of a parallelogram ABCD are
A ( 3, -1 , 2), B (1, 2, -4) and C (-1 , 1, 2). The
coordinates of fourth vertex D are
(a) (1, 1, 1)
(b) (1, -2, 8)
(c) (2,-2,6)
(d) (1, 0, 2)
11.
(a) cos x + x sin x + C (b) -cos x - x sin x + C
(c) sin x + x cos x + C (d) x sin x - cos x + C
A rectangle with one side lying along the x-axis
is to be inscribed in the closed region of the xy
plane bounded by the lines y = 0, y = 3x and y =
30 - 2x. The largest area of such a rectangle is
(a) 135/8 (b) 45
(c) 135/2 (d) 90
If f: R
9.
- ( (- p) A
13.
q) is equal to
(a) pv(- q)
(b) p v q
(C) p /\ (- q)
(d) - p /\ - q
14.
2
6.
With the usual notation
J( [x2]-[x]2 )dx
1s
1
equal to
2 -✓
3
(a) 4+ ✓
7.
2 +✓
3
(b) 4- ✓
15.
(c) 4- ✓
(d) none of these
2- ✓
3
The general solution of
x(l + y2) 112 dx + y(l + x 2) 112 dy = 0 is
1
(a) cos- x+cos- y=C
(b) x2+y2=(l+x2)112+(l+y2)112+C
(d) tan- l x - tan - l y = C
8.
~ 6],
If A=[~
then A 2008 is equal to
1 0 0
(a) A
(b) A- 1
(c) 13
(d) 0
sinx+cosx.
(b) ✓cos 2x + c
(c) ±(sin x-cos x) +c
(d) ±log(sin x-cosx)+c
The equation of the plane containing the line
x+l
y -3
z +2
.
.
- - = - - = - - and the pomt (0, 7, - 7), 1s
3
2
1
(a) x+y+z = 2
(b) x+y+z = 3
(c) x+y+z=0
(d) None of these
The co-ordinates of the foot of perpendicular
from the point A (1 , 1, 1) on the line joining the
points B (1 , 4, 6) and C (5, 4, 4) are
(a) (3,4,5)
(b) (4, 5,3)
(c) (3,-4, 5)
(d) (-3, -4, 5)
(p /\ - q) /\ (- p /\ q) is
(a) A tautology
(b) Acontradiction
(c) Both a tautology and a contradiction
(d) Neither a tautology nor a contradiction
Two finite sets have m and n elements. The total
number of subsets ofthe first set is 56 more than
the total number of subsets of the second set.
Then:
(b) m=6, n=3
(a) m=3, n=6
(c) m = 5,n = 6
(d) None of these
Let f be the function defined by
f(x) ={x 2 _;; :~1 1-1' x
1
(c) (l+x2)112 +(l+y2)1'2 =C
f
16.
*1
X =1
1/2,
(a) The function is continuous for all values ofx
(b) The function is continuous only for x > 1
(c) The function is continuous at x = 1
(d) The function is not continuous at x = 1
The distance ofthepoint(l, -2, 3) from the plane
y
X
x - y + z = 5 measured parallel to the line - = z -1
2
3
_
6
(a) 1
(c) 4
lS
(b) 2
(d) None of these
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2020-10
17.
Target MHT-CET
X +sin X
.
IS
f l+cosx dx
(a) xtan
equal to:
X
2 +c
(b) cot
(c) log(l +cosx)+C
18.
26.
X
2 +c
8 . Then [ a b c] in terms of8 is equal to :
(d) log(x+sin x)+C
(a) (l+cos0)~
The maximum value of z = 6x + 8y subject to
constraints 2x + y::; 30, x + 2y ::; 24 and x 2 0,
y2 0 is
(d) 240
(a) ~
(c) 96
(b) 120
(b) (1 + cos 0) ✓l - 2 cos 20
27.
rr / 2
19.
-
Let a, b and c be non-coplanar unit vectors
equally inclined to one another at an acute angle
J xsin(TC [x] - x)dx is equal to :
(c) (I-cos 8) ✓1 + 2cos 8
(d) None of these
General solution of the equation
sin 2x-sin 4x +sin 6x = 0 is
rr / 3
20.
l
TC
2
6
nTC
(a) -
✓
3
(a) -+-
TC
(b) l- - + -
1 TC
(c) - - - -
(d) -
2
✓
3
21.
For non zero, non collinear vectors p and
O
(b) 2( p
X
8
(a) -
3
29.
q)
30.
24.
(a) 4000n / 3
(b) 400n / 3
(a)
31.
3
x+ y -5✓
2 =0
(1;' 0)
3
2 =0
(b) x+ y-3✓
(b)
(c) 4000n / ✓
(d) None of these
3 cm
The equation of the plane through the line
x +y+z+ 3 =0 =2x - y +3z+ l and parallel to the
. X
y
Z .
Ime - = - = - IS
l
2
3'
(a) x-5y+3z =7
(b) x - Sy+ 3z = - 7
(c) x+5y+3z =7
(d) x + Sy+ 3z = - 7
cs3 ' 0)
(c) (- 7, 0)
(d) None of these
Ifx
1
E
R - {0}, then tan-
[P
+P)
P -P
1
TC
1
(b) - + - cos - (x2)
2
cm 3
3
25.
3
(c) 2x+2y-3✓
2=0 (d) 2x +2y-5✓
2= 0
A ray of light coming from the point (1 , 2) is
(b) /(8)::; 0 \/ 0 ER
(d) /(8)::; 1 \/ 8 ER
The maximum value of z = 5x + 2y, subject to the
constraintsx+y ::;7, x + 2y::; 10, x, y2: 0 is
(d) 70
(b) 26
(a) 10
(c) 35
The volume of the greatest cylinder which can
be inscribed in a cone of height 30 cm and semivertical angle 30° is
cm3
5
(d) -
reflected a t a point A on the x-axis and then
passes through the point (5, 3). The co-ordinates
of the point A is
(c) f (0) 2 1 \/ 0 ER
23.
4
(c) -
The locus of a point that is equidistant from the
(a)
(d) ( p x q)
(c) ( x p)
Let f (8) = sin 8 (sin 8 + sin 38) then
(a) /(8) 2 0 \/0 ER
2
(b) -
lines x+ y -2✓
2 =0 and x+ y - ✓
2 =0 is
q,
q
22.
2
the length of the semi-major axis is
the value of [ipq]i + [Jpq]]+[k pq]k is
(a)
4
A focus ofan ellipse is at the origin. Th e directrix
is the line x = 4 and the eccentricity is _!_. Then
(d) None of these
6
TC
(b) nTC or nTC ±3
TC
(d) nTC or 2nTC± -
6
4
28.
tan 8 + tan48 + tan 78 = tan 8tan 48tan 78
nTC
= nTC
(b) 8 = (a) 8
4
12
= nTC
TC
or nTC± -
TC
(c) nTC±-
6
. TC
- 1- 2 6
6
2
The general solution of the equation
(c) 8
4
2
1
1
(c) - + - cos - (x2) (d) None of these
4
2
dy
2
If y = x x , then is equal to
dx
7t
32
.
(a) (2 In x)
(b) (2 ln x+ l)
2
(c) (In In x + l)xx
(d) None of these
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33.
2020-11
In a triangle ABC, LC = 90°, then
equal to:
(a) sin (A+ B)
35.
36.
(b) sin(A - B)
(a)
y
=
(c)
2
2
(b)
6
(c)
40.
41.
(a) 49or50
(b) 50or51
(c) 51
(d) None of these
The fourth term of an A.P. is tlu-ee times of the
first term and the seventh term exceeds the twice
of the third term by one, then the common
difference of the progression is
46.
10
(b) 3
(b) 13/6
(a) 13/3
(c) 11/6
(d) 11/3
If the curves ay + x 2 = 7 and x 3 = y cut
orthogonally at (1 , 1), then the value of a is.
(a) 5
(b) 6
(c) 7
(d) 8
The value of cos (2cos- 1 x + sin - l x) atx =
2
1
(a) 3
47.
(b) 3
(c) - p A q
(d) - p A - q
2
(c)
3
✓
3
(d)
Fc),where c is a positive
(b) order 2
(d) degree 4
1
48.
If f(x) = -- , the number of points of
1-x
discontinuityoff{f[f(x)]} is:
(a) 2
(b) 1
(c) 0
(d) infinite
49.
If x=a(cost+tsint) and y =a(sint -t cost),
d2
then ---1:.. is
dx 2
½is
(a) sec 3 I
sec 3 t
(c)
50.
(b) p A - q
(d) - 1
2
2
The differential equation representing the family
parameter, is of
(a) order3
(c) degree 3
(a) - - 5
5
Which of the following is logically equivalent to
(a) p A q
3
x 2 -3y 2 = 2x+8 is
✓
6
r;
(d) None
(b) -2...;6 (c) -
- (- p ⇒ q)
(c)
The eccentricity of the hyperbola
of curves y2 = 2c (x +
If the line passing through P(l , 2) making an
angle with the x-axis in the positive direction
meets the pair of lines x 2 + 4xy + y 2 at A and B,
2✓
6
A fair coin is tossed 99 times. IfX is the number
oftimes head occurs, P(X = r) is maximum when r
IS
7
(d) 10
thenPA.PB =
39.
44.
10
2
38.
(c) y=x tan - 1 1og(e / x)
(d) y = e l+tan(y/x)
~ andconditionalprobabilityofAgiven
events A or B happen equals
1
3
1
(a)
(a) y= tan - 1 log(e / x)
(b) y= el+cot (y/ x)
(a) 2
.!.. . The probability that exactly one of the
~J is given by ~ - cos 2( ~ J,then
the equation of the curve is:
=-½(x- ✓3)
(d) None of these
Let A, B be two events such that the probability
Bis
43.
y =I x-21, x = l, x = 3 and the x-axis is
(b) 2
(c) 3
(d) 1
Ifthe slope of the tangent at (x, y) to a curve passing
45.
y+ i=-½(x- ✓3)
ofAis
The area of the region bounded by the curves
tlu-ough ( 1,
-½(x- ✓3)
(b) y -~
42.
(d) sin -A-BJ
( 2
The internal angles of a convex polygon are
inA.P. The smallest angle is 120° and the common
difference is 5°. The number to sides of the
polygon is
(a) 8
(c) 10
(b) 9
(d) 16
In a binomial distribution n = 5, P(X= 1) = 0.4096
and P (X = 2) = 0.2048, then the mean of the
distribution is equal to
(a) 1
(b) 1.5
(c) 2
(d) 2.5
The equation of tangent to the curve
,,;3 1·s
. - 1 2x
y =sm
- - at x=-v;;
1 +x
37.
a 2 + b2
1s
(a) 4
(c) cos (A + B)
34.
a2-b2
at
3
(b) atsec t
?
(d) sec- t
The number of solutions of equation
x 2 - x 3 = 1, - X J + 2 x 3 = 2, x 1 - 2x 2 = 3 is
(a) zero
(b) one
(c) two
(d) infinite
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11111
ANSWER
KEYS
SOLUTIONS
&
~
lll-.....;.;;;;;~~=---=---==------=----=--=-=-=-..:...;...;;........•IIIIIII
(MHT-CET 2020)
Answer KEYS
1
3
4
5
(a)
(c)
(b)
(b)
(a)
51
52
53
54
55
1
2
2
3
4
5
14
15
(c)
(d)
(a)
(a)
(c)
16
17
18
19
20
(a)
(b)
(d)
(d)
(b)
(d)
(b)
(d)
(b)
(a)
61
62
63
64
65
(c)
(b)
(c)
(a)
(b)
66
67
68
69
70
(a)
(b)
(b)
(c)
(a)
(c)
(c)
(c)
(b)
(d)
11
(c)
(a)
(b)
(b)
(d)
16
17
18
19
20
(a)
(a)
(b)
(b)
(b)
8
9
10
(c)
(b)
(c)
(c)
(a)
(a)
(a)
(b)
(a)
(d)
56
57
58
59
60
(c)
(b)
6
6
7
7
8
9
(c)
(d)
(a)
10
11
12
13
12
13
14
15
SECTION-A
PHYSICS
21 (d) 26 (c) 31
22 (c) 27 (c) 32
23 (d) 28 (a) 33
24 (d) 29 (b) 34
25 (c) 30 (c) 35
CHEMISTRY
71 (c) 76 (b) 81
72 (d) 77 (c) 82
73 (a) 78 (b) 83
74 (d) 79 (c) 84
75 (a) 80 (b) 85
SECTION-B
MATHE MATICS
21 (d) 26 (c) 31
22 (a) 27 (a) 32
23 (c) 28 (a) 33
24 (a) 29 (c) 34
25 (a) 30 (a) 35
(b)
(b)
(a)
(b)
(b)
36
37
38
39
40
(d)
(c)
(c)
(a)
(b)
(d)
(b)
(b)
(d)
(d)
86
87
88
89
90
(c)
(a)
(c)
(d)
(d)
(c)
(d)
(b)
(b)
(a)
36
37
38
39
40
(b)
(c)
(a)
(b)
(a)
41
42
43
44
45
(c)
(d)
(c)
(b)
(b)
46
47
48
49
50
(d)
(a)
(d)
(a)
(d)
91
93
94
95
(a)
(c)
(b)
(a)
(b)
96
97
98
99
100
(c)
(b)
(a)
(a)
(a)
41
42
43
44
45
(d)
(d)
(c)
(a)
(a)
46
47
48
49
50
(c)
(c)
(a)
(c)
(a)
92
SECTION-A
PHYSICS
1.
3
O _W£
1
wi
8 = - - , where W = load, £ = length of
3Y I
beam and J is geometrica l moment of inertia for
rectangular beam ,
(a)
I
bd 3
where b = breadth and d = depth
12
-
X 12
3Y b 4
c3
Y b4
(for sq. cross-section)
Wi
4W £3
and 82 = - - - - = - - 3Y(nr4 I 4) 3Y(nr4 )
=-
(for circular cross-section)
Now
For square beam b = d
~ ( n; J
4
Foca beam ofo,cularn-oss-section, / 2
_ 4W
-
81
3nr
4
~ =~
4
3
3nr
(nr2)2 - n
(": b 2 = nr2 i.e. , they h ave same cross-sectional
area)
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MHT-CET 2020
2.
2020-13
7.
(c)
(b) Let the mass per unit area be e r @
2R
T hen the mass of
the complete disc
R
= cr[n(2R)2] = 4ncrR2
The mass of the removed disc = cr(nR2) = ncrR2
Let u s consider the above situation to be a
complete disc of radius 2R on which a disc of
radius R of negative mass is superimposed. Let
0 be the origin. Then the above figure can be
redrawn keeping in mind the concept of centre of
mass as:
z
F
_ Gm(2m)
1
GA -
FGB =
~
J
Gm(2m)
•
•
- - - ( -i cos 30° - j
Fae=
1
sin 30°)
4ncrR 2 ~
•
Gm(2m) •
(icos30°-J sin30°)
1
Resultant force on (2m) is FR
2
X
= 2Gm 2 }+2Gnii(-µfs30°+ ~ )
X
c.m
2
+ 2Gm ](-sin30° -sin 30°)
X
2
= 2Gm }.2Gm
2
J(-;t x~)
= 2Gm 2 ]-2Gm 2}
3.
4ncrR 2 -ncrR 2
(c)
=0 .
c.m
-ncrR 2 x R
3ncrR2
= -- - -
R
3
1
3
=- - ⇒ a=-
2s
I = - -- R+R1 +R 2
(b) Reverse resistance
l
= -=
~I
4.
8.
2
= (4ncrR )xo+(-ncrR )R
c.m
= FGA + FGB + FGC
•
ncrR 2
0
•
-6
= 2x 106 n
0.5 x l0
v 1 = dyl =0.l x l001t cos( 1001tt+2:)
dt
3
(b)
R
v2
= dy 2
Pot. difference across second cell
=-O. l1t sin1tt=O.l1tcos( m+2:)
dt
2
= V=s-IR 2 =0
.
1t 1t 21t-31t
1t
: . Phasediff. = cj>1 -cj> 2 = - - - = - =- 3 2
6
6
5.
(a) L0 =60cm
v=2~J!
2s
.R2 = O
R+R 1 +R 2
R+R 1 +R 2 -2R 2 =0
R+R 1 -R 2 = 0
R=R 2 -R 1
E
v 0 = 256Hz.
1
v oc L
9.
=
(c)
------------------------------------------------------------
:=:=:: 011 ::3::=:=:=:=:=:=:=:=:=:=:=3::=:=:=3::=:=:=:=:=:=
-------------
6.
10
10 = 2 x 3 x 10 - 2 x 100
orm = 6 x 1Q-4kg = 6 x l 0-4x 103 g = 0.6g
(c)
m
x
:::::: Mercury f:::::::::::::::::::::::::::::::3:::::::f::::::::::::
------------------------------As the sphere floats in the liquid. Therefore its
weight will be equal to the upthrust force on it
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Weight of sphere =
i3 1tR3pg
Potential difference across R ,
... (i)
V = IR = ( - E
R+r
Upthrust due to oil and mercury
2 3
2 3
=31tR XCY011g+3 1tR CYHg g
... (ii)
4
2
3
3
2
3
B = µol x ~ = µo 10
2r 2n 4m
10.
(a)
11.
(c) pc =
18.
(d)
(d)
19.
- =-=-
12
pt 2 =
=~=9.6kW
1+ ma
( 0.5)2
1.25
2
l+ - 2-
T2
(b)
16.
=
355
v ' = 600(
) 666Hz
320
(a) Potential at the given point = Potential at
the point due to the shell + Potential due to the
particle
GM 2GM
3GM
a
a
a
(a) In x = A cos rot, the particle starts oscillating
from extreme position. So at t = 0, its potential
energy 1s maximum.
(c) The electron moves with constant velocity
without deflection. Hence, force due to magnetic
field is equal and opposite to force due to electric
field.
E
20
qvB = qE ⇒ v = - =-=40 mis
B 0.5
(a)
IA+ B I=
T = 2•
J;B
✓A 2 +B 2 +2AB cos l20°
-
I
✓A2 +B2 +tAB (1) ( cosl20° = -½)
=N
21.
= ✓A 2 +B2 -A(A)
=B (: . A = B)
(d) It is a one of Fraunhoffer diffraction from
single slit. so for bright fringe where a is the width
of slit.
. 0 =(2n+l) -A.
asm
2
5
"- = 2asin8 = 2 x l.2x10- x 0.0906 = 7248A_
2n+l
2 x l+l
F mg sin a
22. (c) µ=-=~--=tana
R mgcosa
2 2
H1
23. (d)
= 2 u 2sin 0 / 2g -_ tan 2 8
H 2 u sin (90° - 0) / 2g
24.
r=c_l
1 -.!.[2n
l 4MBH) - 2 ~CM¾)
T'-2n (
(d)
p ....._ ___,.._.......,_,. Q
L/2
3
angular acceleration a = g
2L
1
= - x 2 = 1 second.
2
17.
2
(8 = 120°)
~
15.
A2
v'=v(v+vn)
Here, v = 600 Hz, v D = 15 mis
V = 20 mis, v = 340 m/s
5
14.
also wavelength of emitted
T,
T
(d) For stress to be equal, - 1 = ---1...
Ai
A2
Ii Ai 1
V-Vs
13.
"-IR > "-uv
. . ~
1
radiation /1, oc - .
~E
20.
12.
r
R
1+ -
When R = 0, V = 0
R = oo, V = E
Equating (i) and (ii)
-nR pg =-nR 0.8g+-nR +13 .6g
3
3
3
⇒ 2p = 0.8+ 13.6 = 14.4 ⇒ p = 7.2
)R=-E
(b) Current in the circuit,
t
I = -R+r
2
25.
We know that _g___ is energy of capacitor,
2C
so it rep resent th e dimension of en ergy
(c)
= [ML2T- 2].
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MHT-CET 2020
26.
2020-15
=
ri-
VZ Il
100
Ri
= - • - = 50 x 50x- = 1250
2
200
vl Ro
(c) Due to volume expansion of both mercury
and flask, the change in volume of mercury
relative to flask is given by
ti V = Vo [ yL
yg ] ti0 = V [ y L - 3ag] ti0
= 50 [ 180 x 10-6 - 3 x9 x l0-6] (38 - 18)
=0.153cc
28. (a) With the increase in temperature, the surface
tension ofliquid decreases and angle of contact
also decreases.
29_ (b) i = A+ 8m = 60 + 30 = 450
2
2
T2
7i
7i
~ = ~ = 2_
100
100
2
Tl= 2 x T2 = 2 x 280 = 560 K
New efficiency, ri ' = 70%
Tz = 1- ' = l-_2Q_= 30 =2_
7i
-
100
T]
100
10
T '= _!Q x280 = 28 00 =933.3K
3
1
37.
3
Increase in the temperature of high temp.
reservoir= 933.3-560= 373.3 K =380K
(c) As m would slip in vertically downward
direction, then
mg = µN
⇒
vT
(c)
Tz
1-- ⇒ -=l-ri
= 1-
{wM;
30.
(d) T 2 =7°C=(7+273)=280K
Vo lo
Va-lo=---
Vi
27.
36.
(c) Power gain= voltage gain x current gain
N =mg= lOO = 200 Newton
µ
0.5
Same normal force would accelerated M,
~
v~
thus
aM
200
2
= - = 4m/s
50
Taking m +Mas system
F=(m+ M)4= 240N
38.
(c)
tiP
-
P
tiF
ti£
£
x l00=- x l00+2- x l00
F
=6%+2x 3%
32.
(b) According to Einsten ' s photoelectric effect,
39.
the K.E. of the radiated electrons
K.Emax =E-W
1
mv/=(l-0.5) eV=0.5 eV
2
fo.s _
Vl _
33.
34.
m
1 _ 1
d"A
40.
S = ...JI....JL =
I-lg
10- 5
'
x lO0
1-10-5
g
'
'
_!_ = (µ _
f
.
3
f
= 10- Q in parallel
2
(b) Terminal velocity v = 2 r (p - Po )g
, 0
9ri
2 x(2x l0-3 ) 2 x(8 -1.3) x 10 3 x9.8
9 x 0.83
1)
-h
(b) R 1 = 60cm, R2 = cc , µ = 1.6
(b) Here R =lO0Q· I =10- 5 AI=lAS=?
g
h (
dt = eE -? = eE t 2
2n
E
(a) - 0 = c- also k = -and ro= 2nv
"A
B0
These relation gives E 0k = B 0 ro
I R
35.
h
= h
A =}!__=
mv m(eEt I m) eEt
Rate of change of de-Broglie wavelength
V2 - ✓4 - 2
'
m
de-Broglie wavelength,
mv2 2 =(2.5-0.5) eV=2 eV
V2 -
eE
Here, u = 0; a = - ; v = ?; t = t
eE
v=u+at=0+-t
2
1
(a)
41.
(c)
by
l)(-1 __l_)
= (1. 6 -
R1
R2
1)(610 ) ⇒ f = 100 cm.
Thetension T 1 atthetopmostpointisgiven
mv 2
T1 =~-mg
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Target MHT-CET
Centrifugal force acting outward while weight
acting downward.
The tension T 2 at the lowest point
Tz
mv 2
= - - 2 +mg
20
Centrifugal force and weight (both) acting
downward
_mv 22 -mv 12
T2 - T1 20
+ 2 mg
42.
48.
n
49.
43.
(c)
44.
(b)
45.
(b)
Energy, E = 5 x 106 x 1.6 x 10- 19 J
9 X 109
.
5 X 10
y 2 -l
2
1
1
Y -1
~-1
3
2__1
5
51.
52.
--=--+-3
2·
At resonance roL= 1/roC
and i = E/R , So power dissipated in circuit is
P=i2R
(a) Suppose the liquid in left side limb is
displaced slightly by y , the liquid in right limb
will increase by y/2.
The restoring force
F = - PA
(d)
= -pg(3;) x 2A
53.
54.
55.
= 3pgA(-y).
F
a = -=3pgA(-y) / m
X
1.6 X 10-!
⇒ r = 5.2 x 10- m = 5.3 x 10-12 cm.
(d) 't = MB sin 0 ⇒ 'max = NiAB, [0 = 90°]
CHEMISTRY
I
y 1 -l
(92 X 1.6 X 10- 19 )(2 X 1.6 X 10-]9 )
14
50.
3 x ~ = 4 x ~ or ~ = 3v x _3_ =
4/c
2/o
4 4v 8
!0
n1 + n2 = _::L_ + ___:2_
y -1
X
.. r o = - - - ~6- - - - - ~
---9
y= -
47.
No. of capacitor = 8 x 4 = 32
Distance of closest approach
Ze(2e)
ro =
2
4ns 0
)
[x] = [bt2]. Hence [b] = [x/t2] =km/s2
or
46.
(a)
8
(½mv
vf = v~ -2gh or v~ -vf = 2g(40) = 80g
80mg
T2 -T1 =--+2mg=6mg
20
(d) Mutual inductance between two coil in the
same plane with their centers coinciding is given
by
M =.&_(2n2R}N1N2 ]henry.
4n
R1
(d) Let ' n' suchcapacitorsareinseriesandsuch
' m ' such branch are in parallel.
250 x n=1000
:. n=4
... (i)
8
16xn
Also - x m = 16 ⇒ m = - - = 8 ... (ii)
56.
4KO2 + 2 CO2 ➔ 2 KzCO 3 + 302 .
KO2 is used as an oxidising agent. It is used as air
purifier in space capsules. Submarines and
breathing masks as it produces oxygen and
remove carbon dioxide.
(a) Bactericidal are the drugs that kills bacteria.
Ofloxacin works by stopping the growth of
bacteria. This antibiotic treats only bacterial
infections.
(b) .6.U = q + w
=l Ox 1000 - 2 x (20) x 101.3 = 5948 J
(a)
m= E x ixt_ = 31.75 x .5xt,
2
96500 '
96500
t=l2157.48sec.
(d) Aldol condensation is given by only those
aldehydes or ketones which have a-hydrogen
atom on a saturated carbon; a-H present on
unsaturated carbon atom cannot be easily
removed by a base.
(d) For afcc unit cell
(a)
m
✓
la
r=--
a=
. wit
. h, a
0 n companng
OJ=
✓ 3 pgA
m
-
= -OJ 2y
and T
=
57.
(b)
, we get
2n✓
m
3pgA
or
4
4r
✓
2
~
= 2-v2 x 0.14 = 0.39 ::::; 0.4nm.
PV=RT, PV=~RT,
M
120
x .082l x 400
20P=
40
P = 4.92 atm
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MHT-CET 2020
58.
66.
(d)
6
Ntc12
_ _N
_ a_ N_o-=2'-+_H_c_1----+
0-5° diazotisation
6
67
1
(- H 2o)
:?'N;BIF-4__6_-----46FI
59.
60.
61.
67.
-....."
(Balz-Sch1emann
reaction)
.......
..._"
+ BF3+ N2
(b) Benzoic acid is used as preservative as
sodium benzoate.
(a) Only l O aromatic amines undergo coupling
reactions to form a dye.
1
1
B.O. = (1- 0) =
(c) H; : crls1
H2 :crls2cr* Isl
2
2
1
1
68.
K 2SO 4 + 2MnSO 4 +3H 2O+
2Fe(C 2 0 4 )+3H 2 S0 4 +3[0]~
Fe 2 (SO 4 )] +2CO2 +3H 2O
0 required for 1 mol. ofFe(C 2O 4) is 1.5, 50 are
obtained from 2 moles ofKMnO4
2
.·. 1.5 [O] will be obtained from = -5 x 1.5 = 0.6
69.
moles ofKMnO4 .
(c) This reaction occurs according to
Markownikoff's rule which states that when an
unsymmetrical alkene undergo hydrohalogenation, the negative part goes to that C-atom
which contain lesser no. ofH-atom.
CH3-CH 2 -C =CH+HC1~
CH 3 -CH 2 - C = CH2
PH 2o = Mole fraction x total pressure
I
Cl
= ~ x760
10
= 752.4Torr
63.
64.
65.
HI
CO2, SiO2 are acidic, CaO is basic and Sn 0 2
is amphoteric.
(a) Since concentration of ions is the same
(c)
hence Ecell = E~ell
(b) Benzaldehyde forms cinnamic acid as
follows.
CHO
@+
(CIJ,CO), O
5[0]
nascent oxygen
B.O. = 2(2-1) = 2
equal but H! is more stable than H 2 as in the
latter, one electron is present in the anti bonding
(er* 1s) orbital of higher energy.
18
= 0. 1
(b) Moles of glucose = 180
178 2
Moles of water=
· = 9.9
18
Total moles=O.l +9.9 = 10
C 4 H 8 O (R-COCH3)
Thus C4Hg0 should be CH3C8iCOC~, hence
C 4H 10O should be CH3C8iCHOHCH3
(b) The required equation is
2KMnO 4 +3H2SO4 ~
Even though the bond order of H; and H 2 are
62.
(a) [Fe(1½O)5NO] SO4
Let O.N. ofFe bexthen,
1 x (\'.) + 5 x (0) + 1 x (+l)+l x (- 2) = 0
x =+l
(b)
Oxidation
C 4 H 8 C one . H2S04 C4 H 100 ---
CH,cooN';
70.
71.
72.
73.
74.
75.
~CH = ~H.COOH
@
C innamic acid
76.
77.
0.80- 0.6
----=xB; XB =0.25
0.80
(c) MgO being high melting does not catch fire
and hence protects the cooker against fire.
(a)
K 2Cr2O 7 + conc.HCl ➔ Cl 2
(a) Maximum lowering of vapour pressure will
be given by the substance which give maximum
number of particles in solution.
(d) Positive charge t; coagulating power t
so, MgC12 will be most effective.
(a) No compound ofAr has yet been reported
withF2.
(b) Oxygen being more electronegative, will be
best oxidising agent among given options.
(c) t 112 is independent of initial concentration.
(d)
tl/2
cc ao.
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78.
(b)
=-382.64+ (298 x l45.6x10-
3
)
1
79.
80.
81.
= -339.3 kJ mol(c) Polythene is a linear polymer.
(b) Since silica is acidic impurity the flux must
be basic.
CaO + SiO 2 ➔ CaSiO 3
(d} A ~ B, t1H = - 10 kJ mol- 1
It is an exothermic reaction,
(Lill)
= 50-(-10) = 60kJ
(b) c1- is oxidised to Cl2 at anode.
(b) Density= 1.17 g/cc(Given)
Ea(b) = Ea(f) -
82.
83.
As d
Volatile
stable compound
= Mass
Volume
Volume = lee
.-. Mass = d = 1.1 7g
.
No. of moles
Mo 1anty = - - - - - Volume in litre
84.
85.
(d) Both drugs are used as antacids.
(d) Since sucrose is dextrorotatory while
hydrolysis product of sucrose, having equimolar
mixture of glucose and fructose, is laevorotatory.
Hence the hydrolysed product of sucrose is
known as invert sugar and the hydrolysis of
sucrose is known as inversion.
91. (a) This method is veryuseful for removing all
the oxygen and nitrogen present in the from of
impurity in certain metals like Zr & Ti.
Ti+ 212 523K
Til4
1700K
Ti + 212
89.
90.
t1G = AfI - T t1S
1.17 X 1000
36.5 x l
1170
= _ =32.05M
36 5
(d) LiHCO 3 is unstable and exists only in
solution.
(d) P2O5 have great affinity for water, so the
final product will be orthophosphoric acid.
P4O10
2H20
4HPO3
93.
94.
K 2SO 4 +Cr2 (SO 4 )3 +3SO 3 +4H 2O
O.N.of chrorninum changes from +6 to + 3
(b) High density polythene is used for
manufacturing of buckets, dustbins, pipes etc.
0
(a) / ~ \ / C H3
CH3OH
~
CH3
orthophosphoric
acid
86.
(b) ~-keto acid ~
l
96.
Pyrophosphoric
acid
(c) The cyclic portion contains more C-atoms
than acyclic portion. Hence it is derivative of
cyclopentane
2
1
CH 6CH
3
1-(1-methy l)ethyl
cyclopentane
87.
(a)
2RCOOK
Electrolytic
oxidation
2RCOO- + 2K+
Anode
Cathode
At anode
2RCoo· ➔ R - R +2CO2
2K+ + 2e- ➔ 2K
2K+H2O ➔ 2KOH+H2
(c) The lesser the electronegativity of halogen
in NX3 the more is the basic character. N can
donate more electrons in that case.
At cathode
88.
I
O
Clemmensen
Reduction
2H 4 P2 O 7
3
OH OCH 3
t
I
I
2H20
( 2Hz0
H 2S0 4
H 2C-C-CH3
95.
Metaphosphoric
acid
Pure metal
CH 3
COCH3
~
~
[PtCI/NH3) 4]Br2 and [PtBr2(NH3) 4]Cl2 are
ionisation isomers
97. (b) In Ianthan ides, there is poorer shielding of
5 d electrons by 4felectrons resulting in greater
attraction of the nucleus over 5 d electrons and
contraction of the atomic radii.
98. (a) SARAN, a polymer of vin yl chloride
(C8i=CHCI) and vinylidene chloride, is used for
making synthetic hair wigs.
99. (a) Wilkinson's catalyst in [RhCl(PPh 3) 3] , redviolet in colour and has square planar structure.
It is used for selective hydrogenation of organic
molecules at room temperature and pressure.
TiC14 + (C2H 5) 3 Al is Zeigler Natta catalyst.
(C2H 5) 4 Pb is an anti-knocking agent.
cis-platin is used as an anti-cancer agent.
100. (a) Work done during adiabatic expansion
(c)
= C v (T2 -T1)
or
-3000 = 20(T2 - 300) ⇒ T2 = 150K
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MHT-CET 2020
2020-19
SECTION-B
MATHEMATICS
1.
⇒
'
2
k 7)
(+
ER, because k ER and
=4 (k: 7)-7=k
k
is the image of (
y = 3x 1 andy = 30 -2x2
5.
A(y)=(30;y -~)y
6.
=
7.
= ( ~ _ 3) 9 = 15 x 9 = 13 5
2
2
2
7
11 3
)
(~
q)
Ji
y=9 ; A"(y)=-10 < 0
=21 / 2
k:
f is onto.
f is a bijective function.
(a) ~ ((~ p) A q) = ~ (~ p) V ~ q = p V
2 2
2
(c) I= [x ]dx- Ji2[x] dx
6A(y) = (90-3y-2y)y = 90y-Sy2
6A '(y) = 90-10 y = 0
max
x= ( k: )
f[( k:7r ]= 4[(k:7rr-7
= -[xsinx +cosx ]+c
A = (x2 -x 1)y
⇒A
⇒
113
7
113
Now
fx✓l+ c~s 2x dx = -f xcos xdx
X2
'
f(x)=k ⇒ 4x 3 -7=k
~
Xi =3;
=0
⇒ x =x
:. fis one-one.
I
2
f is onto. Let k ER any real number.
2
⇒
l
x - x = 0 because the other factor is non-
zero.
Therefore, the required probability is
P(A2)P(E I A2)
P(A2 / E)=-P-(A--)P_(_E_;_
I A--=i-)_+_P_(A-----'=---)P_(_E_
I _A2-)
1
2
1 1
- x10 4
= _-----=---::-------,-'-----::=
_2_ X 1+ _!_ X _!_ 37
10
10 4
re
(b) - < x < re then
(c)
Xi 3 -X 23_0
- .
⇒ (x1 -x,)[(x1 + x22 )' + 3x:'
~ ~ =I cos X I= - cos X
3.
⇒
⇒ (xi -x 2)(x/ +xix 2 + x/) = 0.
(c) We define the following events :
A 1 : He know the answer
A 2 : He does not know the answer
E : He gets the correct answer
Then, P(A 1) = 9/10, P(A2) = 1 - 9 /10 = 1/10, P(EI
A 1) = I , P(EIA 2) = 1/4.
2.
Xi 3 = X2 3
⇒
(c)
Ji✓2 dx+ f✓✓23 2 dx+ f✓23 3dx- f12 ldx
=4- ✓
2- ✓
3
x(l+ y2)11 2dx+ y(l+ x 2)1i 2dy = 0
⇒
y
Integrating we get
2j;;;i + 2)1 + y 2
= 2c or
(l+x2)112 +(l+y2)112 =c
~~-L---------L..---"'--+ X
Q
4.
x1
X2
(d) We have f(x)=4x 3 -7 , xER.
fis one-one. Let xi' x 2ER and f (x 1) = f(x2).
⇒ 4x 1
3
8.
3
-7=4x 2 -7
⇒ 4x 1
3
= 4 X2
3
9.
2
[60 0~
~i
= 13
1
(b) Let D (x, y, z) be the required point, Then,
the mid-point of diagonal BD is
x+l y+2 z-4)
( _2_ ' _2_ ' _2_
(c)
A =
w~~w~w----=--:--:.J:-=E=E-=s--=o---=o,.......,K....
S:------;-.l.---.,NI
2020-20
Target MHT-CET
Also, the mid-point of diagonal AC is
A(l, 1, 1)
3-1 -1+1 2+2 ) .
,- -,- - 1.e., (1 ,0, 2).
( 2
2
2
But, the mid-points of the diagonals of a
parallelogram always coincide.
:. x+l =l y+ 2 =0 and z- 4 =2
2
' 2
2
So, x = 1, y = -2, andz = 8.
Hence, the required point is D(l, -2, 8).
l0.
I
(c)
13.
14.
x+I
-3
y-3
2
15.
z+2 .
1
a(x+l)+b(y-3)+c(z+2) = 0
... (i)
where-3a+2b+c = 0
... (ii)
If the plane passes through (0, 7, - 7).
a + 4b - Sc= 0
... (iii)
From Eqs. (ii) and (iii),
b
c
-10-4
1-15
-12-2
b
:. lim f(x)
⇒
⇒
y-4
4-4
y-4
St-5 = 0 ⇒ t = 1.
Required foot ofperpendicular is (2+ 1,4,- 1+6)
= (3,4, 5).
(a) Equation ofthe line through (1, - 2, 3) parallel
. x
y
z- l .
tothe I me - = - = - - 1s
2
-6
3
x-l
y+2
z-3
... (i)
= - - = - - =r(say)
2
-6
3
Then, any point on Eq. (i) is
(2r + 1, 3r- 2, - 6r+ 3).
If this point lies on the plane x - y + z = 5, then
(2r+ l)-(3r-2) + (-6r+ 3) = 5
1
c
z-6
i.e.,
5-1
4-6
x-1
z-6
-1
2
0
Any point on this line is (2t + 1, 4, -t + 6). Ifthis
is the foot of perpendicular from A on the line
BC, then d.n. of this perpendicular are
< 2t+l -l , 4-l , -t+6-l> i.e. < 2t, 3, -t + 5 >
Using condition of perpendicularity, we have
(2t) (2) + 3 x 0+ (-t+ 5) (-1)= 0
= oo
:. The function is not continuous at x = 1.
16.
1
1 1
Therefore, the plane (i) becomes
(x+ 1) + (y - 3) + (z+2) = 0
⇒ x+y+z=0
(a) The equations of line BC are (using two
point form)
x-1
x+l
x+
3
x➔l+
⇒
12.
(d)
x 2 -l
Forx < l,f(x)= x 2 + x_
2
3
x 2 -1
x+l
For x > 1, f (x) = - - - - =
2
x -2x+l x-1
---=-- =---
a
2m = 2n + 56
:. Jim f (x) = _!_
2
x➔l-
= - - IS
a
(b)
⇒ 2m-2n =64-8=2 6 -2 3
Slll X -COS X
Any plane containing
(b) (p A - q) A(- p Aq)=(p A - q) A(- q Aq)
=f Af=f
(By using associative laws and commutative
laws)
:. (p A - q) A (- p A q) is a contradiction .
Jsinx + cos x dx
(d)
.JI-sin 2x
sin X + COS X
.
=±.
dx=±log(smx-cosx)+c
11.
B - - - - - - +N
- - - -.... c (5, 4, 4)
(1 , 4, 6)
-7r+6=5 ⇒ r=-
7
.
. . (9
Smce,
thepomt1s
- ,-11
-,-15 J .
7
7
7
I2J
Distancebetween(l, - 2, 3)and ( ~ -~
7' 7 ' 7
( 4~ +
:9 + ~~ J ✓( ~~ J
=
=
.
17.
(a)
I
x +sinx dx
1 +cosx
l
X
X
x+2 sm-cos2
2 dx
2cos 2 ~
J
2
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MHT-CET 2020
2020-21
fx __!_sec
~dx + ftan ~dx
2
2
2
= x tan~ - ftan~ dx + Jtan~ dx + C
2
2
2
18.
y
2
=
= xtan~+C
2
(b) Here,2x +ys;;30,x+ 2y s;; 24,x,y ~ O
The shaded region represents the feasible region,
hence
z = 6x + 8y. Obviously it is maximum at (12, 6).
Hence z = 12 x 6 + 8 x 6 = 120
C(7,0)
(10,0)
+x
J, ~
~>
The region bounded by the vertices
A(O, 5), B(4, 3), C (7, 0).
The objective fonction is maximum at C(7, 0) and
Maxz = 5 x 7 + 2 x O= 35.
y
24.
A
(a)
-~--~~--,-----, X
X + 2y = 24
19.
(b) In the interval ~ to ~ , [x] = 1
3
2
B
~-----:
2
30 tan 30°
r
From geometry, we have - - 30 tan 300
n/ 2
2
(b) We write the given equation as
n
20.
6
or h = 30- ✓
3r
Now, the volume of cylinder,
⇒
tan(0 + 40) = - tan 70 ⇒ tan 50 = tan(-70)
V
50=nTC+(-70) orl20=nTC
r,:; ?
dV
Now, let = O or TC(60r -3-v3r-) = 0
dr
20
3
or
r= ✓
E
I
(d) We can write the given expression
= TCr 2 h = TCr2 (30- ✓3r)
r(
={i.(p X q)}i+{j.(p X q )}] +{k.(p X q)}k
22.
✓3; J
= pxq
Hence, Vmax = TC ( ;
Since for any vector ; ,
= TC 400 X lQ = 4000TC
3
3
(a) Any plane through the given line
2x- y+3z+ 1 +A(x+y+z+3) =0
(From S+ AS' = 0)
a= (;.i)i+(;_J)]+(a .k)k
(a) f (0) = sin 0 (sin 0 + sin 30)
= sin 0 (2 sin 2 0 cos0)
= (2 sin 0 cos 0) sin 20 = (sin 20)2 ~ 0 \7' 0 ER
23.
30-h
30
tan 0 + tan 40 = - tan 70(1- tan 0 tan 40)
0 = nTC /12, n
21.
''
r
✓
3 +TC=[-xcosx+smx] ; 3 = 1- .
:C
.
:.I=fn/n/3 xsin(n-x)dx =fn/n/3 xsinxdx
2
(c) Change the inequalities into equations and
draw the graph oflines, thus we get the required
feasible region as shown below.
25.
.
.
30 -
.
If this plane 1s parallel to the !me
X
y
Z
1 = 2 = 3,
then the normal to the plane is also perpendicular
to the above line.
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2020-22
Target MHT-CET
(2 + 11,) 1 + (11, - 1)2 + (3 + 11,)3 = 0
( ·: l 1l 2 + m 1m2 + n 1n2 = 0)
⇒
29.
(c) ForanypointP(x, y)thatis equidistantfrom
the given line, we have
2 =-(x + y -2✓
2)
x +y - ✓
or 2x + 2 y - 3✓
2 =0 .
3
11,= - 2
and the required plane is x - Sy+ 3z - 7 = 0.
26.
l al= l h l= l c l=l
(c)
-;_b =(l)(l)cos8 =cos8
30.
(a) Letthe co-ordinates ofA be (a, 0). Then the
slope of the reflected ray is
y
and
c. a = cos 8, b. c = cos8
a. a
[ab c] = b. a
C. a
a.
b.
a. b
b. b
C. b
---2
cos8 cos8
cos8
cos8
=
cos8 cos8
C
C
C. C
(5,3)
0
Operate R 1 ➔ R 1 +R 2 +R 3
1
1
= (1 + 2 cos 8) cos 8
cos 8
cos 8 cos8
Operate C 2
➔
C 2 -C1; C 3
➔
C 3 -C 1
0
1
0
= c1 + 2 cos 0) cos 0 1- cos 0
o
cos 0
o
1- cos 0
3
2
5-a
1-a
⇒ --+--=0 ⇒
:. (; b -;;]=(l-cos0)✓1+2cos 0
⇒
sin 2x-sin 4x + sin 6x = 0
(sin2x+ sin6x)-sin4x=O
⇒
2sin4xcos2x-sin4x = 0
(a)
.
sm 4x = 0
⇒
4x = nn
2cos2x-l = 0
⇒
⇒
::,~th! oo-orffinates ofAare
31.
x =-
J-
2
7t
orx=nn±3
6
(a) Perpendicular distance of directrix from
⇒ 2x=2nn±-
e
y
32.
33.
2
y =x x , ln y = x 2 1n x
(d)
2
2
-b 2
sin 2 A - sin 2 B
dy = xx .x(l+2lnx) = xx +1(1+2lnx)
dx
(b) A+ B = 180° -C = 90°
a = 2R sin A, b = 2R sin B, c = 2R sin C
a
2
+ b 2 sin 2 A + sin 2 B
sin(A + B)sin(A-B)
a
(ae, 0)
:. Semi majoraxis = 8/3
-v 2 cos 8 - -v 2 sin 8
2 1
1 dy
--=2xlnx+ x .-=x(l+2lnx)
y dx
x
⇒ a(2- .2!. ) =4 ⇒ a =~3
Y'
-1 ( ✓
2 cos 8+ ✓
2 sin 8)
r;::
r;::
_ 7t _!_
1+ tan8 -7t +
_
- 1( - 1 ( X 2)
-~n
8 --+COS
4 2
l-tan8
4
1
cos2x =-
focus = !!_-ae=4
2
.
4
(1: ,0)
Let x 2 = cos 28 ⇒ 0 :-s; 28 < ~ (": x 2 > O)
(c)
The express10n = tan
7t
7t
28.
3-3a+l0-2a =0
13
= (1 + 2 cos 0) (1 - cos 0) 2
27.
X
3-0
- - = tan 8 (say)
...(1)
5-a
Then the slope of the incident ray
2-0
... (2)
= - - = tan( n - 8)
1-a
from (1) and(2)
·:tan8+ tan(n -8) = 0
2
sin 2 A+sin 2 (90° -A)
x
=
ale
[·: A+B=90°]
= sin 90° sin(A - B) = sin(A _ B)
sin 2 A+cos 2 A
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MHT-CET 2020
34.
2020-23
(b) From geometry, the sum ofall internal angles
=(n-2)x 180°
where n is the number of sides of the polygon.
40.
=cos [ cos- 1 x+cos- 1 x+sin- 1 x]
:. ~[2xl20°+(n-l)x5°]=(n-2) x l80°
2
=cos [ cos-I x+TC / 2] =-sincos- 1 x
⇒ n 2 -25n+l44=0 ⇒ (n-16) (n-9)=0
.
2
. - 1 ~l
= - Slll sm "Ii 1 - x ~ =
Ifn = 16 then the 16th internal
angle=l20° + (16-l) x 5° =195°> 180°
:. n
35.
:;t: 16.
5
2 3
0.2048 = C2p q where p + q = 1
⇒
41.
(d) Since - (p ⇒ q) = p /\ - q
42.
- (- p ⇒ q) = - p /\ - q
(d) The required area is shown by shaded
region
1
4
p=s,q=s
y
Mean=np= 1
36.
(b)
2
-"Ii~
1- xl
~
--Fm' =-iffi--2~
Hence n = 9
(a) 0.4096= 5 C1pq 4
cos[ 2cos- 1 x+sin- 1 x]
(a)
. -I 2x
--=
y = sm
2
l+x
2
dy
TC -
2 tan -I x, f,or x > 1
or
-=---
or
dy )
2 _ 1
( dx x=✓3 = - 1 + 3 - -2
(y = 2 - x)
(y = x - 2)
I+x 2
dx
2
r,::;
Also, when x = -v-', Y =
TC -
2x
TC
TC
3=3
Required Area
3
Hence, equation of tangent is
1
TC
37.
38.
39.
A=
r,::;
y-- = --(x--v3).
3
2
(c) Desired probability
= P(A) + P(B) - 2P(A n B)
and p(A)
B
P(AnB) =]__
P(B)
2
(a) Put (1+
,Ji' 2+ -Ji Jinx2+4xy+y2=0,
we get 3r 2 + 9✓
2r + 13 = O for which product
of the roots is 13/3.
(b) ay + x 2 = 7, and x 3 = y cuts orthogonally.
Now
dy) = - 2x and (dy ) = 3x2
( dx
a
dx
3
3
fIx - 2 p'x = 2f(x- 2)dx
I
I
43.
2
= 2[
x: -2x
(c)
2
Given,!~=~ -cos ( ~ )
= I
Putting y = vx so that dy = v + x dv
dx
dx
dv
2
We get v + x - = v - cos v
'
dx
dx
dv
dx
2
⇒ --=-- ⇒ sec vdv=-cos2 v
x
x
Integrating, we get, tan v = - In x + Inc
tan(~ ) = - In x +Inc
2
or[(- x)(3x
a
2
= -1
)]
(I, I)
2
or --x3=-lora=6.
a
This passes through ( 1, : )
⇒
Inc= 1
1
:.y= x tan- (1og :)
w~..,,,,...,w=-=w...,.....,,.....Jc=E-=E-=B-...:0~0:-nK,.;;S;---;.l~NI
2020-24
44.
Target MHT-CET
(a) Puttingn = 99andp =
1
= (100)( 2 ) = 50
45.
1
2 ,wehave(n + l )p
49.
y = (sin t - t cost). Therefore,
.
.
[-smt+
] =atcost
~
-=a
smt+tcost
dt
so that the maximum value ofP(X = r) occurs at r
= (n + l)p = 50 and at r = (n + l)p-1 = 49
(a) Let the progression be a , a+ d, a + 2d,
Then
X4
= 3x 1 ⇒ a + 3d = 3a ⇒ 3d = 2a
.
dy
[
.
- = a cost-{cost-tsmt}] = atsmt
dt
...(i)
Again x 7 = 2x 3 + 1
⇒ a+ 6d
46.
. dy
= 2(a + 2d) + 1 ⇒ 2d =a+ 1
... (ii)
47.
(c) 2yy 1 = 2c
⇒
2
d
= -(tant)
dx
2
,J3
.
dt
d
=-(tant)dt
dx
c = yy 1
= sec 2 I · dt = sec 2 t · - dx
a/cost
Eliminating c, we get, y 2 = 2 yy 1 ( x + ..j"yy;)
or (y2-2x YY1>2 =4y3yf
It involves only 1st order derivative, its degree is
3 as y~ is there.
48.
(a)
al sin I
--=tant
a/cost
Then, d y _ !!__(dy)
dx 2 dx dx
(x-1) 2 y2
- - - - - = l . Thusa2 = 9 b2 = 3
3
'
9
Using b 2 = a2 (e2 - 1), we get
2
(!)
dx = ( :~)
Solving (i) and (ii) we get
a = 3, d = 2
(c) The given equation reduces to
3 = 9(e -1) ⇒ e =
It is given that x = a(cost+tsint) and
(c)
50.
sec 3 t
= at
(a) The system is Ox 1 + Xz - x3 = 1
- x 1 + Ox2 + 2x3 =2
x 1 - 2x2 + Ox 3 = 3
f{f[f(x)]}=f[r(l~x)]
⇒
=f[ l - ~ J = r( x:l )
1-x
:. f (x) is not defined for x = l ;
Clearly IA l= 0
r(-
1
- ) is not
1-x
defined forx =O.
f {f [f(x)]} is discontinuous at x = 0 and 1
i.e., there are two points of di scontinuity.
NowAdjA- r~
21 211
1
1
: . (Adj A) B -::f. 0 ⇒ system is inconsistent
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MHT-CET 112019 II
General Instructions
■
■
■
■
■
■
■
This question booklet contains 150 Multiple Choice Questions (MCQs).
Section-A: Physics & Chemistry - 50 Questions each and
Section-B: Mathematics - 50 Questions.
Choice and sequence for attempting questions will be as per the convenience of the candidate.
Read each question carefully.
Determine the one correct answer out of the four available options given for each question.
Each question with correct response shall be awarded one (1) mark. There shall be no negative marking.
No mark shall be granted for marking two or more answers ofsame question, scratching or overwriting.
Duration ofpaper is 3 Hours.
SECTION-A
PHYSICS
1.
4.
A sotne of mass 1 kg is tied to a string oflength
2 m long and is rotated at constant speed of 40
ms-1 in a vertical circle. The ratio of the tension
at the top and the bottom is [Take g = 10 ms-2]
(a)
(c)
81
79
19
12
79
(b) 81
(a)
12
(d) 19
(c)
5.
2.
3.
Two coils have a mutual inductance of0.01 H.
The current in the first coil changes according to
equation I = 5 sin 200 nt. The maximum value of
e.m .f. induced in the second coil is
(a) lOnvolt
(b) 0.lnvolt
(c) nvolt
(d) 0.01 nvolt
The radius of the earth and the radius of orbit
around the sun are 6371 km and 149 x 106 km
respectively. The order of magnitude of the
diameter of the orbit is greater than that of earth
by
(a) 1()3
(b) 1()2
(c)
1()4
Two open pipes of different lengths and of same
diameter in which the air column vibrates with
fundamental frequencies 'n 1' and 'n 2' respectively.
When both pipes are joined to form a single pipe,
its fundamental frequency will be
(d) 105
If 'CP' and Cv are molar specific heats of an ideal
gas at constant pressure and volume
respectively, 'y' is ratio of two specific heats and
'R' is univeral gas constant then 'CP' is equal to
Ry
(a)
y-1
l+y
(c)
6.
1-y
(b) yR
R
(d) y-1
In a series LCR circuit R = 300 n, L = 0.9 H,
C = 2 µF, co= 1000 rad/s. The impedance of the
circuit is
(a)
(b) 1300.Q
soon
(c)
4000
(d) 900
n
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TargetMHT-CET
2019-2
7.
The quantity which does not vary periodically
for a particle performing S.H.M. is
(a)
(c)
8.
acceleration
displacement
(b) total energy
(d) velocity
Which of the following combinations of 7
identical capacitors each of2 µF gives a resultant
capacitance of
10
11 µF?
(a)
(c)
(a) 3 in parallel and 4 in series
(b) 2 in parallel and 5 in series
(c) 4 in parallel and 3 in series
(d) 5 in parallel and 2 in series
9.
10.
13.
Bohr model is applied to a particle of mass 'm'
and charge 'q' moving in a plane under the
influence of a transverse magnetic field 'B'. The
energy of the charged particle in then th level will
be (h = Planck's constant)
(a)
2nhqB
nm
(b)
(c)
nhqB
4nm
nhqB
(d)
nm
nhqB
2nm
(a)
(c)
14.
15.
16.
(a)
both P and Q are equally elastic
(b) P is more elastic than Q
(c) P is plastic and Q is elastic
(d) Q is more elastic than P
12.
If WP W 2 and W 3 represent the work done in
moving a particle from A to B along three different
paths 1, 2 and 3 (as shown in fig.) in the
gravitational field of the point mass 'm'. Find the
correct relation between 'Wi', 'W2' and 'W3'
30rnA
20rnA
+ IV
(b) 40rnA
(d) l0rnA
The equation of simple harmonic progressive
wave is given by Y = a sin 2rc (bt- ex)
1
(b) c = - -
(a)
c= na
(c)
c=-
2na
1
(d) c=2rca
1ta
In fundamental mode, the time required for the
sound wave to reach upto the closed end of a
pipe filled with air is 't' second. The frequency of
vibration of air column is
(b) 4(tt 1
(a) (2tt 1
1
(c) 2(tt
(d) (4tt 1
(d) make magnetic induction weak at the centre
Two identical wires of substances 'P' and 'Q' are
subjected to equal stretching force along the
length. If the elongation of'Q' is more than that
of 'P', then
R = 100 Q
The maximum particle velocity will be twice the
wave velocity if
(c) produce magnetic field which is parallel to
plane of coil at any position
11.
(b)W1 < W2 < W3
(d) W l > W 3 > W 2
Assuming that the junction diode is ideal, the
current in the arrangement shown in figure is
+3V
In moving coil galvanometer, strong horse shoe
magnet of concave shaped pole pieces is used
to
(a) increase space for rotation of coil
(b) reduce weight of galvanometer
W 1 < W 3 < W2
W 1 =W2 =W3
17.
Two small drops of mercury each of radius 'R'
coalesce to form a large single drop. The ratio of
the total surface energies before and after the
change is
(a) 2213 : 1
2: 1
(b) ✓
(c) 2 113 : 1
(d) 2 : 1
If radius of the solid sphere is doubled by
keeping its mass constant, the ratio of their
moment of inertia about any of its diameter is
(a) 1: 8
(b) 2: 5
(d) 1 : 4
( c) 2 : 3
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2019-3
l\ffiT-CET 2019
18.
For a metallic wire, the ratio of voltage to
corresponding current is
(a) independent of temperature
24.
(b) increases with rise in temperature
(c) increases or decreases with rise in
temperature depending upon the metal
(a)
(c)
(d) decreases with rise in temperature
19.
20.
A soap bubble in vacuum has a radius of 3 cm
and another soap bubble in vacuum has a radius
of 4 cm. If the two bubbles coalesce under
isothermal condition, then the radius of the new
bubble is
(a) 2.3 cm
(b) 4.5 cm
(d) 7cm
(c) 5cm
(c) attract each other
2
2A
(b) A
(d) 4A
A galvanometer has resistance of 100 0 and a
current of 10 mA produces full scale deflection in
it. The resistance to be connected to it in series,
to get a voltmeter of range 50 volt is
(a) 39000
(b) 40000
(d) 49000
(c) 46000
26.
The angle made by orbital angular momentum of
electron with the direction ofthe orbital magnetic
moment is
(b) 60°
(a) 120°
(c) 180°
(d) 90°
27.
The current in 1 0 resistor in the following circuit
is
neither attract nor repel each other
(b) repel each other
A
25.
Two parallel conductors carrying unequal
currents in the same direction
(a)
A particle executes the simple harmonic motion
with an amplitude ' A' . The distance travelled by
it in one periodic time is
(d) will have rotational motion
21.
A layer of atmosphere that reflects medium
1.lA
1.lA
frequency radio waves which is ineffective
during night, is
22.
(a) Flayer
(b) E layer
(c) stratosphere
(d) thermosphere
A transverse wave is propagating on the
string. The linear density ofa vibrating string
is 10-3 kg/ m. The equation of the wave is
28.
y = 0 .05 sin(x + 15t) where x and y are in
(a)
IA
(b) 0.5A
(c)
1.lA
(d) 0.8A
The wavelength of the first line in Balmer series
in the hydrogen spectrum is ' A'. What is the
wavelength ofthe second line in the same series?
metre and time in second. The tension in the
(a)
string is
23.
(a) 0.2N
(b) 0.250N
(c)
(d) 0.325N
0.225N
20
27 "'
3
(b)
i6"'
The kinetic energy of a revolving satellite
(mass m) at a height equal to thrice the radius of
the earth (R) is
(a)
(c)
mgR
8
mgR
(b)
mgR
2
16
mgR
(d)
4
29.
Work done in stretching a wire through 1 mm is
2J. What amount of work will be done for
elongating another wire of same material, with
half the length and double the radius of cross
section, by 1 mm?
(a)
(c)
1.2 J
8J
(b) 4J
(d) 16J
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2019-4
30.
TargetMHT-CET
The resultant R of P and Q is perpendicular
to
(c)
P. Also I P I = I R I-The angle between P
and Q is [tan45° = 1]
(a)
(c)
31.
32.
6n
7n
(b)
4
7t
(d)
4
(d)
34.
3n
4
L
(a)
(c)
..
36.
2V
8v
(c)
33.
If
-
6L
.JA 2 + B2
3QL3
81t2
QL3
(b)
2
3QL
QL3
(d)
2
4n
47t2
81t2
acceleration
(d) impulse
For transistor, the current ratio 'Pde' is defined as
the ratio of
(a) collector current to emitter current
(b) collector current to base current
(c) base current to collector current
V
4L
X'
The dimensions of torque are same as that of
(a) moment of force (b) pressure
(c)
m
(a)
A thin metal wire oflength 'L' and uniform linear
mass density ' Q' is bent into a circular coil with
'o' as centre. The moment ofinertia ofa coil about
the axis XX' is
~
35.
•
A +B
o·
2m
••
•
C
(A2-B2)]
2
2
X -------._,....,.
A uniform rod of length '6L' and mass '8m' is
pivoted at its centre 'C'. Two masses 'm' and
'2m' with speed 2v, v as shown strikes the rod
and stick to the rod. Initially the rod is at rest.
Due to impact, if it rotates with angular velocity
'w1' then 'w' will be
V
-1[
4
A telescope has large diameter of the objective.
Then its resolving power is
(a) independent of the diameter of the objective
(b) low
(c) zero
(d) high
2L
cos
(d) emitter current to collector current
(b) Zero
37.
A clock pendulum having coefficient of linear
expansion a = 9 x 10- 7 /°C has a period ofO. 5 s at
20°C. Ifthe clock is used in a climate where the
temperature is 30°C, how much time does the
clock lose in each oscillation? (g = constant)
(b) 5 X 10- 1 S
(a) 2.5 X 10- 1 S
(c) 1.125 x lo-6 s
(d) 2.25 x 10-6 s
38.
Two capillary tubes of different diameters are
dipped in water. The rise of water is
}} V
(d) 3L
represents the magnitude of
resultantoftwovectors (A+ B) and (A - B) ,
then the angle between two vectors is
(a) zero in both the tube
(b) same in both the tube
(c) more in the tube oflarger diameter
(d) more in the tube of smaller diameter
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39.
A thin hollow prism ofrefracting angle 3°, filled
with water gives a deviation of 1°. The refractive
index of water is
(a) 1.59
(b) 1.33
(d) 1.51
(c) 1.46
40.
A body is projected vertically from the surface of
the earth ofradius 'R' with velocity equal to half
of the escape velocity. The maximum height
reached by the body is
(a)
(c)
41.
R
5
2
43.
46.
R
4
(b) 6537
A
47.
When photons of energy hv fall on metal plate of
work function 'WO' , photoelectrons ofmaximum
kinetic energy 'K' are ejected. Ifthe frequency of
the radiation is doubled, the maximum kinetic
energy of the ejected photoelectrons will be
(a) K+W0
(b) K+hv
(c) K
(d) 2K
If a star emitting yellow light is accelerated
(b) shining yellow
(c) gradually changing to blue
(d) gradually changing to red
The magnitude ofmagnetic induction at a point
on the axis at a large distance (r) from the centre
ofcircular coil of'n' turns, and area 'A' carrying
current (l) is given by
µo nA
-.(a) B axis =47t
Ir3
2nl
µo
--(c) B axis - 41t · Ar3
If - is the coefficient of performance of a
refrigerator and 'Q 1' is heat released to the hot
reservoir, then the heat extracted from the cold
reservoir 'Q2 ' is
(d) 6351 A
towards earth, then to an observer on earth it will
appear
(a) becoming orange
44.
(a)
In biprism experiment, the distance between
source and eyepiece is 1.2 m, the distance
between two virtual sources is 0.84 mm. Then
the wavelength oflight used if eyepiece is to be
moved transversely through a distance of
2. 799 cm to shift 30 fringes is
(a) 6533 A
(c) 6535 A
42.
(d)
A metal sphere ofradius 'R' and density 'e 1' is
dropped in a liquid of density '., ' moves with
terminal velocity 'V'. Another metal sphere of
same radius and density 'e2 ' is dropped in the
same liquid, its terminal velocity will be
(c)
R
(b) 3
R
45.
(a)
a-1
(b) - Q i
a
(c)
l+a
(d) - Q i
a
The real force 'F' acting on a particle of mass ' m'
performing circular motion acts along the radius
of circle 'r' and is directed towards the centre of
circle. The square root ofmagnitude of such force
is (T = periodic time)
(a)
21t , ---..Jmr
T
(c)
J;;;;
Tmr
41t
21tT
48.
Dimensions of Gyromagnetic ratio are
(b) [L0M-1T 1l 1]
(a) [L1M°T 1l 1]
(c) [L1M°T0I-1]
(d) [L-1M°T 111]
49.
The maximum velocity of the photoelectron
emitted by the metal surface is 'V'. Charge and
mass of the photoelectron is denoted by 'e' and
'm' respectively. The stopping potential in volt
lS
y2
(a)
µo 2nIA
-.-(b) B axis =47t
r3
µo nIA
---(d) B axis41t · r3
(b)
y2
(c)
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50.
The equiconvex lens has a focal length 'f. If the
lens is cut along the line perpendicular to principal
axis and passing through the pole, what will be
the focal length of any half part?
(a)
f
2
(c)
3f
2
52.
57.
When CuSO4 solution in water is treated with
concentrated HCl it turns
(a) Violet
(b) Yellow
(c) Purple
(d) Green
58.
Which of the following polymer is used in paints?
(a) Gutta percha
(b) Melamine
(c) Buna-S
(d) Novolac
59.
Three moles of an ideal gas are expanded
isothermally from a volume of300 cm3 to2.5 Lat
300 K against a pressure of 1.9 atm. The work
done in joules is
(b) +423.56 J
(a) -423.56 J
(d) +4.8J
(c) -4.18 J
60.
Which among the following is used in the
treatment of cancer?
(a) cis-[Pt(en)iC12]
(b) cis-[PtC!i(NH3) 2]
(c) trans-[Pt(en)2C½]
(d) trans-[Pt~)2C!i]
(b) 2f
(d) f
CHEMISTRY
51.
(c) [ ~ )5NO2]SO4
(d) [Pt~)4 C!i]Br2
Which of following methods is used to separate
wolframite and stannic oxide present in
cassiterite?
(a) Hydraulic washing using Wilfley table
(b) Froth :flotation
(c) Hydraulic classifier
(d) Magnetic separation
In the reaction ,
MnO41(aq.)+Br- 1(aq.)
MnO 2 ( s) + BrO31( aq.) , the correct change
in oxidation number of the species involved is
(b) Mn+7 to Mn+2
(a) Br+5 to Br-1
(c) Mn+7 to Mn+3
(d) Br- 1 to Br+s
-+
53.
How many isoprene units are present in abscisic
acid?
(b) Two
(a) Three
(d) Five
(c) Four
54.
Action of hydrogen iodide on anisole gives,
(a) phenol and iodomethane
(b) iodobenzene and methanol
(c) phenol and methanol
(d) iodobenzene and iodomethane
55.
Which among the following compounds is used
to decaffeinate coffee?
(a) Iodoform
(b) Carbon tetrachloride
(c) Methylene dichloride
(d) Chloroform
56.
Which complex among the following gives a
white precipitate on treatment with an aqueous
solution of barium chloride?
(a) [Pt(NH3\Br2]C1i
(b) [Co(NH3) 5 SO4 ]NO2
61.
Which among the following pairs of compounds
in NOT isomorphous?
(a)
(b)
(c)
(d)
NaNO3 and CaCO3
KiSO4 and KiSeO4
NaClandKCl
NaF and MgO
62.
Which among the following compounds is used
as selective weed killer?
(a) Picric acid
(b) 2, 4-dichlorophenoxy acetic acid
(c) 2, 4, 6-trichlorophenoxy acetic acid
(d) Salol
63.
Calculate the difference between hea t of
combustion of carbon monoxide gas at constant
pressure and at constant volume at 27°C ?
(R.= 2CalK- 1 mol- 1)
(b) -600cal
(a) 54cal
(d) 27 cal
(c) -300cal
64.
The conductivity of an electrolytic solution
decreases on dilution due to
(a) decrease in number ofions per unit volume
(b) increase in ionic mobility of ions
(c) increase in percentage ionisation
(d) increase in number ofions per unit volume
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65.
2019-7
Identify B in the following reaction,
Acetaldoxime __N_a_
_,
A
Alcohol
74.
Two electroytic cells are connected in series
containing CuSO4 solution and molten AlC13 . If
in electrolysis 0.4 moles of'Cu' are deposited on
cathode offirst cell. The number of moles of' Al'
deposited on cathode of the second cell is
(b) 0.27 moles
(a) 0.6 moles
(c) 0.18moles
(d) 0.4moles
75.
Mandelonitrile is obtained by the reaction
between hydrogen cyanide and
(a) Propionaldehyde (b) Benzaldehyde
(c) Acetaldehyde
(d) Acetone
76.
The ionic charges on chromate ion and
dichromate ion respectively is
(b) -3, -2
(a) -2,-2
(d) -4, -2
(c) -2,-4
77.
In the reaction,
NaN02
HCI
B+ HzO+ N 2,
66.
(b) C2H5OH
(a) CH3CHzCHzOH
(c) C28sCl
(d) C2HsNHz
Which among the following solids shows Frenkel
defect?
(a) NaCl
(b) CsCl
(d) AgCl
(c) KCl
67.
A cold drink bottle contains 200 mL liquid in which
CO2 is 0.1 molar. Considering CO2 as an ideal gas
the volume of the dissolved CO2 at S. T.P. is
(a) 22.4L
(b) 0.224L
(c) 2.24L
(d) 0.448L
68.
In the reaction,
+2nNa
2n R-X - 0-ry-e-th_e_r_, product
Xis
(a) toluene
(c) benzylalcohol
The product obtained is
(b) n Soldium halide
(a) 2n Alkene
(c) nAlchol
(d) nAlkane
69.
The bacteriostatic antibiotic from the following
70.
What is the percentage of carbon in urea?
(AtmassC= 12, H= 1, N= 14, O= 16)
(a) 20%
(b) 26.6%
(c) 6.67%
(d) 46.0%
79.
a
80.
Calculate Vant Hoff factor for 0.2 m aqueous
solution of KCl which freezes at ---0.680°C.
CK_r= 1.86 Kkgmol-1)
(b) 1.83
(a) 3.72
(c) 6.8
(d) 1.86
81.
Which among the following sets of compounds
is used as raw material for the preparation of
sodium carbonate by solvay process?
(a) NaOH, HCl, CO2
(b) NHFl,HzO,NaCl
(c) NaCl,~,Ca(OH)2
(d) NaCl, CaCO3, HzSO4
82.
What is the H-S-H bond angle is H 2S?
(b) 92.1°
(a) 104.5°
(c) 91°
(d) 90°
(b) Aminoglycosides
(d) Ofloxacin
Nitroalkanes are obtained in laboratory from
primary or secondary alkyl halides by the action
of
(b) NaNO3
(a) AgNO2
(c) AgNO3
(d) HN03
71.
Which of following bonds has maximum bond
length?
(a) C-O
(b) C-H
(c) C-C
(d) C-N
72.
Which of the following sets of components form
homogeneous mixture?
(a) Phenol+ Water
(b) Sugar+ Benzene
(c) Silver chloride+ Water
(d) Ethyl alcohol+ Water
73.
Which among the following compounds in
crystalline form is used for making Nicol's prism?
(a) CaSO4
(b) Na2 AIF6
(c) CaCO3
(d) Al2O3
(d) ethylbenzene
78.
lS
(a) Tetracycline
(c) Penicillin
(b) methylbenzene
-butylene when subjected to hydroboration
oxidation reaction, yields
(a) iso-butyl alcohol (b) sec-butyl alcohol
(c) n-butyl alcohol
(d) tert-butyl alcohol
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83.
TargetMJIT-CET
'K' is Henry's constant and has the unit
89.
Which among the following is NOT a semisynthetic polymer.
(a) Terylene
(b) Viscose-Rayon
(c) Cupra-amrnonium silk
(d) Acetate Rayon
90.
Basesemerization is used in the extraction of
(a) Iron
(b) Copper
(c) Aluminium
(d) Zinc
91.
Which among the following reaction is an example
of a zero order reaction?
atm mo1-1 dm3
(a)
(b) mo1- 1 dm3 atm-1
(c) atmmoldm-3
(d) moJdm-3 atm-1
84.
For the conversion of oxygen to ozone in the
atmosphere, nitric oxide in gaseous phase acts
as
(a) enzyme catalyst
(b) Inhibitor
(c)
homogeneous catalyst
(a) C12Hz2O11(aq.) + HzOo) ➔ C6H12O6(aq.)
(d) heterogeneous catalyst
85.
Which among the following oxides of nitrogen is
called nitrogen sesquioxide?
(a) NO2
(c) N 20 4
87.
Pt
(b) 2NH3(g) ~ N 2(g) + 3Hz
(c)
(d) Bi
(c) Sb
86.
+ C6H12O6(aq.)
Which among the following group 15 elements
does not exhibit allotropy?
(a) N
(b) As
(b) N2O3
(d) N 20 5
(d) Hz(g) + I2(g) ➔ 2HI(g)
92.
2SO 3(g)' identify the correct among the following
relations
-d[SO2(g) ]
- d[O2(g)]
dt
dt
+
(b)
1 d[SO3(g)]
dt
2
(c)
88.
dt
(a) H-TS
T
(c)
qrev
10
M solution is 2.5 x 103
If the Vant Hoff factor for 0.1 M Ba(NO 3)z
solution is 2.74, the degree of dissociaion is
(a) 0.87
(b) 0.74
(c) 0.91
(d) 'if7
94.
What happens when ionic hydrides of S-block
elements in molten state are electrolysed?
(a) Hydride ion migrates at cathode
(b) Dihydrogen is liberated at cathode
(c) Hydride ion reforms metal hydride
(d) Dihydrogen is liberated at anode
95.
Which of following is NOT a property of red
phosphorus?
(a) Insoluble in carbon disulphide
(b) It does not show chemiluminescence by
action of air
(c) If forms phosphine when treated with hot
sodium hydroxide solution
(d) It is non-poisonous
dt
dt
(b) qrev
T
1
93.
d[SO 2(g) ]
For a process, entropy change of a system is
expressed as
The resistance of
ohm. What is the molar conductivity of solution?
(cell constant = 1.25 cm-1)
(a) 3.5 ohm-1 cm2 moJ-1
(b) 5.0 ohm- 1 cm2 mol-1
(c) 2.5 ohm- 1 cm2 mol- 1
(d) 2.0 ohm- 1 cm2 moJ- 1
For the elementary reaction 2SO2(g) + O2(g) ➔
(a)
2HzO20) ➔ 2HzOo) + Oz(g)
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96.
The bond line formula of 1-iodo -2, 3-dimethyl
pentane is
(a)
(b)
(c)
(d)
97.
When propene reacts with HCl in presence of
peroxide, the product is
(a) 1-chloro propane
(b) 1, 1-dichloro propane
(c) 2-chloropropane
(d) 1, 2-dichloro propane
98. Which hydride among the following is strongest
reducing agent?
(a) AsH3
(b) BiH3
(c) PH3
(d) SbH3
99. Which of the following is NOT an antiseptic
compound?
(a) Boric acid
(b) Iodoform
(c) Hydrogen peroxide
(d) Potassium sulphite
100. P-pleated sheets of polypeptide chains are
present in
(a) Secondary structure
(b) Primary structure
(c) Tertiary structure
(d) Quaternary structure
SECTION-B
MATHEMATICS
1.
If P(xp y 1) is a point on the hyperbola
x2 -y2 = a 2, then SP.S'P = .........
2
(a)
(c)
2.
4.
X1
2
(b)
a2
2
XJ
1
e
X1
2
+ YI
a2
(d) X12 + YI2
2
-yl
Ifj(x) = COS
(a)
2
-yl
[
_1
1-(logx)
5.
IfA= [;
(a) 0
(b) 4
(c) 2
(d) 1
Which of the following function is not
continuous at x = 0?
(a)
(c)
3.
e
/(x)
']
I1
/ (x) = (1 + 2x) x ,
{ =e2
,
,thenf(e) = ........
2
l+(logx)
e2
f(x)
(d) 1
The order ofthe differential equation of all circles
whose radius is 4, is ..............
(a) 1
(b) 2
(d) 4
(c) 3
x
:;t:
0
x=O
'
e11 x -1
2
(b)
(c)
2
~] andA=A-1, thenx= ........ .
= 11
e x + 1'
x:;t:O
= -1,
x=O
e5x -e2x
=
(d)
f(x)
=l ,
sin3x
x:;t:O
x=O
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6.
It is observed that 25% of the cases related to
child labour reported to the police station are
solved. If 6 new cases are reported, then the
probability that atleast 5 ofthem will be solved is
19
(b) 1024
(c)
(a)
(c)
12 _
19
(d) 4096
19
2048
7.
(a)
(c)
8.
1
9
2
(b) 9
The area of the region bounded by the curve
y = 2x- x 2 and the line y =xis .......... square units
(a)
1
15.
(c)
9.
3
(d)
15
1
15
f co~x+xsinx dx = ......... .
x +xcosx
xsinx
I+c
(a)
log
(b)
logl
(c)
logl cosx+xsinx l+c
(d)
logl x +x cosx l+c
I x+cosx
x
x+cosx
l+ c
2
Iff(x) = 3x-2 andg(x) = x 2, thenfog(x) = .. ...... .
(a) 3x2 -2
(b) 3x2+2
(c) 3x - 2
(d) 2 - 3x2
7
(d) 6
1
7
7
14.
1
(b) 2
6
7
1
A stone is dropped into a pond. Waves in the
form of circles are generated and radius of
outermost ripple increases at the rate of 5 cm/
sec. The area increased after 2 seconds is .. ...... .
(b) 40cm2/sec
(a) 100ncm2/sec
(c) 50 cm2/sec
(d) 25 cm2/sec
(d) 9
9
(b)
13.
4
7
5
Which of the following is NOT equivalent to
p ➔ q.
(a)
(b)
(c)
(d)
The general solution of x : = y- x tan (:)
p only if q
q is necessary for p
q onlyifp
pis sufficient for q
lS . . ..... .
16.
5
3
The value of f~/ax +bx +cx+k)dx, where
a, b, c, k are constants, depends only on ....... . .
(a) a, b and c
(b) k
(c)
(C)
10.
X
The statement pattern
(p I\ q) /\ [ - r
V
(p I\ q)]
is equivalent to .......... .
(a) r
(c) PA q
11.
17.
sin ( ~) = C
V (-
p
I\
q)
(b) q
(d) p
A bag contains 6 white and 4 black balls. Two
balls are drawn at random. The probability that
they are of the same colour is ...........
a and b
(d) a and k
The general solution ofthe differential equation
ofall circles having centre atA(-1, 2) is ........ .
(a) x 2 + y 2 + x-2y+ c = 0
(b) x 2 + y 2 -2x+4y + c= 0
(c) x 2 +y2 - x+2y+c=0
(d) x2 + y 2 + 2x-4y + c= 0
18.
If A is non-singular matrix such that
(A-21) (A--41) = 0thenA + 8A-1 = ...... .... ..
(a) I
(b) 0
(c) 3 I
(d) 6 I
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2019-11
IfG(3, -5, r) is centroid of triangle ABC where
A(7, -8, 1), B(p, q, 5) and C(q + 1, Sp, 0) are
vertices of a triangle then values of p, q, r are
For a GP, if(m + n)th term isp and(m-n)th termis
. ........... .
q, then m thterm1s
24.
(a) pq
respectively ...... . .
(b) -4, 5,4
(a) 6,5,4
(c) -3,4,3
1
20.
(b)
-tan
(c)
tan
1
-1
2
-1
x+
21.
tan
-1
X
2
2(x + 1)
+c
x+
(c)
3
1
(a)
2✓
3
22.
xlogx
(b) 2✓3
28.
(b) xlogx
2
(c)
23.
xlogx 2
25
(d) logx
sin B
In i1 ABC; with usual notations, if cos A= ---:---C ,
sm
then the triangle is ..... .......
(a) Acute angled triangle
(b) Equilateral triangle
(c) Obtuse angled triangle
(d) Right angled triangle
1
sinx cosx =
Derivative of log/ (logx) with respect to x is
(a)
24
(d) 25
The values ofx in ( O, ; ) satisfying the equation
-1
1
23
27.
✓
3
2
7
(b) 25
The equation of normal to the curve y = loge x at
thepointP(l, 0) is .......... .
(a) 2x+y=2
(b) x-2y= 1
(C) X - y = 1
(d) X + y = 1
2
(c)
I
26.
+c
171t
If e = - - then tane -cote = .......... .... .
3
5
+1
2(x2 + 1)
q
p
;:x) I ~ I ~ I ~ I ~ I ~ I ~
(a)
X
1
(d)
ThenP(2 5 x < S) = ......... .
x+-2- + c
X
(d)
I
1
x----+c
2x(x 2 + 1)
-1
tan
q
Jpq
A random variable X has following probability
distribution
25.
dx _
J-(x2-+-1)2
- .......... .
()
a
p
(c)
(d) -2, 3, 2
(b)
29.
4 are ..........
(a)
1t 1t
6 '12
1t Sn
(b) 12' 12
1t 31t
(c)
s's
1t 1t
(d) 8 '4
If ;
b, b
cand c
are coterminous edges
ofa parallelopiped then its volume is ......... .
+
+
+ ;
(a)
3[a c b]
(b) 0
(c)
2[a b c]
(d) 4[b a c]
If the c.d.f. (cumulative distribution function) is
x -25
given by F(x) =
, then P(27 , x , 33) = ......
10
3
(a)
-
(c)
-
5
1
5
(b)
3
10
(d)
1
10
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30.
The joint equation ofpair ofstraight lines passing
through origin and having slopes (I+ ✓
2) and
37.
r /x2 - a2 dx = ..........
X
(1
31.
+1✓2) is ...........
(a)
2xy+ y2
x 2 -2✓
=0
(b)
x 2 - 2✓
2xy - y2
=0
(c)
x 2 +2xy -
(d)
x 2 +2xy+ y2
(a)
✓x2 -a 2 - acos- 1 ( ~ )+ c
(b)
x.Jx2 - a2 -
(c)
✓x2 -a 2 +asec- 1(~)+c
(d)
.Jx2 - a2
y2 = 0
=0
±tan-I ( ~) + c
+_!_sec- 1 (x) + c
X
x - 2 y - 3 z -5
The angle between lines - - = ~ = - 1
2
y -3 z - 5 .
-= - - = -- 1s ........... .
1
2
2
(a) 30"
(b) (:ff
(d) 90"
(c) 45°
38.
x- 2
The maximum value of z = 9x + l ly subject to
3x+ 2y ~ 12, 2x+ 3y~ 12,x~O,y~ 0 is .......... ...
(a) 44
(b) 54
(c) 36
(d) 48
and -
32.
33.
If the line passes through the points P(6, -1, 2),
Q(8, -7, 211.) and R(5, 2, 4) then value of/\. is ......... .
(a) -3
(b) 0
(c) -1
(d) 2
The equivalent form of the statement ~(p ➔ ~q)
is ................. .
(b) p I\ - q
( C)
34.
35.
39.
p
V -
q
(d) - p
V
40.
q
IfA= {x E R:x2-5lxl + 6=0}, thenn(A) = ........ .
(a) 2
(b) 0
(d) 4
(c) 1
41.
x
x-:;,. 0 is continuous at x = 0 then,j(O) = ..... .
36.
(b) a + b
(d) a - b
42.
The coordinates of the foot of perpendicular
drawn from origin to the plane 2x-y + 5z - 3 = 0
are ........ .
43.
(d)
(1-11)
5' 10 '2
l+ ✓
x
-
•• • • • •••• • ••
(a)
log( e; J
(b)
log( e:J
(c)
log( e:J
(d)
log( e: ]
The number of solutions of sin 2 0 =
is ........ .
(a) three
(c) two
log(l + ax) - log(l - bx)
If the functionj(x) = - - - - - - (a) loga - logb
(c) loga + logb
Jo4_l_dx-
1
2
in[O, 1t]
(b) four
(d) one
p, qand ;
If
then
are nonzero, noncoplanar vectors
[p +q - ; p-q q- ; ] = .........
(a)
3[p qr]
(b) 0
(c)
[pqr]
(d) 2[p qr]
Which ofthe following equation has no solution?
(a)
sec0 = 23
(b) cos0 = ✓
2
(c)
tan0 = 2O19
1
(d) sin0= - 5
The minimum value of z = 1Ox + 25y subject to
0 ~x~3, O~y~3,x+y~ 5 is ....... .
(a) 80
(b) 95
(c) 105
(d) 30
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44.
45.
If.f{x) = 3.x3-9x2 -27x + 15, then the maximum
value of.f{x) is ........... .
(a) 45
(b) 30
(a)
(c) -30
(c)
(d) <56
The equationof the plane passing through the
point (-1, 2, 1) and perpendicular to the line
joining the points (-3, 1, 2) and (2, 3, 4) is ... .... .
(a)
r .(5i + 2) + 2k) = 1
(b)
r .(51 + 2) + 2k) = -1
(c)
(d)
46.
2019-13
r.(5i -2) + 2k) = -5
r.(51 -2)-2k) = 1
49.
Ifthe lengths ofthe transverse axis and the latus
rectum of a hyperbola are 6 and
8
3 respectively,
then the equation of the hyperbola is ..... .... .
(a) 4x2-9y2=72
(b) 4x2-9y2 = 36
(c) 9x2 -4y2=72
(d) 9x2-4y2= 36
47.
48·
The value of
1
tan- 1 -
3 +
1
5+
1
tan-1 -
7+
1
tan- 1 -
8
7t
(b)
37t
(d)
7t
(a)
✓3x 2 -4xy + ✓3/
(b)
x2 + ✓3xy - y2
(c)
3x2 -
4
(d)
x 2 - ✓3:xy - y2
=O
=0
y2 = 0
=O
IfP(2, 2), Q(-2, 4) and R(3, 4) are the vertices of
LlPQR then the eqution of the median through
vertexRis ............
(a) x + 3y+ 9 = 0
(b) x-3y + 9 = O
(c) x - 3y- 9 = 0
50.
4
The joint equation of the lines passing through
the origin and trisecting the first quadrant is ....... .
Ifx =
(a)
tan- 1 -
l l1t
5
-Ja sin- 1 1 ' y= -Ja cos- 1 1 , then
-y
X
· .. . .... . . .. .
IS
(c)
(d) x+3y -9 = 0
X
(b)
y
(d)
-x
y
y
X
dy
=
dx ······
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11111
ANSWER KEYS & SOLUTIONS
---~~~=--=--==------=----=--=-=-=-.:..:...;;.......--1111111
(MHT-CET 2019)
Answer KEYS
SECTION-A
6 (a)
7 (b)
(c) 8 (d)
(d) 9 (c)
(a) 10 (c)
1
2
3
4
5
(b)
11
(a)
12
51
52
53
54
55
(d)
(d)
13
14
15
(b)
(c)
(c)
(c)
(d)
16 (c)
17 (d)
(c)
(b)
(c)
(d)
(d)
(d)
18
19
20
(b)
(c)
(c)
PHYSICS
(b) 26 (c)
(c) 27 (a)
21
31 (d) 36 (b) 41 (None) 46 (c)
(b)
22
32 (None) 37 (d) 42
47 (a)
(c)
(c)
23 (a) 28 (a) 33
48 (b)
38 (d) 43
(b)
24 (d) 29 (d) 34 (a) 39 (b) 44
49 (b)
(c)
25 (d) 30 (d) 35 (a) 40 (b) 45
so (b)
CHEMISTRY
(c)
56
57 (b)
(a) 58 (d)
(a) 59 (a)
(c) 60 (b)
61
66
62
67
63
68
64 (a) 69
65 (b) 70
76 (a) 81
77 (d) 82
78 (a) 83
79 (c) 84
80 (b) 85
(c)
(b)
(d)
(c)
(d)
86
87
(b)
88
(a)
MATHEMATICS
21 (d) 26 (d) 31
22 (c) 27 (b) 32
23 (d) 28 (c) 33
(d)
(c)
24
29 (a) 34
25 (a) 30 (a) 35
(d)
(b)
36 (d) 41
37 (a) 42
38 (d) 43
39 (c) 44
40 (c) 45
71
(b)
72
(d)
(c)
(b)
73
(a) 74
(a) 75
(b)
(c)
89 (a)
90 (b)
91
92
93
94
95
(b)
(b)
(a)
(d)
(c)
96
97
98
99
100
(c)
(c)
(b)
(d)
(a)
SECTION-B
1
2
3
4
5
(d)
(a)
6
7
8
9
(c)
10
(*)
(b)
(d)
(d)
11
12
(a) 13
14
15
(c)
(b)
(c)
(b)
(b)
(d)
(d)
(d)
(b)
16
17
(a) 18
(a) 19
(c) 20
(b)
(a)
(b)
46 (b)
47 (b)
48 (a)
49 (b)
(a)
so (a)
(c)
(b)
(a)
SECTION-A
PHYSICS
mv2
r
...(ii)
Tbottom =-+mg
1.
(b)
mv2
Ttop =--mg
r
Solving (i) and (ii) we get :
...(i)
2
Ttop
Tbottom
=
v - rg
v 2 + rg
79
= 81
...................C ...................
2.
Tbottom
(a)
E=-Mdi =-M_!(5sin2001tt)
dt
dt
=-M x 5 x 200 n cos(200 n t)
mg
IE lmax = 101t volt
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l\ffiT-CET 2019
3.
(c)
4.
(d) v = n11,
= 5c = 5 x 2 µF
[for open pipe in fundamental
11
11
_ 10 F
-11µ
mode 11, = 2/, where l is the length
of the pipe]
So, v=n 1(2/ 1)=ni(2/2)=n 3 2(/1 + /2)
⇒
5.
1
1
1
Il3
n1
n2
9.
(c)
-=-+-
mv
qvB= r
2
...(i)
nh
mvr=-
...(ii)
2n
(a) Cp -C V =R
...(i)
_.!_ mv2
K.E.-
...(ii)
... (iii)
2
Solving (i), (ii) and (iii) we get:
Solving (i) and (ii)
K.E.=
We get : C = Ry
y-1
p
1
nh
nhqB
=-xqBx--=
2
2nm 4nm
2
6.
(a)
1
2 rqvB
2
1 )
z = R + ( roL - roe
10.
(c)
11.
(b)
12.
(c)
13.
(c)
1=
14.
(c)
Particle velocity
PuttingR = 300 n, L = 0.9H, C =2 x 10-6p
and co = 1000 rad/s
We get : z = 500 Q
7.
8.
(b)
C
(d)
-----+----.1
1--+-----1
H
1
Ya11/
3
v-lv = __3__ A= 20mA
1000 100
C
1-I- -
dY
v 1 = - = a2nbcos2n(bt-cx)
dt
So, V 1max=a x 2n x b=2nab
.
ro 2nb b
wave velocity v 2 = - = =K
2nc
c
- - - - - - 1 - - - I H - I5c
-
-----1
C
C
c.q
_..____ _ _ _ __
⇒
=C
=
eq
=
1
5c
(-1 + _!_ + _!_) 1 + 5 + 5
5c C C
15.
1
c=na
(d) For fundamental mode
let time period be T, then
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T
t=4
So,
⇒
T=4t
⇒
_!_=(4tf 1
T
⇒
u=(4tt 1
23.
(a)
So, uinitially = 2 x T x 4nr
(d)
TX 4nR
5
I
oc
⇒
G~
V=
✓G~
_!_m GM= 1 mGM =_!_m R
2
r
2(3R+R) 8 g
2
2
<d)
I =~mr2
⇒
r2
2
24.
17.
r
2
.
1
N ow, Ki nettc energy= mv
(c) ~ig single drop= 2 3 rsmall drop
U=TxA
U finally
GmM
⇒ v2 =
1
16.
mv 2
Q
A )
mean position
O
A )
•
p
1---"""<,...A------<-A---1
in one time period total distance travelled
r2
=A + A+A + A=4A
[ as in each quarter starting from mean
position it travelles A distance as shown]
18.
(b)
R = V and for conductor R increases with
I
25.
(d)
iRg+iR=50
⇒
increase in temperature.
19.
(c)
21.
22.
R=
2
r =r/ +r;
r
20.
i (Rg + R) = 50
= ✓3 2 +42
w 15
v=-=K
1
Now v=/r
⇒ F = v2 µ = (15)2 x (10-3 ) = 0.225N
[Here F = tension force and µ = 1o-3 kg/m]
0
- 100 =49000
lOxl0-3
26.
(c)
27.
(a) Given circuit forms wheat stone bridge:
so,
=5cm
(c) Parallel currents in the same direction attract
each other.
(b)
(c) as y = 0.05 sin(x + 15t)
so,
5
⇒
also
i,(5+1)Q=i2(50 + 10)Q
i1 = 10i2
...(i)
i 1 + i2 = 1.1 A
...(ii)
Solving (i) and (ii) we get i 1 = IA which
passes through 1n resistor
28.
(a)
l
_!_ =K[-1
- _1
2
2
A
⇒
n1
;1
n2
=K(212 - 3~
J
[for first line of Balmer series
n 1 = 2 and n 2 = 3]
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MHT-CET2019
also
2019-17
_l"'2 -_K(-1__l)
22 42
[for second line in Balmer series
38.
(d)
n 1 = 2 and n 2 = 4]
so,
29.
⇒
(d) Work done in streatching a wire
Height in the capillary
1
.
= - x stress x stram x volume
h = 2scos0
pgr
2
nr 2
I
1
1
r
h oc -
= - x Yx(M)2 x 2
so,
30.
31.
32.
33.
34.
35.
w2
( r2 , 2 ( 1, l
~=l~J xl,J
(d)
(d) Resolving power oc , d
Resolving power of a telescope 1s
proportional to the diameter.
(None)
(c)
(b)
Angular deviation 8 = (µ- 1) A
:. 1 = (µ-1)3
3MR 2
3
3
(a) I = - - = Sn 2 .Q.L
2
(a) Torque= Force x distance
Moment of force = Force x distance
So, Moment of force and torque have same
dimension.
36.
39.
(b)
~de
le
=i;
Collector current
1
µ = 1+3
= 1.33
40.
(b) Using conservation of energy
Total mechanical energy at surface = total
mechanical energy at height h
Using this, we have
1
R
1
r
1
4R
r
1
R
Base current
37.
1
4R
(d) LiT = -Ta0
2
= ½ x 9 x 10- 7 x lO x O.5
1 3
R .4
r = 4 / 3R
h =R / 3
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41.
42.
43.
44.
TargetMHT-CET
(None)
(b) K max = hu-cp
47.
F = mw2r
=
: . K 2 =2hu-Wn = k + hu
(c) From Doppler's effect. We know that
frequency increases.
(b)
(a)
47t2
mr -2-
T
:. ✓F = ✓
mr.
48.
(b)
49.
(b)
2;
he
K max =T-cp
- - -r- - - - - ~
•• •• • ••• • • •
• • • • • ••••• • • •••• • ••••••••• •• • • • • • • uu oouoo oo ,
2
1 mv 2
v
Vs = - - - = - 2 e
2 _{!_
m
= µo-3._NJA
B
45.
50.
47t r3
axis
(b) Focal length ofnew lens = 2 x focal length
of convex lens.
CHEMISTRY
(c) Terminal velocity v oc Ps - P1
51.
(d) Wolframite is magnetic in nature whereas
stannic oxide is non-magnetic in nature.
Hence they can be separated by magnetic
seperation method.
52.
(d)
53.
(a) Abscisicacid(molecularformula(C 151½00 4)
~= e2 -cr
v1
e1 -cr
+7
Mn 04 + Br-
-t4
~ Mn 0 2
+5
+ Br 03
Hence (d) is correct option.
46.
(c)
a=
Q2
Q1 -Q2
composed of three isoprene residues and
having a cyclohexene ring with keto and
one hydroxyl group and a side chain with
terminal carboxylic group in its structure.
HC CH
0
COOH
H3
Abscisic acid
54.
a+l
a
(a)
OCH3
6 +m- Anisole
OH
6
Phenol
+CH
31
Iodomethane
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55.
(c) The decaffeination process includes soaking
green coffee in hot water and then some of
solvent or activated carbon is used to extract
the caffeine. The solvent typically used are
methylene dichloride or ethyl acetate.
56.
(c)
fiH-fiU = _.!._ x 2x300
2
= -300cal
64.
(a)
[Co(NH3) 5NO2]SO4 + BaC12 ➔
[Co(NH3)sNO2] Cl2 + BaSO4
volume that carries the current in a solution
decreases on dilution.
(White ppt)
57.
The precipitate of barium sulphate is white
in colour.
(b) When concentrated HCl is added to a very
Conductivity decreases with decrease in
concentration as the number of ions per unit
65.
(b)
Na
C H3 -CH= N-OH---CH3 CH 2 NH 2
Acetaldoxime
diluted solution of CuSO4 , the pale blue
solution slowly turns greenish yellow on
NaN0 2
HCI
the formation of copper chloride complex.
[Cu(HiO)l++4a- ~ [Cuc1J-+6llio
(Pale blue)
58.
59.
(Yellow)
66.
(d)
(d) Novolac polymer is used in paints.
(a) Given, n = 3 moles, v 1 = 0.3L, v2 = 2.5L,
67.
(d)
62.
63.
(b) cis-platin is used in the treatment ofcancer.
(c) NaCl and KCl have same atomic ratio similar
'
molecular formula and similar chemical
properties but different crystal structure.
Thus NaCl and KCl are not isomorphous.
(b) 2, 4-dichlorophenoxy acetic acid is the active
ingredient in many products as an herbicide
to kill weeds on land and in the water.
(c)
(B)
Frenkel defect is found in AgCl because
there is a large difference between the size
of Ag+ and c1-. Hence the cation Ag+
vacant.
0.1 molar = 0.1 mol is present in IL
Givenvolume=200mL ,,,,Q.2L
2
= - x O.l
1
68.
69.
AfI = fiU + fin gRT
1
1
fing =1-1+-=--
2
(a)
alkanes.
Bacteriostatic antibiotics limit the growth
of bacteria by interfering with bacterial
protein production, DNA replication or other
aspects ofbacterial cellular metabolism. This
2
AfI-fiU = fin gRT
(d)
= 0.02 molofCO2
V =0.02 x 22.4=0.448L
The given reaction is an example of Wurtz
reaction which is used in preparation of
1
CO(g) + -02 (g) ~ CO 2 (g)
2
CH 3 CH2OH+H 2O+N 2
No. of mole in 0.2 L liquid
=-423.54J
60.
61.
(A)
occupy the interstitial site by leaving a
corresponding number ofnormal lattice site
p ext= 1.9 atm
Workdone in isothermal process' w = -Pexdv
.". w=-1.9 X (2.5-0.3)
w=-4.18Latm
w=-4.18Latm x 101.325 JL- 1 atm-1
alcohol
70.
group includes tetracyclines.
(a) Alkyl halides react with silver nitrite in
ethanolic solution to give nitro compounds.
71.
R-X + AgNO2 ~RNO2 +Ag l
(b) Bond length order for the given options is,
C-H > C-C > C-N~C-O
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72.
(d) Ethyl alcohol and water, after mixing, can
77.
(d)
very easily become a homogeneous mixture,
because the two liquids are miscible, soluble
in all proportions. The dipoles on the
Acetophenone
ethanol and water molecules cause the
formation of hydrogen bonds between the
Ethylbenzene
reduction
78.
(a)
molecules.
73.
Clemmensen
Molar mass ofurea CN"F½CO :NHi)
= 28 + 4 + 12 + 16 = 60 g/mol.
(c) Nicol's prism is a type ofpolarizer, an optical
60g urea contains 12g C.
device made from calcite crystal. Calcite is a
12
100g urea contains - x 100 = 20% C
60
carbonate mineral and the most stable
polymorph of calcium carbonate.
74.
(b) ApplyingFaraday'ssecondlawofelectrolysis
wt. of Cu
wt. of Al
E
E
Ew of Cu
=---
w
(c)
~
~
Ew of Al
80.
(b)
OH
n-butyl alcohol
a-butylene
of Cu= Atomic wt= 63.5
w
n factor
2
of Al=
79.
Tf = i.Krm
Given, T r = T; -Tr
= 0-(-0.680)
= + 0.680°C
27
3
m
= 0.2
~ = 1.86
0.4x63.5
wt of Al
=
31.75
Thus,
0.680
X
1.86
9
0.680
83
= 0.2 x l.86 = 1.
wt ofAl= 7 .2 g
81.
wt ofAl in moles='!....}__= 0.27 mol
27
75.
= i X 0.2
(c) NaCl, NH3, Ca(OH)2
Ca(OH)2 is used for the regeneration of
ammonia
(b)
2NH4Cl(aq) + Ca(OH)2 (aq/s) ➔ CaCiz(aq)
+ 2NHig) + 2HzO(1)
Benzaldehyde
82.
(b)
83.
(d) mol ctm-3 atm- 1
84.
(c) Nitric oxide (pollutant) act as an homogeneous
Mandelonitrile
catalyst in the conversion ofoxygen to ozone,
since at very high concentration in air it
Both ions contain - 2 charge.
converts into NO2 which generate free oxygen
atom.
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l\1HT-CET2019
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86.
(d) Bi does not exhibit allotropy.
(b) Nitrogen sesquioxide is N 2 O 3 .
87.
(c)
85.
2.74= n(1+ 2 a)
n
-1 d[SO 2 ] = -d[O 2 ] = _!_ d[SO 3]
2
dt
dt
2 dt
d[SO3] _ -2d[Oz]
dt
dt
1 + 2a.
a= 2.74-1 = 0.87
2
94.
(d) Ionic hydrides of S-block elements, in
molten state, liberate dihydrogen gas at
anode on electrolysis.
88.
(a)
anode
89.
(a) Terylene is a synthetic polymer which is
formed by the interaction of ethylene glycol
95.
(c)
phosphorous with cone. NaOH solution.
and terephthalic acid.
90.
91.
Phosphine is formed by heating white
(b) Copper
(b) The decomposition ofammonia on platinum
surface is a zero order reaction.
92.
(b) Resistance (R) = 2.5 x 103 ohm
Cell constant
Conductivity (K) = -R-es_i_st-an_c_e_
l-Iodo-2, 3-dimethylpentane
97.
(c)
1.25cm- 1
Conductivity (K) =
Cl
2.5x103ohm
I
Peroxide
CH3 -CH= C8i+HC1----+ CH 3 -CH-CH3
Propene
K
Molar conductivity (Am) = C x 1000
98.
2-Chloropropane
(b) As we move down the group, M-H bond
dissociation
enthalpy of hydrides
decreases. Therefore, reducing property of
5 10-4 h -l -l
A = x
o m cm x 1000
0.1 mol cm-3
m
(a)
99.
Ba(NO3)z------+ Ba z+ + 2NO
3
nmol
0
n-na.
na.
follows,
PH3 < AsH3 < SbH3 < BiH3
A m = 5 ohm-1 cm2 mo1-1
93.
metal hydrides increases in the order as
0
2na.
Total moles ofparticles
= n-na. +na. +2na. = n(l + 2a)
(d)
100. (a)
Potassium sulphite is not an antiseptic.
Secondary structure of protein refers to the
shape in which a long polypeptide chain
can exist. They are found to exist in two
different types of structures viz. a-helix and
P-pleated sheet structure.
n(l + 2a)
Vant Hafffactor (i) = - - -
n
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SECTION-B
3.
MATHEMATICS
1.
(d) ·: P(x" y) lie on x 2 - y 2 = a 2 •
then; xf - yf = a 2
2
⇒ x1
-a
2
2
Differentiating we get:
2
= Y1
2
(b) Equation of family of circles whose radius is
4is:
(x -a)2 + (y-b)2= 16
... (i)
(where a & bare arbitrary constant)
... (i)
2 (x-a) + 2(y-b)y1
... (ii)
2
·: x -y = a is an equation ofrectangular
hyperbola.
:. e=
✓
2
Again differentiating we get :
SP= ex 1 -a= ✓
2x 1 -a
S'P= ex I +a= ✓
2 x I -a
2 2
2
2
2
: . SP. S'P= e x1 -a = 2x1 -a
⇒ 1+ yf +(y -b)y 2 =O
2
= xf + xf-a = xf + y f (from(i))
2.
(*) f(x)=cos-1 [1-(logx)2]
1+ (logx)2
(1 + yf)
⇒ y -b=----
⇒ f ( u)
... (iii)
Y2
Let 1 + (log x)2 = u
⇒ 1-(logx)2 = 2-u
from (ii) we get:
2-
= cos-1 ( -u-U )
2 l)
= cos - I ( --;;-
x-a =-(y-b)y 1
:. from (i), we get:
(y -b) 2 yf + (y -b) 2
1
⇒j'(u)=
2
⇒ (y - b) -
2
(1 + Y1 )
=16
= 16
u~
(from (iii))
⇒
1
f'(x) = - - - - - = = =
(1 + ((log x) 2 )✓(log x) 2
1
= logx(l + (logx) 2 )
:. Order= 2 & degree= 2
1
1
⇒ f'(e) = log e(l + (log e) 2) = 2
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l\ffiT-CET 2019
4.
7.
(a) A= [: ~]
IAl = 0-1 = -1
:. A- -1[~l ~l]
1
=
1
7
·: =A=A-1
5.
: . t2 = S2-S1=
⇒ x=0
(c)
(a)
8.
11
lim f (x) = lim (1 + 2x) x
n➔ O
n➔ O
&y=x
=e2
From the above equations we get,
x=2x-x2
: . Continuous atx = 0
⇒ x2 -x =0
(b) lim f ( x) = lim (sin x - cos x) = 0 - 1 = -1
n➔ O
lim f(x)
n➔O
= lim \
⇒ x(x-l)=0 ⇒ x = 0,
⇒y
1
= 0, l (respectively)
: . intersecting points of the two curves are
&f(0)=-1
:. Continuous atx = 0
(c)
4
(a) Given curves are y = 2x - x 2
&f(0)=e2
n➔ O
7-3
9-3=-9-=9
(0, 0) and (1, 1)
y
l
x +l
1/x
n➔ Oe
ell x [
(y=x)
1__l_]
ell x
[l _1_]
lim----=---~
= n➔O
II x
e
+ ell x
= (l-O) =l&f(0) = -1
(1 +0)
y'
1
:. not continuous at x = 0
(d)
lim f(x)
n➔ O
= lime
5x
n➔ O
f
1
2
: . required area = (2x -x )dx - f x-dx
0
2x
0
.- e
sm3x
is using L' Hospital's rule:
lim
n➔ O
5e5x - 2e 2x
3cosx
=
5(1)- 2(1)
3
3
- =1
3
:. &f(0)= 1
:. Continuous atx = 0
6.
(d)
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9.
dv
(c) Given: x dy = y-xtan(y)
dx
⇒
x
⇒
... (i)
dx
- - =-tanv
X
dx
cotvdv=-x
Integrating we get :
Put
y
-=v ⇒
X
⇒
⇒
_ _ dy_
dv
y-xv---v+x-.
dx
dx
dv
x-+v=v-tanv
dx
ln (sinv) = -ln (xc)
[from(i)]
dv
x-=-tanv
dx
.
(Cl)
⇒ ln (smv) = ln -;- ·
.
Cl
⇒ smv=- ⇒
X
.
y
xsmv= -=c1.
X
10. (b)
p
q
r
"i°
~p
pAq
~pAq
~rv(pAq)
(pAq)/\
(pAq)/\
[~rV(p/\q)]
[~rv(pAq)]v
(~ pAq)
T
T
T
T
T
T
T
F
F
T
F
T
T
F
F
F
T
T
T
T
T
T
F
T
F
F
F
F
F
F
F
F
F
T
F
F
F
T
F
F
F
T
T
T
F
F
F
T
F
T
T
F
F
T
F
T
T
F
T
F
T
T
T
F
F
F
F
F
F
F
T
T
F
F
T
F
F
F
F
F
(p /\ q) /\ [~ r V (p /\ q)] V (~ p /\ q) = q
11. (c) Total number of balls = 10.
No. of ways of drawing 2 balls out of
12. (b) Let I=
f co~x+xsinx dx
x +xcosx
10= IOC2 =45
No. of ways of drawing 2 white balls out of6
= scx+cosx)- x(l-sinx) dx.
x(x+cos)
6
= C2 =15.
No. of ways of drawing 2 balck balls out of 4
=
f[.!.. _ (1 - sin x) ] dx.
x
4
= C2 =6.
15+6 21 7
:. required probability = ~ =
= .
45 15
(x+cosx)
Put fix)= x + cosx ⇒ f' (x) = 1 - sinx.
⇒
1
1=
.!_
dx.
. EEBOOKS.I
MHT-CET2019
2019-25
⇒
(x+ 1)2+ (y-2)2 = r2
⇒ x2 + 1 +2x +y2+ 4-4y=r2.
⇒ x + y2+ 2x-4y + 5-r2=0.
= log Ix I-log 1/(x)l +c
= log,~
2
I+ c.
~
⇒ x 2 + y2 +2x-4y + c=0,
13. (a) Radius increases at the rate of 5 cm/sec.
.·. radius after 2 seconds = 10 cm.
Now, Area(A) = w2
where (c = 5-r2).
Above equation is the required solution.
18. (d) ·: (A-21)(A-41) =0
(r = radius)
⇒ A 2 -4A-2A + 81=0
dA
dr
., -=21tr.- .
dt
dt
⇒ A 2 - 6A
+ 81= 0
Multiply A-1 both sides we get :
A-1. A.A-6A-1A + 8A-1.I = A- 1.o
⇒ IA - 61 + 8A-1 = 0
⇒ A - 61 + SA-1 = 0
: . after 2 seconds.
2
dA = 2n(10)(5) = 100ncm / sec.
dt
⇒ A + 8A-1 = 61.
14. (a) f(x) = 3x-2andg(x) =x2•
⇒J[g(x)]
= 3(x2) - 2 = 3x2 -2.
15. (c) "q only ifp" is not equivalent" p
➔
19. ld)
Here·' -7 +P +-q + 1 -- 3
~
3
q".
3
16. (b)
-8+q+5p
- -- ~= -5
3
J(ax 5 +bx3 +cx+k)dx
-3
1+5 + 0
and - - -= r
3
⇒
⇒
⇒
p+q -1
-
Sp+q=-7
...(i)
....(ii)
r=2
Subtract (ii) form (i), we get:
p + q - Sp- q = 1 + 7
⇒ -4p = 8 ⇒ p = -2.
from ( 1) we get,
- 2 + q = l ⇒ q = 3.
l
_ a(-3) 6 + b(-3) 4 + c(- 3)2 + k(-3)
[
2
6
4
:. p =-2, q = 3&r= 2.
20. (b) let 1 =
l
dx
f ( x 2 +1)
2
Putx = tan0 ⇒ dx = sec20 d0.
⇒ 1=
f sec22 0 d0 = f sec42 0 de
(tan 0+ 1)2
= 6k.
:. given integral depends only on k.
17. (d) Equation of all circles having centre at
(-l , 2)is :
(x- (-1))2 + (y-2)2 = r2 (r = radius).
sec 0
⇒ 1 = Jcos 2 0d0 = ½J(cos20+l)d0
⇒
1 .
0
1 = -sm20 +-+ c.
4
2
...(1)
·: tan 0 =x
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sinB
23. (d) · · cos A=-.
sinC
⇒
cos A sin C = sin B.
⇒ cosAsinC= sin (n-(A +C))
(": A + B + C = 1t).
⇒ cosAsinC = sin (A+ C)
⇒ cos A sin C = sin A cos C + cos A sin C
X
1
⇒
⇒
⇒
⇒
sin8= p&cos8=
1 +x 2
sin28 = 2sin8cos8 =
Q ·
1 +x
2
For sin A= 0, A= 0° (not possible)
For cos C=0, C=90°
:. ~ABC is right angled triangle.
2
x
(l+x 2 )
24. (b) Let a is the first term & r is the common ratio.
:. p = ar"+n- 1 & q = ar--n-1
⇒ pq = a2rn +n- 1r--n-1
⇒
.
1
1 -I
X
. . I=-.
+-tan x+c.
2
2 (1 +x ) 2
⇒
25. (a)
21. (d) ·: 8 = 171t = 61t - 7t.
3
3
sin A cos C = 0
Either sin A= 0 or cos C = 0.
pq = a 2r2m - 2 = (ar"- I )2
.J"iq = a r m-I = mth term.
X =x
1
2
3
P(X= x)
k
3k
5k 7k
:. tan8 -<:ot8 = tan( 61t-i)- cot( 61t -i)
4
5
6
8k
k
6
·: IP(X) =l
7t
7t
3
3
x= I
=-tan-+ cot-.
⇒ k + 3k+ 5k + 7k+ 8k+ k= 1 ⇒
k =-l
25
:. P(2 ~x< 5) =P(2) + P(3)+ P(4)
1 3
= 3k+ 5k + 7k = 15 x - = -.
25 5
22. (c) Let y= loge2 (logx)
26. (d) ·: y
= log(logx) = log(logx)
= loge x
=-
----=c-'---CC........C..
loge2
⇒
dy
dx
dy _ _1
dx
X
2
⇒
1 1 d
2 logx dx
- = - .---(log x)
dy)
=1.
dx (1,0)
:. equation ofnormal is :
1
1
1
1
=-- -=--- =--x log x 2
2logx·x 2xlog x
(y- 0) =- l (x- l)
⇒ y = - x+ 1 ⇒ x +y= 1.
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MHT-CET2019
27. (b) ·: sinx cosx =
1
4 ⇒ 2sinx cosx = 2
1
. 2 x=-1>
⇒ sm
1
2
n 1t
2x=nn+(-1) -,nEI.
6
7t
30. (a) Equations oflines are :
2)(y-O) &(x-0)
(x -0) = (1 + ✓
=
(-1-)
1+ ✓
2
(y- 0)
Forn=0 x=-.
y
~
1-✓
2
or x=y(l+'.'L.) & x= --r,:- x --r,::1+'.'2 1-'.'2
5n
Forn= 1 x=-.
2) = 0 & x + y (1- ✓
2) =0
or x - y(l + ✓
'
12
'
12
:. joint equation is :
:. x has only 2 values is ( 0,;}
28. (c) ... a+b,b+candc+aare coterminous
[ x-y(l + ✓
2)][ x+ y(l - ✓2)] = 0
⇒ x 2 + xy(l- ✓
2)-xy(l+ ✓
2)
-i(l-(✓
2)2) = 0
edges of a parallelopiped.
Then,itsvolume(v)=[a+b
b+c c+a]
⇒ x 2 +xy- xy✓
2-xy
We know, scalar triple product
-xy✓
2- y2(-1) = 0
⇒ x 2 - 2✓
2xy + y2
Consider [a + b
b+ c
c +a ]
=(a+b). {(b+c) x (c+a)}
=0 •
31. (d) Angle beween the lines :
x-x1 = y-y1 = z-z1
al
= (a+ b).{(bxc)+(bxa)
!Ji
CJ
+(c x c)+ (ex a)}
is:
=a. (bxc) +a .(b xa)+a .(cxa)
-- - --- ---
+b .(bxc)+b .(bxa)+b .(cxa)
:. angle between two given lines is:
CO!q
= I(2)(1) + (-2)(2) + (1)(2)
✓4 + 4 + 1 ✓1 + 4 + 4
+[bba]+[bca]
=[ab c] + [b ~
29. (a)
;]=
2 [a b c]
⇒ case = 0 ⇒
0=90°.
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32. (c) Herethegiven threepointsP(6, -1 , 2),
Q(8,-7, 2A) andR(S, 2, 4) are collinear.
we know that if three points (xi' y 1, z 1),
(x2, y 2 , z) and (x 3,y 3, z) are collinear, then
36. (d) let the co-ordinates of foot of perpendicular
from the orgin (0) to the plane 2x -y + Sx = 3
isP(a, b, c).
:. direction ratios of OP are < a, b, c >
which is also the direction ratios ofnormal to
X1 -X2
YI -y2
Z1 - Z2
X2 -x3
Y2 -y3
z 2 -z3
---=---=---
the given plane.
6-8 -1 + 7 2-2A
--=--=-8-5 -7-2 2A-4
⇒
0
-2
2-2A
= - - ⇒ -4A + 8 = 6- 6A
3
2A-4
-
P(a,b,c)
33. (a) ~(p ➔ ~q)=pA-(-q)=pAq
2x - y+5x= 3
34. (d) x 2 -5 lxl+6 = 0.
Ifx < 0, thenlxl=-x
:. x2 + 5x + 6 =0
⇒ x2+3x + 2x+6 = 0
⇒ x(x +3) +2 (x+ 3) = 0
⇒ (x + 3)(x + 2) = 0
c
a b
... 2- -1---5-- k.
⇒
·: P(a, b, c) passes the given plane
:. 2(2k)-(-k)+5(5k)=3
⇒ x=-3 , -2 .
If x > 0, then Ix I= x
:. x 2 -5x + 6 = 0
⇒ x2 -3x-2x+6=0
⇒ x(x-3)-2(x-3)
⇒
a= 2k, b = -k, c = Sk.
=0
⇒
4k + k + 25k= 3
⇒
k =- =- .
3
30
1
10
(x-2)(x-3) = O
5 1
1
2 1
.·. a=-=- · b=-- and c =-=-
⇒ x=2,3.
10
:. n(A) = 4.
5'
10
10
2
35. (b)
lim f ( x) = lim log(l +ax)- log(l -bx)
x➔O
x➔O
(Qo)
37. (a) Let I=
rJx
2
2
-a dx
X
X
Put x = a sec0
a
b
--+-= lim 1+ ax I-bx (Using L' Hospital's Rule)
x➔O
1
a
b
=-+--=a+b.
1+ 0
⇒
⇒
dx = a sec0 tan0 d0
.Ja2 (sec2 0-1)
1= J- - - - -. asec0tan0d0
a sec0
= Ja tan 2 0.d0 = a J(sec 2 0-l)d0
1-0
f (x) is continuous at x = 0.
f(O) = lim f(x ) = a+b.
x➔O
=a(tan0-0)+c (": Jsec 2 xdx=tanx).
=a✓sec2 0-a-a 0+c
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At(4, 0) ,z= 36.
At
(g g)
5 ' 5 '
z = 108 + 132 = 240 =48.
5
5
: . maximum value ofz is 48.
1
4
39. (c) Let I = f ---ydx
1+vx
0
x ⇒ u2 =x ⇒ 2udu=dx.
put u = ✓
when x = 0, u = 0 & when x = 4, u = 2.
1
2
⇒ I = f -2udu.
38. (d) ·: 3x +2y £ 12 or ~+ y £ 1
0
4 6
l+u
2
2x+3y £ 12 or ~+~£ 1.
= 2f-u-du
6 4
and x 3 0 , y 3 0
0
l+u
put 1 + u = w ⇒ du= dw.
when u= 0, w= 1 & when u= 2, w=3
⇒ I
3
3
= 2f w- J dw = 2f ( l 0
w
I
1)
- dw
w
3
= 2( w-logw] 1
= 2[3-log 3] - 2 [1-logl]
= 6- 2 log 3 - 2 = 4 - 2 log 3
= 4 log e-log3' = log e'-log9 = log( •: )
. 2
40. (c) ·: sm q
1
=-
2
: . Corner points are: (0, 0), (0, 4),(4, 0) and
(g g).
5 ' 5
·: z= 9x + lly.
At(0, 0), z= 0.
At (0, 4), z = 44.
⇒
0 -nn_
+n,
nE I .
4
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:. in [O, 1t], thereareonlytwo
7r
solutions i.e;
41. (c)
3,r
4 and 4 ·
[p+q-r p-q q-r]
=(p+q-r).[(p-q) x (q-r)].
= (p+q-r).[px q - px r-qxq +q X r]
=[p+q-r].[pxq-pxr+qxr] (·: axa=O)
=[p p q]-[P p r]+[p q r]+[q p q]-[ q pr]
+[q q r]-[r p q]+[r P r]-[r qr]
= o-o+[fiqr]-o-[q P r]+o-[r P q]+o-o
[-: [a a EJ = o]
= [fi q r] + [fi q r ]-[fi q r ]
·: [aEc]=[E ca] =-[Ea c]
:. Corner points of the bounded region are:
(3, 2), (2, 3) & (3, 3)
z= lOx +25y .
At (3, 2), z = 30 + 50 = 80 (Minimum).
At(2, 3),z= 20+ 75 =95
At(3, 3),z=3O+ 75 = 105.
44. (b) f(x) = 3x3 -9.x2-27x+l5.
f'(x) = 9x2 -18x-27.
For maxima or minima:
f'(x)= 0 ⇒ 9.x2-18x-27 =O.
⇒ x -2x-3 = O
⇒ x2 -3x + x-3 = 0
⇒ x(x -3) + 1 (x-3) = 0
2
⇒ x=-1,3.
f"(x)=18x-18.
f" (-1)=-18-18=-36<0
f" (3)= 18(3)-18 = 36 > 0.
:. f(x) has maximum value atx =-1.
&max. value=3(-1)3-9(-1)2-27(-1)+ 15
=-3-9+27+ 15=30.
45. (a) We know that equation of plane passing
through a point with position vector
= [fi ii r].
normal to the vector
r
is :
42. (b) cos0 = ✓
2 has no solution, since value of
(r-a)·n=O
cos 0 lies in [-1, 1]
43. (a) z = 1Ox+ 25y subject to :
·.· the plane passes through (-1, 2, 1)
x+y
~
5;x~ 3;y~ 3;x
y
~
O;y
~
a and
:. a= -t + 2) + f
0
Also plane is perpendicular to the line
containing(-3, 1,2)and(2, 3,4)
:. n=5t +2) +2f
:. required equation is:
[r -(-t +2) +k)].(5t +2) +2k) = o
⇒ r .(5t + 2] + 2f)
-[C-t +2] +k).(5t +2] +2k)]=o
⇒ r .(5t +2]+ 2f)-[-5+4 +2J=o
⇒ r.(5t+2}+2k)=l
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y2
x2
46. (b) For - - - = 1
a2
b2
Length of transverse axis = 2a = 6 ⇒ a= 3
2b 2 8
and length oflatus rectum = =a
3
7t
=tan- 1(1)= -
4
48. (a) Let RI and R2 are the two lines, which trisects
the first quadrant (as shown in the figure)
:. equation of hyperbola is :
x2
y2
---=1
9
4
⇒ 4x2 -9y2=36
47. (b) ·: tan- 1 +tan-1y = tan- 1
· tan
..
(;:;),
ifxy < 1.
-I 1
-I 1
-I 1
-1 1
-+tan -+tan - +tan 3
5
7
8
1
slope of R1 = tan 30° = ✓
3
- bn-l
5+31
[ J+
!!
[7+81
tan-I
!! J
and slope off 2 = tan 60° = ✓
3
: . equation of R; is :
y
x=
= tan
-1
-I 15
8
-+tan 14
55
(": t
✓
3
= tan
4
-I 3
-+tan 7
11
passes through centre)
& equation of R2 is :
x= ✓3y
-1
I
(": R2 passes through centre)
:. joint equation is:
31
+2 11
4
= tan-I 7+11
= t -I [4477
an
65
[ 1-Q
77
77
2
2
xy
r;;
x -v3xy - Jl+ y =0
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EquationofRTis (y -4)= ( - ) (x-3)
0-3
✓
3x 2 -3.xy-xy+ ✓
3y2
⇒
✓
3
=O
⇒ ✓3x2 -4.xy+ ✓
3y2
1
or (y -4) =- (x -3) or 3y-12 = x-3
3
orx-3y+ 9 =0.
=0
49. (b) From figure it is clear that Tis the mid point
ofPQ
50. (a)
R(3,4)
. -I
⇒
1
a 5m I log a
d.x
-=~==.--=~✓1-t2
dt 2.Jasin-11
.
co-ordmates
of T = (2-2
- - ,-2 +-4)
2
2
= (0, 3).
dy
-
dt
dy
dt
= -
dx
dt
=
loga0
2
✓1-t2
- loga y
2 ✓1-t 2 - y
- -= --== X
x
2 ✓l-t2 loga x
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MHT-CET 112018 II
General Instructions
■
■
■
■
■
■
■
This question booklet contains 150 Multiple Choice Questions (MCQs).
Section-A: Physics & Chemistry - 50 Questions each and
Section-B: Mathematics - 50 Questions.
Choice and sequence for attempting questions will be as per the convenience of the candidate.
Read each question carefully.
Determine the one correct answer out of the four available options given for each question.
Each question with correct response shall be awarded one (1) mark. There shall be no negative marking.
No mark shall be granted for marking two or more answers ofsame question, scratching or overwriting.
Duration ofpaper is 3 Hours.
SECTION-A
PHYSICS
1.
2.
4.
The path length of oscillation of simple
pendulum oflength 1 meter is 16 cm. Its maximum
velocity is (g = n2 m!s2)
(a) 2ncm/s
(b) 4ncm/s
(c) 81tcm/s
(d) 16ncm/s
A vessel completely filled with water has holes
'A' and 'B' at depths ' h' and ' 3h' from the top
respectively. Hole 'A' is a square of side 'L' and
' B ' is circle ofradius 'r'. The water flowing out
per second from both the holes is same. Then 'L'
(a)
(c)
5.
is equal to
I
-
(a)
3.
MRro
(b)
4t
MRro
t
I
-
I
I
-
r2(n)2(3)2
(b)
I
I
r·(n)2(3)4
(d)
I
r · (n) 2 (3) 4
I
6.
I
/(n)\3)2
A transistor is used as a common emitter amplifier
with a load resistance 2 Kn. The input resistance
is 150 n. Base current is changed by20 µA which
results in a change in collector current by 1.5 mA.
The voltage gain of the amplifier is
(a) CXX)
(b) 1000 (c) 1100 (d) 1200
2t
A circular coil carrying current 'I' has radius 'R'
and magnetic field at the centre is ' B'. At what
distance from the centre along the axis of the
B
8?
(d) 3R
(a) R✓
2 (b) R✓
3 (c) 2R
Two light waves of intensities '11 'and '12'having
same frequency pass through same medium at a
time in same direction and interface. The sum of
the minimum and maximum intensities is
(b) 2(1 1 + 12)
(a) (1 1 + 12)
(c)
7.
MRro
(d) MRrot
magnetic field will be
I
(c)
A dies has mass 'M' and radius ' R'. How much
tangential force should be applied to the rim of
the disc so as to rotate with angular velocity 'ro'
in times ' t' ?
($: +Jr;_)
(d)
($: -Jr;_)
An alternative voltage e = 200✓
2 sin (100 t)
volt is connected to 1 µF capacitor through a.c.
ammeter.The reading of ammeter is
(a) 5 mA (b) lOmA (c) 15 mA (d) 20mA
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2018-2
8.
In the following network, the current flowing
through 150 resistance is
TargetMHT-CET
14.
B
An electron of stationary hydrogen atomjumps
from 4 th energy level to ground level. The
velocity that the photon acquired as a result of
electron transition will be (h = Planck's constant,
R = Rydberg's constant, m = mass of photon)
(a)
2.1 A
(c)
15.
D
9.
10.
(a) 0.8A (b) LOA (c) 1.2A (d) 1.4A
The angle made by incident ray of light with
normal of the reflecting surface is called
(b) angle of incidence
(a) glancing angle
(c) angle of deviation (d) angle ofrefraction
In non uniform circular motion, the ratio of
tangential to radius acceleration is (r = radius of
circle, v = speed of the particle, a = angular
acceleration)
ar2
v2
(d)
2
2
v
r a
v
Ifnumerical aperture ofa microscope is increased
then its
(a) resolving power remains constant
(b) resolving power becomes zero
(c) limit ofresolution is decreased
(d) limit ofresolution is increased
In amplitude modulation
(a) amplitude remains constant but frequency
changes
(b) both amplitude and frequency do not
change
(c) both amplitude and frequency change
(d) amplitude of the carrier wave changes
according to information signal
IfMz = magnetization of a paramagnetic sample,
B = external magnetic field, T = absolute
temperature, C = curie constant then according
to Curie's law in Magnetism, the correct relation
is
2 2
(a)
11.
12.
13.
~ (b)
(a)
T
Mz= CB
(c)
M B
C = -2 T
a2r
v2
CB
M = z
T
T2
(b)
16m
13hR
16m
(d)
✓ 7t:g
T
(c)
16.
17.
18.
19.
l lhR
16m
15hR
16m
A metal wire of density' p' floats on water surface
horizontally. Ifit is NOT to sink in water then
maximum radius of wire is proportional to
(T = surfaceofwater, g= gravitational acceleration)
(a)
(c)
(b)
9Rh
1tpg
(b)
✓7t~g
(d)
1tpg
T
A sphere of mass ' m' moving with velocity 'v'
collides head-on another sphere of same mass
which is at rest. The ratio of final velocity of
second sphere to the initial velocity of the first
sphere is ( e is coefficient of restitution and
collision is inelastic)
(a)
e-1
-
00
½A~
(b)
e
-
(c)
e+l
(d) e
2
For a particle performing linear S.H.M. , its
average speed over one oscillation is
(a = amplitude of S.H.M., n = frequency of
oscillation)
(a) 2an (b) 4an (c) 6an (d) 8an
An ideal transformer converts 220 V a.c. to 3.3
kVa.c. totransmitapowerof4.4kW. Ifprimary
coil has 600 turns, then alternating current in
secondary coil is
2
2
¾A~
¾A~
fA
A conducing wire has length 'L 1' and diameter
' d 1'. After stretching the same wire length
becomes 'L2 ' and diameter 'di' The ratio of
resistances before and after stretching is
(a)
di: d(
(b)
d(: di
(c)
d 2.d2
2· I
(d)
df :d~
(d) c = M2B
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MHT-CET2018
20. The molar specific heat of an ideal gas at
constant pressure and constant volume is 'C/
and 'Cv' respectively. If ' R' is the universal gas
constant and the ratio of'CP' to 'Cv' is 'y' then Cy=
(a)
21.
1-y
l+y (b)
l+y
1-y
R
26.
R
y -1
(c)
2018-3
(d)
y-1
In a capillary tube having area cross-section ' A'
water rises to a height 'h'. If cross-sectional area
is reduced to A , the rise ofwater in the capillary
27.
9
22.
23.
tube is
(a) 4h
(b) 3h
(c) 2h
(d) h
With forward biased mode, the p-n junction
diode
(a) is one in which width of depletion layer
increases
(b) is one in which potential barrier increases
(c) acts as closed switch
(d) acts as open switch
An alternating electric field of frequency 'v' is
applied across the dees (radius R) of a cyclotron
to accelerate protons (mass m). The operating
magnetic field 'B' used and K.E. of the proton
beam produced by it are respectively (e = charge
on proton)
7m1V
- e
2
(d)
7t
28.
25.
A=B+CandB2 =A 2 +C2
(c)
B = A+C and B 2 =A 2 +c2
(d) B=A+CandA 2 =B 2 +c2
A square frame ABCD is formed by four identical
rods each of mass 'm' and length' £' . This frame
is in X-Y plane such that side AB coincides with
X-axis and side AD along Y-axis.The moment of
inertia of the frame about X-axis is
A
4rnl2
3
unit
3
vector
is
m1 2
3
12
represented as
be
29.
2
, n2mv2R
(a)
m v '2n2mv2R2
A ray oflight is incident normally on a glass slab
of thickness 5 cm and refractive index 1.6. The
time taken to travel by a from source of slab is
same as to travel through glass slab. The distance
of source from the surface is
(a) 4cm (b) 8cm (c) 12cm (d) 16cm
A string is vibrating in its fifth overtone between
two rigid supports 2.4 m apart. The distance
between successive node and antinode is
(a) 0.1 m (b) 0.2m (c) 0.6m (d) 0.8m
2 12
(d) ../o.2
(b) ✓
(a) 0.4
OfJ (c) 02
Magnetic susceptibility for a paramagnetic and
diamagnetic materials is respectively
(a) small, positive and small, positive
(b) large, positive and small, negative
(c) small, positive and small, negative
(d) large, negative and large, positive
A mass is suspended from a vertical spring which
is executing S.H.M. offrequency 5 Hz. The spring
is unstretched at the highest point of oscillation.
Maximum speed of the mass is [acceleration due
to gravity g = 10 m/s2]
2 2
2
5 12
~ (b) ~ (c) - - (d)
(0.8i + b] + 0.4k) . Hence the value of ' b' must
(c)
e
24.
(b)
(a)
30.
(c)
If A = 3i-2] + ~B = i-3]+5k:and C=2i+]-4k
form a right angled triangle then out of the
following which one is satisfied?
2
2
2
(a) A= B+C and A =B +c
31.
21rm/s
(b) 1rm/s
I
21t
-mis
(d)
1
- mis
7t
The moment of inertia of a ring about an axis
passing through the centre and perpendicular
to its plane is 'I'. It is rotating with angular
velocity 'ro'. Another identical ring is gently
placed on it so that their centres coincide. Ifboth
the rings are rotating about the same axis then
loss in kinetic energy is
(a)
(b)
Iro2
4
(c)
Iro2
6
(d)
Iro 2
8
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32.
A bomb at rest explodes into 3 parts of same
38.
mass. The momentum of two parts is -3Pi and
2P} respectively. The magnitude of momentum
of the third part is
33.
34.
35.
13 p
(c) 11 P (d) ✓
(a) P
(b) 5P
In a photocell, frequency ofincident radiation is
increased by keeping other factors constant
(v > v0 ), the stopping potential
(a) decreases
(b) increases
(c) becomes zero
(d) first decreases and then increase
A mass attached to one end of a string crosses
top-most point on a vertical circle with critical
speed. Its centripetal acceleration when string
becomes horizontal will be (g = gravitational
acceleration)
(d) 6g
(a) g
(b) 3g
(c) 4g
The expression for electric field intensity at a
point outside uniformly charged thin plane sheet
is (dis the distance of point from plane sheet)
(a) independent of d
d
(b) directly proportional to ✓
A body is thrown from the surface of the earth
with velocity 'u' mis. The maximum height in m
above the surface of the earth upto which it will
reach is (R = radius of earth, g = acceleration due
to gravity)
(a)
39.
A series combination ofN 1 capacitors (each of
capacity C 1) is charged to potential difference
'3V ' . Another parallel combination of N 2
capacitors (each of capacity C2) is charged to
potential difference 'V'. The total energy stored
in both the combinations is same. The value of
C 1 in terms of C 2 is
(a)
(c)
1
36.
37.
Jct
40.
When source of sound moves towards a
stationary observer, the wavelength of sound
received by him
(a) decrease while frequency increase
(b) remains the same whereas frequency
increases
(c) increases and frequency also increases
(d) decreases while frequency remains the
same
The deflection in galvanometer falls to
(¼)
(a)
2
(b)
(½f
(d)
1
( 8.5
)th
41.
th
when it is shunted by 3Q. Ifadditional shunt of
2Q is connected to earlier shunt, the deflection
in galvanometer falls to
(d)
(c)
(c) directly proportional to d
(d) directly proportional to
(b)
2gR-u 2
(b)
C2N1
9N2
Heat energy is incident on the surface at the rate
of 10001/min. If coefficient of absorption is 0.8
and coefficient of reflection is 0.1 then heat
energy transmitted by the surface in 5 minutes
is
(a) 1001 (b) 5001 (c) 7001 (d) 9001
Two metal wires ' P' and ' Q' of same length and
material are stretched by same load. Their masses
are in the ratio m 1 : m 2. The ratio ofelongation of
wire ' P' to that of 'Q' is
(a)
2 .
2
m1 . m2
2 2
42.
Let x = [ a :
]
be the physical quantity. If the
percentage error in the measurement of physical
quantities a, b and c is 2, 3 and 4 percent
respectively then percentage error in the
measurement ofx is
(b) 14% (c) 21% (d) 28%
(a) '7°/4
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43.
Following graphs show the variation of stopping
potential corresponding to the frequency of
incident radiation (F) for a given m etal. The
correct variation is shown in graph
(v0 = Threshold frequency)
49.
50.
44.
45.
(d) (4)
(b) (2)
(a) (1)
(c) (3)
In compound microscope, the focal length and
aperture of the objective used is respectively
(b) large and small
(a) large and large
(d) short and small
(c) short and large
The energy of an electron having de-Broglie
wavelength ''),,.' is (h = Plank's constant, m = mass
of electron)
(a)
h
2m11,
(b)
'n' number ofwaves are produced on a string in 0.5
second. Now the tension in the string is doubled
(Assume length and radius constant), the number
of waves produced in 0.5 second for the same
harmonic will be
(a) n
47.
(b)
✓
2 n (c)
FL
2AY
53.
n
n
✓2
(d)
✓5
The increase in energy of a metal bar of length
'L' and cross- sectional area 'A' when
compressed with a load 'M' along its length is
(Y = Young's modulus ofthe material ofmetal bar)
(a)
48.
52.
(d)
(c)
46.
51.
(b)
FL
(d)
(c)
AY
The ratio of magnetic fields due to a bar magnet
at the two axial points P 1 and P2 which are
separated from each other by 10 cm is 25 : 2.
Points P 1 is situated at 10 cm from the centre of
the magnet. Magnetic length of the bar magnet
is (Points P I and P2 are on the same side of
54.
55.
56.
2018-5
magnet and distance of P 2 from the centre is
greater than distance of P1 from the centre of
magnet)
(a) 5cm (b) 10cm (c) 15cm (d) 20cm
A satellite is revolving in a circular orbit at a
height 'h' above the surface of the earth ofradius
' R'. The speed of the satellite in its orbit is onefourth the escape velocity from the surface of
the earth. The relation between ' h ' and ' R' is
(a) h=2R(b) h=3R(c) h=5R(d) h=7R
A pipe closed at one end has length 83 cm. The
number of possible natural oscillations of air
column whose frequencies lie below 1000 Hz are
(velocity of sound in air = 332 mis)
(b) 4
(a) 3
(c) 5
(d) 6
--------
CHEMISIRY
A certain reaction occurs in two steps as
(i) 2SO2(g) + 2NOi(g) ➔ 2SO~ (g) + 2NO(g)
(ii) 2NO(g) + 0 2 (g) ➔ 2NOi(g)
In the reaction
(a) NO2 (g) is intermediate
(b) NO(g) is intermediate
(c) NO(g) is catalyst
(d) O 2(g)isintermediate
Which among the following equations
represents the first law ofthermodynamics under
isobaric conditions ?
(a) ~U=qp - Pex·LW (b) qv =~U
(c) ~U=W
(d) W= - q
During galvanization of iron, which metal is used
for coating iron surface ?
(a) Copper
(b) Zinc
(c) Nickel
(d) Tin
Formation of PC1 3 is explained on the basis of
what hybridisation of phosphorus atom ?
(b) sp 3
(a) sp 2
(d) sp 3d 2
(c) sp 3d
Identify the element that forms amphoteric oxide.
(a) Copper
(b) Zinc
(c) Calcium
(d) Sulphur
Identifythe product 'C' in the following reaction.
Aniline
. . (CH3CH\O
Antlme Pyridine :,
57.
Br2
A CH,COOH
B _ _ __,,_ C
(a) Acetanilide
(b) p - Bromoacetanilide
(c) p - Bromoaniline
(d) o - Bromoaniline
Identify the functional group that has electron
donating inductive effect.
(a) - COOH
(b) - CN
(c) - CH3
(d) - NO2
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58.
59.
60.
61.
62.
Which among the following metals crystallise
as a simple cube ?
(a) Polonium
(b) Iron
(c) Copper
(d) Gold
Which among the following oxoacids of
phosphorus shows a
tendency of
disproportionation ?
(a) Phosphinic acid (H3PO2)
(b) Orthophosphoric acid (H3PO.J
(c) Phosphonic acid (H3PO3 )
(d) Pyrophosphoric acid (H4 P 2O 7)
What is the oxidation number of gold in the
complex [AuC14 ] 1- ?
(a) + 4
(c) + 2
(d) + I
(b) + 3
Which symbol replaces the unit of atomic mass,
amu?
(b) A
(a) u
(c) M
(d) n
Which of the following compounds reacts
immediately with Lucas reagent?
(a) CH3ettiOH
(b) CH3CttiCttiOH
(c) CH3 - <rH- CH3
68.
69.
70.
71.
72.
OH
CH3
I
(d) CH3 - C- CH3
I
63.
64.
65.
66.
OH
What is the catalyst used for oxidation of SO2
to SO 3 in lead chamber process for manufacturer
of sulphuric acid ?
(a) Nitric oxide
(b) Nitrous oxide
(c) Potassium iodide (d) DiluteHCI
The number of moles of electrons passed when
current of 2 A is passed through a solution of
electrolyte for 20 minutes is
(a) 4.1 x 10-4moJe- (b) l.24 x 10-2 moJe(c) 2.487 x 10-2 mol e-(d) 2.487 x 10-1 moleThe molarity of urea (molar mass 60 g moJ- 1)
solution by dissolving 15 g of urea in 500 cm3 of
water is
(b) 0.5 mol dm-3
(a) 2 mo! dm-3
(c) 0.125 mo! dm-3
(d) 0.0005 mol dm-3
Which carbon atom ofdeoxy Ribose sugar in DNA
I
does NOT contain
67.
-C-OH
I
bond?
(b) C3
(a) C5
(c) C2
(d) C 1
Which of the following carboxylic acids is most
reactive towards esteri:fication ?
(a) (CH3) 3CCOOH
(b) (CH~2CHCOOH
73.
74.
75.
(c) ~CttiCOOH
(d) (C2Hsh)CHCOOH
Molarity is
(a) the number of moles of solute present in
1 dm3 volume of solution
(b) the number of moles of solute dissolved in
1 kg of solvent
(c) the number of moles of solute dissolved in
1 kg of solution
(d) the number of moles of solute dissolved in
100 dm3 volume of solution
Which of the followings is a tricarboxylic acid ?
(a) Citric acid
(b) Malonic acid
(c) Succinic acid
(d) Malic acid
What is the number of donor atoms in
dimethylglyoximato ligand ?
(b) 2
(a) 1
(c) 3
(d) 4
In which substance does nitrogen exhibit the
lowest oxidation state ?
(a) nitrogen gas
(b) ammonia
(c) nitrous oxide
(d) nitric oxide
Which of the following is most reactive towards
addition reaction of hydrogen cyanide to form
corresponding cyanohydrin ?
(a) Acetone
(b) Formaldehyde
(c) Acetaldehyde
(d) Diethylketone
The most basic hydroxide from following is
(a) Pr(OHh (Z = 59) (b) Sm (OHh(Z = 62)
(c) Ho(OHh(Z = 67) (d) La(OH)3 (Z = 57)
What is the SI unit of density ?
(a) g cm-3
(b) g m-3
(c) kg m- 3
(d) kg cm- 3
Which of the following compounds does NOT
undergo haloform reaction?
(a) CH3 -yH-CH, (b) CH,-~-CH,
(c)
76.
77.
78.
OH
0
C 2 H5 -CH - C2H5 (d) CH3 -C-C2H5
I
U
OH
0
Two moles of an idea gas are allowed to expand
from a volume of 10 dm3 to 2m3 at 300 K against
a pressure of 101.325 KPa. Calculate the work
done.
(a) -201.6kJ
(b) 13.22kJ
(c) - 810.6 J
(d) - 18.96kJ
In which among the following solids, Schottky
defect is NOT observed?
(a) ZnS (b) NaO (c) KO (d) CsCI
What are the products of auto-photolysis of
water ?
(a) Hi and 0 2
(b) Steam
(d) Hydrogen peroxide
(c) H3o+and OH-
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79.
Bauxite, the ore ofaluminium, is purified bywhich
process ?
(a) Hoope' s process (b) Hall's process
(c) Mond's process (d) Liquation process
80. Phenol in presence of sodium hydroxide reacts
with chloroform to form salicylaldehyde. The
reaction is known as
(a) Kolbe's reaction
(b) Reimer-Tiemann reaction
(c) Stephen reaction
(d) Etard reaction
81. Which among the following elements of group-2
exhibits anomalous properties?
(a) Be
(b) Mg (c) Ca
(d) Ba
82. Excess of ammonia with sodium hypochloride
solution in the presence of glue or gelatine gives
(b) NIIiNIIi
(a) NaNHi
(c) N 2
(d) NH4Cl
83. What is the density of solution of sulphuric acid
used as an electrolyte in lead accumulator?
(a) 1.5 grnL-I
(b) 1.2grnL-I
(c) 1.8grnL-1
(d) 2.0grnL-1
84. Which of the following polymers is used to
manufacture clothes for firefighters ?
(a) Thiokol
(b) Kevlar
(c) Ncmex
(d) Dynel
85. Which elements is obtained in the pure form by
van Arkel method?
(a) Aluminium
(b) Titanium
(c) Silicon
(d) Nickel
86. Which ofthe following is NOT a tranquilizer?
(a) Meprobamate
(b) Equanil
(c) Chlordiazepoxide (d) Brornopheniramine
87. Conversion ofhexane into benzene involves the
reaction of
(a) hydration
(b) hydrolysis
(d) dehydrogenation
(c) hydrogenation
88. The element that does NOT exhibit allotropy is
(b) arsenic
(a) phosphorus
(c) antimony
(d) bismuth
89. Which of the following reactions is used to
prepare aryl fluorides from diazonium salts and
fluoroboric acid ?
(a) Sandmeyer reaction
(b) Balz-Schiemann reaction
(c) Gattermann reaction
(d) Swarts reaction
2018-7
90.
91.
92.
93.
94.
95.
96.
97.
98.
99.
100.
The correct relation between elevation ofboiling
point and mass of solute is
(a)
K b•W2
M2 = LlTb. W1
(c)
M2 =
LlTb ·Kb
w, . W2
Kb• W1
(b) M2 = LlTb · W2
LlTb · W1
(d) M2 = K b. W2
Which among the group- 15 elements does NOT
exists as tetra atomic molecule?
(a) Nitrogen
(b) Phosphorus
(c) Arsenic
(d) Antimony
Identify the monosaccharide containing only
one asymmetric carbon atom in its molecule.
(a) Ribulose
(b) Ribose
(d) Glyceraldehyde
(c) Erythrose
Identify the oxidation states oftitanium (Z = 22)
and copper (Z = 29) in their colourless
compounds.
(a) Ti3+, Cu2+
(b) Ti2+, Cu2+
(c) Ti4+, Cu 1+
(d) Ti4 +, Cu2+
Arenes on treatments with chlorine in presence
offerric chloride as a catalyst undergo what type
ofreaction ?
(a) Electrophilic substitution
(b) Nucleophilic substitution
(c) Electrophilic addition
(d) Nucleophilic addition
In case ofR, S configuration the group having
highest priority is
(a) -NO;? (b) - ~ (c) -CN (d) -OH
Lactic acid and glycollic acid are the monomers
used for preparation of polymer
(a) Nylon-2 nylon-6 (b) Dextron
(c) PHBV
(d) Buna-N
What is the geometry of water molecule?
(a) distorted tetrahedral
(b) tetrahedral
(c) trigonalplaner
(d) diagonal
With which halogen the reactions, of alkanes
are explosive?
(a) Fluorine
(b) Chlorine
(c) Bromine
(d) Iodine
Calculate the work done during combustion of
0.138 kg ofethanol, C2H5OH(l) at 300 K. Given:
R = 8.314 Jk- 1 mo1-1 molar mass ofethanol = 46
gmol- 1.
(a) -7482J
(b) 7482J
(c) -2494J
(d) 2494J
Slope of the straight line obtained by plotting
log 10k against represents what term?
(a) -E3
(b) -2.303E/ R
(d) -E/ R
(c) -E/ 2.303R
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SECTION-8
MATHEMATICS
!2 +dxl Sx
If
(a) 3
2.
2
24
(b) 4
l
(c)
3
(b)
(d)
2 , are
(c)
(a)
10.
x -3
x
6.
function defined by f(x)
11.
is continuous at
½) = 2 then a + ~
2
-
8
(d)
[~: _\
I
2 -1
=~~3]
[~I
(d)
-1
I
-2
4
k) + "' ( 2i - 2J + k) and
2
is
2
= y+l = z -2
3
2
x-3 = y+ l = z -2
(d)
2
2
3
Lettrs in the word HULULULU are rearrnged.
The Probability of all three L being together is
3
20
2
(b)
5
3
28
5
23
(d)
~o (10
(b)
1
(d)
1~0(10'0 -1)
9_
1)
13.
IfA, B , C are the angles ofti ABC then
cotA.cotB + cotB. cotC + cotC + cotA =
(d) - 1
(a) 0
(c) 2
(b) 1
14.
If
2
d y2 +2x(x + l)dy =
dx
dx
(d) 0
(a) 4
(b) 2
(c) 1
The line 5x + y- l = 0 coincides with one ofthe
lines given by 5x2 + xy- kx -2y + 2 = 0 then the
value ofk is
(a) - 11
(b) 31
(c) 11
(d) -31
(c)
The sum ofthe first 10 terms ofthe series 9 + 99
+ 999 + ... , is
1
3
2
8.
2
2 is
25
(c)
Ify= (tan-1 x)2 then(x2 +1)2
~i
(b)
I
2
(a)
12.
o=2✓x 2 +l+~forx<0)
8
25
2
3
(c)
x 2 -4
= - - , then its range is
x-2
(b) R - {2}
(a) R
(d) R - {-2,2}
(c) R- {4}
Iff(x) = x2 + a for x >
(b)
~
x-3 = y +l = z -2
Iff : R- {2 }
(a) 3
then(A2 -5A)A-1 =
x + 3=y + l =z -2
3
2
2
(b)
5.
x = 0 and f (
4
X
(d)
➔ Risa
2
The equation ofline passing through ( 3, -1 , 2)
and perpendicular to the lines
(a)
y
Y
l
r = (21+ J-3k)+µ(i-2J+2 f )
y
X
(c)
2
~I
I
r = (i + J -
3
x - y3l
dy
-X 3-+ 3) = 2 then -dX =
y
Y
l
3
dx=
1
sin x.cos2 x
(a) secx + log I secx + tanx I+ c
(b) secx . tanx + c
(d) secx + log I secx - tanx I+ c
(c) secx + log I cosecx - cotx I+ c
(b)
[
I
(4, - 1)
X
7.
(a)
(- 1, 4)
[
-l
~i
[-24 =: ~ l
-
J
Iflog 10 (
IfA=
I
4
(d)
The cartesian co-ordinates of the point on the
(a) (- 2,4)
(c) (- 1, - 4)
4.
9.
, then the value of K is
parabola y2 = - l 6x, whose parameter is
3.
2 3]
I
7t
K
1.
J
.J16dx_ 9 x
2
= A sin-1 (Bx)+ C then A +B =
9
(a)
4
(b)
19
4
3
(c)
4
13
(d)
12
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MHT-CET2018
15.
16.
(a)
]dx
=
Jex [2+ sin2x
1 + cos2x
(b) ex tan x + c
(a) ex tan x + c
(c) 2extanx+c
(d) extan2x+c
A coin is tossed three times. If X denotes the
absolute difference beween the number of heads
and the number of tails then P(X = 1) =
(a)
1
2
2
(b)
1
(c)
3
6
(d)
3
26.
4
Hema gets above 95% marks but she does
not get the admission in good college
(b) Hema does not get above 95% marks and
she gets admission in good college
(c) IfHema does not get above 95% marks then
she will not get the admission in good college
(d) Hema does not get above 95% marks or
she gets the admission in good college
Cosl0 .Cos2°.Cos3° ... Cos 179°=
l
(c) - - (d) -1
(b) l
(a) 0
2
17.
If2 sin ( 0+i)
(a)
18.
Jj
= cos(0 -
~), then tan 0, =
1
(b)
-
Jj (c)
1
T3
(d)
-✓
3
The area of the region bounded by x2 = 4y,
y = 1 , y = 4 and the y-axis lying in the first
quadrant is square units.
(a)
22
3
(b)
28
3
(c)
30
(d)
lff(x) =
e• -cosx
x2
28.
21
4
2
19.
27.
, for x ~ 0 is continuous at
(c)
29.
x = 0, then value of (0) is
3
2
5
(b) (c)
(d) 2
3
2
The maximum value of2x + y subject to
3x + 5y ~26 and 5x + 3y~ 30, x <! 0, y<!0 is
(b) 11.5 (c) 10
(d) 17.33
(a) 12
(a)
20.
21.
If
a,b,c
30.
16
31.
[a+ 5+c 5-a c]=
22.
23.
24.
25.
(b) 6
(d) 18
(a) 0
(c) 12
If points P(4 ,5, x), Q(3 , y, 4) and R(5, 8, 0) are
collinear, then the value ofx + y is
(b) 3
(d) 4
(a) -4
(c) 5
If the slope of one the lines given by ax2 +2hxy
+ by2 = 0 is two times the other then
(a) 8h2 = 9ab
(b) 8h 2 = 9ab2
(c) 8h = 9ab
(d) 8h = 9ab2
The equation of the line passing through the
point (-3,1) and bisecting the angle between
co-ordinate axes is
(a) x+y+2=0
(b) -x+y+2=0
(c) x-y+4=0
(d) 2x+y+5=0
The negation ofthe statement : " Getting above
95% marks is necessary condition for Hema to
get the admission in good college".
(-½,%)
81
¼
2
J x.sec x
0
32.
(d)
(½, ½)
A die is rolled. IfX denotes the number of positive divisors of the outcome then the range of
the random variable X is
(a) {1,2,3}
(b) {1,2,3,4}
(c) {1,2,3,4,5,6}
(d) {1,3,5}
A die is thrown four times. The probability of
getting perfect square in at least one throw is
(a)
are mutually perpendicular vectors
having magnitudes 1, 2, 3 respectively, then
If plan es x- cy - bz = 0, cx - y+ az = 0 and
bx+ ay - z = 0 pass through a straight line then
a2 + b2 + c2 =
(b) abc-1
(a) 1 -abc
(c) 1- 2abc
(d) 2abc- 1
The point of intersection ofline represented by
x 2- y2+3y -2 = 0 is
(b) (0,2)
(a) (1,0)
65
(b)
81
(c)
23
81
81
dx =
(a)
2: + log✓
2
4
(c)
l + log ✓
2
(b)
2:-log ✓
2
4
In ~ABC, with usual notations, ifa, b, care in
A.P. Then a cos2 ( ~) +ccos
2
( ~)
=
_c
b
3abc
a
(c) 3- (d) (b) 3
2
2
2
2
Ifx = ea, (sine - cos 0), y = ea (sin 0 + cos 0)
(a)
33.
58
(d)
3-
7t
dy
then - at 9 =- is
dx
4
1
(a)
1
(b) 0
(c)
✓
2
(d)
✓
2
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34. The nwnber ofsolutions ofsin x + sin 3x + sin 5x = 0
43 ·
35.
If tan -I 2x +tan-I 3x =
(a) - 1
36.
37.
38.
39.
40.
41.
42.
(c) 4
(b) 3
(b)
Matrix A" [
3
(d) 5
7t
4 , then x =
(c)
dx
dy = cos ( x + y) is
1
6
(d)
2
i : ;]
X
2-
44.
45.
ilien ilie value of
a31 A31 + a32 A32 + a33 A33 is
(a) 1
(c) - 1
(d) - 13
(b) 13
The contrapositive of the statement : " If the
weather is fine then my friends will come and we
go for a picnic."
(a) The weather is fine but my friends will not
come or we do not go for a picnic
(b) If my friends do not come or we do not go
for picnic then weather will not be fine
(c) If the weather is not fine then my friends
will not come or we do not go a picnic
(d) The weather is not fine but friends will come
and we go for a picnic
Iff(x) = -
1
-- (b) - e
(c) (d) e
e
e
If X~ B(n,p)withn= 10, p = 0.4thenE(X2) =
(c) 3.6
(d) 18.4
(b) 2.4
(a) 4
The general solution of differential equation
(a)
in the interval [ ~ , 3~] is
(a) 2
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The minimwn value ofthe function fl:x) = xlogx is
46.
tan( x ;y) =y+c
(b)
tan(x;y) =x + c
(c)
co{ x;
Y) = y + c
(d)
co{ X;
y) = X+ C
If
planes
and
r.(2i -p]-f)-5=0 include angle
47.
is increasing function then the
X +1
value ofx lies in
(a) R
(b) (-oo,- 1)
(c) (1, oo)
(d) (- 1,1 )
IfX= {4°-3n-l :n EN}andY= {9n-l }:nEN},
thenXnY =
(b) Y
(a) X
(c) cj>
(d) {0}
The statement pattern P A(~p /\ q ) is
(a) a tautology
(b) a contradiction
(c) equivalent top/\ q
(d) equivalent top v q
If the line y = 4x - 5 touches to the curve
y2 = ax3+ bat the point (2, 3) then 7a + 2b =
(a) 0
(c) - 1
(b) 1
(d) 2
The sides ofa rectangle are given by x = ± a and
y = ± b. The equation of the circle passing
through the vertices of the rectangle is
(a) x2 + y2= a2
(b) x2 + y2= a2 + b2
(c) x2 + y2= a2 - b 2
(d) (x - (a)2 +(Y - (b)2 = a2 + b2
(a)
48.
50.
then the
value ofp is
(a) 1,- 3
(b) - 1, - 3
(c) - 3
(d) 3
The order ofthe differential equation ofall parabolas, whose latus rectum is 4a and axis parallel to
the x-axis, is
(a) one (b) four (c) three (d) two
x-1 y + l z -1
y -k
Iflines - - = - - = - - andx-3 = - - =
3
4
2
2
z intersect then the value ofk is
(a)
49.
i
9
-
2
(b)
2
(c)
5
-
2
(d)
7
2
lfa line makes angles 120° and 60°with the positive directions ofX and Z axes respectively then
the angle made by the line with positive Y-axis is
(a) 150° (b) 60°
(c) 135° (d) 120°
L and M are two points with position vectors
2a - b and a+ 2b respectively. The position
vector of the point N which divides the line
segment LM in the ratio 2 : 1 extenally is
(a)
3b
(b)
(c)
5b
(d)
4b
3a +4b
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g-.A~N;.;;.S~W:..:E::.:.:R:.....:K=-=E=-Y=----=S=--------=--=&:___::S=---::0:.....:L=-=U:..:T~IO~N..s
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(MHT-CET 2018)
Answer KEYS
SECTION-A
PHYSICS
1
2
3
4
5
(c)
(c)
(b)
(b)
51
52
53
54
55
(b)
(a)
1
2
3
4
5
14
15
(c)
(d)
(b)
(d)
(a)
16
17
18
19
20
(c)
(b)
(b)
(c)
(d)
(c)
(c)
(a)
(c)
(b )
61
62
63
64
65
(a)
(d)
(a)
(c)
(b)
66
67
68
69
70
(c)
(c)
(d)
(a)
(b)
(c)
(b)
(c)
(b)
(c)
11
(c)
(b)
16 (d)
17 (d)
18 (b)
19 (d)
20 (a)
6 (b)
7 (d)
8 (c)
9 (b)
10 (c)
(b )
56
57
58
59
60
(c)
(d)
(d)
(d)
(a)
6
7
8
9
10
(b)
(b)
(b)
11
12
13
12
13 (b)
14 (d)
15 (a)
26 (c)
(c) 27 (a)
(a) 28 (d)
(b ) 29 (c)
(b) 30 (d)
CHEMISTRY
71 (c) 76 (a)
72 (b) 77 (a)
73 (d) 78 (c)
74 (c) 79 (b)
75 (c) 80 (b )
SECTION-B
MATHEM.ATICS
21 (c) 26 (a)
22 (d) 27 (c)
23 (a) 28 (c)
24 (a) 29 (b)
25 (b) 30 (b)
21
22
23
24
25
(b)
31
32
33
34
35
(d)
(b )
(b)
(a)
36
37
38
39
40
(a)
(d)
(a)
(a)
81
82
83
84
85
(a)
(b)
(b)
(c)
(b)
86
87
88
89
90
(d)
(d)
(d)
31
32
33
34
35
(b )
(c)
36
37
38
39
40
(b)
(a)
(b)
(c)
41
42
43
44
45
(c)
(b)
(a)
(b)
(b)
46
47
48
49
50
(b)
(a)
(d)
(c)
(a)
91
92
93
94
95
(a) 96
(d) 97
(c) 98
(c) 99
(d) 100
(b)
(a)
(a)
(b)
(c)
(c)
(b )
(d)
(a)
(b )
41
42
43
44
45
(a)
(b)
46
47
48
49
50
(d)
(d)
(b)
(b)
(a)
(d)
(a)
(b)
(a)
(c)
(c)
SECTION-A
PHYSICS
1.
(c)
Given:Pathlength = l 6cm
: . Amplitude a=
16
2
Maximum velocity Vmax = aro
2n
2n
= 8 x - = 81t cmls
T
2
= ax -
= 8 cm
Time period T= 2n ) f
I
I
L = (n}2(r)(3)4
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3.
(b) Voltage gain =
V
_2._
⇒ 311 =4/2=4(2.1 -11)
R xl
c
= _ o__
V;
,.,. C~180
R; XJB
2000 X 1.5 X 10-3
3
150x20x10-6 = 3000xl0-6 = lOOO
4.
24
(b) Torque, , = Ia
or, 711 =8.4
MR 2 w
FxR=--x2
t
MRw
: . Tangential force, F = ~
5.
9.
10.
1.2A
Tangential acceleration= ar
2
Let at a distancex from the centre, magnetic
2
ar
ar
:. Ratio = - 2- = - 2
v Ir
v
B
field becomes 8
A,
2
B
µortIR
8
(R2 +x2)3l2
(R2
A,
ll.
(c) d= 2µsina
2N.A
12.
(d) In amplitude modulaion amplitude of the
N.A. limit ofresolution is decrease (c).
carrier wave changes according to
information signal.
312
+x 2 )
or, 8R3 = (R2 + x2)3l2
⇒ 2R = (R2 + x2)112
... (i)
or 4R2 = R2 + x 2 [from squarring both sides
13.
(b) Magnetisation ofa paramagneticMz =
of equation (i)]
Mz =
⇒ 3R2 =x2
:. x = ✓3R 2 = ✓3R
6.
=
Radial acceleration= 2:'.._
r
R
centre
7
(b)
(c)
= µortl
(b) B
8.4
:. 11 =
(b) Imax=(al +a2)2andlmin=(a1-a2>2
14.
(d)
M
;
1
C,: ... (Paranmagnetic)
¼-R [ ;, - ; ,
l
1max + 1min = af + aj + af + aj
= 2 ( af
7.
~I\, = R [~1-116] = 151-6R :.A.= 15R
16
+a?) = 2(11+ Ii)
(d) Alternating voltage, e = e0 sin wt
h
h
P = - or mv= -
From question,
'). _
eo = 200,fi.v, w = 100
15.
(a)
'
· v-
'). , . .
h
mA
15hR
ml6
= --
.
.
T f
Suspens10n tens10n, = £
mg = T.l
nr2pg = Tl
200✓
2 x lOO xl0-6
=2 X
8.
✓
2
}0-2 =2QmA
r2= -
T
npg
(c) l =I 1 +l 2= 2.1A
18/1 =24/2
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16.
(c) Before collision
After collision
20.
C
y ⇒ C = yC
(d) CP - C v = R, __E_=
Cv
v
P
yCv- Cv = R
mV+O=mV1 + mV2
V1 +V2 =V
e=
21.
Coefficient of restitution, e
eV= V2 -V1
2
l
(b) From Jurin's law, h cc - or, rh = constant
r
r 1h 1 = r2h2
⇒ V. = _v -'(e_+---'--I)
.!l = hz
2
2
rz
- 1tr22
A 2-
hi
. V2 _ e+ l
.
.. Ratio,---V
2
17.
2
1tfj
9
(b) Distance travelled in one oscillation= 4a
22.
(c)
23.
(a)
4a
1
= T=4an [:. n= T]
220V·V
= 3.3 x l0 3 V
(b) Given :V=
in
'
out
Power, P = 4.4 kW and no. of turns in
secondary coil, NP= 600
P = V xf.
m
m
4.4 X 1000
220
\ = 9 ⇒ .!l = 3h
rz
rz
P-N junction diode with forward biosed
mode.
2nm
Time period, T = 1/V= - eB
P
mv
R= - = eB
eB
⇒ I. = ---,n
2
= 1tr2
2
h2 = 3h 1 = 3h
total distance
Average velocity = - - - - Time
18.
Cv(r- 1) =R
R
:. Cv = (y-1)
Vz - Vi
Vz -Vi
e=-ui - uz
V- 0
eV + V= 2V
= ⇒
mv 2
[·: F = =eB]
R
2nmv2
P=eBR=e x - - =21DrzvR
2m
20x220
3.3 x l000
e
s
19.
(c)
es
P
Using, R = f
44 4
=- A
33 3
- - - - =-
I =I = J!....
24.
P 2 (2nmvR) 2
KE = - = -'----'--- 2nhnv2R2
·
2m
2m
(b) According to question,
0 Source
~
tXCM
+
ndi
Ri Li A2 Li 4
- = -X - = - X - Rz Lz 12
Lz nd?
4
2
.
R1 dz
:. Ratio R=d2
2
i
Let 'x' be the distance of source from the
surface of glass slab
time taken to travel light, from source to
surface of the glass slab, (t 1) = time taken to
travel in glass slab (t2)
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l k
25=--
X
5
t = - - and t = - - 8
'
3 X 10
'
2
3 X 10
1.6
4n 2 m
8
kA = mg ⇒
C
[ ·: Velocityoflight in glass medium,= M ]
2n5xmg
1.6
or,x=5 x 1.6=8.0cm
(b) Fifth overtone, 2.4 = 6n
A=0.4m=
31.
(b)
0.8
4 =4
26.
(c)
2 ⇒ A,=0.8
(J)
2
OriginalKE=2
=0.2m
1q= ✓4+1+16 =
Clearly,
NewKE=2..!_J
2
.fij
B = A+C and
B 2 = A 2 + C2
32.
(d)
(a) Moment of inertia ofthe frame about X-axis.
ml
3
2
2
-+-+m 1
5
I= -ml
3
28.
A
B
30.
p
.Js~r
34.
(b)
Speed at top most point,
(a)
2 3rg
Centripetal acceleration, a = ~ = =3g
T
c
r
Electric field intensity at a point outside a
⇒✓64+b 2 +0.16 =l ⇒✓0.80+b 2 =l
29.
=
(b) In the photocell, stopping potential directly
proportional to frequency of incident
radiation.
(d) Magnitude of unit vector= 1
⇒ 0.8 + b2 = 1 ⇒ b2 = 0.2 :. b = Joi,
(c) (Relation between magnetic permeability
and susceptibility)
B=(l +X)H
X = for paramagnetic positive and small
X' = for diamagnetic negative and small
2
Iw
4
33.
x
✓(0.8) 2 + (~ 2 +( O.~ 2 = I
w,
=..!.21(w)
2
2
I 2Ioi Ju/
.
Change m KE= - I w - - - = - 2
4
4
Magnitude of momentum of the 3 rd part.
+
D't-------.c
2
2
✓9P2 •P' ✓13
y
ml
3
1
2 Iw2
2
Here, IAI= ✓9+4+1 = -✓
14
2
n
k
Conservation ofangular momentum,
or, Iw = 2Iw 1 ⇒ W1 = -
IBI= ✓1+9+25 = ✓
35
27.
I0nxmxlO
100n2m
l 1W1 =l2W2
'A
:. Distance between successive node and
antinode,
'A
mg
A=k
2n
Vmax = wA= -A=
2nnA
T
5
--=--8
.. 3 X 10
3 X 108
X
25.
⇒ k=l00rr, 2m
35.
v= ~
cr
uniformly charged thin plane sheet= 2 £
0
36.
So it is independent of d
(a) Apparent frequency,
na= n[ v~vs]i.e., frequency increase
(d) Time period, T = 2 n i
/k
1
1
and, frequency, n = T = 2n v--;;;
As frequency increases, so wevelength
decreases.
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37. (d) According to question, the deflection in
(¼)
galvanometer falls to
th
Rwhen
it is
~□
shunted by 3Q.
I
4
2018-15
C2 charged to potential difference, Vare in
parallel,
:. Ceq -N2C2 ; V= V
31
4
E=
From question, total energy stored in both
the combination is same.
. /-- = -
..
3
. 2_.s_
= 31 x 3
R
4
⇒ R=9Q
40.
38.
(a)
15
5/2 ::::} 2
/I = /2
GMm 1 2
GMm
--+-mu =0-+--2
R
R+h
·: l=r+a+t
4 1.
43.
2GMR
h= 2GM-Ru 2 -R
2GMR - 2GMR + R2u 2
2GM-Ru 2
39.
⇒ t=l -0.1 -0.8 =0.1
Fl
(c)
Fl
Y= A/11 'M= YA
(b) Percentage error in the measurement ofx
= 2 lia + 2 11b + lie
b
x
a
c
=2x2+2x3+4
=4+6+4=14%
(a) The variation of m
stopping potential
corresponding to the g,
/
frequency of incident ·8:
radiation (F) as shown <75
below.
-o+-----v,---+F
(b) In compound microscope, the focal length
and aperture of the objective used is
respectively large and small.
(b) de-Broglie wavelength
/ix
R+h
2R
GM -2GM-Ru 2
=
9
m2
MP
A2
A ocm lilQ =Ai=~
42.
R u
2GM -Ru 2
NzN1
m = pV= pxAxl
2Gm-Ru 2
2R
2 2
_
⇒ Ci - Cz
Qt= Q;x t x T(t= cofficientoftransmitance)
Qt= 0.1 X 1000 X 5 = 500J
GM Gm u 2
---2
R+h R
(R +h)
2
Q;= l000J/ m
Coefficient ofabsorption, a= 0.8 coefficient
ofreflection, r = 0.1 Heat energy transmitted
in 5 minutes, Q1 =?
2
2/
I
15
17
l = I + - I = - I or lz=-=2 I 2 I '
17 8.5
1
Let 'h' be the height of the body above the
surface of the earth.
GM
CzNzV2
(b) Heat energy incident on the surface,
1-11 =/2
6
2 _
. . 2 Ni V -
4
9/1 =
1
1
2
-cv
= - c N v2
2
2 2 2
44.
2
Ru
= 2gR-u 2
(a) N 1 number of cap acitors each of capacity,
C 1 charged to potential difference, 3V are in
series.
C1
Ceq =N,· V = 3V
45.
I
h
h
'A.= ----;===
p ✓2mK.E
or,'A.2
2m(K.E)
I
E
=
.!. cv = .!. .s_ 9 v2
2
2 N1
N 2 number of capacitors each of capacity,
2
h2
:. KE.= - 2m11,2
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or, n = l00Hz
Hence frequency of overtones n 1: n 2 : n3 :
------ = 1 : 3 : 3 i.e., 100, 300, 500, 700 and
900Hz
So number of possible natural oscillations
of air column whose frequencies lie below
1000are5.
2018-16
46. (b) Frequency of waves produced in string
when tension in string T,
n=
2~l
When tension in string is doubled i.e., 2T.
n'=-1
2L
{2T
✓2-1 /T
=
iJ--;;;
2L
iJ-;;;
CHEMISTRY
Clearly, n' = ✓
2, n
47.
(b)
FL
51.
52.
FL
(b)
(a)
Al ,', l AY
·: Y =
According to first law of thermodynamics
=q+(- Pex· ~ V) ('.· W= - Pex· ~ V)
~ U=qp - Pex . ~V
Work done / increase in energy
YAL2 F 2 L
= -- = -48.
(a)
53.
2L
2A Y
According to question,
µo
Md1
4n (d?-t2)2
µo
Md2
25
2
54.
4n (d]-t2)
2
( 2 2)
25
(di2-z2)2
2
~x d2 -l
d2
2
2
49.
-t2
55.
(b) Zn forms amphoteric oxide ZnO
ZnO + 2HC1 ~ 2nC12 + 8i0 (acid)
ZnO + 2NaOH ~ Na2ZnO2 + 8i0 (Base)
56.
(c)
2
-/ 2)
400-/ = 5(100
4/ 2 = 100 ⇒ t 2 = 25 or, l = 5 cm
(d) According to question, speed of satellite in
its orbit.
1
(CH 3CO)i0
Pyridine
Ve = 4Ve ,
Aniline
(v e = escape speed)
{GAi
I
✓2GM
Vw =4 (Rf;
50.
Hence, hybridization = sp3
Cl
.!.Q x [ 202 - z2J= 25
10
(b) Zinc is used for coating iron surface.
Because zinc get oxidized first when comes
in contact with moisture and hence iron
suface is protected from corosion.
(b) PC13 - has 3 sigma bond and 1 tone pair.
3+1=4
0p
Cl/ I"-cl
d 1 = 10cm, d2 = 20cm
20
~u = q + w
1 2Gm
V(R+h) =16x (R)
R + h = 8(R)
R + h = BR
7R = h
(c) In case of closed organ pipe, fundamental
frequency
332
n 4L = 4x83x10-2
V
(A)
[§[_
Br
Br
(B)
(C)
(p-bromoaniline)
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57.
2018-17
(c) - C~ is electron donating group which
shows + I effect.
58.
(a)
59.
(c)
4H3PO3
69.
(a) Citric acid is a tricarboxylic acid.
-----43H3 PO4 + PH3
HO
70.
OH
(b) No. of donor atom = 2
(b) In [AuCl4] 1- Let the oxidation numberof
CH 3
HO✓N0,v"OH
Au=x
x + 4(-1) = -l
x-4=-1
CH3
x= - 1 + 4
72.
(c) Nitrous oxide (NP) has the lowest
oxidation state (zero) as it is a neutral
molecule.
(b) Formaldehyde is most reactive towards
73.
(d) La (OH)3 (Z = 57) is the most basic hydroxide
74.
(c)
75.
(c)
71.
x=+3
61.
Vo l. of Solution in dm 3
)lx:l
H 3P03 ------4 H 3 P 0 4 (oxidation)
60.
No. of moles of solute
=-- - - - --
(d)
(phosphonic acid)
H 3P03 ------4 PH 3 (reduction)
.
M oIan ty
68.
(a)
addition reaction .
62.
(d)
3 ° alcohol reacts with lucas reagent
(HCI + anhydrous ZnCl2) immediately &
gives two separate layers.
63.
64.
Because haloform is given by compound
(a) Nitric oxide
(c) Moles of electron
containing
Charge
Current x Time
F
96500
2 X 20 X 60
96500
= 0 _02487
0
II
CH 3 - C - group or R- CH - CH 3 only
I
OH
76.
or 2.487 x 10-2 mo! e65.
(b)
.
No. of moles of solute
M oIanty = - - - - - - - -Volume of solution in (L)
Urea (molar mass) = 60 g/mol
molari
ty
due to lanthanide contration.
kgm-3
= _!_
= 15 x l000 = ~
60 x 500 6x 5 2
= 0.5 mo! dm- 3
66.
(c) C 2
67.
(c) C~CHiCOOH is most reactive towards
77.
78.
(a) Work done is as :W = - PdV
W =-P (V2- V 1)
V 1 = I Odm3 = I0-2 m3
V2 = 2m3
P = 101.325 x I03 pa
W =-101.325 x 103(1.99)
= -201.6kJ
(a) ZnS because it shows Frenkel defect.
(c) Autophotolysis of water is as :-
esterification as bulkier group near the site
Hp ;:::= H + + OHH2O + H + ➔ Hp+
of reaction, slows down esterification.
2H2O ➔ H3O+ + OH-
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2018-18
79.
(b) Hall's process is used to purify the ore of
92.
(d)
aluminium.
(b)
6
OH
N,OH/CH Cl,
O
~
CHzOH
asymmetric carbon atom
CHO
I
93.
(c)
This reaction is known as Reimer-Tiemann
81.
reaction
(a) Be-belongs to second period which exhibits
(b)
94.
(c)
NH2 - NH2 +NaCl+ H 2O
(Hydrazine)
95.
0
a
FeC13
+C!i
Cl
+ HCl
(d) - OH Atomic mass of oxygen is more than
thatofC &N.
1.2 g mL- 1
83.
(b)
84.
(c) Nomex is used to manufacture clothes for
96.
(b) Dextron
firefighters.
85.
(b) Titanium is obtained in pure form by Van
86.
Arkel method.
(d) Bromopheniramine is an Antihistamine.
87.
(d)
n CH3 -
OH
I
C - COOH + n HO- CH2 -
COOH
I
H
Glycolic acid
Lactic acid
Ill
0
0
CH3 - CH2 - CH2 - CH2 - CH2 - CH3
Hexane
Dehydrogenation
Cu1+: [Ar] 4s0 3d10
It is an Electrophillic addition reaction.
~
NH3 + NaOCl~
(Excess)
Ti4+, Cu 1+are colourless compound
Ti: [Ar] 4s23d2
Cu: [Ar] 4s13d10
Ti4+: [Ar] 4s0 3d°
anomalous properties.
82.
glyceraldehyde
*I
OH
80.
CHO
I
H-C-OH
~
0
f
II
o-9H-C-O-CHz-C
CH3
n
Dextron
Benzene
88.
89.
(d) Bismuth does not exhibit allotrophy.
(b) In Balz-Schiemann reaction aryl fluoride is
97.
a
~o
0
Distorted tetrahedral
H/ '-.H
prepared from diazonium salts and
fluoroboric acid.
(a)
98.
(a) Fluorine
dark
+
R-H +F2 ----+R- F+HF
N=NCl-
(alkane)
HBF4
(highly exothermic)
~
99.
(b) Combustion of ethanol is as :C2HPH + 302 -➔ 2CO2 + 3H2O
90_ (a)
91.
t
t
t
l
3
2
t
3
~Tb= KbxW2 xlOOO
W1XM2
0.138 kg= 138/46 = 3 mole
_ KbxW2
M 2~TbxW1
3C2HpH(l) + 9Oz(g) ➔ 6COz(g) + 9Hz0(1)
~n=6-9 = -3
(a) Nitrogen exists as N 2 (diatomic molecule),
not as tetra atomic molecule.
138g
Work = - ~nRT
= -(-3) X 8.3J4 X 300= 7482 J
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100. (c) Ace to Arrhenius equation.
2018-19
y= mx + C
K=Ae-Ea /RT
1
Ea
lnk = lnA--
RT
m=
Ea
log k = log A
-E
a
Y= log k· x = - · Slope =
'
T'
2.303R
-Ea
2.303 R
1
2.303 R x T
SECTION-B
MATHEMATICS
(c) Here,
n
dx
k
1.
f
f
f
f
dx
= -sinx
--dx+ -.-=
tanxsecx + cosec x dx
cos2 x
smx
f 2+18x2 = 24
= sec x + loglcosec x - cot xi + c
0
4.
(cl)
Since,log10 (x:-y:)=2
X +y
log (x 3-y3)-log (x3 + y3) = 2
⇒ log (x3 -y3) = 2 + log (x3 + y3)
Differentiating b/s w.r. t. x
⇒
I
1 [3x2+3yzdy]
[3x2-3yzdy]=
x3 -y3
dx
x3 + y3
dx
3x
2
⇒---
x3-y3
3x 2
x3-y3
⇒ --­
-1
6n
n
· -=tan 3k ⇒ tan-=3k
.. 24
4
2[
1
⇒ 1 = 3K ⇒ K = -
I
2[
]
1
I
]dy
(cl) ·:y2 = -16x
Comparing it with y2 = -4ax
a=4
Parametric equations are
x = -at2, y = 2at
y
dy
x
dx
⇒ -=­
or x =-4(½f ,y =2(4>(½)
or x=-l,y=4
3.
I
⇒ 3x x3_y3- x3+y3 =3y x3+y3 + x3-y3 dx
3
2.
l
2
2
2
3y
3x
[ 3y
dy
x3+y3 = x3+ y3+x3 -y3 dx
(cl)
f sm·
2
2
dx
X cos
2
X
=
2
fsin x+cos x
2
dx
.
Sill X cos X
5.
(a) Heref(x)=x - 4 =(x- 2(x+ 2)=x+2
x-2
(x-2)
:. RangeisR
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Ifthe above equation represents a pair of straight
lines, then
2018-20
6.
(c)
l
ol
x 2 +a
ifx 2':
f(x) = 2.Jx2 + 1 + p ifx < 0
5
is continuous at x = 0
a
h
h g
b f =0
g f C
.-. f(0) = lim_ f(x)
x➔
0
⇒
2
0 + a = Jim 2.Jx +l +P
⇒
a=2 + p ⇒ a-P=2
⇒
x ➔O-
f(½)=(½Y
k
2
1
2
-
0
2
k
-1
2
-1 =0
2
+a=2⇒ a=2-¾=¾
7
-1
.-. P=4-2=4
2
2
9.
. a2 +A.2 =(7..) +(-1) = 49+1 = 50 = 25
I-'
4
4
16
16 8
k 11
1 k k
:. -5--+-+-=0 ⇒ -=- ⇒ k=ll
2 4 4
2 2
(b) (A2 -5A)A-1 =A2A- 1-5AA-1 =A.AA- 1-51
=A-51
..
7.
{1 : ;]-[~ ; ;]
(b) Since, y = (tan- 1x)2
dy
2tan-1 x
l+x 2
⇒ -=---
dx
⇒ (1+x t(:r =4y
2
Again differentiating b/s with respect to x, we
get:
⇒ 4x(l+x 2 )(:~r +2(1+x2t(:)::; =41~
⇒ 4x(l+x 2 ) :~ +2(l+x 2 )2 ::; =4
2 2
⇒ (x2 + 1) d y2 +2x(l + x 2 ) dy = 2
dx
dx
8.
(c) 5x+y-l=0coincides
5x2 + xy-kx-2y+2 =0
=[~: }4 ~ l
1
10.
2
-1
Let a, b, c be d. rs of desired line which is
also perpendicular to the given lines.
:. 2a-2b + c=0
a-2b+ 2c = 0
(c)
a
-4+2
-b
4-1
c
-4+ 2
⇒ --=-=--
a
b
c
⇒ -=-=-
-2 -3 -2
:. direction ratios are < -2,-3, -2 >
Hence equation of desired line is
x-3 y+l z -2 x-3 y+l z -2
- -= -- = --or-- = -- = - -2
-3
-2
2
3
2
1
k
· a=5 b=0 h=- g=-- f=-1 c=2
..
'
'
2'
2'
'
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11.
2018-21
(c) ThewordHULULULUcontains4U,3L&lH
Consider 3L together i.e. we have to arrange 6
units which contains 4U.
Hence number of possible arrangements
16.
HHH ➔ X = 3 -0 =3
TTT ➔ X = 3-0 = 3
HHT ➔ X = 2 - l = 1
HTH ➔ X = 2-l = I
THH ➔ X = 2-l = 1
61
=___:_= 6x5 = 30
4!
Number of ways ofarranging all letters of given
HTT ➔ X = 2-l = l
TTH ➔ X = 2 -l
8!
8x7 x 6 x 5
word= , ,=
x
=8x7x5
34
3 2
8 x7x 5
8x7
6 3
:. P(X = 1) = 8 = 4
28
(b) 9 + 99 + 999 + ........ upto 10 terms
=(10-1) + (100-1) + (1000-1)
+ ........ upto 10 terms
= (10 + 100 + 1000 + .......... upto l0terrns)
- (I+ I+ ... upto 10 times)
17.
0
_ 10[00)' -1]
10-1
10(1010 -1)
9
2sin( e+f ) = cos( 0-i)
9
7t]
⇒
. 0 1t +cos 0sm.
1t
. 0 . 1t
=cos 0 cos-+sm
sm2[sm cos3
6
6
3
⇒
2 -sin0
- +cos0 (✓3)] =cos0 (✓3) +sm0
[ 2
2
2
. (1)2
⇒ sin0+ ✓3cos0= ✓3 cos0+.!.sin 0
10 11 - 10-90
10=---9
=10 -100 _ 100(10
9
9
13.
(d)
10
11
=1
THT ➔ X = 2 -l =l
. d proba b·1·
30
6
3
11ty = - - - = - -=
Hencereqmre
12.
(d) A coin is tossed 3 times.
:. possibilities are
2
1
-✓
3
2
2
⇒ - sin0 = -- cos0 ⇒
-1)
18.
2
r;;
tan0=--v3
y
(b)
(b) We know that ifA + B + C = n, then
tan A + tan B + tan C = tan A tan B tan C
x2 = 4y
1
1
tanBtanC tanAtanC tanAtanB
⇒ cot B cot C + cot A cot C + cot A cot B = 1
⇒ ---- +---- + ----=
-_____
- - - - -........
,.......--_..
......._
_ _ _y=4
y=l
~------'::..+.:::.....------'► X
Wehavex 2 = 4y ⇒ x= 2,Jy
:. area between x = 2,Jy, y= 1 & y=4
1 3 13
A+B=-+-=3 4 12
lS.
a
()
= fex[2(l+sinxcosx)]
fex [2+sin2x]dx
l +cos2x
2cos x
f4
= 2,jydy = 2
1
2
=
[L3/2 ]4
3/ 2 I
2(¾)[Y✓YJ = i(8 - l)= 238
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2
19.
(d)
Now, [a+b+c b-a c]
ex -cosx
x2
f(x)
=(a+ b+ c).[ (b-a)xc] =(a +b+c).(bxc-axc)
Since frx) is continuous at x = 0
⇒
f(O) = lim f(x)
x ➔O
= 2 Ia I.I b x c Icos0° (-: a & (bx c) are parallel)
2
(ex -1) -(cosx -J)
⇒
f(O) = lim
⇒ f(O) = lim e
x➔O
= 21 a I·I b x c I = 21 a II b II c Isin 90°
= 2(1)(2) (3)= 12
X2
x➔ O
x2
-
x2
-2sin2 ~
l - Jim
2
x➔O
22.
PQ=(-l, y-5,4-x)
(d)
x2
QR=(2, 8-y, -4)
·: P, Q, Rare collinear
. X
Sill -
⇒ f(O) = 1+2 lim x ➔O
20.
2
-2
r2 ]
X
. -1
l
2 3
x -= I+-=4
4 2
y-5
4-x
"2= 8-y = ~
⇒ -8
+ y = 2y-lO &4 = 8-2x
⇒ y=2&x = 2
:.I x+y=4 I
(a)
y
23.
(a) ·: ax 2 +2hxy +2by2=0
Let the slope of one line is m.
In slope of other line = 2m.
We know that
a
-2h
m +2m =-& mx2m = b.
b
-2h
⇒ 3m=-&2m
3x+ Sy = 26
Sx + 3y = 30
-2h
⇒ m=- ⇒ m
Corner Points
21.
(c)
z=O
z=2(6)+0= 12
(¾,%)
z=2(¾)+%= ll.5
( 0, 256)
26
z = 2(0) + - = 5.2
5
lal=l, lhl =2, lcl =3
a.b = 5.c = a.c = o
b
Value ofz = 2x+y
(0,0)
(6,0)
2
b
:. 2[ ;:: ) = ~24.
25.
2
a
=-
b.
4h2
=-.
9b2
⇒ 8h
2
= 9ab
(a) y-1 = (-l)(x + 3) ⇒ x+y+z=O
(b) p : Hema gets the admission in good college
q : Hema gets 95% marks
:. given statement can be written as:
p ➔ q
26.
:. its negation is p /\ - q
(a) cosl O cos 2°cos 3°.......cos 179° = 0
Since cos 90° = 0
:. required product = 0
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27.
rc/4
(c) Planes x-cy-bz = O
cx-y+az=O
J xsec
(b)
3 1.
2
xdx
0
bx+ay-z = O
Since the given planes pass through a straight
2
= [xf sec xdx]
line.
-c -b
C -1
a =0
b a -1
=[x.tanx]~
f
d
]
2
-xfsec xdx dx
O dx
rc/4[
14
rc/4
-
f [tanx]dx
0
rc/4 [
]rc/4
- log I sec x I
= [ x. tan x ] O
0
l(l - a 2) + c (- c - ab) -b(ac + b) = 0
1 - a 2 - c2 -abc - abc - b2 = 0
a2 + b2 + c2 + 2abc = 1
a2 + b 2 + c2 = 1 - 2abc
(c) x2 -y2+ x+3y -2 = O
Comparing the above equation with
ax2 +2hxy + by2 + 2gx + 2fy+ c = 0
we get
1
3
a = ! h=O b=-1 g=-, f=- , c = -2
'
'
2
2
'
:. req. point of intersection is:
-
0
:. planes are concurrent
28.
rc/4
=¾-[1og ✓2- log 1]
=!!..- tog ✓
2
4
(c) ·: a, b, care in A.P.
:. 2b = a + c
.......(i)
32.
hf -bg gh - af)
( ab - h 2 ' ab - h 2
2
2
Now, acos ( ~)+ccos ( ~)
=a
[l+cosC]
2
+c
[l +cosA]
2
a + c + a cos C + C cos A
2
29.
30.
(b) Whenweget I, numberofpositivedivisors
are I
When we get 2, number of positive divisors are 2
When we get 3, number of positive divisors are 2
When we get 4, numberofpositivedivisors are 3
When we get 5, number of positive divisors are2
When we get 6, number of positive divisors are 4
Hence range ofrandom variable Xis {I, 2, 3, 4}
(b) P (getting perfect square in atleast one
throw)= 1 - P (not getting perfect square in any
throw)
= 1-(~ x~x¾x~)
r
¾
= 1-(
= 1-
~~ = :~
a+c + b
[·: b = acosC+ccosA]
2
2b+b
3b
2
2
=--=-
33.
[Using equation (i)]
(a) x = e0 (sin 0-cos 0) & y= e8 (sin 0 + cos 0)
:. dx = e 8 (cos0+sin0)+(sin0 - cos0)e 8
d0
= e 8 [2sin0]
& dy = e8 (cos0-sin 0) + (sin 0 + cos0)e 8
d0
. dy
-
dx
dy / d0
e 8 [2cos0]
dx I de
e 8 [2sin0]
= - -=
= e8 [2cos 0)
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TargetMHT-CET
⇒ 6x2 + 6x -x ⇒
⇒
⇒ dy I
dx 0=2:
4
34.
1= 0
6x(x + 1)- l(x + l)=0
(x+ 1)(6x- l) = 0
I
= cot~ = 1
4
:. X=-1, X =(j
(b) sin x + sin 3x + sin 5x = 0
sin 5x + sinx + sin 3x= 0
2sin 3x.cos 2x + sin 3x = 0
:. sin3x[2cos2x + l] = 0
: . sin3x=0or2cos2x + 1 = 0
⇒ sin 3x = sin nn
When x =
1
6,given equation is satisfied.
When x = -1 , we get sum oftwo negative angles,
hence discarded.
I
6
:.x= -
⇒ 3x = nn
n7t
X=-
⇒
3
36.
21 3]5
(c) Horn A = [~
also 2cos2x = -1
⇒
cos2x =-1/2
⇒
cos2x=-cosn / 3
4 7
cos 2x = cos(n-n/3)
⇒
21t
cos2x = cos3
⇒
2n
2x=2nn±3
37.
n1t
7t
X=- X=n1t±3 '
3
35.
x
E[
X
=
(c)
31t]
2,2 gives
38.
7t
7t
X
f(x) = - 2-
x +l
2
(x2 + 1)2
tan -12 x + tan-13 x =
-i(2x + 3x) =7t
l-6x 2
4
5x
l-6x2
(d)
⇒ f'(x) = (x +l)(l)-(x)(2x)
21t & 41t
' 3
3
⇒ tan
we know that,
c3.i IA31 + a32A32+ a33A33 = IAI
= + 1(7-20)-2(7-10) + 3(4-2)
= -13 + 6 + 6 = -1
(b) p = The weather is fine
q = My friends will come and we go for a
picnic.
: . given statement can be written as: p ➔ q
:. its contrapositive is : - q ➔ - p
i.e. Ifmy friends do not come or we do not go for
picnic, then weather will not be fine.
7t
4
⇒ f'(x)
=
l-x 2
2
2
(x + l)
·: f(x) is increasing function.
:. f'(x) > 0
1t
4
⇒ --=tan-
⇒ ~2 = 1
l-6x
⇒ 5x= l-6x2
⇒ 6x2 + Sx-1 = 0
Herex2 + 1 ;c0,
1- x2 > 0,
X E (-) , ])
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39. (a) X=4"-3n-1
40.
41.
2018-25
nEN
&Y=9(n-l)
n EN
⇒ X= {0,9,54,243, ....... }
& Y= {0, 9, 18,27, 36, 45, 54, .......... }
:.XnY=X
(b) p /\ (- p /\ q)
= (p A - p) /\ q
......... (Associative law)
..........(Compliment law)
= F I\ q
=F
..........(Identity law)
(a) Line y=4x-5 ➔ slope oflinem = 4 ...(i)
curve y2 = ax3 + b
:. differentiating w.r.t. 'x'
f'(x)=0 ⇒
⇒
44.
2y dy =3ax 2
dx
45.
I
=
3a x 4
2X3
...(ii)
= 2a
1
1
= -(logl-loge ~-(0-1)
e
e
e
(d) n = I0, p = 0.4, q = 0.6
·: E(x) = np = 4
& V(x) = npq = 10(0.4)(0.6) =2.4
Now, V(x) = E(x2)-[E(x)]2
⇒ 2.4 = E(x2)-(4)2
dx
dy = cos(x + y)
(a)
dy
⇒ -=---
dx
: . from (i) and (ii), we get
4=2a ⇒ a=2
Since, (2, 3) is a point on the curve : y2 = ax3 + b.
:. (3)2=2(2)3 +b
⇒ b=-7
:. 7a+2b=7x2+2(-7) = 0
42.
1
log x = - 1 ⇒ x = e
⇒ E(x2) = 18.4
2
dy 3ax
dx = 2y = slope of tangent
. dy
. . dx (2,3)
l+logx=0
(b)
l+ dy = dV
dx dx
⇒ dy = dV -l
dx
y
x= a
cos(x + y)
Putx + y = V
Differentiating w.r.t. 'x'
dx
dV
I
dx
cosV
⇒ - -1 =--
dV
I
dx
cosV
dV
I + cosV
dx
cosV
⇒ -=--+ l
⇒ - =---
cosV dV =dx
(l+cosV)
⇒---
Integrate both sides, we get :
43.
Centre= (0, 0) &radius = r = ✓a 2 + b 2
:. equation ofcircle
x2 + y2 = a2+ b2
(a) f(x) = x log x
:. f'(x)=l+logx
For minimum value
dV = fdx
f (1 +I +cosV)-1
cosV
⇒f
rl-
f
I V 1dV = dx
2cos 2 -
2
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⇒ 2axy"+ y'3 = 2ay'
V
⇒
1 tan2
V-2-1-=x+C1
⇒ order 2.
48.
2
⇒
(a) Points on the given lines are respectively
(1 ,-1, 1) and (3, k, 0) and their direction ratios are
respectively 2, 3, 4 and 1, 2, 1
Since lines intersect, then lines are coplanar
x + y-tan ( -x+y)
- = x + C1
2
⇒ tan(x;y) =y+C
46.
(d) We have r .(pi-]+2k:) + 3 = 0 and
X2 -X1
a1
Y2 -Y1
b1
2 2 - 21
a2
b2
c2
=0
2 k+l -1
2
Since angle between them is
c1
n
3
4 =0
2
1
:. 2(-5)-(k+ 1)(-2)-1(1)=0
-11 + 2k + 2 = 0
3.
. cose = I ii1.ii2 I
..
lii11 •1°2 I
k=2_
2
49.
n
⇒ cos -
3
Let cos a , cos p & cos y are the direction
cosines of the line. We know that
cos2 a + cos2 p + cos2 y = 1
⇒ (cos 120°) 2 + cos2 p + (cos 60°) 2 = I
(c)
⇒ (-½r +cos2 p + (½f = 1
1 1
1
2
⇒ cos p = 1- 2 = 2 ⇒ cos p = ± ✓
2
⇒ p2 + 5 =6p-4 ⇒ p 2 -6p + 9 = 0
⇒ (p-3)2 = 0 ⇒ p = 3
47.
(d) Equation of parabola whose axis is parallel
to X axis and latus rectum is 4a
(y-k)2 = 4a(x-h)
(where h & k are arbitrary constants)
differentiating b/s, we get
2 (y-k)y' = 4ax
.......(i)
again differentiating b/s, we get.
(y-k)y"+y' 2 = 2a
⇒
2ax
2
-.y"+ y' = 2a
y'
⇒
50.
P = 135°
WehaveL = (2, -l)andM=(l, 2)
and is divided by Nin ratio 2 : 1 externally.
(c)
:. N = (2)(1)-(2)(1) , (2)(2)-(1)(-1)
2- 1
2-1
o,f}-e. N=(0, 5)
i.e. N =(
:. position vector of point N is 5b
from (i)
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MHT-CET 112017 II
General Instructions
• This question booklet contains 150 Multiple Choice Questions (MCQs).
Section-A: Physics & Chemistry - 50 Questions each and
Section-B: Mathematics - 50 Questions.
• Choice and sequence for attempting questions will be as per the convenience of the candidate.
• Read each question carefully.
■ Determine the one correct answer out of the four available options given for each question.
■ Each question with correct response shall be awarded one (1) mark. There shall be no negative marking.
• No mark shall be granted for marking two or more answers ofsame question, scratching or overwriting.
■ Duration ofpaper is 3 Hours.
SECTION-A
PHYSICS
1.
2.
3.
The frequencies for series limit of Balmer and
Pasch en series respectively are ' v 1' and ' v 3 ' . If
frequency of first line of Balmer series is ' v 2 '
then the relation between 'v1' , ' v/ and 'v3 ' is
~ v 1 +~ = ~
00 v~~ = ~
(c) v 1 + v 2 = v 3
(d) v 1 - v3 = 2v1
When three capacitors of equal capacities are
connected in parallel and one ofthe same capacity
is connected in series with its combination. The
resultant capacity is 3. 7 5 µF. The capacity of each
capacitor is
(a) 5µF (b) 6µF (c) 7µF (d) 8µF
Sensitivity of moving coil galvanometer is ' S'. If
shunt of
6.
7.
1
8 th of the resistance of galvanometer
is connected to moving coil galvanometer, its
sensitivity becomes
(a)
4.
5.
s
3
(b)
s
-
6
(c)
s
9
(d)
s
12
Two unknown resistances are connected in two
gaps ofa meter-bridge. The null point is obtained
at 40 cm from left end. A 30 n resistance is
connected in series with the smaller of the two
resistances, the null point shifts by 20 cm to the
right end. The value of smaller resistance in n is
(a) 12
(b) 24
(c) 36
(d) 48
In Fraunhofer diffraction pattern, slit width is
0.2 mm and screen is at 2 m away from the lens. If
8.
wavelength of light used is 5000A, then the
distance between the first minimum on either side
of the central maximum is (0 is small and
measured in radian)
(a) 10-1m
(b) 10-2m
(c) 2 x l0-2m
(d) 2x J0-1m
In series LCR circuit R= 18 n and impedance is 33
Q An rms voltage 220V is applied across the
circuit. The ture power consumed in AC circuit is
(a) 220w (b) 400w (c) 600w (d) 800w
Two parallel plate air capacitors of same capacityC
are connected in series to a battery of emfE. Then
one of the capacitors is completely filled with
dielectric material ofconstant K. The change in the
effective capacity of the series combination is
(a)
~[; :~]
(c)
C[K +l]
(b)
~[; :~]
2 K-1
The polarising angle for transparent medium is
' 0' and 'v' is the speed oflight in that medium.
Then relation between ' 0 ' and ' v' is
( c = velocity iflight in air)
cor{~)
(a)
0 =tan-{ ~)
(b) 0=
(c)
0 = sin- 1 ( ~)
(d) 0 = cos- 1 ( ~ )
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Two identical light waves having phase difference
' <I>' propagate in same direction.When they
superpose, the intensity of resultant wave is
proportional to
9.
10.
(a)
cos 2 <I>
(c)
cos
2
2
(b) cos
(¾J
12.
13.
(
¾J
17.
For a transistor, adc and ~de are the current ratios,
then the value of
11.
(1J
2
(d) cos
TargetMHT-CET
16.
3sin[
P de - 8 dc
A
Udc ·l-'ctc
(a) 1
(b) 1.5
(c) 2
(d) 2.5
A radioactive element has rate of disintegration
10,000 disintegrations per minute at a particular
instant. After four minutes it become 2500
disintegrations per minute. The decay constant
per minute is
(a) 0.2 log 2
(b) 0.5 log0 2
(d) 0.8 loge2
(c) 0.6 log)
When the same monochromatic ray of light
travels through glass slab and through water,
the number of waves in glass slab of thickness
6cm is same as in water column ofheight 7cm. If
refractive index of glass is 1.5, then refractive
index of water is
(a) 1. 258 (b) 1. 269 (c) 1. 286 (d) 1. 310
If the electron in hydrogen atom jumps from
second Bohr orbit to ground state and difference
between energies of the two states is radiated in
the form of photons. If the work function of the
material is 4.2 eV, then stopping potential is
18.
1
(a) 2
n
15.
(b)
1
n
(c)
n2
(d) n
Photodiode is a device
(a) which is always operated in reverse bias
(b) which is always operated in forward bias
(c) in which photo curent is independent of
intensity of incident radiation
(d) which may be operated in forwad or revese
bias.
, wherexandy areinmetre
and time in second. Which of the following is
correct?
(a) Velocityv = 1.5 mis
(b) Amplitude A= 3cm
(c) Frequencyf=0.2Hz
(d) Wavelength 'A.= 10m
Two spherical black bodies have radii 'r 1' and
'r/ .Their surface temperature are 'T1' and ' Tz' . If
r,
(a)
(b)
Tz
(c)
19.
The closed and open organ pipes have same
length. When they are vibrating simultaneously
in first overtone, produce three beats. The lenght
of open pipe is made
n
(b) 4V (c) 6V
(a) 'N
(d) 'iN
The magnetic moment of electron due to orbital
motion is proportional to
(n = principal quantum numbers)
n(½-~J+¾]
they radiate same power, then ..1.. is
'i
13.6
[Energy of electron in nth orbit= - -2- e V]
14.
A wheel ofmoment of inertia 2 kg m 2 is rotating
about an axis passing through centre and
perpendicular to its plane at a speed 60 rad/s.
Due to friction, it comes to rest in 5 minutes. The
angular momentum of the wheel three minutes
before it stops rotating is
(b) 48 kgm2/s
(a) 24kgm2/s
2
(d) 96 kgm2/s
(c) 72 kgm /s
The equation of the progressive wave is y =
20.
I
3 rd and closed pipe is
made three times the original, the number ofbeats
produced will be
(b) 14
(d) 20
(a) 8
(c) 17
A lift of mass 'm' is connected to a rope which is
moving upward with maximum acceleration ' a'.
For maximum safe stress, the elastic limit of the
rope is 'r. The minimum diameter ofthe rope is
(g = gravitational acceleration)
I
(a)
[2m~/a)T
(c)
[
m(!;•)]l
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21. A solid sphere of mass 2 kg is rolling on a
frictionless horizontal surface with velocity 6m/s.
It collides on the free end of an ideal spring
whose other end is fixed. The maximum
compression produced in the spring will be
(Force constant of the spring = 36 Nim)
22.
23.
(a)
.j14m
(b)
.j2.8m
(c)
.}14m
(d)
.j0.7m
A flywheel at rest is to reach an angular velocity
of 24rad/s in 8 second with constant angular
acceleration. The total angle turned through
during this interval is
(a) 24rad (b) 48rad(c) 72rad (d) 96rad
Two uniform wires of the same material are
vibrating under the same tension. If the first
overtone of the first wire is equal to the second
overtone of the second wire and radius of the
first wire is the twice the radius of the second
wire, then the ratio ofthe lengths of the first wire
to second wire is
(a)
24.
25.
26.
1
pm
KT
(b)
KT
pm (c)
28.
Km
pT
(c)
29.
(d)
n:l (d) ¼:l
(c) ✓
The ratio of binding energy of a satellite at rest
on earth's surface to the binding energy of a
satellite of same mass revolving around the earth
at a height h above the earth's surface is
(R = radius of the earth).
2(R+h)
(b)
R
R +h
R+h
2
R
(d)
R
R+h
A particle performing SHM starts equilibrium
position and its time period is 16 seconds. After
2 seconds its velocity is n mis. Amplitude of
oscillation is ( cos45° = ~ )
(a)
30.
2~
(b)
(c)
6~
(a)
3'3 '6
(c)
2'4'6
L 2l SL
LL L
LL L
31.
4~
(d) 8 ~
In sonometer experiment, the string of length
'L ' under tension vibrates in second overtone
between two bridges. The amplitude of vibration
is maximum at
LL SL
(d)
6'2'6
The depth 'd ' at which the value ofacceleration
1
due to gravity becomes - times the value at the
n
earth's surface is (R = radius of earth)
(a) d = R
(n~i)
(c) d=R ( n~l)
32.
(a)
(c)
33.
(b) d=R ( n2~1)
(d) d = R 2
(
n
~I)
A particle is performing SHM starting extreme
position, graphical representation shows that
between displacement and acceleration there is
a phase difference of
pK
Tm
A big water drop is formed by the combination of
' n' small water drops of equal radii. The ratio of
the surface energy of 'n ' drops to the surface
energy of big drop is
(a) n2 :l (b) n : l
(a)
1
(b) (c)
(d)
3
4
5
6
When one end ofthe capillary is dipped in water,
the height of water column is ' h'. The upward
force of 105 dyne due to surface tension is
balanced by the force due to the weight of water
column. The inner circumference of capillary is
(Surface tension of water = 7 x 10-2 Ni m)
(a) 1.5cm (b) 2cm (c) 2.5cm (d) 3cm
For a rigid diatomic molecule, universal gas
CXJlsl:aitR=nCP,where ' C/ is the~olar specific
heat at constant pressure and 'n' 1s a number.
Hence 'n' is equal to
(a) 0.2257 (b) 0.4
(c) 0.2857 (d) 0.3557
An ideal gas has pressure 'p' volume 'V' and
absolute temperature ' T '. If'm ' is the mass of
each molecules and ' K ' is the Boltzmann
constant, then density of the gas is
(a)
27.
1
-
2017-3
Orad
7t
- rad
2
(b)
7t
-rad
4
(d) nrad
The fundamental frequency ofan air column is a
pipe closed at one end is I 00 Hz. Ifthe same pipe
is open at both the ends, the frequencies
produced in Hz are
(a) 100,200, 300, 400...
(b) 100, 300, 500, 700...
(C) 200,300, 400, 500.. .
(d) 200,400, 600, 800
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34.
TargetMHT-CET
For a particle moving in vertical circle, the total
energy at different positions along the path
(a) is conserved
(b) increases
(c) decreases
(d) may increase or decrease
Asimple pendulumoflength 'L' hasmass 'M '
and it oscillates freely with amplitude
'A'. At extreme position, its potential energy is
(g=acceleration due to gravity)
35.
(a)
(c)
MgA
2L
2
MgA 2
(b)
(d)
MgA
2L
37.
')..
(b) '}._oc'}._2_
p
e
e
1
(d) ')..
40.
41.
the angular velocity becomes (
Frequency
(2)
15
2
(b)
2
(c)
38.
Frequency
(4)
(b) 2
(a) 1
(c) 3
(d) 4
According to de-Broglie hypothesis, the
wavelength associated with moving electron of
mass 'm 'is ' \ '. Using mass energy relation and
Planck's quantum theory, the wavelength
associated with photon is ''),, ' . Ifthe energy (E) of
electron and photon is same,ihen relation between
''),,'and''),,' is
e
P
43.
15
A disc of moment of inertia '/1' is rotating in
horizontal plane about an axis passing through
a centre and perpendicular to its plane with
constant angular speed 'roi', Another disc of
moment of inertia '/ / having zero angular speed
is placed co-axially on a rotating disc. Now, both
the discs are rotating with constant angular
speed ' ro2 '. The energy lost by the initial rotating
disc is
+/ ]ro/
(a) _!_[J,//2
Frequency
(3)
¼Jth of the
original in time ' t' and ' n' revolutions are made
in that time. The number of revolutions made by
the fan during the time interval between switch
offand rest are (Angular retardation is uniform)
4n
32n
8n
16n
(a) 15
(c)
(b)
(d)
42.
Frequency
(1)
"',
A parallel plate air capacity ' C' farad, potential
' V ' volt and energy 'E' joule. When the gap
between the plastes is completely filled with
dielectric
(a) both V and E increase
(b) both Van d E decrease
(c) V decrease, E increases
(d) V increases, E decrease
The resistivity ofpotentiometer wire is 40 x l o-8 ohm metre and its area of cross- section is 8x l~m2•
lf0.2 ampere current is flowing through the wire,
then the potential gradient of the wire is
(b) 10-2 V1m
(a) 10-1 Vim
3
(c) I0- V/m
(d) lo-4V/m
A ceiling fan rotates about its own axis with some
angular velocity. When the fan is switched off
15
0
oc ~
p
39.
2MgA 2
L
L
On a photosensitive material when frequency of
incident radiation is increased by 30%, kinetic
energy of emitted photoelectrons increases from
0.4 eV. The work function of the surface is
(b) 1.267 eV
(a) 1 eV.
(c) 1.4eV
(d) 1.8eV
Out ofthe following graphs, which graphs shows
the correct relation (graphical representation) for
LC parallel resonant circuit
36.
(a) ')..p oc
_!_[ 11 -
_!_[~]ro/
1, -12
2
]ro/
_!_[~]ro/
12
(d)
2 11+ 12
2 //2
A particle performs linear SHM at a particular
instant, velocity of the particle is 'u ' and
acceleration is a while at another instant velocity
is 'v' and acceleration is 'W(0 < a < P). The
distance between the two position is
(a)
(c)
u 2 -v 2
(b)
u 2 -v 2
a-p
(d)
a-p
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44.
The observer is moving with velocity 'vo'
towards the stationary source of sound and then
after crossing moves away from the source with
velocity 'v0 '. Assume that the medium through
which the sound waves travel is at rest. Ifv is
the velocity of sound and n is the frequency
emitted by the source, then the difference
between apparent frequencies heard by the
observer is
(a)
45.
2017-5
2nv0
-v- (b)
nv0
-;- (c)
YAaT
(1-aT)
(1-aT)
47.
48.
49.
50.
0
(d)
v
nv
52.
53.
0
A metal rod oflength 'L' and cross-sectional area
'A' is heated through ' 7°C'. What is the force
required to prevent the expansion of the rod
lengthwise
(a)
46.
V
2nv
CHEMISTRY
51.
54.
YAaT
(b)
(1 + aT)
(l+aT)
(c)
(d)
YAaT
YAaT
Two coils P and Qare kept near each other. When
no current flows through coil P and current
increase in coil Q at the rate 10A/s, the emf in
coil Pis 15mV. When coil Q carries no current
and current of 1.8A flows through coil P, the
magnetic flux linked with the coil Q is
(a) 1.4m Wb
(b) 2.2mWb
(c) 2.7 m Wb
(d) 2.9 m Wb
In Young's double experiment, in air interference
pattern second minimum is observed exactly in
front of one slit. The distance between the two
coherent source is 'd ' and the distance between
source and screen is 'D ' . The wavelength of light
source used is
d2
d2
d2
d2
(a)
D
(b) 2D (c) 3D (d) 4D
In communication system, the process of
superimposing a low frequency signal on a high
frequency wave is known as
(a) repeater
(b) attenuation
(c) modulation
(d) demodulation
A bar magnet has length 3 cm, cross-sectional
area 2 cm3 and magnetic moment 3 Am2 • The
intensity of magnetisation of bar magnet is
(a) 2 x 105 Alm
(b) 3 x 105 Alm
5
(c) 4 x 10 Alm
(d) 5 x 105 Alm
The magnetic flux near the axis and inside the air
core solenoid oflength 60cm carrying current '/'
is 157 x 1~ Wb. Its magnetic moment will be
(cross-sectional area of a solenoid is very small
as compared to its length, µ0= 41t x 10-1 SI unit)
(a) 0.25A (b) 0.50A(c) 0.75A (d) 1 A
55.
56.
57.
58.
59.
60.
61.
62.
The work done during combustion of9 x 10-2 kg
of ethane, C2H 6 (g) at 300 K is
(GivenR = 8.314J deg-1,atomicmassC = 12,H= I
(a) 6.236 kJ
(b) - 6.236 kJ
(c) 18.71 kJ
(d) -18.71 kJ
What type of sugar molecule is present is DNA?
(a) D-3-deoxyribose (b) D-ribose
(c) D-2-deoxyribose (d) D-glucopyranose
The molality of solution containing 15.20 g of
urea, ( molar mass = 60) dissolved in 150 g or
water is
(a) 1.689 mo! kg-I
(b) 0.1689 mo] kg-'
(c) 0.5922 mol kg-I (d) 0.2533 mol kg-'
The acid, which contains both -OH and
-COOH groups is
(b) adipic acid
(a) phthalic acid
(c) glutaric acid
(d) salicylic acid
Identify the compound, in which phosphorus
exists in the oxidation state of+ 1.
(a) Phosphonic acid ~PO)
(b) Phosphinic acid (HlO2)
(c) Pyrophosphorus acid (H4Pp5)
(d) Orthophosphoric acid (~POJ
Identify the weakest oxidising agent among the
following.
(b) Na+ (c) Cd2+ (d) 12
(a) Li+
The monomers used in preparation of dextron are
(a) lactic acid and glycolic acid
(b) 3-hydroxy butanoic acid and 3-hydroxy
pentanoic acid
(c) styrene and 1, 3-butadiene
(d) bexamethylenediamine and adipic acid
Which among the following compounds does
not act as reducing agent?
(a) ~O (b) ~S (c) ~Se (d) ~Te
Which of the following processes is not used to
preserve the food?
(a) Irradiation
(b) Addition of salts
(c) Addition of heat (d) Hydration
In case of substituted aniline the group which
decreases the basic strength is
(a) -OC~
(b) -C~
(c) -NH2
(d) -C6H5
(+2) 2-methylbutan-1-ol (-) 2-methylbutan-1-ol
have different values for which property?
(b) Relative density
(a) Boiling point
(c) Refraction index (d) Specific rotation
Which among the following is not is mineral of
iron?
(a) Haematite
(b) Magnesite
(c) Magnetite
(d) Siderite
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2017-6
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
Nitration ofwhich among the following compounds
yields cyclonite?
(a) Formaldehyde
(b) Benzaldehyde
(c) Urotropine
(d) Acetaldehyde ammonia
Calculate the work done during compression of
2 mo! ofan ideal gas from a volume of lm3 to
10 dm3 300K against a pressure of l 00 KPa.
(b) + 99kJ
(a) -99kJ
(c) +22.98kJ
(d) -22.98kJ
Which element among the following does form
p1t - p1t multiple bonds?
(b) Nitrogen
(a) Arsenic
(d) Antimony
(c) Phosphorus
Which of the following statement(s) is/ are
incorrect in case of Hofmann bromamide
degradation?
(a) Reaction is useful for decreasing length of
carbon chain by one carbon atom
(b) It gives tertiary amine
(c) It gives primary amine
(d) Aqueous or alco. KOH is used with bromine
Which of the following statement (s) is/are
incorrect for pair of elements Zr-Hf?
(a) Both possess same number of valence
electrons.
(b) Both have identical sizes.
(c) Both have almost identical radii.
(d) Both of these belong to same period of
periodic table.
Aldehyde or ketones when treated with
C6H5 - NH-Nf1i, the product formed is
(a) semicarbazone
(b) phenlhydrazone
(c) hydrazone
(d) oxime
Solubility of which among the following solids
in water changes slightly with temperature?
(a) KN03
(b) NaN03
(c) KBr
(d) NaBr
What is the quantity of hydrogen gas liberated
when 46 g sodium reacts with excess ethanol?
(a) 2.4 x 10--3 kg
(b) 2 .0 x 10--3 kg
3
(c) 4 .0 x 10- kg
(d) 2.4 x 10-2 kg
Tert-butyl methyl ether on treatment with
hydrogen iodide in cold gives
(a) tert-butyl iodide and methyl iodide
(b) tert-butyl alcohol and methyl alcohol
(c) tert-butyl alcohol and methyl iodide
(d) tert-butyl iodide and methyl alcohol
Name the process that is employed to refine
aluminium.
(a) Hall's process
(b) Mond process
(c) Hoope's process (d) Serperck's process
TargetMHT-CET
73.
74.
75.
76.
77.
78.
79.
80.
81.
The colour and magnetic nature of manganate
ion (MnO/ -) is
(a) green, paramagnetic
(b) purple, diamagnetic
(c) green, diamagnetic
(d) purple, paramagnetic
The osmotic pressure of solution containing
34.2 g ofcane sugar (molar mass= 342 g mol-1) in
lLofsolution at 20°C is (Given R = 0.082 Latm
K-1 mol-1)
(a) 2.40atrn
(b) 3.6atm
(c) 24atrn
(d) 0.0024atm
In assigning R-S configuration, which among
the following groups has highest priority?
(b) -COOH
(a) -S03H
(c) . -0-IO
(d) -C6H5
Which of the following is used as antiseptic?
(a) Chloramphenicol (b) Bithional
(c) Cimetidine
(d) Chlordiazepoxide
In preparation of sulphuric acid from sulphur
dioxide in lead chamber process. What substance
is used as a catalyst?
(a) Manganese dioxide
(b) Vanadium pentoxide
(c) Nitric oxide
(d) Raney nickel
The correct charge on and co-ordination number
of' Fe' in ~[Fe(CN)6] is
(a) +2, 4 (b) +3, 6 (c) +2, 6 (d) +3, 3
Which among the following reactions is an
example of pseudo first order reaction?
(a) Inversion of cane sugar
(b) Decomposition ofH20 2
(c) Conversion of cyclopropane to propene
ofN20 5
(d) Decomposition
.
Th e amme, which reacts with p-toluenesulphonyl
chloride to give a clear solution, which on
acidification gives insoluble compound is
(b) (C2H5) 2NH
(a) C2H5Nf1i
(c) . (C2H 5) 3N
(d) CJ-1iNHC2H5
Which among the following equation represents
Arrhenius equation?
RT
!,_
82.
(a)
k =A,
(c)
k =~
RT
e E.IRT
(b)
k=A.e E·
(d)
k
A
E.
= eRTI
Which of the following compound will give
positive iodoform test?
(a) lsopropyl alcohol
(b) Propionaldehyde
(c) Ethylphenyl ketone
(d) Benzyl alcohol
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MHT-CET2017
83. The first law of thermodynamics for isothermal
process is
(a) q=-W
(b) ~U=W
(c) ~U=qv
(d) ~U=qv
84. The conversion of ethyl bromide using sodium
iodide and dry acetone, this reaction is know as
(a) Swarts reaction
(b) Finkelstein reaction
(c) Sandmeyer reaction
(d) Stephen reaction
85. What is the hybridisation of carbon atoms in
fullerene?
(a) sp3
(c) sp2
(b) sp
(d) dsp 3
86. What is the SI unit of conductivity?
(b) Sm-1 (c) Sm2 (d) Sm--2
(a) Sm
87. Which of the following in Baeyer's reagent?
(a) AlkalineKMnO4 (b) Acidic~Crp7
(c) AlkalineNa2Crp/d) MnO2
88. What is the chief constituent of pyrex glass?
(a) Bp3 (b) SiO2 (c) Aip3 (d) Nap
89. Which of the following compounds has lowest
boiling point?
(a) n-butyl alcohol (b) !so-butyl alcohol
(c) Tert-butyl alcohol (d) Sec-butyl alcohol
90. Identify the invalid equation
(a) !:ili = IJiproducts -IJireactants
(b) !:ili=~U+ p~V
(c) Ml° (reaction) = IR°(product bonds) -IR°(reactant bonds)
(d) !:ili=~U+&lRT
91. The rate constant for a first order reaction is
7.0 x 10-4 s-1• Ifinitial concentration ofreactant
is 0.080 M, what is the half life ofreaction?
(b) 79.2 s
(a) 990 s
(c) 12375 s
(d) 10.10 x 1Q-4s
92. The polymer used in making handles ofcookers
and frying pans is
(b) nylon-2-nylon-6
(a) bakelite
(d) Polyvinyl chloride
(c) orion
2017-7
Which halogen has the highest value ofnegative
electron gain enthalpy?
(a) Fluorine
(b) Chlorine
(c) Bromine
(d) Iodine
94. What is the actual volume occupied by water
molecules present in 20 cm3 ofwater?
(b) 10cm3
(a) 20cm3
3
(c) 40cm
(d) 24.89cm3
95. Which of the following co-ordinate complexes if
an exception to EAN rule? (Given atomic number
Pt= 78, Fe= 26, Zn= 30, Cu= 29)
(a) [Pt(NH)6] 4+
(b) [Fe(CN\]4(d) [Cu~)4 ] 2+
(c) [Zn~\]2+
96. Which among the following equations
represents the reduction reaction taking place
in lead accumulator at positive electrode, while
it is being used as a source of electrical energy?
(b) Pb4+ ➔ Pb
(a) Pb ➔ Pb2+
2
(c) Pb + ➔ Pb
(d) Pb4+ ➔ Pb2+
97. For which among the following equimolar
aqueous solutions Van 't Hoff factor has the
lowest value?
(a) Aluminium chloride
(b) Potassium sulphate
(c) Ammonium chloride
(d) Urea
98. The amino acid, which is basic in nature is
(a) histidine
(b) tyrosine
(c) proline
(d) valine
99. Which element among the following does not
form diatomic molecules?
(a) Argon
(b) Oxygen
(c) Nitrogen
(d) Bromine
100. A molecule of stachyose contains how many
carbon atoms?
(a) 6
(c) 18
(d) 24
(b) 12
93.
SECTION-B
MATHEMATICS
1.
2.
The number ofprincipal solutions oftan 28 = 1is
(a) one (b) two (c) three (d) four
The object function z = 4x 1 + 5x2, subject to
2x1 +x2 :2:7,2x1 + 3x2 ::,15, x2 ::,3, xi' x 2 :2:0has
minimum value at the point
(a) onX-axis
(b) on Y-axis
(c) at the origin
(d) on the line parallel to X-axis
3.
4.
If z 1 and z2 are z-coordinates of the points of
trisection of the segment joining the points
A(2, 1, 4,), B (-1, 3, 6), thenz 1 + z2 =
(b) 4
(d) 10
(a) 1
(c) 5
The maximum value of
logx
f(x)=--(x ;c0,x;c l)is
X
(a)
e
1
(b)
e
(c) e2
(d)
e2
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TargetMHT-CET
2017-8
5.
f:x tan- x dx =
6.
7.
12.
1
- +4 2
TC
(a)
(b)
1
--4 2
TC
13.
8.
(d)
The inverse of the matrix [
[-3 o ol
1
-½ ;
(a)
0
-¾[:-9
9.
If
J
.J9 _116 x
2
10.
1
[-3
_.!_ 3
3
-2
3
ii
~]
~]
0
-1
0
-1
- 9 -2
19
(c)
ii
9
(d)
ii
0(0,0), A(l, 2), B(3, 4) are the vertices of L\OAB
The joint equation of the altitude and median
drawn from O is
(a) x 2 +7xy-y2=0 (b) x 2 + 7xy + y2=0
(c) 3x2 -xy-2y2 = 0 (d) 3x2 + xy - 2y2=0
I
11.
= 0, thenK=?
x= 0(b)continuousatx
ee(c) e
1
2
(d)
(~)=ex
(d) sin (~)=ey
50
(b)
10✓
2
25
(d) 25✓
2
Ifx = f(t) and y= g (t) are differentiable functions
(a)
2
f'(t).g"(t) - g '(t).f "(t)
[f'(t)
r
f'(t) .g"(t) - g '(t).f "(t)
(b)
(c)
(d)
16.
[/ '(t) ]2
g '(t).f"(t)- f'(t) .g "(t)
[f'(t)]3
g '(t).f "(t) + f'(t).g "(t)
[f'(t)]3
The equation of line equality inclined to
coordinate axes and passing through ( -3, 2, - 5) is
(a)
x+3 = y - 2 = z+ 5
1
(b)
1
1
x+3 = y - 2 = 5+z
-1
1
-1
(c)
x +3 = y -2 = z+ 5
-1
1
1
(d)
x +3= 2 - y=z +5
-1
1
-1
Ifthefunctionf(x) = [ tan(¾+x)J" forx;t,0 is
=Kfor
(a) e
(b) sin
d 2y
oft, then dx 2 is
1
dx=asin- 1 (1h) + c, then a+i3=
(b)
=ex
(c)
15.
- 9 -2
ol0 (d) -½[-3- 3
(d) - 10
In L\ABC, ifsin2 A +sin2B= sin2 Cand /(AB) = 10,
then the maximum value ofthe area ofL\ABC is
(a)
0
O is
5 2 -1
-1
7
(a)
l
1+[g(x)J4
2 -3
0
(c)
(b)
14.
1 0
3 3
cos(~)
(c) cos(~) =ey
I
10
1~],
The solution of the differential equation :
(a)
1
f'(x)= - - 4 , then g' (x) is
1 +x
(a) l + [g(x)] 4
(b) l-[g(x)] 4
l+ [f(x)]4
For a invertible matrix A ifA(adjA) = [
then I A I=
(a) 100
(b) - 100 (c)
1 TC
TC
1
(c)
(d) ---4 2
2 4
The statement pattern (- p I\ q) is logically
equivalent to
(a) (pvq)v-p
(b) (pvq)A-p
(d) (p v q) ➔ p
(c) (p A q) ➔ p
If g(x) is the inverse function off (x) and
(c)
i
1
1
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MHT-CET2017
17.
2017-9
27.
JI" log sec dx=
1
6
(a)
If J/logcosxdx= %tog (½),then
If a and pare roots ofthe equationx2 + 51xl-6 = 0,
then the value of I tan- 1 a - tan- 1 Pl is
n;
% log(½)
(c)
1+ % log ( ½)
28.
18.
19.
20.
(d)
3
(d) 4
(a) 1
(c) 3
(b) 2
Which of the following statement pattern is a
tautology?
(a) pv(q ➔ p)
(b) -q ➔ -p
(c) (q ➔ p) v (-p Hq)(d) p" -p
If the angle between the planes
J
r.(m i - + 2k) + 3 = 0 and
A
dy
parameter, then dx =?
(a)
23.
24.
25.
26.
If \
X
2
+4
+ B tan-1 (
)\
f)
X
2
+9
)
dx = A tan-'
1
Y
(b)
X
(c)
(d)
Y
-y
X
29.
The point on the curve y = .Jx -1 , where the
tangent is perpendicular to the line2x+y -5 = 0is
(a) (2,-1)
(b) (10,3)
(d) (5,-2)
(c) (2, 1)
30.
Iff
5
dx = A.Jx
✓xx-7
2
-12x +35 + log µ;I -6
2
3 ,thenm =
(b) x + 2y + z=0
(a) x-2y-z=0
(c) x-2y + z = 0
(d) 2x-2y + z = 0
If lines represented by equation px2- qy2 = 0 are
distinct, then
(b) pq<0
(a) pq > 0
(c) pq = 0
(d) p + q = 0
Let □ PQRS be a quadrilateral. IfMand N are
the mid-points of the sides PQ and RS
respectively, then PS+ QR =
(a) 3 MN (b) 4MN (c) 3 MN (d) 2NM
If slopes of lines represented by kx.2 + 5xy + y2
= 0 differ by 1, then k =
(a) 2
(c) 6
(b) 3
(d) 8
Ifvector r with dc's l, m, n is equally inclined to
the coordinate axes, then the total number of
such vectorse is
(d) 2
(a) 4
(c) 8
(b) 6
-X
2'..
X
+ .Jx -12x+35 +Cl , thenA =
(d) -2
(b) ± 3 (c) 3
(a) 2
21. Ifthe origin and the pointsP(2, 3, 4), Q(l, 2, 3)
and R(x, y, z) are coplanar, then
22.
Ifx = a (t-D ,y= a(t+D,wheretisthe
n;
A
r.(2i-mj-k)-5 = 0is
(d) 4
(c) n:
0
(b)
% log2
A boy tosses fair coin 3 times. Ifhe gets 2X for X
heads, then his expected gain equals to .......... .
A
n;
(a) 2
(a)
1
6
1
30 (d)
(c)
30
(b)
l
(a) -1
(b)
(c)
(d)
2
2
31. At random variableX -B(n, p), if values of mean
and variance of X are 18 and 12 respectively,
then total number of possible values of X are
(a) 54
(b) 55
(c) 12
(d) 18
32. The area of the region bounded by the lines
y=2x+ l,y=3x+ landx=4is
(a)
(c)
33.
16 sq unit
121
6
sq unit
(b)
121
3
sq unit
.
(d) 8 sq urnt
A box contains 6 pens, 2 ofwhich are defective.
Two pens are taken randomly from the box. Ifr.v.
X : number of defective pens obtained, then
standard deviation ofX =
4
(a) ± 3✓
5
(c)
3
(d)
3✓
5
4
16
45
8
(b)
+ C , then A- B =
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2017-10
34. If the volume of spherical ball is increasing at
the rate of 47t cm 3/ s, then the rate of change of
its surface area when the volume is 2881t cm3, is
35.
36.
37.
TargetMHT-CET
(a)
(c)
44.
4
2
(b) -ncm2/s
(a) -ncm2/s
3
3
(d) 21t cm2/s
(c) 41t cm2/s
2
Iff(x) = 1og(sec2x)°°' xforx:;i!:0 = K forx = 0
is continuous at x = 0, then K is
(b) 1
(a) e- 1
(c) e
(d) 0
If c denotes the contradiction, then dual of the
compound statement - p I\ (q v c) is
00
-pV~/\~
~
pv0qv~
~
~
(0.2)8
(b) (0.8)8
1
(d)
C/ 0.2)6 (0.8)2
8
Ifthe distance ofpoints 2i + 3] + Ak from the plane
r·(3i+2] + 6k) = 13is5units, then A. =
17
17
(a)
6,-
(c)
-6,-
(b) 6,
3
17
3
(d) -6,
3
17
3
-p/\~V~
-pv~/\~
The differential equation of all parabolas whose
axis is Y-axis, is
21t
3
(a)
7t
(b)
3
n;
(d) n
2
The particular solution of the differential
equationxdy +2y dx= 0, whenx= 2, y =lis
(a) xy=4
(b) x 2y =4
(c) xy2= 4
(d) x 2y2 = 4
fl ABC has vertices at A = (2, 3, 5),B = (-1 , 3, 2)
and C = (A, 5, µ). If the median through A is
equally inclined to the axes, then the values on
and µ respectively are
(a) 10, 7
(b) 9, 10
(c) 7,9
(d) 7,10
For the following distribution function F (x) ofa rv.x.
(c)
(c)
38.
39.
d 2y
dx 2
-
y
=0
(d)
n
d 2y _dy --0
dx 2 dx
[x] dx = ........... ...., where [x] is greatest integer
function.
(b) 0
(d) 1
(a) 3
(c) 2
The objective function ofLPP defined over the
convex set attains it optimum value at
(a) atleast two of the corner points
(b) all the corner points
(c) atleast one of the corner points
(d) None of the corner points
2
14
3
6
2
a
40.
41.
42.
Ifthe inverse of the matrix [
43.
r ·(i+]+k) = 2
(b)
47.
48.
F(x)
1
(c) r·(3i-3]+3k)=2 (d) r·(i-]+k)=3
Probability that a person will develop immunity
after vaccinations is 0.8. if8 people are given the
vaccine, then probability that all develop
immunity is =
2
0.2 0.37
P(3 < x < 5 ) =
(a) 0.48 (b) 0.37
3
r ·(i+]+k) = 6
1
X
-1]
does not exist, then the value of a is
(d) -2
(b) -1
(a) 1
(c) 0
Iff(X}=xforx :s;0 =0forx> 0,thenf(x)atx=0is
(a) continuous but not differentiable
(b) not continuous but differentiable
(c) continuous and differentiable
(d) not continuous and not differentiable
The equation of plane through (-1 , 1, 2), whose
normal makes equal acute angles with coordinate
axes is
(a)
46.
49.
3
4
5
0.48 0.62 0.85
(c) 0.27
6
1
(d) 1.47
x-1 y+l z -1
The lines-- = - - = - - and
2
2
4
y-k z
-2- = intersect each other at point
x-3
1
(a)
(c)
1
(-2,-4, 5)
(2,4,-5)
(b) (-2,-4,-5)
(d) (2,-5)
8
50.
J sec x dx =
cosecx
(a)
sec 8 x
--+c
8
(b)
sec 7 x
--+ c
(d)
sec 9 x
--+c
9
6
(c)
sec x
--+ c
6
7
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g-.A~N;.;;.S~W:..:E::.:.:R:.....:K=-=E=-Y=----=S=--------=--=&:___::S=---::0:.....:L=-=U:..:T~IO~N..s
111111111111111
(MHT-CET 2017)
WI
1
2
3
4
5
(a)
(a)
(c)
Answer KEYS
(d)
(a)
(b)
6
7
8
9
10
51
52
53
54
55
(c)
(c)
(a)
(d)
(b)
1
2
3
4
5
(b)
(a)
(d)
(b)
(b)
(b)
(b)
(a)
11
12
13
14
15
(b)
(c)
(c)
(d)
(a)
16
17
18
19
20
(c)
(d)
(c)
(c)
56
57
58
59
60
(a)
(a)
(a)
(d)
(d)
61
62
63
64
65
(d)
(b)
(c)
(b)
(b)
66
67
68
69
70
(b)
(d)
6
7
8
9
10
(b)
(a)
(b )
(a)
(d)
11
12
13
14
15
(c)
(c)
(b)
(c)
(a)
16
17
18
19
20
(b)
(d)
(c)
(c)
(c)
(b)
(b)
(b)
(d)
(b)
SECTION-A
PHYSICS
21 (b) 26 (a)
22 (d) 27 (d)
23 (a) 28 (a)
24 (a) 29 (d)
25 (c) 30 (d)
CHEl\flSTRY
71 (d ) 76 (b)
72 (c) 77 (c)
73 (a) 78 (b)
74 (a) 79 (a)
75 (a) 80 (a)
SECTION-B
MATHFMATICS
21 (c) 26 (a)
22 (a) 27 (a)
23 (c ) 28 (c)
24 (c) 29 (c)
25 (c) 30 (d)
31
32
33
34
35
(c)
(d)
(d)
(a)
(a)
36
37
38
39
40
(b)
81
82
83
84
85
(c)
(a)
(a)
(b)
(c)
86
87
88
89
90
(b)
(a)
31
32
33
34
35
(b)
(d)
(d)
(a)
36
37
38
39
40
(b)
41
42
43
44
45
(c)
(d)
(a)
(a)
46
47
48
49
50
(c)
(c)
(c)
(d)
(c)
(c)
(c)
91
92
93
94
95
(a) 96
(a) 97
(b) 98
(b) 99
(d) 100
(d)
(d)
(a)
(a)
(d)
(a)
(a)
(a)
(c)
(d)
41
42
43
44
45
(a)
(a)
(b)
(a)
(a)
46
47
48
49
50
(b)
(d)
(b)
(b)
(b)
(d)
(a)
(b )
(b )
(b)
(b)
SECTION-A
PHYSICS
1.
v1
1 n
(a) Using v = nA, - = A V
v3 =
[-1 __!_)
⇒ __!._= R
'). nf ,q
2
4
Re(312) ~e
= Re(¾-¼)
=
⇒ VJ - V3
⇒ v=Re[~-~)
n1
=Re(_!_)
=Re
2
...(ii)
From eqs. (i) and (ii),
VJ - V3
n2
2.
(a)
= V2 ⇒ VJ -
V2
=V3
Net capacitance between A and B
C'=C+C + C=3C
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rr--,c
:. B = 510-3 m
Distance between 1st minima on either side
=5xl0-3 +5xl0-3 =l0xl0-3 =10-2 m
D
6.
(d) Given, R = l 8Q, Z= 33Q, Vrms = 220V
A.=5x10-7 m
Power consumed in an AC circuit
3.75 µF - - - - - +
.
Net capacitance between A and D
erms
R
p = E;-mg.lnns.COS<p = E?rms·z· Z
3CxC 3C
Ceq= 3C+C =4
:. C= 4Ceq = 4x3.75 =S.00µF
3
3
3.
(c)
S=
G
(Given)
8
...(i)
G
And S = '
n- 1
From eqs. (i) and (ii),
G
7.
I
I
1 2
C
-=-+-=-or C1 =2
Ci CC 5 '
...(ii)
Effective capacity of the series combination
ofcapacitors with dielectric material
G
8= n-1 ⇒ 8=n - 1
:. n=8+ I = 9
Since, the range of galvanometer is
increased by 9 times, therefore its sensitivity
_!_ = _!_ + _l_ . _l_ = _!_[1+ _!__]
Ci
9
(b) Fromquestion, lx= 40cm,IR= 60cm.
using principle ofmetre-bridge,
... (i)
R IR 60 3
When 30Q resistance is connected in series
with the smaller of the two resistances
60
40
CK
2
8.
...(ii)
3
From eqs. (i) and (ii),
X
2
5.
3
⇒
K
C
1]
[ K
K + 1- 2
=c[ 2~~!01 ]= ~[~ :!]
3
⇒ R = 2(X +30)
C
= (K + !) - 2 = C
- - =-=-
2(X +330)
KC ' C2
~C= C2 - C1
40 2
X
Ix
-= - =-=-
X+30
R
C
C
CK
or, C2 = ( l+_!__) ( K+l )
K
:. Change in effective capacitance
reduces to S
4.
220 22
x 0xlS =20x20x2=800W
33x33
(a) Effective capacity of the series combination
of capacitors
=
(b) Polarising angle, tan 0 = µ
C
Also, M= V
3X
2(X +30)
3
9.
or, 9X= 4X+ 120 ⇒ 5X = 120
:. X=24Q
(b) Given d = 0.2 x I 0-3m, D = 2m
andA.=5x 10-7m
7
From B = AD = 5 x 10- x 2
d
o.2 x 10- 3
V
- IV
C
C
or, cot e = - :. e = cot
2
-
(b) Resultant intensity for two coherent sources,
IR =Ii +12 +2✓fiI2 cosq>
For two identical light waves, Ii = I 2 = I
5 x 1010-4
7
2 q>
IR = 41 cos - or, 1R
2
oc
2 q>
cos -
2
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10.
2017-13
(a) As we know, ~de = ~
1- ade
4 1
11= 13.6[ ~ ]= 13.6x¾
(1 - ade) = ade
~de
:. M=l0.2eV
Since, the energy is radiaed in form of
photons,
:. Energy of photons= hv = 10.2 eV
From Einstein's photoelectric equation,
...... (i)
Also, ~de - ade =
ade-~de
From equation (i)
~de(I- ade)
~de
<Xde-~de
hv= q,0 +eY5
10.2eV = 4.2eV + eV5
⇒
1- ade
~ = 1-(1-ade)
ade
:. V5 =6Y
ade
14.
_ 1- 1+ade
11.
<Xde
According
to question,
(b)
N 0=10,000 disintegeration/min
N 1 = 2500 disintegeration/min
t=4min
From the radioactive decay law,
Nt
-Al
-=e
15.
16.
No
2500
or, 10000 = e
AX4
1 -4>..
4>..
⇒ -e
4
12.
⇒ e
nh
And L=..... (i)
2n
..... (ii)
⇒ L oc n
n = principal quantum number
h = planck's constant.
:.M 0 oc n.
(a) Photodiode is a reversed biased p-n junction.
(c) According to question, I= 2kg m 2
t = 5min=5 x 60 = 300s
=4
.
usmg,
=µ g.hg =l.5 x 6=1.286
7
or, µ w
hw
(c) Energy difference between two states
!:ill= E2 - E1 = -13.6 - (-13.6)
= 13.6 _ 13.6
11
12
22
ro - roo
t
⇒ a=--­
ro = ro 0 +at
= µW"hW
22
ro=w 0 +at
= 0-60 = -60 = - 1 rad/s2
300
5
300
For t = 2 min
I
5
= 60-- x l20 = 60 - 24 ⇒ w =36rad/s
hg = thickness of slab and hw = height of
water column.
13.
e xl
(d) Magneticmoment(Mo)=2me
Where, L = orbital angular momentum.
w0 = 60 rad/s, w = 0
⇒ 4A = loge 4⇒ 4A = loge 22
⇒ 4A = 2 loge 2
: . A= 0.5 loge 2
(c) ·: Number of waves in glass slab
= number of waves in water column
:. µg.hg
6eY=eY5
12
Angular momentum,
L = lro = 2 x36 = 72kgm 2/s
17.
(d) Standard equation of wave motion,
Y =A
sin[ 2n(~ -f) +¾]
When compare the given equation with
standard equation we get,
Amplitude, A = 3m
Wavelength, A= 10m
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18. (c)
TargetMHT-CET
Rate of energy radiation.
4
Q = crAT i.e., power, P = crAT
or,
4
T= 4m(g+a) ⇒ d 2 = 4m(g+a)
nd2
nT
t
2
I
:. d=[4m~/a)r
:. Aoe 4
T
21.
If body radiates same power, then
7i 4
A2
Ai
4nr}
4nr1
7i4
-=4 ⇒ --2=4
T2
T2
(c)
1
V
or ' 4L
V
=L
v1
For closed pipe first overtone,
V
v1
3v
2
3V
V
=3 :. -
L
: . .!..kx2 = }_mv2
2
10
=12
L
3
⇒ x 2 = 14 mv
10 k
,
3V
Fundamental frequency v = - ( ) = 2L
f_
2
22.
3
2
m(g ; a)
nr
.
_ m(g+a)
2
nr
or, x=E&m
(d) According to question,
co0 = 0, co= 24rad/s and t = 8s
0 = co 0t +.!..w2 = o+.!..x3x(8)2
=.!2x12=17
12
(b) Maximum tension in the rope = m (g + a)
.. T-
= ~ x 2 x (6)2 = 2 _8
10
36
a= co-coo = 24 = 3rad/s2
8
t
Substituting the given values, we get
Now using,
17 V
V
12L 12' L
Stress in the rope, T =
2
using co= co 0 + at
When length of closed pipe is made 3 times,
V
V
Fundamental frequency v' = -(-) = 4 3L
12L
Beats produced = v - v'
20.
2
1 kx2
.
.
max1mwn compression x =
=---=3
L 4L
V
2L
1
2
I 2 1 2 7
=-mv +-mv =-mv
5
10
2
The potential energy of the spring on
= L
4
When length of open pipe is made
3V
2
2 I 2 2 2
I
=-mv +-x-mr co
2 5
2
For open pipe first overtone,
:. VJ-VJ
Given, mass, m = 2 kg, v = 6 mis and force
constant K = 36 Nim Kinetic energy of
rolling solid sphere
=-mv +-Iw
2
2
. .~ =(~r
19.
(b)
2
= 3x64 =%rad
2
23.
(a) Fundamental frequency of the wire
J-
1
- 2Li
/T _ 1 {I_ 1 fr
f;;; - 2Li vnr?p - 2Liri v~
First overtone of the first wire,
fr __l_ fr
JiI -2/--2_
- 2Lir1 V~ - Li'i V~
...(t).
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Second overtone of the second wire
27.
(d)
p = pm , where m = M mass of each
KT
N
molecule.
Let radius ofbig drop= R
and of small drop= r
Volume ofbig drop = n (Volume ofsmall drop)
irtR 3 =
3
R
24.
3 r1
3 2r2
(a) According to question,
2
forceF= 150dyne 105 xl0-5 N and
Surface tension T=7 x 10-2 N/m
£ 1 =4nR T
2
. _£_
2 = _nr_ _
·: Circumference ofthe capillary x surface
tension = upward force
:.2rtrT=F
(c)
5
= cp
7
26.
(a)
5
7
CP =R =>
7
(a)
Ei=GMm
R
5
..... (i)
Binding energy of revolving satellite at a
height h from the earth surface,
E _ GMm
2 - 2 ( R + h)
CP =R
2
n=-=0.2857
7
Ideal gas equation, p V = nRT
m'
pV = M RT here, m'is the mass of the gas
m'RT
and M molecular weight p = VM
pRT
: .p = - -
M
m'
: .p = V density of the gas
pM
pM
.
P = RT= NkT, N1sAvogadro, number
2
v;;:
...(i)
2
( n 1/ 3 .r )
1
or, ratio ofenergy, £ 2 : £ 1 =
Binding energy on the surface of the earth
Also' Cp -CV =R
or, CP -
2
2
. "dd.1atom1c
. moIecuIe, -CP = -7
For ngi
:. Cv
2
nr
1/ 3
1/3
nr
=~=n
[·: R=n .r]
n .r
28.
CV
R
E1
or 2rtr=F =lOSxlO- s =15 x J0-3 m
7x10- 2
'
T
25.
=> R =n 113 .r
£ 2 = n x 4nr 2 x T
Surface energy of big drop,
3
=l.5x10-2 =l.5cm
= nr
3
3
Surface energy of n drops,
=>!i_=~_r2 =~ ..!L =.!_ [·: 'i =2r2]
Li
3
n.inr3
·· ·· (ii)
From eqs. (i) and (ii),
£
2(R+h)
- 1=
R
E2
29.
(d) Given, particle velocity, v = nmls and time
period T = 16 s
Displacement of the particle, x = A sin wt
Velocity of the particle,
v
dx
=- = Aw cos wt
dt
Angular velocity,
2rt
w =T
21t
...(i)
1t
= - =- = rad/s
16 8
Now from eq. (i),
rt
7t
rt= A x -xcos-x2
8
8
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A
1t
A
33.
1
TargetMHT-CET
(d) Fundamental frequency, for a closed pipe
l=-cos-=-.4 8 ✓
8
2
30.
V
Vt= 4L = lOOHz
2m
:. A=8✓
(d) The figure represents string vibrating in
Fundamental frequency, for an open pipe
V
second overtone between two bridges
VJ = - = 2()()Hz
2L
In a pipe open at both the ends, all multiples
ofthe fundamental frequency are produced.
:. lx200, 2x200,3x200.. .
------L-----+
34.
Clearly, amplitude of vibration is maximum
at
LL SL
31.
(c)
Acceleration due to gravity varies with
depth d as,
35.
i.e., 200,400, 600...
(a) The total mechanical energy remains
conserved, kinetic energy changes into
potential energy and vice-versa. At the
highest point potential energy is maximum
and at the lowest point its velocity and
hence kinetic energy is maximum.
(a) Potential energy of a simple pendulum
=½Mw A =½M.f,A
2 2
g'=g(l - ~)
36.
,
,
g
I
Ad
n accord mg to quest10n, g = n
1 n-1
equation,
KEmax = hvo - <l>o
Initially, hv = 0.4 + <l>o
...(i)
and when the frequency of incident
radiation is increased by 30% then
... (ii)
1.3 hv=0.9+<1>0
From eqs. (i) and (ii)
(n-1)
(d) The relation ofdisplacement and acceleration
0.3<!> 0 =0.9-1.3(0.4)
with time in SHM are shown below,
ir
;;
g
a-a.
+A
o ,____________T_,
(.-.co=lJ
(b) According to the Einstein's photoelectric
d
or, R =1--;;=-n- :. d=R -n-
32.
2
37.
0.38
:. <l>o =-=l.267eV
0.3 resonant circuit, at resonating
(d) In LC parallel
38.
(a)
frequency, current is minimum graph (4)
,_
-A
correctly depicts.
Energy of photon
E =~=>t-. = ~
P
1-. p
2
P
E
Ee= me =pc ⇒ p
p
= -EP
[:.me= p]
C
Clearly, the phase difference between
displacement and acceleration is n.
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39. (b) Note : We have considered that the battery
2017-17
Energy lost ~= E 1- E 2
is kept disconnected from the capacitor.
When dielectric is introduced inside the
parallel plate capacitor, then potential
difference.
.
Also, energy decreases, 1.e., U
40.
= -Uo
K
(b) According to question,
p = 40 X 10-S Qm
A=8 x l0-6 m 2; l=0.2A
.
pl
Resistance, R =
A
⇒ R =E_= 40x10-
8
=Sxl0-2
.!_[
or, M' =
8x10-6
I
A
: . potential gradient of the were
43.
V =IR= 0.2x5x10-2 = 10-2 V/m
I
41.
I
(c) According to question,
co
co
coo= co, co=-; 0 = 2nn
:. a+B=co2(x +y)
4
u2 = co2(x2 _ y2)
v2-u2 = co2 (x-y)(x + y)
⇒ v2 _
2
2
v2-u2= (x-y)(a+ B)
2
CO )
⇒ 2nn = .!2_[
16
16 2a
When the fan is switched off,
co= 0, co 0 = co, 0 = 2nn'
⇒ O= co 2 - 2an'(2n)
:. 2nn' = a or, n' =
42.
(d)
f1co1 =(11 +I2)co2
CO2
11
co,
11 +I2
:.x-y = a+B
44.
u2-v2
ory-x = a +~
(a) From Doppler's effect, when the observer is
moving towards the source and source is
stationary, then the apparent frequency
n'= n( v~vo)
16
15 n
2
From conservation of angular momentum,
as net torque on the system is zero
⇒ -=--
v2-u2
CO
co 2
...(ii)
From eqs. (i) and (ii),
=co -2an(2n)
2an(2n) = co 2 -
... (i)
Also u 2 = co2A 2 - co2x2
and ~2 = co2A 2 - co2y2
using, co 2 = co5 - 2a0
Putting the given values
(:J
(a)
]cof
fil2
2 J1 +12
Let the distance be x when velocity is u and
acceleration a .
And the distance y when velocity is v and
acceleration B.
If is the angular frequency, then
a =co2x and B=co2y
...(i)
When the observer is moving away from
the source and the source is stationary, then
the apparent frequency.
n ,, = - n ( v ~vo )
... (ii)
From eqs. (i) and (ii),
n
2nv0
n' -n "= -(v+v0 -v+v0 ) = - v
V
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45.
(b) Let L 0 be the original length of the wire,
after heating temperature Tlength becomes
'L'. a be the coefficient of thermal expension.
Increase in the length of the rod
M
!!:_= D(2x2-1)1-.. ⇒ !!:...= DIA
2 d
2
2 d2
d2
:.A=-
= aLoT
L=Lo[l+aT]
..... (i)
48.
Also, Young's modulus,
FLo
Y=..... (ii)
AM
Using equation (i) and substituting in
equation (ii), we get
Y=
49.
3D
The process of superimposing the low
frequency signal on a high frequency wave
is called modulation.
(d) From question, L = 3 cm= 3 x 10-2 m
A =2 cm2 =2 x 104 m 2
M=3Am2
(c)
M
Intensity of magnetisation, Im= Lx A
F. Lo(l+aT)
M
A
FLo(l+aT)
or M = - ~ - ~
'
A.Y
From eqs. (i) and (ii),
3A-m2
- 3x2x!0--{5m3
...(iii)
= .!_ x 106 Alm = 5 x 105 A lm
2
FLo(l+at)
AY
50.
CJ.LoT
(c) Magnetic inducion inside the solenoid
B = µoNI
YAaT
.-. F= (l+aT )
46.
Magnetic flux, (j) = BA
(c) Induced emf in coil P
dl
or,
Iep I= M.__g_
<I>
= µoNI.A
L
dt
Putting ep = 15 mV = 15 x 10-2 V
and
dl
__g_
dt
..... (i)
L
<j>L
.
Magnetic moment = NIA = -
µo
= l0 A/s
From question,
15 x 10-3 = M x 10
or, M = 15 x 10-4H
Magnetic flux linked with coil Q
-4
<l>Q=Mlp=l5xl0
L = 60 cm and (j) =1.57 x 10-6 Wb (given)
M = 1.57 x 10-6 x0.6 = 0.75A
4 x 3.14 x 10-7
x l.8
[·: I P= 1.8 A]
=27.0x l0-4
CHEMISTRY
= 2.7x10-3
47.
(c)
=2.7mWb
In YDSE,positionofaminima
y
=
(2n-l}).D
Here, y
51.
d
= ,n = 2
2
Substituting y
=!!:_ and n = 2
2
Work done in a chemical reaction,
W = -~nf.T
Where, ~ng = number of moles of gaseous
products - number of moles of gaseous
reactants.
Reaction involved in combustion ofethane
..... (i)
d
(c)
in eq. (i)
is,
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CzH6(g)+~0 2 (g)~2CO2 (g)+3H 2 O(1)
55
·
(b)
&lg =2 - 4.5= - 2.5
W = (2.5 mol) (8.3 14 JK- 1moJ- 1) x 300 K
Orthophosphorus acid or Hypophosphorus ac id or
phosphonic acid (H3PO3) phosphinic acid (H3PO:z)
Oxidation state : +3
Oxidation state: + I
= 6235.5 J = 6.2355 KJ
l mole ofC2H6 = 30g ofC2H6
Work done during combustion of30 g of
CJ¼;= 6.2355 kJ
Work done during combustion of90g of
6.2355x90
18. 7065 kJ
30
= 18.71 kJ
(c) The sugar molecule present in DNA is
2'-deoxyribose.
C 2H6 =
52.
fl-D-deoxyribose used in DNA
or
D-2-deoxyribose
53.
Pyrophosphorus acid
(H4Pps)
Oxidation state : +3
56.
57.
(a) Molality
Orthophosphoric acid
(H 3PO4)
Oxidation state : + 5
(a) Due to the smaller size oflithium, it has the
highest Hydration Enthalpy which
compensate its I.E. and shows negative E 0
value. Therefore it acts as powerful
reducing agent and hence weakest
oxidising agent.
(a) Monomers used in preparation of dextron
are lactic acid and glycolic acid.
OH
OH
I
I
I
Polymerisation
nCH3- CH- COOH + n CH2 ---'------➔
Number of moles of solute
(m)=-------Mass of solvent (in kg)
Lactic acid
COOH
Glycolic acid
15.2
⇒ _§Q__ = 0.2533
0.150
0.15
⇒ 1.689 mol kg- 1
~
54.
COOH
(d)
~
COOH ,
Pbthal ic acid
CH2 CH 2COOH
I
CH CH COOH
58.
2
2
Adipic acid
59.
- - - CH2COOH
CH2
& COOHOH
60.
"--.CH2COOH ,
Glutaric acid
Salicylic acid
Salicylic acid contains both -OH and
- COOH groups.
(a) All the hydrides, except water CHiO) of
group 16 elements acts as a reducing
agents.
(d) Processes such as irradiation, addition of
salts and heat, antioxidants, emulsifiers are
used to preserve the food.
(d) Electron releasing groups increase electron
density at N-atom hence, such substituents
increase basic nature of aromatic amines.
Option (a), (b), (c) are electron releasing
group whereas (d) : C6 H5 is EWG, thus
decreases the basic strength.
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61.
62.
(d) (+) 2-methyl butane-1--ol and(-) 2-methyl
butan-1-ol are enantiomer. They are nonsuperimposable mirror images of each
other. Hence, they are optically active.
The optical activity of a compound can be
confirmed by the value of specific rotation.
(b) Haematite Fez03
Magnesite MgCO3
Magnetite Fe3O4
Siderite
FeCO3
:. Magnesite is the mineral of magnesium
67.
68.
TargetMHT-CET
(d) Zirconium (Zr) with atomic number 40 and
Hafnium (Hf) with atomic number 72
belongs to period 5th and 6th respectively.
(b) Aldehydes or ketones on treatment
C6Hs-NH-Nttz (phenylhydrazine) gives
phenylhydrazone. This is a nucleophilic
addition reaction.
(Mg).
63.
(c)
R--.......
C=N-NH-G)ls
Urotropine gives highly explosive
cyclonite on nitration.
✓
R--.......
/C = N - NH - C6 Ifs
H Phenyl hydrazone
69.
NO2
I
/
70.
N'-...._
H2f
. /N '-.... /
NO2
CH2
2C 2 H 5OH(/) + 2Na(s)~
2C2 H 5 ONa++H 2 (g) i
IHz
N'-._
N02
Cyclotrimethylene
trinitramine (cyclonite)
64.
65.
66.
(d) The solubility ofNaBr changes slightly with
temperature.
(b) The reaction of ethanol with water:
+3CH2O+NH3
(b) Work done during compression,
W=pext!),.V
Given, p ext= l 00 KPa, T = 300 K
!),.V = V2-V1
=(10-l)dm3 =9dm3
=0.99m3
W = 100 KPa (0.99) m 3
=99kJ.
(b) Nitrogen because of its small size, high
electronegativity, high ionisation energy,
absence of vacant d--orbitals has tendency
to form prc-pn multiple bonds N = N
(b) Statement (B) is incorrect. Hoffmann
bromamide degradation is used to
synthesise primary amine.
71.
2 mole ofNa (46 g) = 1 mole ofHi
= 2 g = 2 x 1o-3 kg
(d) The reaction between tert-butyl methyl
ether with hydrogen iodide:
CH3
I
I
HC-C-O-CH
3
3
+ HI
CH3
Tert-butyl methyl ether
--➔
(cold)
Hydrogen
iodide
CH3
I
I
H C-C- I+ CH3OH
3
CH3
Tert-butyl iodide
72.
73.
Methyl
alcohol
(c) Aluminium is refined by Hoope's process.
(a) Oxidation state ofMn in MnOi- is +6.
Mn (+6) = ls2 2s2 2p6,3s2 3p6 3d1,4s0
Hence, manganate ion MnOi - is
paramagnetic due to presence of unpaired
electron. Also, MnOi-is green in colour.
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74.
2017-21
chloride (Hinsberg reagent). Among which
l O amine on sulphonation gives a product,
which is insoluble in acid.
(a) Osmoticpressure,1t = CRT or 7t=~RT
MV
where, C = concentration of solution.
Given, w= 34.2 g, V = lL, M = 342 g mo1- 1
T = 20°c, c = 20 + 273 = 293 °K
w
H 3C - o - S0 2 Cl +
n=-RT
MV
=
75.
76.
77.
H3c - Q - s 02NHCiH5
342.2 g
N- alkyl toluene
sulphon amide
(Insoluble in alkali)
342g mol- 1
X
0.082 L atm K- 1mol-1 x 293 K
IL
=2.40atm.
(a) In R-S configuration, priority sequence is
decided by the atoms directly attached to
the chiral carbon are arranged in decreasing
atomic number.
From the given groups, sulphur (S) has the
highest atomic number i.e., 16 therefore it
has highest priority.
(b) Bithional is an antiseptic, which is mixed to
medication soaps to impart antiseptic
properties.
Whereas chloramphenicol is antibiotic,
cimetidine is antacid and chlordiazepoxide
is transquilizer.
(c) In the preparation of sulphuric acid Cl½SOJ
by lead chamber process, mixture
containing SO2 air and NO is treated with
steam (1½0). In this reaction, NO acts as a
catalyst.
2SO 2 +
02
( from air)
+ 2H2O + [NO]
81.
-
82.
83.
84.
85.
~
Catalyst
79.
e
- E./RT
__
= _A
eEa/RT
(a) Isopropyl alcohol
...(i)
H3C......._
,......cH - OH
H3C
Catalyst
(b) Coordination number ofFe in~ [Fe(CN)J
is 6 as it is bonded with six CN ligands.
Let x be the oxidation state of Cr
: . x+6(-l) = -3
:. x=+3
(a) Pseudo first order reaction e.g., inversion
of cane sugar is an example of
(c) Variationofrateconstantkwithtemperature
T(K) is given by Arrhenius equation.
k- A
2H 2SO 4 + [NO]
78.
~~~:~~ -➔
86.
87.
88.
89.
will give positive iodoform test.
(a) According to first law ofthermodynamics,
iiU = q + W
where, iiU = Internal energy
q = Heat ; w = Work done
For isothermal process, iiT = 0, iiU = 0
:. q = - W
(b) Alkyl chlorides or bromides reacts with Nal
in dry acetone to give alkyl iodide. This
reaction is known as Finkelstein reaction.
R-X + NaI~ R I + NaX [X = Cl, Br]
e.g., C2H5Br + Nal ~ C2H5I + NaBr
(c) F ullerenes are the allotropes of carbon
structure having cage like with general
formula, C20 (e.g. , C 60, C70 etc). C60 or the
bucky ball consists of60 C-atoms in which
each C-atom in C60 is sp2 -hybridised.
(b) S.I Unit of conductivity (K) is Sm-1
(a) Alk. KMnO4 is called Baeyer's reagent.
(b) The chief consitituent ofpyrex glass is Si 0 2.
(c) For isomeric alcohols, the boiling point
decreases with increase in branching of
carbon chain. Therefore, tert butyl alcohol
has lowest boiling point.
CH3
I
Sucrose
(Cane sugar)
80.
Glucose
Fructose
The concentration of water remains constant
(a) l O , 2° and 3° amines can be distinguished
from each other by p-toluenesulphonyl
H3C - T - CH3
OH
Teri-butyl alcohol
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90.
91.
(c) Relation between heat of reaction (Mir0 )
and bond enthalpies of reactants and
products is
~H, = I:BEreactants - I:BEproducts
~Horeaction
. = I:Hoproduct bonds-I:Horeactant bonds
93.
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(b) Electron gain enthalpy becomes less
(a) Given, k = 7 x 10-4 s-1, [A] 0 = 0.08 M
_ 0.693 _ 0.0693 _ 990
t112-------s
k
7x10-4s
92.
95.
(a) Bakelite is highly cross linked polymer.
Which is used in making handles of
cookers and frying pans, electrical goods,
etc.
94.
(b)
negative on moving from chlorine to iodine.
However, negative electron gain enthalpy
of fluorine is less than that of chlorine due
to small sized of fluorine atom. It has very
high inter electronic repulsion in the
relatively small 2p orbitals. Hence, incoming
electron experience less attraction from the
nucleus.
:. Chlorine has the highest value ofelectron
gain enthalpy.
Half of the volume occupied in water is
empty or unoccupied. Therefore, 10 cm 3of
the actual volume is occupied by water
molecules present in 20 cm3 ofwater.
(d) EAN = Z (atomic number of the metal)-number of electrons lost in the ion formation + number of
electrons gained from the donor atoms of the ligands.
C omplex
Oxidation
state of metal ion
[Pt(NH3)6]4+
+4
76
6
(78 - 4)+(6
= 86 (Rn)
~)
+2
26
6
(26 - 2) + (6
= 36 (Kr)
>1)
+2
30
4
[Fe(CN)6]
4-
[Zn(NH3)4]
2+
A tomic
no.
Coordination
no.
EAN
(30 - 2) + (4 X 2)
= 36 (Kr)
[Cu(NH3)4]
2+
+2
29
[Cu~)4]2+ is an exception to EAN rule.
96.
(d) The reaction involved for lead
accumulator during discharging i.e., when
cell is in the use are
At anode: Pb(s)+
98.
(a)
Overall reaction: Pb(s) + PbOz(s) + 2H+
99.
(a)
+ 2 HSO 4(aq)~ 2PbSOis) + 2Hz0(1)
97.
(d) Number oftotal ions present in the solution
is known as van't Hoff factor.
Urea is a molecular solid hence, does not
undergo association or dissociation
therefore, has the lowest value ofvan' t Hoff
factor (i).
~)
i
r~C
-OH
k2
HN_J;
Histidine
HSO4(aq) ~ PbSOis) + W + 2eAt cathode: PbOz(s) + 3W(aq) +
HSO4(aq)+ 2e-~PbSOis) + 2HzO(l)
(29 - 2) + (4
= 35 (Br)
4
100. (d)
It is basic in nature as it contains more
number of -NH2 groups than -COOH
groups.
Ar (Noble gas) does not form diatomic
molecules. Due to presence of completely
filled valence shell, these gases are highly
stable.
Stachyose contains 24 carbon atoms in its
structure.
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SECTION-8
MATHEMATICS
Corner points z = 4x1 + Sx2
(b) We have, tan 20 = I .
⇒ tan 20 = tan ~ .
4
⇒
n
7t
2
8
⇒
20 = nn +~.
4
0=-n+-.
Also, the value of tan 20 is positive. So, 0 lies in
1st and 3rd quadrants.
0=
2.
n
3.
9n
8 8 , are the two principal solutions.
&
A(3.5, 0)
z = 4 x 3.5 + 5 x 0 = 14 (minimum)
B(7 .5 , 0)
z = 4 x 7.5 + 5 x 0 = 30
C(3, 3)
Z
=
4
X
3+5
X
3 = 27
D(2, 3)
Z
=
4
X
2+5
X
3 = 23
Hence, the minimum value ofz is 14 at point (3 .5, 0)
which lies on X-axis.
(d) Let P & Q are the points with z-coordinates
as z 1 and z 2 respectively which trisect the line
segment AB.
1
(a) The objective function is given as, minimize,
z=4x 1 +5x2
Subject to constraints, 2x 1 + x 2 2:: 7,
2x 1 + 3x2 ~ 15, x2 ~ 3 and x 1, x2 2:: 0
For line 2x 1 + Xi = 7
7
5
Xi
For line 2x1 + 3x2 = 15
p
(2, 1, 4)A
Q
B(- 1, 3, 6)
Then, coordinates of P
2
0
1
=(l x (-1)+2x2 , l x 3+2x l, l x 6+2x4)
1+2
1+2
1+2
3
3
.
l x 6+2 x 4
Now, z-coordmate of P = - - - 1+ 2
0
3
5
3
6
.
6+8
14
l.e. Z1 = - - = 3
3
And coordinates of Q
=(2 x (-l) + lx2 , 2x3 + lxl , 2x6+1x4)
2+1
2+1
2+1
So, z-coordinate of Q =
i.e.
z2
12+4
2x6+lx4
+
2 1
16
=- 3 - = 3
14 16 30
Hence, z1 + z2 =-+-=-=10
3
3
3
x'2
A
5
6
1tB
4.
2x 1 + 3x2 = 15
(3.5, 0) 2x1 + 3xz = 7 (7.5, 0)
Now, the value ofz at corner points are calculated
as:
(b1~
s·mce, f( x ) =logx
--
x
After differentiating on both sides w.r.t.x, we get
1
x.- -logx.l
f'(x) = ~ x ~ - - = 1- logx
x2
x2
For maximum or minimum value of f (x), put
f'(x)=O
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7.
1-logx
⇒
X
= 0 ⇒ log x = 1 ⇒
2
x=e
,,
3+21ogx
Now, f (x)=
3
(a) Given, g(x) = rf{g(x))=x
On differentiating both sides w.r.t. 'x', we get
f(g(x)).g'(x)= 1
1(x)
1
---g'(x)=l
1+ (g(x)) 4
X
1
f"(e) = - - < 0
⇒
e3
g'(x) = 1 + [g(x)]4
After substituting x = e in eq. (i), we get
f(e) =log e =_!
8.
e
e
~) Conside, A = [:
1
Hence,maxirnurn valueoff{x) is -atx = e.
e
1 0
(b)
f x tan-I xdx
0
0
= )(3 X(-])-0)-0(3 X(-1)-0-0)+0(3 X2-5 X3)
=Ix (-3)-0-0=-3
Now,adjA
=
(3x(-l)-0)
-3x(-1)-0)
(3x2 -5 x3)
- (0 -0)
(lx(-1)-0)
- (2xl -5 x0)
(3x0 -0)
-(l x0 -0)
(3xl-0)
[
adj A= [-3
3
=8 - 2
1- +0
=i-½[1-~]=~-½
1 [ 1-tan-1
6.
O
]
-1
pvq ;>-"9 (p V Q) A ::<J
q
~p
T
T
F
F
F
T
T
F
F
F
F
T
F
T
T
T
T
F
F
T
F
F
0
0
-1
0
-9 -2 3
p
F
]
;]
-3
A-1
1
d.
A
I
Hence
= -a~ =- 0
'
IAI
-3
(b) The truth table is given below
T
T
0
-9 -2
1t
~J
~
So, IAI= 3 3 0
5 2 -1
I
5.
1
= -]
[ ·: f ' ( x )
l+x 4
9.
(a)
f ✓9-16x
1
dx
2
1
(¾r
-(x)
dx
2
(~pAq)=(pYq)A~p
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3
Hence, y = -x
2
I . -1 4x
=-sm -+c
3
4
⇒
3x-2y=0
-1
Now, slope of OP= Slope of AB
As
'
f
-1
1
✓9-16x
2
_ )
3 1
( 4-2
dx = asin-l(~x) +c
asin-1(~x)+ c =¾sin-
1
(
1x) +c
=(l=..!_)=-1
4-2
After comparing on both sides, we get
4
1
a=- and~=4
3
Equation of OP is (y-0)=-l(x-0)
y = -x ⇒ x+y = 0
Hence,joint equation of OP and OD is:
(x + y)(3x-2y) = 0
⇒ 3x2 +xy-2y2 = 0
1 1 1 1 3
Hence a + - = - + - = - + - = 1
'~4~44
3
10.
11.
(d)
= -1 [As, OP ..l AB]
(c) Given, f(x)=[tan(¾+x)fx =K
0(0, 0)
As, f(x) is continuous at x = 0,
f(O) = Jim f(x)
x➔O
So, K
. [l+tanx]l/x
= I1m
x➔O
1-tan x
lim[l+tanx
1-tanx
=ex➔O - - -
A
(1, 2)
p D
(2, 3)
B
(3, 4)
Since, 0(0, 0), A(l, 2) and B(3, 4) are the vertices
of~OAB.
Consider that OP and OD are altitude and median
of ~OAB, respectively.
Then, Coordinates ofD
1]I
x
= ei~o( 2tanx )_!_
1-tanx x
HenceK=
12.
/1C~o)= e
[·.-
Jim tanx =l]
x
x➔O
2
(c) We have,
=(1:3,2;4)=(2,3)
10
A(adjA) = [ O
3-0)
So, equation of OD is (y- 0) = ( - ( x - 0)
2-0
As, A(adjA) = IAI I
After comparing on both sides, we get
IAl=I0
0]=10[1 0]=101
10
0 I
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Hence, maximum value ofarea of LlACB
13.
(b) We have, :: = tan(~)+ ( ~)
... (i)
= 50x_!_ = 25
Since, it is homogeneous differential equation
After putting, y= Vx, we get
2
15.
dy =V+x dV
dx
dx
dx
dy
- = f'(t)and- = g'(t)
dt
dt
dV
V +x-= tanV + V
dx
[From(i)]
dy
dy
dt
As,
dx - dx
dV
x - = tanV
dx
dt
1
1
--dV=-dx
tanV
x
After integrating on both sides, we get
fcotV dV = logx + loge
⇒
log sin V = log(xc)
sin v=xc
g'(t)
dx
f'(t)
Now, differentiating again both sides w.r.t. ' x' ,
we get
f
⇒
dy
-=--
1
f --dV = _!_dx
tanV
x
⇒
(a) We have x = f(t) and y = g(t)
After differentiating on both sides w.r. t 't', we get
d2y
dx
f'(t).g"(t)-g'(t).f"(t) dt
2
(f'(t)) 2
dx
f'(t).g"(t)- g'(t).f"(t)
(f '( t ))
2
1
f'(t)
Hence, sin(~)= xc
f '(t).g"(t)- g '(t).f "(t)
14.
(c)
⇒
We have, sin2 A+ sin2 B = sin2 C
a 2 + b 2 = c2
(From Sine rule)
LlABC is right angled triangle and
LACB=90°
So, area of(LlACB) =
=-------
(f'(t))3
16.
I
2ab
(b) Consider(x 1,y1,z 1)=(-3,2,-5)
As, the line is equally inclined to coordinate axes.
/=-1, m= 1 and n=-1
Since, the equation of line passing through
(x 1, y 1, z 1) and direction cosines l, m, n is
By Sine rule's we get
x-x 1 = y-y1 = z-z1
n
l
m
a
c
b
--=--=-sinA sinB sinC
b
sin A sin B
Hence, a= 10 sin A
and b = 10 sin B
x+3 = y-2 = z+5
Hence,
a
-1
1
1
-1
1t
17.
1
2
7t
(d) Wehave, flogcosxdx=-log-
2
0
2
...(i)
AreaofMCB=_.!_(10 sinA)(l0 sinB) [From(i)]
2
1t
1t
= 50 sin A sin B
As, maximum value of sin A sin B =
1
2
2
( 1 )
= 2flog secxdx =flog
- - dx
O
O
cosx
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MHT-CET2017
7t
7t
-
2
2
= -flog (cosx)dx = -flog (cosx)dx
0
0
I
[From(i)]
2m+m-2
2 = ✓m 2 +1+4✓4+m2 +1
=>
I
3m - 2
= ✓(m2 +5)2
7t
18.
= -log2
2
(c) Suppose X be a random variable which
denotes the no. of heads in tossing a coin three
times. X can take value 0, 1, 2, 3.
As, y = ~2x. So, Y can take the values ~0, ~2, ~4
and ~6
1
P(y= 0) = P (0 head) = -
8
1 3m-2
+-=-- 2 m 2 +5
=>
=> m2 + 5=6m - 4 or -m2 -5 =6m - 4
=> m 2 - 6m - 9 = 0 or m2 +6m + 1 = 0
or m 2 + 6m+ 1 = 0
=> (m - 3)2 = 0
21.
3
P(y= 2) = P (1 head) = 8
3
P(y= 4) = P (2 heads) = -
As m 2 + 6m + 1= 0 doesnotgiveanyreal values.
Hence, (m -3)2 =0 => m=3
(c) Wehave,O(0,0,0), P(2,3,4),Q(l ,2, 3)and
R (x, y, z) are coplanar.
So,
8
1
P(y= 6) = P (3 heads) = 8
Hence, expected gain
=>
x -0
y -0
z -0
2-0
3- 0
4 -0 = 0
1-0
2 -0
3 -0
X
y
2
3 4 =0
Z
3
2
19.
=> x(9 - 8) - y(6 -4)+z(4 -3)=0
x-2y +z= 0
=>
= 6+12+6
3
8
(c) The truth table is given below:
p q - p --< ;>Hp
q ➔p
-q ➔ -P
p V(q ➔ p)
p
I\
22.
- p (q ➔ p) v (~p H q)
F
T
T
T
F
T
F
T F F T
FT T F
T
F
F
T
T
T
F
F
T
T
T
F F T T
F
T
T
F
F
T
TT F F
20.
Hence, (q ➔ p) v (- p ➔ q) is a tautology.
(c) Let n 1 and n2 are normals to the planes
r.(rrtl-j + 2k)+3 = 0and
r .(2i -mj- k)- 5 = 0, respectively.
Now, 8 =
2: is angle between the planes.
3
23.
(a) We have, pair ofline is px2 - qy2 = 0 ... (i)
After comparing eq. (i) with ax2 + 2hxy + by2 = 0,
we get a= p , b = - q, h = 0
As slopes of pair of lines represented by
ax2 + 2hxy + by2 = 0
are real and distinct iff h2 - ab > 0
So, 0 + pq > 0
Hence, pq > 0
(c) Consider p, q, r, s, m and n are the position
vectors of P, Q, R, S, Mand N be respectively.
As, M and N are mid-points of PQ and RS
respectively
So
m
'
=p + q
and n
2
=r+s
2
...(i)
Now,PS + QR
= s-p + r-q = (r + s)- (p +q)
= 2n - 2m = 2 MN
[From eq. (i)]
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24.
(c) We have, pair of lines
kx.2 + 5xy+ y2 = 0
... (i)
After comparing eq. (i) with
ax2 + 2hx + by2 = 0, we get
a= k, b = 1 and 2h = 5
Suppose m 1 and m 2 are two slopes of pair of
lines.
Then
-2h
a
m 1 +m2 =-=-5 and m1m2 =-= k
As,
(m 1 -m2 ) 2 =(m 1 +m 2 }2-4m1m 2
b
(1)2 = (-5)2 -4k
4k = 24 ⇒ k =6
(c) We have, vector r with dc's /, m, n is equally
inclined to the coordinate axes.
... (i)
I = m =n
So,
As, t2 + m2 +n2 = 1
[from eq. (i)]
:. 12 + f2 + / 2 = 1
3/ 2 = 1
⇒
⇒
2
15
3
1
-1
A=-andB=10
15
27.
1 1 15+ 10 1
Hence A-B=-+-=--=,
10 15
150
6
(a) It is given that, a and~ are the roots of the
equation
2
x +5lxl - 6 = 0
2
Here, lxl + 6lxl-lxl-6 = 0
⇒ lxl (lxl+6) -l(lxl+6) = 0
⇒ (lxl + 6)(lxl -1) = 0
1
3
/ =± ✓
⇒
1
_,x---tan
_,x-+ C
After comparing on both sides, we get
b
⇒
25.
1
= -tan
10
Jxl = - 6,1
1
As, modulus is always positive.
/=m=n=±-
Therefore,
✓
3
:. vector r = Jri( ±
Therefore, JxJ = 1 ⇒ x = ±1
~ i ± ~ j ± ~ k)
Consider, a= 1and~= -1
Hence,
Hence, total number ofrequired vectors = 23 = 8
26.
1
ltan- 1 o. -tan- 1 Pl= ltan-1 1-tan- (-1)1
(a) Consider I = J( 2
)\
) dx
x +4 X 2 +9
28.
-.!.[Jx +2
1 ctx-J-1-dx]
x +3
-5
2
2
2
2
(c)
We have, x=a(t -fland y=a(t+fl
2
2
2
Then, y2 - x =[a (t+~r - a (t -~r ]
⇒ y2 - x 2 =4a 2
x 1
x C
1
=-tan- 1---tan -1 -+
10
2 15
3
X B
X C
We have I = A tan- 1-+
tan-I -+
'
2
3
After differentiating on both sides w.r.t. 'x',
we get
2y :~ -2x = 0
⇒
2( y : -x) = 0
dy X
Hence - = -y
, dx
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29.
Supposethatslopeofthecurvey= ✓x -1 ism1
(c)
:. m 1 = dy =
~ ✓x -1
dx
dx
31.
2017-29
(b) We have, mean= 18 and variance= 12
So, np= 18 andnpq = 12
1
2✓x-l
npq
np
slope of the line 2x + y- 5 = 0 is m 2
After putting, p =
h-(-2)=-l ⇒ ~=l
.Jx
After substituting x = 2 in y =
-1, we get y = 1
Hence, required point is (2, 1).
(d) Consider, I =
=
32.
f✓: =~ dx
f
=f
x-5
(d)
Hence, total number of possible value ofX
= n + 1= 54 + 1 = 55
For line y = 2x + I,
two points are (0, 1) and (4, 9)
Forliney = 3x + 1,
twopointsare(O, l)and{4, 13)
y
(x-5)(x-5)dx
(x-7)(x-5)
✓x 2 -12x+35
dx
y = 2x + l
J~3=?fl{4, 9)
=_!__f 2x-12+2
2
✓x 2 -12x +35
f
= _!_
2x - 12
dx +
2 R-12x+35
= ✓x 2 -12x+35+f ✓
f
✓x
2
1
dx
-12x+35
1
2
1
3 in np = 8, we get
n( ½) = 18 ⇒ n= 54
' 2 x-1
⇒ x-l=l ⇒ x=2
30.
2
3
2 1
Therefore p = 1-q = 1- - = '
3 3
dy
d
:. m 2 = - = -(5-2x) = -2
dx dx
As, lines are perpendicular ifm1m 2 =-1
So
12
18
:.-=- ⇒ q=-
dx+C
(x -12x+36-1)
Hence, area of shaded region
XJ
Y2
X3
Y3
=
As,
2
2
I= A✓x -12x +35 +loglx-6+ ✓x -12x +35 +Cl
Hence,A= 1
33.
YI
1
=- X2
2
0 1
1
1 = _!__ 4 9 1
2
4 13 1
1
1
2[0-0 + 4(13-9)] = 8 sq units
(d) Given, X is the number of defective pens
obtained. Two pens are defective.
So, X have possible values 0, 1, 2
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ds
dr
-=4X27trdt
dt
ds
1
=}-=8 X1tX6Xdt
36
ds 41t
2
Hence, -=-cm I s
dt
3
35.
E(x
2
2
)
= ~+~ =
15
15
g
15
Standard deviation =
=
(b) Wehave, f(x ) =llog(sec2 xrot2x, forx "# 0
5
As, f ( x) is continuous at x = 0
✓E( x 2 ) - [E(x) ] 2
2
So, f(O) =
~~ [ log ( sec x )
2
•: Volume of spherical ball V =
.
X--)0
4
3
m
3
2
log(l+tan x)
.
1
=} r 3 = 72 X 3 = 8 X 27
tan2 x
X--)01 + tan
2
x
36.
(a) After replacing 'v' by 'A' and' " ' by ' v ' ,
37.
we get dual of the statement - p A (q v c) is
- pv(qAt)
Let vertex of parabola be (0, k) as axis of
parabola is Y-axis
So, equation of parabola is
...(i)
Now, 2887t= .±m3
3
(a)
2
(x-0) = 4a(y-k)
⇒ r=6
After differentiating eq. (i) w.r.t. 't', we get
⇒ x 2 = 4ay -4ak
dV = 41tr2 dr
dt
dt
dr
l
= hm --'--~--'- = hm - - ~
(a) Let r be the radius of spherical ball
⇒ 4rt=4m2 ::
cot x
(¼)-(½Y
=J¥s = 3}s
34.
, forx = 0
k
= _±
y
3
[-.-~~ =47tcm / s]
k
x ----o- - - - -x
1
36
⇒ -=-
dt
k
2
·: Surface area of spherical ball, s = 4nr
After differentiating on both sides, w.r.t. 't', we get
Y'
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MHT-CET2017
After, differentiating both sides w.r.t., ' x', we get
2x = 4a dy
dx
I
I dy
Therefore - = - , 2a X dx
Again differentiating on both sides w.r.t. 'x', we get
d~ (~,:)=
42.
! (21a)
Now, f(0)=0
So, LHL = RHL =f(0)
Hence, f(x) is continuous at x = 0
Here, f'(x) = 1 for x ~ 0,
0 forx > 0
Thus, f(x) is not differentiable at x = 0
(a) Equation of plane which passes through
a= - i + J+ 2k as it is perpendicular to
a= i + }+k will be ~.fi.=a.n
;.(I+]+ f) =(-I+ ]+ 2f).(I +]+ k)
= -1+1+2 = 2
Hence,
X
Hence, ;.(I+]+k:)=2
d2y - dy -- 0
dx 2 dx
43.
38.
(a)
f : [x]dx=f~octx+ f 1 ldx+ f >dx
=[X ] ~ + 2 [ X ]~
44.
(a) The coordinates of given point is (2, 3, A ).
So, equation of the plane is
= (2 -1) +2(3 - 2)=3
39.
(b) We have, probability that a person will
develop immunity after vaccination is 0.8
Hence, probability that a ll 8 persons
develop immunity= (0.8)8
2
r.( 3i + 2] + 6k) =13
(c) Objective function of a LPP defined over
convex set attains its optimum value at
atleast one of the corner points.
==>(xi + YJ +zk:) .( 3i + 2} + 6k) = 13
==> 3x + 2y+6z -13 = 0
Therefore, distance of the plane from the
given point (2, 3, A ) will be
So,
14 -Ii
3 1 =a(9 -2)-14(6 - 6)-1(4-18)
2
==> ±S = 61c - I
✓
49
3
= 7a+ 14
As, inverse of matrix A does not exists.
Therefore, IAI= 0
==> 7a+ 14=0
Hence, a= -2
x
41.
]
3 x 2+2 x3 + 6x1c -13 s[o·
=
1ven
,h2+22+62
1
==> ±35=61c -l
==> 35 =6A -l or - 35=6A -l
17
Hence A = 6 - '
3
,
for x ~ 0
(a) We have, f(x) = { o,'
forx> 0
LHLatx=0= lim_f (x) = lim x
x➔ O
x➔ O
and RHL at x = 0 = Jim f ( x) = lim 0 = 0
x➔O+
x ➔O
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As, AD is equally inclined to both the
coordinates axes.
2017-32
n
46.
n
A-5
µ-8
Therefore, - - = 1 = - 2
2
2n
=-+-=3
2 6
(b) Given, x dy + 2y dx = 0
⇒
dy + 2dx = 0
dy
X
After integrating on both sides, we get
47.
logy + 2 log x = log C
⇒
yx2 = C
⇒
2
A=7
µ -8
48.
And 1=-- ⇒ µ=10
'
2
(b) p(3 < x~5) = p(x=4)+p(x=5)
= (0.62 -0.48) + (0.85 -0.62)
= 0.14+ 0.23 =0.37
49.
(b)
J!-dy + 2 J!-dx = logC
y
X
⇒
A- 5
--=l
Ifx=2theny= I,
So, C = l x22 = 4
Hence, particular solution will be x2 y = 4.
(d) It is given that, A(2, 3, 5), B(-1, 3, 2) and
x-1 y+l z-1
Since ' - 2- = - -2= - -4= A
and
x-3
y-6
2
z
--=--=-
1
... (i)
... (ii)
1
Now, any point on the line (i) is P(2 A+ 1,
C( A, 5, µ) are three vertices of ~ABC.
Let D be the mid-point ofBC
2A-1,4A+ l)
ZA+l-3
I
A-1 5+3 µ+2)
So, coordinates ofD = ( - - , -- , -2
2
2
So,
21.. -l-6
2
4').. - 4 = 2A - 7
41.. + l [from(ii)]
I
⇒
2A = - 3
Hence, point of intersection Pis
= (A-1 4 µ+2)
2 ' ' 2
So, direction ratios of
AD=(A-l_2 4-3 µ+
2
'
' 2
-(')..-5
µ-8)
-1
2 ' ' 2
2
=(-2,-4,-5)
-5)
f
f
= f tan x. sec xdx
= f sec x.secx tanxdx
8
50.
sec x
sinx
-dx
(b) Consider I= - - - d x = - '
cosecx
cos8 x
7
A(2, 3, 5)
6
Let sec x = t
So,
f
⇒
6
sec x . tan x dx = dt,
I= t dt =
7
t7 +c = -sec-+c
x
7
7
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MHT-CET 112016 II
General Instructions
■
■
■
■
■
■
■
This question booklet contains 150 Multiple Choice Questions (MCQs).
Section-A: Physics & Chemistry - 50 Questions each and
Section-B: Mathematics - 50 Questions.
Choice and sequence for attempting questions will be as per the convenience of the candidate.
Read each question carefully.
Determine the one correct answer out of the four available options given for each question.
Each question with correct response shall be awarded one (1) mark. There shall be no negative marking.
No mark shall be granted for marking two or more answers ofsame question, scratching or overwriting.
Duration ofpaper is 3 Hours.
SECTION-A
PHYSICS
1.
2.
In potentiometer experiment, nu! 1 point is
obtained at a particular point for a cell on
potentiometer wire x cm long. Ifthe length of the
potentiometer wire is increased without
changing the cell, the balancing length will
(Driving source is not changed)
(b) decrease
(a) increase
(d) becomezero
(c) not change
An iron rod is placed parallel to magnetic field of
intensity 2000 Am- 1. The magnetic flux through
the rod is 6 x 1o-4 Wb and its cross-sectional
area is 3 cm2. The magnetic permeability of the
rod in Wb A- 1m- 1 is
(a)
3.
4.
10-1 (b) 10-2
(c)
10-3
A/M
(a)
5.
AM
(b)
3-;;;
Afm
(c)
6.
Alternating current of peak value ( ~) ampere
7.
Am
3~M (d) 3M
Interference fringes are produced on a screen by
using two light sources ofintensities I and 91. The
phase difference between the beams is
(d) Io-4
flows through the primary coil of the transformer.
The coefficient of mutual inductance between
primary and secondary coil is 1 H. The peak emf
induced in secondary coil is (Frequency of AC
=50Hz)
(a) IO0V (b) 200V (c) 300V (d) 400V
An electron ofmass m has de-Broglie wavelength
A when accelerated through potential difference
V. When proton of mass M, is accelerated
through potential difference 9 V, the de-Broglie
wavelength associated with it will be (Assume
that wavelength is determined at low voltage)
3V-;
7t
2 at pointP
and 1t at point Q on the screen. The difference
between the resultant intensities at point P and Q is
(d) 81
(a) 21
(b) 41
(c) 61
From Brewster's law, except for polished metallic
surfaces, the polarising angle
(a) depends on wavelength and is different for
different colours
(b) independent of wavelength and is different
for different colours
(c) independent of wavelength and is same for
different colours
(d) depends on wavelength and is same for
different colours
Two particlesX and Yhaving equal charges after
being accelerated through same potential
difference enter a region of uniform magnetic
field and describe a circular paths of radii r 1 and
r 2 respectively. The ratio of the mass ofXto that
ofYis
(a)
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When an electron in hydrogen atom revolves in
stationary orbit, it
(a) does not radiate light though its velocitychanges
(b) does not radiate light and velocity remains
unchanged
(c) radiates light but its velocity is unchanged
(d) radiates light with the change of energy
The magnetic field (B) inside a long, solenoid
9.
having n turns per unit length and carrying
current/when iron core is kept in it is (µ 0 =
permeability of vacuum, x = magnetic
susceptibility)
(b) µ0 nl x
(a) µ0 nl (1- x)
(c) µ 0nz2(1 + x)
(d) µ0nl (1 + x)
10. In balanced meter bridge, the resistance ofbridge
wire is 0.1. n cm. Unknown resistance X is
connected in left gap and 6 n in right gap, null
point divides the wire in the ratio 2:3. Find the
current drawn from the battery of 5 V having
negligible resistance
(a) lA
(b) 1.5A (c) 2A
(d) 5A
11. Three parallel plate air capacitors are connected
8.
in parallel. Each capacitor has plate area
TargetMHT-CET
16.
17.
18.
A
3 and
the separation between the plates is d, 2d and 3d
respectively. The equivalent capacity of
ccmbinatim is (E0 = abiolutepermittivityoffree space)
7E0 A
l 1E0 A
13E0 A
17fo,4
(a) 18d (b) 18d(c) 18d(d) 1&1
12. In an oscillator, for sustained oscillations,
Barkhausen criterion is A~ equal to (A = voltage
gain without feedback and~ = feedback factor)
1
(d) 2
(a) zero (b) (c) 1
2
13. Light of wavelength 'A. which is less than
threshold wavelength is incident on a
photosensitive material. If incident wavelength
is decreased so that emitted photoelectrons are
moving with same velocity, then stopping
potential will
(a) increase
(b) decrease
(c) bezero
(d) becomeexactlyhalf
14. A ray of light travelling through rarer medium is
incident at very small angle ion a glass slab and
after refraction its velocity is reduced by 20%.
The angle of deviation is
4i
00
15.
8
~ ~
~
2
~ ~
Themaximum frequencyoftransmitted radio waves
above which the radio waves are no longer
reflected back by ionosphere is (N = maximum
electron density oflonosphere, g = acceleration
due to gravity)
(a) gN
(b) gN 2 (c) g✓
N (d) g2N 2
Wire having tension 225 N produces six beats
per second when it is tuned with a fork. When
tension changes to 256 N, it is tuned with the
same fork, the number ofbeats remain unchanged.
The frequency of the fork will be
(a) 186Hz (b) 225Hz (c) 256Hz (d) 280Hz
Assuming the expression for the pressure
exerted by the gas on the walls of the container,
it can be shown that pressure is
r
r
r
(a)
[½ kinetic energy per unit volume ofa gas
(b)
[ ¾ kinetic energy per unit volume ofa gas
(C)
[¾ kinetic energy per unit volume ofa gas
(d)
2x
3
kinetic energy per unit volume ofa gas
A mass m 1 connected to a horizontal spring
performs SI-IM with amplitude A . While mass m 1
is passing through mean position, another mass
m2 is placed on it so that both the masses move
together with amplitude A 1. The ratio of
jA
is
(mi < m1)
I
(a)
(c)
19.
[m,:,J
[m,;m,]½
(d) [
m,;m,]'
A particle moves along a circle ofradius rwith
constant tangential acceleration. If the velocity
of the particle is v at the end of second
revolution, after the revolution has started, then
the tangential acceleration is
(a)
20.
(b)
[ m1 : 1mJ2
v2
81tr
v
v
(b)
61tr
(c)
21tr
v
(d)
2
21tr
Two strings A and B of same material are
stretched by same tension. The radius of the
string A is double the radius of string B.
Transverse wave travels on string A with speed
vA and on string B with speed v8 . The ratio ~ is
VB
(a) 4
(b) 2
(c)
2
(d) 4
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21.
22.
(a)
23.
1
3cm
(b)
2
3cm
(c)
3
2cm
29.
30.
(d) 0.2cm
A progressive wave is represented by y = 12 sin
(5t-4x) cm. On this wave, how far away are the
two points having phase difference of90°?
(a)
24.
2016-3
Which of the following quantity does not
change due to damping of oscillations?
(a) Angular frequency(b) Time period
(d) Amplitude
(c) Initial phase
If the end correction ofan open pipe is 0.8 cm,
then the inner radius of that pipe will be
7t
7t
7t
4Gm
r
(a)
16
12
31.
32.
8Gm
(b)
J;
sound in air and -
7t
-cm (b) -cm (c) (d)
2
4
8
Two particles of masses m and 9m are separated
by a distance r. At a point on the line joining
them the gravitational field is zero. The
gravitational potential at that point is
(G = universal constant of gravitation)
r
16Gm
32Gm
--(d) - - r
r
A black rectangular surface of area A emits
energy E per second at 27°C . If length and
(c)
25.
A ring and a disc roll on the horizontal surface
without slipping, with same linear velocity. Ifboth
have same mass and total kinetic energy of the
ring is 4 J, then total kinetic energy of the disc is
(a) 3J
(d) 6J
(b) 4J
(c) 5J
When the observer moves towards the stationary
source with velocity, v 1 the apparent frequency
of emitted note is/1• When the observer moves
away from the source with velocity v 1, the
apparent frequency is / 2. If v is the velocity of
3
of initial value and
temperature is raised to 327°C, then energy
emitted per second becomes
(a)
4E
-
9
(b)
7E
-
9
(c)
IOE
9
-
(d)
(a)
33.
16E
-
9
R
26.
For a gas
C
= 0.4, where R is the universal gas
V
27.
28.
constant and C v is molar specific heat at
constant volume. The gas is made up of
molecules which are
(a) rigid diatomic
(b) monoatomic
(c) non-rigiddiatomic (d) polyatomic
In vertical circular motion, the ratio of kinetic
energy of a particle at highest point to that at
lowest paint is
(a) 5
(b) 2
(c) 0.5
(d) 0.2
Two wires having same length and material are
stretched by same force. Their diameters are in
the ratio 1: 3. The ratio of strain energy per unit
volume for these two wires (smaller to larger
diameter) when stretched is
(a) 3: 1
(b) 9 : I (c) 27: 1 (d) 81: 1
34.
v,
=?
(b) 3
(c) 4
(d) 5
(a) 2
A liquid drop having surface energy Eis spread
into 5 12 droplets of same size. The final surface
energy of the droplets is
(b) 4E
(c) 8E
(d) 12E
(a) 2E
Let M be the mass and L be the length of a thin
uniform rod. In first case, axis ofrotation is passing
through centre and perpendicular to the length
of the rod. In second case, axis of rotation is
passing through one end and perpendicular to
the length of the rod. The ratio of radius of
gyration in first case to second case is
l rel
breadth are reduced to
V
= 2 , then -
(b)
1
1
-
2
(c)
1
-
(d)
1
8
4
A simple pendulum of length l has maximum
angular displacement 0. The maximum kinetic
energy of the bob of mass mis (g = acceleration
due to gravity)
(a) mg! (l + cos 0)
(b) mg! (1 + cos 2 0)
(c) mg/(l-cos0)
(d) mg/(cas0-l)
Angular speed of hour hand of a clock in degree
per second is
I
1
I
(c)
(b)
60
30
120 (d) 720
The value of gravitational acceleration g at a
(a)
35.
height h above the earth's surface is
!,
then
(R = radius of earth)
(a) h = R
(c)
h
=R
3
=R
(b)
h
(d)
h=R
4
2
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36.
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The schematic symbol of light emitting diode
(LED)is
Anode
Anode
(a)
(b)
Cathode
Anode
(d)
Cathode
38.
39.
40.
*~
t
T
(a)
Cathode
Anode
(c)
37.
43.
Cathode
The amount of work done in increasing the
voltage across the plates of capacitor from 5 V
to 10 Vis W. The work done in increasing it from
10 V to 15 V will be
(a) W
(b) 0.6W (c) l.25W(d) 1.67W
Magnetic flux passing through a coil is initially
4 x 1o-4 Wb. It reduces to 10% of its original
value int second. Ifthe emf induced is 0 .72 mV
then t in second is
(a) 0.3
(c) 0.5
(b) 0.4
(d) 0.6
Resolving power of telescope increases when
(a) wavelength of light decreases
(b) wavelength oflight increases
(c) focal length of eye-piece increases
(d) focal length of eye-piece decreases
When light of wavelength A is incident on
photosensitive surface, the stopping potential
is V. When light of wavelength 3A is incident on
3
3
6.
I
·
= - x 10 kgm , density of water= lgcc )
8
(b) T 1 =2T
(a) T1 =3T
(c)
42.
T1 = T
(d)
T1 =
44.
Rpg
2T
2T
(R- r )pg
(d)
(R-r)pg
T
When open pipe is closed from one end, then
third overtone of closed pipe is higher in
frequency by 150 Hz than second overtone of
open pipe. The fundamental frequency of open
end pipe will be
(b) 150Hz
(a) 75Hz
(d) 300Hz
(c) 225Hz
T
A disc of radius R and thickness
I
(a)
45.
wire of radius r (R > r) is inserted symmetrically
5
(b)
6
(c)
I
32
(d)
64
Let a steel bar oflength l, breadth band depth d
be loaded at the centre by a load W. Then the
sag of bending of beam is ( Y = Young's modulus
of material of steel)
(a)
(b)
(c)
(d)
46.
In Bohr's theory ofhydrogen atom, the electron
jumps from higher orbit n to lower orbit p. The
wavelength will be minimum for the transition
(b) n=4~p=3
00 n=5~p=4
47.
Two identical parallel plate air capacitors are
connected in series to a battery of emf V. If one
of the capacitor is completely filled with dielectric
material of constant K, then potential difference
of the other capacitor will become
~
n = 3~p = 2
(~ n = 2~p = 1
K
(a)
2
In a capillary tube ofradiusR, a straight thin metal
R
6 has moment
ofinertia/about an axis passing through its centre
and perpendicular to its plane. Disc is melted
and recast into a solid sphere. The moment of
inertia of a sphere about its diameter is
V
Threshold wavelength for the surface is
(a) 2A
(c) 4t-.
(d) 5A
(b) 3A
The bob of a simple pendulum performs SHM
with period Tin air and with period T 1 in water
Relation between T and T1 is (neglect friction
due to water, density ofthe material ofthe bob is
9
(b)
(R + r)pg
(c)
same surface, the stopping potential is
41.
and one end ofthe combination is dipped vertically
in water such that the lower end of the
combination is at same level. The rise of water in
the capillary tube is
[T = surface tension of water, p = density of
water and g = gravitational acceleration]
(c)
V(K+l)
K-1
KV
(b)
KV
K+l
V
(d)
K(K +1)
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MHT-CET2016
48.
49.
50.
The L-C parallel resonant circuit
(a) has a very high impedance
(h) has a very high current
(c) acts as resistance of very low value
(d) has zero impedance
A galvanometer ofresistance 30 n is connected
toa battery of emf2 V with 1970 n resistance in
series. A full scale deflection of20 divisions is
obtained in the galvanometer. To reduce the
deflection to 10 divisions, the resistance in series
required is
(a) 4030 n
(h) 4000 n
(c) 3970 n
(d) 2000 n
Two coherent sources P and Q produce
interference at point A on the screen where there
is a dark band which is formed between 4th bright
band and 5th bright band. Wavelength oflight
used is 6000 A. The path difference between PA
and QA is
(a) 1.4xJ0--4cm
(h) 2.7xJ0--4cm
(c) 4.5 x J0--4cm
(d) 6.2 x J0--4cm
CHEMISTRY
51.
---.
If 'n' represents total number of asymmetric
carbon atoms in a compound, then the possible·
number of optical isomers of the compound is
(d) 2n+2
(h) n 2
(a) 2n
(c)
The equation that represents general van ' t Hoff
equation is
zn
52.
53.
54.
55.
(a)
rc =!!:_RT
(c)
rc =-RT
V
V
(h) rc = nRT
(d) rc=nVRT
n
Which is the most stable allotrope of sulphur?
(a) Octahedral sulphur
(h) Monoclinic sulphur
(c) Plastic sulphur
(d) Colloidal sulphur
Select the correct statement for thermoplastic
polymer.
(a) It does not become soft on heating under
pressure
(h) It cannot be remoulded
(c) It is either linear or branched chain polymer
(d) It is a cross-linked polymer
How many Faradays of electricity are required
to deposit 10 g of calcium from molten calcium
chloride using inert electrodes?
(Molar mass of calcium= 40 g moJ- 1)
(a) 0.5F (h) IF
(c) 0.25F (d) 2F
2016-5
Name the reagent that is used in leaching ofgold.
(a) Carbon
(h) Sodium cyanide
(c) Carbon monoxide (d) Iodine
57. Which of the following is an analgesic?
(a) Ofloxacin
(h) Penicillin
(c) Aminoglycosides (d) Paracetamol
58. The compound which is not formed when a
mixture of n-butyl bromide and ethyl bromide
treated with sodium metal in the presence of dry
ether is
(a) butane
(h) octane
(c) hexane
(d) ethane
59. What is the general molecular formula of the
products obtained on heating lanthanoids (Ln)
with sulphur?
(a) LnS (h) LnS3 (c) Ln 3 S2 (d) Ln2 S3
60. Butylated hydroxy anisole is a/an
(a) antioxidant
(h) cleansing agent
(c) disinfectant
(d) antihistamine
61. In the cell represented by
Pb(s) IPb2+(1M) IIAg+(lM) IAg(s), the reducing
agent is
(a) Pb
(h) Pb2+ (c) Ag
(d) Ag+
62. Which metal cry.,tallises in a simple cubic structure?
(a) Polonium
(h) Copper
(c) Nickel
(d) Iron
63. The amine 'A' when treated with nitrous acid
gives yellow oily substance. The amine A is
(a) triethylamine
(h) trimethylarnine
(c) aniline
(d) methylphenylamine
64. The element that does not form acidic oxide is
(a) carbon
(h) phosphorus
(c) chlorine
(d) barium
65. While assigning R, S configuration, the correct
order of priority of groups attached to chiral
carbon atom is
(a) CONHi > COCH3 > C8iOH>CHO
(h) CONHi > COCH3 > CHO > CHiOH
(c) COCH3 > CONHi > CHO> CHiOH
(d) CHO > C8iOH > COCH3 >CONHi
66. Bulletproof helmets are made from
(a) lexan
(h) saran
(c) glyptal
(d) thiokol
67. Which metal is refined by Mond's process?
(a) Titanium
(h) Copper
(c) Nickel
(d) Zinc
68. Isopropyl methyl ether when treated with cold
hydrogen iodide gives
(a) isopropyl iodide and methyl iodide
(h) isopropyl alcohol and methyl iodide
(c) isopropyl alcohol and methyl alcohol
(d) isopropyl iodide and methyl alcohol
56.
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2016-6
In face centred cubic unit cell, what is the volume
occupied?
8
4 3
(b) -rcrJ
(a) -nr
3
3
3
64r
16 3
(c) -nr
3
(d) 3✓
3
70. Glucose on oxidation with bromine water yields
gluconic acid. This reaction confirms the
presence of
(a) six carbon atoms linked in straight chain
(b) secondary alcoholic group in glucose
(c) aldehyde group in glucose
(d) primary alcoholic group in glucose
71. How is sodium chromate converted into sodium
dichromate in the manufacture of potassium
dichromate from chromite ore?
(a) By the action ofconcentrated sulphuric acid
(b) By roasting with soda ash
(c) By the action of sodium hydroxide
(d) By the action oflimestone
72. In dry cell, what acts as a negative electrode?
(a) Zinc
(b) Graphite
(c) Ammonium chloride (d) Manganese dioxide
73. Select the compound which on treatment with
nitrous acid liberates nitrogen.
(a) Nitroethane
(b) Triethylamine
(c) Diethylamine
(d) Ethylamine
74. 5.0 gofsodiumhydroxide(molarmass40 gmol-1)
is dissolved in little quantity of water and the
solution is diluted upto 100 rnL. What is the
molarity of the resulting solution?
(a) 0.1 mol dm-3
(b) 1.0 mol ctm-3
3
(c) 0.125 mol dm(d) 1.25 mol dm-3
75. Which of the following compound when treated
with dibenzyl cadmium yields benzyl methyl
ketone?
(b) Acetaldehyde
(a) Acetone
(c) Acetic acid
(d) Acetyl chloride
76. Which halide of magnesium has highest ionic
character?
(a) Chloride
(b) Bromide
(c) Iodide
(d) Fluoride
77. The reaction takes place in two steps as
69.
(i)
78.
NO2Cl(g) ~ NOz(g)+ Cl(g) ,
(ii) NO2Cl(g) + Cl(g) ~ NO2 (g) + Cl2(g)
Identify the reaction intermediate.
(b) NO2(g)
(a) NO2Cl(g)
(d) Cl(g)
(c) Cl2(g)
Which ofthe following amino acid is basic in nature?
(a) Valine
(b) Tyrosine
(c) Arginine
(d) Leucine
TargetMHT-CET
The relation between solubility of a gas in liquid
at constant temperature and external pressure is
stated by which law?
(a) Raoult's law
(b) van'tHoff-Boyle'slaw
(c) van'tHoff-Charles' law
(d) Henry's law
80. Which among the following phenolic compound
is most acidic in nature?
(a) p-aminophenol
(b) Phenol
(c) m-nitrophenol
(d) p-nitrophenol
81. Which among the following solid is a non-polar
solid?
(a) Hydrogen chloride
(b) Sulphur dioxide
(c) Water
(d) Carbon dioxide
82. Identify the metal that forms colourless
compounds.
(a) Iron (Z= 26)
(b) Chrcmium(Z=24)
(c) Vanadium(Z = 23) (d) Scandium(Z = 21)
83. What is the highest oxidation state exhibited by
group 17 elements?
(a) +I
(b) +3
(c) +5
(d) + 7
84. Mathematical equation of first law of
thermodynamics for isochoric process is
(a) AU= q
(b) AU= qv
~ q=-~
~ AU=W
85. Name the catalyst used in commercial method of
preparation of phenol.
(a) Silica
(b) Calcium phosphate
(c) Anhydrous aluminium chloride
(d) Cobalt naphthenate
86. The rate constant and half-life of a first order
reaction are related to each other as
0.693
(a) t,12 = - k (b) t112 = 0.693k
79.
kt _ _
l_
112 - 0.693
(d)
87. What is the combining ratio of glycerol and fatty
acid when they combine to form triglyceride?
(a) 3 : 4 (b) 3:2 (c) 1:3 (d) 1: 2
88. The molecular formula of Wilkinson 's catalyst
used in the hydrogenation of alkenes is
(b) (Ph3P)3 RhCl
(a) Co(CO)8
(c) [Pt(NH3)zC12]
(d) K[Ag(CN)z]
89. The criterion for a spontaneous process is
(a) AG > 0
(b) AG<0
(c) AG=0
(d) AStotal < 0
90. Brown ring test is used for detection of which
radical?
(b) Nitrite
(a) Ferrous
(d) Ferric
(c) Nitrate
(c)
k=0.693t112
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91.
92.
93.
94.
95.
96.
2016-7
The reagent used in Wolff-Kishner reduction is
(a) NHi - NH2 and KOH in ethylene glycol
(b) Zn - Hg / cone. HCl
(c) NaBH4
(d) Na-Hg/H2 O
Which of the following is a neutral complex?
(b) [Co(NH3) 6 ]Cl3
(a) [Pt(NH3)iC12]
(c) [Ni(NH3) 6)Cl2
(d) K4 [Fe(CN)6]
Identify the compound amongst the following
of which 0.1 M aqueous solution has highest
boiling point.
(a) Glucose
(b) Sodium chloride
(c) Calcium chloride (d) Ferric chloride
Which reagent is used in Etard reaction?
(a) Chromyl chloride (b) Ethanoyl chloride
(d) Cadmiumchloride
(c) SnC1 2 andHCl
The most abundant noble gas in atmosphere is
(b) argon
(a) neon
(c) xenon
(d) krypton
Identify an extensive property amongst the
following.
(a) Viscosity
(b) Heat capacity
(c) Density
(d) Surface tension
97.
98.
Which of the following carboxylic acids is a
tricarboxylic acid?
(a) Oxalicacid
(b) Citricacid
(c) Succinic acid
(d) Adipic acid
Average rate ofreaction for the following reaction.
2SO 2 (g) + 0 2 (g) ➔ 2SO 3 (g) is written as
(a)
~[so2]
(b)
_
M
~[02]
~t
~[so
(c)
2]
1
(d) ~[S0 3 ]
~t
2 ~t
99. What is the amount ofwork done when 0.5 mole
ofmethane, CH4 (g), is subjected to combustion
at 300 K? (Given, R = 8.314 JK_-l mol- 1)
(a) -2494J
(b) -4988J
(c) + 4988J
(d) + 2494J
100. Primary nitroalkanes are obtained in good yield
by oxidising aldoximes with the help of
(a) trifluoroperoxy acetic acid
(b) acidified potassium permanganate
(c) concentrated nitric acid
(d) potassium dichromate and dilute
sulphuric acid
SECTION-B
MATHEMATICS
1.
Let X ~ B (n, p ), ifE(X) = 5, Var (X) = 2.5, then
p(X < 1) is equal to
6
} ) II
2.
( } ) IO
(})
(
9
(b)
2
1
3
✓l-x2
(b)
✓l-x 2
1
3
The differential equation of the family of circles
touching Y-axis at the origin is
(c) 3
3.
(a)
(a)
5.
sin- 1(3x-4x3 ) is
(a)
ol
1 1
IfA = 2 l 5 ' then
[
1 2 1
(})
2 (c) 2 (d) 2
..
f
J x ) "h
Denvat1veo tan- l ✓l- x ) wit respect to
(a)
2
4.
2
2
2
(x +y )t-2xy =O
=0
(c)
dy
(x 2-y 2)--2xy=0
dx
(d)
2
-
y
+ 2xy :
(x
(x + y
)
2
):
+ 2xy = 0
(c)
-1
(d) 2
re 5re]
[ 4 ,4 , then the value of c is
(a)
6.
re
3
re
2
(b)
(c)
3re
3
(d) re
The joint equation of lines passing through
the origin and trisecting the first quadrant is
(a)
(b)
(b) 0
IfRolle's theorem for
fix) = ffX ( sin x - cos x) is verified on
(d)
2
1
x 2 + ✓3xy - y 2
2
✓
3xy - y
2
=0
=0
(b)
x
(c)
✓
3x 2 -4xy+ ✓3y 2
(d)
3x
-
2
-
y
2
=0
=0
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2016-8
7.
If2 tan- 1(cosx) = tan- 1 (2 cosecx), then
sin x + cos x is equal to
(a)
8.
2✓
2 (b)
✓
2
1
✓
2
(c)
(d)
f -v,8 + 21x - x
(a)
is continuous at x = 0, then k is equal to
2 1
5'-5'5
(a)
17.
is equal to
½sin-1(x;l)+c (b)
. 1(x+l)
Sill- - +c
3
18.
13.
(a) 0
14.
(d)
(c) -1
Ay,
Ify = em sin- 1 x and (1-x2 ) =
equal to
(c) m2
(b) -m
(a) m
1
2
then A is
(d) - m2
(4ex - 25l
(
)
f l 2ex_5)dx=Ax + Blog 2ex - 5 +c, then
(-✓2)
1
cosec-
(b) A=5andB=-3
(d) A=-5andB=-3
is equal to
(-½)
1
+ cos-
3
4
4
(c) (b)
(d) 0
5
5
5
For what value of k, the function defined
20.
otherwise,
0
2 C
(a+b ) 2 sill
. 2 C
In MBC, ( a-b ) 2 cos -+
- is
2
2
equal to
(b) c 2
(a) b 2
2
(c) a
(d) a2 + b2 + c 2
Derivative oflog (sec 0 + tan 0) with respect to
sec 0 at 0 =
I
tan- 1(✓3)-sec- 1 (-2)
19.
log( 1+ 2x) sinx
then probability of waiting time not more than
4 minutes is equal to
(a) 0.3
(c) 0.2
(d) 0.5
(b) 0.8
12.
(b)
(a)
j½ • 0 ~ X~ 5
0,
0
(a) A=5andB=3
(c) A= -5andB =3
3
f ( X) =
forx=O
k,
1 slll. I ( -X +-1) + c (d) szn. I ( -X - -1) + c
3
3
The approximate value ofj(x) = x 3 + 5.x2- 7x + 9
atx = 1.1 is
(d) 8.3
(a) 8.6
(b) 8.5
(c) 8.4
If random variable waiting time in minutes for
bus and probability density function of x is
given by
(c)
11.
dx
2
f ( x) = !xsin~, for X7- 0
3 4
5'5'5
4
10.
2
x+2 2y-5
Direction cosines of the line - - = - - ,
2
3
z=-1 are
(b)
9.
(d)
TargetMHT-CET
The point on the curve 6y = x 3 + 2 at which
y-coordinate is changing 8 times as fast as
x-coordinate is
(a) (4,11)
(b) (4, -11)
(c) (-4, 11)
(d) (-4,-11)
16. If the function/ (x) defined by
15.
by
f(x) =
for X 7-Q
x2
k,
for X =0
is continuous at x = 0?
(a)
2
(b)
1
2
TC
(c)
90
(d)
90
TC
dy
/1
Iflog 10 lx 2 + y 2 ) = 2, then dx is equal to
( x2 -
21.
TC
4 is
(b)
1
1
(c)
✓
2
(d)
The joint equation of bisectors of angles
between lines x = 5 and y = 3 is
(a) (x-5)(y-3)=0
(b) x 2 - y 2 - 1Ox + 6y + 16 = 0
(c) xy=O
(d) xy-5x-3y+ 15 = 0
(a)
99x
--lOly
(b)
99x
-lOly
(c)
99y
lOlx
(d)
99y
lOlx
✓
2
22.
e-
n/2
sinx)
_} log 2 + sinx is equal to
12
(a)
1
(b)
3
(c) 2
(d) 0
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l
MHT-CET2016
23.
1
f
[
29.
2 ) (x+ran- x)
x + 2a
dx is equal to
X +l
2
(
2016-9
1
( x+ tan- x)
-'------'-+C
loga
30.
The degree and order ofthe differential equation
3
[
25.
1 + ( dy)
dx
]f
2
u+ J+ k) and the plane
2)
. -1[✓
3
-1[✓2)
(b)
Sill
-1[✓
32)
(d)
Sill
cos
(c)
tan
3
2)
. -1[✓
✓
3
The area of the region bounded by the curve
y = 2x- x 2 and X-axis is
(a)
.
2
-squmts
3
(c)
5
-sq units
3
0
(b)
4
.
-squmts
3
(d)
8
-sq units
3
2
If lo;~~x)dx=/ag[logsinx]+c, thenj(x)
28.
is equal to
(a) cotx
(b) tanx
(c) sec x
(d) cosec x
IfA and B are foot ofperpendicular drawn from
point Q(a, b, c) to the planes yz and zx, then
equation ofplane through the points A, Band 0
is
then m + n is equal to
1
(d) -1
(c) 2
l
~
---.========= dx is equal to
~secx+~cosecx
71:
(b)
71:
71:
(c)
(d)
71:
4
6
2
3
If the probability density function of a random
variable Xis given as
Xj
-2
-1
0
1
2
P(X=x1 0.2 0.3 0.15 0.25 0.1
32.
then F(O) is equal to
(a) P(X<0)
(b) P(X>0)
(c) 1-P(X> 0)
(d) 1-{X< 0)
The particular solution of the differential
equationy(l+ logx) dx -xlogx=0, when,
dy
x =e,y= e2 is
(a) y=exlogx
(b) ey=xlogx
(c) xy=elogx
(d) ylogx=ex
33. Mand N are the mid-points ofthe diagonals AC
and BD respectively ofquadrilateral ABCD, then
AB + AD + CB + CDis equal to
(a) 2MN (b) 2NM (c) 4MN (d) 4NM
34. If sin x is the integrating factor (IF) of the linear
differential equation : +Py = Q then Pis
35.
f
27.
(b)
-"[
f
2
r x ( 2I -}+ f) = s
26.
31.
(b) 3and2
(a) 3and7
(c) 7and3
(d) 2and3
The acute angle between the line
(a)
c = ma + nb,
(a)
= 7 (ddxy) respectively are
r = (i + 2J + k) + A,
and
(a)
0
(d) loga(x+ tan-1x)+ c
24.
Ifa= a=i+]-2k,b=2i-] +k:and c=3i-k
36.
(a) log sin x
(b) cos x
(c) tan x
(d) cot x
Which of the following equation does not
represent a pair oflines?
(a) x 2 -x=0
(b) xy -x=0
(c) y-x + I = 0
(d) xy + x +y + I = 0
Probability of guessing correctly atleast 7 out of
10 answers in a 'True' or 'False' test is equal to
11
11
11
27
(c) (d) (b) 64
32
16
32
Principal solutions at the equation sin 2x + cos
2x = 0, where n <x < 2 n are
(a)
37.
7n lln
9 ' 8
(a)
.::.+1--~=0
a b C
.::._l.+~=0
a b C
(a)
--
(b)
(c)
.::__l__~=O
a b C
(d)
.::.+1-+~=0
a b C
(c)
_g_'_g_
lln 15n
9n 13n
8 ' 8
(b)
--
(d)
_g_'_g_
15n 19n
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38. It line joining points A and B having position
vectors 6a - 4b + 4c and --4c respectively and
the line joining the points C and D having
position vectors - a - 2b - 3 c and a + 2b - 5c
intersect, then point of intersection is
(b) C
(d) A
(a) B
(c) D
39.
as[~ ~1],
IfA = [~ 3
(B"-1A-1 1 is equal to
t
(a)
[~
(c)
[~
~2]
~3]
45.
then
46.
(b)
(d)
[~2 !]
~l]
TargetMHT-CET
(a) x,y ;:,:o,x +y ;:,: o, x ;:,:s,y,; 3
(b) x, y ;:,:0,x-y ;:,:o,x s5,ys 3
(c) x,y ;:,: o,x-y ;:,: o, x s5,y;:,:3
(d) x,y;:,:0,x-ys0, x s5,ys3
Direction ratios ofthe line which is perpendicular to
the lines with direction ratios-I, 2, 2 and 0, 2, 1 are
(a) 1, 1, 2
(b) 2,-1, 2
(c) -2, 1, 2
(d) 2, 1,-2
! !],
~1]
Ifmatrix A = [
is equal to
(a)
[ ~2
~[~
such that AX= I, then X
(b)
~[:
~1]
40.
If p : Every square is a rectangle. q : Every
rhombus is a kite, then truth values ofp ➔ q and
p B q are_and _respectively.
(a) F,F
(b) T,F (c) F,T (d) T,T
41. If G(g), H(h) and (p) are centroid orthocentre and
circumcentre of a triangle and xp + yh + zg = 0,
then (x, y, z) is equal to
(a) 1,1,-2
(b) 2,1,-3
(c) 1,3, --4
(d) 2,3, -5
42. Which of the following quantified statement is
true?
(a) The square of every real number is positive
(b) There exists a real number, whose square is
negative
(c) There exists a real number, whose square is
not positive
(d) Every real number is rational
43. The general solution ofthe equation tan2 x = 1 is
44.
7t
(a)
nn+-
(c)
nn±-
4
7t
47.
a·(b xc) = 10 , then 'A, is equal to
00
48.
nn--
49.
(d)
2nn±~
~
7
W
9
Ifrandom variablex- b ( n = 5,P =
~
W
½) ,then
80
40
40
80
(a) 243 (b) 243 (c) 343 (d) 343
The objective function Z = x 1 + x 2 , subject to
the constraints are
x, +X2 s l0,-2x, +3x2 s l5,x, s6, xl' x2;:,: o,
has maximum value _ _ _ _ _ _ _of
the feasible region.
(a) at only one point
(b) at only two points
(c) at every point of the segment joining two
points
(d) at every point of the line joining two points
equivalent to
4
4
The shaded part of given figure indicates in
feasible region,
4
6
P(2 < X < 4) is equal to
7t
(b)
Ifa=i-]+k,b=2i+l]+k,c=i-]+4k and
y-axis
B
C
(3, 3)
(5, 3)
A
(5, 0)
then the constraints are
so.
x-axis
Symbolic form of the given switching circuit is
equivalent to:
(a) p v - q
(b) p A- q
(d) None of these
(c) p B q
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g-.A~N;.;;.S~W:..:E::.:.:R:.....:K=-=E=-Y=----=S=--------=--=&:___::S=---::0:.....:L=-=U:..:T~IO~N..s
111111111111111
(MHT-CET 2016)
WI
Answer KEYS
SECTION-A
PHYSICS
8
(a)
(a)
(a)
9
(d)
10
(a)
(b )
(d)
(d)
(d)
(a)
56
57
58
59
60
(a)
61
62
63
64
65
(b)
(d)
6
7
(c)
(b)
11
12
(b)
2
3
(b)
8
(a)
4
5
9
(d)
10
(a)
13
14
15
(b)
(b)
(b)
1
2
3
4
5
51
52
53
54
55
1
(a)
6
(c)
(b)
(c)
(c)
7
(c)
(a)
(a)
(c)
11
12
13
14
15
(b)
(c)
(a)
(b)
(c)
(a)
(a)
(d)
(d)
(b)
(b)
(b)
(a)
16
17
18
19
20
66
67
68
69
70
16
17
18
19
20
(a)
(b)
(a)
(a)
(c)
(a)
(c)
(b)
(c)
(c)
(a)
(c)
(b)
(b)
(c)
(c)
21
22
23
24
25
(b)
(c)
(c)
(d)
26
27
28
29
30
(a)
(d)
(b)
(a)
(b )
CHEMISTRY
71 (a) 76 (d)
77 (d)
72 (a)
73 (d) 78 (c)
74 (d) 79 (d)
75 (d) 80 (d)
S ECTION-B
MATIIEMATICS
21 (a) 26 (b )
22 (d) 27 (a)
23 (c) 28 (a)
24 (b) 29 (c)
25 (b) 30 (c)
31
32
33
34
35
(c)
(b)
(c)
(c)
81
82
83
84
85
(d)
(d)
(d)
(a)
(a)
(d)
31
32
33
34
35
(c)
(d)
(c)
x
V
(c)
(a)
36
37
38
39
40
(b)
(d)
(c)
(a)
(d)
86
87
88
89
90
(a)
36
37
38
39
40
(a)
(c)
(b )
(b)
(c)
(c)
(a)
(a)
(a)
41
42
43
44
45
(a)
(c)
(d)
(a)
(b)
91
92
93
94
95
(a)
(a)
41
42
43
44
45
(b)
46
47
48
49
50
96
97
(d) 98
(a) 99
(b) 100
(a)
(c)
(b)
(b)
46
47
48
49
50
(a)
(b)
(a)
(c)
(b)
(b)
(b)
(b)
(d)
(a)
(c)
(a)
(b)
(c)
(d)
SECTION-A
PHYSICS
1.
(a) Clearly from figure,
a
l - - - - L-"----+I B
I
I----( ~
Vo
i
.. ---------------------- ------------ ------------ -- ___,
Balancing length x
VxL
-=- ⇒ x =--
2.
L Vo
Vo
here, VO = potenti al difference across
potentiometer wire
V = potential to be measured
L = length ofthe potentiometer wire
·: xocL
: . if length of potentiometer wir e is
increased the balancing length will also
increases.
(c) Given, B 0 = magnetic field after insertion of
iron rod- 2000 Am- 1
Magnetic flux, <)> = 6 x lo-4Wb
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Area ofcross-section, A = 3 cm2 = 3 x 1o-4m
magnetic permeability of the rod,
µ,
For
=~ =-<P-[·: q>= BA]
B 0 AxB 0
M = IP-IQ= 101-41 = 6I
B
So,µ=---r 2000Am-l
3.
(b)
6.
6x10-4Wb
1
:.µ, 3x10-4m2 x 2000Am-l
= 10-3WbA- 1m- 1
From question, peak value ofcurrent
lo
<P = n , lQ =I+ 91 + (-2✓9(1;2)
= 101-61 = 41
:. Difference between the resultant intensity
7.
= ✓2 x lrms =~A
1t
Coefficient of mutual inductance M = I H
Induced emf in secondary coil
(a) According to Brewster's law, tan i = µ
(a)
Clearly, Polarising angle dep~nds on
wavelength and wavelength is different for
different colours oflight.
Force acting on the particle inside magnetic
field
F 8 = qvBsin0
This force F 8 provides necessary centripetal
2
force mv
r
for circular motion of the
charged particle
[·: / = /0 sinmt]
E =M.~
dt
s
⇒ Es= M m/0 cos(mt)
2cos(27t
mv 2
:. - - = qvB sin0
r
Now, for particles x and y and for 0 = 90°
= 1 x 21t x 50 x 7t
x 50 x t)
m v2
____!__..!_=qvxB
(-: m= 21t0)
Fort=0 E =2n x 50 x '
4.
n = 200V
s
m v2
(c) From de-Broglie relation,
A= E_ ⇒ A=
P
___J__J_
r2
h
=
h
.J2m.KE ✓2mqV
1
✓qVm
I
-.Je9VM
...(i)
8.
...(ii)
where, e is the charge on proton, potential
difference = 9V and Mass of proton = m
From eqs. (i) and (ii)
9.
A,: =lVMe⇒Ap=Ae /m
Ap
5.
eVm
3
VM
(c) Resultant intensity ofinterferring wave at 'P'
IP= 11 + 12 + 2.JI 1I2 cosq>
For q> =
(. ·)
... u
mx v x - rt
mx
r1
mYv y
my
r2
----⇒ -=-
1
Forelectron Ae=.JeVm
AP
= qv YB
From eqs. (i) and (ii)
⇒/\.OC--
For proton,
... (i)
r1
2
1t
2,Ip = 1+91 = 101
Again resultant intensity at ' Q'
IQ= l 1 + 1i + 2.JI 1I2 cosq>
10.
r2
(a) As per Bohr's quantisation principle, an
electron revolving in a stationary orbit which
has fixed energy, will not radiate light. Change
in velocity, due to change in direction of
electron revolving in stationary orbit.
(d) Magnetic field inside the solenoid B = µ 0nl
According to question, change in magnetic
field due to insertion of iron core
B' = µB
= µo(l +X)B
.·. B' =µ 0(1 +x)nl
(a) For potentiometer,
R1 -0_
_l1 -_2(··'1-2J
3 . /2 -3
R2
X
2
- = - ⇒ x= 4.Qm- 1
6 3
Total resistance = 6 + 4 = 10.Q
Resistance of wire 0.1 x 100 = 10.Q
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ionosphere gets reflected back by the
I
I
1
:. Reff = 10+ 10 ==> Reff= 5Q.
Current drawn from the battery
V
N.
ionosphare is given by g✓
16.
(a) The fundamental frequency of vibrating
wire is given by
5
l =-=-=IA
R 5
11.
(b)
f1 = .!_
e0A
capacitor C = -d-
Here,µ = mass of string per unit length.
T = tension in the wire
Let x be the frequency of tunning fork
according to question
(x-t) = ±6
.·. Capacitance for
.
first capacitor,
e0 A
c1 = 3d
2 5
:. f1 = 2~ ~ ~ and f2 = 2~
e0 A
second capacitor, C2 = 6d
third capacitor, C3 =
e0A
:.
d
9
Equivalent capacitance of capacitors CP C 2
and C 3arranged in parallel,
ceq =Cl + C2+C3
12.
13.
= &0 A (_!_ + .!_ + .!_i= s 0 A x .!._!_ = l ls0A
d 3 6 9
18
18d
d
(c) Accordmg to Bar ausen criterion if A is
the gain of the amplifying element in the
circuit and Bis the transfer function of the
feedback path, then condition of sustained
oscillation is l~AI = I
(a) According to Einstein's photoelectric
(x+ 6) =
17.
(b)
16
15 (x-6)
:. 15x + 90 = 16x-96
:. x = 186Hz
As per kinetic theory ofgases, the pressure
exerted by the gas on the walls of container
(p) is given by
P = Po+ P1 + P2
I
38v
2
+3gh
For a container,
I 2 Im 2 2 2 1 2
p = -pv = - - .v x-=-.-mv
3
3v
2 32
I
I
i
oc
<p
(b) As given in the question , at glass-air
interface velocity is reduced by 20% of the
velocity oflight.
So, deviation 8 wi II be = 20% ofi
20x i
15.
16
f 2 =-xf
15
15
Equating the two cases offl' we have
.
he
that~-<p = constant
100
16
1.e. p = Po +
:. If wavelength A is decreased, then
stopping potential <p will increase such
14.
15
16
Here
E = kinetic energy
<p = work function
IfE 1s constant, then
f1
f2
-=- ⇒
!¥
==> f2 =-(6+x)
he
equation, ~ = <p + E
.
fr
2'{µ
As we know, capacitance of parallel plate
2
=-KE
3v
18.
V
[-.- KE =½mv2 ]
(a) For a given oscillating mass, potential
energy is given by
PE = .!_kx 2
2
For a body oscillating at x = A, maximum
energy is given by
Emax =.!_kA2
2
5
(c) The maximum frequency of radio waves
which when sent towards the layer of
Also at mean position x = 0.
So,E = 0
1
A oc-✓
m
...(i)
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equation ofprogressive wave, y = A sin (o:t- kx)
wegetA= 12
co= 5
⇒
k=4
When another mass m 2 is placed on mass
m 1. Then, total mass becomes (m 1+ m 2) and
at this point = as x =
When they reach at x = A,
E0
A1
0.
1
... (ii)
-ym1 +m2
Dividing eq. (ii) by eq. (i),
oc
/
Here, (cot- kx) is phase difference=
n
~
19.
1
-( m1: m2
)2
x=-Cm
8
24.
(c)
Let P be the point where gravitational field
is zero so,
Gm
G9m
1
9
-
The velocity of wave travelling on string
(v) is given by
⇒ .J(r-x)2 = ~ ⇒ r - x =3x
:. v = E;;
l [·: ll
⇒
n = 2~
⇒
25.
23.
4
I
and
cm
3
Wehavegiveny= 12sin(5t-4x)cm
Comparing this equation with standard
are
changed
to
3
3
Area becomes
l
3
b
- X-
lb
3
= -
3
A
(·:A = lb)
= -
9
Now for two different cases
E' _ A' (227 + 373}4
A (21 + 213 )4
e-
E' =.!.x(2}4 xE
[·: M=0.8]
b
. 1y.
-l andb
- , respective
(b) The relation between end correction ( M)
and inner radius of the organ pipe (r) is
given by
(c)
r
x=-
When
r
[ ·: Y is same for both the strings.]
(c) The initial phase ((j>) of a pendulum during
damped oscillation remains unchanged.
2
(r- x )2
E = e cr A ( T 4 - T04 )
V8
=-
= ---
(d) According to Stefan's Boltzmann law,
. '!A=f;r
2 =✓4=2
2
:. r=U=U
2
⇒ -( 4Gm:12Gm )⇒-(16~)
A
: . V oc ✓
(A=Area)
The radius ofthe stringAis2randstringBisr.
M = 1.2 x r
0.8
M
x
-( 4~m + G9: x 4) [r- x= : ]
Young's modulus (Y) is given by,
• •
-
⇒
(r-x)2
Now, gravitational potential at this point is
v = ;J
Y= Txl
At1L
:.T x / = YAL1L
= ---
X2
Here, µ=mass per unit length
22.
{gy +---- r - - - - - -@
- - - x- - -P
So, v 2 = 2a x 4nr ⇒ a= Snr (using (i))
v = nA = 2~
21.
2
n
(a) Using third equation ofmotion,
...(i)
v2 = u 2 + 2as
We have given
Initial velocity, u = 0
S=2x2m-=4n:r
(c)
'
2
y2
20.
n
When t=0 4x= -
5t-4x = -
I
n
2
26.
(a)
9
We have given
R
-
= 0.4
CV
⇒
4
(600)
1
9 300
E'=16E
9
...(i)
Here, R = universal gas constant
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Cv = molar specific heat at constant volume
We know that,
C -C
p
C
0.4
v
==}
CV
27.
.
1
2 1
2 2
As for nng, 4 J =-mv +-mR w
cp - CV= R
_P
(·:I = mR2)
= 0.4 + 1 = 1.4
~)J
CV
i.e. Y= 1.4
The gas is diatomic in nature.
(d) We know in vertical circle velocity of a
Js'i;
For disc, .!. mR 2w2 + _!_ mR 2w2 = (~ +
2
4
2 4
30.
(b) We have given
= 3J
_!i = 2
and KE at lowest point ofthe vertical circle
f2
f 1 = apparent frequency heard by the listener
when velocity v 1 is towards the observer.
t'z = apparent frequency heard by the listener
when velocity v I is away from the observer.
Now, the apparent frequency of sound heard
by the listener when observer is moving
towards the source is given by
5mgr
1
(K1)= 2m5gr = -2-
f1
particle at lowest point, v, =
velocity ofparticle at highest point, v h = $g
So, KE at highest point ofthe vertical circle
mgr
1
Kh = 2mrg=-2-
Kh = 2 = ..!.. = o 2
So, required ratio K, 5mgr 5
·
2
(b) Energy per unit volume in string is given by
v+v,
From eqs. (i) and (ii), we get
V
fo
V-V1
f1
= V+V1
-=
V-V1 ... (ii)
V
f2
fo
V+V1
1 F 6./
-=-X- X V 2 A /
U
..
. .(i)
f 2 =(_:f___)fo
1
.
- x stress x stram
2
ie
=( V~v, )ro
Similarly when observer is moving away
from the source, apparent frequency heard
by the listener is given by
mgr
28.
2
2
=..!..xYx(strain)2
2
2
Us= Ys x[ Stress(S) )
SL YL Strain(L)
V
⇒
=A =(~)2
I
r} =f.=9
·1
2
AL
V1
rJ
•
1
(a) For a rolling disc or ring kinetic energy is
5
29.
⇒ V=3V1 ⇒ -=3
1
2
1
2
given by KE=-mv +-lw
2
2
The ring and disc will have same
1
translational kinetic energy, i.e. mv2
2
Rotational kinetic energy of the disc
31.
(c)
SurfaceareaoftheliquiddropA = 4nR2
Let Ebe the surface energy ofliquid drop.
When the drop splits into 512 droplets, the
surface area becomes
Az = 512 x 4nr2 [r =radius ofsmaller drop]
Comparing the volumes of bigger and all
smaller droplets, we get
.
I
4
4
3
3
e -3 nR = 5J2 x -m
..
3
⇒
R
r =-
=.!.mR2w2
4
Rotational kinetic energy ofring
Total area of smaller droplets is
=.!_ mR2 {1)2
Change in surface area Az-A 1
2
A 1 =512 x 4 x n x(~
8
J
= 8A
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(c) Total displacement of hour hand ofa clock
=4n - - -
0 = 2n = 360° (': n=l80°)
Time required for this displacement,
t = l2 x 3600s
(
64
2
2
2
= 4n(8R -R )= 7R
Surface energy, E = AT [A= area, T = tension]
En _ A xT _ 8A _
- - -1 -- - -8
So,
32.
(b)
0
So, angular speed, m= t
Eo A xT A
:.
E = 8E
Moment of inertia ofa thin rod whose axis
is passing through its middle point and
perpendicular to its length is given by
(a) The value of acceleration due to gravity g
at a height h is given by
g' = g ( ~ )2
RC+ h
Here, Re = radius of earth
g = acceleration due to gravity at earth
surface.
ML
l= ... (i)
12
In terms of radius of gyration, it can be
written as
g '= f4 andR e = R
I= MK;
... (ii)
Comparing equation (i) and (ii), we get
2
MK2 = ML
I
12
__!:_
I
So, ¼ = g( R~h
I
2
... (iii)
2✓
3
Moment of inertia of rod whose axis is
passing through one of its end is given by
⇒
36.
ML2 = MK2
3
2
K 2 =~
-J3
... (Vl.)
Again taking the ratio ofK 1 and
Eqs. (iii) and (vi),
We get
33.
Ki from
K 1 L x -J3 _
3 xL
K 2 2✓
37.
(d)
2R = R + h
⇒
R=h
Work done in increasing the voltage from
V 1 to V 2 is given by
= .!.c(v2
-v2)
2
I
2
putting the values, we get
1
= - xC x(l0 2 - 52)
2
I
75C
W = -2 x C x 75= -2... (i)
Again work done when the plate voltage is
increased from IO V to 15 V is given by
-2
W1 =
(c) Potential energy of pendulum, when bob is
at rest, is given by
(PE) = mgl
When bob is displaced by small angular
displacement 8 , the pendulum will lose PE
of bob which gets converted into kinetic
energy (KE). So, from conservation of
energy
Loss in PE = gain in KE
:. KE = mgl-mgl cos 8 = mg/ (1-cos 8)
R
R+h
(+) ~
(-)
An
- o-de- (p
----1
) Vl~( n-)- -C
- a-thode
I =-
I = MK;
... (v)
Comparing equation (iv) and (v), we get
J
(b) The symbol oflight emitting diode (LED) is
ML2
... (iv)
3
In terms of radius of gyration, it can be
written as
1
120
degree/s
35.
2
K =
360
x
12 3600
⇒
1 x C x (l5 2 -102 )
2
125C
I
WI = -2 XC x125= -2-
11
... c··)
Using eqs. (i) and (ii), we get
W
WI
⇒
75C x 2 ⇒ W1 =125 _~
2 x125C
W 75 - 3
Wl= l.67W
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38. (c) We have given,
Initialflux(<!>i)=4 x 10-4 Wb
2016-17
[geff= acceleration due to gravity in water]
Effective value of acceleration due to
gravity when bob is immersed in water, is
given by
Finalflux(<i>z) = 4x10-4 x10
100
=4 x 10-5 Wb
Emf induced (e) is given by
As we know, geff= g (
cr:p)
l
[Here, cr = densityofbob, p = densityofwater]
3
⇒ 0.?2 x l0_3 4 x l0-4 -4 x l0-
5
t
39.
(a)
2-x l0
8
4xl0-5 x9 1
. s
⇒ t =---05
nx10-5 2
Resolving power of a telescope is given by
8
40.
(d)
1
RPoc-
So , T.I
"-
On decreasing the wavelength of light,
resolving power of a telescope increases.
According to Einstein's photoelectric
equation
42.
"
For wavelength 3'A, stopping potential is
2hc
A
41.
f = Yo
0
21
... (ii)
he
-=eY + <1>
3Y
f0 = 0
2 21
V
frequency is f= ; .Third overtone of
4
closed organ pipe at one end is
A
Thus, we get A0 = 5A
(a) Time period of simple pendulum in water
(T) is given by
v~
3
For a closed organ pipe, fundamental
"-o
T=2n er=
pg(R-r)
is given by
6
hc = 5<1> and <l>=hc
"-
2T
For 2nd overtone,
"Subtracting (i) and (ii)
-=eY + 6<1> ⇒
[-:T=2nH]
(d) Fundamental frequency of organ pipe (f0)
Now equation becomes
he -<I>= eY
3A
6
2hc
⇒ --<j>=ev
T.I =3T
(c) Rise ofwater in the capillary tube (h) is given
:. h
43.
y
⇒
h= 2Tcos0
pg(R-r)
In the given case,
cose = 1 as 8 = 0°
For wavelength 'A, stopping potential is Y
Now, equation becomes
... (i)
=2n
by
he
T-<j> = eY
he
--<j> = ev
3
=98[¾i}s[Hf~
RP=-dl.22A
As
3
-_10
= 9.8r-=---~xl_0
f
3
='!_ Yo
4 I
3
We have given, ?Yo - Yo =150
41
21
⇒
⇒
('!__§_JYo =150
4 4 I
Yo =150
41
⇒
y 0 =300Hz
21
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The capacitance of first capacitor becomes
kC, so by charge conservation,
(kC)V 1 =CV2
••• (ii)
2
44.
MR
2
When the disc is melted into solid sphere,
then volume remains same.
: . Volume of disc= Volume of solid sphere
(a) M.0.1. of disc I= -
2
R 4 3
n:R x- = -n:r
6
⇒
R
3
r =-
8
⇒
2
R
r=-
2
2
M.O.I. of solid sphere
2
48.
(a) For parallel resonance L-C circuit, the
2
5mr •
R
2
mR 2 I
=-X mX-=--=5
4
10
5
MR2
[I = moment of inertia of disc = -
45.
2
49.
- ]
(c)
capacitive reaction is equal to inductive
reactance.
The total impedance of the circuit increases
to infinity means the circuit draws no current
from the AC power source.
Total current through the galvanometer is
given by
(b) The sag of bending of beam of length l
I=~
R0 rr
loaded at free end by weight W is given by
WL3
12
So 8
WI3 xl2= WI3
48Ybd 3
4Ybd 3
'
According to Bohr's theory, the wavelength
⇒ °'=1'=2
n~ n;
02 12
3
As the energy difference ~E = E5 - E4 is
very small, so minimum wavelength will take
place for transition ofelectron from n = 5 to
⇒ 12 =!.i_= ioV
Now, I = - - -
Rerr + R s
⇒
C
R s --
rV - R
2
eff
=---2000
sxw--4
=4xl03 -2000=2000Q
So, the resistance of 1970 Q is to be
replaced by 1970 + 2000 = 3970 Q.
.__----1v1-----'
When dielectric is inserted in one of the
capacitor,
K
C
=5x10--4 A
2
2
p=4.
(b) When dieletric is not inserted:C
2000
0 = nl AB (i.e.0ocl)
K
ofradt:;n[er~t~d]is given by
47.
1970+30
(i.e. 20 div).
To get the deflection of 10 divisions, value
of resistance needed to connect can be
obtained as
. of steelbar = bd3
1 = Moment of"mertia
A
2
= 10- A
As this current provides full scale deflection
48Yl
(a)
2
3
o=--
46.
1
K
⇒ V =( l~~ J
3
3
v,
V2
-=- ⇒
50.
"'2n:°
(b) Asilx=[Where, ~x = path difference]
For 4th dark fringe,
o=(2n + l)n:
⇒
.__----1V >-----"
GivenV 1 +V2 =V
o=(2x4 + 1)n:=9n:
&= 1.. 9n =2_1.=2.x6xl0-7
2
2n:
2
= 2.7 x lo--6m = 2.7 x lo--4cm
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CHEMISTRY
51.
(c)
The number of optical isomers depends
upon the number of asymmetric centres (n).
Possible number of optical isomers of the
compound is 2°.
66.
67.
68.
(a) Bulletproofhelmets are made up oflexan.
(c) The Mond's process is used for the
purification ofNi.
(b) Isopropyl methyl ether when treated with
cold hydrogen iodide gives isopropyl
alcohol and methyl iodide.
n
52.
(a) van 't Hoff equation is 7t = V RT
CH3' - .
CH - 0 - CH 3 +HI - - +
53.
(a) Octahedral sulphur (rhombic or a-sulphur)
is the most stable allotrope of sulphur.
(c) Thermoplastic polymers are the linear or
slightly branched polymers in which the
intermolecular forces of attraction are
intermediate between elastomers and fibres.
(a) We require nF to deposit I mo! or 40 g ofCa.
n = 2 (no. of e- involved)
·: 10 g Ca is deposited by 0.5 F.
(b) Leaching of gold is done with the help of
their dissolution in NaCN or KCN or Cu.
(d) Paracetamol is an analgesic.
(d) When a mixture ofn-butyl bromide and ethyl
bromide is treated with sodium metal in the
presence of dry ether, then ethane cannot
be formed because reaction follows
Wurtz- Fittig reaction. It is a type of
coupling reaction.
CH3
54.
55.
56.
57.
58.
/
69.
CH3' - .
CH-OH+CH3I
CH3/
(c) The volume occupied by the face centred
. umt
. ceII
cub1c
16
= Zeff x -4 m 3
3
=-m
3
70.
Dry
ether
(c)
Glucose on oxidation with bromine water
yields gluconic acid. This reaction confirms
the presence of aldehyde group in glucose.
CHO
COOH
I
(CHOH)4 + [O]
Octane
59.
60.
61.
62.
63.
64.
65.
Hexa ne
I
Butane
(d) When lanthanoids (Ln) are heated with
sulphur, then Ln2S3 are formed.
(a) Butylated hydroxy anisole is an antioxidant.
The conjugated aromatic ring ofBHA is able
to stabilise free radicals.
(a) In the cell represented by
Pb(s) IPb2+ (IM) II Ag+ (IM) IAg(s), the
reducing agent is Pb because it readily gets
oxidised to Pb2+
(a)
(d) Secondary amines when treated with
nitrous acid give yellow oily substance. So,
amine ' A' is methyiphenyI amine.
(d) The acidic oxides are formed by the
non-metals (group 14-17) whereas basic oxides
are formed by the metals of group I and
group 2 elements. Ba belongs to group 2.
(b) The correct priority order for the groups
attached to chiral carbon atom is
CONHz > coc~ > CHO > CHiOH
3
71.
72.
73.
Br2+H20
I
(CHOH)4
I
CH2OH
CH2OH
Glucose
Gluconic acid
(a) By the action of concentrated sulphuric
acid, sodium chromate gets converted into
sodium dichromate in the manufacture of
potassium dichromate.
(a) In a dry cell, zinc acts as a negative electrode.
(d) Primary amines on treatment with nitrous
acid liberates nitrogen . Ethylamine
(C2H5NH2) is a primary amine. Hence,
liberates nitrogen on treatment with nitrous
acid.
NaN02 +HCI
+
-
H20
C 2H 5 -N = NCI--=---➔ C 2H 5 OH+N2t +HCI
Diazonium
chloride
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74. (d)
TargetMHT-CET
Given, W(massof solute)=5.0g
m (molar mass of solute) =40 g mo1-1
Volume= lOOmL
Molarity is given as,
OH
Moles of solute
M= Volumeofsolution(inL)
M = mxVolumeofsolution(inmL)
_ 5.0gxl000 _
_
M0xlO0 -1.25moldm 3
4
(d) Acetyl chloride when treated with dibenzyl
cadmium yeilds benzyl methyl ketone.
II
Acetyl Chloride
~"
II
82.
77.
(d)
83.
NO2Cl(g) ~ NOi(g) + Cl(g)
78.
NO2Cl(g) + Cl(g) ~ NO/g) + Cli(g)
(c) Arginine amino acid is basic in nature.
(Basic due to the presence of 'NH' groups)
NH
84.
0
H2NANH~OH
85.
(Arginine) Basic amino acid NH2
79.
80.
meta nitro
phenol
(d) Forscandium(Z= 21)electronic
configuration is 4s23d1• After the removal
of 3 electrons; (Sc3+), acquires a stable
configuration (4s0d 0 ).
Hence, it forms colourless compounds.
(d) The highest oxidation state exhibited by
group 17 elements is + 7.
(a) For an isochoric process, t-,,.V = 0
In this process, Ace to the first law of
thermodynamics
q = t-,,.U-W
q = !-,,.U-pt-,,.V
As t-,,.V= 0
qv= t-,,.U
(d) Cobalt naphthenate is the catalyst used in
the commercial method of preparation of
phenol.
(d) The relationship between solubility of a gas
in liquid at constant temperature and
external pressure is given by Henry's law.
x oc Partial pressure of the gas, p
p = KHx
Here, KH = Henry's law constant
More the value ofKH, lower is the solubility
of gas.
(d) The order for acidity in phenols depends
upon the position of electron withdrawing
groups. - NHi is an electron releasing
(+I-effect)
(+R-effect)
p-amino
phenol
:o =C= o:
.H ~ (µ = o)
Benzylmethyl ketone
ionic character.
Cl(g) is the reaction intermediate involved
in the formation ofNOi(g) and Cli(g).
(Only -/-effect)
the bonds are linear and dipole moment
point in opposite directions, cancel out the
dipole moments, leaving a net polarity of
zero.
C-CH2 - C6 H 5 +CdC12
Here, Ph = Phenyl group
NH2
(d) Carbon dioxide is a non-polar solid because
Dibenzyl Cadmium
(d) Magnesium fluoride (MgF2) has the highest
phenol
o-
0
(-/-effect)
(-R-effect)
para nitro
phenol
+ (C 6H 5CH2 )iCd ~
76.
I
o-
N+
0
2CH3 -
OH
OH
¢Q 6¢
81.
0
2CH 3 -C-Cl
OH
N~ o
Wxl000
75.
group. Hence, it decreases the acidity of
phenol.
p-nitrophenol > m-nitrophenol > phenol >
p-aminophenol.
0-2+
Co
y001
fr-
v,
:::::-....
~
✓
,:;
0
(Cobalt naphthenate)
86.
(a)
0.693
t112= - k
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87. (c) One molecule of glycerol and three
molecules of fatty acids combine to from a
triglyceride.
H 2C-OH
RCOOH
I
HC-OH
I
+
Catalyst
R'COOH
2016-21
94.
95.
(a)
(b)
96.
97.
(b)
(b)
Calcium chloride (1 Ca, 2Cl; ionises)
Ferric chloride (lFe, 3Cl; ionises)
Chromyl chloride is used in Etard reaction.
Argon is the most abundant noble gas in
the atmosphere.
Heat capacity is an extensive property.
Citric acid is a tricarboxylic acid.
I
I
R"COOH
Fatty acid
H 2C-OH
Glycerol
COOH 1
2
II
0
I
H 2C -
II
0 -
C-
O-
i
R ' + 38i0
98.
(b) For reaction, 2SOi(g) + Oi(g)~ 2S0lg)
1 ~[S0 2 ]
2
~t
C -R
Triglyceride
88.
(b)
90.
(c)
91.
(a)
92.
93.
(a)
(d)
= -~[0 2 ] = +.!. ~[S03]
~t
2
~t
So, average rate ofreaction is written as
(b) The molecular formula of Wilkinson's
89.
2
OH
Citric acid
H C-0- C -R
HC -
3
HOOC - CH - C-CH -COOH
0
21
I
I
2
catalyst is (Ph3P)3 RhCl
The criterion for a spontaneous process is
~G< O.
Brown ring test is used for the detection of
nitrate radical.
The reagent used in the Wolff-Kishner
reduction is NH2NH2 and KOH in
ethylene glycol.
[Pt~)2 Cl2] is a neutral complex. This
complex does not have any charge. Thus,
is neutral.
As all the compounds have same
concentration, i.e. 0.1 M. Thus, the
compound that will break into the most parts
has highest boiling point.
Glucose (1 part, covalent; does not ionise)
Sodium chloride (1 Na, 1 Cl; ionises)
- ~[02]
~t
99.
.
(d) 0.5CHig) + 0/g) ➔ 0.5CO/g) + 8i0(1)
100. (a)
~n = 0.5-1.5 = -1
Work done
=-~T=-(-1) x 8.314 x 300=2494J
Primary nitroalkanes are obtained in good
yield by oxidising aldoximes with the help
oftrifluoroperoxy acetic acid.
oRCH = NOH---'[~O]'----'RCH =
Aldoxime
CF3COOOH
L_+-OH
~RCH 2 N0 2
(I nitroalkane)
0
SECTION-B
p(X < 1) = p(X = 0) = nc , p' qn-r
MATHEMATICS
1.
_IOC0 (l)O
(l)IO-O
_ (l)IO -(1)10
- - lxlx -
-
(b) Here, mean E(X) = 5
and variance, Var (X) = 2.5
⇒
np = 5 and npq =2.5
⇒
5q = 2.5 ⇒
Also, p
2
+ q = 1 ⇒ P = 11
2
2.
I
q= -
nx-=5 ⇒ n=10
1
1
2 =2 ·:
np = 5
2
2
(d) Letu - tan-{
bl
v = sin- 1 (3x - 4x3 )
Now, putx = sin 0 ⇒ 0
u = tan_,(
2
2
and
= sin-1(x), then
sin 0
2
.,/1 - sin 0
l
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1
3
and v = sin- 13 sin 8 - 4 sin 8)
sin 8)
⇒ u = tan-1 - - and v = sin- 1 ( sin 3 8)
cos 8
⇒
5.
u=8and v = 38
u = sin- 1x and v = 3sin-1x.
On differentiating both sides w.r.t. x, we get
5
⇒
dx
✓l- x2
and dv
dx
du
l
l
du=dx
dv dv
dx
3.
=3 x
d
dx (sinx - oosx) + (sinx - cosx) dx (e')
= e-' (cos x + sin x) + (sin x -cos x)e-' = 2e-' sin x
We know that, if Rolle's theorem is verified, then
u = tan- 1 (tan 8) and v = sin- 1 (sin 3 8)
=
d
⇒f'(x) =e'
⇒
du
(b) Given,f(x ) =e-' (sin x - cosx)
their exist c E ( ~ , :), such thatf' ( c) = 0
1
2ec sin c = 0 ⇒ sin c = 0
5
C =
E ( ~ , :)
⇒
✓l-x2
6.
~=
3
3
.Ji- x2
(b) Let centre of circle on X-axis be (K, 0).
the radius of circle will be K.
~
(c) In a trisection of
lines in quadrant, angle
90° is divided into three
parts and each part
contain 30°, as shown
in figure
Equation ofline OB is
y
C
B
1
y = tan 30° x ⇒ y= ✓
3x
3y = O
x- ✓
And equation of line OC is
3x-y) = O
y= tan60°x ⇒y = ~ ( ✓
Their combined equation is
(x - ✓
3y)( ✓
3x-y)=O
y'
:. the equation of circle having centre (K, 0)
and radius K is
(x - K)_2 + (y -0)2 = K2
⇒ x 2 + K2 - 2hx + y2 = K2
...(i)
⇒ x 2 - 2Kx + y2 = 0
On differentiating both sides w.r. t x, we get
7.
dy
2x -2K+2y - = 0
⇒
✓3x 2 -xy-3xy+ ✓3i=o
⇒
✓3x2 -4xy+ ✓3i=o
(b)
Here, 2 tan- 1 (cos x) = tan- 1 (2cosec x)
⇒
tan- I - 2cosx
--,,-- = tan
l - cos2 x
dx
⇒
2cosx
dy
K= x+ y dx
!- cos 2 x
cosx
From equations (i) & (ii) we get
⇒
x2 -2( x+ y !)x+ y2
⇒
=0
~
~i
(b) Given,A = [~
1 2 1
Since, the sum of the product of element other
than the corresponding cofactor is zero.
a1 1A21 + a12 A22 + a1023 = O
cosx
1
sin x
sin 2 x
sin x
=l
cot x = I
⇒
x
7t
=-
4
Hence, sin x + cos x = sin
dy
⇒ (x2-y2)+2xy dx =O
4.
2
sinx
⇒
dy
z •.2
-x + y - 2xy dx = O
-2-)
sinx
--~-=-- ⇒ --=--
⇒
...(ii)
-1(
I
7t
4
+ cos
7t
4
I
= ✓
2+ ✓
2= ✓
2
8.
(a) Equation ofgiven line is
x +2 = 2y -5 z +l=0
3
2
5
x+2 y - or
- - =--2 z+ l =0
2
3 '
2
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2 ,0 >
2
22 +(i) +0= ✓4+2._= (25 =2.
2
4 \J4 2
So, DR of given line are < 2,
As
,
:. DCofgivenlineare <
f
9.
(d)
=
10.
dx
2
,
3/2
512 512
=f
✓8+2x - x2
,0 >or <
4 3
5,5,0 >
dx
dx
. -1 (x-l)
f ✓32-(x-1)2
=sm
- 3- +c
(a) Since, j(x) =x3 + 5x 2- 7x + 9
After differentiating on both sides w.r.t.x, we get
f'(x) =3x2 + lOx- 7
As,f(x +tu)= j(x) + tuj'(x)
= x 3 + 5x2 - 7x + 9 + tu x (3x2 + lOx - 7)
After putting x = 1 and tu = 0.1, we get
f(l + 0.1)
= 13 + 5 (1)2-7(1)+9 + 0.l x (3 x 12 + lO x 1-7)
So,f(l.1)= 1 + 5- 7 + 9 + 0.1 (3+ 10-7)
= 8 + 0.1(6) =8.6
I
So, P ( 0 :S x :S 4 )
4
- ~
otherw1se
12.
(b) (a - b)2 cos
2
~
C
2
+(a+ b) sin 2
2
= (a2 + b2- 2ab) cos2
= a 2 ( cos2
C
2
C
+ (a2 + b2+ 2ab) sin2 2
C+sm. 2 C) + b2 (cos2 C+ sm. 2C)
2
2
2
- 2ab( cos
2
~-
2
2
sin ~)
= a2 + b2-2abcoo C
= a2 + b2- 2ab [
0
(b) The equation of the bisectors of the angle
between the lines (x =5) and (y= 3) is
(x-5) _+ y-3
x-5 y -3
✓12 - - ✓12 ⇒ -l- =±-1⇒ x-5 =
⇒ (x - y -
+(y-3) andx -5 = - (y -3)
2)= 0 and (x+y -8) =0
Hence, combined equation of bisectors of angle
between given lines is (x - y - 2) ( x + y - 8) = 0
2x - 2y -16 = 0
(a) Since, 6y = x + 2
...(i)
and~y = 8tu
After differentiating on both sides of eq. (i) w.r.t.x,
we get
6dy = 3x2 ⇒ dy = _!._x2
dx
dx 2
dy
1 2
As ~11 = - L1x ⇒ 8tu= - x tu
'
'J
dx
2
So, x 2 = 16 ⇒ x = ± 4
When x = 4, then 6y = (4)3 +2
So, 6y= 66 ⇒ y = 11
Hence, required point is (4, 11).
16. (a) Given, f(x) =
x sin .!..,for x * 0
(
x
k,
for x=0
As,/(x) is continuous atx = 0
So,LHL= RHL = f{O)
.
.......... (1)
Jim f(x) = limf(0-h)
N ow, LHL = x➔0-
2
2
[·: cos ~ -sin ~ = cosc]
2
14.
15.
4
t
du
1t
n ) =cot-=l
'dve=4
4
⇒ x 2 +xy - 8x - xy - y2+ 8y ⇒ x2 -y2 -1 0x +~+ 16 =O
= f J(x)dx= ( ..!._dx= ..!..[x]4
Jo
Jo 5
5 °
= ..!..(4-0) = 0 .8
5
sece(tane+sece)
= (sec0+tane)xsecetan e = co
Hence - (
0<x<4
(b) Since, j(x) = 5 '
0,
2016-23
(b) Let u = log (sec 0 + tan 0) and v = sec 0
After differentiating on both sides w.r.t. 0, we get
1
du
2
= - - --(sec0tan0+sec 0)
de (sec0 + tane)
dv
- = secetan0
de
du
du=!!_!
d
dv
v de
.J8+1 - (x 2 -2x+ l)
_!_
11.
13.
3
2
a +b -c
2
)
2ab
[·.- cos C = a2 +2:2b_ c2
=c
l
2
1
= lim(O-h)sin-() = lim(-h)sin(-.!..)
h--tO
h--tO
O- h
h
= limhsin_!. =0xfinite wlue lies between -land!
h➔O
h
=0
lim sin_!.= finite value lies between -1 and 1]
[ ·: h-+0
h
andf(O)=k
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Now, from eq. (i), LHL =f(0)
1
1
tan- ( .J3)-(1t-sec- (2))
⇒ 0=k
Hence, k=0
17.
2)+1t-cos-cosec-1 ( ✓
. -1
.
msm x
(c) Given, y
... (i)
e
After differentiating on both sides w.r.t. x, we get
=
dy
-=
dx
⇒
⇒
~
dy
vi-x~ dx
1
x[ mx
1
r-::;
'\Jl-x2
-
l
20.
1t
--+n--
(c)
4
3
Since,
I
After squaring on both sides, we get
2
(1-x
As,
)(:
J
=m
2
y2
(b) Consider, I
=
s[
k,
25
exx2e -5
ldx
= lim
h➔O
f
ex
e-x
=4 f --dx-25 - - d x
2ex -5
2-5e-x
Let 2e-5 = u and2-5e-x= v
⇒ 2exdx = du and se-x dx = dv
2
So, I
-x
log(l + 2(0-h)sin ____2t_(O- h))
1800
(O-h)2
log(l-2h) {-sin
_El_}
180
h➔O
h2
. nh
( - ) Slil -
dv
log(l-2h)
1t
. (- ) . m-180
~x- - x 11
= 11m
2
h➔O
h➔O
-2h
1th
180
180
=4f du -
2sf du
2u
5v
= 2 log u - 5 log v + c
= 2 log (2e-5)- Slog (2-se-~ + c
7t
-5)
tan-I (.J3)-sec-1(-2)
7t
=(-2) X (-1) X 1Xl80 = 90
x = 1]
1 + x = 1and 1·rm sin. 1og-11m
[ ·: x➔O
x➔O
X
X
2ex
=2 log (2ex - 5) - 5 log ----;;+c
= -3log(2e-5) + 5x + c
Therefore, I= 5x-3log(2e - 5) + c
As, I=Ax + Blog(2e-5) + c
Hence, A= 5 andB= -3
=0
h➔O
= lim
e dx=5
[
=0
for X 'F- 0
forx
x➔O-
2ex -5
du
0
As,f(x) is continuous atx = 0
So, LHL =f(0)
·: LHL = lim f(x) = lim f(0-h)
f
⇒ edx = - and
forx
k,
25
= f - 4ex
-dx- -dx
2ex -5
'
X
(1-x'(!)' =Al
4
for x *
0
2
5
12
log(l+2x)sin~
180
Hence,A =m
18.
12
log(l + 2x)sinx
[From eq. (i)]
-~=-~
1t - 121t-31t-41t - 5n
p(x) =
=my
½j
_i±i) _ ;
· -1 d
emsm
x_(msin-1 x)
dx
dy-_e m
sindx
1(
21.
(a)
Since, log 10 [
x:-y:) =
X
2
+y
y2l
= 102
x2 _
[ X2 +y 2
⇒ x2 -y2 = 100(x2 + y 2)
After differentiating on both sides, we get
⇒
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MHT-CET2016
The equation of given line is
J
r = (i + 2] + k) + A(i + + k) and equation of
plane is
2x-2y: =100( 2x+2y:)
dy
dy
x - y - =lO0x + l00ydx
dx
dy
dy -99x
⇒ JOiy dx =-99x ⇒ dx = JOiy
⇒
22.
(cl) Let, I =
f¥
-n
r-(21 - ]+ k) = s
As, b= i +] + k: and
So,
2
log( - s'.n x )dx
2 + smx
.
Slil
e=
fi = 2i - ] + k
(2i-]+kHi+]+k)
A
I2i
2
A
A
A
A
A
- j + k Ii + j + k I
2 - 1 +l
= .J22 +(-1)2 +(1)2.J12 + 12 +12
/(x)= log(~::::) :. /(- x)= log(~:::=:~)
= log( 2 + s~x) = -log(2 - s'.nx) =
2-smx
2+smx
So,f(x) is an odd function.
- f(x)
7t
2
[·: If/(x) is an odd function, then
(c) Consider, I=
Letx+tan- 1x=t
f
l+x
24.
⇒ x2-2x = - y
⇒ x2 -2x+ 1 = - y+ 1
⇒ (x- 1)2= - (y-l)
Which is the equation of parabola whose vertex
is(l, l)anditisopendownward.
y
2
+ x: dx = dt
l+ x
log a
-I
x
+c
loga
(b) The given differential equation is
H:)1 =7( ~:l
After cubing on both sides, we get
r
Ht)']'=?'(~:
25.
(b) The equation of given curve is y = 2x - x 2
=f a1dt =-a'- + c
ax+tan
=
✓
2
2
e =sm. -1[ ✓2)
3
(x2 + 2)a(x+tan-l x)
dx
2
X +1
⇒ ( l + _ l-2 )dx = dt ⇒
So, I
f af (x)dx = 0 ]
_
✓4+1+1 ✓1+1+1 - ✓6 ✓3 = 3
Hence,
26.
f
Hence, !~J(x)dx = O
23.
2
=
As, highest order derivative is 2, and its degree is 3.
Hence, degree= 3 and order= 2
(b) The angle between the line
r =a+ Ab and the plane r •n = d is given by
.
n-b
sm = - 0
1
nb
I
Y'
y=2x - x2
For intersection of the parabola with theX-axis,
put y = 0, then we get
0 = 2x - x 2
⇒ x(2-x) = 0
⇒ x = 0,2
Hence, area of bounded region between the curve
andX-axis
=g ydx
=
f~
2 2
(2x - x2)dx= [ ;
2
x3 ]
-3
o
=[4-¾-0-0] = 1sq units .
I
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After adding eq. (i) and (ii), we get
2016-26
27.
f lo:c~i x) dx = log[logsinx] + c
(a) Since,
2J =
After differentiating on both sides, we get
1.
f(x)
d (logsinx)+0
log(sinx) logsmx dx
1
1-xcosx
xf(x) =
⇒ log(sinx)
logsinx
sinx
k
k
k
A=--,B=--and C=a
b
c
k
k
k
--x--y+-z =0 [FromEq.(i)]
a
b
c
31.
32.
29.
(c)
Given,
a
b
a=i + ]-2k,b = 2f-J + k, c =3i-k
f
"
,..
,,..
,,..
' '
Letlogx=t
So
fo
Let I= 2
⇒ex
~
~ s e ~ dx
n secx + n cosecx
f
f
f.!.ay
!dt + _!_ dx =
X
y
' t
⇒ log t + log x = logy+ log c
⇒ log tx = log ye ⇒ tx = ye ⇒ x log x = y e
Whenx = e theny = e2
Therefore, e log e = e2c
⇒m + n= l + l =2
(c)
1
⇒ -dx=dt
X
'
After equating the coefficient of i, j and k, on
both sides respectively, we get
3 =m+2n, 0=m-nand-1 =-2m + n
⇒ 3 = n + 2n ⇒ n = 1
⇒ m= I andn = 1
30.
7t
21= - Hence I= 2
'
4
(c) Since, cumulative distribution function
F(x) = P(X~x)
So, F(0) = P(X~0)
= P(X= 0)+ P(X= -1) +P(X= -2)
= 0.15+0.3+ 0.2 = 0.65
(a)P(X< 0) =P(X=-1) + P(X=-2)
=0.3 +0.2=0.5
Therefore, P(X< 0) =t- F (0)
(b) P(X> 0) = P(X= 1) + P(X= 2)
= 0.25+0.l = 0.35
Thus, P(X> 0) =t- F (0)
(c) 1-P(x > 0) = 1-0.35 = 0.65
Hence, 1 - P(X > 0) = F(0)
(a) The given differential equation is
f(-1-+_!__Jdx = _!__dy
xlogx x
y
3i -k = (m + 2n)i +(m-n)j+ (-2m + n)k
7t
1 = e 2c ⇒ c
... (i)
Hence, xlogx=X.
33.
~2
e
⇒ y=exlogx
(c) Suppose that the position vectors of A, B ,
C, D, Mand N are a, b, c, d, m and n respectively.
As, Mand N are the mid-points ofAC and BD.
a+c
!!.fcosecx
~dx
fo ~
n cosec x + n sec x
1
=-
e
=
0
(l+logx)dx dy ⇒ (-1-+_!_Jdx =_!__dy
xlogx
y
xlogx x
y
After integrating on both sides, we get
As, 3i-k=m(i+]-2k)+n(2i-] + k)
,...
2
⇒
c
and c=ma+nb
⇒
dx=[x]
y(l + logx{: ]-xlogx = 0
⇒ - ~- L + _:__ = 0 or ~+X. _ _:__ = 0
c
7t
7t
⇒
⇒
b
X
⇒ 2I=f2
0
(a) It is given that, the foot of perpendicular from
point Q(a, b, c) to they.cplaneisA(0, b, c) and the foot
of perpendicular from point Q to the zx plane is
B(a,0,c).
Let the equation of plane passing through the
point (0, 0, 0) be Ax + By + Cz = 0
......(i)
As it is passing through the point A(0, b, c) and
B(a, 0, c).
So, 0 + Bb + Cc=0 andAa + 0 + Cc = 0
⇒ Cc = Bb and Cc= -Aa
Therefore, -Aa = -Bb = Cc= k
a
2
7t
⇒f(x) = cotx
28.
~ !!.fsecx+!!.fcosec
xd
=~~==
fo ~
!!.fsecx +~cosecx
b+d
So m=--andn=-'
2
2
Then, AB + AD + CB + CD
= (b-a) + (d-a) + (b-c) + (d-c)
...(ii)
=2(b + d)-2(a + c)
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=2 x 2n-2 x 2m=4(n-m)=4MN
37.
⇒ 4J+l-7-2-J=10
The given equation is sin 2x + cos 2x = 0
⇒ sin 2x = - cos 2x ⇒ tan 2x = - l
(c)
[·: n< x<2n ⇒ 2n<2x< 4n]
⇒ 3J = 18 ⇒ A = 6
34.
⇒
(d) Since, IF of : +Py= Q is given by
So, sin x = ef pdx
After differentiating on both sides, we get
35.
pdx
38.
cos x = sin x P ⇒ P = cot x
(c) (a) x -x = O ⇒ x(x-l) = 0
2
⇒ x=O and x=l,
This represent a pair oflines.
(b)
.xy-x=O ⇒ x(y-l)=O
⇒ x=O,
y=l,
This represent a pair oflines.
(c) y2-x+ 1 = O
⇒ y 2 =(x-I),
This represent a parabola.
Which does not represent a pair oflines.
+ 1) = O ⇒ (y + l)(x+ l)= 0
y=-1 andx=-1
This represent a pair oflines.
(a) In every true and false question, probability
of guessing correctly, p
guessing wrongly, q =
=
1
2
⇒
⇒
⇒
39.
Here, n = IO
The probability ofatleast 7 correctly guessing
=P(X?:.7)
=P(X= 7) + P(X= 8) + P(X=9) + P(X= 10)
10
C 7 (½r(½Y + cs(½r(½r
10
+
10
C9 (
r(
½
½y +
40.
10
c10 ( ½yo
[·: P(x = r) = ncr pr qn-r]
2
4
-2
6k+ l=-2k+ l = -(8k- l)
6k+l=-2k+ l ⇒ 8k=O
k=O
x = 6 x O, y= -4 x Oandz = 8 x 0-4
⇒ x=O, y=Oandz=-4
This is equal to the B coordinate.
and probability of
1
2.
2 x= Iln 15n ⇒ x= Iln l5n
8 ' 4
8 ' 8
(a) Coordinates of points A and B are given as
(6, -4, 4) and (0, 0, -4) and coordinates ofpoints
CandD are given as (-1,-2, -3) and(l, 2,-5).
Now, equation ofline which passes through (0,
0,-4) and (6, -4, 4) is
x -0 y-0 z+ 4
- - = ~ = + = k [Let]
6
4 4
... (i)
⇒ x = 6k, y = --4k and z = 8k--4
The equation of line which passes through
(-1 , -2, -3) and (1, 2,-5) is
x+l_y+2_ z+3
--- -- - -] + 1 2+ 2 -5 +3
x+l _ y +2 _ 3+3
⇒
- 2- - - 4- - -2
... (ii)
--- --- = ---
⇒ x(y+ 1) + (y
⇒
=
4
As, two lines intersect, so point (6k, --4k, 8k--4)
satisfy eq. (ii), we get
6k + 1 --4k + 2 8k - 4 + 3
(d) .xy+x+ y+l=O
36.
+~)
⇒
IF= ef pdx
cos x = )
3
3
2x=2n+ n 2n+( n
4'
2
41.
1
(a)ItisgiventhatA=[~ ~JB=[~ ~ ]
3
As, (JJ- 1A- 't' = (A- 1t ' (JJ-'t' = AB
[ ·: (ABtl = JJ-l A-l]
[ ·: (A-'t' = A-1]
=[ ~ 3 ~][~ ~1]=[~:~ ~\+0o]=[~ ~2 ]
(a) Given, statementp is true (1) and statement q
is false (F).
So, p ➔ q = T ➔ F = F and p ~ q = T ~ F = F
(b) Since, orthocentre, centroid and circumcentre
ofa triangle are collinear whereas centroid divides
orthocentre and circumcentre in the ratio of2 : 1.
By internally division formula,
2p+lh
=120(½)10 +45(½Yo +1o(½Yo +{½Yo
2+1
=g
⇒
120+45+10+1
210
176
1024
11
64
2p+h-3g = 0
As, x p + y h + z g = 0
Hence, x = 2, y = 1 and z = - 3
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2016-28
42.
43.
(a) The true quantified statement is ' the square
of every real number is positive'.
(c) Since, tan2 x = 1
⇒ tan2 x= 12
7t
⇒
7t
⇒ tan 2 x = tan 2 4 ⇒
⇒
x=n1t±4
(b) In the given figure, OC line passes through
(0, 0) and (3, 3).
So, equation of line is y = x.
Also, shaded portion of this line is towards the
X-axis, sox-y~0.
In the given figure, line AB is parallel to Y-axis.
:. Equation of line AB is x = 5, also shaded
portion of this line is towards the origin, so
x-5 :=; 0 orx:=; 5.
In the given figure, line BC is parallel to X-axis.
Therefore, equation of line BC is y = 3. Also,
shaded portion of this line is towards the origin,
soy-3 :=; 0 or y :=; 3.
Also, the shaded region lies in first quadrant, so
x~0andy~0.
Hence, constraints of given shaded region are
x.y~0,x-y~0, x :=; 5, y :=; 3.
45. (b) Let direction ratios ofa line are (a, b, c).
As, line is perpendicular to the direction ratios
(-1, 2, 2) and (0, 2, 1).
:. ax-1 + bx2+ cx2=0anda x 0 + bx2 + ex 1 = 0
⇒ - a + 2b + 2c = 0 and 0a + 2b + c = 0
a
-b
c
--=--=-⇒
2-4 -1-0 -2-0
b
b
a
c
c
a
⇒
-=-=-or-=-=-2 1 -2
2 -1 2
Hence, direction ratios of a line are (2, -1, 2).
46.
(c)
!]
Given, A=[:
and AX=I
X=A- 11
⇒
⇒ X=A- 1
l [3 -2]
1[3 -2] = 1[3 -12]
=
A-I __
Then,
- IAI --4
1
3-8 -4
=¼[ ~
47.
1
-5 -4
~1]
(a) Given, a=i+J+k, b=2i+)J+k and
A
A
A
c=i-j+4ks
As, ii -(bxc)=IO
1(411.+l)-1(8-1) + 1(-2-11.)=lO
411.+1-7-2-11.=lO
311.= 18 ⇒ 11.=6
⇒
44.
⇒
48.
(b)
i, i]=lO
[~
Since, X-B=( n=5,p=fl
1
3
p(2 < X < 4) = p (X = 3)
p +q= I
=SC
2
3
-+ q =1 ⇒ q =-
(_!_)3(3_)2 =10 X_i_=
5
40
3
3
3
243
(c) Since, objective function is Z = x 1 + x 2 and
given constraints are
x 1 + x 2 :=; 10,-2x1 + 3x2 :=; 15, x 1 :=; 6,xi, x 2 ~O.
3
49.
⇒
"'15
12
Now, the point of intersection oflines x 1 + x2
= 10 and-2x 1 + 3x2 = 15 is B(3, 7) and point of
intersection oflines x 1 = 6 and x 1 + x 2 = 10 is
C(6, 4)
Here, the feasible region is OABCD. The corner
points of the feasible region are O (0, 0), A(0, 6),
B(3, 7), C(6, 4) andD(6, 0).
AtO(0,0)
Z=0+0=0
At A(0,6)
At B(3, 7)
Z=3+7=10
At C(6,4)
2=6+4=10
At D(6,0)
Z=6+0=6
Z =0+6=6
Hence, Z is maximum at each point ofthe segment
joining two pointsB(3, 7) and C(6, 4)
50. (d) Here S 1represent by p and S2 represent by q.
So, given circuit is represented as
(p A q) V (p A q).
This is not equivalent to any of the given options.
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Mock Test-[!]
General Instructions
■
■
■
■
■
■
■
This question booklet contains 150 Multiple Choice Questions (MCQs).
Section-A: Physics & Chemistry - 50 Questions each and
Section-B: Mathematics - 50 Questions.
Choice and sequence for attempting questions will be as per the convenience of the candidate.
Read each question carefully.
Determine the one correct answer out of the four available options given for each question.
Each question with correct response shall be awarded one (1) mark. There shall be no negative marking.
No mark shall be granted for marking two or more answers ofsame question, scratching or overwriting.
Duration ofpaper is 3 Hours.
SECTION-A
PHYSICS
1.
2.
A car runs at a constant speed on a circular track
of radius 100 m, taking 62.8 seconds in every
circular loop. The average velocity and average
speed for each circular loop respectively, is
(b) !0m/s, !0m/s
(a) 0, !0m/s
(c) lOm/s,0
(d) 0,0
The distance of the centres of moon and earth is
D. The mass of earth is 81 times the mass of the
moon. At what distance from the centre of the
earth, the gravitaional force will be zero?
D
3.
4.
5.
2
2D
4D
(c)
6.
An elastic string of unstretched length L and
force constant k is stretched by a small length x.
It is further stretched by another small lengthy.
The work done in the second stretching is :
(a)
(c)
7.
2
1
-k(x+ y)
2
1
2
2
(b)
2 k(x
(d)
2 ky(2x+ y )
9D
(b) 3
(d) 10
(c) 3
In kinetic theory of gases, it is assumed that
molecules
(a) have same mass but can have different volume
(b) have same volume but mass can be different
(c) have different mass as well as volume
(d) have same mass but negligible volume.
Beats are the result of
(a) diffraction
(b) destructive interference
(c) constructive and destructive interference
(d) superposition of two waves ofnearly equal
frequency
A capacitor of capacitance C is charged to a
potential V Ifit carries a charge Q, then the energy
stored in it is
(a)
(b) QV
(a)
+y )
1
A particle starts with S.H.M. from the mean
position as shown in figure below. Its amplitude
is A and its time period is T. At one time, its speed
is half that of the maximum speed. What is this
displacement at that time?
(a)
✓2A
(b)
✓3A
3
2
2A
(c) ✓
3
3A
2
(d) ✓
D
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8.
9.
TargetMHT-CET
100% modulation in FM means
(a) actual :frequency deviation > maximum
allowed frequency deviation
(b) actual frequency deviation = maximum
allowed frequency deviation
(c) actual frequency deviation ~ maximum
allowed frequency deviation
(d) actual frequency deviation < maximum
allowed frequency deviation
In an a.c. circuit, the r.m.s. value ofcurrent, Irms is
related to the peak current, I0 by the relation
(a)
(c)
Inns
Inns
= ✓2 I 0
(b)
Inns
= -I 0
(d)
14---
Inns
(a) 5.f.. 1 -4.f.. 2
18.
Soap
film
0.6g
\ . Straw
12.
13.
14.
15.
19.
For which of the following substances, the
magnetic susceptibility is independent of
temperature?
(a) diamagnetics only
(b) paramagnetics only
(c) ferromagnetics only
(d) diamagnetics and paramagnetics both
Ifthe distance between nuclei is 2 x 10-13 cm, the
density ofnuclear material is
(a)
3.2J x l0-12 kg'm3 (b)
I.6 x l0-3 kgtm3
(c)
2 x 109 kg'm3
1 x 10 17 kg'm3
(d)
Which metal will be suitable for a photoelectric
cell using light ofwavelength 4000A. The work
functions of sodium and copper are respectively
2.0eVand4.0eV.
(a) Sodium
(b) Copper
(d) None of these
(c) Both
A system consists of three particles, each of mass
m and located at (1, 1), (2, 2) and (3, 3). The coordinates of the centre of mass are
(a) (1, 1) (b) (2,2) (c) (3,3) (d) (6,6)
Which one of the following statements is true?
(a) A scalar quantity is the one that is conserved
in a process.
(b) A scalar quantity is the one that can never
take negative values.
(d) 30°
(a) 25°
(b) (f.J'
(c) 45°
The length of elastic string, obeying Hooke's law
when the tension is 5N. The length in metres when
the tension is 9N is -
= ✓2 Io
(d) 6 g
A scalar quantity is the one that does not
vary from one point to another in space.
(d) A scalar quantity has the same value for
observers with different orientations ofthe axes.
A car moves at a speed of20 ms-1 on a banked
track and describes an arc of a circle of radius
40✓
3 m. The angle ofbanking is (g = 10 ms- 2 )
is .f.. 1 metres when the tension is 4N and .f.. 2 metres
10cm - - ~
(b) 0.06g
(c)
17.
= 7t Io
A soap film of surface tension 3 x 1o-2 formed in
a rectangular frame can support a straw as shown
in Fig. Ifg = 10 ms-2, the mass ofthe straw is
0.006g
16.
1
1
7t
(a)
(c)
(b) 5.f.. 2 - 4.f.. 1
(c) 9.f.. 1 -8.f.. 2
(d) 9.f.. 2 -8.f..1
A moving coil galvanometer has resistance of
10 n and full scale deflection of0.01 A. It can be
converted into voltmeter of 10 V full scale by
connecting into resistance of
(a) 9.90 n in series
(b) 10 n in series
(c) 990 n in series
(d) 0.100
A point charge +Q is positioned at the center of
the base of a square pyramid as shown. The flux
through one of the four identical upper faces of
the pyramid is
(a)
(b)
(c)
20.
(d) None of these
The dimensions of impulse are
(a)
[ML T-1]
(b)
[MLY]
(d) [ML-I T-3 ]
[ML0 r 2 J
Three wires are situated at the same distance. A
current of IA, 2A, 3A flows through these wires
in the same direction. What is ratio of F / F 2,
(c)
21.
ij"J! "'°'"'"
1
2
on I and F on 2?
ttt
(c) 9/8
(d) None of these
IA 2A 3A
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MOCK.TEST-I
22.
23.
24.
25.
The escape velocity of a body on the surface of
the earth is 11.2 krn/s. Ifthe earth's mass increases
to twice its present value and the radius of the earth
becomes half, the escape velocity would become
(a) 44.8krn/s
(b) 22.4krn/s
(c) 11.2krn/s
(d) 5.6krn/s
For measuring voltage of any circuit,
potentiometer is preferred to voltmeter because
(a) the potentiometer is cheap and easy to handle.
(b) calibration in the voltmeter is sometimes
wrong.
(c) the potential draws no current during
measurement.
(d) range of the voltmeter is not as wide as
that of the potentiometer.
The ratio of the energy of an X-ray photon of
wavelength 1 A to that of visible light of
wavelength 5000 A is
(a) 1:5000
(b) 5000:1
(d) 25 x 106
(c) 1 :25 x 106
A ray is incident at an angle 60° on a sphere
which is made ofmaterial having refractive index
= ✓3 , find angle by which the emergent ray is
3
30.
31.
32.
33.
deviated
(a) 300
(b)
15°
(c) 45°
(d) 600
26.
27.
28.
29.
A radioactive sample contains 10-3 kg each oftwo
nuclear species A and B with half-life 4 days and 8
days respectively. The ratio of the amounts of A
and B after a period of 16 days is
(a) 1:2 (b) 4:1 (c) 1:4 (d) 2:1
A hammer weighing 3 k~ strikes the head of a
nail with a speed of2 ms- drives it by 1cm into
the wall. The impulse imparted to the wall is
(a) 6Ns (b) 3Ns (c) 2Ns (d) 12Ns
A particle of mass 0.2 kg is moving in a circle of
radius 1 m with f= (2/n) sec- 1, then its angular
momentum is :
(a) 0.8 kg-m2/s
(b) 2 kg-m2/s
2
(d) 16kg-m2/s
(c) 8kg-m /s
A pipe open at both ends has a fundamental
frequency fin air. The pipe is dipped vertically in
water so that half of it is in water. The fundamental
frequency of the air column is now :
3f
f
(b) f
(a) 2f
(c)
(d)
2
4
34.
35.
What is cyclotron frequency of an electron with
an energy ofl 00 e Vin the magnetic field ofl x 10-4
weber / m 2 if its velocity is perpendicular to
magnetic field?
(a) 0.7MHz
(b) 2.8MHz
(c) 1.4MHz
(d) 2.1 MHz
The current I passed in any instrument in
alternating current circuit is I= 2 sin ffit amp and
potential difference applied is given by V = 5 cos
ffit volt then power loss in instrument is
(a) 2.5watt
(b) 5watt
(c) 10 watt
(d) zero
Eddy currents in the core of transformer can't
be developed by
(a) increasing the number ofturns in secondary
coil
(b) taking laminated transformer
(c) making step down transformer
(d) using a weak a.c. at high potential
A body of mass 2 kg is placed on a horizontal
surface having kinetic friction 0.4 and static
friction 0.5. Ifthe force applied on the body is 2.5
N , then the frictional force acting on the body
will be [g = 10 ms- 2]
(a) 8N
(b) 10 N (c) 20N (d) 2.5N
In a photoelectric experiment, with light of
wavelength A, the fastest electron has speed v. If
the exciting wavelength is changed to 5')../4, the
speed ofthe fastest emitted electron will become
(a)
vJ¾
(c)
less than v
(b)
JI
vJI
(d) greater than v
JI
The major contribution of magnetism in
substances is due to
(a) orbital motion of electrons
(b) spin motion of electrons
(c) equally due to orbital and spin motions of
electrons
(d) hidden magnets
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TargetMHT-CET
4
36.
The resistances in the two arms of the meter
bridge are 5Q and RO, respectively. When the
resistance R is shunted with an equal resistance,
the new balance point is at 1.6 / 1. The resistance
'R'is:
(a)
10n
(b)
15Q
sn
37.
38.
39.
40.
(a) 4J
(b)
-; J
(c)
~J
2
(d) zero
41.
43.
A.____...___ ___,
8
11
100-t,
When an object 1s placed at a aistance of25 cm
from a mirror, the magnification is m 1• The object
is moved 15cm further away with respect to the
earlier position, and the magnification becomes
mt Ifmilm2 =4, the focal length ofthemirror is:
(aJ 10cm (b) 30cm (c) 15cm (d) 20cm
A current I flows along the length of an infinitely
long, straight, thin walled pipe. Then
(a) the magnetic field at all points inside the
pipe is the same, but not zero
(b) the magnetic field is zero only on the axis of
the pipe
(c) the magnetic field is different at different
points inside the pipe
(d) the magnetic field at any point inside the
pipe is zero
A body moves a distance of 10 m a long a straight
line under the action of a force of 5 newtons. If
the work done is 25 joules, the angle which the
force makes with the direction of motion of
body is
(a) (J'
(c) 6<J'
(d) 90"
(b) 3(]'
In P-V diagram shown in figure ABC is a semicircle. The work done in the process ABC is
l"(N/m~
Consider the situation shown in figure. If the
switch is closed and after some time it is opened
again, the closed loop will show
O
(a) a clockwise current
(b) an anticlockwise current
•.......✓.
(c) an anticlockwise current and then clockwise
(d) a clockwise current and then an anticlock
wise current.
The equivalent capacitance between A and B is
(in µF)
0
R!'l
(c) 20n
(d) 25Q
42.
(a) 25
(b)
84
25
(c) 9
(d)
44.
45.
46.
':~:r
3 µF
3 µF
3 µF
Moment of inertia does not depend upon
(a) angular velocity of body
(b) shape and size
(c) mass
(d) position ofaxis of rotation
A sound source emits frequencyofl80 Hz when
moving towards a rigid wall with speed 5 mis and
an observer is moving away from wall with speed
5 mis. Both source and observer moves on a
straight line which is perpendicular to the wall.
The number of beats per second heard by the
observer will be [Speed of sound = 355 mis]
(a) 5 beats/s
(b) 10 beats/s
(c) 6 beats/s
(d) 8 beats/s
To get an output I from the circuit shown in the
figure, the input must not be
-------·c:
0'----':_
+V(m3)
_._
i __
c------
2
Water is flowing continuously from a tap having
an internal diameter 8 x 10-3 m. The water velocity
as it leaves the tap is 0.4 ms- 1• The diameter of
the water
stream
at
a
distance
2 x l o-1 m below the tap is close to:
(a) 7.5 x 10-3 m
(b) 9.6 x 10-3 m
3
(d) 5.0 x 10-3 m
(c) 3.6 x 10- m
47.
(a) A = 0, B = 0 , C = 1 (b) A = 1, B = 0,C = 0
(c) A = l,B = 0,C = l (d) A=l , B = l ,C = 0
The ratio of the largest to shortest wavelengths
in Brackett series of hydrogen spectra is
(a) 25/9
(b) 17/6
(c) 9/5
(d) 4/3
IWWW.JEEBOOKS.INI
MOCKTEST-1
48.
49.
Which one did Rutherford consider to be
supported by the results of experiments in which
a-particles were scattered by gold foil?
(a) The nucleus of an atom is held together by
forces which are much stronger than
electrical or gravitational forces
(b) The force of repulsion between an atomic
nucleus and an a-particle varies with
distance according to inverse square law
(c) a-particles are nuclei of Helium atoms
(d) Atoms can exist with a series of discrete
energy levels
A simple pendulum attached to the ceiling ofa
stationary lift has a time period T. The distance
y covered by the lift moving upwards varies
with time t as y = t 2 where y is in metres and t
in seconds. If g = 10 m/s 2, the time period of
pendulum will be
(a)
50.
~T (b)
HT (c)
{¾T (d)
lT
A glass capillary tube ofinner diameter 0.28 mm is
lowered vertically into water in a vessel. The
pressure to be applied on the water in the tube so
that water level in the tube is same as that in the
vessel (in N/m2) is (surface tension of water
= O.D7 Nim, atmospheric pressure= 1OS N/m2) :
(a) 103
(b) 99 X 103
3
10() X 10
(C
@. 10} X J03
5
Benzene reacts with CH3COC1 + AIC13 to give
(a) chlorobenzene
(b) toluene
(c) benzyl chloride
(d) acetophenone
57. Which of the following is the incorrect statement?
(a) NaCl has 6 : 6 coordination and CsCl has
8 : 8 coordination.
(b) In Nap each oxide ion is coordinated by
8Na+ ions and each Na+ ion by4 oxide ions
(c) CsCI structure transform to NaCl structure
on heating
(d) In CaF?istructure each P- ion is coordinated
by 4 Ca + and vice-versa.
58. Which of the following statements is not valid
for oxoacids of phosphorus?
(a) Orthophosphoric acid is used in the
manufacture of triple superphosphate.
(b) Hypophosphorous acid is a diprotic acid.
(c) All oxoacids contain tetrahedral four
coordinated phosphorus.
(d) All oxoacids contain atleast one P = 0 and
one P - OH group
59. Which of the following is most reactive towards
SN2 reaction?
56.
~OCI
(a)¥
CHEMISTRY
51.
52.
53.
54.
55.
The unit J Pa- 1 is equivalent to
(b) cm3
(a) m3
3
(c) dm
(d) None of these
A compound X of formula C3H8 0 yields a ketone
C3H60 on oxidation. To which of the following
class of compounds would X belong?
(a) Aldehyde
(b) Tertiaryalcohol
(c) Secondary alcohol (d) Alkene
The element with which of the following outer
electron configuration may exhibit the largest
number of oxidation states in its compounds :
(a) 3d54s2
(b) 3d 84s2
7
2
(c) 3d 4s
(d) 3d 64s2
The metal oxide which cannot be reduced to metal
by carbon is
(a) Fep3 (b) Alp3 (c) PbO (d) ZnO
In Arrhenius plot, intercept is equal to
(a)
-Ea
R
(b)
(c)
lnK
(d) log 10A
lnA
~OCI
(c)
¥
(d) ~ I
Cl
The equivalent conductance at infinite dilution
of a weak acid such as HF
(a) can be determined by extrapolation of
measurements of dilute solutions of HCl,
HBrandHI.
(b) can be determined by measurement ofvery
dilute HF solutions.
(c) can be determined from measurements of
dilute solutions ofNaF, NaCl and HCI.
(d) is an undefined quantity.
61. Which functional group participates in
disulphide bond formation in proteins?
(a) Thioester
(b) Thioether
(c) Thiol
(d) Thiolactone
60.
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6
62.
TargetMHT-CET
65.
Secondary amines could be prepared by
(a) reduction ofnitriles
(b) Hofmann bromamide reaction
(c) reduction of amides
(d) reduction ofisonitriles
Among [Ni(CO)4] , [Ni(CN)4] 2- and [NiBr4] 2species, the hybridisation state of Ni atoms are
respectively:
(b) sp3, dsp 2, sp3
(a) sp3, ds2p, dsp2
(d) sp3, sp3, dsp 2
(c) dsp2, sp3, sp3
Specific conductance ofa 0.1 N KCI solution at
23°C is 0.012 ohm-1 cm- 1• Resistance of cell
containing the solution at same temperature was
found to be 55 ohm. The cell constant is
(b) 0.66cm-1
(a) 0.06l6cm-1
1
(c) 6.60cm(d) 660cm-1
The rate constant for the reaction
66.
2N 205 ---t 4N0 2 + 0 2, is 3.0 x 10-5 sec-1. If
the rate is 2.40 x 10-5 mol litre- 1 sec-1, then the
concentration ofN2O 5 (in mol litre-1) is
(a) 1.4
(c) 0.04 (d) 0.8
(b) 12
Cryolite is
63.
64.
(a)
Na 3 AlF6 and used in the electrolysis of
alumina for
conductivity.
(b)
decreasing electrical
Na 3AlF6 and used in the electrolysis of
alumina for lowering the melting point of
alumina.
(c)
Na 3 AlF6 and used in the electrolytic
purification ofalumina.
(d)
67.
68.
69.
Na 3 AlF6 and used in th e electrolysis of
alumina.
Which of the following does not contain a
hydrophilic structure ?
(a) Linseed oil
(b) Lanolin
(c) Glycogen
(d) Rubber
Which one of the following is not correct for an
ideal solution?
(a) It must obey Raoult's law
(b) tili=O
(c) till= !!V :ct= 0
(d) All are correct
Which of the following is correct set of physical
properties of the geometrical isomers?
CH3 '-..
H/
/Cl
C = C,
'H
II
Dipole
moment
(a) 1> 11
(b) 11 > I
(c) I > II
70.
B.P.
I > II
11 > I
I > II
(d) II > I
II > I
Baking powder contains:
(a)
MP.
Stability
11 > 1
11 > 1
1> 11
1> 11
1> 11
11 > 1
1> 11
1> 11
NaHCO3 , Ca CHiPO2) 2 and starch
(b) NaHCO3, Ca(8iPO2) 2
(c)
71.
NaHCO3, starch
(d) NaHCO3
Which reaction is not feasible?
(a)
2JU+Br2 ➔ 2KBr+I 2
(b)
2KBr + 12 ➔ 2JU + Br2
(c)
2KBr +Cl 2 ➔ 2KCI + Br2
(d)
2H 20 +2F2 ➔ 4HF+02
72.
Teflon and neoprene are
(a) copolymers
(b) condensation polymers
(c) homopolymers
(d) monomers
73. Which of the following reagents will convert
p-methylbenzenediazonium chloride into
p-cresol?
(a) Cu powder
(b) 8i0
(d) C 6HpH
(c) ~PO2
74. According to lUPAC nomenclature sodium
nitroprusside is named as:
(a) Sodium pentacyanonitrosylferrate (III)
(b) Sodium nitroferrocyanide
(c) Sodium nitroferricyanide
(d) Sodium pentacyanonitrosylferrate (II)
75. One mole of calcium phosphide on reaction with
excess water gives
(a) one mole of phosphine
(b) two moles of phosphoric acid
(c) two moles of phosphine
(d) one mole of phosphorus pentoxide
76. The rate constant of a reaction is 3.00 x I 0 3 L
mo1- 1 sec-1• The order of this reaction will be:
(b) I
(d) 3
(a) 0
(c) 2
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MOCK.TEST-I
77. Which of the following statements is not true?
(a) Paramagnetic substances are weakly
attracted by magnetic field.
(b) Ferromagnetic substances cannot be
magnetised permanently.
(c) The domains in antiferromagnetic
substances are oppositely oriented with
respect to each other.
(d) Pairing of electrons cancels their magnetic
moment in the diamagnetic substances.
78.
©
+ CH3CHO
7
82.
83.
dil. NaOH
A
.A.
(Major)
will beOH
(a)
I
C 6H 5 CH -CH 2 CHO
84.
Match the columns
Colwnn-1
Column-II
(Example of solid)
(Type of solid)
Ag
A. Molecular solid I.
B. Ionic solid
II. SiC
C. Metallic solid
III. C04
N MgO
D Covalent solid
(a) A-IV, B-Ill, C -1, D-11
(b) A-II, B-IV, C-1, D-Ill
(c) A-Ill,B-Il, C-1,D-IV
(d) A- Ill, B -IV, C-1, D - II
HBr reacts with CH2 = CH - OCH3 under
anhydrous conditions at room temperature to
give
(a) BrC8i-C8i-OC~
(b) ~C-CH(Br)-OC~
(c) C~CHOandC~Br
(d) BrCHiCHOandC~OH
Silver benzoate reacts with bromine to form
(b) C6H5CH=CH-CHO
79.
80.
81.
(c) C6H5C8iC8iCHO
(d) Both (b) & (c)
A blue colouration is not obtained when
(a) ammonium hydroxide dissolves in copper
sulphate
(b) copper sulphate solution reacts with
K 4 [Fe(CN)6]
(c) ferric chloride reacts with sod. ferrocyanide
(d) anhydrous CuS04 is dissolved in water
Which of the following statements is not correct?
(a) Physical adsorption is due to van der Waal 's
forces.
(b) Chemical adsorption first decreases with
increase in temperature.
(c) Physical adsorption is reversible.
(d) Adsorption energy for a chemical
adsorption is generally greater than that of
physical adsorption.
When 0.01 mole ofa cobalt complex is treated
with excess silver nitrate solution, 4.305 g silver
chloride is precipitated. The formula of the
complex is
(a) [Co(NII:i)3Cl3]
(b) [C~)5Cl]Cl2
(c) [Co(NR:i)JC13
(d) [Co(NR:i)4Cl2]N03
85.
Which L-sugar on oxidation gives an optically
active dibasic acid (2 COOH groups)?
(a)
H~ r~H
HO
(c)
(b)
H
CH20H
:+g~
H=t=OH
CH20H
H~+~H
H=t=OH
CH20H
(d)
Hi+~H
HO=t=H
CH20H
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8
86.
87.
88.
89.
90.
91.
92.
TargetMHT-CET
A solution containing components A and B
follows Raoult's law when
(a) A- B attraction force is greater than A-A
andB-B
(b) A- B attraction force is less than A-A and
B-B
(c) A- B attraction force remains same as A-A
and B-B
(d) volume of solution is different from sum of
volume of solute and solvent
Find the charge in coulombs required to convert
0.2 mole VO3- 2 into VO4- 3 .
(a) 1.93 X 104
(b) 9.65 X 104
(d) 9.65 x 105
(c) 1.93 x 105
The alcohol which does not give a stable
compound on dehydration is
(b) methyl alcohol
(a) ethyl alcohol
(c) n-Propyl alcohol (d) n-Butyl alcohol
The simplest way to check whether a system is
colloidal or not is by
(a) Tyndall effect
(b) Brownian movement
(c) Electrodialysis
(d) Measuring particle size
CFC which is a main reason behind air pollution, is
produced by
(a) sewage pollutant (b) aerosols
(c) industrial remains (d) all the three
Which of the following halide is 2° ?
(a) Isopropyl chloride (b) Isobutyl chloride
(c) n-propyl chloride (d) n-butyl chloride
The equilibrium constant for a reaction A+ 2B
~ 2C is 40. The equilibrium constant for
reaction
1 .
C ~ B+-A1s
2
(a) 40
(b)
[410r
(c)
(d)
-1 ]
112
93.
40
[ 40
Best method for preparing primary amines from
alkyl halides without changing the number of
carbon atoms in the chain is
(a) Hoffmann bromamide reaction
(b) Gabriel phthalimide synthesis
94.
95.
96.
97.
(c) Sandmeyer reaction
(d) reaction with~
Sulpha drugs are used for
(a) precipitating bacteria
(b) removing bacteria
(c) decreasing the size of bacteria
(d) stopping the growth of bacteria
When petroleum is heated gradually, the first
batch of vapours evolved will be rich in
(a) kerosene
(b) petroleum ether
(d) lubricating oil
(c) diesel
On boiling an aqueous solution ofKCIO3 with 12
the products obtained are
(a) KIO3+ Cl2
(b) KC!+ Ip5
(c) KIO4+Cl2
(d) No reaction takes place
In the reaction:
CH3OH
98.
99.
oxidation
A
NH3
B ; A and B
respectively are
(a) HCHO, HCOONH4
(b) HCOOH, HCOONH4
(c) HCOOH, HCON8:i
(d) HCHO,HCON8:i
The chemistry oflithium is very similar to that of
magnesium even though they are placed in different groups. Its reason is
(a) Both are found together in nature
(b) Both have nearly the same size
(c) Both have similar electronic configuration
(d) The ratio of their charge and size (i.e. charge
density) is nearly the same
Consider the equation Z
= PV . Which of the
RT
following statements is correct?
(a) When Z > 1, real gases are easier to
compress than the ideal gas
(b) When Z=l , real gases get compressed
easily
(c) When Z= l, real gases are difficult to
compress
(d) When Z> 1, real gases are difficult to
compress
100. How many propagation reactions occur
simultaneously in a binary copolymerization
process?
(a) 2
(c) 1
(d) 3
(b) 4
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MOCK.TEST-I
9
SECTION-8
9.
MATHEMATICS
1.
2.
Let n (U) = 700, n (A) = 200, n (B) = 300,
n (A nB) = 100, then n (A' n B') is equal to
(a) 400
(b) fill
(c) 300
(d) None of these
The domain and range of the relation R given
6
by R = {(x, y) : y = x + -; where x, y
E
N
X
and x < 6} is
(a) {1, 2, 3}, {7, 5}
(c) {2, 3}, {5}
3.
I+x
(c) x
11.
(d) -x
Therangeofthefunctionf(x)= .J3x2 -4x+5 is
l fl]
(a)
-oo,
(c)
5.
1/x
(b)
10.
(b) {1, 2}, {7, 5}
(d) None of these
If3j(x)-f(~) = Iogx4, thenj(e-x) is
(a)
4.
The length of the tangent drawn from any point
on the circle x 2 + y2 + 2fy + A = 0 to the circle
x 2 +y2+2fy+ µ= 0, whereµ > A> 0, is
[
J¥, J
12.
00
13.
tan A+ tan(60° + A)- tan(60°-A) is
6.
tan 3A
2
7.
(b)
2 tan 3A
(c) 3 tan 3A
(d) None of these
For which real values of x and y, the equation
sec 0 =
4xy
2
(b)
(c)
(d) m + l
14.
15.
is possible ?
(x+ y)
(a) x=y
(b) x >y
(c) x<y
(d) None of these
If Sn denotes the sum of first n terms ofanA.P,
.Jµ2 - A.2
9
(d)
1600
9
From eighty cards numbered 1 to 80, two cards are
selected randomly. The probability that both the cards
have the numbers divisible by 4 is given by
(a)
9
(a)
21
316
whose first term is a and Snx is independent of
Ifill (c)
(b)
(b)
1600
19
316
(d) None of these
4
Ifz is a complex number such thatz + lzl= 8 + 12i,
then the value of lz21 is equal to
(a) 228
(b) 144 (c) 121
(d) 169
If 5x+ 1 > -24and 5x-l < 24, thenx E (-a, a). The
valueof'a' is
(a) 2
(c) 4
(b) 3
(d) 5
The tens digits ofl ! + 2! + 3 ! + .... + 49! is
(b) 2
(a) 1
(c) 3
(d) 4
Inthebinomialexpansioo(a+bx)-3 =
1
9
8 + 8x+ ... .,
then the value of a and b are :
(b) a=2, b=-6
(a) a =2, b=3
(c) a =3, b=2
4
s
-Jµ+A
Find the length ofintercept on the line 4y = 3x-48
by the parabolay2 = 64x.
(c)
The value of
(a)
(a)~
16
•
8
d(l+x2 + x4
If dx l + x + x
(d) a=-3 , b=2
J= ax
3
+ bx, then
X
(a) a = 4,b = 2
(c) a =-2, b = 4
x, then SP =
(a)
8.
P3
(b) P 2 a
(c)
Pa 2
(d) a 3
The locus of the moving point whose
coordinates are given by (e1 + e-1, e1 -e-1) where
tis a parameter, is
(b) x+y =2
(a) xy = I
(c) x 2 -y2 = 4
(d) x 2 -y2 = 2
17.
(b) a=4,b=-2
(d) Noneofthese
The mean weight per student in a group ofseven
students is 55 kg. If the individual weights of six
students are 52, 58, 55, 53, 56 and 54, then the
weight of the seventh student is
(a) 55kg (b) 60kg (c) 57kg (d) 50kg
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10
18.
19.
TargetMHT-CET
Letf(x) = [x]2 + [x + 1]-3 where [x] = the greatest
integer function. Then
(a) f(x) is a many-one and into function
(b) f(x) = 0 for infinite number ofvalues ofx
(c) f(x) = 0foronlytworealvalues
(d) Both (a) and (b)
G is the centroid of the !1ABC,
GA+GB+oc
(a)
(c)
3sinnx,
5
Iff{x)= {
x
2k,
3n
25.
iscontinuousatx = 0,
x=0
22.
5
(b)
10
(d)
3n
2
The value of the integral
2 loge x
(a)
1
26.
27.
(loge x )2
e-loge2
(c) e-2log2 e
The solution of :
(a)
y
(b)
I
(c)
e-
fex dx
fln(e +l-y)dy
e
(d)
0
f In y dy
I
If two events A and B are such that
P(A) = 0.3, P(B) = 0.4 and P(A n B) = 0.5
29.
then
p(~)
=
Au B
(a)
0.9
(b) 0.5
(c)
0.6
(d) 0.25
If m (tc 1) be a cube root ofunity and
(I + m2f = (1 + m4f, then the least positive
value of n is
(a)
2
30.
(d)
(b) 0 only
(d) None of these
I
= xlxl + c
y =-+c
2
X
(a) (a,a) (b) (0,a) (c) (0,0) (d) (a, 0)
Which of the following is not the area of the
region bounded by y = e and x = 0 and y = e?
(a) e-1
is :
x2
x3
y =-+ c
2
24. IfA, B and C are the vertices of a triangle whose
(c)
0
is
The normal to the curve x = a(l + cos 0), y = a
sin0 at '0' always passes through the fixed point
is
(b) e-log2 e
(d) e-loge4
= lxl
sin 0 cos 0
-sin0 -x
e
28.
l dx
The determinant
independent of
(a) x only
(c) x and 0 both
Which one of the following statements is
correct in respect of the curve 4y - x2 - 8 = 0 ?
(a) The curve is increasing in (- 4, 4)
(b) The curve is increasing in (- 4, 0)
(c) The curve is increasing in (0, 4)
(d) The curve is decreasing in (-4, 4)
1
fel---
23.
re
(c)
3
COS
x#0
3n
10
(d)
x
then the value ofk is equal to
21.
a +b+c
~ ~
If A = [~
] and I is the unit matrix of
a b -1
(a)
- - -a-b- -c
a+b +c
(b)
0
3
order 3, then A 2 + 2A4 +4A6 is equal to
(d) 61
(a) 7A8 (b) 7A7 (c) 81
20.
is
then
position vectors are ;, b and ; respectively and
2
(b) 3
(c) 5
(d) 6
If ncr denotes the number of combination of n
things taken r at a time, then the expression
ncr+I +nCr-1 + 2x nCr equals
(a)
n+ICr+I
(c)
n+2Cr+I
WWW.JEEBOOKS.INI
11
MOCKTESf-1
31.
The number of integral terms in the expansion of
(3 ½+ 2½)500 is
(a)
32.
33.
128
(b)
129
(c)
251
(a)
(d) 512
The points (4, 7, 8), (2, 3, 4), (-1 ,-2, 1) and (1, 2, 5)
are the vertices of a
(b) rhombus
(a) parallelogram
(c) rectangle
(d) square
39.
(a)
3
bn
-1
17
19
(b)
i -2] +k
on the
is equal to:
9
.!.2_
5
16
(d)
(c)
✓3
19
19
✓
3
(d)
The equation of the plane which makes with
co-ordinate axes, a triangle with its centroid
(a, p, y) is
(a)
Then find Jim bn ·
(c)
5
4i -4] + 7k
9
40.
3
-
(b)
The projection of the vector
vector
Let the sequence <bn> of real numbers satisfies
the recurrence relation bn+1 = .!..(2bn + .!.32.J
2 , bn ,e o·
2
19
ax+py+yz=3 (b)
ax+py+yz=I
n ➔ao
34.
(a) 10
(b) 15
(c) 5
(d) 25
Let p and q be any two logical statements and
r :p ➔ (
~ p V q) . Ifr has a truth value F, then
the truth values ofp and q are respectively:
(a) F, F
(b) T, T (c) T,F (d) F, T
2a
41.
2 !Ox -10-x
35.
X1
Yi
x2
2c -½
y2
If 2b
=
y3
abc
2
* 0, then the area of the
x is
The inverse off(x) = x
3 10 + 10-
triangle whose vertices are (
1
(a)
3
l +x
log10 1- x
(b)
l
2+3x
loglO 2 -3x
I
2 -3 x
log lO 2+3x
2
and ( ; ,
1
(c)
3
2+3x
log!O 2-3x
(d)
6
(a)
36.
If tan-I ~ < ~, x
N, then the maximum value
(c)
(b) 5
(d) None of these
2
!]
a I
andA- 1= [
~: -
I:
2
l
42.
I
-abc
4
(b)
1
- abc
(d)
8
~
],
(c)
(R)
1
sin-
l+k
The value of
dy
Let y = x 3 -8x+ 7 and x = .l{t). If dt = 2 and
(a)
x = 3 att = 0, then the value of dx att = 0 is
dt
4
The angle at which the curve
5 / 2 -3 / 2 1/2
43.
8
1
intersects the y-axis is :
(b)
(a) tan- 1(k2)
2
then the value of a + c is equal to
(a) 1
(b) 0
(c) 2
(d) none of these
38.
is
3
re
ofx is
(a) 2
(c) 7
37. ffA{
E
~)
~ , ~ ) , ( x; ,1)
(c)
3rc 2
64
3rc 2
256
r
4
(d)
y
= kek:x
coc 1(k2)
1
4
sec- .J1+k
x (sin 4 x cos4 x) dx is
(b)
3rc 2
128
(d) None of these
IWWW.JEEBOOKS.INI
12
44.
TargetMHT-CET
Shamli wants to invest t50,000 in saving
certificates and PPF. She wants to invest atleast
t 15,000 in saving certificates and at least t20,000
in PPF. The rate of interest on saving certificates
is 8% p.a. and that on PPF is 9% p.a. Formulation
of the above problem as LPP to determine
maximum yearly income, is
(a)
47.
(a)
48.
MaximizeZ = 0.08x+0.09y
Subject to, x + y ~ 50,000, x
~
The d.r. ofnormal to the plane through (1, 0, 0),
(0, 1, 0) which makes an angle n /4 with plane
x+y=3are
15000,
y ~20,000
~
(b)
1, 1, ✓
2
(c) 1, 1,2
(d) ✓
2 , 1, 1
The differential equation ofall parabolas having
their axes ofsymmerty coinciding with the axis of
Xis
(a)
(b) MaximizeZ = 0.08x+0.09y
Subject to, x + y ~ 50,000, x
1, ✓
2 ,1
yd2y +(dy)2 =0
dx 2
dx
15000,
y ~ 20,000
(c) MaximizeZ = 0.08x+0.09y
Subjectto, x + y ~ 50,000, x
~
15000,
(c)
y ~20,000
(d) MaximizeZ=0.08x + 0.09y
Subject to, x + y ~ 50,000, x
~
15000,
49.
y ~20,000
45.
Suppose X follows a binomial distribution with
parameters n and p, where O < p < 1, if
P(X = r)/P(X = n - r) is independent ofn and r, then
(a)
(d) None of these
Let f(x) be a continuous function such that the
area bounded by the curvey= :f(x), x-axis and the
lines
a2
x = 0 and x = a is -
a
7t
+ - sin a + - cos a, then
2
2
2
1
(b) p= 3
1
p= 2
(a)
1
(c) p= -
(d) None of these
4
(b)
2
1
(d) None of these
3
IfX is a binomial Variate and P(X) is the probability
function then the value ofX for which the value
(c)
46.
f
x+3,J;J+~
x(l +
rx)
.
dx 1s equal to
50.
(a)
~x 213 +6tan-1 x 116 +C
2
ofp(X) is the maximum, given n = 9, P =
(b)
~x 213 -6tan-1 x" 6 +C
2
(a) 3 or 2
(c) 4 or 2
(c)
-~x 213 +6tan-1 x I16 +C
1
5 is
(b) 2or 1
(d) none of these
2
(d) None of these
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Mock Test-~
General Instructions
■
■
■
■
■
■
■
This question booklet contains 150 Multiple Choice Questions (MCQs).
Section-A: Physics & Chemistry - 50 Questions each and
Section-B: Mathematics - 50 Questions.
Choice and sequence for attempting questions will be as per the convenience of the candidate.
Read each question carefully.
Determine the one correct answer out of the four available options given for each question.
Each question with correct response shall be awarded one (1) mark. There shall be no negative marking.
No mark shall be granted for marking two or more answers ofsame question, scratching or overwriting.
Duration ofpaper is 3 Hours.
SECTION-A
(a)
PHYSICS
1.
2.
3.
4.
5.
The maximum velocity (in ms-1) with which a car
driver must traverse a flat curve ofradius 150 m
and coefficient of friction 0.6 to avoid skidding is
(a) 60
(b) 30
(c) 15
(d) 25
A ring ofmass m and radius r is melted and then
moulded into a sphere. The moment of inertia of
the sphere will be
(a) more than that of the ring
(b) less than that of the ring
(c) equal to that of the ring
(d) None of these
The young's modulus of a wire of length l and
radius r is y N/m 2 . If the length and radius are
reduced to £/2 and r/2, then its young's
modulus will be
(a) y/2
(b) y
(c) 2y
(d) 4y
When the light is incident at the polarizing angle
on the transparent medium, then the completely
polarized light is
(a) refracted light
(b) reflected light
(c) refracted and reflected light
(d) neither reflected nor refracted light
A simple pendulum ismadeofabodywhich is a
hollow sphere containing mercury suspended by
means ofa wire. Ifa little mercury is drained off,
the period of pendulum will
remain unchanged
(b) increase
(c)
decrease
(d) become erratic
l
6.
Which of the following is not correct about
relative magnetic permeability (µr)?
(a) It is a dimensionsless pure ratio.
(b) For vacuum medium its value is one.
(c) For ferromagnetic materials µr > > 1
7.
A non-linear polyactomic gas molecule (like NH3)
have how much degree of freedom?
(d) 3
(a) 5
(b) 6
(c) 4
A transverse wave is represented by y = A sin
(cot- kx). For what value of the wavelength is
the wave velocity equal to the maximum particle
velocity?
(d) For paramagnetic materials µr < 1.
8.
(a)
9.
nA
2
(b)
nA
(c) 2nA
(d) A
In an induction coil the current increases from 0 to
6 amp in 0.3 sec by which induced emfof30 volt is
produced in it then the value of coefficient of self
inductance ofcoil will be
(a) 3H
(b) 2H
(c) 1 H
(d) 1.5H
WWW.JEEBOOKS.INI
14
10.
11.
12.
13.
TargetMHT-CET
The X-rays of wavelength 0.5 A are scattered by
a target. What will be the energy of incident
X-rays, if these are scattered at an angle of72°?
(a) 12.4lkeV
(b) 6.2keV
(c) 18.6keV
(d) 24.82keV
The centre ofmass of two particles lies on the line
(a) joining the particles
(b) perpendicular to the line joining the particles
(c) at any angle to this line
(d) None of these
A transistor has three impurity regions. All the
three regions have different doping levels. In
order of increasing doping level, the regions are
(a) emitter, base and collector
(b) collector, base and emitter
(c) base, emitter and collector
(d) base, collector and emitter
If ar and at represent radial and tangential
accelerations, the motion of particle will be
uniformly circular, if
(a) ar = 0 and a 1 = 0 (b) ar = 0 but a 1 0
(c) ar
0 and a 1= 0 (d) ar
0 and at
0
Which of the given graphs proves Newton's
law of cooling?
*
14.
(a)
l.- I
c
_g°
*
*
~----
(b)?
C,
*
~
17.
18.
19.
A pipe of length 85 cm is closed from one end.
Find the number of possible natural oscillations
of air column in the pipe whose frequencies lie
below 1250 Hz. The velocity of sound in air is
340m/s.
(b) 8
(c) 6
(d) 4
(a) 12
Joule - second is a unit of
(a) energy
(b) torque
(c) power
(d) angularmomentum
Magnetic lines of force due to a bar magnet do
not intersect because
(a) a point always has a single net magnetic
field
(b) the lines have similar charges and so repel
each other
(c) the lines always diverge from a single force
(d) the lines need magnetic lenses to be made
to interest
20.
21.
~
Time
- - + Time
A Carnot engine whose sink is at 300 K has an
efficiency of 40%. By how much should the
temperature of source be increased so as to
increase, its efficiency by 50% of original
efficiency ?
(a) 325 K (b) 250K (c) 380K (d) 275 K
A horizontal force of l ON is necessary to just
hold a block stationary against a wall. The
coefficient of friction between the block and the
wall is 0.2. The weight ofthe block is
(a)
20N
(b) SON
(c)
(d) None of these
-
15.
16.
Time
The mass number ofHe is 4 and that for sulphur is
32. The radius ofsulphur nuclei is larger than that
ofhelium by
(a) Jg
(b) 4 (c) 2
(d) 8
In a Young's double slit experiment, the
separation of the two slits is doubled. To keep
the same spacing of fringes, the distance D of
the screen from the slits should be made
(a)
D
2
22.
(b)
D
✓
2
(c) 'JD
(d) 4D
23.
IOON
lON
(d) 2N
In an oscillating LC circuit with L = 50 mH and
C = 4.0 µF , the current is initially a maximum.
How long will it take before the capacitor is fully
discharged for the first time :
(b) 14 x I0-4s
(a) 7 x 1Q-4s
(c) 28 x 10-4s
(d) none
Pre-emphasis in FM system is done to
(a) compress modulating signal
(b) expand modulating signal
(c) amplify lower frequency component of the
modulating signal
(d) amplify higher frequency component of the
modulating signal
lWWW.JEEBOOKS.INI
15
MOCKTESf-2
24.
25.
A body of mass m moving with velocity 3 km/h
collides with a body of mass 2 mat rest. Now the
coalesced mass starts to move with a velocity
(a) lkm/h
(b) 2km/h
(c) 3 km/h
(d) 4km/h
The horizontal component ofthe earth 's magnetic
30.
perpendicular magnetic field
26.
2.8xl0-4tesla
(b)
2.1 x 10-4 tesla
(c)
7.2xl0- 5 tesla
(d)
3.6 x 10-5 tesla
If
A =4i+6] and B =2i+ 3].Then
(c)
(d)
A .B
(b)
- - =-
(c)
A xB
(a)
33.
In the Rutherford experiment, a -particles are
scattered from a nucleus as shown. Out of the
four paths, which path is not possible?
~
(c) C
28.
34.
~
by the equations y 1 = 0.1 sin ( 1001tt + ~) and
= 0.1
cos 7tt. The phase difference of the
velocity of particle I with respect to the velocity
ofparticle 2 is
(a)
29.
~
3
(b)
-n
6
(c)
~
6
(d)
-n
3
The wavefronts of a light wave travelling in
vacuum are given by x + y + z = c. The angle
made by the direction of propagation of light
with the X-axis is
(b) 45°
(a) (J'
(d) cos- 1(1/ ✓
3)
(c) <xf'
I/ /
- ·-
-3 N
(b) -30N (c)
3N
(d) 30N
A charged particle q is placed at the centre O of
cube of length L (A B CD EFG H). Another
same charge q is placed at a distance L from 0.
Then the electric flux through ABCD is
(b) zero
(d) A
Two simple harmonic motions are represented
y2
xi'i
(a) q /4n e 0 L
~
(b) B
.,
/X
/
32.
IA I
(a) D
X
/
in the position ofminimum deviation, it produces
a deviation of30°. The angle ofincidence is
(b) 45°
(c) 15°
(d) (:Jf
(a) 300
An object ofmass 10 kg moves at a constant speed
of 10 ms-1• A constant force, that acts for 4 sec on
the object, gives it a speed of 2 ms-1 in opposite
direction. The force acting on the object is
(d) angle between A and B is 30°
27.
5 ✓
2Ba2
10Ba2 wsinwt
/
A prism has a refracting angle of600. When placed
0
IB I 2
-=-
_ _xS
31.
= 29
(a)
B. It has 10 turns.
The emf induced is
(a) B a 2 w sin wt
(b) B a2 w cos wt
field is 3.6 x 10-5 tesla where the dip angle is 60°.
The magnitude of the earth's magnetic field is
(a)
A square loop of side a is rotating about its
diagonal with angular velocity w in a
35.
(c) q/2 n e 0 L
(d) q/3ne 0 L
Spherical wavefronts, emanating from a point
source, strike a plane reflecting surface. What
will happen to these wave fronts, immediately
after reflection?
(a) They will remain spherical with the same
curvature, both in magnitude and sign.
(b) They will become plane wave fronts.
(c) They will remain spherical, with the same
curvature, but sign of curvature reversed.
(d) They will remain spherical, but with
different curvature, both in magnitude
and sign.
Of the two eggs which have identical sizes,
shapes and weights, one is raw, and other is half
boiled. The ratio between the moment ofinertia
of the raw to the half boiled egg about central
axis is
(b) greater than one
(a) one
(d) not comparable
(c) less than one
IWWW.JEEBOOKS.INI
16
36.
37.
TargetMHT-CET
A current carrying conductor placed in a
magnetic field experiences maximum force when
angle between current and magnetic field is
(a) 3ro'4 (b) rr/2
(c) n/4
(d) zero
In a photoelectric effect measurement, the
stopping potential for a given metal is found to
be VO volt when radiation of wavelength "-o is
used. Ifradiation ofwavelength 2 "-o is used with
the same metal then the stopping potential (in
volt) will be
(a)
38.
(a) 6.0 µF
(b) 4.0 µF
43.
4.~
a
3.0
6.0
-0
(d) 3.0 µF
A capillary tube is immersed vertically in water
and the height of the water column is x. When
this arrangement is taken into a mine of depth d,
the height of the water column is y. If R is the
44.
X
radius of earth, the ratio - is:
y
(1-!)
(b)
(1-:)
45.
(c)
40.
41.
( ~::)
✓
2
(d)
2R
c-v
c✓
2
A spherical ball of iron of radius 2 mm is falling
through a column of glycerine. If densities of
glycerine and iron are respectively 1.3 x 1o3 kgtm3
and 8 x 103 kgtm3. ri for glycerine
= 0.83 Nm-2 sec, then the terminal velocity is
(a) 0. 7 mis
(b) 0.07 mis
(c) 0.007 mis
(d) 0.0007 mis
A potentiometer wire oflength Land a resistance
rare connected in series with a battery of e.m.f.
E0 and a resistance r 1. An unknown e.m.f. E is
balanced at a length l of the potentiometer wire.
The e.m.f. E will be given by:
E0r
~
2.0
(a)
(c)
)
(
b
(c) 2.0 µF
39.
(b)
✓2 ( c+v)
(c+ v)
he
he
(c)v0 + - (d) Yo--2e1c0
2eA 0
The equivalent capacitance between a and b for
the combination of capacitors shown in figure
where all capacitances are in microfarad is
1.0
D•······Qs
( c+v)
c-v
(d)
42.
(b) 2V0
~o
(a)
( ~:: )
The resistance of an ammeter is 13 Q and its
scale is graduated for a current upto 100 amps.
After an additional shunt has been connected to
this ammeter it becomes possible to measure
currents upto 750 amperes by this meter. The
value of shunt-resistance is
(a) 2Q (b) 0.2n (c) 2kQ (d) 20Q
A whistle S of frequency f revolves in a circle of
radius Rat a constant speed v. What is the ratio
of largest and smallest frequency detected by a
detector D at rest at a distance 2R from the centre
of circle as shown in figure ?
(take c as speed of sound)
46.
l
(a) (r+r1)°L
(b)
(c)
(d)
E0 l
L
LE0 r
Two vibrating tuning forks producing waves
given by
y 1 = 27 sin 6007tt and y2 = 27 sin 604 7tt are held
near the ear of a person, how many beats will be
heard in three seconds by him ?
(a) 4
(b) 2
(c) 6
(d) 12
Two bodies of masses 4 kg and 9 kg are
separated by a distance of 60 cm. A 1 kg mass
is placed in between these two masses. If the
net force on I kg is zero, then its distance from
4 kg mass is
(a) 26cm (b) 30cm (c) 28cm (d) 24cm
The diagram below shows a junction with
currents labeled 11 to 16 . Which of the following
statements is correct?
(a) 11 + J3 = 16 + 14
(b) 11 + I2 = I6+ I4
(c) 14 + 13 = 16
(d) 12 = 16 + 14
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17
MOCKTEST-2
47.
48.
When a 8 kg mass is hung vertically on a light
spring that obeys Hooke' s law, the spring
stretches by 4 cm. The work required to be done
by an external agent in stretching this spring by
8 cm will be(g= 9.8 m/sec2)
(a) 4.2 joule
(b) 6.2 joule
(c) 5.2 joule
(d) 3.2joule
A shell of mass Mand radius R has a point mass
m placed at a distance r from its centre. The graph
ofgravitational potential energy U(r) vs distance
rwill be
52.
(b) cflsp 3 in case of strong field ligand
53.
54.
55.
U (r)
49.
U (r)
Which set of following characteristics for ZnS
crystal is correct?
Coordination number (4: 4); eep ; Zn 2+ ion
in the alternate tetrahedral voids
(a)
GivenV =40V
Source' V = V0 sin (100nt+~)
'
R
6 .
(b) Coordination number (6: 6); hep ; Zn2+ ion
in all tetrahedral voids.
(c)
Peak value of current in the circuit is
(a)
10✓
2A
(b)
15✓
2A
(c) 20✓
2A
(d) 25✓
2A
A film of water is formed between two straight
parallel wires oflength 10 cm each separated by
0.5 cm. If their separation is increased by I mm
while still maintaining their parallelism, how much
work will have to be done? (Surface tension of
water=7.2 x 10-2 N/m)
(a) 7.22 x 10----6 J
(b) 1.44 x 10- 5 J
(c) 2.88 x 10-5 J
(d) 5.76 x 10- 5 J
56.
l % HgSO4
A
The correct order of decreasing polarisability of
following ions is
(a)
57.
The end product (C) in the following sequence of
reactions is
HCeeCH
Coordination number (6: 4); hep; Zn2+ ion
in all octahedral voids
(d) Coordination number (4: 4); eep; Zn2+ ion
in all tetrahedral voids.
CHEMISTRY
51.
(c) cflsp 3 always
(d) sp3cf2 always
Collision theory is applicable to
(a) first order reactions
(b) zero order reactions
(c) bimolecular reactions
(d) intra-molecular reactions
Which one of these is not compatible with
arenes?
(a) Greater stability
(b) Delocalisation of re-electrons
(c) Electrophilic additions
(d) Resonance
In an L-C-R series circuit connected to an AC
V L = 40V and V c = 1ov. Resistance R = 4n.
SO.
(a) acetic acid
(b) isopropyl alcohol
(c) acetone
(d) ethanol
Octahedral complex of Cr(III) will be
(a) sp3cf2 in case of weak field ligand
B
20% H2SO4
58.
Cl- , Br-, I- , F-
(b)
F-,1-,Br- , C1-
(c) F- , c1- , Br-, 1(d) 1- , Br- , c1-, FFor a first order reaction, A ➔ products the
concentration of A changes from 0.1 M to 0.025
Min 40 minutes.
The rate ofreaction when the concentration ofA
is0.0lMis:
(a) 1.73 X 10-5 M/min
(b) 3.47 x lo-4M/min
(c) 3.47 X 10-5 M/min
(d) 1.73 x lo-4 M/min
One litre oxygen gas at S.T.P will weigh
(a)
1.43g
(b) 2.24g
(c)
11.2g
(d) 22.4g
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18
59.
60.
TargetMHT-CET
Which of the following is not the property of
natural rubber?
(a) Low tensile strength
(b) High water absorption capacity
(c) Soft and sticky
(d) High elasticity
Which of the following will not give iodoform
test?
(a) Isopropyl alcohol
67.
A graph was plotted between molar conductivity
of various electrolytes (NaCl, HCl and NH4 OH)
and ✓
c (in mo! L- I) . Correct set is :
(b) Ethanol
✓
c
(c) Ethanal
(a)
(b)
(c)
(d)
(d) Benzyl alcohol
61.
62.
63.
A deep brown gas is formed by mixing two
colourless gases which are
(a) NO2 and 0 2
(b) NzOandNO
(c) NOandO2
(d) Nif:iandHCl
18 g of glucose (C6H 1zOJ is added to 178.2 g of
water. The vapour pressure of water for this
aqueous solution is
(a) 76.00torr
(b) 752.40torr
(c) 759.00torr
(d) 7.60torr
16 g of oxygen and 3 g of hydrogen are mixed
and kept at 760 mm of Hg pressure and 0° C. The
total volume occupied by the mixture will be nearly
(a) 22.4 litres
64.
68.
69.
(b) Ii
(d) Water gas
Metals like Pt and Pd can adsorb large volume of
hydrogen under specific conditions. Such
adsorbed hydrogen by the metal is known as
(a)
occluded hydrogen
(b) absorbed hydrogen
(c)
reactive hydrogen
(d) atomic hydrogen
(b) 33.6 litres
70.
(c) 448 litres
(d) 44800mL
An organic amino compound reacts with aqueous
k
In -
(b)
X
k
-
X
(c) C~CHzNHCHzC~
(d) (C~CHz)3N
72.
Chemical formula for iron (III) hexacyanoferrate
(II) is
FeiFe(CN)J
Fe4 [Fe(CN)J 3
hydrogen is most
Methane
Ethylene
73.
(c)
k+x (d)
k
At anode in the electrolysis of fused NaCl
(a) Na+ isoxidized
(b) C~CHzNHz
(a) Fe[Fe(CN)J
(b)
(c) Fe3 [Fe(CN)J4
(d)
In which of the following
acidic?
(a) Acetylene
(b)
(c) Ethane
(d)
If concentration ofreactants is increased by 'x',
then k becomes
(a)
71.
(a) C~Nttz
66.
In the metallurgy of zinc, the reducing agent
employed in reducing the zinc oxide to crude
zinc metal in the last stage is
(a) Al
(c) Coke
nitrous acid at low temperature to produce an
oilynitrosoamine. The compound is
65.
I (NaCl), II (HCI), ill, (NHpH)
I (HCI), II (NaCl), ill, (NHpH)
I (NHpH), II (NaCl), ill, (HCl)
I (NHpH), II (HCI), m, (NaCl)
(b) c1-isoxidized
(c) C l is reduced
(d) Na is reduced
The correct decreasing order of priority of
functional groups is
(a) - SO 3H, - OH, - COCI, ~C = C~
(b) - COOH, - SO3H, - COOR, - OH
(c) - C = C, - NHz, - OH, ~C= 0
(d) - CN, - CONHz, ~C = 0, - OH
The main element ofsmog is
(a)
0 3 and PAN
(b) 0 3
(c)
PAN
(d) PPNandPBN
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MOCKTESf-2
74.
19
Which of the following monosaccharide is a
pentose ?
(a)
Galactose
(c) Fructose
75.
76.
78.
NiCii-
(Z of Ti= 22, Co= 27, Cu = 29, Ni = 28), the
colourless species are:
(d) Arabinose
(a)
Cu2Cl2 and NiCli-
(b)
TiFJ- and CtliC12
(c)
CoFJ- and NiCii-
(d)
TiFJ- and CoFJ-
Which group contains coloured ions out of
2. Ti 4+
Out of TiFJ- , CoFJ-, Cu 2Cl 2 and
(b) Glucose
1-Chlorobutane on reaction with alcoholic potash
gives
(a) 1-butene
(b) 1-butanol
(c) 2-butene
(d) 2-butanol
1. Cu 2+
77.
81.
3. Co 2+
(a)
1,2, 3,4
(b)
(c)
2,3
(d) 1, 2
4. Fe 2+
82.
1, 3, 4
In a solid lattice the cation has left a lattice site
and is located at an interstitial position, the lattice
defect is :
(a) Interstitial defect (b) Valency defect
(c) Frenkel defect
(d) Schottky defect
The IUPAC name ofthe compound shown below
is:
83.
Equal moles ofwater and urea are taken in a flask.
What is mass percentage ofurea in the solution ?
(a) 7.692%
(b) 769.2%
(c) 76.92%
(d) 0.7692%
Surface tension oflyophilic sols is
(b)
Hi0.
more than that of Hi0.
(c)
equal to that ofHiO.
(a)
lower than that of
HiO
depending
(d) either less or more than
upon the nature of disperse phase.
84.
The reaction ofKMnO4 and HCI results in
(a)
oxidation of Mn in KMnO4 and production
ofCI2
(b) reduction of Mn in KMnO4 and production
ofHi
(a)
3-bromo-1-chlorocyclohexene
(b)
l-bromo-3-chlorocyclohexene
(c)
(d) reduction of Mn in KMnO4 and production
ofCI2
(c) 2-bromo-6-chlorocyclohex-l-ene
(d) 6-bromo-2-chlorocyclohexene
79.
Phosphine is not obtained by which of the
following reaction
(a)
80.
oxidation ofMn in KMn O 4 and production
ofHi
85.
White Pis heated with NaOH
Chlorination of toluene in the presence of light
and heat followed by treatment with aqueous
NaOHgives
(a)
o-Cresol
(b) RedP is heated with NaOH
(b) p-Cresol
(c) Ca3P 2 reacts with water
(c)
(d) Phosphorus trioxide is boiled with water
(d) Benzoic acid
A drug that is antipyretic as well as analgesic is
(a) chloropromazine hydrochloride
(b) para- acetamidophenol
(c)
chloroquin
(d) penicillin
86.
2,4-Dihydroxytoluene
Consider the following complex
[Co~) 5CO3 ]ClO4 _The coordination number,
oxidation number, number of d-electrons and
number of unpaired d-electrons on the metal
are respectively
6, 3, 6,0
(b) 7, 2, 7, 1
(c) 7, 1, 6,4
(d) 6, 2, 7,3
(a)
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87. In the diazotization ofarylamines with sodium
COOH
nitrite and hydrochloric acid, an excess of
hydrochloric acid is used primarily to
(a) supress the concentration of free aniline
available for coupling.
(b) supress hydrolysis of phenol.
(c) ensure a stoichiometric amount of nitrous
acid.
(d) neutralise the base liberated.
@ @
(,)@ (d)@
(a)
OH
88. Which ore contains both iron and copper?
(a) Cuprite
(c) Chalcopyrite
89.
(b) Chalcocite
(d) Malachite
93.
According to Le-Chatelier 's principle, adding
heatto a solid
~
Alum helps in purifying water by
(a) forming Si complex with clay particles.
(c)
(a) temperature to increase
Consider the following statements for condensation
polymerization -
I.
Bifunctional orpolyfunctional monomers
(a)
II.
Loss of each kind of functional group in
each step for bifunctional species
(c) amount ofliquid to decrease
94.
(d) amount of solid to decrease.
Monofunctional or polyfunctional monomers
(b) AzB
(c)
A 4B 3 (d)
96.
Which one of the following reaction occurs at
the cathode?
Which of the following are true?
(a) I and II
(b) I, II and III
(a)
20H-~H 2 0 + 0+2e-
(c)
(d) ill and IV
(b)
Ag~Ag+ + e-
(c)
Fe 2+ ~ F e 3+ +e-
(d)
Cu 2+ + 2e- ~ C u
I and III
Aldehydes and ketones are distinguished by
which of the following test?
(a) Lucas test
(b) Tollen 's test
(c) KMn04 solution (Baeyer's test)
(d) None of these
' Z' in the following sequence ofreactions is
W _ Z_n_/_H_
C_IX
97.
Lead pipes are not suitable for drinking water
because
(a) a layer of lead dioxide is deposited over
pipes
(b) lead reacts with air to form litharge
(c)
lead reacts with water containing air to form
Pb(OH)2
(d)
lead forms basic lead carbonate
NaN0 2 ) y
HCI
A 3B 4
Among the following actinide pairs, the maximum
oxidation states is shown by
(b) Np and Pu
(a) U and Np
(c) PuandAm
(d) UandPa
byproduct molecule
N.
AB 2
95.
III. Always accompanied by the release of a
92.
aluminium which coagulates the mud
particiles.
(d) making mud water soluble.
In a solid 'AB' having the NaCl structure, ' A'
atoms occupy the corners of the cubic unit cell.
If all the face-centered atoms along one of the
axes are removed, then the resultant stoichiometry
of the solid is
(b) temperature to decrease
91.
NHz
(b) sulphate part which combines with the dirt
and removes it.
liquid equilibrium will cause
the
90.
(b)
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MOCKTEST-2
98.
21
Imino acid among these compounds is
(a) serine
99.
(c) tyrosine
(d) lysine
What is the structure of the major product when
phenol is treated with bromine water?
OH
Br~
(a)
¢
(b) proline
y
0
Br
Bry y Br
½J_
(b)
Br
H
(c)
OH
(d)
& "'
Br
100. The presence or absence of hydroxyl group on
which carbon atom of sugar differentiates RNA
and DNA?
(d) 4th
(a) pt
(c) 3rc1
(b) 2nct
Br
SECTION-B
MATHEMATICS
1.
In a class ofl00 students, 55 students have passed
in mathematics and 67 students have passed in
physics. Then the number of students who have
passed in physics only is
(a)
2.
4.
(b) 33
(c)
10
(a) 0 for all x ER
(b)
2x for all x E R
2x,forx ;::: 0
(d)
{O, forx;::: 0
2x, forx < 0
{ 0, forx<0
7.
Let A= {x, y, z} and B = {a, b, c, d}. Then,
which one of the following is not a relation
from A to B?
(a)
{(x, a), (x, c)}
(b)
{(y, c), (y, d)}
(c)
{(z, a), (z, d)}
(d)
{(z,b),(y,b), (a,d)}
5.
(b) 2
(c)
3
8.
(b)
m 2 -m(4r+ 1)+4r + 2 = 0
2
2
Two tangents PQ and PR drawn to the circle
(a)
75 sq. unit
(b) 73 sq. unit
(c)
72 sq. unit
(d) 74 sq. unit
Two dice are thrown together. Then the
probability, that the sum of numbers appearing
on them is a prime number, is
7
12
18
(b)
13
(c)
36
(d)
11
36
If z and ro are two non-zero complex numbers
(a) -i
yr
m 2 -m(4r-1) + 4r 2 -2 = 0
2
such that lzrol=I and Arg(z )-Arg(ro) = ~,
2
then zro is equal to
(d) 4
Ifthe coefficients of rth, (r + !)th, and (r + 2)th
terms in the the binomial expansion of (1 +
are in A.P. , then m and r satisfy the equation
(a)
m -m(4r-1) + 4r + 2=0
5
sin 2 A+ sin 2 B + sin 2 C-2cosAcos BcosC =
I
(d)
(a)
A, B, C are the angles of a triangle, then
(a)
m 2 -m(4r+ 1)+4r2 -2 = 0
x2 +y-2x-4y-20 = 0frompointP(l6, 7). Ifthe
centre of the circle is C then the area of
quadrilateral PQCR is
(d) 45
Iff(x) =x and g(x) =Ix I, then (f+ g) (x) is equal to
(c)
3.
22
6.
(c)
9.
2
I
(b)
2
I
(c)
-1
(d)
1.
2a
If- + -+-=-,where a, b EN, then
9! 3!7! 5!5! b!
the ordered pair (a, b) is
(a)
(9, 10) (b) (10, 9)(c) (7, 10) (d) (10, 7)
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10.
Ifthe third term in the expansion of [x + xlog10 x ]5
is 106, thenxmaybe
(a)
11.
(b)
✓
10
(c)
10
(d) 10-21s
Find the equation of set points P such that
PA 2 + PB2 = 2K2 , where A and B are the points
(3, 4, 5) and (-1, 3, -7), respectively:
(a)
12.
1
(a)
K2 -109
(b)
2K 2 -109
(d)
4K 2 - 10
(c)
17.
13.
-
e
(d) None of these
19.
(a) p and q both are true
(c) pis false and q is true
Let f : [4, oo) ➔ [1, oo) be a function defined by
20.
f(x) = 5x(x- 4) , then f-l (x) is
(a)
2-.j4+log 5 x
(b)
(C)
_ Jx(x-4)
( 51
(d) None of these
2+.j4+1og 5 x
cor- 1 2 + cor-1 8 + cor-1 18 + cor- 1 32 + .... is
(c)
n:
4
(b)
b
C
bx+c
ax+b
bx+c
0
=O,
(b) GP.
(d) None of the above
1
the function f[ f {flx)}] are
(b) {0,1}
(a) {0,-1}
(c) {1,-1}
(d) None of these
The area enclosed between the curves y = ax2
and x = ay2 (a > 0) is 1 sq. unit, then the value of
n:
2
21.
1
✓
3
(b)
2
(c)
(d)
3
f cosx-smx
is equal to
dx .
(a)
3
~log[tan(1+ ;)[+c
(b)
~ log[cot(i)[ + C
(c)
3
~Iog[tan(~- ;)[+c
(d)
~ log[tan(i-f)[+c
The sum of the infinite series
(a) n:
(ax+b) / x
Iff{x) = l-x ,thenthepointsofdiscontinuityof
(a)
(d) None of these
15.
b
a lS
(b) p and q both are false
14.
a
1
Ifp and q are two statement then (p B ~q) is true
when-
~l
(d) None of these
(a) A.P.
(c) H.P.
18.
(c)
00
then a , b, care in :
x ➔O
(b)
[(11~)1
(b)
Ifthedeterminant
~=
Jim (cosecx) 111ogx is equal to:
(a) 0
~J
Us ~J
Go
dn
-(log x) =
dxn
(n-1)!
(d) None of these
(a)
(n-2)!
(c)
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MOCKTEST-2
22.
Let
23
ABCD
be
If
parallelogram.
a
The dice is tossed and it is told that either the
face I or face 2 h as s hown up, t hen the
probability that it is face 1, is
AB=i+3}+7k, AD =2i+3}+ -5k and p
is a unit vector parallel to AC, then jJ is equal
(a)
to
1
-(2i + j +2k)
3
1
-(3i + 6} + 2k)
7
A
(a)
A
A
(c)
23.
A
•
I
•
•
•
(b)
-(2i-2j+k)
3
(d)
-(6i + 2} + 3k)
7
I
•
•
The two linesx = ay + b , z = cy + d andx = a'y+ b',
z = c'y + d' will be perpendicular, ifand only if
29.
30.
(d) (a + a')(b + b') +(c + c ') = 0.
5
(d)
21
f[x 2 ]dx is
(a)
2- ✓
2
2
(b) 2+ ✓
(c)
✓
2 -I
(d)
If O ~ x
~
· 2
1t and 8 Ist0
x
-✓
2- ✓
3 +5
+ 8 lcos
2
x
= 30, then x=
(a) 1t ! 6 (b) 1t /2 (c) 1t / 4 (d) 31t / 4
Ifx = I + a+a2 + .................... toinfinity and
y= 1 +b+ b2 + ................... to infinity, wherea, b
are proper fractions, then 1 +ab+ a 2b2 + .....to
infinity is equa l :
The equation of the tangent to the curve
(a)
y = e-lxl at the point where the curve cuts the
linex = 1 is
(a)
(b)
xy
x+ y- 1
31.
(d) None of these
(d)
xy
xy
~-y+l
x+y+ I
The slopes of the lines which mal<e an angle 45°
with the line 3x -y = -5 are
Maximiz.eZ=4x+ 6y,subjectto3x+2y~ 12,x+y~4,
(a)
x, y~ 0, is
(a)
16at(4,0)
(b) 24 at (0, 4)
(c)
24 at (6, 0)
(d) 36 at (0, 6)
32.
given by dy _ 2'..+
Sx
= 0 if thepoint
dx x (x +2)(x-3)
33.
(5, a) lies on the curve, then the value of a is
(c)
67
(b) 5 sin
12
5 log
7
ii
34.
7
ii
(d) None of these
For a biased dice, the probability for the different
faces to turn up are
Face
1
p
0.10
IfP
1,-1
(b)
1
2
, -1 (c)
1,
1
2
(d)
-2,
I
2
= (x,y), F 1 = (3, 0), F 2 = (-3, 0) and
l 6x2 +
The gradient ofthe curve passing through (4, 0) is
(a)
xy
x - y -1
(c)
(b) y+ex = I
e(x+y)= 1
(c) y+x=e
27.
10
16
2
28.
(c) aa' + bb' +cc'= 0
26.
21
5
(c)
A
(b) aa' + bb' + cc' + 1 = 0
25.
(b)
0
•
(a) aa' +cc' + 1 = 0
24.
16
-
35.
2
3
4
5
6
0.32
0.21
0.15
0.05
0.17
25y2 = 400, then PF1 +PF2 equals
(b) 6
(d) 12
(a) 8
(c) 10
Product ofreal roots ofthe equation i1-x2+ lxl +9 = 0
(a) is always positive (b) is always negative
(c) does not exist
(d) None of these
7- z
, where z = 1 + 2i, then 1/(z)I is
Ifj(z) = - 1-z 2
equal to :
(a)
El
(c)
21 z l
2
(b)
12 1
(d) None of these
(r·
The solution set of the inequality 5•+2 > ;
(a)
(- 2, 0)
(b)
(-2, 2)
(c)
(-5, 5)
(d)
(0, oo)
5
is
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36.
3 7.
The number of ways in which first, second and
third prizes can be given to 5 competitors is
(b) ffi
(c) 15
(d) 125
(a) 10
The number ofdissimilar terms in the expansion
of(a + b)0 is n + 1, therefore number ofdissimilar
terms in the expansion of (a + b + c) 12 is
(a)
38.
If
13
(b) 39
(c)
78
(d) 91
y=(1+~)(1+~)(1+~}---{1+~) and
(a)
44.
40.
(b)
82
1
2
(c)
50
Iff(x) = sinx + cosx,g(x) = x
is invertible in the domain
2
(d) 80
-
(l+x)ex
I, theng(f(x))
(a)
loglcos(xex )I + C (b)
loglcot(xex)I + C
(c)
loglsec(xe-x)l + c (d)
loglsec(xex)l+ c
If (a x E)2 + (a.b) 2 = 676 and I b I= 2 then I ii I
is equal to
(a) 13
(b) 26
(c) 39
(d) None of these
46. The area enclosed between the curves y 2 = x and
y=lxlis
(a) 1/6
(b) 1/3 (c) 2/3
(d) 1
47. A coin is tossed 7 times. The probability that at
least 4 consecutive heads appear is
45.
3
48.
(d) [0,1t]
ThematrixA =
[-! -:
I
(a)
43.
is
49.
2 -I
(d) None of these
Consider the system of equations :
x + ay=0, y+az = 0and z+ax = 0. Thentheset
ofall real values of 'a' for which the system has
a unique solution is:
(a) R- {1}
(b) R-{-1}
(c) {1,-1}
(d) {I, 0, -1}
If Y =
(a-x)~-(b- x ) ~
.Ja-x +.Jx-b
wherever it is defined is
dy
then dx
16
(b)
5
32
· 2 X )e- 2sin
f( X ) = (Sill
(c)
2
X
3
32
(d)
I
8
· j(X ) =
; max. j(X ) -mm.
1
1
2e - ~
(a)
1
e2
(b)
(c)
1
(d) Noneofthese
.
dy ex(sin 2 x+sin2x) .
The solut10n of dx = y( 2 logy+ l)
1s
(a) y(logy)- ~ sin 2 x + c = 0
(b) y(logy)- ~ cos2 x+c = 0
(c) y2 (logy) +~ cos2 x+ c= 0
(d) None of these
idempotent matrix (b) involutory matrix
(c) nilpotent matrix
42.
~i
2x + (a +b)
2.J(a- x )(x-b)
.
1s equal to
f cot(xex) dx
(a)
41.
2x-a-b
2.Ja-x.Jx-b
x* O,
(a) n!
(b) (n-1)!
(c) (-l?(n-1)!
(d) (-1? n!
Mean of 100 items is 49. It was discovered that
three items which should have been 60, 70, 80
were wrongly read as 40, 20, 50 respectively. The
correct mean is
(a) 48
(b)
(a+b)
2.J(a-x)(x-b) (d)
(c)
dy
then dx whenx =-1 is
39.
x +(a+b)
.J(a-x)(x-b)
7t
50.
fxf(sin x)dx is equal to
0
7t
(a)
7t
1tf f(cosx)dx
(b)
1tf f(sinx)dx
0
0
1t/ 2
1t/2
(c)
ff f(sinx)dx
0
(d)
7t
f f(cos x)dx
0
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Mock Test-[@]
General Instructions
■
■
■
■
■
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This question booklet contains 150 Multiple Choice Questions (MCQs).
Section-A: Physics & Chemistry - 50 Questions each and
Section-B: Mathematics - 50 Questions.
Choice and sequence for attempting questions will be as per the convenience of the candidate.
Read each question carefully.
Determine the one correct answer out of the four available options given for each question.
Each question with correct response shall be awarded one (1) mark. There shall be no negative marking.
No mark shall be granted for marking two or more answers ofsame question, scratching or overwriting.
Duration ofpaper is 3 Hours.
SECTION-A
1.
2.
Which of the following relationship between the
acceleration and displacement x of a particle
involve SHM?
(a) a = 2x
(b) a =4x2
(c) a=-5x
(d) a=-3x2
What will be the maximum speed of a car on a
road turn ofradius 30 m ifthe coefficient offriction
between the tyres and the road is 0.4 (Take g
=9.8m/s2)
(a) 10.84 mis
(c) 8.84m/s
3.
4.
(a)
5.
1
-10
4
6.
84
(c) 10
If the electric flux entering and leaving a closed
surface are 6 x 106 and 9 x 106 respectively, then
the charge inside the surface of permittivity of
free space i;0 is
25
(c)
9
3 µF
3 µF
(d)
7.
8.
1
-lo
2
(d) zero
(b)
3 µF
(d) 6.84m/s
(b)
The equivalent capacitance between A and B is
(in µF)
(a) 25
(b) 9.84m/s
When a body undergoes a linear tensile strain it
experiences a lateral contraction also. The ratio
of lateral contraction to longitudinal strain is
known as
(a) Young's modulus (b) Bulk modulus
(d) Hooke's law
(c) Poisson's ratio
When an unpolarized light of intensity 10 is
incident on a polarizing sheet, the intensity of
the light which does not get transmitted is
(b) -EO X 106
(d) 3i;0 x 106
(a) i;0 x 106
(c) -2i;0 x 106
PHYSICS
9.
A voltmeter essentially consists of
(a) a high resistance, in series with a galvanometer
(b) a low resistance, in series with a galvanometer
(c) a high resistance in parallel with a galvanometer
(d) a lowresistance in parallel with a galvanometer
A nucleus splits into two nuclear parts which
have their velocity ratio equal to 5 : 1. What will
be the ratio of their nuclear radius?
(a) 5113:l(b) 1:51/3 (c) 3112:l(d) 1:3112
In a stream line (laminar flow) the velocity of
flow at any point in the liquid
(a) does not vary with time
(b) may vary in direction but not in magnitude
(c) may vary in magnitude but not in direction
(d) may vary both in magnitude and direction
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TargetMHT-CET
26
10.
11.
When two quantities are divided, the relative
error in the result is given by
(a) the product of the relative error in the
individual quantities
(b) the quotient of the relative error in the
individual quantities
(c) the difference of the relative error in the
individual quantities
(d) the sum of the relative error in the individual
quantities
e
13.
(a) 45°
(b) 30"
(c) 90"
(d) fff'
In semiconductors, at room temperature
(a) the conduction band is completely empty
(b) the valence band is partially empty and the
conduction band is partially filled
(c) the valence band is completely filled and
the conduction band is partially filled
(d) the valence band is completely filled
For an AM wave, the maximum voltage was found
to be 10 V and minimum voltage was 4 V. The
modulation index of the wave is
(a) 0.33
14.
17.
A and B are two vectors and 0 is the angle
3(A .B), the value
between them, if I A x B I= ✓
of is
12.
16.
(b) 0.43
(c)
0.56
18.
19.
(d) 0.64
The four wires from a larger circuit intersect at
junction A as shown. What is the magnitude and
direction of the current between points A and B?
20.
(a) 2 A from A toB
(b) 2A from B to A
Two coaxial solenoids are made by winding thin
insulated wire over a pipe of cross-sectional area
A = IO cm2 and length = 20 cm. If one of the
solenoid has 300 turns and the other 400 turns,
their mutual inductance is
(µ 0 =4rc x 10-7 TmA-1)
(a) 2.4rcxI0- 5 H
(b) 4.8rc x lo-4H
(c) 4.8n x J0-5 H
(d) 2.4n x Jo-4 H
An organ pipe open at one end is vibrating in
first overtone and is in resonance with another
pipe open at both ends and vibrating in third
harmonic. The ratio oflength of two pipes is
(a) 1:2 (b) 4:1 (c) 8:3 (d) 3 : 8
The angular velocity of the earth with which it
has to rotate so that acceleration due to gravity
on 60° latitude becomes zero is (Radius of earth
= 6400 km, at the poles g = 10 ms-2)
(a) 2.5 x 10-3 rad/s
(b) 5.0 x 10-1 rad/s
(c) 10 x 10 1 rad/s
In the figure is shown
(d) 7.8 x 10-2 rad/s
~
J
fc
Young 's double slit
· ~ Fi --·· _
experiment. Q is the
~~~
c
position of the first
s1t ~
......_ ,.
bri~ht fringe on the right side of 0 , Pis the
11 fringe on the other side, as measured from
Q. If the wavelength of the light used is 6000 x
10-10 m , then S 1B will be equal to
(a) 6 x lo-6m
(b) 6.6xlo-6m
(c) 3.138 x 10-7 m
(d) 3.144 x 10-7 m
Figure consists of two NOT gates followed by a
NOR gate. This combination is equivalent to a
single
B
(c) 3A from A to B
6A
(d) 2A from B to A
15.
Two identical particles are located at -; and
y
with reference to the origin of three dimensional
co-ordinate system. The position vector of centre
of mass of the system is given by
➔
(a)
➔
➔
x- y
(b)
➔
x+ y
2
➔
(c)
➔
➔
(x- y)
(d)
21.
➔
x- y
2
22.
(a) NAND gate
(b) AND gate
(c) ORgate
(d) XORgate
A particle describe a horizontal circle ofradius
0.5 m with uniform speed. The centripetal force
acting is IO N. The work done in describing a
semicircle is
(c) 5 nJ (d) lOrcJ
(a) zero (b) 5 J
A current of5 ampere is flowing in a wire oflength
1.5 metres. A force of7.5 N acts on it when it is
placed in a uniform magnetic field of2 tesla. The
angle between the magnetic field and the direction
of the current is
(c) (ff'
(d) 90"
(b) 45°
(a) 30"
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MOCKTESf-3
23.
27
A particle describes uniform circular motion in
a circle of radius 2 m, with the angular speed
1
of2 rad s- • The magnitude of the change in its
1t
velocity in
24.
25.
2
s is
(a)
Oms-1
(b)
(c)
8ms-1
(d) 4m s-1
A I 00 turns coil of area of cross section 200 cm2
having 2 Q resistance is held perpendicular to a
magnetic field ofO. l T. Ifit is removed from the
magnetic field in one second, the induced charge
produced in it is
(a) 0.2C (b) 2C
(c) O.lC (d) IC
The adjoining figure shows graph of pressure
and volume of a gas at two tempertures T I and
T 2. Which of the following inferences is correct?
p
(d) None of these
26.
28.
~~
ION
(b) SN
(c)
32.
(c)
!SN
(d) 30N
In an experiment to measure the internal
resistance of a cell, by a potentiometer, it is found
that the balance point is ata length of2 m, when the
cell is shunted by a 5 Q resistance and is at a length
of3 m when the cell is shunted by a IO Q resistance.
The internal resistance ofthe cell is then
i
(a)
A machine gun has a mass 5 kg. It fires 50 gram
bullets at the rate of 30 bullets per minute at a
speed of 400 ms- 1• What force is required to keep
the gun in position?
(a)
27.
2✓
2ms- 1
The binding energy of deuteron is 2.2 MeV and
that of He is 28 MeV. Iftwo deuterons are fused
to form one iHe, then the energy released is
(a) 23.6MeV
(b) 19.2MeV
(c) 30.2MeV
(d) 25.8MeV
30. A glass slab ofthickness 4 cm contains the same
number of waves as 5 cm ofwater when both are
traversed by the same monochromatic light. If
the refractive index ofwater is 4/3, what is that of
glass?
(a) 5/3
(b) 5/4
(c) 16/ 15 (d) 1.5
31. Two concentric uniform
shells of mass M 1 and M 2 are
as shown in the figure. A
particle of mass m is located
just within the shell M2 on its
inner surface. Gravitational
force on 'm' due to M 1 and
M2 will be
29.
33.
34.
zero
(d) None of these
The ionization energy of hydrogen atom is
13.6 eV. Following Bohr's theory, the energy
corresponding to a transition between 3rd and
4th orbit is
(a) 3.40eV
(b) 1.51 eV
(c) 0.85eV
(d) 0.66eV
A 100 N force acts horizontally on a block of 10
kg placed on a horiz ontal rough surface of
coefficient of friction µ = 0.5. Ifthe acceleration
due to gravity (g) is taken as 10 ms- 2 , the
acceleration of the block (in ms- 2) is
(c) 5
(d) 7.5
(a) 2.5
(b) 10
In the circuit given below, what will be the reading
of the voltmeter?
(a) I.SQ (b) lOQ (c) 150 (d) 1 Q
For transmission of e .m .wave of audible
frequency, these waves are superimposed with
waves of
(a) frequency less than 20 Hz
(b) frequency less than 10 KHz.
(c) frequency in the audible range.
(d) radio-frequency.
100
200V, IOOHz
(a)
300V (b) 900V (c) 200V (d) 400V
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28
35.
If the moment of inertia ofa disc about an axis
tangential and parallel to its surface be I , then
what will be the moment ofinertia about the axis
tangential but perpendicular to the surface?
6
3
3
5
(b) -J
(c) - I (d) -J
5
4
2
4
A simple pendulum performs S.H.M. about x = 0
with an amplitude a, and time period T. The speed
of the pendulum at x = a/2 will be
(a)
36.
-J
a ✓3
(a)
42.
'TtT
43.
na ✓3
(b)
2T
na
(d)
T
A ring ofmass m and radius R has four particles
each of mass m attached to the ring as shown in
figure. The centre of ring has a speed v0 • The
kinetic energy of the system is
(c)
37.
(a)
(b)
3mv5
(c)
5mv02
(d)
6mv5
A bar magnet ofmagnetic moment M and length
Lis cut into two equal parts each oflength L/3.
The magnetic moment of each part will be
(b) M/4
(a) M
(c) ✓
2 M (d) M/3
39. Nickel shows ferromagnetic property at room
temperature. If the temperature is increased
beyond Curie temperature, then it will show
(a) anti ferromagnetism
(b) no magnetic property
(c) diamagnetism
(d) paramagnetism
40. Consider two hot bodies B I and B2 which have
temperatures 100°C and 80°C respectively at t = 0.
The temperature ofthe surroundings is 40°C. The
ratio of the respective rates of cooling R 1 and R 2
of these two bodies at t = 0 will be
(b) R 1 :R2 =5:4
(a) R 1 :R2 =3:2
(d) R 1 : R 2 = 4 : 5
(c) R 1 : R 2 = 2 : 3
41. Find the minimum thickness of a film which will
stronglyreflectthe light ofwavelength 598 nm. The
refractive index of the material ofthe film is 1.25.
(a) 118nm
(b) 120nm
(c) 218m
(d) 225mm
38.
Water rises in a capillary tube to a certain height
such that the upward force due to surface tension
is balanced by7.5 x lo-4N force due to the weight
of the liquid. If the surface tension of water is
6 x 10-2Nm- 1, the inner circumference of the
capillary tube must be
(a) 1.2s x 10-2m
(b) o.so x 10-2m
(c) 6.5 x 10-2m
(d) 12.5 x 10-2m
Figure shows three
oscillating LC circuit
with identical inductors
and capacitors. If t I' t2 ,
t3 are the time taken by
(I)
(IT!)
(II)
the circuits I, II, III for
fully discharge, then
(a)
t 1> t2> t3
t2< t 1< t3
(b) ti < t2 < t3
N2
(c)
(d) t3 =
Two sources P and Q produce notes offrequency
660 Hz each. A listener moves from P to Q with a
speed ofl ms- 1. If the speed of sound is 330 ml
s, then the number ofbeats heard by the listener
per second will be
(a) zero (b) 4
(c) 8
(d) 2
45. A liquid does not wet the sides of a solid, if the
angle of contact is
(a) Zero
(b) Obtuse (more than 90°)
(c) Acute (less than 90°)
(d) 90° (right angle)
46. A steel ring ofradius rand cross sectional area A
is fitted onto a wooden disc of radius R (R > r ). If
the Young's modulus of steel is Y, then the force
with which the steel ring is expanded is
(b) AY(R-r)/r
(a) AY(R/r)
(d) Yr/AR
(c) (Y/A)[(R-r)/r]
47. An ideal gas is initially at P 1, V1 is expanded to
P 2 , V2 and then compressed adiabatically to
the same volume V 1 and pressure P 3 • If Wis
the net work done by the gas in complete
process which of the following is true ?
(b) W< 0 ;P3 > P 1
(a) W> 0 ;P3 > P 1
(c) W> 0 ;P3 < P 1
(d) W< 0;P3 < P 1
48. A coaxial cable consists ofa thin inner conductor
fixed along the axis of a hollow outer conductor.
The two conductors carry equal currents in
opposites directions. Let B 1 and B 2 be the
magnetic fields in the region betweem the
conductors and outside the conductor,
respectively Then,
(a) B 1 ;,t 0, B2 ;,t 0
(b) B 1 = B2 = 0
(c) B 1 ;,t0, B2=0
(d) Bl =0,B2;,t0
44.
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29
MOCKTEST-3
49.
A drop of water is placed on a glass plate. A
double convex lens having radius of curvature
ofeach surface is 20 cm is placed on it. The focal
length of water is (µw = 4 / 3)
58.
i
) ; ~=
50.
(a) -20cm
(b) 60cm
(c) 20cm
(d) -60cm
A source oflight is placed at a distance of 50 cm
from a photocell and the stopping potential is
found to be V 0. If the distance between the light
source and photocell is made 25 cm, the new
stopping potential will be
(a) 2V0 (b) Vd2 (c) V0
(d) 4V0
CHEMISTRY
51.
52.
53.
54.
55.
56.
57.
Which one of the following complexes will most
likely absorb visible light?
(At nos. Sc =21, Ti = 22, V = 23, Zn = 30)
(a) [Sc(HiO)J 3+
(b) [Ti(NHJ6]4+
(c) [VCNI½)J 3+
(d) [Zn~)6]2+
Calcination is used in metallurgy for removal of
(a) moisture
(b) water and CO 2
(c) CO 2 and H 2 S
(d) H 2 OandH 2 S
If the rate of a gaseous reaction is independent
of pressure, the order ofreaction is:
(d) 3
(a) 0
(b) 1
(c) 2
Which amino acid is achiral?
(a) Alanine
(b) Valine
(c) Proline
(d) None of these
1-Phenylethanol can be prepared by reaction of
benzaldehyde with
(a) methyl bromide
(b) ethyl iodide and magnesium
(c) methyl bromide and aluminium bromide
(d) methyl iodide and magnesium
The acidic, basic or amphoteric nature ofMnp7,
V 20 5 and CrO are respectively
(a) acidic, acidic and basic
(b) basic, amphoteric and acidic
(c) acidic, amphoteric and basic
(d) acidic, basic and amphoteric
The number of P - 0 - P bonds in cyclic
metaphosphoric acid is
(a) zero (b) two (c) three (d) four
59.
60.
61.
62.
63.
In the electrochemical reaction
2Fe 3+ +Zn~Zn 2 + + 2Fe 2 + ,
on increasing the concentration ofFe2+
(a) increases cell emf
(b) increases the current flow
(c) decreases the cell emf
(d) alters the pH of the solution
The general formula Cn8in0 2 could be for open
chain
(a) carboxylic acids (b) diols
(c) dialdehydes
(d) diketones
In a cubic lattice A atom occupy all the corners.
If B atom occupy one of the opposite face, and
atom C occupy the remaining faces. The simplest
formulae of the compound is
(a) ABC3 (b) ABC2 (c) ABC (d) AB2C
Out of the following isomeric alcohols containing
five carbon atoms, the alcohol that exhibits optical
isomerism is
(a) 1-pentanol
(b) 2-pentanol
(c) 3-pentanol
(d) 2-methyl-2-butanol
Reaction of alkyl halides with aromatic
compounds in presence of anhydrous AICJ3 is
known as :
(a) Friedel Craft reaction
(b) Corey house synthesis
(c) Kolbe 's synthesis
(d) Beckmann rearrangement
The molar ionic conductances of the octahedral
complexes:
(I)
PtCI 4 .5NH 3
(Ill) PtCI 4 .3NH3
Follow the order
(a) I < II <III < IV
64.
65.
(1I)
PtCI4 .4NH3
(IV) PtCI 4 .2NH3
(b)
IV < IIl < II < I
(c) III < IV < II < I
(d) IV < IIl < l < II
Which one ofthe following binary liquid systems
shows positive deviation from Raoult's law?
(a) Benzen~toluene
(b) Carbon disulphide-acetone
(c) Phenol-aniline
(d) Chloroform-acetone
Calcium carbide when treated with water gives:
(a) ethylene
(b) methane
(c) acetylene
(d) ethane
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30
66.
TargetMHT-CET
The standard reduction potentials at 298K for the
following half reactions are given against each
73.
Ee
s c3+ / Sc2 +
2
Zn + (aq)+2e- ~ Zn(s);--0.762V
70.
(a) Zn (s)
(b) Cr (s)
(c) 8i(g)
(d) Fe3+(aq)
Which polymer is used for making magnetic
recording tapes?
(a) Dacron
(b) Acrilan
(c) Glyptal
(d) Bakelite
Carbylamine reaction is used for the detection of
74.
(a) aliphatic 2° amines.
(b) aliphatic I O amines.
(c) aromatic I O amines.
(d) Both (b) and (c).
Which one of the following is not applicable to
the phenomenon of adsorption?
(a) ~H > 0
(b) ~G < 0
(d) ~H < 0
(c) ~S < 0
For a reaction, activation energy (Ea) = 0 and rate
75.
'
+
Cu 2 /Cu
= 0.34
0.692 min-I
24
I (8l) .
(c)
2.303
24
(d)
2.303
. -1
- Iog (8)
- mm
24
1
og
mm
-1
In Bosch 's process, which gas is utilised for the
production of hydrogen gas ?
(b) Water gas
(a) Producer gas
(a)
3.2 x 10- 12 s- 1
(b)
3.2 x l06 s- 1
(c) Coal gas
(d) None of these
In the commercial electrochemical process for
aluminium extraction the electrolyte used is
(c)
6.4 x 1012 s- 1
(d)
6.4 x I06 s- 1
(a)
value of the rate constant at 310 K
72.
/Cr
= --0.90 Ee
= +1.57
Which of the following statements is incorrect?
(a) Sc3+ has good stability due of [Ar]3d 04s0
configuration.
(b) Mn 3+ is more stable than Mn2+.
(c) Cr2+ is reducing in nature.
(d) Copper does not give Hi on reaction with
dil. 8iSO4.
The decomposition of a substance follows first
order kinetics. Its concentration is reduced to
118th of its initial value in 24 minutes. The rate
constant of the decomposition process is
(a) 1/24 min-I
constant (k)=3.2xl06 s-1 at300K. What is the
71.
Mn 3+ /Mn 2+
2H+(aq)+2e- ~ 8i(g) ; 0 .00V
Cr
(b)
69.
'
Ee 2+
Which is the strongest reducing agent?
68.
Ee
= -0.37
Cr3+(aq)+3e- ~ Cr(s);--0.740V
Fe3+(aq)+e- ~ Fe 2+ (aq) ;0.770V
67.
On the basis of data given below,
Which one of the following is a non-benzenoid
aromatic compound?
(a) Aniline
(b) Benzoicacid
(c) Naphthalene
(d) Tropolone
Which of the following is the key step in the
manufacture of sulphuric acid ?
(a) Burning ofsulphur or sulphide ores in air to
generate so2
(b) Conversion of SO2 to SO3 by the reaction
with oxygen in presence of catalyst.
(c) Absorption ofSO 3 in 8iSO4 to giveoleum.
(d) Both (b) and (c)
76.
A1(0H)3 in NaOHsolution
(b) An aqueous solution of Al2 (so 4)3
(c)
A molten mixture of Al2O3 andNa3AIF6
(d) A molten mixture of A1 2O 3 and Al(OH)3
77.
A system absorbs 10 kJ of heat and does 4 kJ of
work. The internal energy of the system
(a) increases by 6 kJ
(b) decreases by 6 kJ
(c) decreases by 14 kJ
(d) increases by 14 kJ
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78.
Reagents capable of converting cyclohexanone
to N-ethyl cyclohexylamine is
31
83.
Cloud or fog is a colloidal system in which the
dispersed phase and the dispersion medium are
84.
(a)
gas, liquid
(b) liquid, gas
(c)
liquid, liquid
(d) solid, liquid
Which ofthe following ions will exhibit colour
in aqueous solutions?
79.
La 3 +(2 = 57)
(b)
Ti 3+ (2 = 22)
(c)
Lu 3+ (2 = 71)
(d)
Sc3+(2=21)
CH 3CH 2 Br and NH 3
(b)
CH 3CH 2 NH 2 and H 2 / Pt
(c)
CH 3CH = 0 and NH 3
(d)
LiAlH4 followed by H 2O and then
Williamson's synthesis?
CH 3CH 2 Br
(a)
85.
Which of the following cannot be made by using
Methoxybenzene
Which one is the most likely structure of
(b) Benzyl p-nitrophenyl ether
CrC1 3. 6H2 O if 1/3 of total chlorine of the
compound is precipitated by adding AgNO3
(c)
(a)
CrC~.6Hp
(d) [CrC1<8iO)5 ] C½,8iO
The rate ofreaction ofwhich of the following is
not affected by pressure
(a)
PC13 + Cl2 ~PC1 5
(b)
Nz +3H2~2NH3
(c)
N 2 +O2 ~2NO
Methyl tertiary butyl ether
(d) Di-tert-butyl ether
86.
1 M, 2.5 litre NaOH solution is mixed with
another 0.5 M, 3 litre NaOH solution. Then find
(b) [Cr(1½O)3Cl3].(8iO)3
(c) [CrC12<8iO)4 ] Cl.28iO
80.
(a)
(a)
out the molarity ofresultant solution
87.
(a)
0.80M
(b)
(c)
0.73M
(d) 0.50M
I.OM
In the manufacture of bromine from sea water,
the mother liquor containing bromides is treated
with
88.
(d)
81.
82.
2S0 2 +0 2 ~2S03
(a)
carbon dioxide
(b) chlorine
(c)
iodine
(d) sulphur dioxide
The oxidation potentails ofAandB are+2.37 and
+ 1.66 V respectively. In chemical reactions
Among Al2O 3, SiO2, P2O 3 and SO2 the correct
order of acid strength is
(a)
(a) Alp3 <SiO2< SO2 < P2O 3
(b) SiO2< so2 < Alp3 < Pp3
(c)
(c) SO2<P2O 3< SiO2 < A1p3
(d) Alp3< SiO2< Pp3< SO2
Which of the following statements about
amorphous solids is incorrect?
(a) They melt over a range oftemperature
(b) They are anisotropic
(c) There is no orderly arrangement ofparticles
(d) They are rigid and incompressible
A will be replaced by B.
(b) A will replace B.
AwillnotreplaceB.
(d) A and B will not replace each other.
89.
Adenosine is an example of
(a)
nucleotide
(c) purine base
90.
(b) nucleoside
(d) pyrimidine base
Which of the folliowing metal oxides is antiferromagnetic in nature?
(a)
MnO (b) TiO2 (c) VO2
(d) Cr02
WWW.JEEBOOKS.INI
TargetMHT-CET
32
91.
Which one of the following is the correct order
of acidic strength?
(a) CFFOOH> CHC12COOH> HCOOH>
C 6H5C8iCOOH> Cff:iCOOH
(b) CH3COOH > HCOOH > CF 3COOH >
96.
97.
CHClFOOH > C6H5C8iCOOH
92.
(c) HCOOH > C 6H 5C8iCOOH > CF3COOH >
CHC1iCOOH> Cff:iCOOH
(d) CF3 COOH > CH3 COOH > HCOOH >
CHC1iCOOH > C6H5C8iCOOH
The following compounds differ in
_,...,...H H......._
H......._
/ Cl
c1,. . . . . .c = c,c1 CI,. . . . . .c = C.... H
93.
(b) conformation
(a) configuration
(d) chirality
(c) structure
Assume that a particular amino acid has an
isoelectric point of 6.0. In a solution at pH 1.0,
which of the following species will predominate?
R
R
(a)
+I
H NCHCO2H
3
(b)
R
(c)
94.
98.
+I
H 3NCHCO2
I
H 2NCHCO2H
R
(d)
I
H2NCHCO2-
Which one of the following forms micelles in
aqueous solution above certain concentration?
(a)
Dodecyltrimethylamrnonium chloride
(b) Glucose
(c) Urea
95.
(d) Pyridinium chloride
The relationship between the dissociation energy
ofN2 and N 2+ is :
(a) Dissociation energy ofN/ > dissociation
energy ofN2
(b) Dissociation energy of N 2 = dissociation
energy ofN2+
Dissociation energy of N 2 > dissociation
energy ofN2+
(d) Dissociation energy of N 2 can either be
lower or higher than the dissociation energy
Which has the maximum number of molecules
among the following ?
(a) 44gCO2
(b) 48gO3
(c) 8 g 8i
(d) 64 g SO2
Which one of the following statement is not
true?
(a) In vulcanization the formation of sulphur
bridges between different chains make rubber
harder and stronger.
(b) Natural rubber has the trans -configuration
at every double bond
(c) Buna-S is a copolymer of butadiene and
styrene
(d) Natural rubber is a 1,4-polymerofisoprene
Which compound undergoes nucleophilic
substitution with NaCN at the fastest rate?
(a)
Br~
(b) B e ~
(c)
Br~
(d)
99.
Antibiotics that are effective against Grampositiveor Gram-negative bacteria X. Antibiotics
that are effective against a single organism or
disease are Y
What isX and Y?
(a) X = Broad spectrum antibiotics.
Y = Narrow spectrum antibiotics.
(b) X = Broad spectrum antibiotics.
Y = Limited spectrum antibiotics.
(c) X = Narrow spectrum antibiotics.
Y = Limited spectrum antibiotics.
(d) X = Narrow spectrum antibiotics.
Y = Broad spectrum antibiotics.
100. Rate ofSN2 will be negligible in:
Br
(a)
(c)
ofN/
Br~
6
6
Br
(b)
Br
Br
(c)
6
6
(d)
IWWW.JEEBOOKS.INI
33
MOCKTEST-3
SECTION-8
1.
Ify =
(a)
2.
3.
MATHEMATICS
+ sec2x, then
8.
cos2x
y:,::; 2
(b)
y:,::; 1
(c) y ~ 2
(d) l<y <2
IfA is the set of even natural numbers less than
8 and B is the set of prime numbers less than 7,
then the number of relations from A to B is
(a) 29
(b) 92
(c) 32
(d) 29 - 1
20 teachers ofa school either teach mathematics
or physics. 12 of them teach mathematics while 4
teach both the subjects. Then the number of
teachers teaching physics only is
(a)
12
(b) 8
9.
10.
5.
6.
Let A(2, - 3) and B (-2, 1) be vertices of a
triangle ABC. If the centroid of this triangle
moves on the line 2x+3y = 1, then the locus of
the vertex C is the line
(a) 3x-2y=3
(b) 2x-3y=7
(c) 3x + 2y= 5
(d) 2x+ 3y= 9
The equation ofthe parabola having axis parallel
to y-axis and which passes through the points
(0, 4), (1, 9) and (4, 5) is
(a)
-19 2 79
y=-x +-x+4
12
12
(b)
-19 2 79
y=-x +-x-4
12
12
19 2 79
y=-x +-x+4
12
12
(d) None of these
(c)
7.
[
-l+ ✓
-3
2
(a) 2
(c) -1
12.
21C7 (d)
30Cs
If number of terms in the expansion of
(d) 610
(a) 7
(b) 8
(c) 9
The ratio in which the line joining (2, 4, 5), (3, 5,-4)
is divided by the yz plane, is
(a) 2:3 (b) 3:2 (c) -2:3 (d) 4:-3
The integer n for which
x➔ O
Xn
number is
(d) 4
(a) 1
(b) 2
(c) 3
13. Which of the following is the inverse of the
proposition? "If a number is a prime then it is
odd."
(a) Ifa number is not a prime then it is odd
(b) Ifa number is not a prime then it is not odd
(c) Ifa number is not odd then it is not a prime
(d) Ifa number is not odd then it is a prime
14. The marks of some students were listed out of
75. The SD of marks was found to be 9.
Subsequently the marks were raised to a maximum
of 100 and variance ofnew marks was calculated.
The new variance is
(a) 144
(b) 122
(c) 81
(d) None of these
If f(x)
= _x_ , then (fofo........of)(x) is equal to :
x-1
(d) 1
21Cs (c)
. (cosx-l)(cosx-ex).
.
h m - - - - - - - 1 s a fimte non-zero
15.
100 [ -1- ✓
-3 )100 .
1s equal to
) +
2
(b) 0
30C7 (b)
(x-2y+3z? is 45 then n =
(c)
4.
3x .5Y =75 and 3Y .5x =45 is
(a) 0
(b) 1
(c) 3
(d) Noneofthese
The number of ways in which an examiner can
assign 30 marks to 8 questions, giving not less
than 2 marks to any question, is :
(a)
11.
16
(d) None of these
In a G.P. ofpositive terms, ifanyterm is equal to
the sum of the next two terms then the common
ratio of the G.P. is
(a) sin 18°
(b) 2 cos 18°
(c) cos 18°
(d) 2sin 18°
The number of ordered pairs (x, y) satisfying
(a)
(c)
19 times
X
x-1
19x
x-1
(d)
X
WWW.JEEBOOKS.INI
34
16.
TargetMHT-CET
LetA= [~ ~] and(A + I) 50 - 50A = [:
!],
find abc + abd + bed + acd
(a) 0
(b) -1
(c) 1
(d) None of these
17.
I sin A sin 2 A
Ifin a triangle ABC, I sin B sin2 B
21.
J(x) = sin
plog
22.
23.
I+ 3
12(log4)3 ,x
=0
may be continuous at x = 0, is
(a) l
(b) 2
(c) 3
(d) None of these
19.
If
((ax b) x (c x d)).(a x d) =0 , then which
of
must lie in the plane of cand d
dx
~ - - equals
f___
3 sin x
cosx+ ✓
(a) log tan (~+-2:) +C
2 12
_2:)
(b) log tan (~ _
+C
2 12
(a)
k =2_
(c)
k=±-
(a)
k> l
(b)
2
1
k=-2
1
(d) k can take any value
2
The function.f{x) = sin x- kx - c, where k and
c are constants, decreases always when
(b) k~l (c) k<l
(d) k:s;l
J_2_-_ 3_x_ dx _
3x~
-
(a)
2 logc: 3 )
(c)
3
4logC 3 )
(d) None of these
If y = tan
(c) either b or c must lie in the plane of aandd
20.
represent
25.
(b) either a or d must lie in the plane of b and c
a orb
Fi '½,k)
Corner points of the feasible region for an LPP
are (0, 2) (3, 0) (6, 0), (6, 8) and (0, 5). Let
F = 4x + 6y be the objective function.
The minimum value ofF occurs at
(a) (0, 2) only
(b) (3, 0) only
(c) the mid-point ofthe line segment joining the
points (0, 2) and (3, 0) only
(d) any point on the line segment joining the
points (0, 2) and (3, 0)
a,b,c,d are necessarily coplanar
(d) either
Under what condition do \
24.
the following is always true?
(a)
½log tan (f- 1~) +C
8
,x;t: O
[ l
x2
(d)
direction cosines of a line?
triangle is
(a) equilateral or isosceles
(b) equilateral or right-angled
(c) right angled or isosceles
(d) None of these
The value ofp for which the function
X
~2 log tan (~+
-2:) + C
2 12
= 0 then the
lsinCsin 2 C
18.
(c)
_1(
(3 2
2
log. (e/ x ))
+ log. xJ
_
+ tan 1 1_ 6 log
•
log,(ex2 )
ex
d 2y
then - 2 is
dx
(a) 2
(b)
(c) 0
(d) -1
lWWW.JEEBOOKS.INI
MOCKTEST-3
26.
27.
28.
35
Three persons, A, Band C, fire at a target in turn,
starting with A. Their probability of hitting the
target are 0.4, 0.3 and 0.2 respectively. The
probability of two hits is
(a) 0.024 (b) 0.188 (c) 0.336 (d) 0.452
The area enclosed by the curve x 2 y = 36, the
x-axis and the lines x = 6 and x = 9 is
(b) 1
(d) 2
(a) 6
(c) 4
A random variable X assumes values which are
n+l
n
rational numbers of the form - - and - - ,
n+ 1
n
wheren = 1, 2, 3, .....
34.
The number of solution oflog5inx 2tanx > 0 in the
interval ( 0,
35.
(c) 2
(d) 3
(b) l
(a) 0
How many numbers lying between 500 and 600
can be formed with the help of the digits 1, 2, 3, 4,
5, 6 when the digits are not be repeated?
(b) 40
(a) 20
36.
%) is
expansionof(½x
P(X < 1) = P(X > 1)
(b)
1
P(- <X<l)<P(X>l)
2
(c)
29.
P(X >
(c)
37.
) < P(X < 1)
2
1
(b)
50
31.
32.
33.
IO
is:
60
423
(d) None of these
then the value of x is given by
(a)
2,2±
(b) 2 ± ✓
3 ,3
(c)
3±
(d) None of these
x2
+x+l,
100 99
2
f'( 1) = mf' (0), where m is equal to
(b) 0
(a) 50
(c) 100
(d) 200
38.
If the function f : R ➔ A given by is
+2
100
2
2
r;;)x -4x + 3 {
r;;)x -4x + 3
If ( 7-4v3
+ 7+4v3
= 14,
x99
f(x)= - + -+ ... -
90
(d)
The sum of 11 terms of an AP. whose middle
term is 30,
(a) 320
(b) 330 (c) 340
(d) 350
The intercept cut off by a line from y -axis twice
than that from x-axis, and the line passes through
the point (1, 2). The equation of the line is
(a) 2x+y=4
(b) 2x +y+ 4=0
(c) 2x-y=4
(d) 2x-y +4 =0
The length of intercept, the circlex2 + y2 + 10x6y + 9 = 0 makes on the x-axis is :
(d) 8
(b) 4
(a) 2
(c) 6
.fi_
.fi_ , 2
10
)
For the function
f(x)=
X
30.
114
(b)
x'oo
9
100 (c)
(d) 80
13
3
1
IO
+x-
243
(d) All above are correct
A card is drawn at random from a pack of 100
cards numbered 1 to 100. The probability of
drawing a number which is a square, is
(a)
112
70
(a)
(a)
(c) 00
The coefficient of x 2 term in the binomial
39.
+l
issurjection, thenAis
(a) [O, I) (b) (0, I) (c)
Ifx2 + y2 + l- = ?,then
(0, l]
(d) [O, 1]
xy
yz
xz
+ tan- 1 + tan-1 zr
xr
yr
tan- 1 -
re
(a) re
(c)
40.
0
cose
IfA = [ . e
-Sill
(a)
(b)
2
(d) None of these
sine]
l
e then Jim -An is
n ➔oo n
cos
anullmatrix
(b) an identity matrix
(d) None of these
WWW.JEEBOOKS.INI
TargetMHT-CET
36
41.
If a system of equation - ax+ y + z = 0
x-by+z= 0
(b)
l
l +C
logx-+ ~
x +--3
(c)
loglx+Jx +3J+c
X
x+y-cz=0 (a,b,c,t-l)
X2
has a non-zero solution then
1
1
1
--+--+--=
l+a l+b l+c
(c) 2
(b) 1
(a) 0
42.
(d) 3
The function f(x) = [x]2- [x2] (where [y] is the
greatest integer function less than or equal toy),
is discontinuous at :
(a) all integers
(b) all integers except 0 and 1
47.
2
(d) None of these
Two spheres of radii 3 and 4 cut orthogonally
The radius of common circle is
(a)
48.
12
(b)
12
5
r
0
(d) all integers except 1
43.
✓
12
- 5
(d)
Ju
A curve passing through (2, 3) and satisfying the
differential equation
(c) all integers except 0
(c)
ty(t) dt = x2y (x), (x > 0) is
(a) x 2 +y2 = 13
The maximum value of In x in ( 2, oo) is
X
(a)
44.
1
(b) e
(c) 2/e
(d)
x2
lie
(c)
-
Ify =j(x) makes +ve interceptof2 and 0unit on x
and y axes and encloses an area of 3/4 square
8
y2
+-
=1
18
(d) xy= C
e37
2
unit with the axes then
f xf'(x)dx is
49.
(a) 3/2
45.
46.
f
2
dx is equal to
(x - l)
4
2
xJx +3x +1
rcsin(rcloge x) dx .
1s equa1 to
X
I
0
(c) 5/4
(d) -3/4
(b) 1
For the LPPMinz =x1 + x2 such that inequalities
5x 1 + 10x2 ~ 0, x 1 + x 2 ~ I, x 2 ~ 4 and x" x 2 ~ 0
(a) There is a bounded solution
(b) There is no solution
(c) There are infinitie solution
(d) None ofthese
f
(b) 20
(a) 2
50.
The vectors
AC
= 5i -
(c)
2
TC
AB = 3i + s] + 4k
(c) 2rc
and
J
5 + 2k are the sides of a triangle
ABC. The length of the median through A is :
(a)
✓
13 units
(b)
2✓
5 units
(c)
5 units
(d)
l0units
WWW.JEEBOOKS.INI
Mock Test-~
General Instructions
■
■
■
■
■
■
■
This question booklet contains 150 Multiple Choice Questions (MCQs).
Section-A: Physics & Chemistry - 50 Questions each and
Section-B: Mathematics - 50 Questions.
Choice and sequence for attempting questions will be as per the convenience of the candidate.
Read each question carefully.
Determine the one correct answer out of the four available options given for each question.
Each question with correct response shall be awarded one (1) mark. There shall be no negative marking.
No mark shall be granted for marking two or more answers ofsame question, scratching or overwriting.
Duration ofpaper is 3 Hours.
SECTION-A
PHYSICS
1.
The dimensional formula of angular velocity is
(a) [MLY-11
(b) [M°L01]
(c) [ML0r 2J
2.
3.
4.
5.
6.
7.
A
(d) [M°L0 r'J
A ball ofmass 150 g, moving with an acceleration
20 m/s2, is hit by a force, which acts on it for 0.1
sec. The impulsive force is
(a) 0.5N (b) 0.1 N (c) 0.3N (d) 1.2N
When the base current in a transistor is changed
from 30 µA to 80 µA , the collector current is
changed from 1.0 mA to 3. 5 mA. Find the current
gain j3.
(a) 30
(c) 45
(d) 50
(b) 40
In an L.C.R. series a.c. circuit, the current
(a) is always in phase with the voltage
(b) always lags the generator voltage
(c) always leads the generator voltage
(d) None of these
For an A.M. wave, the maximum and minimum
amplitude is found to be 20V and 4V. Find the
modulation index(m).
(a) 3/5
(b) 5/3
(c) 2/3
(d) 3/2
Let V and E denote the gravitational potential
and gravitational field at a point. It is possible
to have
(a) V=0andE=0
(b) V=0andE ;c0
(c) V ;c 0andE = 0
(d) All ofthe above
To get output 1 for the following circuit, the
correct choice for the input is
B
C o - - - - - - - ; __
8.
9.
10.
11.
_,,
(a) A=0,B=l , C=0 (b) A=l,B=0,C=0
(c) A = l,B = l,C = 0 (d) A = l,B = 0,C = l
The Poisson's ratio ofa material is 0.5. Ifa force
is applied to a wire of this material, there is a
decrease in the cross-sectional area by 4%. The
percentage increase in the length is :
(a) 1%
(b) 2%
(c) 2.5% (d) 4%
If two waves of same frequency and same
amplitude, on superposition, produce a resultant
disturbance of the same amplitude, the wave
differ in phase by
(a) 1t
(b) 2n/3 (c) rr/2
(d) n/3
A hoop rolls down an inclined plane. The fraction
of its total kinetic energy that is associated with
rotational motion is
(a) 1 : 2 (b) 1: 3 (c) 1 : 4 (d) 2 : 3
2
An unpolarised beam of intensity 2a passes
through a thin polaroid. Assuming zero
absorption in the polaroid, the intensity of
emergent plane polarised light will be
(a) 2a2
(b)
a2
(c)
✓
2 a 2 (d)
a2
✓
2
WWW.JEEBOOKS.INI
38
12.
13.
14.
TargetMHT-CET
Demagnetisation of magnets can be done by
(a) rough handling
(b) heating
(c) magnetising in the opposite direction
(d) All the above
The Kirchhoff's first law {Li = 0) and second law
(LiR = LE), where the symbols have their usual
meanings, are respectively based on
(a) conservation of charge, conservation of
momentum
(b) conservation of energy, conservation of
charge
(c) conservation of momentum, conservation
of charge
(d) conservation of charge, conservation of
energy
At 10° C the value of the density of a fixed mass
of an ideal gas divided by its pressure is x. At
110°C this ratio is:
(a)
X
(b)
19.
20.
(c)
X
21.
(a)
(c)
22.
30µC
(b) 60µC
15 µC
(d) 90µC
Cj
A bullet of mass 'a' and velocity 'b ' is fired into a
large block of wood of mass 'c'. The bullet gets
embedded into the block of wood. The final
velocity of the system is
(a)
(d)
15.
va cos 20
(d) va
383 X
283
283 x
383
The capacitor, whose capacitance is 6, 6 and 3 µF
respectively are connected in series with 20 volt
line. Find the charge on 3µF.
The fundamental radio antenna is a metal rod
which has a length equal to
(a) ').., in free space at the frequency of operation
(b) ')..,/ 2 in free space at the frequency of
operation
(c) ')..,/4 in free space at the frequency of
operation
(d) 3')..,/4 in freespaceatthefrequencyofoperation
A particle is moving in a circular path of radius a,
with a constant velocityv as shown in the figure.
The centre ofcircle is marked by 'C'. The angular
momentum from the origin O can be written as:
(a) va (I + cos 20)
Y
(b) va (1 + cos 0)
23.
b
(b)
--x C
a+b
a+b
- -xa
C
(c)
_a_x b
(c)
T2 > T3 > T1
a+c x b
a+c
(d)
a
A rain drop of radius 0.3 mm has a terminal
velocity in air = I mis. The viscosity of air is
8 x I o-5 poise. The viscous force on it is
(a) 45.2 x 10-4 dyne (b) 101.73x J0-5 dyne
(c) 16.95 x 10-4 dyne (d) 16.95 x 10-5 dyne
The plots of intensity versus wavelength for
three black bodies at temperatures T1, T2 and T3
respectively are as shown. Their temperature are
such that
20V
16.
17.
18.
At what distance from a long straight wire
carrying a current of 12 A will the magnetic field
be equal to 3 x 10-5 Wb!m 2?
(a) 8xJ0-2 m
(b) )2 x J0-2 m
2
(d) 24 x J0-2 m
(c) 18 x 10- m
IfN0 is the original mass of the substance of
half-life period t I fl = 5 years, then the amount of
substance left after 15 years is
(a) Nof8 (b) N0/16 (c) Nof2 (d) Nof4
A rectangular coil of I 00 turns and size 0.1
m x 0.05 mis placed perpendicular to a magnetic
field of0.1 T. The induced e.m.f. when the field
drops to 0.05 Tin 0.05s is
(a) 0.5V (b) l.OV (c) 1.5V (d) 2.0V
(d) T3 > T2 > T 1
24.
25.
The ratio of intensities of two waves is 9 : I .
They are producing interference. The ratio of
maximum and minimum intensities will be
(a) 10 :8 (b) 9:1
(c) 4:1 (d) 2:1
The ratio of escape velocity at earth (vJ to the
escape velocity at a planet (vp) whose radius
and mean density are twice as that of earth is :
(a)
1:2
(c)
1: 4
2
(b) 1:2 ✓
(d) 1: 2
lWWW.JEEBOOKS.INI
MOCKTEST-4
26. Ifx, v and a denote the displacement, the velocity
27.
and the acceleration of a particle executing simple
harmonic motion oftime period T, then, which of
the following does not change with time?
(a) aT!x
(b) aT+2w
(c) aT/v
(d) a 2 T2 + 4n2 v2
If in acircularcoilAofradius R,current I is flowing
and in another coil B ofradius 2R a current 21 is
flowing, then the ratio of the magnetic fields BA
and
produced by them will be
(a) 1
(b) 2
(c) 1/2
(d) 4
The Young's mcxlulus of the material of a wire is
2 x 1010 Nm-2 . If the elongation strain is 1%, then
the energy stored in the wire per unit volume in
Jm-3 is
(a) 106
(b) 108
(c) 2 x 106 (d) 2 x 108
ABC is an equilateral triangle. Charges +q are
placed at each comer as shown as fig. The electric
intensity at centre O will be
39
33.
~
f
Bs,
28.
29.
(a)
(a)
34.
35.
_1_~
41tE
r
0
36.
30.
31.
4n Eo r2
(d) zero
A spring of spring constant 5 x 1o3 N /m is
stretched initially by 5 cm from the unstretched
position. Then the work required to stretch it
further by another 5 cm is
(a) 18.75J(b) 25.00J(c) 6.25J (d)l2.50J
A ray is incident at an angle of incidence ion one
surface of a prism of small angle A and emerges
normally from the opposite surface. If the
refractive index of the material of prism is µ, the
angle of incidence i is nearly equal to
A
µA
A
(c) µA (d)
2µ
2
µ
Two particles ofmass m I and m 2 (m 1 > m 2) attract
each other with a force inversely proportional to
the square of the distance between them. If the
particles are initially held at rest and then
released, the centre of mass will
(a) move towards m 1 (b) move towards m 2
(c) remains at rest
(d) None of these
(a)
32.
--~
C
-
b +c = J
(b)
At a certain place, horizontal component is ,Jj
times the vertical component. The angle of dip at
this place is
(a) 0
(c) n/6
(d) n/8
(b) rr/3
Four curves A, B, C andD are drawn in the figure
for a given amount of a gas. The curves which
represent adiabatic and isothermal changes are
C and D respectively
j
(b) D and C respectively
P
(c)
A and B respectively
(d) Band A respectively
37.
38.
(b)
39.
J+c=J
E+e = J
(d)
(c) d+ e= J
When the current in a coil changes from 8 amp to
2 amp in 3 x 1o-2 seconds, the emf induced in the
coil is 2 volt. The self inductance of the coil is
(a) lOmH (b) 20mH (c) 5mH (d) lmH
(a)
_ _ _ _ _ _ _:.:. +q
(c)
J
Six vectors, ii through have the magnitudes
and directions indicated in the figure. Which of
the following statements is true?
v--+
In Young's experiment, the distance between the
slits is reduced to half and the distance between
the slit and screen is doubled, then the fringe width
(a) will not change
(b) will become half
(c) will be doubled
(d) will become four times
Two thin, long, parallel wires, separated by a
distance ' d' carry a current of ' i' A in the same
direction. Theywill
(a) repel each other with a force of µ 0i2/(2nd)
(b) attract each other with a force of µ 0i2/(2nd)
(c) repel each other with a force ofµ 0 i2/(2nd2)
(d) attract each other with a force of µ 0 i2 /(2nd2)
If specific resistance of a potentiometer wire is
10-7 Om, the current flow through it is0.l A and
the cross-sectional area of wire is 10-6 m 2 then
potential gradient will be
(b) 10-4 volt/m
(a) 10-2 volt/m
(c) 10--<ivolt/m
(d) lo-8volt/m
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40
40.
TargetMHT-CET
A thin liquid film formed between a U-shaped
wire and a light slider supports a weight of
1.5 x 10-2 N (see figure). The length of the slider
is 30 cm and its weight negligible. The surface
tension ofthe liquid film is
41.
45.
A block of mass 0.1 kg is held against a wall
applying a horizontal force of5 Non the block. If
the coefficient of friction between the block and
the wall is 0.5 , the magnitude of the frictional
force acting on the block is:
'
(a)
0.0125Nm-1
(b)
0.1 Nm-1
(a)
2.5N
(b) 0.98N
(c)
0.05Nm-1
(c) 4.9N
(d) 0.49N
Film
(d) 0.025Nm-1
w
A car is negotiating a curved road of radius R.
The road is banked at an angle 0. the coefficient
of friction between the tyres of the car and the
road is µ 5• The maximum safe velocity on this
road is:
gR[ µ +tan 0 J
tan0 (b)
gR2[µ1-µ+tan0J
energy of emitted electrons is
(b) 3.2 X 10-I? J
(a) 3.2 X 10- 19 J
(c)
47.
(c)
42.
(d)
g [~+tan0J
R2 1-~ tan0
Two capillary oflength Land 2L and ofradius R
and 2R are connected in series. The net rate of
flow offluid through them will be (given rate to
48.
43.
44.
(b)
2-x
8
(c)
5
- X
7
(d)
(a)
re ,Ju (b)
(c)
!!:_,Ju (d) 2rc,./Lc
2
}._ re,Ju
2
LJ
(d)
virtual and inverted
Two simple pendulums of length 1 m and 4 m
will be again in phase after the shorter pendulum
has completed number of oscillations equal to:
(a) 2
5
(c) tJ4
(d) 1611.
(a) 411.
(b) "At t < 0, the capacitor is charged and the switch
is opened. At t = 0 the switch is closed. The
shortest time T at which the charge on the
capacitor will be zero is given by:
real and erect
in the same direction at the same instant. They
7
-X
Sound waves oflength 11. travelling with velocity
v in a medium enter into another medium in which
their velocity is 4 v. The wavelength in 2nd
medium is
(c)
respectively are both given small displacement
4
8
- X
9
real, inverted and smaller in size
(b) real, inverted and of same size
the flow through single capillary, X = nPR )
811L
(a)
(d) 3.2 x 10-11 J
An object is placed at a distance of40 cm in front
(a)
g[~+tan0J
R 1-µ 2 tan0
3.2 x 10-16 J
ofa concave mirror of focal length 20 cm. The
image produced is
1-~ tan0
5
When ultraviolet light ofenergy6.2 eV incidents on
aaluminimum surface, it emits photoelectrons. Ifwcrk
function for aluminium surface is 4.2 eV, then kinetic
5
5
(a)
46.
49.
(b) 7
(c) 5
(d) 3
The ionisation potential ofH-atom is 13.6 V. When
it is excited from ground state by monochromatic
radiations of 970.6
A, the number of emission
lines will be (according to Bohr's theory)
(a)
SO.
(c) 6
10
(b) 8
(d) 4
A particle moves in a circle of radius 30 cm. Its
linear speed is given by : v = 2t, where tin second
and v in mis. Find out its radial and tangential
acceleration at t = 3 sec respectively.
(a) 220 m/sec2, 50 m/sec2
(b)
110m/sec2,5m/sec2
(c)
(d)
120 m/sec2, 2 m/sec2
110 m/sec2, 10 m/sec2
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MOCKTESf-4
51.
41
(c)
Ph -
Which of the following statements is true?
(d)
CH 2 =CH-CH 2 -Cl
(a) HCIO4 is a weaker acid than HC1O3
(c)
53.
(d) In aqueous medium HF is a stronger acid
thanHCl
How many unit cells are present in a cube-shaped
ideal crystal ofNaCl of mass 1.00 g?
[Atomic masses: Na= 23, Cl = 35.5]
(a) 2.57 x 1021 unit cells
(b) 5.14 x l021 unitcells
(c) 1.28 x 1021 unit cells
(d) 1.71 x 1021 unit cells
In a cubic closed packed structure of mixed oxides,
the lattice is made up of oxide ion, 20% of
tetrahedral voids are occupied by divalent x2+
ions and 50% of the octahedral voids are
occupied by trivalent y 3+ ions. The formula of
the oxide is
59.
What is X and Y in the given reactions ?
2Xz(g)+2HzO (I) ➔ 4W(aq) + 4X-(aq) + Oz(g)
C8:iCHzCH(C8:i)C(C8:i)2CHzCHzC8:i?
Y 2 (g) + HzO (I) ➔ HY(aq) + HOY(aq)
(b) 4
sc
0
(c) 5
(d) 6
/',.
H,
.
~~
(A);
Product (A) of the reaction is:
(a) Propanol
(b) Ethanol
(c) Butanol
(d) Pentanol
Excess of copper in toxic proportions in plants
and animals can be removed by chelating with
(a) EDTA
(b) ethane-1,2-amine
(c) oxalate ion
(d) D-penicillarnine
60.
3A ➔ 2B , rate ofreaction d[B] is equal to
dt
61.
(a)
X = Cl,Y = F
(b) X = Cl , Y = Br
(c)
X = F , Y = Cl
(d) X=I, Y = F
The structural feature which distinguishes
pro line from natural a-amino acids?
(a)
_i d[A]
(b)
(c)
_3_ d[A]
(c)
_.!_ d[A]
3 dt
(d)
(d) Pro line is a secondary amine
Ethyl alcohol is used as a preservative for chloroform
because it
(a) (C8:i)zCHBr or C8:i-CHz-CHz-Br
(b) C8:i-CHz-CHz-Br
or C8:i-CHz-CHz-I
prevents aerial oxidation ofchloroform
(c)
decomposes phosgene to CO and Cl2
(d) removes phosgene by converting it to ethyl
carbonate
+ 2 d[A]
dt
In the given pairs of alkyl-halide, in which pair
the first compound is more reactive than second
compound towards SN2 reaction?
Proline is a dicarboxylic acid
(b) prevents decomposition of chloroform
3 dt
2 dt
Proline is optically inactive
(b) Proline contains aromatic group
(a)
(a)
57.
Br
How many primary carbon atoms are there in
10% NaOH
56.
58.
8:iPO3 is a stronger acid than H 2 SO3
(a) 3
55.
Br or
or H 2C=CH-Cl
(b) HNO 3 is a stronger acid than HNO2
52.
C8:i- CHz-CHz -
CHEMISTRY
62.
A compound ofa metal ion M x + (z = 24) has a
spin only magnetic moment of
../Is
Bohr
magnetons. The number of unpaired electrons
in the compound are
(a) 2
(b) 4
(c) 5
(d) 3
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TargetMHT-CET
42
63.
64.
6.3x 10-2
Specific conductance of0. l M HNO3 is
ohm- 1 cm- 1• The molar conductance of the
solution is
(a) 100 ohm-I cm2
(b) 515 ohm-I cm2
2
(c) 630 ohm-I cm
(d) 6300ohm-I cm2
2-Butyne contains :
(a) sp hybridised carbon atoms only
(b)
(c) Hall-Heroult method
(d) Van Arkel method
70.
Buna-N synthetic rubber is a copolymer of:
(a) HzC = CH-CH=CHzandH5C6 -CH=CHz
(b) HzC = CH-CNandCHz=CH-CH = CHz
(c) HzC = CH-CNand H 2C = CH-C = CH 2
I
CH 3
sp 3 hybridised carbon atoms only
(c) Both sp and sp 2 hybridised carbon atoms
(d)
(d) Both sp and sp 3 hybridised carbon atoms
65.
66.
The reducing power of divalent species
decreases in the order
(a) Ge > Sn > Pb
(b) Sn > Ge > Pb
(c) Pb > Sn > Ge
(d) None of these
H 2C = CH-CH = CH 2
71.
(b) Hydrolysis of gem-dihalides
internal energy change (L'1U) when I mol ofwater
(a) 41.00kJmol-I
(b) 4.l00kJmol-I
(c) 3.7904kJmol-I
(d) 37.904kJmol-I
68.
A galvanic cell is composed of two hydrogen
electrodes, one of which is a standard one. In
which of the following solutions should the
other electrode be immersed to get maximum
e.m.f :
(a) 0.1 MHCl
(b) 0.1 MHzSO4
(c) 0.1 MNHpH
(d) 0.01 MHCOOH
The following set of reactions are used in
refining zirconium.
523 K
(pure)+ 212
This method is known as
(a) Distillation
JSOOK
(d) Stephen's reaction
72.
73.
The molecule having smallest bond angle is:
Zr (impure) + 212
(c) Dry distillation of calcium carboxylates
The number of ions produced by the complex
[Cr<M½)4C~]ClO3 is
2
(b) 3
(c) 4
(d) 6
Saline hydrides react explosively with water, such
fires can be extinguished by
(a) water
(b) carbon dioxide
(c) sand
(d) None of these
Which of the following IS not a
disproportionation reaction?
(a)
67.
69.
By which one of the following reaction ketones
cannot be prepared?
(a) Hydration of alkynes
Assuming that water vapour is an ideal gas, the
is vapourised at I bar pressure and I 00°C,
(given : molar enthalpy ofvapourisation ofwater
at I bar and 373 K = 41 kJ mo1- 1 and R = 8.3 J mo1-I
K- I)will be
Cl
I
H2C = CH-C =CH 2 and
Zr
74.
75.
(a)
P4 + 5OH- --► H2PO2 +PH3
(b)
CI 2 + Ofr--► Cl- + HCIO
(c)
2H2O2 ~2H2O+O2
(d)
PbO2 +H2O~PbO + H2O2
When bromination of aniline is carried out by
protecting - NHz. The product is
(a) o-bromoaniline
(b) 2, 4, 6 tribromoaniline
(c) p-bromoaniline
(d) mixture ofo-and p-bromoanilines
(b) Liquation
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MOCKTEST-4
76.
43
H
,Nl(YNH'
In the following sequence ofreactions,
CH3CH20H
P+I2 >A--M~g-
B-H_C
_H_O~
ether
(c)
the compound D is
(a) propanal
(c) n-butyl alcohol
77.
79.
80.
81.
/:1~
Which of the following statements about a
catalyst is/are true?
A catalyst accelerates the reaction by
bringing down the free energy ofactivation.
(b) A catalyst also takes part in the reaction
mechanism.
(c) A catalyst makes the reaction more feasible
by making the l1G0 more negative.
(d) A catalyst makes the equilibrium constant
of the reaction more favourable for the
forward reaction.
The reaction A ➔ B follows first order kinetics.
The time taken for 0.8 mole ofA to produce 0.6
mole ofB is I hour. What is the time taken for
conversion of0.9 mole ofA to produce 0.675 mole
ofB?
(a) 2 hours
(b) I hour
(c) 0.5 hour
(d) 0.25 hour
When salicylic acid is treated with acetic
anhydride we get
(a) aspirin
(b) paracetamol
(c) salol
(d) none of these
Identify incorrect statement:
(a) Cup is colourless.
(b) Copper (D compounds are colourless except
when colour results from charge transfer.
(c) Copper (I) compounds are diamagnetic.
(d) cl½s is black.
Which of the following compound is used for
preparation ofmelamine formaldehyde polymer?
(a)
@(~
-....;::
(d)
(b)
.,...-N ....._N
H
,M
NHi
NH,
~
N
H2N
82.
83.
84.
A match box exhibits
(a) cubic geometry
(b) monoclinicgeometry
(c) tetragonal geometry
(d) orthorhombic geometry.
The nodal plane in the n-bond of ethene is
located in
(a) the molecular plane.
(b) a plane parallel to the molecular plane.
(c) a plane perpendicular to the molecular plane
which bisects the carbon - carbon cr -bond at
right angle.
(d) a plane perpendicular to the molecular plane
which contains the carbon - carbon cr -bond.
If the elevation in boiling point of a solution of
non-volatile, non-electrolytic and non associating
solute in a solvent CKt, = x K kg mo1- 1) is y K, then
the depression in freezing point of solution of
same concentration would be (Kr of the solvent
= zKkgmol- 1)
2xz
(a)
85.
86.
N
N
NHi
(b) butanal
(d) n-propyl alcohol.
(a)
78.
NY
y
xz
yz
(b)
x
(c)
Y
(d) yz
2x
Na 2 SO 3 and NaHCO 3 may be distinguished
by treating their aqueous solution with :
(a) MgO
(b) MgSO4
(c) litmus solution.
(d) dil. acid
Two separate bu! bs contain ideal gases A and B.
The density of gas A is twice that of gas B. The
molecular mass ofA is half that ofgas B. The two
gases are at the same temperature. The ratio of
the pressure of A to that of gas B is :
(b) 1/2
(c) 4
(d) 1/4
(a) 2
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44
87.
88.
TargetMHT-CET
The migration of colloidal solute particles in a
colloidal solution, when an electric current is
applied to the solution is known as:
(a) Brownian movement
(b) Electroosmosis
(c) Electrophoresis
(d) Electrodialysis
Arrange ce+3, La+3, Pm+3 and Yb+3 in increasing
order oftheir ionic radii.
95.
hormone?
96.
89.
90.
2X 2 (s)+3Y 2+ (aq)~2x~+ (aq)+3Y(s)
91.
92.
93.
94.
(a) + 0.105 V
(b) + 0.2955 V
(c) 0.0985V
(d) -0.2955 V
Flux is used to :
(a) Remove silica.
(b) Remove silica and undesirable metal oxides.
(c) Remove all irnpurities from ores.
(d) Reduce metal oxide.
The rate of reaction between A and B increases
bya factorofl00, when the concentration ofA is
increased 10 folds, the order of reaction with
respect to A is
(a) 10
(c) 4
(d) 2
(b) 1
Phenacetin is used as
(a) antipyretic
(b) antiseptic
(c) antimalarial
(d) tranquillizer
The correct order of magnetic moments (spin only
values in B.M.) among is
Estradiol
(b) Prostaglandin
(c)
Progesterone
(d) Estrone
All form ideal solution except
C 6H6 and C6H5C1½
(b) C 2H6 and C 2H5 I
(c) C 6H5Cl and C 6H 5Br
(d) C 2H 5 I and Ci85OH.
97.
(c) Yb+3 < Pm+3 < La+3 < ce+3
(d) Pm+3 < La+3 < Ce+3 < Yb+3 .
Which of the following will be most stable
diazoniurn salt RN2+x-?
(a) C1½N/X(b) C 6H 5N/ X(c) C1½CHiN/ x(d) C6HsCHiN/ xThe equilibrium constant for the following
general reaction is 1030 • Calculate E0 for the cell
at298 K.
(a)
(a)
(a) Yb+3 < Pm+3 < Ce+3 < La+3
(b) ee+3 < Yb+3 < Pm+3 < La+3
Which one of the following is a non-steroidal
98.
An aromatic ether is not cleaved by HI even at
525 K. The compound is
(a)
C 6H5OC~
(c)
C 6H5OC3H,
(b) C 6H5OC6H5
(d) Tetrahydrofuran
In CH3C8iC8il, the C-1 bond is formed by the
overlapping of
99.
(a)
2sp3 - 2pz orbitals (b) 2sp3 - 3pz orbitals
(c)
2sp3 -4pz orbitals (d) 2sp3 -5pzorbitals
Among the following compounds, the increasing
order of their basic strength is:
(I)
(a) (I) < (II) < (IV) < (III)
(b) (I) < (II) < (III) < (IV)
(C) (II) < (I) < (IV) < (III)
(d) (II) < (I) < (Ill) < (IV)
100. MF + XeF4 ~ '.N (M+= Alkali metal cation)
The state of hybridisation of the central atom in
'A' and shape of the species are:
(b)
[Fe(CN) 6 ]4- > [MnC1 4 ]2- > [CoC1 4 ]2[MnCl4] 2- > [Fe(CN)6] 4- > [C0Cl4)2-
(c)
[MnC1 4 ] 2- > [CoC1 4 ] 2- > [Fe(CN) 6] 4-
(b) sp3d3, distorted octahedral
(d)
[Fe(CN) 6 ]4- > [CoC1 4 ]2- > [MnCl4)2-
(c)
(a)
(Atomic nos. : Mn = 25, Fe = 26, Co = 27)
(a) sp3d, TBP
sp3d3, pentagonal planar
(d) No compound formed at all
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MOCKTEST-4
SECTION-8
MATHEMATICS
1.
In a battle 70% of the combatants lost one eye,
80% an ear, 75% an arm, 85% a leg, x % lost all the
four limbs. The minimum value ofx is
(a)
2.
3.
10
(b)
8.
12
(c) 15
(d) None of these
The relation Rde:fined on the set A= {l, 2, 3, 4, 5} by
R= {(x,y): Ix 2 -y2 I< 16} is given by
(a) {(l, 1), (2, 1), (3, 1), (4, 1), (2, 3)}
(b) {(2, 2), (3, 2),(4, 2),(2,4)}
(c) {(3,3),(3,4), (5,4),(4,3),(3, l)}
(d) None of these
lfj{x + y) = f(x) + 2y 2 + kxy andj{a) = 2 ,j{b) = 8,
then.f{x) is of the form
(a)
2x2
9.
(b) 2x2 + 1
f(x)
= /J, g(x) = x
10.
(c)
11.
= 1+rb +r 2b +r 3b + ... oo,
th en a
1·
s
(c)
logs-1 (
A
(d) None of these
12.
(b) abc; iO.. = 1
(d) (abc)213 ; ifA. = 2
(a)
(-oo,log 2 (✓
2+1))
(b)
(0, oo)
(c)
(½, log2(✓2-1))
(d)
(-oo,
log2 (✓2-l)] u[½, oo)
The bisector of the acute angle formed between
the lines 4x-3y+7=0 and 3x-4y+l4=0
(a)
has the equation :
(a)
x + y+3=0
13.
(b)
55
(b) 66
(c)
77
(d) 88
For positive numbers x, y, z the numerical value
x-y-3=0
(d) 3x + y- 7 = 0
x-y+3=0
2
Two circles S 1= x + y2 + 2g 1x + 2f1y + c 1 = 0and
S2 = x 2+ y2 + 2g2x + 2f'iy + c2 = 0 cut each other
orthogonally, then :
(c)
7.
;(a,b, c,l > 0)isequalto-
The number of seven digit integers, with sum of
the digits equal to 10 and formed by using the
digits 1, 2 and 3 only, is
B
6.
I
j
1; iO.. = 1
abc; in = 1/3
log8 (A)
A-1)
3
\ },, / X
Solution of 2x + 2lxl ~ 2✓
2 is
b
equal to
(a)
x➔O
(a)
If A= 1+ ra + r2a + r3a + .. m
an d B
ax +bx + ex
liml
X
(d) None of these
5.
The xy-plane divides the line joining the points
(-1,3, 4)(2,-5,6)
(a) internally in theratio2 : 3
(b) externally in the ratio 2 : 3
(c) internally in the ratio 3 : 2
(d) externally in the ratio 3 : 2
X
(c) f(x)= - ,g(x)= 1
2
(d) None of these
4
(
(b) f(x)=sin2x + cos2x ; g(x)= 1
(b)
4
(c)
(c)
1
(d) x 2
Which pairs of function is identical?
(a)
3
(a)
2x2 -
4.
(a) 2g 1g2 + 2f/2 = c 1+ c2
(b) 2g 1g 2 -2f/2 = c 1 + c2
(c) 2g 1g 2 +2f1f2 = c 1-c2
(d) 2g1g2-2f/2 =C1-C2
A point is selected at random from the interior of
a circle. The probability that the point is close to
the centre, then the boundary of the circle, is
logx z
ofthe determinant log y x
log 2 x
(a) 0
(c) 1
log y z is
5
(b) log x log y log z
(d) 8
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46
14.
Negation of the statement (p
I\
r) ➔ (r v q) is
(a) -(pAr) ➔ -(rvq)
(b) (- pv-r)v(rvq)
(c) (p I\ r) I\ (r I\ q)
(d) (pAr)A(-rA - q)
21.
(b) reflexive, transitive but not symmetric
(c) symmetric, transitive but not reflexive
(d) neither transitive nor reflexive but symmetric
Ify = m log x + nx2 + x has its extreme values
at x = 2 and x = 1, then 2m + 10n =
(b) -4
(a) -1
15.
If/ (x) =
l
✓
l+h-~
for-1:,;
X
X
<0
22.
IS
2x +3x -2,
continuous at x = 0, then k =
(b) -3
(c) -2
(d) -1
The area enclosed between the curve
16.
23.
y = loge(x+e) andthecoordinateaxesis
17.
(b) 2
(a) 1
(c) 3
(d) 4
The differential equation ofthe family ofcurves
for which the length of the normal is equal to a
constant k, is given by:
(a)
24.
(c)
(d)
18.
f
(y:r
y(:r
(y :r
4
3
2
3
(b)
If x + iy =
COS
3
. .
0 +1
=k2 - y2
25.
ThematrixA= [
= k2 + y2
= k2 + y2
dx-
+a2
26.
-
Sill 0 +
8
3
(d)
I
3
then 4x - x 2 - .y2
2
(c) 4
(d) 5
!]
~
is
2
-2 -1 -3
(a)
idempotentmatrix (b) involutorymatrix
(c)
nilpotent matrix
n-1
X
X2n
(c)
reduces to:
(a) 2
(b) 3
dx
(b)
the value of k.
(d) 5
(a) 2
(b) 3
(c) 4
The projection oflinejoining (3, 4, 5) and ( 4, 6, 3)
on the line joining (-1 , 2, 4) and (1, 0, 5) is-
(a)
= k2 _ y2
y2 dy
(d) -3
AB+AC+AD+AE+AF = kAD , then find
2
(a) -4
(c) -2
IfABCDEF is a regular hexagon and
Ifx = exp
{
tan -I
(d) None of these
l~)1} ,
( y- x
2
dy
then dx equals
2x [1 + tan (log x)] + x sec2 (logx)
(b) x [1 + tan (logx)] + sec2 (logx)
(a)
19.
J
(a)
na tan
(c)
~sm
n .
-J(XnJ
-;; + C (b)
-1
x
n
~cos
-I
x
[---;;
nl +C
(c) 2x [I + tan (logx)] + x 2 sec2 (logx)
(d) 2x [I + tan (logx)] + sec2 (logx)
27.
The value of
° is equal to
(b) 41
(c) 42
(a) 40
(d) 0
Let R be a relation defined by a Rb, a ;?: b where
a and b are real number then R is :
(a) reflexive, symmetric and transitive
dt
t(l + t) is equal to
L
e
e
The sum of the rational terms in the expansion of
(✓2 + 3115 )1
20.
[---;;nl +C (d)
-J[Xn)
---;; +C
n
~tan
(a)
0
(c)
log(-1)
l +e
(d) log(l+e)
WWW.JEEBOOKS.INI
47
MOCKTEST-4
28.
A coin is tossed thrice. If E be the event of
showing at least two heads and F be the event of
35. Ifall the solutions of a cos x +a-cos x
= 6 (a > 1)
are real, then the set of values ofa is:
showing head in the first throw, then find P ( ; ) .
1
1
4
3
(b) (c) (d) 4
4
2
3
An aeroplane flying horizontally 1 km above the
ground is observed at an elevation of 60° and
after 10 s the elevation is observed to be 30°. The
uniform speed of the aeroplane in kilometre per
hour is
(a)
29.
30.
31.
(a)
60✓
3
(b)
(c)
240✓
3
(d) 480
(c)
[l
2]
3 + 2✓
3n + 7, then what is the sum of its first 50 terms?
(a) 3925 (b) 4100 (c) 4175 (d) 8200
LetA(l, k), B(l, 1) and C (2, 1) be the vertices of
a right angled triangle with AC as its hypotenuse.
Ifthe area ofthe triangle is lsquare unit, then the
set of values which 'k' can take is given by
(a) {-1,3}
(b) {-3,-2}
(c) {1,3}
(d) {0, 2}
If the ellipse -
4
y2
+-
1
=1
37.
Let f: ( 4, 6) ➔ (6, 8) be a function defined by
f(x) = x+[%]
(where [.] denotes the greatest
integer function), then
Let f(x)
(b)
-x-2
~
x-2
(~
--
If f(x)
=
meet the ellipse
xe
-u.r~) , *
x
,x=0
0
39.
Let fbe a positive function if
11 =
k
k
1-k
1-k
Jxf{x(l-x)}dxand 12 = ff{x(l-x)}dx
where 2k- 1 >0, then 11 : 12 is equal to
1
34.
(d) None of these
2../x-1-5
In a test of Statistics marks were awarded out of
40. The average of 15 students was 38. Later it
was decided to give marks out of 50. The new
average marks will be
(a) 40
(b) 47.5 (c) 95
(d) 41.5
then f(x) is
x=0
✓x-l
(c)
O
(d) neither differentiable nor continuous at x = 0
1 < x < 26 be real valued function. Then/'(x)for
1 < x < 26is
(b)
x+[f]
11
(a) discontinuous every where
(b) continuous as well as differentiable for all x
(c) continuous for all x but not differentiable at
= ✓x-l + ✓x+24-10✓x-1;
(a) 0
is equal to
x-[f]
( 1
38.
r- 1(x)
(a)
{
(b) b <4
(d) Both (b) and (c)
(d) None of these
Four couples (husband and wife) decide to form
a committee of four members. Find the number of
different committees that can be formed in which
no couple finds a place.
(a) 12
(d) 24
(b) 14
(c) 16
a = b2 - !Ob + 25 then which of the following
is true?
(a) 4 < b < 6
(c) b > 6
(b) (612)
36.
2
2
. fiour ct·1stmct
y =1 m
. pomts
. and
-X - + -;;:
1
33.
[3+2✓
2,+ oo)
If the nth term of an arithmetic progression is
x2
32.
240
(a)
(a)
40.
2
(b) k
For any vector
(c)
1
-
a, the value of
(a' x [)2 + (a" x })2 + (-;{ x i:)2
(a)
-2
3a
(b)
(d)
2
-2
a
(c)
is equal to
-2
2a
(d)
-2
4a
WWW.JEEBOOKS.INI
48
41.
TargetMHT-CET
FortheLPPMinz=x 1 + x 2 such that inequalities
5x 1 + 10x2 ~ 0, x 1 + x 2 :,; 1, x2 :,;4 andx 1,x2 ~O
(a) There is a bounded solution
(b) There is no solution
(c) There are infinitie solution
(d) None ofthese
42.
(b)
47.
n!
1
(c) 1- n
f
I
n!
1- -
a In
xvl-x 3
[~+bl
~
vl-x 3 +l
48.
(a) b = l ,a= l
2
(c) b = l , a=-3
l
(d) b = land a=-3
(a)
(c)
49.
44.
A point on the parabola
y2 = l 8x
at which the
ordinate increases at twice the rate of the
abscissa is
(b)
(2,-4)
(b) A+I
A-I
2
2
(c) 2(A-I)
(d) 2A+ I
The integral factor of differential equation
(x 2 + 1/Y + 2xy = x 2 -1 is
dx
+ k, then:
l
(b) b = -1 , and a=3
3
ofxis
(b) 5
(a) 2
(c) 7
(d) Noneofthese
IfAisasquarematrix suchthat(A-2I)(A + I)=O,
thenA- 1 =
(a)
(d) None of these
dx
~
If tan -I ~ < 2: , x E N , then the maximum value
n:
There are n letters and n addressed envelopes,
the probability that all the letters are not kept in
the right envelope, is
(a)
43.
46.
50.
2x
x2 +1
x 2 -1
(d) None of these
x2 + 1
Area bounded by the curves y = e", y = e-x and
the straight line x = l is (in sq. units)
(a)
l
e+ e
(b)
l
e+-+2
(c)
1
e+ --2
e
(d)
1
e--+2
45.
9)
-9
( g' 2
x-3
(2, 4)
e
(a)
l
(b) 2
y-4
z-5
2
2
- =-
1
plane x + y + z = 17 is
(d)
e
The distance from the point (3, 4, 5) to the point
where the line -
(c)
x 2 +l
(b)
- =-
(c) 3
- meets the
(d)
✓
2
Which of the following is the greatest?
(a)
(b)
(C)
(d)
3tc 2_31c 2 + 3'c 2 _
_ 31c 2
I
2
0
···
31
32c 2 _32c 2 + 32c 2_ + 32c 2
I
32
0
I
···
32c 2 + 32c 2 + 32c 2 _ + 32c 2
32
I
2 ·· ·
0
34c 2_ 34c 2 + 34c 2 _ + 34c 2
0
32
I
2 ···
WWW.JEEBOOKS.INI
Mock Test-~
General Instructions
■
■
■
■
■
■
■
This question booklet contains 150 Multiple Choice Questions (MCQs).
Section-A: Physics & Chemistry - 50 Questions each and
Section-B: Mathematics - 50 Questions.
Choice and sequence for attempting questions will be as per the convenience of the candidate.
Read each question carefully.
Determine the one correct answer out of the four available options given for each question.
Each question with correct response shall be awarded one (1) mark. There shall be no negative marking.
No mark shall be granted for marking two or more answers ofsame question, scratching or overwriting.
Duration ofpaper is 3 Hours.
SECTION-A
PHYSICS
1.
2.
3.
4.
5.
The magnetic field at a point due to a current
carrying conductor is directly proportional to
(a) resistance of the conductor
(b) thickness of the conductor
(c) current flowing through the conductor
(d) distance from the conductor
The work done in placing a charge of
8x 10-18 coulomb on a condenser of capacity
100 micro-farad is
(a) 16xl0-32 joule (b) 3.lxl0-26 joule
(c) 4xl0- 10 joule
(d) 32xl0-32 joule
Light ofwavelength 6000 A falls on a single slit
of width 0.1 mm. The second minimum will be
formed for the angle of diffraction of
(a) 0.08 radian
(b) 0.06 radian
(c) 0.12radian
(d) 0.012radian
A body executing linear simple harmonic motion
has a velocity of3 mis when its displacement is 4
cm and a velocity of4 mis when its displacement
is 3 cm. What is the amplitude of oscillation ?
(b) 7.5cm
(a) 5cm
(c) 10cm
(d) 12.5cm
If the mass of earth is eighty times the mass of a
planet and diameter of the planet is one fourth
that of earth, then acceleration due to gravity on
the planet would be
(a) 7.8m/s2
(b) 9.8m/s2
2
(c) 6.8m/s
(d) 2.0m/s2
6.
A steel wire oflength £ has a magnetic moment
M . It is bent in L-shape (Figure). The new
magnetic moment is
(a) M
M
2
(b) ✓
(c)
M
2
(d) 2M
7.
At a certain place, the angle of dip is 30° and the
horizontal component ofearth's magnetic field is
0.50 oerested. The earth's total magnetic field (in
oerested) is
1
1
3
(b) 1
3
(a) ✓
(c) ✓
(d)
8.
In an LR-circuit, the inductive reactance is equal
to the resistance R ofthe circuit. An e.m .f. E = E0
cos( mt) applied to the circuit. The power
consumed in the circuit is
2
2
(a)
9.
(b)
!_g__
(c)
E5
(d)
E5
8R
2R
4R
Why is the Wheatstone bridge better than the
other methods of measuring resistances?
(a) It does not involve Ohm's law
(b) It is based on Kirchoff's law
(c) It has four resistor arms
(d) It is a null method
WWW.JEEBOOKS.INI
50
10.
11.
12.
13.
TargetMHT-CET
The gap between the frequency of the side bands
in an amplitude modulated wave is
(a) twice that of the carrier signal
(b) twice that of the message signal
(c) the same as that of the message signal
(d) the same as that of the carrier signal
The density of a material in CGS system is
8 g / cm3. In a system ofa unit in which unit of
length is 5 cm and unit of mass is 20 g, the density
of material is
(a) 8
(c) 50
(b) 20
(d) 80
Excitation energy of a hydrogen like ion in its
excitation state is 40.8 eV. Energy needed to
remove the electron from the ion in ground state
is
(a) 54.4eV
(b) 13.6eV
(c) 40.8eV
(d) 27.2eV
A block B is pushed momentarily along a
horizontal surface with an initial velocity V. Ifµ
is the coefficient of sliding friction between B
and the surface, block B will come to rest after a
time
g
(a) ~ (b) V
V
V
V
(c)
14.
15.
16.
g
(d)
17.
The effective capacitance of combination of
combination of equal capacitors between points
A and B shown in figure is
(a)
(c)
(d)
18.
19.
20.
c
c~c
(b) 2C
I II
3C
C
A
C
B
I
I
cc_J_ c
I ""I I
C
2
In a photoelectric experiment the stopping
potential for the incident light ofwavelength 4000A
is 2 volt. Ifthe wavelength be changed to 3000 A,
the stopping potential will be
(a) 2V
(b) zero
(c) less than 2 V
(d) more than 2 V
When the current in a coil changes from 2 amp.
to4 amp. in 0.05 sec., an e.m.f of8 volt is induced
in the coil. The coefficient of self inductance of
the coil is
(b) 0.2 henry
(a) 0.1 henry
(d) 0.8 henry
(c) 0.4 henry
The correct option for getting X = 1 from the
given circuit is:
J/JJJJJ/J/J/f/
A~-.-----...
B---,.--L...-__,
g(µ)
Two identical spheres ofgold are in contact with
each other. The gravitational attraction between
them is
(a) directly proportional to the square of the
radius
(b) directly proportional to the cube of the
radius
(c) directly proportional to the fourth power
of the radius
(d) inversely proportional to the square of the
radius
The coefficient ofperformance of a refrigerator
is 5. Ifthe inside temperature of freezer is -20°C,
then the temperature of the surroundings to
which it rejects heat is
(a) 41°c (b) 11°c (c) 21°c (d) 31°c
In Young's double slit experiment, the slits are 3
mm apart. The wavelength oflight used is 5000
A and the distance between the slits and the
screen is 90 cm. The fringe width in mm is
(a) 1.5
(b) 0.ol5 (c) 2.0
(d) 0.15
C
C
AB(BC
- - -x
C~--,_
21.
BC
__J
(a) A = B = C = 1
(b) A = B = 1 &C = 0
(c) A=C= 1 &B=0 (d) A=0 &B = C= 1
The linear velocity of a rotating body is given by:
v=ro x r
If~ =i-2]+2k and 7 =4]-3k , then the
magnitude of v is
(a)
✓'29 units
(b)
-,J3l units
..J37
22.
(d) .f,i1 units
(c)
units
A ship ofmass 3 x 107 kg initially at rest, is pulled
bya forceof5 x 104 N through a distance of3m.
Assuming that the resistance due to water is
negligible, the speed of the ship is
(a) 1.5 m/sec.
(b) 60 m/sec.
(c) 0.lm/sec.
(d) 5m/sec.
WWW.JEEBOOKS.INI
MOCKTEST-5
23.
A particle of mass 2 kg is moving such that at
time t, its position, (in meter) is given by
2
r(t) = 5i - 2t
The angular momentum of the
particle at t = 2s about the origin (in
kg m-2 s-I) is:
J.
(a)
24.
25.
26.
27.
28.
-80k
(b)
30.
(1 oi - 16})
(c) -40k
(d) 40k
A metallic wire oflength 2.0 mis elongated by 2.0
mm. Area of cross-section of the wire is 4.0 mm2.
The elastic potential energy stored in the wire in
elongated condition is [young's modulus of the
metallic wire is= 2 x 10 11 N/m 2]
(a) 8.23 (b) 0.83 (c) 6.23 (d) 0.63
An ideal gas A and a real gas B have their volumes
increased from V to 2 V under isothermal
conditions. The increase in internal energy
(a) will be same in both A andB
(b) will be zero in both the gases
(c) ofB will be more than that ofA
(d) ofA will be more than that ofB
An electron moving with kinetic energy 6x 10-16
joules enters a field of magnetic induction
6 x 10-3 weber/m 2 at right angle to its motion.
The radius of its path is
(a) 3.42cm
(b) 4.23cm
(c) 5.17cm
(d) 7.7cm
An iron rod oflength 2m and cross-sectional area
of50 mm2 stretched by 0.5 mm, when a mass of
250 kg is hung from its lower end. Young 's
modulus of iron rod is
2
18
(a) 19.6x1020 N / m 2 (b) 19.6x10 N / m
(c) 19.6 x 10 10 N / m 2 (d) 19.6 x l015 N / m 2
All batteries are having emf 10 volt and internal
resistance negligible. All resistors are in ohms.
Calculate the current in the right most 2Q resistor.
31.
51
a result of the collision, the two masses stick
together. The kinetic energy of the composite
mass will be
(a) ffiO
(b) 800
(c) 1000 (d) 1200
A radioactive source of half-life 2 hours emits
radiation of intensity which is 64 times the
permissible safe level. The minimum time in hours
after which it would be possible to work safely
with the source is
(b) 8
(c) 6
(d) 24
(a) 12
A hospital uses an ultrasonic scanner to locate
tumours in a tissue. The operating frequency of
the scanner is 4.2 MHz. The speed of sound in a
tissue is 1.7 km/s. The wavelength of sound in
tissue is close to
(a)
4 x l0-4 m
(b)
32.
33.
34.
(c)
(d) 8 x l0-3 m
A particle executes simple harmonic motion
between x =-Aandx =+ A The time taken for it
to go from O to A/2 is T 1 and T 1 and to go from
A/2 to A is T 2. Then
(a) T 1 < T 2
(b) T 1 > T 2
(c) T 1 =T2
(d) T 1 =2T2
The moment of inertia of a thin uniform rod of
mass M and length L about an axis passing
through its midpoint and perpendicular to its
length is 10 . Its moment of inertia about an axis
passing through one of its ends and
perpendicular to its length is
(a) I 0 +ML2/2
(b) I 0 +ML2/4
(c) I 0 + 2ML2
(d) I 0 + ML2
The centre of mass of triangle shown in figure
has coordinates
y
(a)
2
'_ ~ Jt
llli:----w,
___, ,_,..,,.,~-:-~to..].,. . -2---~
10
' - - - - - ---W,W,21',--- 10
(a)
29.
25
-A
12
(b)
25 A
6
12
(d) _i_A
(c)-A
25
25
A mass of20 kg moving with a speed of l0m/s
collides with another stationary mass of 5 kg. As
8x10-4m
4xl0-3 m
h
b
h
h
b
x=2,y=2
(c)
X=3,y=3
(d)
35.
b
(b)
x=3,y=3
I
l,.•=====
. b-__
..,.__~x
A particle Pis moving in a circle ofradius ' a'
with a uniform speed v. C is the centre of the
circle and AB is a diameter. When passing
through B the angular velocity ofP about A and
Care in the ratio:
(a) 1: 1 (b) 1: 2 (c) 2 : 1 (d) 4: 1
WWW.JEEBOOKS.INI
TargetMHT-CET
52
36.
37.
When light passing through rotating nicol is
observed, no change in intensity is seen. What
inference can be drawn ?
(a) The incident lig ht is unpolarized.
(b) The incident light is circu larly polarized.
(c) The incident light is unpolarized or
circularly polarized.
(d) The incident light is unpolarized or
circularly polarized or combination of both.
An infinitely long thin straight wire has uniform
1
linear charge density of
cm- 1. Then, the
is slightly increased. The frequency of the piano
string before increasing the tension was
43.
38.
39.
(c)
(256-S)Hz
(d) (256+5)Hz
Water flows in a stream line manner through a
capillary tube ofradius a, the pressure difference
being P and the rate flow Q. If the radius is
(a) 4Q
44.
a
2
and the pressure is increased to
45.
!ILL_
40.
41.
42.
(d)
!I~
1
(a)
46.
T/✓
2
(b) 2T
(c)
2T ✓
2
(d) 4 T
A tuning fork of known frequency 256 Hz makes
5 beats per second with the vibrating string ofa
piano. The beat frequency decreases to 2 beats
per second when the tension in the piano string
C
2
I
3 respectively. Then
and ✓
✓
3
(b)
✓3
2
2
(c)
✓
3
(d)2
A certain number of spherical drops ofa liquid of
radius 'r' coalesce to form a single drop ofradius
'R' and volume 'V' . If'T' is the surface tension of
the liquid, then:
Distance --+
Distance --+
covered
covered
A coil having 500 square loops each of side 10
cm is placed normal to a magnetic field which
increases at the rate of I Wb/m 2 • The induced
e.m.f. is
(a) 0.1 V (b) 5.0V (c) 0.5V (d) J.0V
An ideal gas is found to obey an additional law VP2
= constant. The gas is initially at temperature T
and volume V. When it expands to a volume 2 V,
the temperature becomes
(a)
Q
8
the refractive index ofglass with respect to water is
Distance --+
covered
J
(c)
(d)
2
(b) -F
(a) F
(c) 3F
(d) -3F
The refractive indices of glass and water with
respect to air are
!r=__ ~) ! ~
Distance --+
covered
Q
A circular coil ABCD
carrying a current i is
placed in a uniform
magnetic fie ld . If the
magnetic fo rce on the
1
(a)
(c)
(b) Q
segment AB is F , the
force on the remaining
segmentBCDA is
(c) g_ (d) Q
(a) 2
(b) ✓
2
✓3
3
A lead shot of 1 mm diameter falls through a long
column of glycerine. The variation ofits velocity
v with distance covered is represented by
(b) (256-2)Hz
2P, the rate of flow becomes
Q
Q
(256 + 2)Hz
reduced to
3
magnitube of electric intensity at a point 18 cm
awayis: (Giveni:0 = 8.8 x I0 12C 2 Nm-2 )
(a) 0.33 x 10 11 NC-1 (b) 3 x 10 11 NC-1
(c) 0.66 x 1011 NC-1 (d) 1.32 x J0 11 NC-1
In an oscillation ofL.C circuit, the maximum charge
on the capacitor is Q. The charge on the capacitor,
when the energy is stored equally between the
electric and magnetic field is
(a)
47.
(a)
energy = 4VT(~-~) is released
(b)
energy = 3VT (
(c)
energy = 3VTU- ~) is released
~+ ~)
is absorbed
(d) energy is neither released nor absorbed
Two bodies A and B are placed in an evacuated
vessel maintained at a temperature of27°C. The
temperature of A is 327°C and that ofB is 227°C .
The ratio of heat loss from A and Bis about
(a) 2 : 1 (b) 1:2 (c) 4:1 (d) 1 : 4
IWWW.JEEBOOKS.INI
MOCKTESf-5
48.
When the road is dry and the coefficient of the
friction is µ, the maximum speed of a car in a
circular path is 10 ms- 1• Ifthe road becomes wet
53.
and µ'=~, what is the maximum speed
54.
permitted?
(c)
49.
10✓
2 ms- 1
(b)
!Oms- 1
(d)
5✓
2 ms- 1
A light ray is incident perpendicularly to one
face of a 90° prism and is totally internally
reflected at the glass-air interface. If the angle of
reflection is 45°, we conclude that the refractive
indexn
1
2
(a) n > ✓
(b)
n>✓
2
(c)
n<✓
2
(d)
2
n<✓
55.
(a)
A whistle of frequency 385 Hz rotates in a
horizontal circle of radius 50 cm at an angular
speed of 20 radians s- 1• The lowest frequency
heard by a listener a long distance away at rest
with respect to the centre of the circle, given
velocity of sound equal to 340 ms- 1, is
(a) 396Hz(b) 363Hz(c) 374Hz (d) 385Hz
d 4 (in weak ligand fields)
(d) d 4 (in strong ligand fields)
(c)
56.
57.
58.
Which of these does not influence the rate of
reaction?
(a) Nature of the reactants
(b) Concentration of the reactants
(c) Temperature of the reaction
(d) Molecularity of the reaction
3-Hexyne reacts with N a/liq.~ to produce
(a) cis-3-Hexene
(b) trans-3-Hexene
(c) 3-Hexylarnine
(d) 2-Hexylamine
Total volume of atoms present in a face-centred
cubic unit cell ofa metal is (r is atomic radius)
52.
The radii ofNa+ and CJ-ions are 95 pm and 181
pm respectively. The edge length of NaCl unit
cell is
(b) 138pm
(a) 276pm
(c) 552 pm
(d) 415 pm
Aluminium oxide may be electrolysed at l 000°C
to furnish aluminium metal (At. Mass= 27 amu;
l Faraday = 96,500 Coulombs). The cathode
reaction is AJ3+ + 3e- ➔ Al
To prepare 5.12 kg of aluminium metal by this
method would require
(a) 5.49 x 107 C ofelectricity.
(b) 1.83 x 107 C ofelectricity.
(c) 5.49 x 104 C ofelectricity.
(d) 5.49 x 10 1 C ofelectricity.
59.
16
3
3
24
3
3
(a)
12 3
-1tr
3
(b)
-m
(c)
20
-1tr 3
3
(d)
-7tf
CHEMISTRY
51.
d 5 (in strong ligand field)
(b) d 3 (in weak as well as in strong fields)
1
50.
53
Among the following, the wrong statement is
(a) PMMA is plexiglass
(b) SBR is natural rubber
(c) PTFE is teflon
(d) LDPE is low density polythene
Hydride ion transfer takes place in:
(a) Frankland method
(b) Wurtz reaction
(c) Cannizzaro reaction
(d) Wolff-Kishner reduction
The value of the ' spin only' magnetic moment
for one of the following configurations is 2.84
B.M. The correct one is
Which one of the following pairs is isostructural
(i.e., having the same shape and hybridization)?
(a)
[ BCl3 and BrCl3]
(b)
[ NH3 and NO 3]
(c)
[NF3 and Bf:3]
(d)
[ BF4 and NH! ]
WWW.JEEBOOKS.INI
54
60.
TargetMHT-CET
Consider the following sequence ofreactions :
Compound[A]
Reduction )
The compound [A] is
(a) C8:iC8iCN
(c) CR:iNC
61.
62.
::r
) CH 3CH, OH
(b) CR:iNO2
(d) CR:iCN
~1-
69.
Which of the following is chalcopyrite?
(b) FeS2
(c) KMgCl3.68iO
(d) Alp3.28iO
lfx is the specific resistance of the solution and
N is the normality ofthe solution, the equivalent
conductivity of the solution is given by
(a)
(c)
I000 x
N
(b)
IO00N
(d)
X
64.
HN02
[Fe(H2O 6
and [Fe(CN
differ in:
(a) geometry, magnetic moment
(b) geometry, hybridization
(c) magnetic moment, colour
(d) hybridization, number of d-electrons
(a) CuFeS2
63.
[BJ
68.
b= ;,
70.
1000
66.
67.
(d) it forms XeOt"-which is explosive in nature
The rate ofa firstorderreaction is 1.5 x 10-2 mol L-1
min- 1 at 0 .5 M concentration ofthe reactant. The
half life of the reaction is
(a) 0.383 min
(b) 23.1 min
(c) 8.73min
(d) 7.53min
Bauxite ore is made up of
Alp3 + SiO2 + TiO2 + Fepy This ore is treated
with cone. NaOH solution at 500 Kand 35 bar
pressure for few hours and filtered hot. In the
filtrate the species present is/are
Nx
(a)
Nx
(b) Na2Ti(OH)6 only
1000
(c) NaAl(OH)4 and N¾SiO3
71.
oxidised by heating with alkaline
KMnO4 to give
65.
The reason for not storing XeF6 in a glass or a
quartz vessel is that
(a) it forms an explosive having the formula
XeO2F2
(b) it forms an explosive having the formula
XeOF4
(c) it forms XeO2 which is explosive substance
(a)
CH2O+CH3CO(CH2)4COOH
(b)
CO 2 +CH3COCH 2COCH 2CH 2COOH
(c)
CH 2O + CH3 COCH 2COCH 2CH 2COOH
(d) the corresponding tetrol
The reagent commonly used to determine
hardness of water titrimetrically is
(a) oxalic acid
(b) sodium thiosulphate
(c) sodium citrate
(d) disodium salt ofEDTA
The charge on colloidal particles is due to
(a) presence of electrolyte.
(b) very small size of particles.
(c) adsorption of ions from the solution.
(d) none of these.
The E 0 at 25° C for the following reaction is 0.22
V. Calculate the equilibrium constant at 25° C:
H 2 (g) + 2AgCl(s)~ 2Ag(s) + 2HCl(aq)
(a) 2.8 x 107
(b) 5.2 x 108
6
(c) 5.2 x 10
(d) 5.2 x I 03
72.
73.
74.
NaAl(OH)4 only
(d) Na2 SiO3 only
Which one of the following is employed as a
tranquilizer?
(a) Naproxen
(b) Tetracycline
(c) Chlorpheninarnine
(d) Equanil
Primary amines can be distinguished from
secondary and tertiary amines by reacting with
(a) Chloroform and alcoholic KOH
(b) Methyl iodide
(c) Chloroform alone
(d) Zinc dust
In HS-, 1-, RNHi and NH3, order of proton
accepting tendency will be
(a) 1- > N8:i > !lNHi > HS(b) HS- > RNlii > N8:i > 1(c) RNlii > N8:i > HS- > 1(d) NH3 > RNH2 > HS- > 1One litre hard water contains 12.00 mg Mg2+.
Milli-equivalents of washing soda required to
remove its hardness is :
(b) 12.16
(a)
3
(d) 12.16 x 10-3
(c) I x 10-
IWWW.JEEBOOKS.INI
78.
Cr20~-(aq) + H 2 0 ~ 2CJ{)~- (aq) + 2H+ (aq)
The oxoanion has
(a) same oxidizing property in acidic and alkaline
solutions.
(b) better oxidizing property in acidic solution.
(c) better oxidizing property in alkaline solution.
(d) no oxidiz ing property in acidic or alkaline
solution.
The respective compounds A and B are
0
(a)
O
COCH3
and
6
55
The dichromate ion is in equilibrium with
chromate ion in aqueous solution as :
79.
COCH3
80.
The correct sequence which shows decreasing
order of the ionic radii ofthe elements is
(a)
AJ3+ > Mg 2+ > Na+ > F- > 0 2-
(d)
0 2- > F- > Na+> Mg 2 + > AI 3+
Which of the following will give a pair of
enantiomorphs?
(a)
[C~)J[Co(CN)J
(b) [Co(en)2C½]Cl
(c)
[Pt~)J [PtClJ
(d) [C~\Cl]NO2
81.
In the following reaction
RedP + HI
CH
2 sOc2H s + 4[H]-------+
B + H2O~C + HCl
Compound (A), (B) and (C) will be respectively
77.
(a)
PCl5,POCl3,H3PO3
(b)
PCl5 , POCl3 ,H3PO4
(c)
SOCl2, POCl3,H3PO3
(d)
PCl3,POCl3 , H3PO4
Camphor is often used in molecular mass
determination because
(a) it is readily available
(b) it has a very high cryoscopic constant
(c) it is volatile
(d) it is solvent for organic substances
82.
83.
(a) ethane
(b) ethylene
(c) butane
(d) propane
The solubility of a specific non-volatile salt is 4
gin 100 g ofwater at 25°C. lf2.0 g. 4.0 g and 6.0
g of the salt added tol00 g of water at 25°C , in
system X , Y and Z . The vapour pressure would
be in the order
(a) X < Y < Z
(b) X > Y > Z
(c) Z > X = Y
(d) X > Y = Z
The gas which is least adsorbed on charcoal
(under identical conditions) is
(a)
HCl
(b) 0 2
(c)
CO2
(d) ~
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56
84.
TargetMHT-CET
Which one of the following chemical units is
certainly to be found in an enzyme?
90.
OH
(a)
'•·o~
H
HO
0····
91.
H
I
(b)
(o)
· N- IT....
0
0
92.
(a) Antacid
(b) Analgesic
(c) Antimicrobial
(d) Antiseptic
Mark the correct statement
(a) Methylamine is slightly acidic.
(b) Methylamine is less basic than ammonia.
(c) Methylamine is a stronger base than ammonia.
(d) Methylarnine forms salts with alkalies.
Ary! halides can not be prepared by the reaction
ofaryl alcohols with PC13, PC1 5 or SOC1 2 because
(a) phenols are highly stable compounds.
(b) carbon-oxygen bond in phenols has a
partial double bond character.
(c) carbon-oxygen bond is highly polar.
(d) all of these.
Which of the following structures represents
thymine ?
0
O)V'-R
~Jl--R
(d)
85.
87.
88.
I
o.:::,...._N
(b)
(o)
CH 3 (CH 2 )iOH
Amalgams are
(a) always in liquid state.
(b) highly coloured alloys.
(c) alloys which have a great resistance to
abrasion.
(d) alloys which contain Hg as one of the
constituents.
Which of the following is most stable?
(b) Ph2Ctt+
(a) Ph3C+
(c) PhC~
(d) Tropyliumcation
For which of the following changes, 11Htc i1U
(a) N 2 (g) + 0 2 (g) ➔ 2NO(g)
(b)
H 2 (g) + Cl2 (g)~2HCl(g)
(c)
(d)
C(s)+0 2 (g)~C0 2 (g)
CaC0 3 (s)~CaO(s)+ COz(g)
\Nl
N
f~
O.:::,...._NjJ
I
(CH 3)zCHOH
The drug
(b)
I
H
93.
CH
I
z
CH 2 -NH2
(d)
NJJ
i'5-c~
HO
N
Which of the following expressions correctly
represents the equivalent conductance at
infinite dilution of Al 2 (S0 4 ) 3. Given tha t
o
Ao
sol- are the equival e nt
A Al3+ and
conductances at infinite dilution of the
respective ions?
(d)
is used as:
H
f;;
HO~
H
89.
HN:'.)01
Ol ~R
0
The reaction of Lucas reagent is fastest with :
(a)
86.
(a)
94.
( A : 13+ + A; 0
l_ )x 6
2-Bromopentane is heated with pota ssium
ethoxide in ethanol. The major product obtained
is
(a) 2-ethoxypentane (b) pentene-1
(c) trans-2-pentene (d) cis-pentene-2
WWW.JEEBOOKS.INI
MOCKTEST-5
95. In any period, the valency of an element with
respect to oxygen
(a) increases one by one from IA to VIIA
(b) decreases one by one from IA to VIIA
(c) increases one by one from IA to IVA and
then decreases from VA to VIIA one by one
(d) decreases one by one from IA to IVA and
then increases from VA to VIIA one by one
96. In face centred cubic lattice, a unit cell is
shared equally by how many unit cells
(a) 2
(b) 4
(c) 6
(d) 8
97.
98.
Which one of the following reactions of xenon
compounds is not feasible?
(a) 3XeF4 + 6H 2 O ~
2Xe + XeO 3 + 12HF + 1.50 2
(b) 2XeF2 + 2H 2O~2Xe + 4HF + O 2
(c) XeF6 + RbF ~ Rb[XeF7]
(d) Xe03 + 6HF ~ XeF6 + 3Hp
Which of the following is an example of SN2
reaction?
57
CH3 -CH-CH3
I
OH
(c)
CH3CH2OH
(d)
(CH 3hC-Br+OH- ~
-HzO
CH2 = CH2
(CH3hCOH+Br99. Isopropyl alcohol is obtained by reacting which
of the following alkenes with concentrated HzSO4
followed by boiling with HzO?
(a) Ethylene
(b) Propylene
(c) 2-Methylpropene (d) Isoprene
100. Which of the following monomers form
biodegradable polymers?
(a) 3-hydroxybutanoic acid
+ 3-hydroxypentanoic acid
(b) Glycine + amino caproic acid
(c) Ethylene glycol + phthalic acid
(d) Both(a)and(b)
SECTION-B
MATHEMATICS
1.
If n(A) = 1000, n(B) = 500 and ifn(A n B) ~ 1 and
n(A u B) = p, then
(a) 500:c;p::;IO00
(b) 1001:c;p::;1498
(c) 1000:c;p:,; 1498 (d) 1000:c;p:,; 1499
2.
1
Letf(x) =x,g(x)= - andh(x)=flx)g(x).
3.
Then, h (x) = I if and only if
(a) xis a real number
(b) xis a rational number
(c) xis an irrational number
(d) xis a non-zero real number
The set of values of x for which
4.
5.
X
tan3x-tan2x
..
- - - - - = 1 IS.
1+ tan3x tan2x
(a) <I>
(b) 4
(c)
(d)
{me+¾: n = 1,2,3, ....
6.
Ifa, b, c, dare distinct integers in A. P., such that
2 2 2
.
2
d = a +b +c ,thena + b + c+d1s :
(a) 0
(b) 1
(c) 2
(d) Noneofthese
The lines x + 2y-5 = 0, 2x-3y + 4=0,
6x+4y-13=0
(a) are concurrent
(b) form a right angled triangle
(c) form an isosceles triangle
(d) form an equilateral triangle
The area of an equilateral triangle inscribed in
the circle x 2 + y2 + 2gx + 2fy + c = O is
(a)
3✓3 I 2 + f2 -c)
-\g
(b)
3✓3 (g2 +f2-c)
2
4
J
J
(c)
3✓3 (g2 +f2 +c)
4
(d) None of these
{zmc+¾:n= l,2,3, ....
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TargetMHT-CET
58
7.
Ifz =
I
z2 =
Then the function is
(a) discontinuous at x = nn: + n:/4
(b) continuous at x = nn: + n:/4
(c) discontinuous at all x
(d) None of these
and
✓2[cos2:+isin2:]
4
4
✓3[cos~+ i sin~], then lz 1 z21is equal to
✓
m,. Value ofm is
8.
(a) 6
(b) 3
(c) 2
(d) 5
Find the 7th term from the end in the expansion
2
of( x- x 2 /
9.
ioc4
(b)
IOC4.24x
(c)
24. x 2
(d)
10C4.24(:2)
The roots of the equation
abc 2 x 2 + 3a 2 cx + b 2 cx -6a 2 -ab+ 2b 2 = 0 are
non-real
rational ifa, b, c, are rational
irrational ifa, b, care rational
None of these
12.
(a)
4
5
(b)
1/ 5
(c)
18.
19.
dx
1/10 (d) 9/10
14.
(b) = 0ifa= I
(d) all of these
If f(x) = sin x, when xis rational }
= cos x, when xis irrational
l
3 sq. unit,
then the roots of the equation x 2 + 2x = a, are
(a) --4and2
(b) 2and4
(c) -2 and--4
(d) 8 and-8
If[sin- 1 cos- 1 sin- 1 tan- 1 x] = I, where[.] denotes
the greatest integer function, then x belongs to
the interval
(a) [tan sin cos I, tan sin cos sin I]
(b) (tan sin cos I, tan sin cos sin I)
(c) [-1, 1]
(d) [sin cos tan I , sin cos sin tan I]
The solution to of the differential equation
( X + I) -dy - y
= e3x ( X + 1)2 IS.
= (x+ 1)e 3x +c
(a)
y
(b)
3y = (x+ 1)+e3x +c
(c)
- - =e
(d)
ye-3x =3(x+ 1)+ c
3y
x+ l
3x
+c
20.
A father has 3 children with at least one boy. The
probability that he has 2 boys and 1 girl is
(b) 1/3
(a) 1/4
(c) 2/3
(d) None of these
21.
If
The determinant 2a + 1 a+ 2 I is
3 1
3
(a) > 0ifa > l
(c) < 0ifa < I
b
If the area enclosed by y 2 = 4ax is
2
a +2a 2a + 1 I
13.
~2] is an orthogonal matrix,
17.
(a)
11.
2
16.
r
The limit of the series I
as n
2
4
r=I l+r +r
approaches infinity, is
I
I
(c) (b) (d) I
3
2
4
The mean and median of 100 items are 50 and 52
respectively. The value oflargest item is 100. It
was later found that it is 110 and not 100. The
true mean and median are
(a) 50.10, 51.5
(b) 50.10,52
(c) 50,51.5
(d) None of these
The probability that in the random arrangement
ofthelettersoftheword 'UNIVERSITY', the two
I's does not come together is
½[~ :
then
(a) a=-2, b=-1
(b) a= 2, b= 1
(d) a=-2, b = 1
(c) a = 2,b = -l
Find the angle between the tangent to the curve
y2 = 2ax at the points where x = a/2.
(b) 90"
(a) 180"
(c) O"
(d) None of these
n
10.
IfA=
a
0
(a)
(a)
(b)
(c)
(d)
15.
6
dx
f-= p(x) then, f--dx is equal to
x+x
x +x
x
7
7
(a) lnl x l-p(x)+c
(c) x -p(x)+c
(b) lnl xl+p(x) + c
(d) x+p(x)+c
WWW.JEEBOOKS.INI
MOCKTEST-5
22.
The distance between the planes
29.
x+2y-2z+l=0 and 2x+4y-4z+5=0 is
23.
(a)
2 units
(c)
2
➔
1
1
4
units
units
(d) 4 units
'
➔
,,
➔
I-
30.
a is equal to :
(a)
2✓51+2..fs]+ ✓Sk
(b)
2✓5[-2✓5J+ ✓5k
(c)
✓
5t+ ✓5}+ ✓5k
(d)
✓
5i+2✓5]+ ✓5k
If
f(x) = 2sin- 1 .JI-x + sin-I (2.Jx(l-x) ),
where x
(a)
' '
Ifa=2i-2j+kand c = -i+2k
then I c
24.
(b)
E (
0,
31.
½),
then/'(x) is
59
The horizontal distance between two towers is
60 metres and the angular depression of the top
of the first tower as seen from the top of the
second. is 30°. If the height of the second tower
be 150 metres, then the height ofthe first tower is
32.
33.
150-60✓3m
(b) 90m
(c) 150-20✓3m
(d) None of these
Let the perpendiculars from any point on the
line 7x + 56y=0upon3x + 4y=0and5x-12y=0
be p and p', then
(a) 2p = p'
(b) p = 2p'
(c) p = p'
(d) None of these
The length of the latus rectum of the parabola
which has focus at (-1 , 1) and the directrix is
4x + 3y-24 = 0is
(a) 4
(c) 8
(b) 6
(d) 10
7
- i then z 14 =
3-4i
(a) 27
(b) 27 i (c)
If z =
i1 4 i
(d)
-27 i
Number of integral values of x satisfying the
2
3 )6x+IO-x
inequality ( <
4
(b) 6
(a) 5
(c)
2
(a)
.Jx(l-x)
(b) zero
2
(c)
25.
26.
27.
28.
(d)
n:
34 •
IfRbe a relation < from A = {l , 2, 3, 4} to
B = {1, 3, 5} i.e.,
(a, b) ER <=>a < b, then RoR- 1 is
(a) {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}
(b) {(3, 1),(5, 1), (3,2), (5, 2), (5,3), (5, 4)}
(c) {(3, 3),(3,5), (5,3), (5,5)}
(d) {(3, 3), (3, 4), (4, 5)}
If S(p, q, r) = (~p) v [~ (q /\ r)] is a compound
statement, then S(~p, ~q, ~r) is
(a) ~S(p, q, r)
(b) S(p, q, r)
(c) p v (qAr)
(d) p v (q v r)
The co-ordinates of the points A and B are
(2 , 3, 4) and (-2, 5, -4) respectively. If a point
P moves so that PA 2 - PB2 = k where k is a
constant, then the locus of P is
(a) -8x+4y-16z+l6 = k
(b) -8x-4y-16z-16 = k
(c) -8x + 4y -16z-16 = k
(d) None of these
Let A be a set of n ( ~ 3) distinct elements. The
number of triplets (x, y, z) ofthe elements ofA in
which at least two coordinates are equal is
(a) np3
(b) n 3 _np3
(c)
3n2
35.
36.
37.
27
- is
64
7
(d) 8
sin(A-B) , then a 2 , b 2 , c 2
,11a uAABC, sinA = --'----'-
T-
sinC sin(B-C)
are sueh t h at
(a) theyareinG.P.
(b) theyareinH.P.
(c) theyare inA.P.
(d) b 2 =a 2 + c 2
Three numbers are in G.P. such that their sum is
38 and their product is 1728. The greatest number
among them is :
(a) 18
(b) 16
(c) 14
(d) Noneofthese
Find the number of integral solution of the
equationx +y+ z=20andx> -1,y> -2 andz> -3.
(a) 2s c 23
(b) 17c2
(c) 23 C 2
(d) None of these
The coefficient of x 100 in the expansion of
200
L
.
(l + x) 1 is :
J=O
(a)
(200)
100
(b)
(c)
(200)
101
(d)
Gi~)
(~i~)
(d) 3n 2 (n- l)
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TargetMHT-CET
60
38.
Derivative of (
✓x + .);z)
2
(a)
~
(b)
(c)
.Jx2 + l
(d)
✓
x+l
is
X
1
(a)
1--1
(b)
x2
x2
(c)
39.
(d)
l+x2
lff R ➔ R,g: R ➔ Randh : R ➔ Raresuch that
ftx) = x 2, g(x) = tan x and h (x) = log x, then the
value of [ho (got)], if x =
(a) 0
40.
45.
1
(b)
-/
1
0
~ll
2
46.
\ll+x~
The maximum value of P = x+3ysuchthat
2x +y~2O, x +2y~2O, x~ O, y~O is
(a) 10
(b) ffi
(d) None of these
(c) 30
IfA= [~
(d)
(a)
10
47.
:
(b) 299A
(c)
(d) None of the above
Let fbe the function defined by
and
1
f(x) ={x 2 _;~ :~11-1' x ~d
J /2,
k
(a)
(b)
(c)
(d)
(a) 7
(b) -7 (c) 15
(d) -11
Letj(x) be a function defined as follows:
f(x) = sin(x2 -3x), x ~ O; and 6x +5x 2 , x > 0
Then atx = O,j(x)
(a)
(b)
(c)
(d)
100
2100A
2 101 A
A-1 = _!_adj(A), then k is
41.
~] thenA
will be :
(c) -1
1
Ifmatrix A=[:
J;
~
has a local maximum
has a local minimum
is discontinuous
None of these
48.
X
=1
The function is continuous for all values ofx
The function is continuous only for x > 1
The function is continuous at x = 1
The function is not continuous at x = 1
The value of
x
(a)
fe
(J+x+x2)
1an -1 x _
_ _ _ dx
2
is
I+ x
/an - 1 x+C
-I
1t
2
42.
f [(x+n) +cos (x+3n)]dx is equal to
3
49.
2
2
(c)
y+3
2
z- 4
-]
32
7t
7t4
7t
x-4
y+4
z+I.
32
2
I
2
(b)
- +-
- - = - - = - - 1s:
(d)
2:_ 1
(a)
cos-
(c)
cos-
2
43.
x+l
2
- - = - - = - - and
31t
(a)
(c) e1"" x +2x+C (d) None of these
The angle between two lines
4
For non zero, non collinear vectors p and q,
2
(i)
1
(¼)
(b)
cos-
1
(¾)
(d)
cos - I (
1
¾)
the value of [ipq]i +[Jpq]J+ [k pq]k is
50.
44.
(a)
O
(c)
(q
X
p)
(b)
2( p
(d)
(p
X
X
q)
q)
The area bounded by the x-axis , the curve
y = f(x) and the lines x = 1, x =b, is equal to
A fair die is thrown twenty times. The probability
that on the tenth throw the fourth six appears is
20 c x5 6
12O x 5 7
(a)
(c)
10
620
(b)
610
84x5 6
(d)
None of these
~-✓
2 for all b > I, then ftx) is
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Mock Test-rn]
General Instructions
■
■
■
■
■
■
■
This question booklet contains 150 Multiple Choice Questions (MCQs).
Section-A: Physics & Chemistry - 50 Questions each and
Section-B: Mathematics - 50 Questions.
Choice and sequence for attempting questions will be as per the convenience of the candidate.
Read each question carefully.
Determine the one correct answer out of the four available options given for each question.
Each question with correct response shall be awarded one (1) mark. There shall be no negative marking.
No mark shall be granted for marking two or more answers ofsame question, scratching or overwriting.
Duration ofpaper is 3 Hours.
SECTION-A
PHYSICS
1.
2.
3.
4.
5.
The fundamental frequency ofa closed end organ
pipe is n. Its length is doubled and radius is
halved. Its frequency will become nearly
(b) n/3
(a) n/2
(c) n
(d) 2 n
Ifthe density ofa small planet is the same as that
of earth, while the radius of the planet is 0.2 times
that of the earth, the gravitational acceleration on
the surface of the planet is
(a) 0.2g (b) 0.4g (c) 2g
(d) 4g
Which of the following statement is correct?
(a) Gauss's law is valid only for symmetrical
charge distributions.
(b) Gauss' s law is valid only for charge placed
in vacuum.
(c) The electric field calculated by Gauss 's law
is the field due to the charges inside the
Gaussian surface.
(d) The flux of the electric field through a closed
surface due to all the charges is equal to the
flux due to the charges enclosed by the surface.
Wavefront is the locus of all points, where the
particles of the medium vibrate with the same
(a) phase
(b) amplitude
(c) frequency
(d) period
A bar magnet oflength '£' and magnetic dipole
moment 'M' is bent in the form ofan arc as shown
in figure. The new magnetic dipole moment will
be
(a)
3
-M
1t
2
(b) -M
1t
(c)
(d)
6.
7.
8.
M
~
•
.r
\
/4
r\
-~
ir
2
M
The transformer voltage induced in the
secondary coil ofa transformer is mainly due to
(a) a varying electric field
(b) a varying magnetic field
(c) the vibrations ofthe primary coil
(d) the iron core ofthe transformer
In the experiment of potentiometer, at balance
point, there is no current in the
(a) main circuit
(b) galvanometer circuit
(c) potentiometer circuit
(d) both main and galvanometer circuits
Radiations of two photon' s energy, twice and
ten times the work function of metal are incident
on the metal surface successsively. The ratio of
maximum velocities ofphotoelectrons emitted in
two cases is
(a) 1 : 2 (b) 1 : 3 (c) 1 : 4 (d) 1 : 1
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62
TargetMHT-CET
9.
(a) remains stationary
(b) is attracted by the loop-A
(c) is repelled by the loop-A
(d) rotates about its CM, with CM fixed
(CM is the centre of mass)
A proton moving with a velocity3 x 105 mis enters
a magnetic field of0.3 tesla at an angle of30" with
the field. The radius of curvature ofits path will
be ( elm for proton = I 0 8 C/kg)
(b) 0.5cm
(a) 2cm
(c) 0.02cm
(d) 1.25cm
A wire suspended vertically from one of its
ends is stretched by attaching a weight of
200N to the lower end. The weight stretches
the wire by I mm. Then the elastic energy
stored in the wire is
(a) 0.2J (b) !OJ (c) 20J (d) 0.1 J
A car is moving in a circular horizontal track of
radius 10 m with a constant speed of 10 mis. A
bob is suspended from the roof of the car by a
light wire oflength 1.0 m. The angle made by the
wire with the vertical is
If a vector
vector 4
10.
11.
12.
13.
14.
2i + 3} + 8k
is perpendicular to the
J- 4i + ak , then the value of a is
(d) -I
(a) 1/2
(b) -1/2 (c) I
A wirehasamass0.3 ± 0.003 g, radius0.5 ±0.005
mm and length 6 ± 0.06 cm. The maximum
percentage error in the measurement of its
density is
(c) 3
(b) 2
(d) 4
(a) l
In a transistor, the change in base current from
100 µA to 125 µA causes a change in collector
current from 5 mA to 7 .5 mA, keeping collectorto-emitter voltage constant at 10 V. What is the
current gain of the transistor?
17.
18.
(d) 25
(a) 200
(c) 50
(b) 100
If the terminal speed ofa sphere of gold (density
= 19.5 kg/m3) is0.2 mis in a viscous liquid(density
= 1.5 kg/m3), find the terminal speed of a sphere
of silver (density= 10.5 kg/m3) of the same size
in the same liquid
(b) 0.133mls
(a) 0.4mls
(c) 0.1 mis
(d) 0.2 mis
Two gases A and B having the same temperature
T, same pressure P and same volume V are mixed.
If the mixture is at the same temperature T and
occupies a volume V, the pressure ofthe mixture is
(c) P/2
(d) 4P
(b) P
(a) 2P
A system goes from A to B via two processes I
and II as shown in figure. Ift.U 1 and t.U2 are the
changes in internal energies in the processes I
and II respectively, then
(a) relation between t.U 1 and t.U2
tS::
19.
(a)
20.
kC
(a)
(c)
16.
(1 + k
2kC
l+ k
(b) C(k+ I)
(d) None of these
Two identical circular loops ofmetal wire are lying
on a table without touching each other. Loop-A
carries a curent which increases with time. In
response, the loop--B
7C
7C
3
(c)
21.
(d)
6
7C
4
The least coefficient offriction for an inclined plane
inclined at angle a with horizontal in order that a
solid cylinder will roll down without slipping is
2
2
(a) -tan a
(b) -tan a
(c)
tana
(d)
7
5
-tana
7
If the magnetic dipole moment of an atom of
diamagnetic material, paramagnetic material and
ferromagnetic material are denoted by µd, ~ and
µf respectively, then
(a) µd = OandµP ,e O (b) µd;eOandµp = O
(c) µP = 0 and µr * 0 (d) µd 0 and µr * 0
In Young's double slit experiment shown in
figure S 1 and S 2 are coherent sources and S is
the screen having a hole at a point 1.0mm away
from
the central line.
.... .ls,
Centreof
I
screen
White light (400 to0.5m~ ... ~ s
Screen
2
1
700nm) is Sent
hole I.Omm
through the slits.
'
s0cm
's
Which wavelength passing through the hole has
strong intensity?
(b) 700nm
(a) 400nm
(d) 667nm
(c) 500nm
*
V
Two capacitors of capacitance C are connected
in series. If one of them is filled with dielectric
substance k, what is the effective capacitance ?
(b)
3
can ~otbe determined P
(b) t.U 1 -t.U2
~
A~
B
(c) t.U 1 < t.U2
1
(d) t.U 1 > t.U2
15.
Cf
22.
t.
1
IWWW.JEEBOOKS.INI
MOCKTESf-6
23. The equation ofplane progressive wave motion is
30.
. 2n ( vt-x ) . Velocity of the particle is
y =a sm
T
dy
vdx
dy
(c)
(d) - v dx
If a body cools down from 80°C to 60°C in 10 min
when the temperature of the surrounding is 30°C,
then the temperature of the body after next 10
min will be
(a)
24.
(a)
25.
dv
ydx
dv
- ydx
26.
27.
28.
(d) None of these
32.
+111 y + n + n
the binding energy per nucleon ofX and Y is 8.5
MeV whereas of 236U is 7.6 MeV The total energy
liberated will be about
(b) 200MeV
(a) 2000MeV
(c) 2MeV
(d) 200keV
An audio signal represented as 25 sin 2n (2000 t)
amplitude modulated by a carrier wave : 60 sin
2n(100, 000)t. The modulation index of the
modulated signal is
(a) 25% (b) 41.6% (c) 50% (d) 75%
A ball of mass 10 g moving perpendicular to
the plane of the wall strikes it and rebounds in
the same line with the same velocity. If the
impulse experienced by the wall is 0.54 Ns, the
velocity of the ball is
(a) 27 ms-1
(b) 3.7 ms- 1
(c) 54ms-1
(d) 37ms-1
In Fig. ABC is the cross section of a right - angled
prism and ACDE is the cross section of a glass
slab. The value of0 so that incident normally on
the face AB does not cross the face AC is (given
sin-I (3/5) = 37°).
A
E
(a)
e:"'.:37°
(b) 0 < 37°
(c)
0:"'.:53°
31.
(b) 48°C
(c) 30°C
In a fission reaction
~~6 U ➔ 111 X
The phase difference between the beams is
(b)
50°C
:£
II
.,
63
Two beams of light having intensities I and 41
interfere to produce a fringe pattern on a screen .
33.
34.
35.
D
29.
C
(d) 0 < 53°
Two bodies of masses 2 kg and 4 kg are moving
with velocities 2 mis and 10 mis respectively along
same direction. Then the velocity of their centre
ofmass will be
(a) 8.1 mis
(b) 7.3 mis
(c) 6.4mls
(d) 5.3 mis
%at
point A and n at point B. Then the difference
between the resulting intensities at A and B is
(a) 21
(b) 41
(c) 51
(d) 71
A straight wire of diameter 0.5 mm carrying a
current of 1 A is replaced by another wire of 1 mm
diameter carrying same current. The strength of
magnetic field far away is
(a) twice the earlier value
(b) same as the earlier value
(c) one-halfofthe earlier value
(d) one-quarter of the earlier value
An inductor, a resistor and a capacitor are joined
in series with an AC source. As the frequency of
the source is slightly increased from a very low
value, the reactance of the
(a) inductor increases (b) resistor increases
(c) capacitor increases(d) circuit increases
A ring ofmass m and radius r is melted and then
moulded into a sphere. The moment ofinertia of
the sphere will be
(a) more than that of the ring
(b) less than than of the ring
(c) equal to that of the ring
(d) None of these
A drop of oil is placed on the surface of water.
Which of the following statements is correct?
(a) It will remain on it as a sphere
(b) It wi II spread as a thin layer
(c) It will partly be a spherical droplet and partly
a thin film
(d) It will float as a distorted drop on the water
surface
A police car moving at 22 mi s, chases a
motorcyclist. The policeman sounds his horn at
176 Hz, while both of them move towards a
stationary siren of frequency 165 Hz. The speed
of the motorcycle, ifit is given that he does not
observe any beats is
Pol ice car
--+
22 mis
( 176 Hz)
(a)
Motorcycle
~
Stationary siren
(165 Hz)
33mls(b) 22mls(c) zero
(d)
ll mls
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TargetMHT-CET
64
36.
3 7.
38.
The maximum velocity of a particle, executing
simple harmonic motion with an amplitude 7 mm,
is 4.4 mis. The period of oscillation is
(a) O.Ols (b) 10s (c) O.ls (d) lOOs
The radii ofcircular orbits of two satellites A and
B of the earth, are 4R and R, respectively. Ifthe
speed of satellite A is 3 V, then the speed of
satellite B will be:
(c) 12V (d) 3 V/2
(a) 3 V/4 (b) 6V
Unpolarized light is incident on a plane sheet on
water surface. The angle of incidence for which
the reflected and refracted rays are perpendicular
to each other is ( µ of water =
39.
1
(a)
sin-
(c)
tan-I
(¾)
(b)
(1)
(d)
16 ,__
25 o
21,__
(c)
40.
42.
(¾)
sin- (½)
tan-
(d)
mv2
(b)
(b)
43.
C
lV
/\
(c)
3V
(d)
1.5V
2µJ'./ \'\µFB
~~
A
2µF
A particle of mass 10 gm is describing S.H.M .
along a straight line with period of 2 sec and
amplitude of l Ocm. Its kinetic energy when it is
at 5 cm from its equilibrium position is
(b) 3.75,r 2 erg
(a) 37.5,r2 erg
(d) 0.375,r2 erg
Two waves having the intensities in the ratio of9
: 1 produce interference. The ratio ofmaximum to
the minimum intensity, is equal to
(a) 2:1 (b) 4:1 (c) 9:1
(d) 10:8
A particle is going parallel to x-axis with constant
speed v at a distance a from the axis. Then its
angular velocity about an axis passing through
the origin 0, at the instant when radial vector of
the particle makes angle 0 with the x-axis is
(c) 375,r2 erg
1
44.
1
45.
20,__
27 o
25,__
16
V
2
(b) -cos 0
(a)
2a
o
A body of mass (4m) is lying in x-yplane at rest.
It suddenly explodes into three pieces. Two
pieces, each of mass (m) move perpendicular to
each other with equal speeds (v). The total kinetic
energy generated due to explosion is
(a)
41.
20 o
(b)
(a) 2V
¾)
The wavelength of radiation is "-o when an
electron jumps from third to second orbit of
hydrogen atom. For the electron to jump from
the fourth to the second orbit of the hydrogen
atom, the wavelength ofradiation emitted will be
(a)
between A and B. The voltage between B and C
is
Imv
(c)
V
46.
2
2
(c) 2 mv2
(d) 4 mv2
A block rests on a rough inclined plane making
an angle of30° with the horizontal. The coefficient
of static friction between the block and the plane
is 0.8. Ifthe frictional force on the block is l ON,
the mass of the block (in kg) is
2
(take g = 10 m / s )
(a) 1.6
(b) 4.0
(c) 2.0
(d) 2.5
Three capacitors are connected in the arms of a
triangle ABC as shown in figure 5 V is applied
~sin0
Currents of a 10 ampere and 2 ampere are passed
through two parallel thin wires A and B
respectively in opposite directions. Wire A is
infinitely long and the length ofthe wire Bis 2 m.
The force acting on the conductor B, which is
situated at 10 cm distance from A will be
(a) 8 x 10-5 N
(b) 5x 10-5 N
(c)
47.
8n x 10-7 N
(d) 4n x 10-7 N
A force of 103 newton, stretches the length of a
hanging wire by 1 millimetre. The force required
to stretch a wire of same material and length but
having four times the diameter by 1 millimetre is
(a)
4 x 103 N
(b)
16 x 103 N
(c)
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MOCKTEST-6
48.
49.
SO.
65
Two coils, one primary of 500 turns and one
secondaryof25 turns, are wound on an iron ring
ofmean diameter 20 cm and cros&-sectional area
12 cm2. Ifthepermeabilityofiron is 800, the mutual
inductance is :
(a) 0.48H (b) 2.4H (c) 0.12H (d) 0.24H
A 5V battery with
internal resistance
20 and a 2V battery
with
internal 5V
2V
10n
20
in
resistance 10 are
connected to a 100
resistor as shown in
the figure.
The current in the I on resistor is
(a) 0.27 AP2 toP1
(b) 0.03AP1 toP2
(c) 0.03 AP2 to P 1
(d) 0.27 AP1 to P2
Water rises to a height of 10 cm in capillary tube
and mercury falls to a depth of3. I cm in the same
capillary tube. If the density of mercury is 13.6
and the angle of contact for mercury is 135°, the
approximate ratio of surface tensions of water
and mercury is
(a)
l:0.15(b)
1:3
(c)
1:6
(d) 1.5:l
CHEMISTRY
51.
52.
53.
54.
Which of the following lanthanoid ions is
diamagnetic?
(At nos. Ce = 58, Sm = 62, Eu = 63, Yb = 70)
(a) Sm2+ (b) Eu2+ (c) Yb2+ (d) Ce2+
For fee ifAB is just like the rock salt like structure
then, A+ and B- are located at(a) A+ - Tetrahedral voids ; B- - Corner
(b) A+- Comer and faces ; B- - Octahedral voids
(c) A+- Octahedral voids ; B- - Comer and faces
(d) N - Comer and faces; B- - Octahedral and
tetrahedral voids
Second and successive electron affinity of an
element
(a) is always successive (energy is released)
(b) is always positive (energy is absorbed)
(c) can be positive or negative
(d) is always zero
Hydrogenation of benzoyl chloride in the
presence of Pd and BaS04 gives
(a) benzyl alcohol
(b) benzaldehyde
(c) benzoicacid
(d) phenol
XeO4 molecule is tetrahedral having :
(a) Two pn - dn bonds
(b) One pn - dn bonds
(c) Four pn - dn bonds
(d) Three pn - dn bonds
56. When CuS04 is electrolysed using platinum
electrodes,
(a) copper is liberated at cathode, sulphur at
anode.
(b) copper is liberated at cathode, oxygen at
anode.
(c) sulphur is liberated at cathode, oxygen at
anode.
(d) oxygen is liberated at cathode, copper at
anode.
57. Silver is monovalent and has atomic mass of 108.
Copper is divalent and has an atomic mass of
63.6. The same electric current is passed for the
same length of time through a silver coulometer
and a copper coulometer. If 27 .0 g of silver is
deposited, then the corresponding amount of
copper deposited is
(a) 63.60g
(b) 31.80g
(c) 15.90g
(d) 7.95g
58. XeF6 dissolves in anhydrous HF to give a good
conducting solution which contains:
(a) Wand XeF7 ion
55.
(b)
HF2 and XeF{ ions
(c)
HXeF and F- ions
6
(d) none of these
59. Primary and secondary ammes can be
distinguished by:
(a) Schiff's reagent
(b) Carbylamine reaction
(c) Hoffinann's bromamidereaction
(d) Biuret reaction
60. A mixture of benzaldehyde and formaldehyde
on heating with aqueous NaOH solution gives.
(a) benzyl alcohol and sodium formate.
(b) sodium benzoate and methyl alcohol.
(c) sodium benzoate and sodium formate.
(d) benzyl alcohol and methyl alcohol
61. Which of the following modes of expressing
concentration is independent of temperature ?
(a) Molarity
(b) Molality
(c) Formality
(d) Normality
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TargetMHT-CET
66
62.
63.
64.
The best method for the separation of
naphthalene and benzoic acid from their
mixture is:
(a) distillation
(b) sublimation
(c) chromatography (d) crystallisation
The gaseous product formed when HOC! reacts
with 8i02 in acidic medium is
(a) H2
(b) C1 2 (c) 0 2
(d) HC102
The pH of 10- 10 M NaOH solution is nearest to:
(a) 6
(b) -10 (c) 4
(d) 7
(c)
I
66.
67.
If 1.!.. moles of oxygen combine with Al to form
2
Al2 0 3 the weight of Al used in the reaction is
(Al=27)
(a) 27g (b) 54g (c) 49.5g (d) 31g
Which of the following statement is wrong?
(a) Polar stratospheric clouds (PSCs) are
clouds formed over Antarctica.
(b) Acid rain dissolves heavy metals such as
Cu, Pb, Hg and Al from soil, rocks and
sediments.
(c) 8iS04 is major contributor to acid rain,
HN03 ranks second and HCl third in this
respect.
(d) Fishes grow in warm as well as in cold water.
If one strand of DNA has the sequence
ATGCTTGA, the sequence in the complimentary
strand would be
(b) TACGTAGT
(a) TCCGAACT
(d) TAGCTAGT
(c) TACGAACT
68.
70.
71.
72.
y
WhatisY?
CH3 -CH-CH2 -CH2 -OJ
CH 3
74.
I
I
CH3 CH3
The IUPAC name of the complex
[Co(NH3)i8i0)4]Cl3 is
(a) Diamminetetraaquacobalt (III) trichloride
(b) Diamminetetraaquacobalt (11) chloride
(c) Diamminetetraaquacobalt (III) chloride
(d) Tetraaquadiamminecobalt (III) trichloride
During the charging oflead storage battery, the
reaction at anode is represented by :
(a) Pb 2+ +SO~- ~PbS04
(b)
73.
(a)
I
CH3 CH3
69.
65.
CH3 -CH-CH-O-CH-CH-CH3
PbS0 4 +2H20~
Pb0 2 + so~- + 4H+ + 2e2
Pb~Pb + +2e-
(c)
(d) Pb2+ +2e- ~ P b
The most reactive compound for electrophilic
nitration is:
(b) Nitrobenzene
(a) Benzene
(c) Benzoic acid
(d) Toluene.
Which of the following polymer is an example of
fibre
(a) silk
(b) dacron
(c) nylon-6,6
(d) all of these
The organic compound with two asymmetric
carbon atoms is
(a) 3,4-dimethylheptane
(b) 3-methyl-1-pentene
(c) 2-chloropentane
(d) 5-ethyl-2,3 -dimethylheptane
Zinc and mercury do not show variable valency
Ii ked-block elements because
(a) they are soft.
(b) their d-shells are complete.
(c) they have only two electrons in the
outermost subshell.
(d) their d-shells are incomplete.
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MOCKTEST-6
75.
76.
77.
Select the correct statement
(a) The non-stoichiometric form of NaCl is
yellow and that ofKCl is blue lilac.
(b) Solids containing F-centres (Farbe) are
paramagnetic
(c) Conduction by electrons is known as n-type
super conduction
(d) All the above are correct
What is the decreasing order of strength of the
bases ?
OH-, NH2, HC = c- and CH 3CH 2 ?
(a) CH 3CH2 > NH2 > HC = c- > OH(b) HC = c- > CH 3CH 2 > NH 2 > OH(c) OH-> NH 2 > HC = c- > CH3CH2
(d) NH2 > HC = C- >OH-> CH3CH2
A graph plotted between log k vs 1/T for
calculating activation energy is shown by
67
81.
82.
83.
84.
85.
78.
79.
80.
The geometry of the compound [Pt(NR:i)2Cl2] is
(a) squareplanar
(b) pyramidal
(c) tetrahedral
(d) octahedral
Which of the following statements is correct?
(a) RNA controls the synthesis of proteins.
(b) The sugar present in DNA is D-(-)-ribose.
(c) RNA has double stranded a-helix structure.
(d) DNA mainly occurs in the cytoplasm of the
cell.
A colloidal solution is subjected to an electrical
field. The particles move towards anode. The
coagulation of same sol is studied using NaCl,
BaC12 and A1Cl 3 solutions. Their coagulating
power should be
(a) NaCl > BaC1i > AIC13
(b) BaC12 > AIC13 > NaCl
(c) AIC13 > BaC13 > NaCl
(d) BaC12 > NaCl > AIC13
86.
87.
88.
On electrolysis of dilute sulphuric acid using
platinum electrodes, the product obtained at the
anode will be
(a) hydrogen
(b) oxygen
(c) hydrogen sulphide(d) Sulphur dioxide
How many EDTA ( ethylenediaminetetraacetic
acid) molecules are required to make an
octahedral complex with a Ca2+ ion?
(a) One
(b) Two
(c) Six
(d) Three
The stablity of lyophillic colloids is due to which
of the following?
(a) Charge on their particles
(b) Large size of their particles
(c) Small size oftheir particles
(d) A layer of dispersion medium
Which of the following is not correct regarding
terylene?
(a) Step-growth polymer
(b) Synthetic fibre
(c) Condensation polymer
(d) Thermosetting plastic
An ideal gas obeying kinetic theory of gases
can be liquefied if
(a) its temperature is more than critical
temperature Tc
(b) its pressure is more than critical pressure Pc
(c) its pressure is more than Pc at a temperature
less than Tc
(d) it cannot be liquefied at any value of P and T
Doping ofAgCl crystals with CdC12 results in
(a) Frenkel defect
(b) Schottky defect
(c) Substitutional cation vacancy
(d) Formation ofF - centres
Benzene can be obtained in the reaction:
(a) Ethene + 1,3-butadiene
(b) Trirnerisation of ethyne
(c) ReductionofPhCHO
(d) All of these
In countries nearer to polar region, the roads are
sprinkled with CaC12 • This is
(a) to minimise the snow fall
(b) to minimise pollution
(c) to minimise the accumulation of dust on the
road
(d) to minimise the wear and tear of the roads
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68
89.
90.
TargetMHT-CET
Acetanilide on nitration followed by alkaline
hydrolysis mainly gives:
(a) o-Nitroaniline
(b) p-Nitroaniline
(c) m-Nitroaniline
(d) 2, 4, 6-Trinitroaniline
A substance initial concentration (a) reacts
according to zero order kinetics. What will be the
time for the reaction to go to completion
a
(a)
91.
k
(b)
a
a
(c)
(d)
96.
III
(2)
(a)
@ - cH2 - CH2 - CH3
(b)
@ - H - CH2 - CH3
2k
a
k
2k
Arrange the following amines in the decreasing
order of their basicity
~
The final product (III) obtained in the reaction
sequence -
1
OH
0
2
(c)
NH
@ - ! - ocH2 - CH3
~
0
(d)
@ - ~ - CH2 - CH3
97.
1> 3 > 2
1> 2 > 3
(a)
(c)
92.
93.
94.
95.
If 1
(b) 3 > 2 > 1
(d) 2 > 1 > 3
1
2 moles of oxygen combine with Al to form
Al2 0 3 the weight of Al used in the reaction is
(Al=27)
(a) 27g (b) 54g (c) 49.5g(d) 31g
Which of the following terms indicates to the
arrangement of different protein subunits in a
multiprotein complex ?
(a) Primary structure
(b) Secondary structure
(c) Tertiary structure
(d) Quaternary structure
Ifchloroform is left open in air in the presence of
sunlight, it gives
(a) carbon tetrachloride
(b) carbonyl chloride
(c) mustard gas
(d) lewisite
Which one of the following alcohols is least
soluble in water?
(a) CH 30H
(b) C 3H 7 0H
(c) C 4 H 9 0H
(d) C 10 H 2 i0H
Which of the following statements is not true
about enzyme inhibitors?
(a) Inhibit the catalytic activity of the enzyme
(b) Prevent the binding of substrate
(c) Generally a strong covalent bond is formed
between an inhibitor and an enzyme
(d) Inhibitors can be competitive or non competitive
98. Identify the incorrect statement among the following.
(a) Br2 reacts with hot and strong NaOH solution to give NaBr and H20.
(b) Ozone reacts with S02 to give S03.
(c) Silicon reacts with NaOH(aq) in the presence of air to give Na2Si0 3 and HzO.
(d) Cl2 reacts with excess ofNH3 to give N 2
andHCI.
99. Mn04has the strongest and weakest oxidising
power in
(a) alkaline and acidic medium.
(b) alkaline and neutral medium.
(c) acidic and neutral medium.
(d) acidic and alkaline medium.
100. 3 moles of ethanol react with one mole of
phosphorus tribromide to form 3 moles of
bromoethane and one mole of X. Which of the
following is X?
(a) Hl04
(c) HP03
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69
MOCKTEST-6
SECTION-8
MATHEMATICS
1.
2.
3.
7.
Given n(U)=20, n(A)= 12,n(B)=9,n(AnB)=4,
where U is the universal set, A and B are subsets
ofU, then n((A u B)c) =
(a) 17
(b) 9
(c) 11
(d) 3
Which of the following functions are periodic?
(a) f(x) = logx,x > O
(b) f(x)=eX,x ER
(c) f(x)=x-[x],x ER
(d) f(x) =x+ [x] ,x ER
The least difference between the roots, in the
first quadrant ( 0:,; x:,;
%),of the equation
Letz= log 2 (1 + i), then (z +
(a)
ln4+1t
z )+ i (z- z )=
n-ln4
(b)
ln4
(c)
8.
ln4-n
n+ln4
(d)
ln4
ln2
Six dice are thrown. The probability that different
numbers will turn up is :
(a)
9.
ln2
129
1296 (b)
1
54
(c)
5
324
(d)
5
54
dy
Ify = (1 + xll4 ) (1 + x 112 ) (1 - xl/4 ), then dx is
equal to
2
4cos x(2-3sin x) + (cos 2x + 1) = 0 is
(a)
4.
7t
6
(b)
7t
-
4
(c)
7t
-
3
(d)
(a)
7t
2
If Sn denotes the sum ofn terms ofan AP., then
Sn+3 -3 Sn +2 + 3 Sn+! - Sn =
(a)
5.
6.
10.
0
(b)
1
(c)
1
2
11.
(d) 2
The values of k for which the line
(k-3)x-(4-k2)y + k2- 7k + 6 = 0 is parallel to
thex-axis, is
(a) 3
(b) 2
(c) 1
(d) 4
If OA and OB are the tangents from the origin to
the circle x 2 + y2 + 2gx + 2.fy + c = O and C is
12.
and
2
1 / 2
-v c(g + f - c)
2
14.
(b)
.Jc(g2 + f2 - c)
(c)
c.Jg2+f2 - c
(d)
.Jg2+f2-c
(b) -1
13. If-; =i+2J+3k,
the centre ofthe circle, the area ofthe quadrilateral
OACBis
(a)
1
(c)
X
(d)
✓
x
Identify the false statements
(a) ~ [p v (~ q)]=(~ p) v q
(b) [p v q] v (~ p) is a tautology
(c) [p /\ q) /\ (~ p) is a contradiction
(d) ~[p v q]=(~ p) v (~ q)
The mean ofl 3 observations is 14. Ifthe mean of
the first 7 observations is 12 and that of the last
7 observations is 16, what is the value of the 7 th
observation ?
(a) 12
(b) 13
(c) 14
(d) 15
In how many ways can 12 gentlemen sit around a
round table so that three specified gentlemen are
always together?
(a) 9!
(b) 10!
(c) 3! 10! (d) 3! 9!
b =2i+3J + k , 7 =3i + J+2k
aa +13b +y e = -3(i -k) , then
the
ordered triplet (a, 13, y) is
(a) (2,-1,-1)
(b) (-2, 1, 1)
(c) (-2,-1, 1)
(d) (2, 1,-1)
If y = a log x + bx2 + x has its extreme value at
x = 1 and x = 2, then ( a, b) is :
(a)
(1,½)
(c)
(2,~1)
C
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70
15.
TargetMHT-CET
Let R be the relation over the set of straight lines
ofa plane, such that/ 1 R 12 ~ / 1 J_ /2. Then, R is
(a) symmetric
(b) reflexive
(c) transitive
(d) an equivalence relation
16.
sin (x +a)
Evaluate integral - - ~ dx.
sin (x +b)
J
(a) x cos (a-b) + sin (a -b) loglsin (x+ b)l + C
(b) x sin (a-b) + cos (a-b) log lsin (x+ b)I + C
Ifthe middle point ofthe sides ofa triangle ABC
are(O, O); (l, 2)and(-3, 4), then theareaoftriangleis
(b) 20
(a) 40
(c) 10
(d) ©
2n
n+l
n
_
+
5
3 2
Jim -------,-----,- is equal to
24.
n ➔oo 5n +2n +3 2n+3
(d) 0
(a) 5
(b) 3
(c) 1
25. Ifp and q be the roots of the quadratic equation
x2 -(a-2) x -a.-1 = Othen minimum value of
p 2 + q2 is equal to
(a) 2
(b) 3
(c) 6
(d) 5
26. The area of the region lying between the line
23.
x - y + 2 = 0 and the curve x = Jy is
(a) 9
(b) 9/2
(c) x cos (a+ b) + sin (a + b) log lsin (x -b)I + C
17.
18.
19.
20.
(d) x sin (a + b) + cos (a + b) log lsin (x-b)I + C
IfAis idempotent and A + B = I, then which of the
following is false?
(a) Bis idempotent
(b) AB = O
(c) BA=O
(d) None of these
2t +(✓
3t
If (✓
(d) 2
(a) 1
(b) - I
(c) 0
Let L be the line of intersection of the planes
2x + 3y+ z= 1 andx + 3y + 2z= 2. IfLmakesan
angle a with the positive x-axis, then cos a
equals
22.
1
(b)
✓
2
(c)
1
✓
3
35
6
(b)
2
35
(c)
3
35
28.
(d)
6
35
(d) None of these
.
1-sinx+cosx
The function f(x) =
.
is not
1 +smx + cosx
defined atx = 7t. The value of/(1t), so that/ (x) is
continuous at x = 1t, is
I
I
(a) - - (b) (c) -1
(d) I
2
2
10/3
35 2
· ····< r-l)(_!_)r, thenthis
5
r!
is the term ofbinomial expansion
If(r + l) th term is
(a)
(1-¾r2
(i-¾rl/2
(b)
29.
IfA + B + C = 1t, then cos2A+cos2B+cos2C
+ 4 sin A sin B sin C is equal to :
(d) 3
(a) 0
(b) 1
(c) 2
30.
( x + ~r + ( x 2+ x12
(d)
2
A boat is to be manned by eight men of whom 2
can only row on bow side and 3 can only row on
stroke side, the number of ways in which the
crew can be arranged is
(a) 43©
(b) 57©
(c) 5930
(d) None of these
A bag contains 4 red and 4 blue balls. Four balls
are drawn one by one from the bag, then find the
probability that the drawn balls are in alternate
colour.
(a)
27.
then the number
of values of x is
(a) 2
(b) 4
(c) 1
(d) None of these
The value of a for which the function/(x) = a sin
x + (1/3) sin 3x has an extremum atx = n/3 is
(a)
21.
= (✓!3t 1 2 ,
(c)
r r
+ (x 3+ x\
....upto n terms is
x 2n -1
(a)
- --
x 2 -1
x2n +2 +l
X -
----:--
x2n
+ 2n
(b)
X 2n + 1
X 2n + 2 _ l
- -- X - -- --2n
x2+ l
x 2n
(C)
x 2n - 1
-----,,---x2 - 1
x 2n -1
X
- --
x 2n
-
2n
( d) None of these
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71
MOCKTESf-6
31.
Two pairs of straight lines have the equations
y2 + xy - I2x2 = 0 and ax2 + 2hxy + by = 0. One 37.
line will be common among them if
(a) a=-3(2h + 3b) (b) a = 8(h-2b)
(c) a = 2 (b + h)
32.
Ifthe focal distance ofan end of the minor axis of
(c)
33.
x2 y2
-2+ -2= l
k
h
0
(b)
I
(c)
ro
(d)
ro
(b)
(c) 4n-~
2
38.
1-cosx
l+ cosx
X
2
2
(d) None of these
The equations 2x + 3y+ 4 = 0; 3x + 4y + 6 = 0 and
4x + 5y + 8 = 0 are
(a) consistent with unique solution
(b) inconsistent
(c) consistent with infinitely many solutions
(d) None of the above
7t
4
39.
The value of flog e (1+ tan x )dx is
The value of (1 + 2ro + oi)3" -( I + ro + 2ro2) 3" is :
(a)
34.
x2
y2
- + 2
= l (d)
k 2 k -h 2
X
(a)
(d) Both (a) and (b)
any ellipse (referred to its axis as the axes of x
and y respectively) is k and the distance between
the foci is 2h, then its equation is
Ifx E (71t, 81t), then tan -I
0
2
Letpis a non-singular matrix such that
(a)
7t
(c)
1t loge 2
1+p +p2+ ... +p"= O(Odenotes the null matrix),
thenp- 1 is
(a) pn
(b) _ pn
(c) -(1 + p + .... + pn) (d) None of these
35.
The value of
xsin- 1 x
40.
.
f \/1-x~ dx 1s equal to :
~
36.
xsin- 1 x+C
(c)
x-✓O-x2 )sin-1 x+C
(d)
✓(sin-Ix) +C
The constraints
- x 1 + x2 :S 1, -x 1 +3x2 :S 9, x 1,x2 ;;;:: 0 define on
(a) Bounded feasible space
(b) Unbounded feasible space
(c) Both bounded and unbounded feasible
space
7t
- loge 2
8
Ify = logn x, where logn means log log log ...
(repeated n time), then x log x log x log2 x log3 x
. .. logn- 1 x logn x dy is equal to
dx
(a)
(b)
(d)
41.
42.
logx (b)
lqr x
(c)
1
logx (d)
Let f(x), g(x) be two continuously differentiable
functions satisfying the relationships f'(x) = g(x)
and f"(x) = -f(x).
Leth(x) = [f(x)] 2 + [g(x)]2. Ifh(0) = 5, then h (10)=
(a) 10
(b) 5
(c) 15
(d) None of these
.
x - 2 y+l z -1 .
The hne, - - = - - = --=-i- mtersects the
2
3
curvexy = c 2, z = 0 if c is equal to
1
(a) ± 1
(b) +
- -3
(c)
±✓
5
(d) None of these
(d) None of these
IWWW.JEEBOOKS.INI
72
43.
TargetMHT-CET
2x+a ; x 2'. -1
If f(x) =
and
{ bx 2 +3; x < -1
g(x)=
46.
dy
=
dx
; 0 :,; X :,; 4
x+4
The solution to the differential equation
yf'(x)-y2
f(x)
where f(x) is a given function is
{ -3x-2 ; -2 < x < O
(a)
f(x) = y(x + c)
(b)
f(x)=cxy
If domain of g (f(x)) is [-1 , 4], then-
(c)
f(x) = c(x + y)
(d)
yf (x) = ex
(a)
(c)
a=O, b > 5
a=2, b > IO
(b) a = 2, b >7
(d) a = O, b e R
47.
i,
If an = 2n + 1 and C r = nc r then
x-l, x < 0
44.
If/(x) =
{
x = 0, then
(a)
(n - 1)( 2nCn)
(b) n(2nCn )
x >0
(c)
2
(n + l)( nCn)
(d) (n + l)(nCn / 2)
x,
(a)
(b)
(c)
45.
48.
The maximum value of z = 6x + 8y subject to
constraints 2x + y :,; 30, x + 2yQ4 and x 2'. 0, y 2'. Ois
(a) ~
(b) 120 (c) 96
(d) 240
49.
IfA ~ [
Jim f (x) = I
x ➔O+
lim f(x)
x➔O-
=1
f(x) is discontinuous at x = 0
~ ~l
and A-' - [:
n
then ilirnlu,
(d) None of these
of x is equal to
A force F = 2i + j - k acts at a point A, whose
position vector is 2i - j. The moment ofF about
the origin is
(a) i + 2J-4k
(b) i-2J - 4k
(c) i + 2) + 4k
(d) i-2) + 4k
(a) -3
(b) 3
(c) -2
(d) 6
Ifthe mean ofa binomial distribution is 25, then
its standard deviation lies in the interval given
below
(a) [0, 5) (b) (0,5] (c) [0,25) (d) (0,25]
SO.
lWWW.JEEBOOKS.INI
Mock Test-[!]
General Instructions
■
■
■
■
■
■
■
This question booklet contains 150 Multiple Choice Questions (MCQs).
Section-A: Physics & Chemistry - 50 Questions each and
Section-B: Mathematics - 50 Questions.
Choice and sequence for attempting questions will be as per the convenience of the candidate.
Read each question carefully.
Determine the one correct answer out of the four available options given for each question.
Each question with correct response shall be awarded one (1) mark. There shall be no negative marking.
No mark shall be granted for marking two or more answers ofsame question, scratching or overwriting.
Duration ofpaper is 3 Hours.
SECTION-A
PHYSICS
1.
2.
Kepler's second law regarding constancy of areal
velocity of a planet is a consequence of the law
of conservation of
(a) energy
(b) angular momentum
(c) linear momentum
(d) None of these
Which of the following is not correct for elastic
potential energy of a strained body.
1 AY
(a) U= - - f 2
2 L
(b) U =
(c) U =
(b) U =
3.
4.
1
2
B
5.
6.
stress x strain
2
1
~ ~ D'(
.
stress x stram x volume
1
2
x maximum stretching force x
extension
A liquid does not wet the sides of a solid, if the
angle of contact is
(a) Zero
(b) Obtuse(morethan 90°)
(c) Acute (less than 90°)
(d) 90° (right angle)
A wavefront AB passing through a system C
emerges as DE. The system C could be
~
(a) a slit
(b) a biprism
(c) a prism
(d) a glass slab
At the centre ofa cubical box+ Q charge is placed.
The value oftotal flux that is coming out a wall is
(a) QIE0 (b) Q / 3i:0 (c) Q / 4i:0 (d) Q / 6i:0
If we double the radius of a coil keeping the
current through it unchanged, then the magnetic
field at any point at a large distance from the
centre becomes approximately
(a) double
(b) threetimes
(c) four times
(d) one-fourth
A steel wire oflength f has a magnetic moment
M. It is then bent into a semicircular arc. The new
magnetic moment is
(a)
M
7t
8.
E
(b)
2M
7t
(c)
3M
(d)
7t
4M
7t
The energy of electron in the nth orbit of
d
.
-13.6
h ydrogen atom 1s
expresse as E 0 = --eV.
n2
The shortest wavelength of Lyman series will be
(a) 910A
(b) 5463A
(c) 1315 A
(d) None of these
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TargetMHT-CET
74
9.
When a ferromagnetic material is heated to
temperature above its Curie temperature, the
material
(a) is permanently magnetized
(b) remains ferromagnetic
(c) behaves like a diamagnetic material
(d) behaves like a paramagnetic material
A particle of mass m moves a long line PC with
velocity v as shown. What is the angular
momentum ofthe particle about P?
(a)
16.
C
(a) mvL
(b) mvl
(c)
17.
mvr
(d) zero
o
Two drops of the same radius are falling through
air with a steady velocity of 5 cm per sec. If the
two drops coalesce, the terminal velocity would
be
(a) lOcmpersec
(b) 2.5cmpersec
(c) 5 x (4) 113 cm per sec (d)
12.
13.
14.
Which one of the following is not measured in
units of energy ?
(a) Couple x angle
(b) Moment of inertia x ( angular velocity) 2
(c) Force x distance
(d) Impulse x time
Ground wave propagation is possible for
(a) low radio frequency over a short range
(b) high radio frequency over a short range
(c) high radio frequency over a long range
(d) low radio frequency over a short range.
Forces of 4 N and 5 N are applied at origin along
X-axis and Y-axis respectively. The resultant force
will be
(a)
(c)
15.
5 x fj cm per sec
✓41N, tan- 1( ¾)
(b)
✓41N, tan- 1
B
0
1
0
1
y
1
1
0
1
(b) Y=
A.B
(d) Y = A x B
(c) Y = A - B
A wire is placed parallel to the lines offorce in a
magnetic field and a current flows in the wire.
Then
(a) the wire will experience a force in the
direction of the magnetic field
(b) the wire will not experience any force at all
(c) the wire will experience a force in a direction
opposite to the field
(d) it experiences a force in a direction
perpendicular to lines of force
In the circuit diagram shown, Xe= 100 n,
XL = 2000&
R = 100 n . The effective current through the
(a) 4
(c) 2
18.
19.
20.
(b) 3
(d) 5
20ovf
The threshold frequency for a photosensitive
metal is 3.3 x 10 14 Hz. If light of frequency
8.2 x l 0 14 Hz is incident on this metal, the cut-off
voltage for the photoelectric emission is nearly
(b) 3V
(c) 5V
(d) 1V
(a) 2V
Assuming the radius ofthe earth as R, the change
in gravitational potential energy of a body of
mass m, when it is taken from the earth's surface
to a height 3R above its surface, is
3
(a) 3mgR
(b)
- mgR
1 mg R
(d)
2
(c)
4
3
mg R
An electric fan has blades of length 30 cm
measured from the axis ofrotation. If the fan is
rotating at 120 rpm, the acceleration of a point on
the tip of the blade is
(a)
-✓41N,tan- 1 (¾)(d) - ✓41N, tan- 1 (1)
A
1
0
0
1
A+B
source is 2✓
x A then find value ofx.
(1)
The expression corresponding to the truth table
Y=
1600ms- 2
(b) 47.4rns-2
(c) 23.7 ms- 2
21.
(d) 50.55 ms-2
We increase the charge on the plates ofa capacitor,
it means,
(a) increasing the capacitance
(b) increasing P.D. between plates
(c) decreasing P.D. between plates
(d) no change in field between plates
WWW.JEEBOOKS.INI
MOCKTEST-7
22.
23.
24.
Two waves are represented by the equations
y 1 =asin(ffit+ kx +0.57)mandy2 = acos(c:ot+ kx)
m, where x is in meter and t in sec. The phase
difference between them is
(a) 1.0 radian
(b) 1.25 radian
(c) 1.57 radian
(d) 0.57 radian
In a room where the temperature is 30°C, a body
cools from 61 °C to 59°C in 4 minutes. The time (in
minutes) taken by the body to cool from 51 °C to
49°C will be:
(a) 8
(c) 6
(b) 5
(d) 4
The surface tension of water is 75 dyne/cm.
Find the minimum vertical force required to pull a
thin wire ring up (refer figure) ifit is initially
resting on a horizontal water surface. The
circumference ofthe ring is 20 cm and its weight
is0.1 N:
75
ffl
25.
26.
27.
28.
29.
0.225N
(c)
0.115N
(d)
0.130N
Resistance of 12 0 and XO are connected in
parallel in the left gap and resistances of9 0 and
7 0 are connected in series in the right gap ofthe
meter bridge. If the balancing length is 36 cm,
then the value of resistance X is
(a) 720 (b) 540 (c) 360 (d) 640
A coil ofresistance 4000 is placed in a magnetic
field. Ifthe magnetic flux q> (wb) linked with the
coil varies with time t (sec) as q> = 50t2 + 4. The
current in the coil at t = 2 sec is
(a) 0.5A (b) 0.IA (c) 2A
(d) IA
A particle of mass IO kg is moving in a straight
line. If its displacement, x with time tis given by
x = (t3 - 2t- I 0) m, then the force acting on it at
the end of 4 seconds is
(a) 24N (b) 240N (c) 300N (d) 1200N
At the magnetic north pole of the earth, the value
ofthe horizontal component of earth's magnetic
field and angle of dip are respectively
(a) zero,maximum
(b) maximum, minimum
(C) maximum, maximum
(d) minimum, minimum
Four masses are fixed on a massless rod as shown
in the adjoining figure. The moment of inertia
about the dotted axis is about
~
~
ffl
2kg
5kg
5kg
2kg
i - -0.4m - -.........- - 0.4 m - t
30.
31.
(a) 0.125N
(b)
0.2m
0.2m
32.
33.
34.
35.
1 kgm2
(a)
2kgm2
(b)
(c)
0.5kgm2
(d) 0.3kgm2
Two radioactive materials X 1 and X 2 have decay
constants I 0A. and A respectively. If initially they
have the same number ofnuclei, then the ratio of
the number of nuclei ofX 1 to that ofX2 will be
1/e after a time
(a) 1/IOA (b) I/I IA (c) 11/IOA (d) 119A
If two vessels A and B contain the same gas
but the volume of vessel A is twice that of B
and temperature and pressure of gas A is twice
that of gas in B, then the ratio of gas molecules
in A and Bis
(a) 1:2 (b) 1:4 (c) 4:1 (d) 2:1
Ifthe temperatures of source and sink ofa Carnot
engine having efficiency ri are each decreased
by 100 K, then the efficiency
(a) remains constant (b) becomes I
(c) decreases
(d) increases
In Young's experiment, two coherent sources are
placed 0.90 mm apart and fringe are observed one
metre away. Ifit produces second dark fringe at a
distance of I mm from central fringe, the
wavelength of monochromatic light used would
be
(a) 60 x lo-4cm
(b) 10 x Io-4cm
(c) 10 x 10-5 cm
(d) 6 x 10-5 cm
The Young's modulus of steel is twice that of
brass. Two wires of same length and of same
area of cross section, one of steel and another of
brass are suspended from the same roof. If we
want the lower ends of the wires to be at the
same level, then the weights added to the steel
and brass wires must be in the ratio of:
(a) 2: 1 (b) 4: 1 (c) 1 : 1 (d) 1 : 2
A simple pendulum oscillates in air with time
period T and amplitude A. As the time passes
(a) T and A both decrease
(b) T increases and A is constant
(c) T remains same and A decreases
(d) T decreases and A is constant
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76
36.
Find emfE ofthe cell as shown in figure.
12V
(b) lOV
1n
E
A f--~ l-='--E---'Ww----1 B
IA
12V
43.
F
(d) 5V
38.
39.
40.
41.
I
D ~~ l--___,,,w,....---4,__, C
(c)
37.
20
15V
(a)
L---+----'oJ_ _ _ __J
E
2A
Two coils have a mutual inductance 0.005 H. The
current changes in the first coil according to
equation I = 10 sin rot, where 10 = 10A and ro = 100
n radian/sec. The maximum value of e.m.f in the
second coil is
(a) 2'1t
(c) n
(b) 5n
(d) 4n:
A parallel beam oflight is incident on the surface
of a transparent hemisphere of radius R and
refractive index 2.0 as shown in figure. The
position of the image formed by refraction at the
first surface is :
(a) R/2
(b) R
(c) 2R
(d) 3R
A single slit Fraunhoffer diffraction pattern is
formed with white light. For what wavelength of
light the third secondary maximum in the
diffraction pattern coincides with the second
secondary maximum in the pattern for red light
ofwavelength 6500 A?
(a) 4400A
(b) 4100A
(c) 4642.8A
(d) 9100A
A train moving at a speed of220 ms- 1 towards a
stationary object, emits a sound offrequency 1000
Hz. Some of the sound reaching the object gets
reflected back to the train as echo. The frequency
ofthe echo as detected by the driver ofthe train is
(speed of sound in air is 330 ms- 1)
(a) 3500Hz
(b) 4000Hz
(c) 5000Hz
(d) 3000Hz
The amplitude ofa particle executing SHM is 4
cm. At the mean position the speed ofthe particle
is 16 cm/sec. The distance of the particle from
the mean position at which the speed of the
particle becomes 8✓3 emfs, will be
42.
?,cm
(a) 2✓
(b) ✓3 cm
(d) 2 cm
(c) 1 cm
A body of mass 0.4 kg is whirled in a vertical
circle making 2 rev/sec. If the radius of the circle
is 1.2 m, then tension in the string when the body
is at the top of the circle, is
44.
TargetMHT-CET
(a) 41.56N
(b) 89.86N
(c) 109.86N
(d) 115.86N
The ratio of the accelerations for a solid sphere
(mass ' m' and radius ' R') rolling down an incline
of angle '0' without slipping and slipping down
the incline without rolling is:
(a) 5:7 (b) 2:3 (c) 2:5 (d) 7:5
A transverse sinusoidal y
wave moves along a
string in the positive xdirection at a speed of 10
X
emfs. The wavelength of
the wave is 0.5 m and its
amplitude is IOcm.Ata
particular time t, the snap-shot ofthe wave is shown
in figure. The velocity of point P when its
displacement is 5 cm is
(a)
✓3n Jm / s
(b)
50
(d) - ✓
3n i m i s
50
50
Assuming the sun to have a spherical outer
surface ofradius r, radiating like a black body at
temperature t°C, the power received by a unit
surface, (normal to the incident rays) at a distance
R from the centre of the sun is
(c)
45.
(a)
(c)
46.
✓
3n •
---j m i s
50
✓3n i m i s
r 2 cr(t + 273) 4
4nR2
r 2 cr(t + 273) 4
R2
(b)
16n2 r 2 crt 4
R2
(d)
4nr 2 crt4
R2
An electric charge +q moves with velocity
~ = 3i + 4J+ k in an electromagnetic field given
by
47.
E= 3i + J+ 2k
and
B= i + J- 3k
The y-
component of the force experienced by + q is:
(a) llq (b) 5q
(c) 3q
(d) 2q
A transistor-oscillator using a resonant circuit
with an inductor L (of negligible resistance) and
a capacitor C in series produce oscillations of
frequency f. IfL is doubled and C is changed to
4C, the frequency will be
(a) 8f
(c) t72
(b)
fl
2-.fi.
(d) t74
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77
MOCKTESf-7
48.
A rectangular block is placed on a rough
horizontal surface in two different ways as shown,
then
56.
57.
jJ_
(a)
1 . . . . . .1..
(b)
(a) friction will be more in case (a)
(b) friction will be more in case (b)
(c) friction will be equal in both the cases
(d) friction depends on the relations among its
dimensions.
49.
SO.
Three condensor each of capacitance 2F are put
in series. The resultant capacitance is
(a) 6F
(b) 3/2F (c)
2/3F (d)5F
If a motorcyclist skids and stops after covering a
distance of 15 m. The stopping force acting on
the motorcycle by the road is 100 N, then the
work done by the motorcycle on the road is
(a) 15001
(b) -15001
(c) 7501
(d) Zero
CHEMISTRY
51.
In which of the following compounds, nitrogen
exhibits highest oxidation state?
(a) N 2H 4 (b) ~ (c) N 3H (d) NHzOH
52.
The nature of curve ofE~ell vs. log Kc is :
(a) straight line
(b) parabola
(c) hyperbola
(d) elliptical curve
Formation of alkanes by action of Zn on alkyl
halides is called:
(a) Frankland's reaction
(b) Cannizaro's reaction
(c) Wurtz's reaction
(d) Kolbe's reaction
CdO has NaCl structures with density 8.27 glee.
If the ionic radius of 0 2- is 1.24 A, determine
ionic radius ofCd2+:
(a) 1.5 A (b) 1.1 A (c) 1.9 A (d) 1.5 A
Indicate the nature of bonding in CC14 and CaHz
(a) Covalent in CCl 4 and electrovalent in CaHz
(b) Electrovalent in both CC14 and CaHz
(c) Covalent in both CCl 4 and CaJ-1i
(d) Electrovalent in CCl 4 and covalent in CaHz
53.
54.
55.
58.
59.
60.
61.
62.
63.
What is the weight of oxygen required for the
complete combustion of2.8 kg of ethylene?
(a) 2.8kg (b) 6.4kg (c) 9.6kg (d) 96kg
Nucleophilic addition reaction will be most
favoured in
(a) (C1½)2C = 0
(b) C1½CHzCHO
(c) ~CHO
Knowing that the chemistry oflanthanoids(Ln)
is dominated by its + 3 oxidation state, which of
the following statements is incorrect?
(a) The ionic size ofLn (III) decrease in general
with increasing atomic number.
(b) Ln (III) compounds are generally colourless.
(c) Ln (III) hydroxide are mainly basic in
character.
(d) Because of the large size of the Ln (III) ions
the bonding in its compounds is
predominantly ionic in character.
The rate constant of a reaction is 10.8 x 10-5 mo!
ctm-3 s- 1. The order of the reaction is
(d) 3
(a) zero (b) I
(c) 2
The most durable metal plating on iron to protect
against corrosion is
(b) copper plating
(a) nickel plating
(d) zinc plating
(c) tin plating
One Faraday of electricity is passed through
molten Al 20 3, aqueous solution of CuSO4 and
molten NaCl taken in three different electrolytic
cells connected in series. The mole ratio of Al,
Cu and Na deposited at the respective cathode
is
(b) 6: 2: 3
(a) 2: 3 : 6
(c) 6: 3 : 2
(d) 1 : 2: 3
Producer gas is the mixture of:
(a) CO + N 2
(b) CO+Hz
(c) CO + water vapours
(d) N 2 +CH4
Hydrogen can be fused to form helium at
(a) high temperature and high pressure
(b) high temperature and low pressure
(c) low temperature and high pressure
(d) low temperature and low pressure
IWWW.JEEBOOKS.INI
78
64.
Steam reacts with iron at high temperature to give
hydrogen gas and Fe 3 0 4 (s). The correct
expression for the equilibrium constant is
(a)
(c)
65.
66.
67.
68.
(b)
4
[PH2 ] [Fe304]
4
[PH20] [Fe]
(d)
[PH)4
4
[PH20 ]
a-
71.
[Fe30 4 ]
[Fe]
The reaction A ➔ B follows first order kinetics.
The time taken for 0.8 mole ofA to produce 0.6
mole ofB is I hour. What is the time taken for
conversion of0.9 mole ofA to produce 0.675 mole
ofB?
(b) 0.25 hour
(a) 0.5hour
(c) 2 hours
(d) 1 hour
The pyrimidine bases present in DNA are
(a) cytosine and thymine
(b) cytosine and uracil
(c) cytosine and adenine
(d) cytosine and guanine
The most basic compound among the following
is:
(b) Benzylamine
(a) Acetanilide
(c) p-Nitroaniline
(d) Aniline
Which ofthe following has minimum flocculation
value for positively charged sol?
(a)
69.
p2
H2
2
PH20
70.
(b)
so~-
(d)
[Fe (CN)J4-
72.
(a)
CH3C-O-
(II)
0
CH 30-
NaOH
CH3CHCH2CHO
I
(c)
O+ No;------,VNO,
(d) Both(a)&(b)
73.
The number ofunpaired electrons in the complex
[Cr~)6]Br3 is (Atomic number ofCr= 24)
(a)
74.
4
I
(b)
(c)
2
(d) 3
For orthorhombic system axial ratios are
*
a* b c and the axial angles are
* 90°
(a)
a=~= y
(b)
a=~=y=90°
(c)
a=~= y=90°,~ -:P.90°
a-:P.~ * y =90°
p- vs T plot in the Ellingham diagram slopes
(d)
75.
~
downward for the reaction
(Ill) CN0
3
C~OH + HCOONa
OH
II
(IV) H C
NaOH
2HCHO
(b) 2C~CHO
The decreasing order of nucleophilicity among
the nucleophiles
(I)
TargetMHT-CET
(C) (IV) > (Ill) > (II) > (I)
(d) (I) > (TI) > (Ill) > (IV)
In which of the following compound does
hydrogen exhibit a negative oxidation state:
(a) UH
(b) HzO
(c) HO
(d) none of these
Adiabatic expansions of an ideal gas is
accompanied by
(a) decrease in Lill
(b) increase in temperature
(c) decrease in ~S
(d) no change in any one of the above
properties
Which of the following is disproportionation
reaction?
~[ ~ -
II
0
(a) (Ill) > (TI) > (I) > (IV)
(b) (TI) > (Ill) > (I) > (IV)
O-
1
➔ MgO
(a)
Mg+-02
2
(b)
2Ag+-02
2
(c)
C+-0 2
2
(d)
l
C0+-02
2
IS
I
I
➔ Ag20
➔ CO
➔ CO2
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MOCKTEST-7
76. The values ofheat of formation ofSO2 and SO3 are
79
82.
-298.2 kJ and -98.2 kJ respectively. The heat of
formation ofthe reaction
SO 2 +(1 / 2)02
➔ SO 3
(a) -200kJ
(c) + 200kJ
77.
The most probable product in the reacion given
below is
/"-I__"' H S0
\_J 6H~
will be
2
(b) -356.2kJ
(d) -396.2kJ
Amphoteric oxides are
(a)~
(a) ZnO, Kp, SO3
(b) ZnO, Pz05 , Clz07
(c) SnO2 ,Alz03 , ZnO
(d) PbO2 , SnO2, SO3
78.
Before introducing FeO in blast furnace, it
converted to Fe2O3 by roasting so that
(a)
it may not be removed as slag with silica
(b) it may not evaporate in the furnace
(c) presence of it may increase the m.pt. of
charge
(c)
83.
R'
80.
84.
85.
86.
(c) both are included in stereoisomerism
(d) they have no similarity
The electronic configuration of gadolinium (At.
No. 64) is
(a)
[Xe]4/8 5d16s 2
(b)
7
[Xe]4/ 5d 6s
(c)
[Xe]4J 3 5d 5 6s 2
(d)
[Xe]4f 6 5d 2 6s 2
1
2
/
~~
OH
OH
2
H
(B)
Ring (A) is pyranose with a - glycosidic
link
0 2 and Xe have comparable ionisation
energies
(d) Both (a) and (c)
A similarity between optical and geometrical
isomerism is that
each
gives equal number of isomers for a
(a)
given compound
~:,:><i:°~t
(A)
0 2 and Xe have comparable sizes
(b) if in a compound one is present then so
is the other
81.
0
(a)
(b) both 0 2 and Xe are gases
(c)
The correct statement about the following
disaccharide is
"~
'
HO
H
OH
The formation of Ot[PtF6 J- is the basis for the
formation of xenon fluorides. This is because
(a)
0(
1
(d) None of these
79.
4
87.
(b) Ring (A) is furanose with a - glycosidic link
(c) Ring (B) is furanose with a - glycosidic link
(d) Ring (B) is pyranose with P- glycosidic link
Which of the following compound will undergo
electrophilic substitution more readily than
benzene?
(a) Nitrobenzene
(b) Benzoic acid
(c) Benzaldehyde
(d) Phenol
Equal volumes ofO. l M HCI and 0.1 M NaOH are
mixed. The concentration ofthe resulting solution
will be
(a) 0.1 M (b) 0.05M(c) 0.2M (d) 0.0M
Acidified KzCrz07 solution turns green when
Na2SO3 is added to it. This is due to the formation
of:
(a)
Crz(SOJ3
(b) Cr~-
(c)
Crz(SO3) 3
(d) CrSO4
Which of the following is not used in FriedelCrafts reaction?
(a) N-Phenyl acetanilide
(b) Bromobenzene
(c)
Benzene
(d) Chlorobenzene
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80
88.
89.
TargetMHT-CET
Polyvinylalcohol can be prepared by
(a) polymerization of vinyl alcohol.
(b) alkaline hydrolysis of polyvinyl acetate.
(c) polymerization ofacetylene.
(d) reaction ofacetylene with 1½SO4 in presence
ofHgSO4•
Which one of the following sets forms the
biodegradable polymer?
(a) C1½=CH-CN and C1½= CH-CH=C1½
(b) 1½N - C1½- COOH and
1½N-(C1½)5 -COOH
(c) HO-C1½-C1½-OH and
Z in the above reacting sequence is
(a) CH3CH2CH2NHCOCH3
(b)
(c)
96.
97.
Hooc-@-cooH
(d) @ - c H = C1½ and
90.
91.
92.
C1½ = CH-CH=C1½
When 2-methoxypropane is heated with HI, in
the mole ratio 1 : 1, the major products formed are
(a) methanol and 2-iodopropane
(b) methyl iodide and 2-propanol
(c) methyl iodide and 2-iodopropane
(d) methanol and 2-propanol
When mango is placed in dilute aqueous solution
ofhydrochloric acid, it
(a) shrinks
(b) swells
(d) Nothing happens
(c) bursts
The geometry of [Ni(CN) 4 ] 2and
[Ni(PPh3)iC1 2] are
93.
94.
95.
(a) both square planar
(b) tetrahedral and square planar
(c) both tetrahedral
(d) square planar and tetrahedral
Which of the following is not true?
(a) Some disinfectants can be used as
antiseptics.
(b) Sulphadiazine is a synthetic antibacterial.
(c) Aspirin is analgesic as well as antipyretic.
(d) Polystyrene is used to make non-stick
cookware.
Which of the following is true in respect of
chemical adsorption?
(a) Afl < 0,~S > 0, ~G > 0
(b) ~H<0,~S < 0, ~G < 0
(c) Afl > 0,~S > 0, ~G < 0
(d) Afl>0,~S < 0,~G>0
CH3CH2Cl
NaCN
X
Ni / H2
y
acetic anhydride
z
98.
CH3CHzCHzNHz
CH3CH2CH2CONHCH3
(d) CH3CH2CH2CONHCOCH3
The appearance of colour in solid alkali metal
halides is generally due to
(a) Schottky defect
(b) Frenkel defect
(c) Interstitial positions
(d) F-centre
Given below, catalyst and corresponding
process/reaction are matched. The one with
mismatch is:
(a) [RhCl(PPh3) 2] : Hydrogenation
(b) TiC14 + Al (C28s)3 : Polymerization
(c) Vp5 : Haber-Bosch process
(d) Nickel : Hydrogenation
Identify the incorrect statement, regarding the
molecule XeO4 :
(a)
XeO4 molecule is tetrahedral
(b) XeO4 molecule is square planar
(c)
99.
There are four pre - drc bonds
(d) There are four sp3 -p, a bonds
Which one of the following compounds has the
most acidic nature?
~Q CHpH
(a)~
(b)
@-OH
0-
OH
(c)
OH
0-CH-o
I
(d)
100. Which is correct statement?
(a) Starch is a polymer of a-glucose
(b) In cyclic structure offructose, there are four
carbons and one oxygen atom
(c) Arnylose is a component of cellulose
(d) Proteins are composed of only one type of
amino acids
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MOCKTEST-7
81
SECTION-8
MATHEMATICS
1.
2.
A set A has 3 elements and another set B has 6
elements. Then
(a) 3::; n(A u B)::;6 (b) 3::; n(AuB)::;9
(c) 6::; n(AuB)::;9 (d) o::; n(AuB)::;9
A real valued function f (x) satisfies the functional
equation
(c)
3.
8.
2nn ±2:.+~
4
2
( x I a)- a, when x < a
9.
If f(x)=
0, whenx=a, then
{
(c)
4.
2nn ±2:.-~
4
If an=
(b)
nn+(-lf 2:.
12
(a)
2
12
n radical
10.
signs then by methods of mathematical induction
which is true
5.
6.
7.
(a)
an > 7 V n ~ l
(b)
an < 7 V n ~ l
(c)
an < 4 V n ~ 1
(d)
an < 3 V n ~ 1
Let x 1 and y1 be real numbers. Ifz 1 and z 2 are
complex numbers such that lz 1I= lz21= 4, then
2
lx1z1 -y1z21 + IY1Z1 + x1 zzl2 =
(a) 32(x/ +y/)
(b) 16(x/ +y/)
(c) 4(x/ + y/)
(d) 32(x/ + y/) lz 1 + zzi2
Iff(x) = x sin x, then f{
(b)
a -( x I a), when x > a
limf(x)=a
(b) f (x) is continuous at x = a
(c) f(x) is discontinuous at x = a
(d) None of these
The probability of getting sum more than 7 when
a pair of dice are thrown is
7
5
(a) 36
(b) 12
(c)
11.
7
12
(d) None of these
f
Evaluate
(a)
x2 +l
dx
X +X 2 +1
4
tan -I
1
( cx 2 -1)1
l
j+c
✓
3x
_/ (x 2 -1)1
tan
.J3x
+c
l
(b)
.J3
(c)
cos-
(d)
sec-
%) is equal to
1
(b) 1
(a) 0
(c) -1
(d)
2
Which ofthe function defined below is one-one?
(a) f: (0, oo) ➔ R , f(x) =x2 -4x + 3
2
x ➔a
(d) None
✓7 + ✓7 + .J1 + ...... having
J
Given the system of straight lines:
a(2x + y-3) + b(3x + 2y-5) = 0, the line of the
system situated farthest from the point ( 4, -3)
has the equation
(a) 4x + lly-15=0 (b) 7x + y-8=0
(c) 4x+3y-7=0
(d) 3x-4y+ l=0
(.J3-l)sin0 + (.J3+1)cos0=2 is
(a)
X
e +~
e
(d) f:R ➔ R, f(x) = £n(x 2 +x + l)
f(x-y) =f(x)f(y)-f(a-x)f(a+y)
where a is a given constant and/(0) = l,f(2a-x)
is equal to
(a) -f(x)
(b) f(x)
(c) f(a) + f(a-x)
(d) f(-x)
General solution of the equation
f : R ➔ R,f(x)=
l
1 (cx
l
1(
j
2 -1)1
.J3x
)
+c
cx 2 -1)1
.J3x
j +c
f:[0, oo) ➔ R,f(x)=x2 +4x-5
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TargetMHT-CET
82
12.
2
2
Find the minimum value of e<2x - 2x-l)sin x.
20.
(a)
Vectors
a and b are inclined at an angle 8 =
13.
(b) 2
1
(c) 0
(d) None of these
The number ofreal roots of the equation
is equal to
12-11-lxlll=lis
(a)
14.
(a) 1
(c) 5
(d) 6
(b) 3
In the expression (x + l)(x+4)(x + 9)(x + 16)...... .
15.
(x + 400), the coefficeient of x is
(a) 2870 (b) 2100 (c) 4001 (d) 1900
The area enclosed between the curves
19
120°. If I a l=I bI= 2, then [(a+ 3b) X (3a + b)
21.
16.
17.
Y '(Y 2 -
=y
y3 - 3.xy = C
(c) x 3
(a)
+y2 -3x-4y = 0
X
22.
(b)
(c)
x +y2+3x+4y = O
192
r-z
q
r-z =0, then the value of
r
q-y
y
Z
(c) 2
(d) 4pqr
(b)
(a) 0
Ifcos x = b. For what b do the roots ofthe equation
formanA.P.?
(a)
✓3
(b)
2
2
24.
(c) -1
(d) Noneofthese
Ifthe perpendicular distance ofthe point (6, 5, 8)
from the Y-axis is 5l unit, then"' is equal to
(b) 3
(d) 2
(a) 5
(c) 4
The three planesx+y = 0,y+ z= 0 andx+ z = 0
(a) meet in a unique point
(b) meetinaline
(c) meet taken two at a time in parallel lines
(d) None of these
25.
lfsin- 1 x+sin - 1 y+sin- 1 z = n
2
23.
2
x + y2-3x +4y = 0
If p -x
(d)
p q r .
- +- + - IS
-
X2
q-y
p- x
.
IS
(b) y3 + 3.xy = C
3xy = C
(d) y3 - .xy = C
Equation of the circle concentric with the circle
x 2 +y2 -3x + 4y-c = 0 and passing through the
point (-1, - 2), is
(a)
18.
X)
(c) 300
(b) 275
p
l andh
..
t ex-ax1s,1s
y= Ioge ( x+e,
) x=logey
(a) 2 sq unit
(b) 1 sq unit
(c) 4squnit
(d) Noneofthese
The letters ofthe word MODESTY are written in
all possible orders and these words are written
out as in a dictionary then the rank of the word
MODESTY is
(a) 5040 (b) 720 (c) 1681 (d) 2520
The solution of the differential equation
190
J2
3
then
the
value of
(d)
19.
2
2
XIOO
+ y100 + 2 100 _ _ _3_ _ _ is
XIOI + y101 + 2 101
(a)
0
x +y2-7x+7y=0
( 4x _l)3
The value of Jim
x➔O
X
sin -
2
4
, is
log(l + 3x)
(a)
~(ln4)2
(b)
~(ln4)3
3
Cc)
Ic1n4)2
(d)
I(ln4) 3
2
3
2
26.
(b)
I
(c) 2
(d) 3
Two dice are thrown n times in succession. The
probability ofobtaining a double-six atleast once is
(b)
35)n
l- ( 36
(d) None of these
IWWW.JEEBOOKS.INI
MOCKTEST-7
27.
What is
83
f(ex+1r dx equal to?
(a)
In(ex +l)+c
(c)
-ln(e-x +l)+c (d) -(ex +l)+c
34.
X+A, x < 3
28.
If/ (x) =
4,
35.
x = 3 is continuous at x = 3,
!
3x-5, x > 3
29.
then').,=
(b) 3
(c) 2
(a) 4
(d) 1
The base ofa cliffis circular. From the extremities
of a diameter of the base the angles of elevation
of the top of the cliff are 30° and 60°. Ifthe height
of the cliffbe 500 metres, then the diameter ofthe
base of the cliff is
(a)
30.
31.
1000✓3m
(b)
of z
= x+iy
(a)
x+y-1=0
(b)
x-y-1=0
(c)
x+ y +l=0
(d)
x- y +l=0
2m
(d) 2000✓
Ifthe amplitude ofz-2-3i is n/4, then the locus
J" (f(l+x)Jl /x
37.
p belongs to the set :
(b)
(a) {2,-5}
(c) {-2, 5}
(d)
then
38.
2
of
the
circle
2
x + y + 2g'x + 2f'y + c' = 0 then the length of
39·
40.
33.
(b)
(
)2 , x>-1
x+l
(c)
✓
x+i,x?.-1
(d)
✓
x-1, x?.0
2✓g 2 +f 2 +c
(d)
r are perpendicular to q+ r, r + p
respe ctively
and
if
p+q
If p, q and
5✓
2 (b) 10
(d) 5
(c) 15
If7 points out of 12 are in the same straight line,
then the number of triangles formed is
(a) 19
(b) 185
(c) 201
(d) None of these
Ifthe ratio of the 7 th term from the beginning to
(a)
the common chord of these two circles is
(c)
-✓
x -1,x ?.0
Ip+ q+ r I is
2
circumference
(d) e3
I p + q I= 6, I q+ r I= 4✓
3 and I r + p I = 4 then
{3,-5}
Ifthecircle x +y2+2gx+2fy+c=O bisects
the
(c) e2
(a)
and
{-3, 2}
(b) e½
1
equals
Suppose f(x) = (x + 1)2 for x ?. -1. Ifg(x) is the
function whose graph is the reflection of the
graph off(x) with respect to the line y = x, then
g(x)equals
are roots of the equation
p I= ✓IO,
(b)
x~l~
Then
is
p
8
Let f: R ➔ R be such thatf{l) = 3 and f'(l) = 6.
(a)
1000 / ✓3m
3
x 2 + px + p = 0, such that I a 4
32.
36.
2000 / ✓3m
(c)
If a and
3
5
(c)
(d) 1
8
8
IfA is 3 x 2 matrix and B is a matrix such that A ' B
and BA' are both defined. Then, order of matrix
Bis(a) 3 x 4 (b) 3 x 2 (c) 4 x 4 (d) 4 x 3
The statement "If22 = 5 then I get first class" is
logically equivalent to
(a) 2 2 = 5 and I do not get first class
(b) 2 2 = 5 or I do not get first class
(c) 2 2 "# 5 or I get first class
(d) None of these
1
(a)
2✓g' 2 +f' 2 +c'
There are four letters and four envelopes, the
letters are placed into the envelopes at random,
the probability that all letters are placed in the
wrong envelopes is
the 7th term from the end in
them n equals to
(a) 10
(b) 9
(
(c) 8
1
~ + '}/3
)n is
1
6
(d) 12
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TargetMHT-CET
84
41.
np
The area between the parabola y = x 2 and the
45.
line y = xis:
1
-sq.units
6
(a)
(b)
1
.
-sq.umts
(c)
Jxsin 2 xcos 2 x
I
-sq.units
3
7t2
(a)
32
(d) None of these
2
(c)
2
I+a +a
42.
4
2 2
2 2
l + ab + a b
l+ac + a c
If l+ab+a 2 b 2
l+b 2 +b4
l + bc + b 2 c 2
2 2
l+bc+b c
l+ac+a c
2 2
2
l+ c +c
43.
(c) 2
1
(b)
46.
4
47.
= (a-b/ (b-cl (c-al, then k is
(a) -1
(d) -2
(a)
44.
Ifl r
2✓
3 (c)
(b)
a
a
r
r
I> land x = a + -+ 2
b
b
r
r
8
2
(a) I
(b) 2
(c) 0
(d) None of these
The image of the pair oflines represented by:
ax2 + 2hxy + by = 0 by the line mirror y = 0 is
(a)
ab
C
C
2r
(b)
ax2 -2hxy -by2 =0
(c)
48.
(d) 4
The mean mark in statistics of 100 students in a
class was 72. The mean mark of boys was 75,
while their number was 70. The mean mark of
girls in the class was
(a) 65
(b) (i)
(c) 66
(d) 62
+ ....to oo ,
x, x:<S; 1
49.
If f(x) =
2 ....to oo
Y = b--+--
and z = c+
2
bx2 + 2hxy + ay= 0
(d) ax2 - 2hxy + by = 0
2
2✓
2
(d) None of these
(b) bx2 - 2hxy + ay = 0
~+ L = l .IfA(x + y) is any point on the ellipse,
16 8
then the maximum area ofthe triangle AS I S2 (in
square units) is
7t
32
Find the minimum value of eC2x - 2x-l)sin x .
(a)
Let S 1, S 2 be the foci of the ellipse
2
dx is equal to
0
{ x 2 +bx+c, x > I
, then find the
values of b and c if.f(x) is differentiable at x = 1.
+
C
4r
ac
b
xy
+ ...to oo, then - =
z
(c)
be
a
50.
(d)
(a)
b= c= 1
(b) b = -1, c = 1
(c)
b = 0, c = I
(d) b=-1, c = 0
Maximum value of I 2x + 3y subject to constraints
x;::o: 0,y;::-: 0,x +y:<S; 5 and 3x + y:<S;9 is
(b) 36
(c) (i)
(d) 40
(a) 15
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g-.A~N;.;;.S~W:..:E::.:.:R:.....:K=-=E=-Y=----=S=--------=--=&:___::S=---::0:.....:L=-=U:..:T~IO~N..s
111111111111111
(Mock Test-1 )
WI
Answer KEYS
SECTION-A
PHYSICS
1
(a)
6
2
3
(d)
(d)
4
5
(c)
7
8
9
10
51
52
53
54
55
(d)
(a)
(c)
(a)
(b)
(b)
56
57
58
59
60
(d)
(b)
(b)
(d)
(c)
(d)
(d)
(b)
(d)
(c)
1
2
(c)
6
(a)
(a)
(b)
3
(d)
4
5
(c)
(c)
7
8
9
10
(c)
(a)
(c)
(a)
11
12
(d)
13
14
15
(b)
(d)
61
62
63
64
65
(d)
(b)
(b)
(d)
11
12
13
14
15
(a)
(c)
(b)
(d)
(d)
(a)
(b)
16
17
18
19
20
(d)
(b)
66
67
68
69
70
(b)
(d)
16
17
18
19
20
(c)
(c)
(a)
(c)
(c)
(a)
(b)
(c)
(d)
(a)
(a)
21
22
23
24
25
(a)
26 (c)
27 (a)
28 (a)
29 (b)
30 (b)
31
32
33
34
35
(d)
(b)
(d)
(d)
(b)
36
37
38
39
40
(c)
78
79
80
81
82
83
84
85
(d)
(b)
(d)
86
87
88
89
90
(b)
(c)
(b)
(d)
CHEMISTRY
71 (b) 76 (c)
72 (c) 77 (b)
73
74
75
(b)
(a)
(c)
(b)
(b)
(b)
SECTION-B
MATHEMATICS
21 (c) 26 (d)
22
23
24
25
(c)
(a)
(a)
(b)
27
28
29
30
(a)
(d)
(b)
(c)
31
32
33
34
35
(a)
(c)
(a)
(c)
(c)
(b)
(b)
(d)
(d)
(c)
(c)
(c)
(a)
(b)
(a)
(b)
36
37
38
39
40
(b)
(b)
(a)
(a)
(c)
41
42
43
44
45
91
92
93
94
95
41
42
43
44
45
(c)
(d)
(d)
(a)
(a)
46
47
48
49
50
96
97
(b) 98
(d) 99
(b) 100
(a)
(a)
(b)
(b)
(b)
(a)
(a)
(d)
(b)
(d)
(d)
(b)
(c)
(a)
(a)
46
47
48
49
50
(c)
(b)
(a)
(b)
(a)
(b)
(b)
SECTION-A
PHYSICS
2.
1.
(a)
(d)
7
Distance covered in one circular loop = 2m
=2x 3.14x 100=628m
Gmm
2
~(D-x)
or G(8lm) = Gm
x2
(D- x)2
628
Speed =-=10m / s
62.8
Displacement in one circular loop= 0
. =-.0- = 0
Ve1oc1ty
trme
Gme
~
1/
;::::D
9D
x=
3.
4.
w·
(d)
(c)
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86
5.
TargetMHT-CET
(d) Work done in storing a charge Q in a
capacitor is stored in capacitor as its energy U
⇒ (11,o)copper =
2
1
1
Q
U=W=-QV=-= -CV 2.
2
2C 2
6.
(d)
I 2
1
2
WI= -kx and w2 =- k(x+ y)
2
2
I
2 I 2
W=W2 -Wj = - k(x+ y) - - kx
2
2
14.
(b)
v=w[A 2 -x 2 J 112 ⇒ x=
(b)
.
Vmax
Given that v = -
2
- =
2 2]1/2
so,
8.
(b)
A2 - ~
4co2
= m1X1 + m2X2 + ffi3X3
m1 + m2 + m3
&y= m1Y1 + m2y2 +m3y3
m1 + m2 + m3
m
[ T'
2
A - :
here m 1= ~ = m 3= m
2
(x +x +x )m
3
SO X =1- - 2- - ~
=2,
m+m+m
Aw
2 .
(Y1 +Y2 +y3)m
y=~----=2
m+m+m
r::;
So coordinates ofC.M. ofthree particle are
=::!]._A
[
2
actual frequency deviation
x 00°/4
1
max. allowed frequency deviation
15.
16.
(2,2)
(d)
(d) Angle of banking is tan 0
202
v2
= -=--=-rg 40✓
3 xlO
1
3
tan = ✓
(M)actual x 1OO%
(M)max
if(L'lf) actual= (M) max
m=l00%
9.
(d)
10.
(c)
11.
(a)
(d) Density of nuclear material = mass/volume
12.
To eject photo-electrons from sodium the
longest wavelength is 6188 A and that for
copper is 3094 A.
Hence for light ofwavelength 4000 A, sodium
is suitable.
The coordinates ofC.M ofthree particle are
X
I
=-ky(2x+ y)
2
7.
2
4 x 6188 = 3094 A
e
17.
(b)
Y=
10
m x IO = 2 x 3 x IO - 2 x 100
orm=6 x Jo-4kg =6x Io-4 x J03 g=0.6g
:.
e = 30°
Let f. 0 be the unstretched length and f. 3
be the length under a tension of9N. Then
4Ro
A (.e1 - Ro)
These give
10-27
4
-m
4
3
9
Further, --;;---;;- = o
-c 1 - -c o
3
o
-c z - -c o
Substituting the value of f. 0 and solving,
we get f. 3 = 5f. 2 -4f. 1
6.6 X 10- 34 X 3 X 108
- - - - - - - = 6188 A
( 11,0) sodiumxl. x -19
2
6 10
18.
(c)
V
10
R = - - G = - - -10 = 990 n in series.
lg
0.01
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87
MOCK.TEST-I
19.
(c)
. m
. pyrann'd = - Q .
Flux gomg
TBl/2
2Eo
16
= 8=2
which is divided equally among all 4 faces.
:. Flux through one face = -
Q
8"o
20.
21.
22.
(a) Impulse= force x time
=MLr2 x T=[M Lr 1J.
(a)
(b) Escape velocity
v
e
= ✓2GMe
R
e
v'
'
e
27.
= ✓2GM;
28.
29.
R'
e
= 4: 16, = 1 : 4
(a) As we know, limpulsej = !change in momentum!
= IP2-P 11= I0-mv 11= I0-3 x 21 = 6Ns
(a)
(b) The
fundamental
frequency in case (a) is
f =~
2£
The
fundamental
frequency in case (b) is
, _ _v_ = ~=f
f - 4(RI 2) 2£
v'e = 2ve = 2 x 11.2 = 22.4 km/s
23.
(c)
24.
(b)
E = hv = h ~ :.
A
25.
_§_ = A. 2 = SOOO
E2
I
A.1
30.
(b)
31.
32.
(cl)
(b)
33.
(cl)
34.
(cl)
(d) From Snell's law,
sin60°
sinr
,,;
Limitingfriction= 0.5x2xl0=10N
The applied force is less than force of
friction, therefore the force of friction is
equal to the applied force.
= " 3 or
---------
--♦-----------------------
he
1
2
-mv = - - ~
2
A.
-------
60
Clearly, v' > i v
.
✓
3
I
sm r= 2 x ✓3 =2
26. (c)
r = 30°
Thus, 8=60°
Ratio ofnumber ofhalflife taken is given
as:
After 16 days
35.
36.
(b)
(b) This is a balanced wheatstone bridge
condition,
⇒
R = 15O
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TargetMHT-CET
88
37.
(d)
m = -~=-c~f
Now m1
f 2 ➔ frequency heard by observer after reflection
J
355 5
= [ ~ x][
- ] x180=180 Hz
355-5
355
= -C5~ f
J ... (i)
... (ii)
40-f
m1
f2-fi = 5Hz
46.
47.
(a)
(a) For Brackett series
48.
49.
(b)
(b) Distance covered by lift is given by
y = t2
:. Acceleration oflift upwards
40- f
:. mz = 25 _ f or4= 25 _ f orf=20cm.
38.
(d) There is no current inside the pipe.
Therefore
fB.df = µOJ
39.
⇒ 1=0
B=O
W
25
1
W=F s cos 0 cos0=-=-- =,
Fs 5x10 2'
(c)
0 = 60°.
2
d y
d
2
g
=-=-(2t)=2m / s =dt2
dt
5
40.
41.
From Bernoulli's theorem,
(c)
I
2
I
2
P0 +- pv1 +pgh=P0 +- pv2 + O
2
2
V2 =.Jv?
T' =
+2gh= ✓0.16+2 x l0x0.2 = 2.03m/s
From equation of continuity, A 2v 2 =A 1v1
n2
7t_____l_ X V2
4
42.
43.
44.
g
n..2 ⇒ Dz =Di ~ =3.55 X
=7t-Vj
4
V2
50.
(b)
w-3 m
(d) According to Lenz's law, when switch is
closed, the flux in the loop increases out of
plane of paper, so induced current will be
clockwise.
(d)
(a) Moment of inertia is given by
i=l
45.
2n~
Thus, it does not depend on angular
velocity.
(a) Frequency heard by observer directly
.
355-5
commgfromsource = --x180 = 175Hz.
355+5
l g =
g+5
2,ff.
f = J¾
-g
T.
5
2 x 0.07
2T
----; = 0.14 x l0-3
.
2T
Pressure applied, = Pa - x 103 N/m 2
r
= 105 - 103= 99
CHEMISTRY
51.
(a) Joule is the unit of work and Pascal is unit
of pressure.
JPa-1 =_!__= Work = Nm =m3
Pa Pressure Nm- 2
52.
(c)
C3H 80 ~ C3H 6 0 (Ketone)
(X)
OH
I
[O]
0
II
CH3-CH-CH3~CH3-C-CH3
Ketone
2° Alcohol
Ketones are oxidation products of 2°
alcohols.
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MOCK.TEST-I
53. (a) The element with outer electron configuration
3d54s2 is Mn which exhibits oxidation states
from+2to+7.
54. (b) Al2O 3 cannot be reduced by carbon.
55. (b) According to Arrhenius equation,
60.
(c)
89
destabilize the carbocation intermediate ofthe
SN 1 mechanism, a benzylic chloride that
disfavours the SN 1 mechanism.
Acc. to Kohlrausch law,
Aeq (NaF) + Aeq (HCl)-Aeq (NaCl)
k = A .e- Ea l RT
=
where k = rate constant
61.
(c)
2R-S-H
R-S-S-R
Thiol
Disulphide
Ea
or 1n k = lnA--
RT
A = frequency factor or pre-exponential
factor
Ea= Energy ofactivation.
In Arrhenius plot, ln k vs 1/T
62.
63.
CN- being a strong field ligand pairs up
64.
(b)
65.
(d)
lnk
@
66.
(d)
0
(b)
unpaired electron in Ni 2+.
Specific conductance of the solution
(K) = 0.012 ohm-1cm-1and resistance (R) =
55ohm.
Cell constant = Specific conductance
x Observed resistance = 0.012 x 55
=0.66cm-1.
Rate=k[Ni05] ;
2.4x10-5 =3.0x10-5[N2O5]
:. [N2O5] = 0.8
Acetophene
58.
67.
II
H-P-H
I
Hypophosphorous acid
0
'-. H
68.
(HlO2) is a monobasic acid. i.e., it has only
one ionisable hydrogen atom or one OH is
0
t
69.
(b)
Na 3 AIF6 is cryolite and used in the
electrolysis of alumina to lower the melting
point and increase electrical conductivity.
(d) Linseed oil, lanolin and glycogen attract
water hence contain a hydrophilic structure,
but rubber does not attract water and thus
does not contain a hydrophilic structure.
(c) For an ideal solution, D.H = O, ~V = O
Hence, option (c) is incorrect.
(c) In compounds
CH3 ~
/H
C=C~
H /
Cl
present H-P-OH
I
59.
RNH-CH3
secondary amine
(b) Ni shows sp3, sp3 and dsp2-hybridisation
in Ni(CO) 4, [NiC1 4] 2- and [Ni(CN)4 )2respecti vely.
i
57.
4[H]
alkyl isocyanide
R
(d)
R-N ➔ c
(d)
Slop is - Ea and intercept in lnA.
56.
A eq (HF)
H
(d) 4-nitrobenzyl chloride is most likely to react
by the SN2 mechanism as the strongly
electron-withdrawing nitro group would
I
II
I has more dipole moment than II, hence its
boiling point will be higher. Melting point
depends on symmetry, therefore I has higher
melting point than II. Steric crowding in II is
more than in I therefore I is more stable than
II.
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90
TargetMHT-CET
70.
(a) Baking powder has starch, NaHCO3 and
Ca(8:iPO2) 2.
71.
(b)
CH(OH)CH2CHO
@
2KBr + I 2 ~ 2KI + Br2 (not possible)
Because Br- ion is not oxidised to Br2 with
12 due to higher electrode (oxidation)
potential ofl2 than that of bromine.
72.
73.
CH = CHCHO
@
(c)
~
¢
N+cc
(b)
. __..__
'I
OH
tt2o
¢ +N,+HCI
Cinnamaldehyde
79.
(b)
80.
81.
(b)
2CuSO4 +K4[Fe(CN)6]~
Cu 2[Fe(CN)6] + 2K2SO4
CH3
p- cresol
74.
75.
76.
(a) IUPAC name of sodium nitroprusside
Nai[Fe(CN)5NO] is sodium pentacyanonitrosylferrate (III)
2 x O.N. ofNa + O.N. ofFe + 5 x O.N. ofCN
+ 1 x O.N. ofNO=0
2 x (+1)+O.N. ofFe+ 5 x (-1)+1 = 0
O.N. ofFe = 5 -3 = + 2, hence ferrate (II)
(c) Ca3P 2 + 6Hp ➔ 3Ca(OH)2 + 2PH3 ; i.e 2
moles of phosphine are produced from one
mole of calcium phosphide.
(c) As we know that, units ofrate constant.
= (unit ofconc.) 1-n (unit oftimet1
= (mol L- 1) 1- n (sect1
On comparing these units with the given
units of rate constant, we get
(mol L- 1) 1- n (sect 1 = Lmo1- 1 sec- 1
⇒ Ln-l mo1 1-n sec- 1 = L moJ-1 sec-1
On comparing the powers, we get
(-H20)
Chocolate ppt.
(c)
Number of moles ofAgCl
=
4305
= 0.03 mol
143.5
0.01 mol. ofcomplex ➔ 0.03 mol ofAgCl
1 mol. of complex ➔ 3 moles ofAgCl
Hence, the compound has three ionisable
Cl atoms. Thus formula ofthe complex must
be [C~)JC13.
82.
83.
(d)
(b) Methyl vinyl ether under anhydrous
condition at room temperature undergoes
addition reaction.
HBr
CHrCH-O-CH 3
I
n-l=l ⇒ n=2
77.
78.
Br
So, reaction is of second order.
(b)
(b) Aldol formed in aromatic aldehydes itself
loses water molecule without heating
because double bond formed is more stable
due to conjugation with benzene ring.
85.
86.
CHO
@+CH,CHO
Hunsdiecker reaction
dd.N,OH
C 6H 5 Br+CO 2 +AgBr
(a) (a) and (d) are L- sugar but (a) gives an
optically active dibasic acid.
(c) These two components A and B follows the
condition of Raoult's law, if the force of
attraction between A and B is equal to the
force ofattraction between A and A or Band
B.
87.
(a) Charge=0.2 x l Faraday
= 0.2 x 96500 coulombs
= 19300 = 1. 93 x 104 coulombs
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MOCK.TEST-I
88. (b) Dehydration of CH30H gives carbene
91
For reaction,
(methylene), an unstable intermediate.
1
C ___. B + -A
~
Carbene
89.
(a) Tyndall effect is the simplest way to check
K'
colloidal system since path of light beam
becomes visible due to scattering oflight.
90.
(b)
91.
(a) Isopropyl chloride CH3 -CH-CH 3
I
92.
K'
93.
K=
[A I~
2=40
...(ii)
[c]
=[~f2 =[410r2
(b) Gabriel phthalimide synthesis is the best
method of preparing primary amines from
alkyl halides without changing the number
of carbon atoms in the chain.
(d) For reaction, A+ 2B ~ 2C
[c]2
[~ 4 1/2
Dividing (ii) by(i)
20
Cl
2
...(i)
0
0
0
0
0
0
~ KOH(,1,4~+~➔ @;'-R
1 NaOH/H2 0
@¢
0
R - NH2 +
primary amine
- +
ONa
- +
ONa
0
94.
(d) Sulpha drugs (antibacterials and antibiotics)
are group of drugs which are derivatives of
sulphanilamide.
Petroleum ether has lower boiling point than
all the other three products.
95.
(b)
96.
(a)
97.
(b) C~OH
2KC10 3 + 12
➔
2KI03 + Cl 2
98. (d)
99. (c)
100. (b)
Due to diagonal relationship.
In binary copolymerization, there are two
different chain radicals which can add both
the monomers, though not necessarily with
same ease, the system characterizes four
simultaneous propagation reactions.
Oxidation
HCOOH
(A)
HCOONH 4
(B)
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92
TargetMHT-CET
SECTION-8
MATHEMATICS
1.
(c)
5.
The given expression
n(A'nB') = n(AuB)' = n(U)-n(AuB)
A
= tan
= n (U)-[n (A)+ n (B)-n (An B)]
= 700-[200 + 300-100] = 300
2.
(c)
[ ✓
3 +tanA] [ ✓3-tanA]
3 tan A - 1+ ✓3 tan A
+ 1- ✓
3
=tanA+[ 8tanA ]=9tanA-3tan 3
l-3tan 2 A
l-3tan 2 A
(a) When x = 1, y = 7 EN, so (1 , 7) E R
When x = 2, y = 2 + 3 = 5 E N, so (2, 5) E R
=3 _(3tanA-tan3 A) =3tan3A
l -3tan 2 A
Again for x = 3, y = 3 + 2 = 5 E N, (3, 5) E R
Similarly for x = 4, y = 4 +
y=5+
6
4 !I' N and for x = 5,
6.
6
(d)
3/(x)-
1(D
3/(D- f(x) =
= logx
4.xy
2
zl
(x+ y )
⇒
1
;
2
⇒
Domain of R = {1, 2, 3} and Range of
R = {7, 5} .
3.
4.xy
(x+ y)
Since range of sec 0 is ( ---oo, -1] u [l, oo).
S 11' N. Thus, R = {(1, 7), (2, 5), (3, 5)}
4
.
.
29
()
a G1ven equation, sec =
X= X
(x +y)2 -4xy:,; 0
-4.xy :,; 0
⇒
x2+y2+2xy
⇒ (x-yf:,; OBut(x- y )2i0foranyx,yER
(x-y)2 = 0 ⇒ x=y
log(~r
After solving we get j{x) = log x
nx [2a + ( nx-l)d]
f (e- x) = log, e-x = - x
4.
7.
(b)
snx
= ~2~---~ [2a + (x-l)d]
2
5x
(c) /(x) is defined if3x2 -4x + 5 2 0
n[(2a-d) + nxd ]
(2a-d)+xd
For
Which is true for all real x
Domain of f(x) = (-oo, oo)
Lety = ✓3x 2
nx to be independent ofx
sx
2a - d =0 ⇒ 2a = d
-4x+5
now, SP=
⇒ y 2 =3x2 -4x+ 5 i.e. 3x2 -4x + (5 - y 2)=0
For x to be real , 16 - 12 (5 - y 2 ) 2 0
5
⇒y 2
J¥
8.
p
2
2 [2a + (P- l)d] = P a
(c) Let (e 1 + e- 1, e1- e- ~
= (h, k)
or h=e' +e- 1 and k=e'-e-1
Squaring and subtracting, we get
h2 _ k2 = ( e1 + e-1 )2 _ ( et _ e - t )2 = 4
Therefore, the locus is x 2 - y 2 = 4.
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93
MOCKTESf-1
9.
(a) Let the radius of the first circle be CT= r 1.
Also, let the radius ofthe second circle be CP = r 2.
15.
Given expansion is (a+ bx)-3 which can be
(b)
written as
In the triangle PCT, Tis a right angle
122
- ✓ 2 -CT2 =-yr1-ri
So, PT-PC
10.
(By using (I + x)-3 = I -3x + 6x2 - ........)
(c) 4y = 3x-48 ⇒ m = 3/4,c = -12
y 2 =64x ⇒ a= 16
2
Length of intercept = - ; a(l + m )( a - me)
m
11.
.J
(b) Let total no. of numbers divisible by 4
and -3ba-4 = 9. 2-3 ⇒ b = -6
between 1 to 80 is n ;
4 + (n - 1)4 ⇒ 80 = 4 n ⇒ n = 20
20
c
Required probability =
16.
soc:
=
dx
⇒ -2x+ 4x 3 = ax3 +bx
y=l2 ...(ii)
⇒ a=4
(x= -5) So, z=-5 + 12i
⇒ Iz I= .J25 + 144 = 13 ⇒ Iz 2 I= I z 12 = 169
14.
17.
Given inequality is 5x + 1 >- 24
⇒
5x > - 25 ⇒ x >-5
Also,5x-l < 24
(c) The total weight of seven students is
52 + 58 + 55 + 53 + 56 + 54 = 328 kg
Hence, the weight of the seventh student is
5x < 25 ⇒ x < 5
Hence,-5 < x < 5
⇒ x E (-5, 5)
(a) We know that 1! + 2! + 3! + 4! = 33
Also,5!= 120,6!=720, 7! = 5040,8! = 40320and
9! =362880. Thus, tensdigitofl! + 2! + .... +9! is 1.
Also, note thatn! is divisible by 100 for all n ~ 10.
Therefore, the tens digit of 1! + 2! + .... + 49! is 1.
andb = -2.
55 x 7 = 385kg
The sum of the weights of six students is
(d)
⇒
(l+x2 +x4 )
⇒ .!!:___(l- x2 +x4 ) = ax3 +bx
2
=8 ... (i) &
(b) We have,
dx
316
x+iy+.jx 2 +y =8+12i
⇒ x+ ✓x 2 +y2
⇒ a=
.!!:_[(I +x2 +x4)(1 -x2 +x4) ] = ax3 +bx
19
(d) z+ l z 1=8+12i
⇒
13.
2
⇒ a
⇒ 80 =
12.
-3 =-=
1 2-3
8
4
9
3
1600
= - X16 16(1 + - )(16+ 12 X-) = - 9
9
4
16
385-328 = 57 kg.
18.
(d) f(x) = [x]2 + [x + l]-3 = {[x] + 2} {[x]-1}
So, x = 1, 1.1, 1.2, ..........
⇒ f(x)=0
f(x) is many one.
only integral values will be attained.
f(x) is into.
IWWW.JEEBOOKS.INI
94
19.
2
(a)
~ ~ ~ ~
~
TargetMHT-CET
~i
I=
A = [~
][~
] = [~
0 0 1
a b -1 a b -1
f
I
(
loge2
1
I
t - 2 ) e1 dt
f
I
=
t
(
loge2
1 -1
t +2
)
1
e dt
t
eloge2
t ]'
- .:._
= e - - - = e -2log 2 e
- [ t loge 2
loge 2
23.
(a)
dy
dy
dy
dx =ixl ⇒ dx =x forx:2:0 & dx = -xfor
x<0
fdy= fxdx
20.
*
⇒
From (i) and (ii) y =
24.
3
lim f(x) = Jim sin nx = /(0)
5x
x ➔O
x ➔O
⇒
S
x2
2
...(ii)
+c1
~ +c
2
(a) Let A, B, C are the vertices of a I::. whose
position vectors are
a, b and C respectivety.
Let G be the centroid of !::.ABC. : . Centroid of
3 Sin 7tX
31t COS 7tX
/S
= 31t
Now: lim - - = J.·1m -5x
5
'x➔O
x➔O
31t
⇒ y= -
fdy = -lxdx
3sin nx
0
iscontinuousatx = 0
f(x) = ~ , x
{
2k, x = 0
(a)
...(i);
triangle (G)
31t
= 2k ⇒ k = 10 (usingL.'Hospita!Rule)
a+b+c
3
Consider, GA+ GB + GC
2
21.
(c)
r=la
x +8
4
Giventhat4y-x 2 -8 = 0 ⇒ y = --
rJ+lb
a+b+c'\
a+b+c'\
3
3
)
.ffi
. .
dy 2x
D1 erentiatmgw.r.t. x _ = _
4
dx
For increasing function dy > 0
dx
1 - - - - =-[2a-bc+2b -a - c+2c -
3
So,
2x
->0 ⇒ x>0
x
4
25.
Thus, the curve is increasing in (0, 4).
22.
(c) Let
1
}
fel2 -1oge
-1 - 2 dx
x ( loge x)
(b)
-
-
a - b]= 0.
sin0 cos0
- sin0 - x
cos 0
l
I
x
=x(x 2 - l) - sin0(-xsin0-cos0)
+ cos0(-sin 0 + x cos0)
Put loge x = t ⇒ x = e ⇒ dx =
1
e1 dt
Alsoifx = 2 then t = loge 2 and ifx = e then t = 1
=-2-x+xsin2 0+sin0cos0-cos0sin0+x ros2 0)
=x3 - x+x=x3
lWWW.JEEBOOKS.INI
MOCK.TEST-I
26.
95
⇒ P(AnB)=0.5 ⇒ P(A)-P(AnB)=0.5
dx = -a sin 0 and dy = a cos 0
(d)
d0
d0
⇒ P(AnB)= P(A)-P(AnB) =0.7-0.5 =0.2
p(_!_)
- P(A n B)
A u B - P(A) + P(B)-P(A n B)
dy ... ---cote.
dx
:. The slope of the normal at 0 = tan 0
:. The equation of the normal at 0 is
=
y-asin 0 = tan0(x -a-a cos 0)
29.
⇒
ycos0-asin0cos0
= xsin0-asin0-asin 0cos0
⇒ xsin0-ycos0=asin0 ⇒
(b)
0.2
= 0.25
0.7+0.6-0.5
(l+olt =(l+ro4 t
⇒ (-rot = (l+rot = (-ro2 t ⇒ ron = l ⇒ n = 3
y=(x-a)tan0
which always passes through (a, 0)
e
27.
f
= n+IC
(a) Requiredarea = iny dy
r
+ n+IC
r+I
= n+2C
r+I
I
31.
(c)
General Term T
= (y lny- y)j = (e-e)- [-1] = 1
y=e
32.
+ =
r 1
c
500-r _i:_
r3
2
22
The above term is integral if r is even. Also
0:,; r:,; 500
Sor=0,2,4, 6, ......., 500
(a) Let the points are A, B, C and D respectively
Mid point ofAC is
(i
2_ ~) .
4 - 1 7 - 2 8 + 1) or
( 2' 2' 2
2'2'2
(0, 1)
x' - - - - - -........- x
0
y'
Mid point ofBD is
2+1 3+2 4+5)or
( 2 ' 2' 2
Also,
500
e
e
I
I
(i 2_ ~)
2 ' 2 ' 2·
Thus AC and BD bisect each other. Further,
fIn ydy = fln(e + 1- y)dy
AC= ✓(4+1)2 +(7+ 2)2 +(8-1)2 = ✓25+81+49= ✓l55
I
Further, required area = ex 1- Jex dx
:. AC'# BD. Hence, ABCD represents a
parallelogram.
0
28_ (d)
p(~)
= P[Bn(AuB)]
AuB
P(AuB)
33.
(c) Let Jim bn = b Now,
n~
P [BnA) u (Bn B)]
P (A)+P(B)-P(A n B)
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96
125
lim bn+I = ~[2 lim bn +
or n➔oo
n➔oo
3
lim bn2
n ➔oo
l
TargetMHT-CET
38.
ltis given that when t= 0,x= 3. Therefore, when
t = 0,
125
3
3b
35
(c) p ➔ (~ p v q) has truth value F.
It means p ➔ ( ~ p v q) is false.
It means pis true and ~ p v q is false.
⇒ p is true and both ~ p and q are false.
⇒ p is true and q is false.
(b~
•
J
Ify =
1
or x=
2
2 lOx -10-x
-
- -- -
3 10x + 10-x'
1o2 x =
2
39.
(a) The projection of
--
2 - 3y
Here,
1t
3
ii:b .
lbl
a='i-2}+k, b=4'i-4}+1k
cl -
2] +k).(41 -4] + 1k)
✓(4)2 +(-4)2 +(7)2
4+8 +7
19
19
.
= --;===== = - - = - umts
✓16+16+49 ✓
81
9
(b) We have,
X
is
:. Required projection
2+3y
log10 2-3y
11:
~ on b
3y+2
. _1
_ 1
2+3x
.. f (x) - 2 loglO 2 - 3x.
tan -1
...(1)
19=-dx / dt
=
36.
dy / dt
= dx / dt
.
dy
dy
Smcewhen t = 0 - = 19 and - = 2, from(!)
' dx
dt
3
⇒ -=2 ⇒ b = 125orb =5.
34.
dy
Also, dx
2
dy
- =3x 3 - 8 = 19.
dx
125]
orb= -1 ( 2b+b2
3
b
(a) We have y = x 3 - 8x + 1 :. dy = 3x2 - 8
dx
- < - ⇒ tan
(
tan - 1 -X) <tan -1t
3
1t
40.
⇒ ~ < ✓3 ⇒ x < ✓311: = 5.5 (approx.)
Let us take a triangle ABC and their vertices
A (a, 0, 0), B (0, b, 0) and C (0, 0, c)
Therefore the equation of plane is
(c)
7t
37.
.... (i)
:. The maximum value ofx is 5.
(b) We have,
1
-
0
[
0
1
4(1-a) 3(a-l)
Now, given centroid of LiABC is (a,~. y)
As we know, centroid oft.ABC with vertices
(x 1, y 1, 2 1), (x2 , y2 , 2 2) and (x3, y3, 2 3) is given by
l
(
1 [1 o ol
2(c+l)=010
c+
2+ac
0 0 1
Comparingtheelementswegetc+ 1 =0 ⇒ c=-1
⇒ a= 1
and a - 1 = 0
xi + xz +x3
3
'
Y1
+yz +y3
3
'
21 + 2 2
+ 2 3)
3
'
: . By using th is formula, we have
a+O+O = a ⇒ a = 3 a . O+b+O = A.
3
"
3
..,
⇒ b = 3~
and O+ O+ c = Y
3
⇒ c= 3Y
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97
MOCKTESf-1
Now, put the values of a, b, c in equation (i),
which gives
43.
(c)
LetI = fo" x (sin4 x cos4 x)d.x
x
_xyz
y
z
- + - + - = 1 . . -+ - +- = 3
3a 3~ 3y
a ~ y
41.
(d) Let the vertices ofa triangle be
= nfo" sin 4 x cos 4 xdx-1
(;, ~) ,(;,y:) and(;, y:)
J"sin x cos xdx = 2.-2 J" sin xcos xdx
2
:. ] = -1t
0
Area of the triangle=
XI
2:'.!.
a
a
2b
X2
Y2
X3
Y3
C
C
1
=
b
44.
12
1t
4
4
4
4
0
3 · l · 3 · l 1t
8 ·6·4·2 2
3n 2
256
7t.- - - . - = -
(a) Let Shamali invest t x in saving certificate
and t y in PPF.
.·. x + y ~ 50000, x ~ 15000 and y~20000
Total income =
8
9
x+
Y
100
100
:. Given problem can be formulated as
Maximize Z = 0.08x + 0.09y
Subject to, x + y ~ 50000, x ~ 15000, y ~ 20000.
P(X = r)
45.
"Crpr(l-p)n-r
(l-p)n-2r
"Cn- rPn-r(l-p)r
Pn-2r
-(1~pr' -(~-f''
1
abc 1
X- = - .
4abc 2
8
= - X42.
(a) P(X = n-r)
(b) Given Y = kekx . The curve
and
m-1>0
.·. ratio will be independent ofn and r if( 1/p}-1 = 1
⇒ p = 1/2
intersects the y-axis at (0, k)
46.
dy)
_ k2
So, ( dx (O,k ) -
(a)
Putx = z6 ⇒ dx = 6z5 dz
y
3 4 + 6tan-l z + C -- -3 x 2/3 +6tan-lxl /6+C
=-z
If0 is the angle at which 1
the given curve intersects the y-axis, then
2
47.
2
1t
2
k -0
tan( - - 0) =
=k
2
1+ 0.k 2
⇒
0 = cot
-I
2
(k )
2
(b) Equation of plane through (1, 0, 0) is
a(x -l) + by +cz= 0
(i)
⇒
...(i)
passes through (0, 1, 0). -a + b = 0
b = a; Also,
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98
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49.
(b) We have,
a2
a
J
0
⇒ 2a2 = c2 ⇒ c = ✓
la .
f{a) = a + _!_ (sin a + a cos a)-
2
y2 = l(x + h) , where / and h are arbitrary
constants. Differentiating (i) we get
dx
Differentiating again,
Put a =
...(2)
7t
Differentiating w.r. t. a, we get
2a i.e. l, l , ✓
2.
Sod.rofnormalarea, a ✓
The equation of such a parabola is
48. (a)
2y dy = I
a
f(x) dx =-+-sina+-cosa
2 2
2
50.
f; r(f) f
=
+
~ sin a
2
½- f = ½
(b) Bydefinition ofmode, the required value of
Xis the mode. Here (n + l)P = (9 + 1)
1
5=2
= integer ⇒ bimodal, modes being 2 and 2 - 1.
WWW.JEEBOOKS.INI
(Mock Test-2)
Answer KEYS
SECTION-A
PHYSICS
1
2
3
4
5
51
52
53
54
55
(b)
6
(b)
7
(b)
8
9
10
(b)
(b)
(c)
(c)
(c)
(c)
(a)
56
57
58
59
60
(d)
(b)
(c)
(d)
(d)
(d)
(b)
(a)
(d)
(d)
11
12
13
14
15
61
62
63
64
65
(a)
(d)
(c)
(b)
(c)
(c)
(b)
(d)
(c)
(d)
16
17
18
19
20
66
67
68
69
70
(c)
(c)
(d)
(a)
(b)
(a)
(b)
(c)
(a)
(d)
21
22
23
24
25
(d)
(a)
(d)
(a)
(c)
26
27
28
29
30
(b)
(c)
(b)
(d)
(d)
CHEMISTRY
71 (b) 76 (b)
72 (b) 77 (c)
73
74
75
(a)
(d)
(a)
78
79
80
(a)
(b)
(b)
36
37
38
39
40
(c)
(d)
(a)
(a)
(a)
41
42
43
44
45
(a)
(b)
(a)
(c)
(d)
46
47
48
49
50
(b)
(c)
(a)
(d)
(d)
86
87
88
89
90
(a)
(a)
(c)
(d)
(a)
91
92
93
94
95
(b) 96
(b) 97
(c) 98
(d) 99
(b) 100
(d)
(c)
(b)
(a)
(b)
(d)
(c)
(a)
(a)
(d)
36
37
38
39
40
(b)
(d)
(c)
(c)
(b)
41
42
43
44
45
(b)
(b)
(b)
(d)
(a)
46
47
48
49
50
(a)
(b)
(d)
(a)
(d)
31
32
33
34
35
(b)
81
82
83
84
85
(b)
(c)
31
32
33
34
35
(b)
(b)
(c)
(b)
(a)
(b)
(b)
SECTION-B
MATIIEMATICS
1
2
3
4
5
(d)
(c)
(d)
(b)
(c)
6
7
8
9
10
(a)
(a)
(c)
(a)
(c)
11
12
13
14
15
(b)
(c)
(c)
(b)
(c)
16
17
18
19
20
(d)
(b)
(b)
(a)
(a)
21
22
23
24
25
(d)
(c)
(a)
(d)
(d)
26
27
28
29
30
(c)
(d)
(d)
(a)
(a)
SECTION-A
PHYSICS
1.
(b) For negotiating a circular curve on a levelled
road, the maximum velocity of the car is
4.
5.
Vmax = ~
Hereµ = 0.6, r= 150 m,g= 9.8
.'. vmax= .Jo.6 x 150 x 9.8 '.::: 30m / s
2.
3.
(b) Because radius of the sphere will be very
less in comparison to ring (although mass
is equal).
(b) Young's modulus ofwire does not vary with
dimensions ofwire.
6.
When the light is incident at the polarising
angle on the transparent medium, the
reflected light is completely polarised.
(b) When some mercury is drained off, the
centre of gravity of the bob moves down
and so length of the pendulum increases,
which result increase in time period .
(d) Relative magnetic permeability
(b)
µr=
magnetic permeability of material(µ)
permeabi Ii ty of free space (µ 0 )
It is a dimensionless pure ratio and for
paramagnetic materials µr > 1.
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100
7.
8.
(b)
17.
(c) y=Asin(rot-kx)
Particle velocity, vp =
dy
dt = A
ro cos (rotf =
kx)
.'. vpmax=A ro
wave velocity=
k
(J)
:. 'A,=2rcA
(d)
1250
0.85 X 4
Aro= k
1
2 TC
A= - Butk= k
'A
i.e.,
(2n-l)u
L
~1250
4
⇒ (2n-l)x340 ~
(J)
9.
(c) Lengthofpipe = 85 cm = 0.85m
Frequency of oscillations of air column in
closed organ pipe is given by,
19.
⇒ 2n-l:::12.5"'6
(d) Joule-second is the unit of angular
momentum.
(a)
20.
(b) We know that efficiency of Carnot Engine
18.
Af = 6A, Llt = 0.3s, E= 30V
= 7i -Tz
7i
di
E=Ldt
where, T 1 is temp. of source & T2 is temp. of
sink
L = 30 x 0.3 = 1.5 H.
.'. 0.40 =
6
7i -
⇒ 7i -300 = 0.407i
300
7i
10.
(d)
he 6.6xl0-34 x 3xl0 8 J
Energy = - = - - - - - - 'A
0.5xlO-lO
6.6xl0-34 x3xl0 8
- - -11
- - - - e V =24.82 keV
5x10- xl.6x10- 19
12.
13.
(a) The centre of mass of two particles lies
always on the line joining the two particles.
(d)
(c)
14.
(b)
11.
When hot water temperature (T) and
surrounding temparature (T0) readings are
noted, and log(T- T0 ) is plotted versus time,
we get a straight line having a negative slope;
as a proof ofNewton's law of cooling.
⇒ 7i
3
3
= 00 = 000 = SOOK
.6
6
Now efficiency to be increased by 50%
0.67i = 300
7i -300
.·. 0.60 = ~7i- -
21.
⇒
T.1 - 300 = 0.6T.1
Q.47i = 300 ⇒ 7i = 3QQ = 300 X lQ = 750
.4
4
Increase in temp = 750- 500 = 250 K
(d) For the block to remain stationary with the
wall
J = µN
f=W
JON
µN=W
22.
16.
[3=/3,
(c)
m.
or
d
D'')...
- (2d)
D'='2D
w
0.2 x 10 = W ⇒ W
(a) Time period,
T = 2rc/ic =
JON
= 2N
2rc✓(50 X 10-3 ) X 4 X 10-6
= 28 X lQ-4 S
Time taken by capacitor to charge fully,
T
-4
t= -=7xl0
4
s
WWW.JEEBOOKS.INI
MOCKTEST-2
23. (d) Pre-emphasis of higher frequency
component is required in FM-system
because high frequency terms of
modulating signal have small amplitude and
therefore small power relative to those of
low frequency term.
In the reproduced program at the o/p, these
high frequency terms have poor SIN ratio and
at time noise may completely mask the signal
at these high frequencies, so it is necessary
to provide pre-emphasis of high frequencies.
24. (a) Applying law of conservation of
momentum,
m 1u 1 + m2u2 = (m 1 + m2)v
or, m 1u 1 = (m 1 + m 2)v
⇒
m (3 x 1000) = 3m(v)
101
29.
30.
e = - dq> = -~(10Ba 2 cos rot)= 10Ba2 sin rot( ro ).
dt
dt
31.
32.
3.6x10-S = B x _!_
(b)
i = A+om = 60° +30° = 450
2
2
10 ms- 1,
(b) Here u =
t = 4 s, a = ?
33.
34.
35.
(b)
(c)
(b) A raw egg behaves like a spherical shell and
a half boiled egg behaves like a solid sphere
Ir
Is
36.
(c)
37.
(d)
2
2
2 / 3 mr = ~>l
2 / 5 mr2 3
he
,
he
eV0 = --W0 and eV =---W0
Ao
2 Ao
Subtracting them we have
⇒ B = 7.2 x 10-5 Tesla
e(Vo-V')
I
26.
(b)
A
xB =
J
v= -2 ms- 1,
Using a = v-u = - 2 - 10 =-3 m / s 2
t
4
:. Force, F = ma= 1Qx(-3)=-30N
3600
1000
⇒
v = - - m I s = I km / h
3600
25. (c) Horizontal component of earth ' s field,
H = Bcos0, since, 0 = 60°
(d)
(d) qi = n BA cos 0 = 10 B a 2 cos rot
k
4 6 0
2 3 0
=~[1-.!..]
Ao
2
= ~ or
no
V ' -- Vo - he
-2eA.o
= i(0-0)- J(0-0) + k:(12-12) = 0
38.
27.
(c) As a-particles are doubly ionised helium
He++ i.e. Positively charged and nucleus is
also positively charged and we know that
like charges repel each other.
28.
(b)
v1 = dyl = 0.1 x I 00rc cos ( 1OOrct + 2:.)
3
dt
(a)
Rearranging the circuits, we get the
following circuit.
J1.L..----U::.;I:
:~;:
C
~
-------11------1
:. equivalent capacitance between A andB,
2
v2 = dy = -0.lrcsinrct = O.lrccos(rct+2:.)
dt
2
2rc- 3rc
4x4
CAB = - - = 2µF
4+4
and equivalent capacitance between C and D,
6
re
6
8x8
CcD =-=4µF
8+8
:.
Cab = 2µF + 4µF = 6µF
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102
39.
40.
(a)
(a) We know
-
I
1s
44.
(c)
ro 1= 600n, roi = 604n,
f, = 300Hz, fi= 302Hz
Beat frequency, f2 - f 1 = 2 Hz
⇒ Number of beats in three seconds = 6
G
= l+-
s
45.
(d)
•
x
A
Jlo •
C
9kg
60cm
(a)
or
Largest frequency (f1)
L
t fr
(f)
owes equency 2
Largest frequency will be detected when the
source approaches detector along the line
joining and the smallest frequency will be
detected when the source recedes the
detector along the line joining them
46.
(b)
2
X
- =--- ⇒ x=24cm
3
(60-x)
By using Kirchhoff's first law
1, + 15 = 16
... (i)
12 = 14 + 15
... (ii)
Adding (i) and (ii), we get
1, + 12 = 16 + 14
47.
48.
(b)
(c) Gravitational P.E. = m x gravitational
potential U = m V, so the graph ofU will be
same as that ofV for a spherical shell.
c+v
c-v
42.
B
1kg
4kg
S ⇒ 20
41.
...
(60-x)
49.
50.
(a)
(b) Increment in area of soap film = A 2 -A 1
= 2 x [(lO x 0.6)-(l0x 0.5)) x lo-4 =2 x lo-4m2
Work done = Tx !1.A
= 7.2 x 10-2 x 2 x lo-4 = 1.44 x 10-SJ
2
(b) Terminal velocity, v O = 2 r (p - Po )g
9ri
2x(2 x 10-3) 2 x (8-l.3) x 103 x 9.8
CHEMISTRY
51.
(c)
9 x 0.83
=0.07ms-1
HC = CH
l%HgSO4
20%H2SO4
43.
(a) EMF, E = Kl where K =
V
L potential gradient
CH 3CH(OH)CH 3 ~ C H 3COCH3
V
iR
( E 0r l /
K=-=- = 1 - ) L
L
\r+r1 L
52.
E 0 rl
So, E =Kl= (r + r )L
1
(c) Cr(III) has three 3d unpaired electrons with
two vacant orbitals available for bonding.
The outer orbital bonding is not required.
53.
(c)
[BJ
Acetone [C]
Applicable to bimolecular reactions.
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MOCKTEST-2
54.
55.
56.
57.
103
In arenes, 1t electrons are delocalised, hence
arenes do not undergo addition reactions
easily. Aromatic compounds (arenes) are
highly stable and show resonance, e.g.
benzene.
(a) ZnS has cubic close packed (ccp) structure.
The s2- ions are present at the corners of
the cube and at the centre of each face. Zinc
ions occupy half of the tetrahedral sites.
Each zinc ion is surrounded by four sulphide
ions which are disposed towards the corners
ofa regular tetrahedron. Similarly, s2- ion is
surrounded by four Zn 2+ ions.
(d) The larger the size of anion the more is its
polarizability
(b) For a first order reaction
(c)
PH 2o
99
= · x760=752.4Torr
10
63 ·
(d)
2
.-. Total number of moles =
64.
(c)
65.
(d)
66.
(a)
67.
(b)
68.
(c)
22.4 L of 0 2 at STP = 32 g
1.43 g
(d)
60.
(d)
C 6 H 5CH 2OH does not give iodoform test
because it has neither CH3CO- group nor
CH 3CHOH group.
I
R
61.
(c)
2NO + 0 2
➔
Since the organic amino compound on
reaction with nitrous acid at low temperature
produces an oily nitrosoamine so the
organic amino compound is a secondary
aliphatic amine.
Note : This reaction is used as a test for
aliphatic amines since no other class of
amines liberates N 2 gas on treatment with
HN02 •
Chemical formula of iron (III)
hexacynaoferrate (II) is FeiFe(CN) 6hIn HC ea CH hydrogens are acidic since
carbon is sp hybridised.
Ionic molar conductivity ofH+ is very high
and NH4OH is a weak electrolyte.
Zinc oxide is mixed with powdered coke
and heated to 1673 K in a fire clay resort
when it is reduced to Zinc metal.
2NO 2 brown
ZnO+C
62.
180
178 2
· = 9.9
18
Totalmoles=0.l +9.9= 10
1673K
Zn + CO
At 1673 K, Zinc being volatile, distills
over and is condensed.
(b) Moles of glucose=__!!_= 0.1
Moles of water =
1
2 2=2
+
= 44800mL
R = k[A]1 = 3.47 x 10-2 x 0.0l
= 3.47 x 10-4mol L-1 min- 1
59.
3
V = nRT = 2 x 0.082 x 273 = 44 _ L
8
1
p
= 2.303log 4 = 2.303x0.6020 = 3 .47 xl0-2
40
40
32
1 L of 0 2 at STP = - - x 1 = 1.428 g =
22.4
16 1
n of 0 2 =-=32 2
3
n of H 2 =-
k = 2.0303 log-a- = 2.303 10 __2.:.!_
a-x
t
40
g0.025
58. (a)
= Mole fraction x Total pressure
69.
(a)
70.
(d)
Rate constant does not change with
concentration.
71.
(b)
c1- is oxidised to Cl2 at anode.
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104
72.
73.
74.
75.
(b) Correct order of decreasing priority is
- COOH, - SO3H, - COOR, - OH.
(a)
(d) Arabinose is an aldopentose HOCH2(CHOH)3-CHO
(d)
+2
O.S of Mn changes from +7 to +2 hence
reduction occurs and Cl2 is formed.
85.
]-Butene
2KMnO4+l6HCl ➔
2 MnCh + 2KC1 + 8H 2 O + 5Cl 2
(a) CH3---CH2---CH2---CH2---Cl + KOH (Ale)
1-Chlorobutane
76.
+7
84.
(d)
-6~
6
__
3c
_12_, h_v
(b) Cu 2 + [Ar]3d 9 ;Ti4+ [Ar]3d 0 ;
heat
2
Co + [ Ar ]3d
7
;Fe2+ [Ar
]3d
6
CCI,I
aq. NaOH
~
1,3,4 are coloured ions.
Frenkel defect is due to dislocation of ion
from its usual lattice site to interstitial
position.
77.
(c)
78.
79.
(a)
(b) Red P does not react with NaOH to give
PH3 •
80.
81.
(b)
(b) The colour exhibited by transition metal ions
is due to the presence ofunpaired electrons
in d-orbitals which permits the d - d
excitation of electrons.
86.
(a)
87.
(a)
88.
(c)
89.
(d)
90.
(a)
In TiFJ--Ti is in + 4 O.S.; 3d0 -colourless
In CoFJ--Coisin + 3 O.S; 3d 6-coloured
In ~Cl2-Cu isin +1 O.S.; 3d10-colourless
In Nied- -Ni is in+ 2 O.S; 3d 8 -coloured
82.
(c)
lf8iO = x mole
Mass ofx mole of8iO = 18x g
Then urea= x mole
0
II
Mass ofx mole ofNH 2 - C- NH 2 = 60x g
Total mass ofthe solution = l 8x + 60x = 78x g
60x
83.
Mass% ofurea= - x 100 = 76.92%
78x
(a) Surface tension of lyophilic sols is lower
than water (dispersion medium).
[Co(NH3) 5CO 3]ClO 4 . Six monodentate
ligands are attached to Co hence C. N. of
Co = 6;
O.N.=x+5 x (0)+ 1 x (-2) + 1 x (-1)=0 :.
x = + 3; electronic configuration ofCo3+[Ar]
3d64s0 hence number of d electrons is 6.
All d electrons are paired due to strong
ligand hence unpaired electron is zero.
Excess ofHCI is used to convert free aniline
to aniline hydrochloride otherwise free
aniline would undergo coupling reaction
with benzenediazonium chloride.
Cuprite: Cup; Chalcocite: ~S; Chalcop)fite
: CuFeS2 ; Malachite: Cu(OH)2.CuCO3.
Solid '-i:::"=~Liquid
It is an endothermic process. So when
temperature is raised, more liquid is formed.
Hence adding heat will shift the equilbrium
in the forward direction.
III is not true because in some reactions,
there is no elimination of any molecule.
Besides, monofuntional monomers fail to
complete the reaction. At each step of
reaction, two functional groups, one ofeach
kind, are lost.
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MOCKTEST-2
91.
92.
105
(b) Tollen's reagent is ammonical AgNO 3 •
Aldehydes form silver mirror with it and
ketones do not show any change. So
Tollen 's reagent is used to distinguish
between aldehydes and ketones.
(b)
95.
96.
97.
98.
(b) Neptunium (Np) and plutonium (Pu) show
highest oxidation state of+ 7.
(d) Reduction occurs at cathode.
(c)
(b) Proline contains imino (secondary amino),
'
/ NH group.
99.
~
y I
HNo, ,
H 2SO 4
~
VI
(a)
zn1Hc1
(acidicreduction)
(W)
Phenol has activating (electron releasing)
-OH group and bromine water supplies Br+
ion easily, hence under such conditions
reaction does not stop at monobromo or
dibromo stage but a fully brominated (2,4,6,tribromophenol) compound is the final
product.
+3B,, - - - > B,* B,
(X)
(Y)
(Z)
Br
93.
94.
Alum coagulates mud particles and helps
in purifying water.
(d) Before removing face centered atoms:
The number of'A' atoms
2, 4, 6-Tribromophenol
(c)
[There are 8 'A' atoms at the corners and 6
'A' atoms at the face centers]
The number of'B' atoms
100. (b)
RNA has D (-)-Ribose and the DNA has
2-Deoxy D (-)-ribose as the carbohydrate
unit.
H O t ~ OOH
H
H
4
l
H
3
2
H
OH OH
Ribose
= (12x¾) + (l x 1)=4
5
[There are 12 B atoms at the edges and 1 'B'
atom at the centre ofthe unit cell]
After removing two face centered 'A' atoms
along one of the axes.
The number of'A' atoms
H O C ~ OOH
4
l
H
H
H
3
2
H
OH H
2-Deoxy ribose
[There are now only 4 atoms]
From the structures it is clear that 2nd carbon
in DNA does not have OH group.
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106
SECTION-8
where L = length oftangent and r= radius ofcircle.
MATHEMATICS
1.
2.
(d) Heren(M)=55, n(P)=67,n(MuP)=lOO
since n (M u P) = n (M) + n (P) - n (M n P)
100= 55 +67-n (M n P)
n(MnP) = 122-100 = 22
: . n(Phy.,icsrnly)=n(P)-n(M n P)=67-22=45
(c)
L = .js; = 15andr = .J1 + 4+20 = 5
7.
(2, 5), (3, 2),
(3, 4), (4, 1),(4, 3), (5,2), (5,6),(6, 1), (6, 5),}
Given functions are : f(x) = x and g (x) = lxl
Probb
a 1·1·1ty = -15 = -5
36 12
:. (f+g)(x)=f(x) + g(x)=x + lxl
According to definition of modulus function,
X + X,
(f+ g)(x)= {
X -X,
X~ 0
X< 0
=
{ 2X,
X~ 0
0,
X< 0
3.
(d) In option ( d), a t A .·. It is not a relation.
4.
(b)
2
2
Hence the required area= 75 sq. units.
(a) Event = {(l, 1), (1,2),(1 , 4),(1, 6), (2, 1),(2, 3),
8.
Consider Izro l=I z II ro l=I z II ro l=I zro I= 1
(c)
Consider
Arg(zro) = arg(z) + arg(ro) = -arg(z) + argro
2
sin A+ sin B + sin C
TC
=-
= 1- cos 2 A+ 1- cos 2 B + sin 2 C
= 2 -cos 2 A - cos(B + C) cos(B -C)
2
:. zro=-1
9.
= 2-cosA[cosA-cos(B-C)]
1
1
1
1
1
= -+ - + -+ - + 1!9! 3!7! 5!5! 3!7! 9!1!
= 2-cosA[-cos(B + C)-cos(B-C)]
= 2 + cosA.2cosBcosC
.·. sin2 A + sin2 B + sin2C-2cos A cos B cos C = 2
5.
(c)
Given mcr-J, mer, mcr+I areinA.P.
= __!__(210-1)-t._ _!'._
2mcr =m Cr-I +m Cr+I
10!
10.
10!
b!
(given)
⇒ a = 9, b = 10
(c) Put log 1o.x = y, the given expression becomes
(x+xY )5 .
⇒ m -m(4r+1)+4r -2 = 0.
2
6.
2
(a) Area PQCR = 2Li PQC= 2 x
T3 = 5 C 2 .x3 (xY )2 =10x3+2Y =10 6 (given)
1
2Lxr
⇒
(3+2y) log 10 x=51og 10 10 = 5
⇒
(3+2y )y = 5
⇒
5
y =l, - -
2
⇒ logt0x=l
5
or log 10 x=--
2
:. x=l0or x =(l0t512
11.
(b)
Let the coordinates of point P be (x, y , z).
Here, PA 2 = (x-3)2 + (y-4) 2 + (z-5)2
PB2 = (x + 1)2 + (y-3)2 + (z + 7) 2
WWW.JEEBOOKS.INI
MOCKTEST-2
By the given condition PA 2 + PB2 = 2K2
We have
(x-3) 2 + (y-4) 2 + (z-5)2 + (x+ 1)2
107
-1(- 2) =tan- i((2n+l)-(2n-l))
=tan
+ (y-3)2 + (z+ 7) 2 = 2K2
= 2K2 -109
4n 2
= tan- • (2n + 1)-tan- 1 (2n-1)
i.e. 2x2 +2y2+2z2 -4x-14y+4z
12.
"'
Sn = 1)tan-1(2n+l) -tan-1 (2n-1)}
Let y = lim(cosec x) 1110gx
(c)
l + (2n + 1)(2n - 1)
x ➔O
n=l
Taking log on both sides, we get
7t:
7t:
7t:
= tan- 1 oo- tan- 1 I =-- -=2 4 4
Iogy= lim log cosec x [ -oo tiorm ]
x➔ O
logx
oo
.
-cotx
x ➔ O 1/ X
= I1 m - -
(By L' Hopital rule)
= -lim-xx ➔ O tanx
⇒
log y= -1
⇒ y =e
I
-I
=-
e
Continuing in this way, we get
I
Hence, required limit = e
13.
(c) WeknowthatpBqistrue ifpandqbothare
true or false.
sop B ~ q is true when ifp and ~q is true.
In factA2" =
i.e.,p is true and q is false.
or p and ~q is false, i.e. p is false and q is true.
14.
17.
C~Jv
n EN
(b) We have determinant
(b) Let
y = 5x(x-4 ) ⇒ x(x -4) = log 5 y
a
b
b
C
ax+b
X
t. =
bx+c =0
ax+b bx+ c
0
4±.j16+41og 5 y
⇒ x = - - - -=(2±.J4+log 5 y)
2
But x:=::4, so x = (2+.J4+log 5 y)
..
15.
(c)
Ifx = I then t, =
C (x) = 2 + .J4+ log5 x
LetS00 =cor 12+cor 1 8 + cor 1 18 +
t. =
-1
1
:. T0 = cor 1 2n2 =tan - 2
2n
b
a+b
b
C
b+c =0
a+b b+c
1
cor 1 32+ ....
a
[C3
a
b
b
C
0
0
0
=0
a+b b+c -(c+a +2b)
➔
C3 - (C1 +C2 )]
lWWW.JEEBOOKS.INI
TargetMHT-CET
108
⇒ (a+c+2b) (ac-b 2 )=0
[byexpanding]
21.
⇒ b 2 =ac anda + c = -2b
a, b, care in GP.
18.
(d) Let y= Iog x
⇒ Yt
22.
1
(b) We have, f(x) = - - .
1-x
As at x = 1, f(x) is not defined, x = 1 is a point of
discontinuity of f(x).
1
-1
X
X
2
=- , Y2 =2, Y3 =3, ...., Yn =
(c) Let
(-lt-1(n-l)!
n
X
=
AB
X
i +3}+7k
and
AD
21+ 3} -si:
= (i +3}+7k) +(2i+3} - 5k)
AC = AB + AD
j 1 )
x- 1
1
lfx;tl, f[f(x)]=t\ 1-x = 1-1 / (1 - x) = -x-
= 3i +6}+2k
:.x = 0, 1 arepointsofdiscontinuityoff[f(x)].
Ifx ;t 0, x;tl
x -1)
fl:f { f(x)}] = f ( -x- =
1
(x -1) = x .
1- - x
19.
(a) y=ax2 &x = ay2
Since
p is a unit
vector parallel to
Points of intersection are O (0, 0) & A( -; ,-;)
~x
AC therefore
2
1
•
•
•
= -(3i + 6J + 2k)
7
0
:. Area=
1t(J¥-ax }x
I
I
=-2.._ __l_
3a2 3a2 = 3a 2 = 1 ⇒ a = ✓
3
20.
(a)
=
f
dx
cosx-sinx
lf
sec(
=f
x - b = L = z - d. x - b' = L= z - d '
a
c ' a'
c' ·
1
1
23.
(a)
24.
For perpendicularity oflines aa'+ 1+ cc'= 0
(d) We have equation of tangent to any curve
2
f(x)at(x i, y 1)is (y-y1)= dyl
(x - x1)
dx (x1,Y1 )
dx
r;;
v2cos
(
x+¾) dx
= llogltan(¾+f + i)l +c
x+-n)4
Given curve is y = e-l xl
Point ofintersection is ( 1,
S o, y = e
3
= llog ltan(f+ :)l+c
(
dy)
dx x = l
-x
⇒
¼) at x = 1, Ix I= x
dy= - e-X
dx
= - e-1
WWW.JEEBOOKS.INI
MOCKTEST-2
109
Therefore, equation of tangent is
25.
27.
(d) Let E : ' face I comes up' and F: 'face 1 or 2
comes up'
1 -1
y-- = -(x-l) ⇒ x + ey = 2
e
e
(d) We have, minimized Z = 4x + 6y
Subject to 3x + 2y:c:; 12, x + y~4, x, y~0
Let £1: 3x + 2y= 12
£2 : X +y=4
£3 : x = 0 and £4 : y = 0
Shaded portion ABC is the feasible region, where
A(4, 0), C(0, 4), B(0, 6).
(·: E c F)
EnF = E
⇒
:. P(E) = 0.10 and P(F) = P(l) + P(2) = 0.10 + 0.32
= 0.42
Hence, required probability
y
I
f
= 0d.x+
fz
0
26.
NowmaximizeZ = 4x + 6y
ZatA(4, 0)=4(4)+ 6(0) = 16
ZatB (0, 6)= 4(0) + 6(6) = 36
Z at C(0, 4) =4(0) + 6(4) = 24
Thus, Z is maximized at B(0, 6) and its maximum
value is 36.
(c) The differential equation is
dy
dx
_x_=
x
✓
2
✓
3
2
I
✓
2
✓3
f ld.x + f 2dx+ f 3d.x
= [x][2 +[2x]Jz +[3x]F3
=✓
2-1+2✓3-2✓
2 +6-3✓
3 = 5- ✓
3- ✓
2
29.
5x
(x+2)(x-3)
(a)
2
· 2
Wehave, 8lsm x +8lcos x=30
Now check by options, put x =
/6
· 2
then (81)5 m
1t
+ (8It
05 2
1< /
6
~
6
= 30
X
Solution is
Y(;) J(;) (x +~~x _3)dx m(: =~ )+c
=
x
=
It passes through (4, 0), so C = - In 6
2
:. y=xln{ (x+ )}
6(x-3)
Putting (5, a), we get a= 5
30.
(a) If a, ar, ar2, ar3 ......... are in G.P., then
sumofinfiniteGP.= a + ar + ..... +oo = -a-
1-r
where 'a' is the first term and 'r' is the common
ratio ofGP.
Given x = I+ a+ a 2 + .....oo
ln(
7
)
12
This is a GP, with common ratio 'a'.
WWW.JEEBOOKS.INI
TargetMHT-CET
110
1
x -1
34.
⇒ x= -- ⇒ x - ax=l ⇒ a= -X
1-a
(a)
z = 1 + 2i ⇒I z I= .J1 + 4 = .Js
7 z
7 -l-2i
f(z)=~ =
1-z
l-(1 +2i) 2
2
Again, y = 1 + b + b + ......oo This is also a G.P.,
with common ratio 'b'.
6 - 2i
1
y- 1
1- b
y
6- 2i
3- i
-----= -- = -l-(1-4 +4i) 4 -4i
2-2i
⇒ y= -- ⇒ b= --
⇒ lf(z) I=J ; : ;iJ = 11;:;]1
Now, consider 1+ab+ a 2b 2 + .....oo
which is again a GP with common ratio 'ab'.
✓
9+l
= ✓4+4 =
1
Sum= - - = - - - - 1- ab
_ x -1 _y -1
1
X
y
35.
~
~ - xy+x+ y- 1
31.
3
tan 2: = 1 -m2
4
1+3m2
(d)
xy
x+ y - 1
✓
5
2
2
(d) We have
1).!.. ⇒ sx+2 > 5_3. ⇒ x+2>--2
5x+2 > 25
(
X
X
X
I ⇒ l + 3m2 =3 -m2
[·: base 5 > 1]
⇒
or 1+ 3flli
= -(3-flli)-2=-4m2 or m 2 = - 2
x 2 +2x+2
2
x+2+-> O ⇒ ---- >
X
'2
⇒
2
The ellipse can be written as, ~ + L = 1
25 16
(c)
36.
e2 = 1-16/25=9/25 ⇒ e=3/5
Foci ofthe ellipse are(± ae, 0) = (± 3, 0), i.e ., F 1
andF2
:. We h ave PF1 + PF2 = 2a = 10 for every point
Pon the ellipse.
33.
(a) Consider eqn i1x2 + lxl + 9 = 0
Product of real roots
9
= 2 > 0, Vt ER
t
x > O or x
(0, oo)
(b) First prize can be given in 5 ways. Then second
E
prize can be given in 4 ways and the third prize in 3
ways (Since a competitior cannot get two prizes) and
hence the no. ofways. = 5 x 4 x3 = 60 ways
Herea2 = 25, b2 = 16, butb2 =a2 (1 - e2) ⇒ 16/25
= 1-e2
⇒
0
X
[·:x 2 +2x+2>0V xeR]
2
32.
1
O⇒->
X
1
m = -2 2
lzl
37.
(d)
(a+b+c) 12 = [(a+b) + c] 12
= 12Co(a + b) 12 +
12C1 (a+ b)1 1c+ ... + 12C12c12
The RH.S. contains, 13 + 12 + 11 + .... + 1 terms
= 13(13+1) = 9lterms
2
Also no. of term in the expansion of(a + b + c)" is
given by n + 2c 2•
Thus fior n = 12 '· n + 2c 2 =
14C
2
14 x 13
= -2- = 91 .
Product of real roots is always positive.
WWW.JEEBOOKS.INI
111
MOCKTESf-2
42.
38.
(c) y= ( 1+~)(1+~)(1+~}-{1+~)
:
= (-
;2
)(1+~)(1 +~}-.(1 +;)
+(1+±)(-
39.
Now, IA I = [1-a(-a2)] = 1 +a3 ,t0
So, system has only trivial solution.
Now, IAI = 0 onlywhena= - 1
So, system of equations has infinitely many
solutions
which is not possible because it is given that
system has a unique solution.
Hence set of all real values of'a' is R- {- 1}.
= (-1)(-1)(-2)(-3) ....(1-n)
43.
(b)
=
5000
Correct mean = - - = 50
100
40.
y=
(a - x)3/ 2 +(x - b)3 / 2
.Ja-x+.Jx-b
( ~ + ~ X a - x - ~ ~ +x - b)
(b) f(x)=sinx + cosx, g(x) = x 2 - 1
⇒ g(((x))= (sinx + cosx)2 - I = sin 2x
.Ja - x+.Jx- b
=a-b-.Ja- x .Jx - b
=
or dy
dx
Clearly g (((x)) is invertible in -~ ~ 2x ~ ~
2
~i
a O I
:2)(1 +~}-.(1+;)
= (-1 )°{1)(2)(3)....(n - 1) = (-l?(n-1) !
(c) Surn ofl 00 items = 49 x 100 = 4900
Sum of items added = 60 + 70 + 80 = 210
Sum of items replaced = 40 + 20 + 50 = 110
Newsum= 4900+210-110 = 5000
~
A = (~
+ ... +(1+±)(1+~)(1+~}-{- ;z)
·: ~ x= - I
(b) Given system of equations is homogeneous
which is
x+ay = 0; y+az = 0;
z+ax=0
It can be written in matrix form as
1
1
.Jx - b -
2.Ja - x
.Ja-x
2.Jx - b
2
2x - a - b
7t
7t
4
4
- 2.Ja-x.Jx - b
⇒ -- ~X~ -
44 .
(d) Let I
=
(l+x)ex dx
f cot(xex )
Put x~ = t ⇒ (x~ + ~) dx = dt ⇒ ex (x + 1)
dx = dt
25 - 24+0
I
40 - 40 + 0
O+O+Ol
= -15+15+0 - 24+25+0 0+0+0
[
- 8+ 10 - 2 0+0+ 1
- 5+6 -1
dt
:. I= cot(t)
45.
(a)
= l~lsect
l+ C=loglsec{u!)l+ C
(i'i x b)2+(i'i·b) 2 =676
Cl a 1-1EIsin en)2 + Cl aI ·IEI cos 0)2 = 676
⇒ a 2 b2 sin 2 0+a 2 b 2 cos 2 0=676 [(n)2 = l]
Hence, the matrix A is involutory.
⇒
a 2b 2 (sin 2 0 + cos 2 0)=676
IWWW.JEEBOOKS.INI
TargetMHT-CET
112
⇒
a2
= _67_6 = 676
b2
48.
4
Let t = sin 2 x; t
[0, l] ; f(x) = g(t) =te- 21
E
g '(t) =(l-2t)e- 21 ;
1- 1 26
1a- 1= ~676
4 ⇒ a = 2 ⇒ 1a I= 13
46.
(d)
g'(t)= O at t = 1/ 2;
g(_!_) =_!_
2e
2
(a) The area enclosed between the curves
y2=xand y= Jxl
From the figure, area lies between y2 = x and y = x
g(0)=0andg(l)=e- 2
:.
gmax. = 1/ 2 e andgmin. =0
:. max.f(x) -min .f(x) = _!__
2e
49.
dy
(a)
dx
ex (sin 2 x + sin 2x)
= -'-------
y(2logy+l)
f(2ylogy+ y)dy = f ex(sin x+sin2x)dx
⇒
2
On integrating by parts, we gety2 (logy)= eX sin 2
x+c.
Y'
7t
50.
:. Required area= J~(y 2 - y 1)dx
(d)
7t
I=Jxf(sinx)dx=J(rc-x)f(sinx)dx
0
0
7t
7t
J
= re f(sin x)dx - I
⇒
J
21 = re f(sin x)dx
0
.·. Required area =
2[x 3/2]1 1[x 2]1
-
3
O
2
0
I=
2
1
--- = 3 2 6
47.
0
it
it / 2
0
0
f Jf(sin x)dx = re Jf(sinx)dx
it/ 2
(b) We have a result that if a coin is tossed
(m+n)times (m>n). Theprobabilityofatleastm
= re
Jf(cosx)dx
0
n+2
consecutive heads is
2
m+ I . Herem= 4, n
=3
3+2
5
:. Required prob = 24+ 1 =
32
WWW.JEEBOOKS.INI
(Mock Test-3)
Answer KEYS
1
2
3
4
5
51
52
53
54
55
1
2
3
4
5
(c)
(a)
(d)
(b)
(d)
(c)
(b)
(a)
(d)
(d)
(c)
(a)
(b)
(d)
(d)
6
7
8
(d)
(a)
12
(d)
(c)
(b)
13
(b)
9
14
15
(c)
10
(a)
(d)
56
57
58
59
60
(c)
(c)
(c)
(a)
(b)
6
7
8
(a)
(c)
9
10
(b)
(c)
(b)
(d)
(a)
(a)
(a)
(b)
16
17
18
19
20
61
62
63
64
65
(b)
(a)
(b)
(b)
(c)
66
67
68
69
70
(a)
(d)
(d)
(a)
(b)
11
(a)
(c)
16
17
18
19
20
(a)
(a)
(d)
(c)
(c)
11
12
13
14
15
(b)
(a)
(a)
(b)
SECTION-A
PHYSICS
21 (a) 26 (a)
22 (a) 27 (b)
23 (c) 28 (d)
24 (c) 29 (a)
25 (a) 30 (a)
CHEMISTRY
71 (d) 76 (c)
72 (b) 77 (a)
73 (b) 78 (b)
74 (d) 79 (c)
75 (b) 80 (c)
SECTION-B
MATIIEMATICS
21 (c) 26 (b)
22 (b) 27 (d)
23 (a) 28 (d)
24 (d) 29 (a)
25 (c) 30 (b)
31
32
33
34
35
(b)
(d)
(c)
(c)
(b)
36
37
38
39
40
81
82
83
84
85
(d)
(b)
(b)
(b)
(d)
86
87
88
89
90
31
32
33
34
35
(a)
(d)
(a)
(a)
(a)
36
37
38
39
40
(a)
(c)
(d)
(d)
(a)
41
42
43
44
45
(a)
(a)
(c)
(b)
(c)
91
92
93
94
95
(a) 96
(a) 97
(a) 98
(a) 99
(c) 100
41
42
43
44
45
(b)
(d)
(d)
(d)
(a)
(b)
(b)
(b)
(a)
(a)
(c)
(a)
(b)
(a)
(b)
46
47
48
49
50
46
47
48
49
50
(b)
(b)
(c)
(d)
(c)
(c)
(b)
(a)
(c)
(c)
(a)
(b)
(d)
(a)
(c)
SECTION-A
⇒
PHYSICS
Acceleration should be like, a= - kx.
1.
(c)
2.
(a) r=30mandµ=0.4.
Vmax
= .Jµrg = ✓0.4 X 30 X 9.8 = 10.84rn/s
3.
(d)
4.
2
(b) I= I 0 cos e
Intensity ofuntransmitted light
Io
Io
- Io--=-
2
5.
(d)
2
By Gauss law, we know that
~ = _9__ Here, Net electric flux, ~ = ~2 co
I
Intensity ofpolarized light = ;
=9
6.
X
106 - 6 X 106 = -
q
co
⇒q=3
X
~,
106 X C
.
0
(d)
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TargetMHT-CET
114
7.
(a) For conversion of a Galvanometer to a
voltmeter, we connect a large resistance R
18.
(a)
in series with the Galvanometer.
8.
g ' =g - cilRcos 2 'A. ⇒ O= g - oiRcos 2 60°
0= g _
(b) As momentum is conserved, therefore,
m
A1 v 2 I
- 1= = = mz
A2
v1
~=
·· R2
1/3
A1
=
( A )
2
\/Ji
4
400 s
= 2 _Sx l0-3 rad
5
19.
_
cu2 R ⇒ m= 2 /g = _I_ rad
(.!.5
)1/ 3
=
s
(a) Path difference, S 1B =Ill= n'A..
As P is the position of 11 th fringe from Q,
I : 5113
so from O it will be 10.
:.1:u=n'A.=l0'A.
9.
(a) In stream line flow velocity of flow at any
10.
(d)
= 10 x 6000 x 10-10 = 6 x lo-6 m
point in the liquid does not vary with time.
11.
(d)
A
A
A+B=C
IA x Bl= ✓3(A.B)
20.
(b)
B
B
⇒ ABsine = ✓3ABcose
⇒ tan e = ✓3 ⇒ e = 60°
12.
(c)
13.
(b)
14.
(c)
10-4 = _i_ = 0.43
10 + 4 14
Kirchhoff's junction rule states that the
algebraic sum of all currents into and out of
any branch point is zero: LI = 0. By
convention, the sign of current entering a
21.
22.
23.
junction is positive and current leaving a
(a)
(a)
A
B
A B A+B C
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0 =AND gate
0
1
W = F s cos 90° = zero
1t
(c) Given m= 2rads-1 r = 2m t = -s
'
'
'
2
Angular displacement, 0
junction is negative.
15.
16.
(b)
(d)
1t
4A+ 5 A-6A + IAB = 0, therefore IAB=- 3A.
The wire between points A and B carries a
= mt = 2 x - = re rad
2
current of3A away from the junction.
Linear velocity, v= r x m= 2 x 2 = 4m s-1
➔
r
M
➔
=
➔
➔
m 1 r 1 +m2 r 2
m 1 +m 2
=
➔
m(x + y)
2m
➔
.-. change in velocity, t:.v
➔
x+ y
2
4rrx l0-7 x300x 400 x !OO x !0-4
0.2
= 2 x 4 x sin (
24.
. e
= 2v sm 2
f)
= 8 ms-1
(c) Initial magnetic flux linked with the coil is
e
= BA cos = 0.1 x 200 x 10-4 x coso0
= 2 x 10-3 Wb
<l>i
17.
(a)
Final magnetic flux linked with the coil is<!>r= 0
WWW.JEEBOOKS.INI
MOCKTEST-3
By
115
Faraday's
28.
(d)
Since radio frequencywaves can travel long
distances because these waves are of wave
length ofthe order of 100 m and their energy
content is quite large therefore e.m. wave of
audible frequency are superimposed with
radio frequency waves.
29.
(a)
1D
law,
2
~ 2 He
4
Energy released = 28-2 x 2.2 = 23.6 MeV
(Binding energy is energy released on
formation ofNucleus)
Induced current
I=~= 0.2V = 0.IA
R
25.
20
30.
(a) Given that w µg =
Induced charge q = It = 0.1 x 1 = 0.1 C
(a) For a given pressure, volume will be more if
temperature is more (Charle's law)
5
4
and a µ w =
4
3
5 4 5
.'. aµ g =w µ g xaµw =4 x 3=3
31.
32.
(b) Gravitational force will be due to M 1 only.
(d) E=E4 -E3
13 6
13 6
= - 42· -(- 32· ) = -0.85 + I .51
=0.66eV
From the graph it is clear that V2 > V 1 ⇒ T 1
> T2
26.
(a)
33.
(c)
a = F-µR = 100-0.5x(10x10)
10
m
y2 = VJ+(VL-Vc )2
34.
(c)
. d change in momentum
F orce reqmre =
time taken
35.
(b)
(50 X JO-)
36.
(a)
X
30) X 400-(5 X 0)
27.
(b) In case ofinternal resistance measurement
by potentiometer,
V1 =~
V2 .e 2
{ER1 /(R 1 +r)} _ R 1 (R2 +r)
{ER2 l(R2 +r)} R2 (R1 +r)
R 2 =100
ms-2
SinceVL=Vc henceV = VR=200V
v = ffi.Ja 2 - y 2
= - - - - - - - - - 10 N
60
5
At
x=0,V=ffi✓a2 -o2
v'
✓
3
V
2
=ffia.
✓
3
or v' = -ffia
2
:.
2
5(10+r)
3 = 10 ( 5 +r) or20 + 4r=30 + 3rorr
=100
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116
46.
37.
(c)
38.
(d)
39.
(d) Beyond Curie temperature, ferromagnetic
(b) Let T be the tension in the ring, then
T.2nr
Y=---A.2n(R-r)
Tr
A(R-r)
substances behaves like a paramagnetic
:. T = Y A(R-r)
r
substance.
40.
(a) Initially att = 0
Rate of cooling (R) ex: Fall in temperature of
47.
(b) In the first process
body (0-00)
⇒
41.
Wis+ ve as L'1Vis
positive, in the
second process W
is - ve as t-. V is ve and area under
the curve of
second process is
more
Net Work < 0 and alsoP3 > P 1•
0 -00 100-40 3
- = -1 - = ---=R2 0 2 -00
80-40 2
R1
(a) For strong reflection, the least optical path
difference introduced by the film should by
)../2. The optical path difference between the
waves reflected from the two surfaces of
the film is 2 µd.
Thus, for strong reflection, 2µd = ).J2.
48.
589
'"A.
d = 4µ = 4 x l.25 = 118nm.
42.
(a) Weight ofthe liquid column= T cos0 x 2m.
For water 0= 0°. Here weight ofliquid column
W = 7 .5 x 1o-4N and T = 6 x 10- 2N/m. Then
circumference, 2m =W IT= 1.25 x 10-2m
43.
(c) Time period,
~
[ As
LC , T2 = 2nff,
7i = 2n✓
(b)
t-.f
f
=~
C
=
(Beats)/ 2
⇒
f
v
=-C
0
2fv = 4.
C
(~-1)(-1
__!_)
3
-20
00
⇒ Beats=
50.
45.
f B.dT= µ L I]
= 2n.J2LC .
Clearly t2 < t 1 < t3.
44.
Apply
Ampere's
circular law to the
coaxial circular loops
L 1 and L 2 . The
magnetic field is B 1 at
all points on L 1 and B2
at all points ofL2. LI -:tc0 for L 1 and Ofor L2.
Hence, B 1 -:tc- 0 but B2 = 0
(c)
:.f=-60cm.
(c) Since, stopping potential is independent of
distance hence new stopping potential will
remain unchanged i.e., new stopping
potential = V0 .
(b)
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MOCKTEST-3
117
CHEMISTRY
51.
52.
(c)
The absorption of visible light and hence
coloured nature of the transition metal
cation is due to the promotion of one or
more unpaired - d - electron from a lower to
higher level withing same d-subshell. Hence
higher will be the number of unpaired
electron higher will be the absorpion in
visible light.
The electronic configuration of the given
elements is
Sc3+ (18) = ls2 2s2 2p6 3s2 3p6 3rfJ 4s0 - no
unpaired e-.
Ti4+ ( 18) = ls2 2s2 2p6 3s2 3p6 3rfJ 4s0 - no
unpaired e-.
y 3+ (20) = ls2 2s2 2p6 3s2 3p6 3d2 4s0 - Two
unpaired e-.
Zn2+ (28) = ls2 2s2 2p6 3s2 3p6 3d10 4s0 no unpaired e-.
57.
(c) In cyclic metaphosporic acid number of
P--0-P bonds is three.
58.
(c) Nernst equation Ecen =
2+J2 [z 2+]
n
increasing
E ocell _ RT ln[Fe
nF [Fe3+] 2
59.
[Fe2+] will decrease the Eceu·
(a) CnRzn02 is general formula for carboxylic
acids.
60.
(b) A: B: C =
61.
(b) Those compound which have asymmetric
Carbon or chiral carbon atom (*) show
optical isomerism,
1
8
x 8:
1
2
x 2:
1
2x 4
=
1: 1:2
H
(b) Calcination decomposes carbonates into
their respective oxides and used for removal
ofvolatile impurities like Hp and CO2•
I.
I
CH3-C-CHz-CH 2-CH3
OH
2-Pentanol
Bauxite
CaCO 3 ~
Limestone
53.
(a)
62.
Alumina
CaO
a Lewis acid (like A1Cl3, FeBr3 etc.) is used
+ CO 2
Calcium oxide
rate oc [Preactant ]
(a) Friedel Craft reactions are examples of
aromatic electrophilic substitution. In this,
as catalyst.
0
C6HsCH 3 + HCl
i.e., rate= k
54.
So, the order of reaction will be zero.
(d) All are chiral.
C6Hs
55.
56.
(d)
I
1-Phenylethanol ( CH 3CHOH) is a
2° alcohol and can be prepared by the
reaction of benzaldehyde with Grignard
reagent C~Mgl.
(c) Mnp7 is acidic, Vz0 5 is amphoteric acid
and CrO is basic.
63.
(b)
PtC14 .5NH3: [Pt(NH3)sCl]Cl3
➔
[Pt(NH 3)sC1] 3+ +3Cl- (4 ions)
PtC14 .4NH3: [Pt(NH3)4Cl2]Cl2 ➔
[Pt(NH 3)4Cl2 ]2+ + 2Cl-(3 ions)
PtC14 .3NH3: [Pt(NH3hCl3]Cl ➔
[Pt(NH3)}Cl3r + c1-
(2 ions)
PtCl 4 .2NH3 : [Pt(NH3)iCl 4 ]
Nonionic
(no ion)
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118
64.
(b)
65.
(c)
c=>=
+ 2Hp
CaC2
NCH2CH3
Calcium carbide
~
HC =CH+ Ca (OH)2
Acetylene
66.
(a) Since oxidation potential of Zn is highest
67.
(d)
68.
(d) R-NIIi + CHC1 3
0-- NHCH2CH3
79.
(c) The ions present in the ionisation sphere
are precipitated.
hence strongest reducing agent.
ale. KOH
EB
(Where, R = Alkyl or Ary! Group)
69.
(a)
70.
(b)
71.
(d)
72.
(b)
73.
(b)
Enthalpy change during adsorption is
negative. As in adsorption, there is
decrease in residual forces of the surface
which result in decrease in surface energy
in form ofheat.
When E 8 = 0, rate constant is independent
oftemperature.
Amongst all tropolone is a non-benzenoid
aromatic compound.
The key step in the manufacture ofHzSO4
is catalystic oxidation ofSO 2 with 0 2 to give
SO3 in presence ofV2O 5 .
Mn 2+ (d 5) is more stable than Mn3+ (d 4),
thus E~n3+ / Mn 2+ = +ve
74.
(d)
Hence [CrCli(H 2O)4 ]Cl.2H 2O contains
1/3 Cl in ionisation sphere to be precipitated
by AgNO3 as AgCI.
e
----► R - N=C
80.
(c)
N2 +O2~2NO; ~n=O
81.
(d)
As the size increases, the basic nature of
oxides changes to acidic nature i.e., acidic
nature increases.
SO 2 > P 2O 3 > SiO 2 > A1 2O 3
Acidic
a-x
=
2.303 I
og
1
(b)
(b) Amorphous solids are isotropic, because
83.
(b)
these substances show same properties in
all directions.
Cloud and fog are colloidal system having
dispersed phase liquid and dispersion
medium gas
84.
(b)
La
(c)
77.
(a)
24 1 24
Lu 3+ : 68 e-= [Xe] 4J1 4
Sc3 + : 18 e-= [Ar]
catalyst
CO2+ 2H2
85.
(d) The
86.
(c)
q=+ l0kJ, w=-4kJ
~E = q+w
= 10-4 = 6kJ
So, energy increases by 6 kJ
78.
(b)
:54e-=[Xe]
1
water gas
76.
3+
Ti 3+ : 19 c= [Ar] 3 d (Colour)
. 1
= 2.303 iog 8 rmn-
~O + Hf+ Hi)
Amphoteric
82.
8
75.
Weak
acidic
SO 2 and P 2 0 3 are acidic as their
corresponding acids HzSO3 and ~PO3 are
strong acids.
k = 2.303 log-a-
t
H 2 / Pt
reduction
c=>,=o+ H 2NCH2CH3 ➔
two components shou ld be
(C~)3CONa + (CH3) 3CBr. However, tertalkyl halides tend to undergo elimination
reaction rather than substitution leading to
the formation of an alkene, Me2C = CHz
From molarity equation
M 1V 1 +M2V 2 = M/V 1 +V2)
1X 2.5 + 0.5 X 3 = ~ X 5.5
4
M3 = - =0.73M
5.5
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MOCKTEST-3
87.
119
(b) Bromide in the mother liquor is oxidised to
Br2 by Cl 2 which is a stronger oxidising
agent. 2Br- +Cl 2 ➔ Br2 +2Cl-
(b) A is more reactive than B, because it has
high oxidation potential. Therefore, A will
replaceB.
89. (b) Adenosine is a nucleoside which contains
a fine carbon ribose sugar and a base
(adenine).
90. (a) MnO
91. (a) Carboxylic acids are acidic in nature
because of stabilisation (i.e., dispersal of
negative charge) ofcarboxylate ion. So any
factor which can enhance the dispersal of
negative charge of the carboxylate ion will
increase the acidity and vice versa. Thus
electron-withdrawing substituents (like
halogens , -NO 2, -C 6H5 etc.) would
disperse the negative charge and hence
stabilise the carboxylate ion and thus
increase acidity of the parent acid. On the
other hand, electron-releasing substituents
would intensify the negative charge,
destabilise the carboxylate ion and thus
decrease acidity of the parent acid.
Now, since alkyl groups are electronreleasing, their presence in the molecule will
decrease the acidity. In general, greater the
length of the alkyl chain, lower shall be the
acidity of the acid. Thus formic acid
(HCOOH), having no alkyl group, is about
10 times stronger than acetic acid
(Cif:,COOH). Thus correct order of acidic
strength is
CF3COOH> CHC12COOH > HCOOH>
C6H5C8iCOOH> C~COOH
92. (a) Given structures are representing cis-trans
isomerism (geometrical) hence differ only
in configuration.
93. (a) In acidic medium Zwitter ion convert into
88.
+
NH3--CH--coo- + H+
I
+
NH-CH-COOH
3
I
R
94. (a) Micelle formation is shown by surfactants
detergents (Dodecyl trimethyl ammonium
chloride) in their aqueous solutions.
95. (c) Dissociation energy of any molecule
depends upon its bond order. Bond order
2
96.
in N 2 molecule is 3 while bond order in N
is 2.5. Further we know that more the Bond
order, more is the stability and more is the
bond dissociation energy.
(c)
No. of molecules
44
Moles of CO2 =
=I
NA
44
48
Moles ofO3 =
=1
NA
48
8
Moles of Hi = = 4
4NA
2
64
Moles ofSO2 = 64
97.
=1
NA
(b)
Natural rubber
(All cis configuration)
98.
(a)
Rate ofSNZ cc Steric crowding near reaction centre ·
99.
Narrow spectrum antibiotics are effective
against Gram-positive or Gram-negative
bacteria. Limited spectrum antibiotics are
effective against a single organism or
disease.
100. (c) At a bridge head position SNl and SN2 do
not takes place.
(c)
R
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120
SECTION-8
MATHEMATICS
1.
(c)
Given y =cos2 x+sec2 x
⇒
1
1
2
y=cos x + --2 (·: cos x = --)
cos x
secx
⇒
6.
y=ax 2 +bx + c
COS X
and 5 = 16a + 4b + c ⇒ 16a + 4b = I
⇒
1
y=(cosx---) + 2
⇒
y=(cos x -sec x }2+2
2
19
79
a=--and b=12
12
( cos x - sec x )2
= 0 or positive
2
2.
(a) A = {2,4,6}, B = {2,3,5}
3.
Number of relations from A to B = 23 x 3 = 2 9
(b) Let n(P) = Number ofteachers in Physics
n(M) = Number of teachers in Maths
n(PuM) = n(P)+n(M)-n(PnM)
19 2 79
y=--x +-x+4
12
12
7.
⇒
Let
-1+i ✓3
2
= ro then
-l- ✓3i
2
= ro
2
where ro = cube root of unity
-1+0 100 [ -1-0 ) 100
+
)
[
2
2
.
+ ar" + 1
Consider - - -
l=r + r2 ⇒ r2 + r-l=0
⇒ r=
5.
(c)
(d) Giventn = tn +l+ tn +2
⇒ ar" - 1 = ar"
. . . (5)
Substituting the values of a, band c from (2) and
( 5) in (1 ), we obtain the equation ofparabola as
20 = n(P) + 12-4 ⇒ n(P) = 12
Only Physic' s teacher = 8
4.
.. .(4)
( ·: c = 4)
Solving (3) and (4), we get
COSX
~
. .. (1)
Since it passes through the points (0, 4), (1 , 9)
and(4, 5),
4 = 0+0+c ⇒ c = 4
.. .(2)
. .. (3)
9= a+ b+ c⇒a+b= 5
( ·: c = 4)
2
1
y =cos x+--+2-2
2
As
.. y = 2 or y
(a) The equation ofparabola parallel to y-axis is
-1 ± ..,t'i"+4
\ 100
( -1+ ✓
3iI
2
=l
-1 + ✓
5 .
r=---, smcer > 0
2
Therefore r = 2 sin 18°
(d) Let the vertex C be (h, k), then the
2
J
+l
-1- ✓3 i
2
\ 100
I
J
= (OJ 00 + (0200 =co+ (02 = -1
3
(-: c.o = 1 and 1 +
centroid of
!1ABC is e-~+h, -3+3l + k) or
(
8.
ro + ro 2 = 0)
(b) The equation are 3x. 5 Y = 75
...(1)
and 3 Y• 5x = 45
...(2)
Dividing the two equations, we get
2h
It lies on 2x + 3y = 1 ⇒ ⇒
2h+3k = 9
3
(¾r-y
= :: =
-
¾⇒
X-
y=- J
•. •(3)
2+k = 1
:. Locus of Cis 2x + 3y = 9
Multiplying equations (1) and (2), we get
(15t+Y = 45 x 75 = (15) 3 ⇒ x + y = 3
. . .(4)
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9.
121
solving (3) and (4)we get x = l, y = 2
Hence, only one ordered pair that satisfying given
equations
(c) 30 marks to be alloted to 8 questions. Each
question has to be given z 2 marks
Let questions be a, b, c, d, e,f, g, h
14.
The inverse ofp ⇒ q is - p ⇒ - q
i.e., ifa number is not a prime then it is not odd.
(a) Given, a=9.
Let a student obtains x out of75. Then his marks
out of I 00 are
~da + b +c+ d+e +f+g + h=30
4x
3 •Each observation is multiplied
Let a= a 1 + 2 so, a 1 z 0
b = a2 +2 so, a 2 zO,...... ,a8 zO
4
by 3
So, a1 + a 2 + ...... + a8 } =
30
+2+2+ ...... +2
New a=i x 9=12, Variance = a 2 = 144.
3
a 1 +a2 + ...... + a 8 =30-16= 14
So, this is a problem of distributing 14 articles in
8 groups.
Number of ways= J4 +s- 1c 8_ 1 = 21 C 7
(b) No. ofterms in the expansion = o+3-IC3_ 1
:. o + 2 c2=45 ⇒ n=8
(a) Let the point R divides the line joining the
pointsP (2,4, 5)andQ(3, 5,-4) in theratiom: n.
⇒
10.
11.
m
R
P(2, 4, 5)
15.
n
⇒
3m-2n __ ⇒
0
3m-2n= 0
m+n
12.
(c)
2
n
3
.
⇒
⇒
(cosx-l)(cosx-ex)
Xo
3m=2n
17.
2
13.
(a) AsA2 = 0, N = 0 V kz2.
(A + I)5°=1 + 50A ⇒ (A + I)5° -50A=I
Thus,
a= 1, b = 0, c = 0, d = 1
abc + abd +bed+ acd = 0
(a)
sinA sin2 A
sin B sin 2 B = 0
sinC sin 2 C
⇒ (sin A-sin B)(sin B-sin C)(sin C-sin A)
= bm - - - - - - - - - - -
⇒ sin A
Xo
isnon-zero ⇒ n=3.
(b) p: A number is a prime
q: It is odd.
We havep ⇒ q
X
(fofof... ..of)(x) =f(fof)(x) =f(x)= x-1
19 times
. (-~: +x4: +....-J-x-x + ...... )
x➔O
X
(fofof)(x) = f(fof)(x) = f(x) = x-1
'---v--'
16.
l1m - - - - - - -
x➔O
X
x -1
x-1
= -1- =x.
x -x+l
x-1
x-1
Q(3, 5,- 4)
3m-2n, 5m-4n, -4m+5n)
m+n
m+n
m+n
m
X
x-1
_x__ l
x -1
Since, the point Rison yz-plane, therefore
x-coordinate will be zero.
⇒
·: f(x)= x-l :. (fof)(x) = f{f(x)} = f
X
The coordinate ofR is
(
X
(a)
18.
=0
= sin B or sin B = sin C or sin C = sin A
:. atleast two of A, B, Care equal.
Hence the triangle is isosceles or equilateral.
(d) For/(x)tobecontinuousatx=0, weshouldhave
l~o f(x)=f(0)= 12(log4)
3
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122
TargetMHT-CET
lim f(x)
oo ➔O
I I
or, -+-+k 2 = I
2 4
px2
= (log 4) 3 · 1 · p · x➔O
lim
l
x2
(
1 2
1 4
(b) Let f (x ) = sin x - kx - c where k and c
are constants
f'(x) = cos x - k :. f decreases if cos x ~ k
Thus, f (x) = sin x - kx - c decrease always
when k :::_ I.
23.
(a) Put I+ x = t 2 ⇒ dx = 2tdt
Then integral is
J
= 3p (log 4)3 · Hence p = 4.
19.
(c)
3
((ax b) x (c x d)).(a x d) = o
20.
(c)
⇒ I=f
dx
f cosx+ ✓3 sin x
dx
. ]
2[21cosx+ 2✓3 smx
}
2
t2- J
3
=[21n t -l J -6=2log
t+ I 2
e2
I_6 =21oge-2e33-
c or b must lie in the plane of a and d.
I=
3[
2 (t2 -l)t
[a c d][b ad]= o
Either
2
2
l = f 2 - 3(t -l)2tdt=2f - - -3 t
⇒ ([acd ] b -[bcd]a).(axd) = O
⇒
1
k=± 2
22.
1
- x - - x + ...
3
18
⇒
24.
(d) Construct the following table of objective
function
Corner Point
Value of F= 4x+6y
(0, 2)
4 x 0+ 6 x 2 = 12
(3, 0)
(6, 0)
4 X 3+ 6 XO= 12
4 X 6 + 6 X0 = 24
(6, 8)
(0, 5)
4 x 6 + 6 x 8=72
4 x 0 + 6 x 5 = 30
} f-minimurn
f- rmxirnurn
Since the minimum value (F) = 12 occurs at two
distinct com er points, it occurs at every points
of the segment joining these two points.
⇒
I=
½.J cosec( x+¾) dx
25.
(c)
fcosecxdx = log I(tanx / 2) I+ C
I = -1 . log tan (X
- +71:)
- +C
2
21.
(c) For (
2
12
~ ,½,k) to represent direction
= tan
_1(1-2
logex
- --) +tan -I( 3+2logex)
1+21ogex
l-3.2logex
= tan- 1 ( l) -tan- 1 (2logex) + tan- 1 (3) + tan- 1
(2 logex)
cosines, we should have
lWWW.JEEBOOKS.INI
MOCKTEST-3
= tan- 1 (1) + tan- 1 (3)
dy =0
dx
26.
123
30.
So,
11
(b) Required probability
31.
= [(1-P(A)]P(B)P(C) + P(A) [(1-P(B)]P(C)
+ P(A)P(B)[(l - P(C)]
= (1-0.4)(0.3)(02)+ (0.4)(1-0.3)(0.2)+ (0.4)
(0.3) (1-0.2)
= 0.036 + 0.056 + 0.096 = 0.188
Desired area =
f2
(a) Let the line make intercept 'a' on x-axis.
Then, it makes intercept '2a' on y-axis. Therefore,
~ + Y =1
a
2a
It passes through (1, 2), so, we have
1 2
-+-=l ora =2
a 2a
Therefore, the required equation ofthe line is given
by
X
36
11
the equation of the line is given by
36
(d) y= - 2 ,x=6,x=9
9
= 30
= -[2a+IOd]=- x 2[a+5d]=ll x 30=330
2
2
P(A' nBnC)+P(AnB' nC)+P(AnBnC')
27.
(b) Middle term =
⇒ a + 5d=30S 11
6th term
X y
- +2 4
dx
6x
32.
= 1 or 2x + y = 4
(d)
Given equation of circle:
x2
+ y2 + 1Ox - 6y + 9 = 0 ....(i)
and we know the general equation of the circle is
x 2 + y 2 + 2gx + 2.fy + c = 0 ....(ii)
28.
(cl)
P(X < 1) =
On comparing equation (i) and (ii), we get
_n_)
i>(x
n=l
n
=
g = 5,f= -3andc = 9
+1
= f(½)n+l =
n=l
Now, the length of intercept on x-axis
2
= 2.Jg -c =
2
33.
Similarly, P(X > 1) =
1
1
2 <X<l
)
2
=
2✓16
= 8 units
(1 + 4✓3)(1 - 4✓3) = 1,
r;;)x
1 = 14 where y = ( 7-4-...,3
y+y
L 21 )n+I
2
- 4x + 3
(
⇒ y 2 -14y + 1 = 0 ⇒ y= 7 ± 4✓3
n=2
Nowy =7 +4 ✓3 ⇒ x 2 -4x+ 3 = -1 ⇒ x = 2, 2
1
= -<P(X >1)
4
29.
Since
=
:. The given equation becomes
00
Also, P(
(a)
2✓(5)2 -9
Alsoy = 7-4 ✓
3 ⇒ x2-4x + 3 = 1 ⇒ x = 2 ±
Note that P(X > 3/2) = 0 < P (X < 1)
(a) n(S) = 100; E = square of terms lies
between 1 to 100.
= 1,4, 9, 16, 25, 36, 49, 64, 81, 100; n(E)= 10
n(E)
Required probability = n(S) =
10
1
=
100 10
34.
,fi,
(a) logsinx 2tanx > 0; sin x > 0, sin x -ct= 1
0 < sin x < 1 in ( O,~) ; 2 tanx < 1 (not possible)
Thus, the equation has no solution.
WWW.JEEBOOKS.INI
124
35.
TargetMHT-CET
(a) There must be 5 at hundred place, now 2
numbers to be chosen from 5 numbers i.e.,
0
Spz = 5 X 4 = 20.
36.
+
-1
(a) General term of the given binomial series is
or x 2 y + y = x 2 or x =
given by:
y
✓1-y
y
exists if l - y ~ 0 er 0::,:;y< 1 Hence,A E [0, 1).
39.
10 x 9x8 x7 1
=-----x
4x3x2xl
2
· 36
70
=-x
(c)
2
xy yz xz xyz
+- +- - zr xr yr r 3
( x2 + y2 +z2l
243
Thus coefficientofx 2 =
37.
70
243
.
i-l
Given,
XIOO
x99
40.
99
98
f'(x)= 100x + 99x + ... + 2x + l + 0
100
99
2
n
-I
7t
00 = -
2
cosne
-
x2
X
2 -
+1
co~ ne
n ➔ oo
1 n
⇒ Jim-A
n➔oo n
Since f: R ➔ A is surjective, A must be the range
off(x).
n
[ - sinnne
n ➔ oo
1+1 + 1...+1+1
'------v--"'
100 times
⇒ f'(l) = l00
...(ii)
Again, putting x = 0, we get
f'(0)=0+0 + ... + 0 + 1 ⇒ f'(0) = l ...(iii)
From eqs. (ii) and (iii), we get; f' (1) = l00f ' (0)
Hence, m = 100
(a) The domain off(x) is all real numbers.
sinnel
-
n
. cos n0
. sin n0
IIm - - = 0 , 1Jill - - = 0
n
n
100 times
Letf(x)=y, i.e.,y = -
sinn8 ]
cosn8
But - I ::,:; cos n8 ::,:; 1 and - 1 ::,:; sin n8 ::,:; I
(1)99 +198 + ... +1+1
f' (1) =
An = [ cosn8
(a)
⇒ .!.A" =
[·: f(x) = x" ⇒ f'(x)=nxn- ]
... (i)
⇒ f'(x) = x9'1+ x98 + ... + x + l
Putting x = 1, we get
38.
tan
J
r2
-sinn8
1
=
=
x 2
f(x)= - + -+ ... + - + x+l
100 99
2
⇒
xy
yz
xz
+ tan- 1 + tan- 1 zr
xr
yr
(b) tan- 1 -
=
-a
41.
(b)
tl.
=
[o0 o0]
1
-b
=0
-c
for non-zero solution
⇒
abc -a-b -c- 2 = 0 ⇒ abc=a + b + c+ 2
1
1
1
No"'--+--+-, l+a l+b l+ c
WWW.JEEBOOKS.INI
MOCKTEST-3
125
2
3
3
=[x f (x)] - - = 2/(2)-4
o 4
3+ 2 (a +b+c)+(ab+bc+ac)
1+ (a +b+c)+(ab+bc+ac) +abc
3
3
=0-4 (·: f(2) = 0) = -4.
3+ 2 (a +b+c) +(ab+bc + ac)
1 +2 (a+b+c)+2+ab +bc+ac
42.
45.
(d) f{x) = [x] 2-[x2] =(-1)2-(0)2 =0,-l<x < 0
(a) It is clear from the graph that it is bounded
solution.
⇒ 0<x 2 <1
f(x)=0-0=0, 0:<,;x < landf(x)=l-1=0,
3 andf(x) = 1-3 = -2, ✓3 :<,;x < ✓
4
1 :<,;x < ✓
:. From above it is clear that the function is
n V n E I except at x = 1.
discontinuous at ✓
43.
lnx
(d) Let y=-;
X
1
dy
dx
x. - -lnx.l
X
1-logx
x2
x 1 +x2 = I
5x 1 + !Ox2 = 0
.
dy
For maxuna, put dx = 0
⇒
46.
1-lnx
--=0 ⇒ x=e
x2
(a)
J
(x2 -1)
dx =
x.Jx4 +3x2 +1
d 2y
Now, =
2
dx
2
x (-_!_J-(1-lnx)2x
J
(x2 -1)
dx
x2 /x2 +3+-1V
x2
X
(x2)
2
d2y
Atx=ewehave - 2 <0
dx
. y=1
.
I
:. Th emax1mumvaueatx=e1s
e
44.
[ Putting x +
~ = z ⇒ (1- x12 }x =dz]
3
2
(d) We have ff (x)dx = - ; Now,
0
4
2
2
2
0
0
0
fxf'(x)dx = xf f'(x)dx- f f(x)dx
WWW.JEEBOOKS.INI
TargetMHT-CET
126
47.
(b) For the orthogonal section C 1P and C 2P
are pendicular where C 1 and C2 are centres of
sphere of radii 4 and 3 respectively
I=
=
50.
371t
1t
1t+l 8.21t
0
0
1t
Jsin t dt = fsin t dt + fsin t dt
7t
21t
0
0
fsin t dt + 18 Jsin t dt = 2 + 0 = 2
(c) Letthegivenvectorsbe AB=3i+5]+4k
J
and AC= Si - 5 + 2k
A
Now C 1P=4 andC2P=3,so tan0=
3
.
3 12
OP=C 1Psm 0 =4x-=5
5
48.
",J'-.,
✓x
,,,
4
:. Radius of circle of intersection
J'-.,
,.x~
<-,',
l'x
.....
t',f7
M
B
C
Let AM be the median through A
(d) Differentiate .xy(x) = x2y'(x) + 2xy(x)
1- AM=-(AB+AC)
2
or
or
dy
x - +y = O
dx
.xy(x)+x2y'(x)= O or
lny + lnx = lnc or
xy = c
(a) I=
f
A
A
X
Put re log x = t
A
A
A
A
A
A
A
= -(8i +6k) = (4i + 3k)
re sin(rcloge x) d
I
e
A
2
1
e37
49.
!
= -[(3i +5} +4k)+(5i -5) + 2k)]
X
2
:. Length of the median AM = ✓4 2 + 32 = 5 units
⇒
re
-X dx = dt
WWW.JEEBOOKS.INI
(Mock Test-4)
UI
1
2
3
4
5
51
52
53
54
55
1
2
3
4
5
(d)
(c)
(d)
(d)
(c)
(b)
(a)
(c)
(c)
(d)
(a)
(d)
(a)
(b)
(c)
6
7
8
9
10
56
57
58
59
60
Answer KEYS
(d)
(d)
(d)
(b)
(a)
11
(b)
12
(d)
(d)
(d)
13
14
15
(a)
(a)
(a)
(a)
16
17
18
19
20
(c)
(a)
(b)
(d)
(b)
(c)
(d)
61
62
63
64
65
(d)
(d)
(c)
(d)
(a)
66
67
68
69
70
6 (c)
7 (a)
8 (c)
9 (d)
10 (d)
11
12
13
14
15
(d)
(c)
(d)
(d)
(c)
16 (a)
17 (b)
18 (a)
19 (b)
20 (b)
(d)
(d)
(c)
(d)
(b)
SECTION-A
PHYSICS
21 (c) 26 (a)
22
23
24
25
(a)
(b)
(c)
(b)
27
28
29
30
(a)
(a)
(d)
(a)
CHEMISTRY
71 (d) 76 (d)
72 (a) 77 (a)
73 (c) 78 (b)
74 (d) 79 (a)
75 (d) 80 (a)
SECTION-B
MATIIFMATICS
21 (d) 26 (a)
22 (b) 27 (a)
23 (a) 28 (b)
24 (b) 29 (c)
25 (c) 30 (c)
(c)
(c)
(c)
31
32
33
34
35
(a)
(c)
81
82
83
84
85
(c)
(d)
31
32
33
34
35
(a)
(a)
(b)
(b)
(c)
(a)
(b)
(a)
36
37
38
39
40
(c)
(d)
86
87
88
89
90
(c)
(c)
36
37
38
39
40
41
42
43
44
45
(b)
(b)
(d)
(b)
(b)
91
92
93
94
95
(c)
(c)
(c)
(c)
(c)
41
42
43
44
45
(b)
(a)
(d)
(a)
(a)
46
47
48
49
50
(a)
(a)
(c)
(b)
(b)
(a)
(c)
(c)
96
97
(a) 98
(c) 99
(b) 100
(d)
(b)
(d)
(c)
(c)
46
47
48
49
50
(b)
(a)
(b)
(b)
(a)
(c)
(a)
(a)
(c)
(c)
SECTION-A
4.
PHYSICS
5.
1.
2.
3.
(d) Angular velocity co =
t0
= [M0 L0r
_Am_ M 1 -M 2 _ 20-4 _ _!i_3_
1
]
Ac
150
(c) Mass = 150 gm = --kg
1000
Force= Mass x acceleration
5
= l 0 x20N=3N
1000
Impulsive force= F.tit = 3 x 0.1 = 0.3 N
(d) We know that ~
(3.5- 1.0) X 10-3
(80-30) X }0-6
(d)
(c) modulutaion index (m)
= 50
M 1 +M 2
20+4
6.
7.
(d)
(d)
8.
ld)
9.
(b) As R 2 = a 2 + b 2 + 2 ab cos
~
24
3
!-,,r / r -05-2. b.r _..!_M
Mll _ _ _ 2'r - 2!
2
2
2
<I>
2
: . a =a +a +2 a coscp ,
cos <1>
1
= - 2 , <1> =
21t
3
WWW.JEEBOOKS.INI
128
10.
(a) Total energy of rolling body
= translational K.E. + Rotational K.E
17.
TargetMHT-CET
(a) After every half-life, the mass of the
substance reduces to half its initial value.
= ½Mv~.m + ½Ic.mffi2
Where I is the moment of inertia about an
ax is passing through its C.M. &
perpendicular to the plane of body.
For hoop 1cm = MR2, vc.m. = Rffi
So Rotational K.E
Total energy
=
2
½Ic.mco
2
½Mv:.m+ ½Ic.mCO
No
2
5years
5 years
5years
18.
(a)
e = d$ = ~(NBA)= NA dB
dt
dt dt
=100 x 0.1 x 0.05 x ( O. l- 0 ·05) = 0.5 V
0.05
- - - - - - - - = l: 2
½MR 2(J)2 + ½MR 2(J)2
11.
12.
13.
14.
(b) Intensity of light transmitted by polariser
is half of intensity of unpolarised light.
(cl)
(cl) Kirchhoff's first law is based on conservation
of charge and Kirchhoff's second law is
based on conservation of energy.
(cl) Let the mass of the gas be m.
At a fixed temperature and pressure, volume
is fixed.
Density of the gas, p = m
V
19.
20.
(c)
(a)
21.
(c)
22.
(a)
m 1 v 1 +m 2 v 2
axb+0
a(b)
m 1 +m 2
a+c
a+c
v=~~-~~
F = 6 7tll rv = 6 x 3.14 x (8 xI0-5) x 0.03 xl{)()
= 4.52 x 10-3 dyne
23.
1
(b) According to Wien's law "-m oc T and from
the figure ('A.m)l < ("-mh < ('A.m)i therefore
Ti > T3 > T2.
24.
p
m
m
Now-=-=-p PV nRT
(c)
!l_ _ a/
9
a
3
12
1
a2
1
--=
- o r -1= 2
a2
. 1m ax _ (3+1)2
.. 1mm - (3-1) 2
⇒ ~ = x (By question)
25.
nRT
16
4
=4 =-
(b) As we know, escape velocity,
⇒ xT = constant ⇒ x T
1 1 = x2 T 2
⇒x
X1T1
2
283
383
⇒ --=-x
T2
283K]
383K
15.
(a)
16.
(a) Current (I)= 12 A and magnetic field (B)
= 3 x 10-5 Wb/m 2 . Consider magnetic field
Ratio Ve = 1 :
VP
26.
B at distance r.
Magnetic field , B = µof
2nr
2✓2
(a) For an SHM, the acceleration a= -ffi 2 x
2
where ffi is a constant. Therefore, !!.. is a
X
constant. The time period Tis also constant.
aT
Therefore, is a constant.
X
WWW.JEEBOOKS.INI
MOCKTEST-4
27.
129
2
(a) In coil A B = ~ nl
'
4n R
p isothcnnal > p adiabatic
Tiso1h nnal > T adiabatic
⇒ S1
ope of curve for isothermal change
< slope of curve for adiabatic change.
So, curve B shows isothermal change and
curve A shows adiabatic change.
I
:. B ex:- .
R'
~-_!J__,& _~- 1
Hence, B2 - R1
28.
(a) Y=2x l0 10 Nm-2;
l2 - 2 -
t:J.l
1
=0. 0l
Work done per unit volume
=
1
2 x stress
=½ y(
~Ir
.
I
x strain = x Y x strain2
(cl)
38.
(b)
~ =7 andW= (d / 2 ) = 4~
2
29.
2
1
U = .!.x 2 x I0 10 x(--) = U = 10 6 Jm-3
100
2
(cl) Unit positive charge at O will be repelled
equally by three charges at the three comers
oftriangle.
30.
Bysymmetry, resultant E atOwould be zero.
1
3
(a) w; =- x 5 x l0 x (0.05)2
2
1
3
2
⇒ ff; =- x5x l0 x (0.10)
2
F
F - µOlJ 12 µ01· 2
----- = --
39.
2nd
2nd
£
(attractive as current is in the same direction)
(a) Potential gradient = Potential fall per unit
length. In this case resistance of unit length.
1
R =pt= 10- x 1 = 10_1 0
A
10-6
Potential fall across R is
V= f.R = O. l x l0- 1 = 0.01 volt/m.
!:J.W =.!_ x 5x10 3 x 0.15 x 0.05 = 18.751.
2
31.
32.
33.
34.
As refracted ray emerges normally from
opposite surface, r2 = 0
As A= r 1 + r2 :. r 1 =A
sin i
i1
i .
Now, µ=-.-1 =-=-;1=µA
r1 A
Sill 'i
(c) The centre of mass remains at rest because
force of attraction is mutual. No external
force is acting.
35.
36.
= 10-2 volt / m
(c)
40.
41.
8 2
( - ) ⇒ L= l0mH
dlldt ⇒ 2 = L 3x10-
:. 8=30° = n / 6radian
(c) Curve A, B shows expansion. For expansion
ofa gas,
w isothennal > wadiabatic
2
= J.Sx l0- N =0.025Nm - 1
2L
2x 0.3 m
(b) On a banked road,
V
2
V
V
I
tanli=-=-- = H ✓
3V ✓
3
At equilibrium, weight of the given block is
balanced by force due to surface tension,
i.e., 2L. S = W
V~ax =( µ 5 + tan0)
Rg
1-µ 5 tan0
Maximum safe velocity ofa car on the banked
road
(a) According to Faraday's law of electromagnetic inductions,
(c)
(cl)
or S = ~
(c)
e= IL
(2D)'),..,
D').,,
37.
max -
42.
Rg [ µs + tan 0 ]
1-µs tane
.
. given
.
by R = -8riL
(a) Fl u1'd resistance
1s
4
nr
When two capillary tubes are joined in
series, then equivalent fluid resistance is
811L
811 x 2L
1tR
n(2R)
4 +---4
Rs = R1 + R 2= - -
lWWW.JEEBOOKS.INI
TargetMHT-CET
130
As £1 < £2 therefore T 1 < T 2
Let longer length pendulum complete n
oscillation and shorter length pendulum
complete (n + 1) oscillation. For unison
swinging
= (811L)
x.2_
4
nR
8
Rate of flow
-
P
Rs
nPR4
8
811L
9
= - - X-
8
-x
9
[ as X = n:11:4 ]
43.
44.
(n + l)T1 = nT2
(a) From v = n A, we find 'A, oc v because freq. n is
constant. Therefore, new wavelength= 4 A.
(c) The time period of LC oscillations,
(n+ l) x 2njf = (n)x2nH
⇒ n= 1
:.n+l = l + l = 2
T=2nJ'ic.
The time at which charge on the capacitor
will be zero is
i.
49.
1
970.6 X 10-lO
So t=!::..-Jic.
⇒-----
2
45.
46.
47.
µ=0.5
(b) The magnitude of
the frictional force f
has to balance the
weight 0.98 N acting SN
downwards.
Therefore the
frictional force
= 0.98N
(a) Ek=E-~0 =6.2-4.2=2.0eV,
Ek=2 X 1.6 X 10-19 =3.2 X 10-19 J
(b) Objectdistanceu = -40cm
Focal length f = -20cm
According to mirror formula
1
1
U
V
- +-
1
1
1
Number
N= n(n-1)
2
SN
50.
(c)
-v
u
emission
(-40)
= - - - = -1
(-40)
The image is of the same size and inverted.
(a) Let T I and T 2 be the time period of the two
pendulums T1 = 2nlf and T2 = 21t~
line
= 4 x3 = 6
2
Given:r = 30cm 0.3mandv=2t
Radial acceleration at t = 3 sec
dv
2
a 1 =-=2 m/sec
dt
CHEMISTRY
+5
I -2+ 1
1
- = - - = - - or v=-40cm.
40
V
40
Negative sign shows that image is infront
ofconcave mirror. The image is real.
Magnification, m = -
of
2
2
4 (3 2
a = ~ = ~ = x ) = I20 m/sec 2
r
r
0.3
0.3
and tangential acceleration
1
= - or - = - - V f
U
f
1
1
1
1
I
or-+---- = +v -20 (-40) -20 40
48.
(c)
+3
51.
(b)
The HN03 is stronger than HN02 . The
52.
more the oxidation state ofN, the more is
the acid character.
(a) Since in NaCl typeofstructure4 formula units
form a cell.
58.5 gm. ofNaCl = 6.023 x I023 atoms
6.023 X 10 23
atoms
58.5
4 atoms constitute 1 unit cell
I gm ofNaCl =
23
.
6.023 X 10
- - - - atoms constitute
58.5
6.023 x 1023
58.5 X 4
= 2.57 x 1021 unit cells.
= ----
WWW.JEEBOOKS.INI
131
MOCKTEST-4
62.
53.
(cl) Magnetic momentµ=
n = number of unpaired electrons
(c)
✓
15
Thus there are five 1° carbon atoms.
54.
(c)
CH3CHO
63.
(c)
=.Jn(n+2) :. n = 3
Molar conductance of solution is related to
specific conductance as follows :
CH3 - CH = CH- CHO
NaOH
A
56.
(cl) D-penicillamine is used in treatment of
Wilson's disease which is a rare genetic
disorder of Cu metablism, penicill amine
treatment relies on its binding to
accumulated Cu and elimination through
urine.
(b)
d[B]
dt
2 d[A]
3 dt
~
58.
64.
1
10
xz+
y3+
2x20
-100
0.4
4
50
100
0.5
5
65.
Hence formula X 4 Y 5O10
59.
60.
61.
(c)
2F 2 (g)+28iO(1) ➔ 4W(aq)
+ 4P----(aq) + Oi(g)
Cl2 (g) + 28iO (l) ➔ HCl (aq) + HOCl
(cl) Prolinecontains an imino group i.e.,
secondary amine.
(cl) CHC13 on exposure to air forms phosgene
which is poisonous gas and removed by
converting it into diethyl carbonate (which
is non-poisonous substance).
0 2/light
COC1 2 +HCl
Phosgene
(Poisonous)
COCl2 + 2C2H50 H - (C2H5)zC0 3 +2HCI
Diethyl carbonate
(non- poisonous)
(cl)
= 6.3 x 10-2 x 104 ohm- 1cm2 mol- 1
= 630 ohrn- 1 cm2 mol-I
We know that carbon having
(i) 4 cr bonds correspond to sp3
(ii) 3 cr and 1 rt bond correspond to sp2
(iii) 2 cr and 2 rt bonds correspond to sp
(I) (2)
(b) Sphere Tetrahedral void Octahedral void
o z-
....(a)
1000
x ----(O.lmol / cm3)
due to partial D.B.
character rate of
SN2 decreases
Cl > ~
x 1000
C
Am = (6.3 x 10-2 ohrn-1 cm-I)
---=---- ⇒ -- =- ---
57.
K
where C is molar concentration.
Putting 1< = 6.3 x 10-2 ohm-I cm-1 and
C = 0.lM
3A-.+2B
Rate of appearance of B is equal to rate of
disappearance ofA.
1 d[B]
1 d[A]
2 dt
3 dt
(cl) RateofSN2
=
m
Hz!Ni > Clf:i-C8i-C8i-C8i-OH
55.
.Jn(n+2) where
66.
67.
(3) (4)
H 3C- C = C- CH 3
(4)
(1)
(2) (3)
No. of bonds: 4cr
2cr 2cr
4cr
23C 23C
sp sp
sp 3
Hybridisation : sp3
3
Thus, 2-butyne has sp and sp hybridised
carbon atoms.
(a) The stabilityof+2 O.S. follows the order:
Pb2+ > Sn2+ > Ge2+
Hence order of reducing power is :
Ge > Sn > Pb
(cl) Given ~H = 41 kJ mo1- 1 = 41000 J mo1- 1
T = 100°C = 273 + 100=373 K
n= l
~U= m - illlRT= 41000-(l x 8.314 x 373)
= 37898.88 J mo1-1 = 37.9 kJmo1-I
(cl) Bond angle decreases progressively from
H 2O
➔
H 2S ➔ H 2Se ➔ H2 Te
due to
decreasing bp-bp repulsions as the
electronegativity of the central atom
decreases down the group. 8i0 has smaller
bond angle in comparison to NH3 due to
presence of two lone pair of electrons.
Hence smallest bond angle is in 8iTe.
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TargetMHT-CET
132
68.
(c) For given cell;
Ecell
69.
70.
71.
72.
2.303
0.8
k = --Iog _ or k=2.303 log4
1
02
again a=0.9 mo!, a-x=0.9-0.675
= 0.225mol
lRHs
[H+
RT
= -log [ ]
F
H+ LHS
for max. emf [H+]LHs should be min. and
that is for NH4OH (aq).
(d) Vapour phase refining method is used for
the purification of titanium, zirconium etc.
and is called Van Arkel method.
(b) Buna - N is a copolymer ofbutadiene.
(C1½ = CH - CH = C1½) and acrylonitrile
(C1½=CHCN).
(d) Stephen's reaction is used to prepare
aldehydes only.
(a)
k = 2.303 10 ~
t
g 0.225
2 303
2.303log4 = ·
log 4
t
Hence, t = I hour
79.
(a)
OH
@'
[Cr(NH3) 4Cl;]ClO 3 ➔ [Cr(NH3) 4Cl T + ClO2
COOH
1H3CO)iO
NaOH
Acetyl salicylic acid
(Aspirin)
Salicylic acid
2ions
73.
74.
75.
(c) Fire due to action ofwater on saline hydrides
cannot be extinguished with water or CO2.
These hydrides can reduce CO2 at high
temperature to produce 0 2 .
(d) Disproportionation involves simultaneous
oxidation and reduction of the same atom
in a molecule.
(d)
HCHO
80.
81.
82.
83.
84.
(a) Cup is yellow in colour.
(c)
(d) Match box is orthorhombic.
(a) The 7t bond is formed by the sideways
overlapping of two p-orbitals of the two
carbon atoms.
The molecular plane does not have any 1t
electron density as the p-orbitals are
perpendicular to the plane containing the
ethene molecule. The nodal plane in the 1tbond of ethene is located in the molecular
plane.
(b) Given I<i, = x K kg moJ-1
~Tb = kb x m
: . y= x x m
We know
~Tr= lcr x m
On substituting value of m,
CH2CH3
I
H-C-OH
I
H
~T
(D)
n-propylalcohol
77.
78.
85.
(a)
(b)
A ➔ B, For a first
order reaction
Given a=0.8 mo!, (a-x) = 0.8-0.6 = 0.2 mo!
(b)
f
= yz
X
2MgSO 4 + 2 Na2CO3 + H2O
--➔
MgCO3.Mg(OH)i + 2Na2SO4 +CO2
Basic magnesium carbonate
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MOCKTEST-4
86.
(c)
133
97.
PMw = dRT
PA dA MB 4
-=-X--=pB dB MA 1
87.
88.
89.
98.
(c)
(a) In lanthanides there is a regular decrease in
the atomic radii as well as ionic radii of
trivalent ions as the atomic number
increases from Ce to Lu. This decrease in
size of atoms and ions is known as
lanthanide contraction. Although the atomic
radii do show some irregualrities but ionic
radii decreases from La to Lu. Thus the
correct order is.
Yb+3 < Pm +3 < ce +3 < La +3
86pm 98pm
103pm
106pm
(b) Arene diazonium salts are most stable
among the given options because of the
dispersal of +ve charge on the benzene ring
due to resonance.
99.
(b) Due to greater electronegativity of
sp2-hybridized carbon atoms ofthe benzene
ring, diaryl ethers are not attacked by
nucleophiles like 1-.
(d) Carbon belongs to 2nd period, while iodine
belongs to 5th period, hence the C-1 bond
in C~CH2 CH2 I must be formed by the
overlapping of2sp 3 orbital ofC with the 5pz
orbital of iodine.
(c) (I)
+ Reflect
the lone pair of electron is less easily
available for protonation.
+ Reflect
6x FE0
90.
(b)
logl030 =
91.
the lone pair of electron is not available for
protonation.
(Ill)
K = 10 2.303 RT
0
6
xE
0.0591
⇒ E 0 =0.2955V
JC More +I, less H-bonding
(b) Flux is used during metallurgy to remove
92.
93.
(d)
(a)
94.
(c)
O
silica and undesirable metal oxides.
Rate= K[A ]2 [B]n
[Fe (CN) 6]4- ➔
-
CH3
+ I, H-bonding
+ I more preferred than H-bonding, is due to
steric hindrance to H-bonding in l O amine.
(IV)
11qu1u1: I: I [TI I: I: I: I
- no. of unpaired electrons = 0
!I III I
[MnCli] - ➔ 1 1 1 1 1 [TI
-no. of unpaired electrons= 5
2
I: I: I: I
0
I I I [TI I: I: I: I
[Coc4f- ➔ l1q1q 1 1 1
-no. of unpaired electrons= 3
The greater the number of unpaired
electrons, greater the magnitude of
magnetic moment. Hence the correct order
will be
[MnC14 ] 2-
95.
96.
>
[CoC14 ] 2-
> [Fe(CN)J4-
+ I, H-bonding
NH
~
More H-bonding, less +I effect
Unstable Thus, the correct order is
(II) < (I) < (IV) < (Ill)
100. (c)
MF + XeF4 ~ M + [ XeF5]
sp 3d3, Pentagonal planar
(b) Prostaglandin is a non-steroidal hormone.
(d) C 2H 5I and C 2HpH form non-ideal solution.
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134
TargetMHT-CET
SECTION-8
Now, let (h, k) be the point which is equidistant
from the lines 4x-3y+ 7 = 0 and 3x-4y + 14 = 0
MATHEMATICS
1.
2.
3.
4.
(a) Minimumvalueofn=l00-(30+20 + 25 + 15)
= 100-90= 10
(d) HereR = {(x,y): lx2-y2 I< 16}
and given A = { 1, 2, 3, 4, 5}
R = {(1, 2)(1, 3) (1 , 4); (2, 1)(2, 2)(2,3) (2, 4);
(3, 1); (3, 2) (3,3) (3, 4); (4, 1) (4,2) (4, 3); (4, 4), (4, 5),
(5 , 4)(5, 5)}
(a) f(x+y)=fix)+2y2 + kxy
fil + y) = 2 + 2y 2 + ky, puttingx = 1
putting y = 1,./{2) = 8 = 2 + 2 + k ⇒ k =4
:. f(l + y) = 2 +2y 2 +4y = 2(y+ 1)2 : . f(x) = 2x2
(b) For checking equal function
4h - 3k + 7
3h - 4k + 14
Th en ---.==== = +---.====
✓42+(-3)2
✓32+(-4)2
⇒
7.
S.
4h-3k+7 = ±(3h-4k+l4)
⇒ h + k-7 = 0 and 7h-7k + 21 =0
Hence locus of(h,k) is x +y - 7 =0 andx-:y+ 3 =0
(a) The circles x 2 + y2 + 2gx + 2fy+ c = 0 and
x 2 +y2 + 2g 1 x+2f1y + c 1=0
are orthogonal, if 2gg 1 + 2ff1 = c + c 1
Thus, in the given question, the condition will be
2gl g2 + 2f1f2 =cl+ Cz·
(c) n(S) = the area of the circle ofradius r
(a) Domainoff(x) = Rbutrange = [0,oo)
n(E) = the area of the circle ofradius
Domain ofg (x) = R, range = R
Domain same but range is different so it is
not an equal function.
r
2
n(~J
n(E)
1
:. Theprobability = - - = - -2 = - .
4
n(S)
nr
(b) Domainoff(x) = R
Domain ofg (x) = R
Domain and range both same so it is an
equal function.
9.
(c) Domain off(x) = R- {0}
(d) Suppose xy-plane divides the line joining
the given points in the ratio"- : 1. The coordinate
of the point of division are
Domain ofg(x) =R
Not equal function as domain is different.
5.
(c)
This point lies on xy-plane.
1
A=-- ⇒ 1-r
a
1-ra
1
.
. . a log r = log
a
1 A-1
=l--=-A
A
b
1 B-1
=1--=-B
B
=- ⇒ r
A
B=-- ⇒ 1-r
1-rb
1
b
I
=- ⇒ r
B
(A-1)
A
jB-1)
B
6A+4 =0 ⇒ A=-i
')._+J
2
Hence, xy-plane divides externally in the ratio 3 : 2.
10.
ax + bx + ex ) ")., /x
(d)
Consider Jim
x➔O [
and b Jogr = Jo'
")., . (ax-1+-
-hm 3 x➔O
bx-1
X
X
3
cx-lJ
+-
X
=e
6.
(c) If a point is equidistant from the two
intersecting lines, then the locus of this point is
the angle bisector of those lines.
= e").,IJ (log a + log b + log c)
=
e")., / 3(1og abc) =(a b c )")., / 3
WWW.JEEBOOKS.INI
MOCKTEST-4
11.
135
2
2x + 2lxl 2 2✓
(d)
Case I.
x 2 0,
...(i)
then Eq. (i) becomes
2x+2x<'.2 ✓
2 ⇒ 2
X
r,:;
2-v2 ⇒ x2
15.
.
✓l+kx- ✓1-kx
x➔O-
X
(c) L.H.L. = hm - - - - - = k
2
1
RH.L = lim (2x +3x-2) = -2
2
x➔O+
Case II. x < 0, then eq. (i) becomes
2x +Tx 2 2✓
2
16.
Since it is continuous, L.H.L = R. H. L ⇒ k = -2
(a) Required area (OAB)
y
⇒ t+! 2 2✓2 , where2x = t
8:...----y
.l.!;:
= log,,(x +e)
t
⇒ t 2 -2✓
2t+l 2 0
⇒ x :s; log2 (✓
2-1)
0
fln(x + e)dx
Also, 0< ✓
2-1<1, log 2 (✓
2-1) <0.
:. The solution is
(--oo,
12.
13.
1-e
J
log 2 (✓2-l))]u[½, oo
=
(c) We have to form 7 digit numbers, using
the digits 1, 2 and 3 only, such that the sum of
the digits in a number= 10.
This can be done by taking 2, 2, 2, 1, 1, 1, 1, or by
taking 2, 3, 1, 1, 1, 1, 1.
17.
1
[xln(x+e)-J--xctx]'
x+e
0
(b)
=
Sincelengthofthenormal =
.
7! 7!
.. Numberofways =-+-=77.
3!4! 5!
According to the question y
log a
(d) Replace logba by log b
y2[1+(:rJ =k ⇒
logx
1
: . ! 1 . = - - - - -x logx
log x logy logz
logx
1.
y✓l+(:r
✓1 + ( : )
2
=k
Squaring on both side, we get
2
log y
logz
3logy
logz
log y
5logz
y2+y2(:r =k
2
Take log x, logy, log z common from Ci, C2 , C3
respectively.
dx
f-x
__
x2n +a2
n-1
0 0
!1.=l
1
14.
3 1=1
5
2 0=lx2x4=8
1 0 4
(d) We know that- (p ➔ q) = p A -q
:. -((p Ar) ➔ (rv q)) = (p Ar) A [- (rv q)]
ee(pAr) A (-rA-q)
18.
(a) Let I =
Let xn = t ⇒ n . xn-l dx = dt
[xn]
-1 1
+C
= -tan
na
a
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136
19.
TargetMHT-CET
2) 1 0-r(311sy,
(b) HereTr+ 1 = 10 cr( ✓
wherer = O, 1,2, ....,10.
We observe that in general term Tr+ 1 powers of
2 and 3 are
I
C
F
1
2 (10-r) and 5 rrespectivelyand O~ r~ 10.
A
So both these powers will be integers together
onlywhenr
B
= (AC+CD)+(AE+ED)+AD
=Oor 10
= AD+AD + AD = 3AD
.·. Sum ofrequired terms = T 1 + T 11
0
= 10c ( ✓
2)10 + 1oc
20.
21.
23.
(311s) 10= 32 + 9 = 41
10
(b) Let R be a relation defined by aRb,
a z b, where a and bare real number
Reflexivity : Ifa is real number (given)
⇒ R is reflexive.
then a z a is true
Symmetry : Ifa and b are two real numbers such
that a z b then b z a is not true
⇒ R is not symmetric.
Transitivity : Ifa, band care the real numbers
then a z b, b z c ⇒ a z c ⇒ R is transitive
Hence, R is reflexive, transitive but not symmetric.
(d) Let y = mlogx + nx2 + x
m
dy
= - + 2nx + 1;
dx
x
andDr'soflinePQare(l + 1), (0-2), (5-4)=2,
-2, 1
2
-2 1
De's ofline PQ =
,2
2 +(-2)2 +l 3 3
.J
: . Projection ofline segment AB on the line PQ is
3
(b) x + i y = - - - - cos0+i sin0+ 2
cos0+i sin0+2
3
1
m + 2n + 1 = 0. Thus, we have m + 8n + 2 =
0
:. 6n + l
=0
6n+I = 0 }
:. 3m + 2 = 0 ⇒ n =
1
22.
(b)·: AB= ED and AF= CD, So
AB+ AC+ AD+ AE + AF
= ED+AC+AD+AE+CD
⇒ --=-----
x+iy
⇒
-6
-4 5
2
m=-- Hence 2m + 10n = - - - = - 3
3
'
3 3
,-
2 -2 1
3 ' 3 '3
24.
=0
(a) Let A= (3, 4, 5), P= (-1, 2, 4); B= (4, 6, 3)
andQ=(l , 0, 5)
:. Dr'soflineAB are(4-3),(6-4),(3-5) = 1,2,-2
dy
At x = 2 - = 0
' dx
:. ; +2n (2) + 1 = 0; At x = 1, :
k =3
x-iy
=.!_[(cos0+2)+i sin0]
(x+iy)(x-iy) 3
X
⇒
1
X
⇒
2
+y
2
+y
3
2
X
2
X
=-(cos0+2)
2
1
- = -cos 0
3 3
1 . 0
y
and --~-=-sm
x2 + y2 3
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MOCKTESf-4
137
Squaring and adding, we get
(x 2
On differentiating w.r. t. x, we get
r -:y2r
:y2-¾
2
I
+(x 2
2
⇒--- (3-4x)+l
X +y
⇒ 3-4x
2
dy
2 sec (log x)
- = 2x tan (logx) +x -~~~ + 2x
dx
x
I
9
dy
⇒ dx = 2x [I + tan (logx)] + x sec2 (logx)
=0
= -x 2 - y2
⇒ 4x-x 2 -y 2
=3
= [log t - log(t + 1)
e
J:e
1/e
= log-- log-1+e
1+ 1/e
Again, A3=A-A2
=[-2~
!][ ~ ~
2
-1 -3
e
e
= log--log-=0
l+e
l+e
28. (b) S = { HHH, HHT, HTH, HTT, THH, THT,
TTH, TIT}
E = {HHH, HHT, HTH, THH}; F = {HHH, HHT,
HTH,HTT}
E n F= {HHH, HHT, HTH}; n(E n F) = 3, n(F) = 4
~i
-1 -1 -3
E)
n(EnF) 3
:. Reqd prob. = P ( F = n(F) =
4
o o ol
[0 0 0
29.
(c)
= 0 0 0 =O
1 km
Thus, 3 is the least positive integer such that
A3 = 0. So, A is nilpotent with index 3.
26.
(a) Given that, x = exp tan {
l
1 (y -
2
x
1J}
d = Hcot30° -Hcot60°
Time taken = IO second
: . speed
~
Taking log on both sides, we get
logx=tan-
⇒
1
l~)
X
2
10
= 240✓3
30.
2
y- x
= cot30° -cot 60° x 60 x 60
( y-x21
=tan(logx)
(c)
As given, n th term is: T = 3n + 7
0
Sum ofn term, S0
= L T0
⇒ y= x 2 tan(Iogx) +x2
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138
= 3n(~ + 1) + 7 n = n[ 3n + ~ + 14]
5
4
5
= 38x- = 47.5.
4
3x50+17]
2
35.
(a) Let a cos x = y. The equation converts to
1
y
y+ -=6 ⇒ y
(a) The vertices ofa right angled triangleA(l, k),
B(1, 1) and C(2, 1) and Area of MB C = 1 square
unit
6
32
..· y = ± 2✓
y
&
B(l , l)
⇒
32.
±(k -1)=2
1 ⇒
⇒
-1 :=; log a (3 ± 2✓
2) :=; 1
C(2,1)
2) ~ -1 and loga (3 + 2✓
2) :=; 1
:. loga (3-2✓
⇒ 3 - 2✓
2 ~a - I and 3 + 2✓
2 :=; a
1
k=-1,3
(c) Given
10b + 25
Now, a> 1 ⇒ b 2 - 1Ob+ 25 > 1
(a)
/(x)= ✓x-1+ ✓25+(x-1)-1~
=✓x-1 + ✓(5- ✓x-1) 2
= ✓x -1 + 15- ✓x -1 I =5
[·:v'x-1<5 forl<x<26]
f'(x)=O
(b) Let a student gets x marks out of 40. He
.
gets -5x marks out of 50. Thus, each obseratlon
4
2 :=; a
r;; ~ .!_ and 3 + 2✓
3+2-vL a
1
⇒ a ~ 3 + 2✓
2 and a ~ 3 + 2✓
2
a= b2 -
⇒ b -10b + 24 > 0 ⇒ (b-6)(b-4) > 0
34.
⇒
2 (l)l(k-l)l=l
2
33.
= 3+2✓
2
-
: . for all real roots we must have
We know that, area of right angled triangle
1
-6y +l=O
Since a > 1 and -1 :=; cos x :=; 1
X
2 x BCxAB=
2
⇒ acosx = 3± 2✓
2 ⇒ cos X = log a (3± 2✓
2)
0
=
1
5
multiplied by - giving mean
1 7
= 50[ ~ ] = 25 x 161 =4175
31.
.
4
=n[3n;l7]
Sum of50 terms= Sso = 50 [
.
will be multiplied by - . Hence, mean 1s a so
:.aE[3+2✓
2, + oo)
36.
(c) The number of committees of 4 gentlemen
=4C4 = l
.
.
The number of committees of 3 gentlemen, 1 wife
= 4c3 X Icl
( ·: after selecting 3 gentlemen only 1 wife is left
who can be included)
The number ofcommittees of2 gentlemen, 2 wives
= 4Cz X zc2
The number ofcommittees of I gentleman, 3 wives
=4Cl x3C3
The number of committees of4 wives= 1
: . The required number of committees
=1+4+6+4+1=16
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MOCKTEST-4
37.
139
Since f :(4, 6) ➔ (6, 8) ⇒ f(x) = x + 2
(c)
41.
C 1 (x) = x-2
(c)
38.
f(0)
= O;
(a) It is clear from the graph that it is bounded
solution.
-(~+~)
= xe
f(x)
RHL. lim (0 + h)e- 21h = lim _h_ = 0
h➔Oe 2 l h
h➔O
-(¾-¾) = 0
L.HL. lim (0 - h)e
h➔O
therefore, f(x) is continuous.
-(¾+¾)
-0 = 0
RH.D= lim (O+h)e
h➔O
x 1 + x2 = I
h
L.H.D.= lim (0 -h)e
5x 1 + 10x2 = 0
-(¾-¾)
-0 = l
-h
therefore, L.H.D. RH.D.
f(x) is not differentiable atx = 0.
h➔O
42.
*
1
11 =
(c)
Jxf{x(l - x)}dx
We know, if q is the term used for the probability
of the letters which are not kept in the right
envelope.
1-k
k
=
I
- ( ·: Total letters = n) i.e., P = n!
n!
k
39.
(b) Probabilityofall the letters kept in the right
envelope is
f (k+I-k-x)f[(k +I - k- x )
1-k
Thenp + q = l
k
= J(l- x)f{(l- x)x}dx=
1-k
k
Jr{x(J- x)}dx- J xr{x(l- x)} dx
1-k
1-k
1
q = I-p = 1--.
n!
{1-(k + 1-k-x)}]dx
k
⇒
43.
(b) I =
Jx
b
l-x 3
=
fx
R
2
3
l-x 3
Put 1-x 3 = t 2 ⇒ -3x 2 dx=2tdt
40.
(c)
ax i
Let a= xi+ y] +zk
= z] - yk
⇒ (ax T)2
Similarly, (a x ]) 2
= y2 + z 2
= x 2 + z 2 and
(axf)2 =x 2 + y2
⇒ (ax T) 2 +(ax ])2 +(ax f )2
= 2(x 2 + y2 +z2 ) = 2a 2
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140
44.
TargetMHT-CET
(a)
y
2
dy
dx
dy
dx
48.
9
y
=18x ⇒ 2y- = 18 ⇒ - = -
.
dy
9
Given -=2 ⇒ - = 2 ⇒
dx
y
(a) We have
(.x2 + 1) dy + 2xy = x 1 - 1
dx
9
y =-
2
⇒
· ·
Puttmg
m y2
= 18 x ⇒ x = -9
8
2
Here, P = ~ and Q = x - l
2
2
x +1
x +1
:. Required point is(¾,¾)
45.
f~dx
(c) WeknowthatnC/ + nc/+ ... +nc/
Integrating factor= efPdx = e
Let x 2 + I = t ⇒ 2xdx = dt
=2ncn
and nc/ - nc/ + ... + nc/
0, if nisodd
= { ncn12 (-lt12 ,if niseven
!dt
:. I.F = e J1
49.
C/-
46.
31 C/+ 31 C/- ... - 31 C 2= 0
From this 31
31
32c 2_32c 2+32c 2_
+32c 2= _32c
0
I
16
2 ···
32
34c 2_34c 2+34c 2_ +34c 2=_34c
0
I
2 · ··
32
17
32c 2 + 32c 2 + 32c 2 _
+ 32c 2 = 64c
I
0
2 · ··
32
32
Obviously 64 C32 is greatest.
(b) We have,
tan
⇒
-I nX 3
7t ⇒ tan (
-<-
tan
-I -nX) < tan-3
7t
~ < ✓3 ⇒ x < ✓3n = 5.5 (approx.)
7t
47.
dy
2xy
x 1 -l
-+=
2
2
dx x + 1 x + 1
the maximum value ofx is 5.
(a) (A-2I)(A +I) = 0 ⇒ AA-A-21 = 0
:. A-I = A-I
2
x +1
2
=elogt =e'og (x +l)=x2+ l
(c) Given curves are y = eX and y = e-x
Now, eX=e-x ⇒ x = O
f(ex-e-x)dx = (ex+e-x\
I
:. Area = A =
I
0
= [(e+e-1)- (e0 +e-o )J
50.
1
=e+ -2.
e
(c) Anypointonthelineis(r+3,2r + 4, 2r + 5).
It lies on the plane x+y+z=l7,
(r + 3)+(2r+4) + (2r+5)=17 i.e r = l
Thus the point of intersection of the plane and
the line is (4, 6, 7)
Required distance = distance between (3, 4, 5) and
(4,6, 7)
= ✓{(4 - 3) 2 +(6 -4) 2 +(7 -5) 2} = 3
2
lWWW.JEEBOOKS.INI
(Mock Test-5)
Answer KEYS
SECTION-A
1
2
3
4
5
51
52
53
54
55
1
2
3
4
5
(c)
(d)
(d)
(a)
(d)
(c)
(a)
(b)
(c)
(d)
(d)
(d)
(c)
(d)
(b)
12
13
14
15
(c)
(a)
(d)
(c)
(d)
16
17
18
19
20
(d)
(b)
(d)
(b)
(b)
(d)
(b)
(b)
(d)
(d)
61
62
63
64
65
(c)
(a)
(b)
(b)
(d)
66
67
68
69
70
(c)
(a)
(b)
(a)
(b)
(a)
(d)
(b)
(a)
11
12
13
14
15
(b)
(a)
(d)
(b)
(a)
16
17
18
19
20
(b)
(a)
(a)
(c)
(b)
10
(b)
(c)
(c)
(d)
(b)
56
57
58
59
60
6
6
7
8
9
7
8
9
10
11
(b)
PHYSICS
(a) 26 (a)
(c) 27 (c)
(a) 28 (a)
(b) 29 (b)
(b) 30 (a)
CHEMISTRY
71 (d) 76 (b)
72 (a) 77 (b)
73 (c) 78 (b)
74 (a) 79 (d)
75 (c) 80 (b)
SECTION-B
MATHEMATICS
21 (a) 26 (d)
22 (c) 27 (c)
23 (b) 28 (b)
24 (b) 29 (c)
25 (c) 30 (c)
21
22
23
24
25
31
32
33
34
35
(a)
(a)
(b)
(c)
(b)
36
37
38
39
40
(c)
(a)
(b)
(a)
(b)
41
42
43
44
45
(a)
(c)
(d)
(b)
(b)
46
47
48
49
50
(c)
(a)
(d)
(b)
(c)
81
82
83
84
85
(a)
(d)
(b)
(b)
(d)
86 (d)
87 (a)
88 (d)
89 (a)
90 (c)
91
92
93
94
95
(b) 96
(d) 97
(c) 98
(c) 99
(a) 100
(c)
(d)
(a)
(b)
(d)
31
32
33
34
35
(d)
(d)
(c)
(c)
(a)
36
37
38
39
40
41
42
43
44
45
(b)
(c)
(d)
(d)
(c)
46
47
48
49
50
(b)
(d)
(a)
(b)
(c)
(a)
(a)
(b)
(a)
(c)
SECTION-A
PHYSICS
1.
2.
3.
(c) The magnetic field at a point due to a cur-
(d)
rent carying conductor is directly proportional to the current flowing through the
conductor.
The work done is stored as the potential
energy. The potential energy stored in a
capacitor is given by
l Q2
l
2 C
2
(s x 10-
18
)2
U=--=- x ~ - ~ lOO x l0-6
(d) Wave length, 'A, = 6000 A
= 6000 X 10-lOm
Slit width a = 0.1 mm = 0.1 x 10-3 m
In case of diffraction at single slit, the
position of second minima is given by
02
=2')..,
a
Substituting the values, we get,
e2 =2x6000xl0-10
0.lxlO-3
=0012
.
di
ra an.
= 32x 10-32 J
WWW.JEEBOOKS.INI
142
4.
9.
(a) Velocity in SHM is given by
V
10.
= ffi.Ja2 -y2
At y= 4 cm= 0.04 m, v = 3 m / s
11.
:. 3 = ffi✓a 2 - (0.04) 2
At y = 3 cm = 0.03 m, v = 4 mis
5.
TargetMHT-CET
(d)
(b) In an amplitude modulated wave side
band frequency gap is twice that of the
message signal.
(c) n 1u 1 = n 2u 2
....(1)
:. 4=ffi✓a 2 -(0.03) 2
....(2)
Dividing(2) by(l), we get a = 0.05 = 5 cm
(d) Since gravitational acceleration on earth is
:. n 2 =
12.
(a) Excitation energy L'lE = E 2 - E 1 = 13.6 z2
1
2
[i; - 2]
⇒ 40.8 = 13.6 Xi X z2 ⇒ Z = 2.
defined as g = GMe ............ (i)
2
e
Re
4
Now required energy to remove the electron
from ground state
mass of planet is Mp = Me & radius
80
2
R - Re
p
-4
13.
GMp
..)
- - ...... (11
S0 gp =
Ri
From (i) & (ii), we get
+l3.~Z = 13.6(Z) 2 = 54.4 eV.
(I)
(d) Friction is the retarding force for the block
F=ma=µR=µmg
Therefore, from the first equation of motion
v = u-at
2
0 = V-µg x t
Mp R e
ge
2
= - =2m/s
gp =ge - 2 x 5
Rp Me
14.
( as g= 10m/s2)
6.
(b) Magnetic moment, M = ml
⇒
F= G m1m2
M =m,
£
r2
where mis the polestrength.
= ✓(l/2) +(£/2) =
2
15.
£
✓2
(c)
(d)
R
z
~
273-20
= 253
T1- (273- 20) T1- 253
1518
:. T 1= - - =303.6
5
or, T 1= 303.6-273=30.6c;31°C
2
EoR
222
⇒ - x -- x - ⇒ P = -
-J2 z-h.
(2r)2
5T 1-(5 x 253) = 253
5T 1=253+(5 x 253)=1518
8.
Eo
G~nr3 p x ~nr3 p
3
3
So,
B =__.!!._=~= 0.50 x 2 = l /✓3
,fj
cos e cos 30°
Eo
µg
= _in:2p2r4
9
ie. Fcx:r4 ~
Coefficient of performance,
5=
7.
V
⇒ -=t
(c) The gravitational force ofattraction between
two identical spheres ofradius r is
Therefore distance between poles
2
n1:: = s[ 210] [fT = 50.
2
E0 R
.
E2
~
G1venX = RsoZ = v2R ⇒ P=--=
_o
2
4R
4R
L
_ (d)
16
~ = AD=5000 x lO-IOx0.9m
3 x 10-3
d
= J.5 x l04 m = 0.l5mm
WWW.JEEBOOKS.INI
MOCKTEST-5
17.
~)
143
A.~l:}
25O x 9.8
~
y = F l A= 5Ox 10-6
M If 0.5 x 10-3
27.
(c)
28.
2
(a) The simplified circuit is
4
The figure shows two independent
balanced wheatstone Bridges connected in
parallel each having a capacitance C. So,
19
·
20.
21.
22.
(d)
(b1~
eVs =
B x(assume)
2
IOV
he
T- Wo. ID.decreases, V increases
5
p
i:=Mdi or8=M[(4 - 2)]
dt
0.05
8xO.O5
M = - - - = 0.2 henry
2
O(assume)
We have to find I.
Let potential of point P be 0. Potential at
other points are shown in the figure apply
Kirchoff's current law at B where potential
is assume to be x volt.
(b)
(a)
(c)
V
i
J
k
=I
-2
0
4
2
-3
x-1O + x-1O + x-2O + (x-1O)-O =O
2
4
2
4
v = i[6-8]+ ][0+3] + k[4-0]
v =-2i+3]+4k ⇒ lvl= -✓29 units .
⇒
x - IO + 2x - 20 + x - 20 + 2x - 20 = 0
F= ma ⇒
⇒
6x = 70
a= F = 5xl04 = ~x10-3ms-2
m
Also,
v2 -
3xlO7 3
u2 = 2as
I=
⇒
23.
(a)
19.6xl010N/ m2
JO
cnet = CAB = 2C
18.
⇒
v2 - 0 2 = 2 x ~ x l0-3 x3=1O-2
3
⇒ v=O.l ms- 1
Angular momentum L = m (v x r)
29.
⇒
35
x = - volt
3
20- 35
3 = 25 A
4
12
(b)
2
2kg(: x r) =2kg(4tj x 5i-2t ])
2O x lO + 5 x O=(2O + 5) v.lJ'S ⇒ vsy, =8m / s
K . E. of composite mass
= 2 kg(-2O tk:)=2kg X-2O x2 rn-2 s-1 k: = -80 k:
= ~(20 + 5) x (8)2 = 8OOJ
2
24.
25.
(b)
(b) Under isothermal conditions, there is no
30.
31.
change in internal energy.
26.
(a)
Ek
I
2
= -rnv
2
or rnv
~
Ek m and
= ._i2
mv .J2Ek m
r=-=-'----
Bq
Bq
(a)
(a) Frequency(n)=4.2MHz=4.2 x 1O6 Hzand
speed of sound (v) = 1.7 krn/s= 1.7 x 103 mis.
32.
(a)
Wave length of sound in tissue
3
(A.) = ~ = l.7 x l0 = 4 x l0-4m_
n 4.2 x l0 6
lWWW.JEEBOOKS.INI
144
33.
34.
TargetMHT-CET
(b) By theorem ofparallel axes,
p
I =I + Md2
I = I~+ M (U2)2 = 10 + MI}/4
As - = constant or T ex: P, thus T becomes
T
(c) We can assume that three particles of equal
mass mare placed at the corners of triangle
42.
T/✓2
(c) A tuning fork offrequency 256 Hz makes 5
beats/second with the vibrating string of a
piano. Therefore, the frequency of the
vibrating
string
of
piano
is
(256 ± 5) Hz. i.e., either 261Hz or 25 I Hz.
When the tension in the piano string
increases, its frequency will increases. Now
since the beat frequency decreases, we can
conclude that the frequency of piano string
is251Hz
11 =0i+O}, r2 = bi+O] and r3 = 0i+ly
mir1+mzrz + m3r3
b.
h.
m1 + mz + m3
3
3
:. rem= - - -- - - - = - i + - j
i.e. coordinates ofcentre of mass is (
35.
¾,~)
(b) From the geometry of the figure, the angle
traverses about A and C are 0 and 20 re-
4
spectively. So
43.
(d)
n(2P)(~ )
2
8ri £
Q' =
Q
8
4
[ ·.- Q
e
20
ro A = - and roe = - = 2ro A .
t
t
36.
37.
38.
44.
(b) Here,
_!_ Q2
2C
2 2C
:. q=
✓
2.
]
FAB + FscDA = 0
⇒ FBCDA =-FAB =-F
(c)
(a)
(b) If q is the required charge, then
:i_
= n~ae
(": FAB
45.
= F)
(b)
Q
39.
(a) When a body falls through a viscous liquid,
its velocity increases due to gravity but after
some time its velocity becomes uniform
because of viscous force becoming equal
to the gravitational force. Viscous force itself
is a variable force which increases as
velocity increases, so curve (a) represents
the correct alternative.
40.
(b)
41.
(a)
e= d<J> = i_(NBA) = NA dB = 500 x l0-2
dt dt
dt
x 1 = 5.0V
Since VP2 = constan t,
w
46.
(c)
47.
(a)
p
48.
(d)
a µg
aµw
- ~- 1/ ✓
3 -
✓3
2
As surface area decreases so energy is
released.
Energy released = 4nR2T[n 113 - I)
where R = n 113r
E1
yp2 = 2VP'2
... P'--
-
µg -
Ez
4
cr(T1 - Tcj)
cr(Tf - Tcj)
(600)4 - (300)4
4
2: 1
4
(500) - (300)
✓
2
lWWW.JEEBOOKS.INI
MOCKTESf-5
49.
145
other molecule of carbonyl compound. In
the final step there is a exchange of proton
from acid to alkoxide ion to get stable
product.
(b) The incident angle is 45°.
Incident angle > critical angle, i > ic
:. sin i > sinic or sin 45 > sinic
. .
1
Sill l e = -
50.
(c)
n
. 450 1
1
1
> - or->:.sm
n
✓
2 n
Velocity of source
V5
= rro = 0.50 x 20 = 10 ms-
n' =-v-n = 340 x385
340+10
v+v5
H-lLt ~- H - ~ ~
r;:;
⇒ n>v2
~--'-Formaldehyde
I
(i)
(c)
= 374 Hz
In a fee lattice, the distance between the
cation and anion is equal to the sum oftheir
radii, which is equal to half of the edge
length ofunit cell,
More stable
Less stable
55.
(d) d
5-
d 3-
Edge length
= 2r++2r=(2 x 95 +2 x 181) pm
= (190 + 362) pm = 552 pm.
(a) 27 g of Al is obtained by charge of
3 X 96500C.
1 gm ofAl is obtained by charge of
54.
(b)
µ = ✓3(5)
11 11 11
(c)
H
I
2H-C=O
NaOH
0
II
H-C-0Na+CH 30H
Mechanism : First ofall, base OH- acts as a
nucleophile and attacks one of carbonyl
compounds to generate a hydroxy alkoxide
ion which acts as a hydride ion donor to the
eg
=
,hs = 3.87B.M.
I IJIJ
t2g
eg
µ = ✓4(4+2)
5. 12 X 1000
SBR is styrene-butadiene rubber, is a
synthetic rubber.
In the Cannizzaro reaction, two moles of
carbonyl compounds having no a-hydrogen
atom when treated with strong alkali undergo,
redox or disproportionation reaction.
rn
d 4- in weak ligand field
d
= 5.49 X 107C.
53.
I
t2g
:. 5.12 x 103 g ofAl is obtained by charge of
27
in weak as well as in strong field
11 11 11
3 x 96500 C.
27
X
eg
µ= ✓n(n +2) = ✓3 = 1.73B.M.
r+= 95 pm, r-= 181 pm
96500
I [I]
t 2g
2
= 3X
strong ligand field
11~11~11
i.e. r+ +r- =!!.. (wherea = edgelength)
52.
Formaldehyde
1
CHEMISTRY
51.
I
H
O- H
4
-
=
=4.89B.M.
in strong ligand field
11~ 11 11
I ITJ
t2g
µ= ✓2(4)
56.
✓2A
eg
=
✓8 =2.82 B.M.
(d) Molecularity of the reaction does not
57.
(b)
58.
(b)
influence the rate ofreaction.
Reduction ofalkynes with Na/liq. Nlf:i gives
trans-alkenes.
The face centered cubic unit cell contains 4
atom
Total volume of atoms
= 4 x ircr 3 = ~rcr 3
3
3
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TargetMHT-CET
146
59.
(d)
~
BF4 hyl:ridisation sp3, tetrahedral structure.
V
NH! hybridisation sp 3 , tetrahedral
0
(i)KMn04,0H-
~
O
v coOH
heat; (ii) H+
+ CO2
structure.
60.
CH CN
(d)
3
Reduction> CH
- CH - NH
3
2
J
65.
(d) It forms calcium and magnesium complex
with Ca2+ and Mg2+ ions present in hard
water.
66.
(c)
67·
(a)
2
HONO
CH3 -CH2 -OH+ N2 + H2 O
61.
2
Fe2+in[ Fe(H2O)6 ] +
(c)
3d
4s
4p
4d
⇒
:l- 1----r-............
11~111111111 [TI] I "E. 1-1~ 1·n. 1 .-:,I-u~l,.,..,
~
2
Hyb. : sp 3d
68.
(b)
2 x 0.22
0.0591
0
E = - - IogKeq;logKeq
2
0.0591
7.44 or Keq:::; 2.8 x 10
2XeF6 +SiO 2 ~
(glass)
7
2XeOF4 +SiF4
(explosive nature)
Colour: Pale green µ = 4.9 B.M.; octahedral
4
Fe 2+in [Fe(CN6)] -
3d
11~ 11~ I1~ I'1l- 1·H-1
CJ I"E-1"E- I"1l- I
~
Hyb.: d
62.
2
2XeO 2 F2 + SiO 2 ~ 2XeO 3 + SiF4
4p
4s
(explosive)
69.
r = k[ A] or k = [A]
Colour: Yellow; µ = O; octahedral
(a) Chalcopyrite: CuFeS2
⇒ k= l.5xl0-
2
Fool's gold : FeS 2
Further, t112
70.
(a)
_ 0.693 _ 0.693 _ 23 l
- ------k
3 x 10-2
.
.
mm
In bauxite ore, only Alz03 reacts with cone.
NaOH and forms sodium meta aluminate.
This further dissolves in water.
Aiz03 + 2HzO + 2NaOH
K X 1000
64.
1000
.·A
. eq
xN
N
(b) Alken es are oxidatively cleaved by hot alk.
KMnO 4 in the following way. The terminal
CHz group(= CH2) is completely oxidised
to CO2 and HzO ; a monosubstituted atom
of a double bond is converted to aldehyde
which is further oxidised to carboxylic acid,
and the disubstituted atom of a double
bond is oxidised to ketone.
=3 x 10-2
0.5
Camalite : KMgCl3.6HzO
63.
products
r
s/
Bauxite : AiiO3.2HzO
(b) Specific resistance = x
Specific conductance ( or conductivity)
➔
(b) For a first order reaction, A
SOOK
35 bar
2NaAIO2 + 3HzO
NaA1O2 + 2HzO ➔ NaAl(OH)4
71.
72.
(d) Equanil is an important medicine used in
depression and hypertension.
(a) 1° amines (aliphatic and aromatic) react with
CHCl/ KOH to yield isocyanide (foul
smelling) This is known as carbylarnine test
which is not given by 2° and 3° amines.
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MOCKTEST-5
73. (c) Strong base has higher tendency to accept
the proton. Increasing order of base and
hence the order of accepting tendency of
proton is
I- < HS- < NH3 < RNH 2
74.
(a) Mg 2+ +Na 2CO 3 ~MgCO 3 +2Na+
147
79.
80.
lgeq.
lgeq.
1 geq. ofMg2+= 12gofMg2+= 12000mg
= lOOOmilli eq. of Na 2 CO 3
(d) All the given species contains 10 e- each
i.e. isoelectronic.
For isoelectronic species anion having high
negative charge is largest in size and the
cation having high positive charge is
smallest.
(b) Non superimposable mirror images are
cal led optical isomers and may be described
as 'chiral' . They are also called enantiomers
and rotate plane polarised light in opposite
directions.
:. 12mgMg2+ = 1 millieq.NaFO3
75.
(c)
0
C~H
H2S04, Hg2+
9H
0 -C = Ctti
~
~
o -C - CH3
81.
[A]
0
6
{;,CH
Due to electronegative nature
transferred toward benzene ring
(b)
PC15 +H2O~POCl3 + 2HCl
(A)
Red P / HI
Cleavage of
ethers
C 2H 5 OC2Hs ----➔ 2C2Hsl
Red P / HI
Red uction
2C 2H6
Ethane
(d) Solution X is unsaturated so v.p. will be
more, solution Y and Z are saturated so v. p.
ofY = v.p. of Zand 2 gm of solute would be
present in form of solid in system Z.
83. (b) The more readily soluble and easily
liquefiable gases such as~' HCl and SO2
are adsorbed more than the so called
permanent gases like 0 2• This is due to the
van der Waals or intermolecular forces
which are involved in adsorption.
84. (b) Peptide bonds are present in enzymes.
82.
H 2 S04 , Hg2•
of > C - 0 , 1t electrons are
76.
(a)
(8)
POC13+ 3H2O ~ H3PO4 + 3HC1
(B)
77.
78.
(b)
(b)
(C)
Solvent having high cryoscopic constant
(camphor) can be used in determination of
molecular masses of organic compounds
like naphthalene, anthracene etc. , by
cryoscopic method.
E
0
2_
J+
Cr20 7 /Cr
= 1.33 V;
85.
(d) Lucas reagent is anhydrous ZnC½ and cone.
HCI. It is used to distinguish between I O , 2 °
and 3° alcohols.
3° alcohols ➔ Immediate turbidity
2° alcohols ➔ Turbidity after 5 minutes
1° alcohols ➔ No turbidity at room temp.
W WW.JEEBOOKS.INI
148
TargetMHT-CET
CH3CH(Br)CH2CH2CH3
CH3
CH 3
-b- OH is a tertiary alcohol, hence
CH 3CH = CHCH2CH3
2-Pentene (maj or) trans
I
CH3
86.
87.
88.
89.
90.
91.
92.
+CH 2 =CHCH2CH2CH3
it will give fastest reaction with Lucas
reagent.
(d) Amalgams are alloys having Hg as one of
the constituents.
(a) Same as above, in Ph 3C+, +ve charge can
delocalise over three benzene rings.
(d)
Aff
= L'.U + L'.ngRT ; L'.ng = I in (d);
L'.ng
1-Pentene(minor) cis
Since trans- alkene is more stable than cis,
thus trans-2-pentene is the main product.
95.
(a)
6
( )
9
•
In other cases.
(a) Given drug is histamine which is used as
Antacid.
(c) Methyl amine is a stronger base than
ammonia due to +I effect. The alkyl groups
which are electron releasing groups increase
the electron density around the nitrogen
thereby increasing the availability of the
lone pair of electrons to proton or lewis acid
and making the amine more basic
NR:i
c~~
Kb= 1.8 x 10- 5
44 x 10-5
(b) This method is not applicable for the
preparation ofaryl halides because the CO bond in phenol has a partial double bond
character and is difficult to break being
stronger than a single bond.
(d) The correct structure of thymine is
B
97.
OH
98.
N~
H,
HO~)
Thymine (T)
93.
94.
C
=0
Equivalent conductance of an electrolyte
at infinite dilution is given by the sum of
equivalent conductances of the respective
ions at infinite dilution.
(c) Potassium ethoxide is a strong base, and 2bromopentane is a 2° bromide, so elimination
reaction predominates
99.
An isolated/cc cell is shown here. Each
face of the cell is common to two adjacent
cells. Therefore, each face centre atom
contributes only half of its volume and
mass to one cell. Arranging six cells each
sharing the remaining half of the face
centred atoms, constitutes f ee cubic
lattice. e.g., Cu and Al.
(d) The products of the concerned reaction
react each other forming back the reactants.
XeF6 +3H 2O ~ XeO3 +6HF ·
(a) Only I O alkyl halides (i.e. C~Br) undergo
SN2 reaction.
(b) Since the compound is formed by hydration
of an alkene, to get the structure of alkene
remove a molecule ofwater from the alcohol.
(c)
CH3 CHCH 3
I
OH
-H 2o l CH2
= CHCH3
Propylene
Isopropyl alcohol
100. (d)
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MOCKTEST-5
149
SECTION-8
MATHEMATICS
1.
(cl) n(A) = 1000,n(B) = S00,n(A n B)~ 1,
n(A u B) =p;n(AuB) =n(A)+ n(B)-n(AnB)
p = 1000 + 500-n (AnB)
1 :,;n(AnB):;;500
2.
Hencep:,; 1499 and p ~ 1000
1000 :,;p:,; 1499
(cl) D(j) = R , D(g) =R- {O}
From
~QLC, QL = CQ sin 60° =
1
D(h) = R-{0}andh(x)=f(x)g(x) =xx - = l
3.
:. QR=2QL= ✓
Now, area of MQR
X
h(x) = 1 if and only ifx ER - {0}
3.
(c)
⇒ tan(3x-2x)=tan
⇒
4.
tanx
7t
=tan- ⇒
4
3✓3 (g2 +f2 -c)
=
4
-
4
7t
x=(nn+ 4'
n=l,2,3, ......)
7.
(a)
lz 11=
(a.+3p)2 =(a.-3p)2 +(a.-13)2 +(a.+13)2
⇒ a. 2 -6a.13+13 2 =0 ⇒ a. =3±2✓
2
=
p
a., P must be rational number
8.
~ cannot be irrational.
2
I=
✓~+2= ✓3
4 4
lz1 z2i= lz1I lz2i= ✓
2·✓
3 =✓
6
(cl) The 7th term from the end= 5th term from
4
[·.-GX-%) = -1]
9.
Lines I and II intersect at the point (1, 2) and (1, 2)
does not belong to III. Hence, the lines are not
concurrent, i.e., they form a right angled triangle.
(b) Given circle is x 2 + y2+ 2gx + 2fy + c = 0
...(1)
Let C be its centre and PQR be an equilateral
ea
✓3[cos~+isin~]
beginning
13
(b) Lines II and Ill are at right angles
triangle inscribed in the circle, then C
.fi. and z2 =
✓3[]._+i
✓23]·' lz
2
T5 =
6.
z 1 = ✓2[cos¾+isin¾]
= ✓2[~+i ~]=l+i
(cl) Let a = a. - 3P,, b = a. - P , c = a.+ P and
d =a.+ 3P then
5.
✓g 2 +f 2 -c
4
4
7t
2
✓3. QR2 = ✓3 ·3(g 2 +f2 -c)
=
.
tan 3x - tan 2x
G1ven - - - - - = 1
1 + tan3xtan2x
✓3 ✓g 2 + f 2 - c
(-g, - f)
and radius ofthe circle CQ = ✓g 2 + f 2 - c
10c4x 6
(-4)
X
=
10c4 . 24 (~)
X
(b) The equation is
abc 2 x 2 +(3a 2 c+b 2 c)x-6a 2 -ab+2b 2 =0
Discriminant
D = (3a 2 + b 2 ) 2 c 2 -4abc2 (-6a 2 -ab+ 2b 2 )
= 9a 4 c 2 +b4 c 2 + 6a 2b 2 c 2 +24a3 bc 2
+4a 2 b 2 c 2 -8ab3c 2
4 2
2 2 2
4 2
3
= 9a c + 16a b c +b c +24a bc
2
-8ab3c 2 -6a 2b 2c 2
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150
TargetMHT-CET
= (3a 2 c + 4abc - b 2 c)2
Since the discriminant is a prefect square,
therefore the roots are rational provided a, b, c,
are rational.
10.
(a)
LetTr =
13.
(cl) Let ll =
a 2 +2a 2a+ l 1 a 2 +2a-32a-20
2a + 1 a + 2 1 = 2a - 2
a -1 0
3
3
1
3
3 1
r
2
I+ r + r
[Applying R 1 ➔ R 1 -
4
2
.
a +2a-3 2a-21
Za _ 2
a _ 1 [Expanding along C 3]
l
=
T
r
=I
I
I{
1
}
2r
2 (r 2 +I)2 -r2 2 r 2 -r + I + r 2 + r +I
_ ,(a+3)(a- l) 2(a -l), _
2 la+3 21
2(a- 1)
a-1 - (a-l)
2 I
I
= -Car -ar+I)
2
I
where ar = - -(r- l)r + l
14.
= (a-1)2.(a + 3-4) = (a-1) 3
Clearly, ll> 0 ifa> l; ll= Oifa= 1 andll < Oifa < 1.
(b) The function can be continuous only at
those points for which
.
15.
:t
a-- r=l
11.
Tr = Lim.!..{1
n--- 2
⇒ ¾[~ ! ~m
:Ex
M=-=50 :.:Ex- = 5000
n
12.
X
⇒ 1[~ : ~M~ l ~H~ I~l
l
} = _!_
2
(n + l)n + 1
(b) Given, n = JOO, M = 50, Median = 52
:. Correctedmean =
= cos X ⇒
TI
= nn + 4
(a) As A is an orthogonal matrix,
AAT = I
Sill X
:. Lim
Ri and}½ ➔ }½ - RiJ
~2
5000-100+ 110
JOO
= 50.10
Median remains same.
(a) Total no. of arrangements of the letters of
the word
0
9
J[~ r ~l
1
a +4+2b
2a+2-2b
2a +2 -2b a 2 +4+ b 2
UNIVERSITY is ~ .
2!
No. ofarrangements when both I's are together= 9 !
So. the no. of ways in which 2 I's do not together
-[~~ ~]
= 10! -9!
2!
~ -91
.
..
2!
.
:. Requrredprobab1hty = lO!
⇒
⇒
10!-9! 2!
lO!
⇒
16.
2!
10 x 9!-9!.2!
10!
9![10-2)
10 x 9!
8
10
4
5
(b)
a + 4 + 2b= 0,2a + 2-2b=Oanda2 + 4 + b2 = 9
a+ 2b+4 = O, a-b+ 1 = Oanda2 + b2 = 5
a =- 2, b = -1
We have, y2 = 2ax
..(i)
Put x =
i ;y2
= 2a ( ~)
⇒ y=± a
lWWW.JEEBOOKS.INI
MOCKTEST-5
151
y(-1-) = f
:. Thepointsare (i,a) and (i,-a)
dy
⇒ _L = e 3xdx + a = ~+a
x+l
3
a
y
=2a ⇒ -=-
dx
⇒ _i2:'.__ = e3x + c c = 3a
At (~,-a) ; dy =~=~ = -1 =m2 (say)
dx y -a
2
x+l
'
(b) Consider the following events :
A : Father has at least one boy
B : Father has 2 boys and one girl
Then, A = one boy and 2 girls, 2 boys and one girl,
3 boys and no girl A nB = 2 boys and one girl.
Now, the required probability is
Since m 1m 2 = - 1, the two tangents are at right
angles.
P( A I B) = P( A n B)
P(A)
20.
dy a a
a )
At ( - ,a ; - = - = - = 1 =m 1 (say)
2
dx y a
17.
3x
f
Differentiating (i) with respect to x, we get
dy
2ydx
e3x(x+l).-l-dx+a
x +l
x+l
(a)
r4 f a
y= Jo
~
(a·X-\/4a-x)dx
21.
(a)
0
3
2
16a
½~ ·:
3
-1H~rl
22.
18.
Putting the value of a in x2 + 2x- a = 0, we get its
roots i.e., --4 and 2.
(a) We have, 1 ~ sin- 1 cos-1 sin-1 tan-1
19.
x~2
⇒ sin 1 ~ cos- 1 sin- 1 tan- 1 x ~ 1
⇒ cos sin 1 ~ sin-1 tan- 1x ~ cos 1
⇒ sin cos sin 1 ~ tan- 1 x ~ sin cos 1
⇒ tan sin cos sin 1 ~ x ~ tan sin cos 1
x E [tan sin cos 1, tan sin cos sin 1]
(c)
The given equation is
7t
dy _--2:'.._ = e3x(x + 1)
dx x+l
=
0
a4
)
dx
=f (1x(l+x+x)-1
6
)
]4/a -2[(4ax)3! 2]4/a
0
x(l+x
6
0
_!_ = [ ax2
3
f -x6-7 dx= f - x6- dx
6
x+x
~
dx
-1 = f4 /aaxdx- f4 /a\/4ax
3
=_!_.
f _!_dx-f
x
1
- -dx = lnlxl-p(x)+c
x+x7
(c) Givenplanesare x+2y -2z+l=0
and 2x+4y-4z +5 = 0
These plane are parallel Put x
= 0,y = 0
in
1
2
so, co-ordinate of a point on the plane
x+2y -2z+l=0 ⇒ z= -
x +2y -2z+ 1= 0 are (
o,o,½)
:. Required distance= Length of the
perpendicular for ( 0, 0,
½)
on the plane
(2x+4y-4z+5 = 0)
1
0+0-4x-+5
2
✓4 + 16+16
The solution is
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152
23.
(b)
31.
Ifa=2i-2}+k and e= - i+2k
2
focus from directrix
2
lcl= ✓C-1) +2 = ✓1+4 = ✓5
leI_;= .Js.c2'i -2] +k)
le1.a =2✓5'i-2✓5J +Jsk
24.
(b)
TargetMHT-CET
(d) Length of latus rectum= 2 x distance of
32•
(d)
z
7 -i
4i
=3-
X
= 21 + 25i + 4 =
✓
x = cos 0
x E ( 0,
½) or ✓x = cos 0
or 0 E (
¾, ~)
or 20 E
E (
( ~,
0,
16 + 9
~J
ll-4+3-241
= 2 x ' - - - - ~ = 10
5
3+ 4i
3 + 4i
25(1 + i) = (1 + i)
25
z 14 = (l+i)14 = [(l+i)2]7
= (2i)7 = 27 /
7
= -2 i
2
n)
33.
or f(x) = 2sin-1 ✓1-cos2 0 +sin- 1 (2✓cos 2 0sin 0)
(c)
(¾rx+IO-x < :
2
2
⇒ (¾rx+IO-x < (¾Y
= 2sin-1(sin 0) + sin-I (2sin 0cos0)
25.
26.
27.
28.
29.
= 20+sin- 1(sin20) = 20+n-20 = n
orf(x) = 0.
(c) We have, R = {(l, 3); (I , 5); (2, 3); (2, 5); (3, 5);
(4,5)}
R- 1 = {(3, l); (5, 1); (3 , 2); (5, 2); (5, 3); (5,4)}
HenceRoR- 1 = {(3, 3); (3, 5); (5, 3); (5, 5)}
(d) S(p,q,r)=(~ p) v [~(qAr)]
S(~ p, ~ q, ~ r) =~ (~ p) v [~ (~ q A ~r)]
= p V [~ (~ q) V ~ (~ r)] = p V (q V r)
(c) ·: PA 2 -PB2 =k
:. [(x-2)2 +(y-3)2 + (z-4)2]
-[(x+ 2)2 + (y-5) 2 + (z+ 4)2] = k
or-8x+ 4y -16z- 16 = k,
(b) Desired number = n 3 - np3
(c) (150 -h)cot30°=60
B
⇒
150-20✓3
h=
iE
⇒
(asbase(3/4) < 1)
6x+ I0-x2 > 3
x 2 -6x-7 < 0
(x+ 1) (x - 7) < 0
Thus, integral values ofx are 0, 1, 2, 3, 4, 5 and 6.
34
_ (c)
sinA = sin0--B) ⇒ sin(!3+C)
sinC sin(!3-C) sin0-+ B)
sin0-- B)
sin(!3- C)
⇒ sin 2 B-sin 2 C = sin 2 A - sin 2 B
⇒ sin 2 A, sin 2 B, sin 2 C and hence a 2 ,b2 ,c 2
35.
areinA.P.
(a) Let the required three numbers ofG.P. be
a
- , a andar.
r
Then, their sum =!!..+a + ar = 38
r
⇒
al( 1
2')
+rr+ r j=38
... (i)
0
V)
___ 1
60m
30.
0
(c) Any point on the line 7x + 56y = 0 is
( XJ, -
a
product = - x a x ar = 1728
r
a 3 = (12) 3
a = 12
11
⇒
...("")
Substitute the value of a, in equation (i), we get
2
75:1). i.e., ( X1, - X81 J
12 x ( l +\+r
⇒
:. The perpendicular distance p and p' are
3x 1 -
4x 1
-
p=
8
5
⇒ p=p'
~ and p'=
2
5X1
12x 1
+ -8
13
~
2
l
= 38
6+6r+6r 2 =19r ⇒ 6r2 -13r +6= 0
2
3
:. r=-or3
2
Hence, therequirednumbersare 18, 12, 8or8, 12, 18
Greatest number = 18
⇒
(3r-2)(2r - 3) = 0
IWWW.JEEBOOKS.INI
MOCKTESf-5
36.
153
(a) Since as per the give condition x > - 1, so
xis non negative integer,
y > -2 soy=-1 + band similarly
Z > 3 SO z = - 2 + C
or (x)+(- l + b) +(-2+c)=23
40.
(a)
j
C100X
100
+ .... +
j
C200X
......(i)
Also we know A- I == adj(A)
IA I
'
.......(ii)
:. By comparing (i) and (ii) IA I= k
3 -2
I A I= 1
⇒
2
1
0
200
4
-1
1
= 3 (2 + 1) + 2 ( I + 0) + 4 (1-0) = 9 + 2 + 4 = 15
:. Coefficient ofx 100 in the expansion of
41.
(1 + x)I == JC100
~1]
1
1
and A -I == _!_adj(A)
k
{l+x) j _
-1+ j C1x+ j C2 x 2 + j C3x 3 + ..... .
+
[i -,i2
0
or x+b+c=23
and we need to find the number of non negative
integral solution of the equation x + b + c = 23
which is
23+ 3- tc3 - I = 25C2 = 25C23
37.
If A ==
(c)
(b) ./(0) = sin O= 0, /(0+) ➔ o+
/(0-) == lim sin(x 2 -3x) == lim sin(h2 + 3h) ➔ o+
x➔O-
Coefficient ofxIOO in the expansion of
200
h ➔O
Thus, /(0+) > /(0) and /(0- ) > /(0).
.
I: (1 + x)1 will be
J=O
200
equal to I: JCwo
Hence, x = 0 is a point ofminima.
7t
2
j=IOO
42.
== tooc,oo +'°' C100 +102 c,oo +
····· .... +
200
I=
(c)
J[(x+n}3+cos2(x+31t)]dx
371
2
c,oo
Put x + 7t == t
== 200]
- 200
C100 ( 100
38.
(b) We have,
=
!
"
J
2
3
J
2
2
[t + cos t)dt = 2 cos tdt
I=
! {(✓x l J}
"
0
2
+
7t
2
{x+~+2}
d -I
d
d
== dx (x)+ dx (x )+ dx (2) = 1+ (-1) x-2+ 0
=
f(I + cos2t)dt == f +O
0
43.
We can write the given expression
(d)
....
--
.......
--q)}j +{k .(p
== {i.(p X q )}i+{j.(p
= 1-_!_
39.
"
2
...
X
x2
(a) ho (go f) (x) = h [go f) (x)]=h[g(f(x)]
= pxq
= h [g (x2)] = h (tanx2) = log (tanx 2)
Since for any vector -;,
At x ==
1; ,
, . . - - ,.
X
q )}k
a =(a .i)i+(a .j)j+(a .k)k
value == log [tan(¾)] = log 1 = 0
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154
TargetMHT-CET
b
44.
(d) Given
x 2 -1
For x > 1, f(x) = ---::-- - x 2 -2x+l
Jf(x)dx = Jb 2 + 1- ✓2
I
45.
x➔ I +
X
f(b) = ~ ⇒ f(x) = ~
2
\fb +1
\fx 2 +1
(c) Obviously,P=x+3ywillbemaximrnat(O, 10).
:. P=0 + 3x 10 = 30.
:. The function is not continuous at x = I.
48.
(a) Put x = tan 0 ⇒ dx = sec 2 0d0
I=
=
y
2x +y=20
J
e
e I + tan 0 + tan 2 0 .sec 2 ecte
1+ tan 2 0
2
e (tan0+sec 0)d0
f
8
0
49.
-I
= e tan0+c =xe1an x +c
(b) The angle 0 between the two lines
X - Xt
46.
0n
DnD ~J Dn
=2
A 3 =22 A,
:. An =2n-1
= 2A
A 4 = 23A
Dn
⇒
AIOO = 2100-1 A
:. A100 = 299A
47.
For x < 1, f(x) =
(d)
.
1
x ➔C
2
50.
x 2 -I
x+l
=- x 2 + 2x-3 x + 3
= Z-Z1
2 x 2 +2x 2+(-2)xl
· cos e = --;;===-;====..
✓4 + 4 + 1-v'4+4+1
4 _
⇒
yl
a 1b1 + a 2b2 + a3b3
cos e = -;=====--;====
==
/2
2
2/2
2
2
-va 1 + a 2 + a 3 -vb1 + b2 + b3
Now in the given equation: a 1= 2, 82 = 2, a3 = -1
b 1 = 1, b2 = 2, b3 = 2
A3 = 2 [l11l] ' A- 23[I11I]
2
=y-
X- X2
y - y2
Z-Z2
and - - = - -= - - is given by:
b1
b2
b3
(b) LetA=
A2 =
x-1
:. lim f(x) = ao
Differentiate with respect to b
b
X+I
1
0 = cos- (~) ·
(c) Desiredprobability= probabilityofgetting3
sixes in first 9 throws x getting six in the 1Othrow
(1)6 (5)6 6I
3
-_ 9 C 3
-
6
-
x-
:. ltm f(x)=-
lWWW.JEEBOOKS.INI
(Mock Test-6)
Answer KEYS
SECTION-A
PHYSICS
1
2
3
4
5
(a)
(a)
(d)
(a)
(a)
6
7
8
9
10
(b)
(b)
(b)
(b)
(d)
11
12
13
14
15
(b)
(c)
(a)
(b)
(a)
16
17
18
19
20
(c)
(b)
(d)
(d)
(c)
21
22
23
24
25
(a)
(c)
(d)
(b)
(b)
26
27
28
29
30
(b)
(a)
(b)
(b)
(b)
31
32
33
34
35
(b)
(b)
36
37
38
39
40
81
82
83
84
85
(b)
(a)
(d)
(d)
(d)
86
87
88
89
90
31
32
33
34
35
(d)
(c)
(a)
(a)
(c)
36
37
38
39
40
(a)
(b)
(b)
(a)
(b)
(c)
(b)
(b)
41
42
43
44
45
(c)
(a)
(c)
(b)
(a)
46
47
48
49
50
(d)
(c)
(c)
91
92
93
94
95
(a)
(b)
(d)
96
97
98
(b) 99
(d) 100
(a)
(c)
(d)
(c)
(d)
41
42
43
44
45
(b)
(c)
(a)
(c)
(c)
46
47
48
49
50
(a)
(c)
(a)
(b)
CHEMISTRY
51
52
53
54
55
(c)
(c)
(b)
(b)
(c)
56
57
58
59
60
(b)
(d)
(b)
(b)
(a)
61
62
63
64
65
(b)
(b)
(c)
(d)
(b)
66
67
68
69
70
(d)
(c)
(a)
(c)
(b)
71
72
73
74
75
(d)
(d)
(a)
(b)
(d)
76
(a)
77
(b)
78
79
80
(b)
(a)
(c)
(c)
(b)
(a)
(b)
(a)
SECTION-B
MATIIEMATICS
1
2
3
4
5
(d)
(c)
(a)
(a)
(a)
6
7
8
(b)
(c)
(c)
9
(b)
10
(d)
11
12
13
14
15
(c)
(d)
(a)
(d)
(a)
16
17
18
19
20
(a)
(d)
(c)
(d)
(c)
21
22
23
24
25
(b)
(d)
(b)
(d)
(d)
26
27
28
29
30
(c)
(c)
(b)
(b)
(a)
(b)
(c)
(a)
(d)
(b)
(b)
(a)
(a)
SECTION-A
~ = ~ = 0.2R = 0.2
PHYSICS
g
1.
(a) Frequency does not depend upon radius.
2.
As length is doubled, fundamental
frequency becomes half.
We know that,
(a)
R
R
g'=0.2g
3.
(d)
4.
(a) Wavefront is the locus of all points, where
5.
the particles of the medium vibrate with
the same phase.
Magnetic dipole moment
M=m x £,M'=mx r
From figure
(a)
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156
11 •
. = -M c when VCE is constant.
(b1~ Current gam
Ms
2 ·5 x l0-3 = 0.l x 103 =100
25 x 10-6
[Af8 = 125 µA-100 µA = 25 µA
Afc = 7.5 mA-5 mA = 2.5 mA]
£=
nr
or
3
12.
3e
(c)
0.2
1t
:.vr,
2
13.
8.
(b)
(b)
2
2
mv 1
As P 1V 1 = P 2 V2 or
14.
~ - ✓ Wo
9.
(b)
15.
16.
➔
A · B =0
/\I\
I\
(a)
(c)
Ifthe current increases with time in loop A,
then magnetic flux in B will increase.
According to Lenz's law, loop-Bis repelled
by loop -A because current in loop B will be
antiparallel to that in A.
(2i+3j+8k ) · (4j-4i +a k ) = 0
-8 + 12 + 8a= 0
10.
(d) Density, p = M
V
,t:,,.
___E_
x lOO
p
P1V1
=V
~u1 = ~ U2
3
1\/\/\
P2
= P x2 V = 2 P
V
(b) Change in internal energy do not depend
upon the path followed by the process. It
only depends on initial and final states i.e.,
_ .!_
9W0
For two vectors to be perpendicular to each
other
➔
= 0.lm / s
(a) Here, initiallyP 1 = P, V 1 = V + V = 2 V ;
Finally, P2 = P ; V 2 = V
=2W0 -W0 =Wo and
v2
9ri
= (10.5-1.5) ⇒ vr, =0.2 x i_
(1 9.5-1.5)
2
18
vT2
(b)
1
2r (d 1 - d 2 )g
= ---=---~-
1t
1t
7.
2
vT
r= -
m x 3£
3
so, M' = m x r = - - = -M
6.
.
.
Termmal velocity,
17. (b) r=
1
⇒ a=--
mvsin e
3 X 105 Sin 30°
Be
0.3 x10 8
2
3x 105 x .!..
- - --'2
"- = 0.5 x l0-2 m = 0.5cm.
7
3x l0
= _!!_
nr2£
[Mf + - + -M,]
= -
M
2&
r
£
x l00
18.
. energy = -1 x F x x
(d) Elastic
2
F = 200N, x= l mm= 10-3 m
0.003
0.005 0.06 ] 00
xl
=4
- + 2 - -+ [0.3
0.5
6
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MOCKTESf-6
19.
(d) Given; speed = l Omis; radius r = l Om
60-T = T / 2 ⇒ 120-2T=.:!:_
20
40
2
Angle made by the wire with the vertical
102
v2
tan0=-=--=l
rg lO x lO
F
µ= R
⇒
re
0=45°=4
mg sin a
20.
(c)
21.
(a) The magnetic dipole moment ofdiamagnetic
mgcosa
⇒ T = 48°C
25. (b) Binding energy
= 117 X 8.5 + 117 X 8.5-236 X 7.6
= tan a
= 234 X 8.5-236 X 7.6
= 1989-1793.6 = 200MeV
Thus, in per fission of Uranium nearly 200
material is zero as each ofits pair ofelectrons
have opposite spins, i.e., µd = 0.
Paramagnetic substances have dipole
moment > 0, i.e. µP 0, because of excess
ofelectrons in its molecules spinning in the
same direction.
*
Ferro-magnetic substances are very strong
magnets and they also have permanent
magnetic moment, i.e. µf 0.
Wavelength for which maximum obtained at
the hole has the maximum intensity on passing. So,
MeV energy is liberated
26.
B
(b) Modulation index = A
B = 25,A= 60
⇒ M.l. = ~ = 0.416 ⇒ m%
= 41.6%
60
*
22. (c)
27.
(a) As the ball, m = 10 g = 0.01 kg rebounds
after striking the wall
:. Change in momentum=mv-(-mv) =2mv
Inpulse = Change in momentum = 2mv
tlD
x= - d
o-
:. v = Impulse= 0.54 N s = 27 rn s- 1
2 x 0.01 kg
2m
o-
xd 1 x 1 3 x 0 .5 x I 3
A, - - ------- nD -
n X 50 X 10-2
1 X 10-6
1000nm
n
n
28.
(b) A = 90° -0
.
6/5 4
cos0 > smec = - = 2/3 5
n = l, 11, = 1000 nm ➔ Not in the given range
(0c is critical angle)
n = 2, A= 500nm
23.
24.
(d)
(b)
i5
e < cos- 1 = 37°
Apply Newton's law of cooling,
~T
-t= -k(Tav -T.e)
20
IO= -k (70-30)
A
B..__----~C
29. (b)
.......... (1)
60 -T =-k(60+T _ 30)
10
2
.......... <2)
30.
(b) IA
= 1+41+2✓I x 4Jcosn l 2 = 51
and 18 = 1+41 + 2✓1 x 4Jcosrc=f
Divideeq. (2) byeq. (1)
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31.
32.
. 1s
. .m d epen d ent o f
B = -µoi an d so 1t
2nr
thickness.
The current is same in both the wires, hence
magnetic field induced will be same.
(a) Thereactance of inductor, XL= roL
(b)
The reactance of capacitor, X e = _l_
roe
where ro = 27tll & n is the frequency ofA. C
source.
33.
34.
(b)
(b) The surface tension of oil is less than that
of water, so the oil spreads as a thin layer.
35.
(b)
176(V-Vo)
v-22
'"A
5 16 20
-=-x - = '"Ao 36 3
27
40.
= 165 V+ Vo
(b) By conservation of linear momentum
V
2mv 1=
Here v = 3 30 mis, after simplifying, we get
36.
v0 =22m/s
(a) Maximum velocity,
Vmax
=aro ⇒ vmax
⇒ T=
37.
✓2mv ⇒
v1 =
F2
V
m
As two masses
of each of mass
2n
=axT
,__ _ m
_ v
m
move perpendicular
to each other.
Total KE generated
3
2na =2x3.14x7xl0- ~o.Ols
Vmax
4.4
2m
1
I
I
2
2
2
= -mv +-mv +-(2m)v1
2
2
2
(b) Orbital velocity of a satellite in a circular
orbit ofradius a is given by
mv 2 3
= mv2 +--=-mv 2
2
41.
38.
(c)
Given, refractive index, µ =
mg sin0 = fs(for body to be at rest)
4
3
According to Brewster ' s law when
unpolarised light strikes at polarising angle
ip on an interface then reflected and
refracted rays are normal to each other and
is given by:
⇒ m
x 10 x sin 30° = 10
⇒ mx
taniP = µ
.
... Ip=
tan-I
(c)
2
5 = IO ⇒ m = 2.0 kg
(4)3
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MOCKTESf-6
42.
(a) The equivalent circuit diagram as shown in
46.
the figure.
(a) Force acting on conductor B due to
conductor A is given by relation
F =
µol1f2l
~~~
2nr
/-length of conductor
r-distance between two conductors
7
:.F = 4n x !0- x !O x2x2 =S x 10_5 N
2 x nx0.I
The equivalent capacitance between A and
Bis
C
eq
47.
constant)
If diameter is made four times then force
required will be 16 times, i.e., 16 x 103 N
= 2µF x 3µF + 2 F=~ F
2µF+3µF
µ
5µ
Total charge of the given circuit is
16
Q =-µFx5V= 16µC
l
2
= YxA x L ⇒ F ex: r (Y., landandLare
F
(b)
48.
(d)
49.
(c)
Applying Kirchoff's loop law in AB P2P 1A ,
we get
5
-2i + 5-10 i1 = 0
.....(i)
Q 1 =(2µF)x5V=10µC
Q2=Q - Q 1 = 16 µC- 10 µC =6 µC
Voltage between B and C is
B
P,
!"""'-" ...... !
= Q2 = 6µC = 2 V
BC 3µF 3µF
V
SY!
100
2n1
i
=.......... ·-······ '
43.
(c)
2
=
44.
½x lOx
(2;r
Again applying Kirchoff's loop law in P2
CDP I P 2 weget' lOi I + 2 -i +i I = 0 -...(ii)
2
2
2
[10 -5 ] = 375 n erg
5
From(i) and (ii) Iii1 +2 - [ - ~0ii
]=o
(b) As intensity of wave ex: (amplitude)2
50. (c)
1max
I nun
.
45.
D
A
. energy K = 1 mm 2(a 2 - y 2)
Ki netlc
(a1 +a 2 )
(a1 - a2)
2
2
16
=-
h = 2a cos 0 ⇒
rpg
0
ex: ~
cose
..
⇒ ratio IS 4 : 1.
4
!O x !
cosl35°
1
= - - x - - - - ~cos00 - 3.l x l3.6
6
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CHEMISTRY
51.
52.
53.
(c) Sm2+(Z= 62)[Xe]4/6 6s0-6 unpaired eEu2+(z= 63) (Xe]4/7 6s0 - 7 unpaired eYb2+(z = 70) [Xe]4f 14 6s0 - 0 unpaired eCe2\Z= 58) [Xe]4f 15d1 6s0 -2 unpaired eOnly Yb2+ is diamagnetic.
(c) AB is just like NaCl. Thus twelve A+ are at
edges and 1 within body of fee i.e. in
octahedral voids and six B- at faces and 8 at
comer.
(b) Let's take the example of oxygen
56.
(b)
CuSO 4 ~ Cu 2 + + SO~H2O ~ H+ + OHAt cathode : Cu z+ + 2e- ➔ Cu
57.
(d)
:. Wcu
= 7.95g
O(g) + e- - - - t 0 -(g) + e- - - - 0 2-(g)
- EA1
+EA2
Energy is required to add an electron to the
negatively charged species due to electron
- electron repulsion.
54.
55.
(b)
59.
60.
(b)
(a) Benzaldyde and formaldehyde, both do not
have a - hydrogen atom, so both will
undergo Cannizzaro reaction; here
formaldehyde will always be oxidised to
formate while the other aldehyde
(C6 H 5CHO or any other aldehyde not
having a-H, viz- Me3CCHO) will always be
reduced to corresponding alcohol ( crossed
Cannizzaro reaction)
(b)
(c) Xenon undergo sp3 hybridization.
lli]
11~11~1 1~1
5s
5p
(ground
~ ~ - ~ ~ - ~ _ _ , state)
5d
I
OCHO
[illl 1l 1l1I
5s
HF+ XeF6 ~ XeF; + HF2
58.
5p
Benzaldehyde
+HCHO
NaOH
Formaldehyde
In the fourth excited state xenon atom, has
8 unpaired electrons
Benzyl alcohol
61.
I1 I 1 I 1 I 1 I
5d
One s and three p orbital undergo sp3
hybridization. Four sp3 hybrid orbitals form
four cr bonds with oxygen atoms. They are
a sp3-p. Four prc-drcbonds are also formed
with oxygen atoms by the unpaired
electrons.
62.
sod. formate
(b) The molality involves weights of the solute
and the solvent. Since weight does not
change with the temperature, therefore
molality does not depend upon the
temperature.
(b) Among the given compounds naphthelene
is volatile but benzoic acid is non-volatile
(it forms a dimer). So, the best method for
their separation is sublimation, which is
applicable to compounds which can be
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161
MOCKTEST-6
63.
converted directly into the vapour phase
from its solid state on heating and back to
the solid state on cooling. Hence it is the
most appropriate method.
(c) HOCI + Hp2 ~ 8:iO+ + CI-+ 0 2
64.
(d) Given concentration ofNaOH = 10-
10
I
I
CH3
OH
M
CH3 - CH - CH 2 - CH 2 - O-CH2 -CH2 - CH- CH3
NaOH~Na+ + OH10-I0M
CH3 -CH- CH2 - CH2
I
10-I0
CH3
:. [OH-] fromNaOH= 10-IO
We have to consider dissociation ofHzO
I
CH3
Y
69.
(c)
70.
(b) During charging, the lead storage battery
behaves like an electrolytic cell. So, at anode
the reaction is
[OH-] from H 2 O = 10-7
Total [OH-] = 10-7 + 10-Io
PbSO 4 +2H 2O ~
1001
= 10-7 (0.001 + 1) = 10-1 (
]
1000
PbO 2 + 4H+ +SO~-+ 2e71.
= 10-IO xlOOl
= -(loglOOl x l0-10 ) =- 3.004+ 10=6.9996
pH = 14-pOH= 14-6.996 = 7.004
.-. pHono- 10 MNaOHsolution is nearest
to 7.
65.
(b)
72.
TI.
3
2Al+-O 2 ➔ Al2O3
2
3
According to equation
mole of 0
2
combines with 2 mole Al.
2 mole Al = 54 g
(d) Due to + I-effect of the CH3 group, toluene
has much higher electron density in the ring
than benzene, nitrobenzene and benzoic acid
and hence it is most reactive towards
nitration.
(d) Silk is protein fibre. Dacron is polyester fibre
and nylon-6,6 is polyamide fibre .
*
*
oo ~ - ~ - ~ -rn-rn-~
-~
ICH CH
I
3
3
(3 , 4-dimethylheptane)
2
74.
(b)
Zn and
30
80
Hg have their d orbitals
completely filled, so they do not show any
66.
(d)
67.
(c) InaDNAmolecule,A ===T(Two H-bonds)
75.
C ::: G (Three H-bonds)
Purine ➔ Adenine (A), Guanine (G)
Pyrimidine ➔ Cytosine (C), Thymine (T)
So the complimentary sequence of
ATGCTTGAis TACGAACT.
76.
variable valency.
(d) All the given statements are correct.
(a) Stronger the acid, weaker the conjugate
base. Since acid character follows the order
H 2O > HC =CH> NH3 > CH3 - CH3
(Acid character),
the basic character oftheir conjugate bases
decreases in the reverse order, i.e.,
CH 3 CH 2 = c- > HC > NHz- > OH(Basic character)
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77.
1
(b) A graph plotted between log k vs- for
T
calculating activation energy is shown as
from Arrhenius equation
logk= logA
78.
79.
80.
81.
86.
(c)
87.
(b)
88.
(a) CaC1 2 acts as a non-volatile solute and
results in depression in freezing point. Thus,
snow fall is reduced and prevents blocking
ofroads in the polar region.
(b)
89.
a
2.303 RT
(a) [Pt~)zC12] O.S. of Pt is +2; electronic
configuration ofPt2+= [Xe]4f 14 5d 8 . Ligand
NR:i results in pairing ofd-electrons leaving
one d-orbital empty therefore hybridisation
is dsp 2 and geometry is square planar.
(b)
(c) The movement towards anode shows that
sol is negative. For coagulation ofnegative
sol cation with higher charge is more
effective.
(b) At the anode, the following reaction are
possible
2soi- ➔ S2 o~-(aq)+2e-
83.
84.
85.
(a)
(d)
(d)
(d)
Red hot tube
500°C
0
E
.... (ii)
For dilute HzSO4 reaction (i) is preferred
to produce 0 2 gas. But for cone. HzSO4 ,
reaction (ii) occurs.
EDTA has hexadentate four donor O atoms
and 2 donor N atoms and for the formation
of octahedral complex one molecule is
required.
The stability oflyophilic colloids is due to
layer of dispersion medium around sol
particles.
Terylene is a fibre, and not a thermosetting
plastic because on heating they melt and
do not show plastic property while rest
options are true regarding terylene.
Ideal gas cannot be liquefied at any value
ofP and T since there are no intermolecular
interactions between molecules.
0
0
II
II
© No,, $-C-C:;~ ~
NH-C-CH3
N02
N02
90.
91.
(a) For zero order reaction tcompletion = a/k.
(a)
92.
(b)
2H 20(1) ➔ 0 2(g) + 4H+ (a q) + 4e- ....(i)
82.
3HC=CH
93.
94.
95.
96.
3
2Al + -0 2 ➔ Al203
2
3
According to equation
mole of 0 2
2
combines with 2 mole Al.
2 mole Al = 54 g
(d) Quaternary structure refers to the overall
structure ofa multiprotein complex whereas
primary, secondary and tertiary structure
refer to the different structural levels of a
single protein.
(b)
(d) Solubility of alcohol in water decreases with
increase in molecular mass due to increase
in water repelling alkyl part in alcohol.
(a)
CH3 -CH 2 -COOH
CH3 -CH 2 -CO-Cl
(!)
COCHzCH3
C6H6
Aici;
@
(JI)
Wolff-Kishner
reduction
~CH,CH,
(ill)
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MOCKTEST-6
97.
163
(c) Some drugs do not bind to the enzyme's
active site but bind to a different site of
enzyme which is called allosteric site, which
changes the shape ofthe active site, in such
a way that substrate cannot recognize it. If
the bond formed between an enzyme and
inhibitor is a strong covalent bond and
cannot be broken easily the enzyme is
blocked permanently. The body then
degrades the enzyme-inhibitor complex and
synthesises the new enzyme.
98.
(d) Chlorine reacts with excess ofammonia to
produce ammonium chloride and nitrogen.
3Cl2 + 8NII:i (excess)~ 6NH4Cl + N 2
99.
(c)
E
0
_
Mn04 1Mn
E~n
04
2+
/ Mn0
2
(acidicmedium)=l.51V ;
(alkaline medium) = 0.60 V
E~no / MnO~- (neutral medium) = 0.56 V
4
3C 2 H 5 OH+PBr3 ~ 3C 2 H 5 Br+H 3PO3
100. (d)
[X]
SECTION-B
6.
MATHEMATICS
1.
2.
3.
(d) n(A u B) = n(A) + n(B)- n(A n B)
= 12+9-4 = 17
Now, n((AuBf)=n(U)-n(AuB) =20 -17 =3
(c) l(x) = logx, is not periodic.; l(x) = e\ is not
periodic.
l(x)=x-[x] = {x}, has period l;f(x)=x+ [x], is
not periodic.
(a) We have,
(b) Area of quadrilateral = 2 [ area of!:l. OAC]
= 2 . .!_0A.AC =
2
.js;.,Jg2 + 1 2 - c
4cos x(2-3sin 2 x) + (cos 2x + 1) = 0
⇒
4cos x(3cos 2 x-1) + 2cos 2 x = 0
⇒
2cos x(6cos 2 x +cos x-2) = 0
⇒
2cos x(3cos x + 2)(2cos x-1) = 0
Point is (0, 0)
S1 = c ,
:. Area= ,Jc(g2 + 1 2 -c)
7.
⇒
⇒
z = log 2 (1+i) = log 2 (✓
2eirr / 4 )
(c)
1 . 7t 1
=2+ 14 og2 e
either cos x = 0 which gives x = n I 2 or
COSX=-2 / 3
Which gives no value ofx for which 0 ~ x
or
~
n I2
cosx = 112, which gives x = n / 3
Hence, (z + z) + i(z- z)
So, the required difference = n / 2 - n / 3 = n / 6
4.
(a)
Sn+3 -3Sn+2 + 3Sn+I - Sn
= (Sn+3 -Sn+2)-2(Sn+2 -Sn+! )+ Sn+l -Sn
= tn+3 - 2tn+2 - tn+l = 0
5.
(a) Any line parallel to x-axis of the form y = p
i.e. coefficient ofx = 0
:. In equation (k-3)x-(4-k2)y+k2- 7k+6 =0
Coefficientofx=k-3=0 :. k=3
8.
1t
1t
ln4-7t
= 1--log2 e = 1 - - - = - - 2
21n2
ln4
(c) The number of ways ofgetting the different
numbers 1, 2, ..... , 6 in six dice= 6 !.
Total number of ways= 66
Hence, required probability
6!
=~=
lx2x3 x 4x5 x 6
66
5
324
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9.
(b) Wehave, y=(l+x 114)(I+x112)(1-x114 )
15.
= (1-x112)(l + x112) = 1-x
_._dy=-1
dx
10.
16.
(cl) Since ~ (p v q) ;:;~ pA ~ q
(By De-Morgans' law)
(a) 11 R 11 ⇒ 11 is not perpendicular to 11
( :. Ris not reflexive)
11 R 12 ⇒ 11 ..l 12
⇒ 12 ..l ! 1 ⇒ 12 R 11• Hence, R is symmetric
11 R 12 and 12 R 13 ⇒ 11 R 13
( :. Ris not transitive)
(a) Put x + b = t ⇒ dx = dt
Also, sin (x + a)= sin (t-b +a)
= sin t cos (a - b) + cos t sin (a - b)
.'. ~ (p V q) ;c~ p V ~ q
11.
12.
13.
f
:. (d) is the false statement
(c) Total sum ofl 3 observations= 14 x 13 = 182
Sumof14observation = 7 x 12+7 x 16= 84 x 112
= 196
So, the 7th observation = 196 -182 = 14
(cl) It is obvious by fundamental property of
circular permutations.
(a) Equating the components in
f
= sin tcos(a-b)_+cos t sin(a-b) dt
smt
=
a(i +2]+ 3k:)+~(2i +3]+k)+y(3i + ]+2k)
= -3(i-k) , we have
17.
a + 2 ~ + 3y = - 3
....(i)
2a + 3 ~ + y = 0
....(ii)
3a + ~ + 2y = 3
....(iii)
sin (x+a) dx
sin(x+b)
Solving the equations (i), (ii), & (iii) we get
J[cos(a - b) + sin(a - b)cot t] dt
= t cos (a- b) + sin (a -b) loge lsin ti+ C
= (x+ b) cos(a-b)+ sin (a-b) logelsin (x + b)l + C
= x cos (a - b) + sin (a- b) loge lsin (x + b)I + C
[Absorbing b cos (a- b) in C], CE R
(cl) A + B=I ⇒ B=I-A
NowB 2 = (I-A) (I-A) = 12 -AI-IA + A 2
= 1-A-A+ A = I-A = B
:. Bis idempotent
Now,AB =A(I -A) =AI - A 2 =A-A = O
And BA= (I-A)= IA-A2 =A-A= 0
a = 2, ~ = -1, y = -1.
14.
(cl) We know, any :function f(x) has extreme value
at the points where its first derivative is zero.
Given:y=alogx + bx 2 +x
... (i)
⇒
Differentiate equation (i) dy = ~ + 2bx + 1
dx x
Which is ofthe form cosx 12 a+sinx 12 a=l.
=~+2b.1+1
( dy)
dx x=l 1
(
dy)
=~+2b.2+1
dx x=2 2
⇒ a+ 2b+ l = 0
... (ii)
19.
⇒ a+8b+2=0
⇒ a+8b = -2
(
2
✓
13
_
)x/2 + ( - 3 )x/2 -1
✓
13
... ~=2.
2
(cl) If.f{x) has an extremum at x = rc/3, then
f'(x) = 0 at x = rc / 3. Now,
... (iii)
f(x) = asinx+.!.sin3x
3
From equation (ii) and (iii), a + 2b =-1
:. f'(x) = acosx+cos3x; f'(rc / 3) = 0
a + 8b=-2
⇒
1
2
-6b = 1 ⇒ b = - - and a=-6
3
or acos(rc / 3)+cosrc=0
ora = 2.
WWW.JEEBOOKS.INI
MOCKTEST-6
20.
165
(c) Let the direction cosines of line L be /, m, n,
then
2/+3m+n=0
... (i)
and/+ 3m + 2n=0
... (ii)
on solving equations (i) and (ii), we get
23.
n
l
m
--=--=-6-3 1-4 6-3
24.
l
m n
- =- =3 -3 3
⇒
(b) If the given mid points be D, E, F; then the
area of ~DEF is given by
1
1
2[0(2-4)+ 1(4-0)-3(0-2)]= 2[0+4+6]=5
⇒
Area of the triangle ABC = 4 x 5 = 20
(d)
.
5 n+1+ 3 n_ 2 2n
.
5 _5 n+ 3 n_ 4 n
hm-----= hm-----n ➔oo 5n + 2n + 32n+3
n➔oo 5n + 2n + 27. 9n
z2 + m 2 + n2 = 1
3
1
1
1
!=--=- m=-- n=✓
27
✓
3'
✓
3,
✓
3
⇒
0+0-0 = 0.
0+0+27
= lim
m n
l
I
3= -3 =3= ✓
27
n➔oo
25.
(d) p 2 + q2 = (p + q)2-2pq= a 2 -2a + 6
p 2 + q2 = (a- 1)2 + 5 ~5
26.
(c) Required area =
Line L, makes an angle a with +vex-axis
:. l=cosa
21.
22.
2
1
2
Required number of arrangement
= 5c 2 X 3c 3 X 4! X 4! = 5760
(d) E 1 : Event that first drawn ball is red, second
is blue and so on.
E 2 : Event that first drawn ball is blue, second is
red and so on.
4
x
4
x
3
x
3
7
6
5
P(E) = P(E1) + P(E2)= 2 x
4 4 3 3
[ r
x2
x3
6
s·1·6·s = 35
8 10
3 3
=2+4--=-
x'
27.
(c) f{x) =
2cos 2 ~ -2sin ~cos~
2
2
2
2
2cos ~ + 2sin ~cos~
2
2
2
8 7 6 5 and P(E2)
4 4 3 3
= -x- x - x 8
(Y1 - Y2)dx
= f [(x+2)-(x )dx= - +2x - Jo
2
3
⇒ cosa = ✓
3
(b) First we have to select 2 men for bow side
and 3 for stroke side. The number of selections
of the crew for two sides= 5 c2 x 3C3
For each selection there are 4 persons on both
sides, who can be arranged in 4! x 4!ways.
P(E1) =
s:
X
.
X
cos - -sm -
2
2
X
. X
cos-+sm2
2
rt X)
rt
= tan ( - - - atx = rt /(rt)= -tan- = -1
4 2
.
'
4
WWW.JEEBOOKS.INI
TargetMHT-CET
166
32.
28.
(b) Tr+! = 3.5 .... (2r-1)(.!_)r
r!
5
29.
x2
y2
a2
b2
-+-=l
Let e be the eccentricity of the ellipse.
Since distance between foci = 2h
2ae = 2h ⇒ e = h
...(1)
Focal distance ofone end of minor axis say (0, b)
isk
a+e(O) = k ⇒ a = k
...(2)
From (1) and (2), b2 = a 2 (I -e2) = k 2 -h 2
The equation of the ellipse is
112
which is the (r + l)th term of (
(c) Let the equation of the ellipse be
1-¾r
x2
y2
-+
=l.
k2 k2 -h2
(b) IfA+ B + C=rc,
33.
then cos mA + cos mB + cos mC
(a) We have,
(1 +ai2 + 2ro )3n-(1 + ro + 2ro 2) 3n
. mA . mB . mC
= 1- 4 sm-sm-sm2
2
2
We know that, 1+ ro + ro2 = 0 and ro3 = 1
For m=2: cos2A+cos2B+cos2C
given expression is equal to
= l-4sinAsinBsin C
30.
⇒ cos2A+cos2B + cos2C -t4sinAsinBsinC=l
(a) The series is
(1 1
= (ro)3n -(ro2)3n = (ro3t-(ro3)2n = 1-1 = O
1 ....)
(x 2 +x 4 + x 6 + ... )+ -2 + 4+6+
X
X
34.
X
+ (2 + 2 + ..... )
(a) Given that, pis a non-singular matrix such
that
l + p + p2 + .... +pn=o
⇒
⇒
(1 + p)(l +p+p2 + ... + pn) = O
1 _ pn+ I = 0 ⇒ pn + I = 1
⇒
pn x pl = 1
p-1 = pn
x2n _ 1 x 2n+2 +l
=---x---+2n
x2 -1
x2n
31.
(d)
y2 + xy-12x2 = 0
⇒ (y + 4x) (y-3x) = 0 :.
35.
(c) Let I =
f
. -1
xSm
.Ji-x
x dx
2
Take, sin-1x = t
⇒ x = sin t
y
- = 3, -4,
dx=dt
X
The two pairs will have a line common if
3or-4willbearootofb
(fr +2h (f) +a=
:. 9b + 6h + a=0 or 16b-8h + a=0
~
0
I
X
f
=
sin t.t dt
'
:. cost
= t.(-cos t)-
= ✓1 -
x2
f(-cos t)dt
= - t cos t + sin t + C
= -c✓i-x 2 )sin-1 x + x +C
WWW.JEEBOOKS.INI
MOCKTEST-6
36. (b) It is clear from the graph, the constraints
define the unbounded feasible space.
167
7t
4
f{log 2- log(l + tan x)}dx
=
0
=
37.
7t
7t
4
4
0
0
floge 2dx - Jloge (1 + tan x) dx
x)
1-cosx
tan _, - - = tan- 1 ( -tan1+cosx
2
(c)
1t
2 I = - loge 2
4
=tan-1 tan ( 4n- X) =4n- X
2
2
40.
X
]
71t X
so tan-<0
[ ·:7n<x<8n ⇒ -<-<4n,
2
2
2
38.
1t
I = - loge 2
8
(b) ·: y = lognx
On differentiating w.r.t. x, we get
x log x log2 x log3 x ... logn- Ix logn x dy
dx
(a) Consider first two equations :
2x + 3y=-4 and 3x + 4y = -6
_ x log x log 2 x log3 x ... logn-l x logn x. l
We have 1'1=1~ !l = -1*0
= lognx
1
x = -2andy = 0
Now, this solution satisfies the third, so the
equations are consistent with unique solution.
7t
4
Jlog (1 + tan x)dx
...(i)
(b)
Sincef(x) = g(x), f'(x)=g'(x)
Putf'(x) = -f(x). Hence g'(x) =-f(x)
wehaveh' (x)=2f(x)f(x)+2g(x)g'(x)
= 2[f(x) g(x) + g(x) [-f(x)]]
-4 31
4 =2
i'lx = -6
(d) Let I=
x logx log2 x log3 x ... logn-l x
-
41.
39.
⇒
= 2 [f(x) g(x)-f(x) g(x)] = 0
:. h(x) = C, a constant :. h(0) = C i.e. C = 5
h(x) = 5 for all x. Hence h (I 0) = 5.
42. (c) We have, z = 0 for the point where the line
intersects the curve. Therefore,
x-2
3
0
y+l
2
0-1
-1
-- = -- = --
7t
⇒
y+l
x-2
-3- = 1 and -2- = 1 ⇒ x = 5 and y = 1
Put these value in xy = c2 , we get, 5 = c2
=
7t
7t
4
4
flog
0
{
f
1-tanx}
2} dx
1+
- - - dx = log { - l+tan x
l + tanx
O
43.
⇒ c=±✓S
(a) f(4) = g(4) ⇒ 8+a = 8 ⇒ a = 0
f(-1) =-2 for a = 0; f(-1) > f (4); b + 3 > 8 ⇒ b> 5
WWW.JEEBOOKS.INI
168
44.
(c) Clearly from curve drawn of the given
function f(x) is discontinuous at x = 0.
TargetMHT-CET
2
2
47. (c) Sn=aoCo + a!Cl +a2C/+ ........ + ancn2
Sn= anC/ + an_ 1Cn- /+an_/ + ........ + a0 C/
2Sn = (a0 + an) C/ + (a 1+ an_ 1) C/ + ....... + (a0 + a0) C0 1
= (2n + 2) (C/ + C/ + C/ + ..........+ C 2)
0
(0,1/4) )
0
48.
(0,- 1)
45.
(c)
Force (F) = 2i+ j-k and its position vector
of A= 2i-j. We know that the position vector of
a force about origin (r) = (2i -})- (0i + OJ+ Ok) or
r = 2i-j.
Therefore, moment of the force about origin
j
=rxF= 2
-1
2
1
: . Sn = (n + 1) 2ncn
[·: a0 + an = a 1+ an_ 1+ ..........= 2n + 2]
(b) Here,2x + y:;;30, x+2y:s; 24,x,y ~0
The shaded region represents the feasible region,
hence
z = 6x + 8y. Obviously it is maximum at (12, 6).
Hence z = 12 x 6 + 8 x 6 = 120
y
k
0 =i+2J+4k.
-1
--t'~--..--,., ,. . - --x
X
dy
dx
y2
f'(x)
f(x)
⇒ ----y=---
49.
+ 2y= 24
(a) Now AA-1 = I
f(x)
1
-2 dy
-1 f'(x)
. .d b
D lVl e yy2 y - - y - - = - - dx
f(x)
f(x)
-1
Put Y
= z ⇒ -y
-2
dy dz
-=dx dx
_dz _ f'(x) (z) = __l_
dx f(x)
f(x)
dz
dx
f'(x)
f(x)
1
f(x)
1
⇒ - + -- z =--
f f'(x) dx
I.F. = e f(x) = elogf(x) = f(x)
1
- + -=0 ⇒ x =-3
3 X
50.
(a)
Standard deviation a= ✓npq ~ 0
Now mean = np =25 and q < 1
:. The solution is z(f(x)) = ff(~) (f(x) )dx + c
⇒ y- 1 (f(x))=x + c ⇒ f(x)=y(x+c)
So cr = ✓npq
<Fr =5
:. 0 :;; a < 5
WWW.JEEBOOKS.INI
(Mock Test-7)
UI
Answer KEYS
SECTION-A
PHYSICS
1
2
(b)
(b)
6
7
3
(b)
8
4
9
5
(c)
(d)
10
51
52
53
54
55
(c)
(a)
(a)
(b)
(a)
56
57
58
59
60
1
(c)
(a)
(a)
6
7
8
(b)
(d)
(b)
9
(b)
(a)
10
(b)
2
3
4
5
(c)
(b)
(a)
(d)
(d)
(c)
(c)
(b)
(a)
(d)
(b)
(b)
16
17
18
19
20
(b)
(d)
(a)
(b)
(c)
61
62
63
64
65
(a)
(a)
(a)
(b)
(d)
66
67
68
69
70
(a)
11
12
(b)
16
17
18
19
20
11
12
13
14
15
13
14
15
(c)
(d)
(a)
(a)
(a)
(c)
(a)
(a)
(b)
(d)
(b)
(a)
(c)
(a)
(b)
(b)
(d)
21
22
23
24
25
(b)
(a)
(c)
(d)
(c)
26
27
28
29
30
(a)
(b)
(a)
(b)
(d)
CHEMISTRY
71 (a) 76 (c)
72 (a) 77 (c)
73 (d) 78 (a)
74 (b) 79 (d)
75 (c) 80 (c)
SECTION-B
MATHEMATICS
21 (c) 26 (b)
22 (c) 27 (c)
23 (d) 28 (d)
24 (a) 29 (b)
25 (c) 30 (d)
31
32
33
34
35
(d)
(d)
(d)
(a)
(c)
81
82
83
84
85
(b)
(c)
(a)
(d)
(b)
86
87
88
89
90
31
32
33
34
35
(c)
(b)
(b)
(b)
(c)
36
37
38
39
40
36
37
38
39
40
(d)
(b)
(c)
(c)
(c)
41
42
43
44
45
(d)
(a)
(a)
(a)
(c)
46
47
48
49
50
(a)
(b)
(c)
(c)
(d)
(a)
(a)
91
92
93
94
95
(b) 96
(d) 97
(d) 98
(b) 99
(a) 100
(d)
(c)
41
42
43
44
45
(a)
(c)
(c)
(a)
(a)
46
47
48
49
50
(a)
(d)
(a)
(b)
(b)
(b)
(c)
(d)
(a)
(b)
(b)
(b)
(b)
(a)
(b)
(b)
SECTION-A
PHYSICS
1.
(b) Since areal velocity A & angular
3.
(b)
4.
(c) A slit would give divergent; a biprism would
give double; a glass slab would give a parallel
wavefront. Edge is downward.
(d) According to Gauss' Law
momentum L of a planet are related by
5.
equation
A = _f._ , where M is the mass of
2M
planet. Since in planetary motion L is
constant ( iext. = O) , hence A is also
constant.
2.
fE.ds =
Qenclosed by closed surface = flux
Eo
so total flux = Q/i:0
Since cube has six face, so flux coming out
through one wall or one face is Q/6i:0 •
(b)
WWW.JEEBOOKS.INI
TargetMHT-CET
170
6.
(c)
B .
axis
2
_vo_I _ _R_
= (µoNI)R 2
2x 3
vo
Boc R 2
7.
(b)
So, when radius is doubled, magnetic field
becomes four times.
Let pole strength = m
12.
(d)
13.
(a)
14.
(a)
When wire is in form ofarc, then the distance
2£
between poles = 7t
So, M'= m2£
9.
10.
r2
Since the attenuation of ground waves
increases with increase in frequencies so
only low frequency- radio waves uses this
mode of propagation for short distances.
R= ✓4 2 +5 2 = ✓41N
The angle
= 2M
7t
(a)
r2
or
So, M = mC
8.
= (2113 r) 2 = 2 213
e will be given by
[2]
7t
SN
1
1
- = R[-(1)2
--_!_]⇒'· = _!_<><910A.
'-min
oo
mm R
.'
4N
(d)
(d) Let a particle A of mass m whose position
vector is r w.r.t. the point Pat any instant
in an inertial frame.
15.
16.
17.
18.
(b) Y = A. B = (A+ B)
(b)
(d)
(a) K.E. = hv -hvth = eV0 (V0 = cutoffvoltage)
⇒ V0 = ~(8.2 x 1014 -3.3 x 1014 )
19.
,.,2v.
e
(b) Gravitational potential energy (GPE) on the
surface of earth,
Ei = - GMm
From the formula,
p = mv
Then, angular momentum
⇒
11.
(c)
R
£= r X p
£ = rxpsin0
0 is the angle between rand p.
So, £ = 0
Therefore, 0 = 0°
IfR is radius of bigger drop formed, then
GPE at 3R, E2
=
GMm
(R+3R)
GMm
---
4R
Change in GPE
- E
-
E _
2 -
GMm
GMm _ 3GMm
- ~
1 - - ~ + -R-
±nR3 =2x±m 3 orR = 2 113 r
3
3
As
v 0 oc r 2
3
= -mgR
4
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171
MOCKTEST-7
20.
(c)
2
Centripetal acc.= ro r= 4n v2r
= 4 x (3.14)2 x
21.
(b)
22.
(a)
2
120
60
x 1.2._ = 23.7 ms- 2
100
[ ·: ro = 2nv]
·: q oc V forq = CV
⇒ as charge on capacitor increases means
P.D. between plates increases.
Here,y1 =asin(rot+kx + 0.57)
and y2 = a cos (rot+ kx)
28.
(a) At magnetic north pole ofearth, H = 0 and 8
= 90", maximum.
29.
(b)
I = 2 x 5 x(0.2)2 + 2x 2 x(0.4)2 = lkgx m2
30•
ld)
~
N
(d)
= a sin [%+(cot + kx)]
=
23.
24.
25.
= N oe-IOAt ,
2
= N oe- At
PAVA = PsVs
TA
Ts
7t
⇒
1
t=9A.
VA= 2Vs; TA= 2Ts; PA = 2Ps
= nAR = nsR
2 -0.57
3 4
· 1 -0.57 = 1.57-0.57 = 1 radian
2
(c)
(d) Freq= mg +2 [T(21t R)] [T = 75 x m-3 N/m]
= 0.1 + 2 [75 x 10-3 (0.2)] = 0.130N
(c) Let p be the resistance per unit length
then, P = 36p, Q = 64p
R=
N
~ U
-I
N1
=e
= e • 9A.t = 1
N2
'
31.
Phase difference, L\<j> = <j>2- <j> 1 =
1
11A
PAVATs
119
Ps VsTA
(2Ps )(2Vs) (Ts)
=2
Ps Vs (2Ts)
32. (d)
33. (d) For dark fringe
12
X
S = 16
X+12 '
')J)
x=(2n -1) 2d
Now, for meter bridge
26.
p
R
Q
s
12X
- --
36
: . A.=
- =-
(X + 12)16
64
12X=9X + 108 = X =36O
(a) According, to Faraday's law of induction
2xd
(2n-l)D
=
2 X 10-3 X 0.9 X 10-3
(2 x 2-l)xl
A.= 0.6x l0-6 m =6 x 10-5 cm
34.
(a)
d<j>
Induced e.m.f. E = - - = -(I00t)
dt
Young's modulus
WI
Y = - .A L\l
A, l, M
Y2
Induced current i at t = 2 sec.
=
27.
Brass
l~I
W1 = W2
Y1
Y2
= + 10400~ 2 = +0.5Amp
[ ·: A, I, L\l same
(b) m = 10kg, x = (t3 -2t-10)m
dx
- =
dt
l, A , M
YI
Steel
for both brass and steel]
2
V
= 3t 2
-
d x
2 =a= 6t
' dt 2
At the end of4 seconds, a = 6 x 4 = 24 m/s2
F = ma = 10 x 24 = 240N
·
]
-W1 = -Y1 = 2 [Ysteel/Ybrass = 2 given
W2 Y2
35.
(c)
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172
36.
TargetMHT-CET
41. (d) At mean position velocity is maximum
(d) By junction rule at point B
-I+ 1A + 2A=0
.
I . e. ,
By Loop rule,
-3x2-J x l-E + l2 = 0
:.v =mJa 2 -y2
E=5V
37.
(b)
42.
e = M di =0.005 x i_(i 0sinrot)
dt
dt
:. emax=0.005 x l0 x 1001t = 51t
µ
I
u
µ-I
(c) Using, --- = V
R
or
[·: cosrot=l]
2
v
2-1
ao
R
(c)
(2n+l)1c D
2a
= 0.4 x (l5.08)2 -(0.4x9.8)
2
(4 + 1)0
For red light, x = -'------'-- x 6500A
2a
= 45.78-3.92 = 41.56N
43.
(6 + 1)0
For other light, x = - - - x 1cA
2a
xis same for each.
40.
1
R2
For solid sphere slipping on inclined plane
without rolling, acceleration
a2 = gsin 0
Therefore required ratio =
f'=(v+u)f
v-u
330 220
+
)1000 = 5000Hz
330-220
K2
l+ -
27 x 6500 = 4642.8A.
where f = original frequency of source of
sound
f' = Apparent frequency of source because
of the relative motion between source and
observer.
(a) For solid sphere rolling without slipping on
inclined plane, acceleration
g sine
a =---
(c) Frequency of the echo detected by the
driver of the train is
(According to Doppler effect in sound)
/'=(
Given: Mass (m) = 0.4 kg
Its frequency (n) = 2 rev/sec
Radius (r) = 1.2 m. We know that linear
velocity of the body (v) = ror = (27tll)r
= 2 x 3.J4 x 1.2 x 2= 15.08m/s.
Therefore, tension in the string when the
body is at the top of the circle (T)
r
X = - -- -
5 x 6500 = 7 x 1c ⇒ 1c =
(a)
mv2
= - - -mg
v = 2R
39.
⇒ 8✓3=4J42 -y2
⇒ 192 = 16(16- y2 ) ⇒ 12 = 16-y2 ⇒ y = 2cm.
= 0.0005x irocosrot
38.
Vmax
16
vmax = ma ⇒ cu= a- = -4 = 4
So, 1=3A
= - - =-- =
44.
45.
~
a2
5
(a)
(c) Power radiated by the sun at t°C
= a(t + 273) 4 4nr 2
Power received by a unit surface
a(t + 273)4 4nr 2
4nR2
= - - ----=----
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MOCKTEST-7
46.
173
(a) Lorentz force acting on the particle
F = q[ E+ ~ X B]
2.303RT
Slope= ~
~ log l<,:
= q [3I+ }+ 2k + i(-1 2 -1)
From (i) and (ii) , we get
-n F E:en = -2.303 RT log Kc
- ](-9-1)+ k(3 -4)]
o
2.303RT
Ecell = - - - logKc
FY = l lq}
47.
nF
(b) We know that frequency of e lectrical
Comparing equation (3) with y= mx + c
oscillation in L.C. circuit is
f- l
2n
....(iii)
2.303RT
c=0m = - - -
/I
Vic
'
53.
nF
(a)
Now, L=2L & C = 4C
CH 3 -X ~
1 Jl
1 fT
f' = 2n
x
= 2n
V2L.4C
Vic
1
2✓2
(b·'1
54
•
⇒ f' = -1 - x f
Zn
·
CH 4 Frankland ' sReact:ton.
4 x 128
8 27 = ---------,--6.023 x l0 23 a 3
·
⇒
a = 46.8 x 10--9 cm = 4.68A
2✓
2
49.
(c)
(c)
50.
(d) Though an equal and opposite force acts
48.
4.68A
1.24A + rCd2+ = - 2
on the road but since road does not undergo
any displacement, hence no work is done
on the road.
CHEMISTRY
51.
(c) Compotmd
Oxidation number of
nitrogen
56.
(c) C 2H4 + 3 0 2 ~ 2CO2 + 2Hz0
28 g ofC2H4 undergo complete combustion
by = 96 g ofO2
- 1/3
-1
(a)
(a)
28 g 96 g
-2
-3
52.
55.
110° = -2.303 RT log K c
....(i)
2.8 kg of C 2 H 4 undergo complete
combustion by
and also 110° = - n F E:en
....(ii)
= 9.6 kg of 0 2.
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174
57.
58.
TargetMHT-CET
(c) Aldehydes are more reactive than ketones
due to +I effect of- C8:J group. There are
two - C8:J group in acetone which reduces
+ve charge density on carbon atom of
carbonyl group. More hindered carbonyl
group too becomes less reactive. So in the
given case C8:JCHO is the right choice.
(b) Most of the Ln 3+ compounds except La3+
and Lu3+ are coloured due to the presence
off-electrons.
64.
(b) 3Fe(s)+ 4HzO(stearn)~
Fe3O4 (s) + 4 Hz (g)
~=
(pH2)
4
(PH20)
4 ( only gaseous products and
reactants are considered).
65.
(d)
A
B
t= 0
0.8
0
59.
(a) Mo! dm- 3 s- 1 units are for zero order.
t= 1
0.8-0.6
60.
(d) This is because zinc has higher oxidation
t= 0
0.9
potential than Ni, Cu and Sn. The process
ofcoating of iron surface with zinc is known
t= ?
0.9-0.675
61.
a
AJ + +3e- 3F
IF
2
Cu + +2e- 2F
IF
AI
I mol
1/3 mo!
Cu
0.675
0.8
a
In second case - a-x
0.9
=- - = 4
0.225
Since the ratio is the same, hence time will be
same. Therefore I hr.
Mn+ +ne- ~ M
3
0
= 4
In first case - - = a-x 0.2
as galvanization. Galvanized iron sheets
maintain their lustre due to the formation of
protective layer of basic zinc carbonate.
(a) The charge carried by I mole of electrons is
one faraday. Thus for a reaction
nF = I mole ofM
0.6
66.
(a)
68.
(d)
67.
(b)
For positive charge colloids coagulating
power t coagulation value ,I.._ [Fe(CN)6]4--_
69.
I mo!
1/2 mo!
(b) The stronger the base the more is the
nucleophilic character and vice versa.
Basic character order is
The mole ratio of Al, Cu and Na deposited
at the respective cathode is .!.:.!.: I or 2 : 3 : 6.
3 2
62.
(a) Producer gas is a fuel gas and is a mixture of
Hence the nucleophilic character is above
the same.
COandN2.
63.
(a) A fusion reaction between hydrogen nuclei
is difficult because positively charged
nuclei repel each other. However, at very
high temperatures ofthe order of I 06 to 107
K, the nuclei may have sufficient energy to
overcome the repulsive forces and thus
fuse. This is why, fusion reactions are also
called thermonuclear reactions.
70.
71.
(a) LiH is an ionic hydride, in which an electron
is transferred from Li hence Li+ and H- are
formed.
(a) ~E =~Q-W
For adiabatic expansion, ~Q = 0
⇒ ~=-W
The negative sign shows decrease in
internal en ergy, which is equal to the work
done on the system by the surroundings.
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MOCKTEST-7
72.
73.
175
(a) In this reaction, one molecule is oxidised
and other is reduced simultaneously.
(d) In [Cr ~)JBr3, Cr is in+3 oxidation state
3d
24Cr
74.
75.
11 11 11
(c)(jy
OH
II
IO carbocation
(5-membered ring)
4p
4s
IXIXI ~ ~
(b) For orthorhombic system, a =
(c)
4p
I1 11 11 I 1 I1 I DJ
3d
+3 .--....----,---.....-,..--,,
2P
4s
82.
30v
2
Ring expansion
P= y = 90°.
leads to relief in
steric strain
C(s)+ _!_ 0 2 (g) ➔ CO(g); ~S increases.
+
6
4
5
3° carbocation
2
(6-membered ring, more stable)
Hence, as the temperature increases, T~S
increases and hence ~G (~H - T~S)
decreases. In other words, the slope of the
curve for formation of CO decreases.
However, for all other oxides, it increases.
:~~ex
or~
5
3° carbocation
76.
(c)
1
SO 2 +-0 2 --tSO3
2
~ =~
77. (c)
78.
;
(S03)-~; (SO2)
= -98.2 + 298.2 = 200 kJ/mol
Basicity ofoxides decreases in a period and
increases in a group.
:. SnO2, Al2O 3 and ZnO are amphoteric
oxides.
(a) FeO is capable forming slag with SiO2
SiO 2 + FeO ➔ FeSiO 3
79.
(d) (i)
The first ionization energy of xenon
(1, 170 kJ mol- 1) is quite close to that
of dioxygen (1 ,180 kJ mol- 1) .
(a)
(d) Due to + M effect of the - OH group in
phenol, electron density in the ortho and
para positions of the phenol nucleus
increases hence phenol will undergo
electrophilic substitution easily than
benzene. The other three compounds have
electron withdrawing groups, hence they
will undergo electrophilic substitution with
a difficulty than benzene.
85. (b) Solution will be neutral. Concentration of
each will be 0.05 M since volume got
doubled.
86. (a) The green colour appears due to the
formation ofCr3+ ion
83.
84.
(ii) The molecular diameters ofxenon and
dioxygen are almost identical.
Based on the above similarities Barlett (who
prepared o ; [PtF6J- compound) suggested
that since oxygen combines with PtF6, so
xenon should also form similar compound
with PtF6.
80.
(c)
81.
(b)
Similarity between optical and geometrical
isomerism is that both are included in stereo
isomerism.
Electronic configuration of gadolinium is
[Xe] 4/75 d 16s 2
Cr2 0 ~- +3SO~- +8H+ - - t
3SO~- +2Cr 3+ +4H 2O
87.
88.
(a) N-Phenylacetanilide precipitates out to form
a complex with anhydrousA1Cl3.
(b) Vinyl alcohol, CHi=CHOH, monomer of
polyvinyl alcohol exists mainly as C~CHO
; hence polyvinyl alcohol is best prepared
by the alkaline hydrolysis of polyvinyl
acetate which in turn is prepared by the
polymerisation ofvinyl acetate.
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TargetMHT-CET
176
89.
(b) Biodegradable polymer is Nylon-2-Nylon-6
which is copolymer of glycine <HiN - C1½COOH) and amino caproic acid
<HiN-(C8i)5 -COOH).
n1½N-C8i-COOH +
glycine
nIIiN - (C8i) 5- COOH
amino caproic acid
1
CH3CHzCHzNHCOCH3
96.
0
-f HN -
0
II
II
CH2 - C - HN - (C&1 - C tn
97.
z
(d) The appearance ofcolour in solid alkali metal
halide is due to presence off-centre defect
in the crystal structure.
(c)
nylon - 2 - nylon - 6
90.
V20 5 is used as catalyst in contact process
of manufacturing 1½S04 .
(b)
0
I
CH3
CH3
")cHOCH3 +HI ~
CH3....-
98.
(b) Mango swells due to osmosis.
(d) [Ni(CN)4 ]2- is dsp 2 hybridised.
[Ni(PPh3)zC1 2 ] i.e., Ni(II) :3d 8 4s 0 4po
(sp3 hybridisation as weak field ligands PPh3
and Cl do not force the two unpaired 3d
electrons to be paired up.
93.
94.
#
Xe
I ..
0 o U
CH)+ ") CHOH
CH3....2-Propanol
91.
92.
(b)
(b) Phenol is most acidic because its conjugate
base is stabilised due to resonance, while
the rest three compounds are alcohols,
hence, their corrosponding conjugate bases
do not exhibit resonance.
100. (a) Starch is also known as amylum which
occurs in all green plants. A molecule of
99.
starch (C 6 H100 5 )n is built of a large
number of a-glucose rings joined through
oxygen atom.
(d)
(b) 11H < 0, 11S < 0,11G < 0
SECTION-B
MATHEMATICS
1.
2.
(c) We have
minn(AuB) = max {n(A), n(B)} = max {3,6} = 6
Maxn(AuB)= n(A)+n(B) = 9; .-. 6:<,;n(AuB):<,;9
(a) f(2a-x)= f(a -(x-a)) = f(a)f(x-a)-f(0)
f(x)= f(a)f(x-a)-f(x) =- f(x)
[·: x = 0,y = 0, f(0) = J 2 (0)- J\a)
⇒ J 2 (a) = 0 ⇒ f(a)=0]
⇒
3.
f(2a -x) = - f(x)
(a) Let ✓3 + 1 = r cos a, and ✓3 -1 = r sin a
r
2
= (✓3 +1)2 +(✓3-1)2 = 8 i.e. a=rr/12
From the equation, r cos (0- a)= 2
⇒
cos(S-n/12) =11 ✓
2 =cos(n/4)
0 = 2nn ± rr/4 + rr/12
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177
MOCKTESf-7
4.
10.
(b) a 1 = ✓
7 < 7 . Let am<7
(b) Here n (S) = 6 2 = 36
Let E be the event "getting sum more than 7" i.e.
sumofpairofdice= 8, 9, 10, 11 , 12
Then am + 1 = ✓7 + am
{~ : ~
⇒ a 2m+ l =7+am < 7 +7 < 14.
⇒ am +
1
./14 < 7;
<
So by the principle of
5.
mathematical induction an < 7 V n.
(a) I x1z1 - y1z212 + I Y1Z1-x1z2 12
6.
= I x 1z 112 +I y 1zi!2-2Re(x 1y 1z 1z:i)
+ I Y1Z1 12+ Ix1z212 + 2Re(x1y1z1z2)
2
2
2
2
= x/ I z11 +y/ Iz2 l +y/ I z 11 + x/ I z2 1
2
2
2
2
I z2 1 + Y/ I zl 1 + x/ I z2 1
= x/ I z1 1 +
= 2(x/+ y/) (4 2) = 32(x/ + y/)
(b) ·: f(x)=xsinx
7.
11.
(b)
d
f'(x)=dx(x sinx)
12.
x➔a+
(6,6)
h➔O
l
Hence it is continuous at x = a.
2
-1)1
j +c
l ✓3x
(a) Let y = e(2x 2-2x- l)sin2 x
= sin x [2(2x2- 2x) cos x + (4x -2) sin x]
du
dx
= O ⇒ sinx = O ⇒ x= nrc
d2 u
d
- 2 = sinx -d [2(2x2-2x-l)cosx+(4x-2)sinx]
X
dx
+ cos x [2 cosx (2x2- 2x - l) + (4x - 2) sinx]
2
d u
At x = nrc - 2 = 0 + 2 cos2 nrc(2n2 rc2- 1) > 0
' dx
Hence at x = nrc, the value of u and so its
corresponding the value ofy is minimum and
minimumvalue = eO = I
- a)=O
a
x) = lim {a -(a+ah)2 } = 0
h➔ O
_J (x
du
Now dx = (2x2- 2x- 1)2sinxcosx+(4x-2)sin2x
2
-a] = Jim f(a - h)
d (x - 1/x)
(x - l/x) 2 + 3
and u = (2x2 -2x- l ) sin2 x
-1
y- 1= _ _ (x-1) ⇒ 3x-4y+l=O
3 1
4-1
(b) /(a) =O
and lim f (
(6,5)
✓3tan
(d) The given system of lines passes through
2
(5,6)
1- f 2l + l / x2 2 ctx-f
I
(b) By definition only f (x) = x 2 + 4x - 5 with
f(x)= Jim [x
x➔ax➔a- a
(6,4)
(6,2)}
1
-I (x-1/x)
✓
3 tan
✓
3
+c
f'(~) = sin~+~cos~ = l
lim
(5,5)
x +l+l/x
the point of intersection of the straight lines
2x + y-3 = 0 and 3x + 2y-5 = 0 [L 1 + 1cL2 = 0
form], which is (1, 1).
The required line will also pass through this point.
Further, the line will be farthest from point(4,-3)
if it is in direction perpendicular to line joining
( I, l)and(4,-3).
:. The equation of the required line is
9.
4 6
(5,3)
(6,3)
:. Req. probabil ity= n(E) = _!2 = _2_
n(S) 36 12
domain [O, oo) is one to one.
8.
(5,4)
:. n(E)= 15
d .
.
.
d
= smx-x+x - smx =sm x+xcosx
dx
dx
⇒
(4,4)
.
1.e. E = ( , )
Y/
⇒
(3, 5)
(4, 5)
13.
(c)
l2- ll- l x lll = l ⇒ 2-ll-lxll=±l
⇒I 1-1 x
II = I or 3
If 11- 1x j = I ⇒ 1- I x I= ±1 ⇒I x I= 0 or 2
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TargetMHT-CET
178
⇒ x=0or±2
f ~ dy
:. If = e Y
Solution is
If 11-l x II =3 ⇒ 1-1 x 1=±3 ⇒1 x l= - 2 or4
14.
⇒1 XI= 4 ⇒ X = ±4
[·: IX I* -2]
:. Solution set is {-4, -2, 0, 2, 4}, hence 5 real
roots in all.
(a) (x+ l)(x +4). (x + 9)(x + 16)......(x + 400)
= x20 + (12+ 22 + 32+ ...... + 202) xl9+ ....... .
3
y .x
= f y .y dy + A ⇒ xy = ~ +A
l -
18.
20(20+1)(2 x 20+1)
= 2870
6
(a) The required area
coeff. ofx 19 =
15.
= e logy = y
3xy = C Where C = - 3 A
⇒
(b) The equation oftwo concentric circles differ
only in constant terms. So let the equation of the
required circle be : x 2 + y2 -3x +4y + l = 0
It passes through (-1, -2), so we have
1 + 4+3-8 + l = 0 ⇒ l =0,
Hence required equation is x 2 + y2 - 3x + 4y = 0
y
19.
hm
x➔O
= lim
x➔O
x= -e
=
= f1O- e loge(x+e)+ 100
e -x dx
0
20.
( 4 x -1)3
.
(b)
4
3
(cl)
x2
sin -
4
log(! + 3x)
(4x - 1}3. (x / 2)2 .
3x
.!
x3
sin x 2 / 4 log(l + 3x) 3
3
(toge 4) .l.loge(e)=
((ii+ 3b) x (3ii + b)J
2
4
3
3
(loge 4) .
= [ii x 5+ 9b x iiJ 2
= (-8ii X i,)2 = 64(1ii II b Isin 120°11)2
= [ x log(x+e)-f - x- dx]o -[e-x]o
x+e
1-e
= [x log(x +e) -
x+ e log(x + e)]?-e + 1
= e + (1 - e) + 1 = 2 sq. unit.
16.
17.
(c) Words start with Dare 6! = 720, start with E
are 720. start with MD are 5 ! = 120 and start with
ME are 120. Now the first word starts with MO is
nothing but MODESTY. Hence rank of
MODESTY is 1681.
(a) Given differential equation is y' (y2 - x) = y
⇒
⇒
2
dy
(y - x) = y
dx
-
⇒
dx
-
dy
21.
(c)
dx
1
-+x.-= y
dy
y
This is the Linear differential equation in x
q- y
p- x
q
p- x q - y
r-z
r-z =0
r
Apply R 1 ➔ R 1- ~ and Rz ➔
= y - -X
y
p
⇒
X
O
-z
0
y
- z =0
p- x
q- y
Rz- ~' we get
r
x[yr + z(q-y)]-z[0-y(p-x)] = 0
[Expansion along first row]
⇒ xyr + zxq + yzp = 2xyz ⇒ .£. + .9. + !_ = 2
X
y
Z
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179
MOCKTESf-7
22.
(c) Forb=-1,cosx= b ⇒ cos x = -1 which is
satisfied for x = 1t, 3n , Sn etc. which forms an
A.P. with common difference 2n.
For no. other value ofx out of
23.
So the probability ofnot getting a double -six in n
1
2
and
✓
3
Probabi Ii ty of obtaining a double-six atieast
2 , the
roots will form an A.P.
(d) Foot of perpendicular from (6, 5, 8) on Yax.is is (0, 5, 9).
Required distance = ✓(6 - 0) 2 + (5 - 5) 2 +(8 - 0) 2
once= 1- (
27.
24.
51c=
Letl+e-x = t
(a) The planes x +y = 0 i.e. x = -yand y+ z= 0
X
I=
z Anypomt
.
1 = =T = 1 .
y
on this line is
(t, -t, t). This point lies in the plane x + z = 0 ift + t
= 0 ⇒ t = O . So the three planes meet in a unique
point (0, 0, 0).
(c)
1
Jex +l x
J(ex + 1)-l dx
=
Let I
(c)
= ~
-J~I+e- x
10 ⇒ A.= 15° =2
. z = -ymeet m
. th e I'me
1.e.
25.
35)n
36
-x
= IO unit
⇒
35)n
36
throw = (
28.
lim
-J!dt
= - logt + c= -log(l +e-x)+c
t
f(x) = /(3) =
⇒ lim
lim
x➔3-
J(x)
/(x) = 4
x➔ r
or lim 3- h + 1c = 4
2
1
- e- xdx=dt
(d) By definition of continuity, we know that
x➔ 3 +
3
We have sin-1 x + sin- 1 y + sin-1 z = n
and sin- x ::s; ~ it is possible only when
⇒
⇒ 3+
"- = 4 ⇒ 1c = I
h➔O
29.
(b)
3,
d 2 = h cot30° = 500✓
sin- 1 x=2:. ⇒ x=l
2
XIOO
3
+ ylOO + ZIOO
XIOI
26.
(b)
+ YIOI + ZIOI
= 3-1 =2.
The probability ofgetting a double -six in one
1
36
The probability ofnot getting a double -six in one throw
throw=
= l-__!___=35
36 36
Diameter d
= 500✓3 + SOO .fj = 2
3
30.
(d)
z-2 -3i = x+iy -2-3i= (x-2)+i(y-3)
tan -I ( y - 3)
x-2
⇒
ozo m
v3
= 2:. ⇒ y - 3 = tan 2:. = I
4
x -2
4
x - y+l = 0
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180
31.
3P 0
. eqn. 1s
. x 2 + px+ 4
=
()
c ffIVen quad ratlc
So, a+ P = - p, ap =
3p
4
32.
33.
4
⇒
±M
p 2 -3p-10-0
2
:r
39.
(b) Numberoftrianglesformed = 12C3 - 7C3 = 185
40.
.
(b) Given
T
= 6
Tn- 7+ 2
~r-
6
c
n 6(
⇒
c~r
n- 12
1
=-
- T7-
1
= 6
Tn- s
1
⇒ 'c,-,(~l'(Af'
n-12
6
n-12
⇒6 3
= 6-1
6
Since all 4 letters are to be placed in wrong
envelopes then required probability
n-12
..· -3 = -l ⇒ n = 9
41.
(b) Let the order ofB be m x n .
Since, A is 3 x 2 matrix .·. A' is 2 x 3 matrix .
Given that, A'B is defined .
Number of column of A' must be equal to
number ofrows ofB :. m = 3
Also, since BA' is defined .
Number of columns ofB must be equal to
number ofrows ofA' : . n = 2 : . order ofB is 3 x 2 .
35. (c) Let p and q be two proposition given by
p: 2 2 = 5, q: 1 get first class
Here give statement is p ➔ q
So contrapositive ofp ➔ q is -q ➔ - p
i.e. ifl do not get first class then 22 5.
1
7
~~
-⇒ 2 3 .3 3
34.
2
Ip 1 = 50
2
= 50 ⇒ I + q + r I = 5✓
= [;, - ;, + ;, - ........... (-1)° ~,]
½-¾+ 2~ = i
L
IP+ ci + r 1 = L IP1
⇒ p=-2,5 ⇒ p E {-2,5}
(b) The common chord will be the diameter of
the smaller circle, whose circumference is
bisected.
(b) We know from the above given formula that
probability that no letter is in right envelope out
of n letters and n envelopes is given by
= [ ; ! - ; ! + ; !] =
(a) By given condition,
2
M
3 X P -10
TargetMHT-CET
(d) Clearly g(x) will be inverse of f(x)
⇒ g(x) = ✓
x -1
38.
Now,givenla-PI=
⇒ a -P=
⇒ (a-P)2 = 10 ⇒ a 2 + P2 -2aP= IO
⇒ (a+ p)2-4ap = IO
⇒ p 2 -4
37.
(a) For points of intersection of the equation
of parabola
y= x 2
... (i)
and equation of straight line: y = x
... (ii)
We have: x2 -x=0 ⇒ x(x-1)=0
x= 0 or x =
l ⇒ y=0ory=
1
Hence , the coordinates of their points of
intersection are O (0, 0) and P (1, 1).
2
y=x
*
II x
36.
(c)
lim (/(l+x))
x➔O
/(1)
I'
I (/(l+x)- /(!))
=/'.!1o~
/(l)
/'(I)
= ef(I) = e2
Required area (shaded region)
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MOCKTEST-7
I
= f(x -x
2
181
ar
br
abr 2
xy=-X-=-r-1 r+l r 2 -1
[ 2 3]I
)dx = _)(_ _ _)(_
2
0
3
0
... (2)
Dividing (2) by ( 1), we get
=[
42.
(½-½J-o] =¼sq. units
xy abr 2 r 2 -1 ab
- = - - X- - = z
c
r 2 -1 cr 2
(c)
7t
l+a 2 +a4
l+ab+a 2 b2
2 2
2
~= l+ab+a b
l+ac+a2 c2
4
l+ac+a 2 c2
2 2
l+b +b
l+bc+b c
l+bc+b2c2
l+c 2 +c4
2
45.
J
(a) Let I = x sin 2 x cos 2 x dx
...(i)
0
7t
a
2
= 1 b b
2
1 a
a
2
1 b b
2
1 a
c2 1 c
1 c
2
2
2
I= J(%-x}in x cos x dx
=(a-b)2(b-c)2(c-a)2
...(ii)
0
c2
7t
2
2
43.
J
2
By adding (i) and (ii) : 21 = % sin 2 x cos 2 x dx
Equation of ellipse is ~ + L = 1
16 8
(c)
0
2
where, a= 4, b = 2✓
. .
E ccentnc1ty, e =
7t
~
[b2
l--;; = / - 16 =
2
1
or
✓
2
21
f
= ~ sin 2 2x dx
8 0
Area is maximum when vertex is (0, b)
.
[·: sin2x = 2sin xcos x]
1
:. M axunumarea= -x2aexb
2
1
7t
= x2x4x2✓2x ✓2 =8sq.units
2
44.
(a) Since Ir I> 1,
,~r
f (l-cos4x)dx
7t 2
=-
1
8
0
1
a
ar
x=--=-1_ _!_ r-1
r
. . I
Slffil1ar y, Y =
b
(
)
l- _ _!_
46.
br
and
r+l
=-
(a) Let y = (2x 2 -2x-l)sin2 x
e
and u = (2x2 -2x-1) sin2 x
r
du
Now dx =(2x2-2x- l) 2 sin xcosx+ (4x-2) sin2 x
..(1)
= sin x [2(2x2 - 2x) cos x + (4x-2) sin x]
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182
orb +c= 0
du
dx
= 0 ⇒ sinx=0 ⇒ x= n1t
2
d u
-
dx
TargetMHT-CET
...(1)
d
=sinx -d [2(2x2 -2x-l)cosx +(4x-2)sinx]
2
X
+ cos x [2 cosx (2x2 -2x- 1) + (4x -2) sinx]
Also,f( J+) =f(J-)
50.
or lim f'(x) = lim f'(x)
x➔I+
x➔ l-
or 2 +b= l or b = -1 :. c = 1.[From (l)]
(b) Given, constraints arex ~ O,y ~ O,x + y ~ 5
and 3x + y~ 9andz = 12x + 3y
y
d2 u
Atx=n1t, - 2 = 0 + 2cos 2 n1t(2n 2 1t2 - l) > 0
dx
47.
Hence at x = n1t, the value of u and so its
corresponding the value of y is minimum and
minimum value = e0 = I
(d) Each point (x,y) has an image in liney= Oas
(x, - y). So, replacingy by-y in the given equation,
we get the image as ax2- 2hxy + by = 0.
48.
(a)
70x75+30 xx =?2 ⇒ x= 65
100
49.
(b)
f(x)
=
x, x ~ I
y'
{ x 2 +bx+c, x > I
l, X < I
:. f'(x) = {
2x+b, x > I
.f{x)isdifferentiableatx = I.
Then, it must be continuous atx = I for which
lim f (x) = lim f(x)
x ➔I+
x➔ l-
Here, feasible region ofOABC
AtpointO (0, 0), z= 12 (0) + 3 (0) = 0
AtpointA(3,0),z = 12(3) + 3 (0) = 36
At point B (2, 3), z = 12 (2) + 3 (3) = 33
At point C (0, 5), z = 12 (0) + 3 (5)= 15
Hence, maximum value is 36.
or 1 + b+c= l
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