Mahaentrance
Sample Test Paper
Physics
Q.1.
Two wires A and B of equal length and equal cross-sectional area but different
materials are stretched by the same force. If extensions produced in wires A and B
are in the ratio of 1 : 3,
(a) 9 : 1
Q.2.
(b) 1 : 9
(c) 3 : 1
(d) 1 : 3
The diagram shows the energy levels for an electron in a certain atom. Which
transition shown represents the emission of a photon with the most energy? .
n4
n3
n2
I II
(a) III
Q.3
Q.4.
(b) IV
n1
(d) II
(a) zero
(b) l + h
(c) 2h
(d) h
If the length of second's hand in a stop clock is 3 cm, the angular velocity and linear
velocity of the tip is
(b) 0.2547 rad/s, 0.314 m/s
(d) 0.1047 rad/s, 0.00314 m/s
Permanent magnet has properties retentivity and coercivity respectively
(a) high-high
Q.6.
IV
(c) I
Water rises to a height h in a capillary tube lowered vertically into a water to a depth
l. The lower end of the tube is closed inside the water and the tube is taken out of
water and opened. If l < h, then the length of water column remaining in the tube is
(a) 0.2047 rad/s, 0.0314 m/s
(c) 0.1472 rad/s, 0.063 m/s
Q.5.
III
(b) low-low
(c) low-high
(d) high-low
A weightless thread can bear tension upto 3.7 kg-weight. A stone of mass 500 g is
tied to it and removed in a circular path of radius 4 m in a vertical plane.
If g =10 m / s 2 , the maximum angular velocity of the stone is
(a) 2 rad/s
(b)
21 rad/s
(c) 16 rad/s
(d) 4 rad/s
Q.7. A planet has (1/49) times the mass of the earth and (1/4) times the radius of the earth.
The ratio of the earth's acceleration due to gravity on the surface of the planet
and earth is
(a) 4 : 7
Q.8.
(b) 4 : 49
(d) 16 : 49
Induced emf in the coil depends upon
(a) conductivity of coil
(c) rate of change of linked flux
Q.9.
(c) 2 : 7
(b) amount of flux
(d) resistance of coil
With in depletion region of p-n junction diode
(a) p-side is positive and n-side is negative (b) p-side is negative and n-side is positive
(c) both sides are positive or both negative (d) both sides are neutral
Q.10. 27 small drops each having charge q and radius r coalesce to form big drop. How
many times charge and capacitance will become?
(a) 3, 27
(b) 27, 3
(c) 27, 27
(d) 3, 3
Q.11. Light of frequency v falls on material of threshold frequency vo. Maximum kinetic
energy of emitted electron is proportional to
(a) v - vo
(b) v
(c) v  v 0
(d) vo
  t x 1 
Q.12. A wave equation is given by y  4 sin      where x is in cm and t in sec.
  5 9 6 
Which of the following is true?
(a)  = 18 cm
(b) v = 4 m/s
(c) a = 0.4 m
(d) f = 50 Hz
Q.13. A light emitting diode (LED) has a voltage drop of 2 V across it and passes a current
of 10 mA. When it operates with a 6 V battery through a limiting resistor R, the value
of R is
(a) 40 k 
(b) 4 k 
(c) 200 
(d) 400 
Q.14. A silicon optical fibre has a core refractive index of 1.50 and a cladding refractive index
1.47. What is the numerical aperture for the fibre?
(a) 0.90
(b) 0.60
(c) 0.45
(d) 0.30
Q.15. The minimum potential difference between the base and emitter required to switch a
silicon transistor `ON' is approximately
(a) 1 V
(b) 3 V
(c) 5 V
Q.16. Fleming's left and right hand rules are used in
(d) 4.2 V
Q.17
(a) DC motor and AC generator
(b) DC generator and AC motor
(c) DC motor and DC generator
(d) both rules are same, any one can be used
The angle between particle velocity and wave velocity in a transverse wave is
(a) zero
Q.18
Q.19
(c)  / 2
(d) 
An artificial satellite is moving in a circular orbit around the earth with a speed equal
to half the magnitude of escape velocity from the earth. The height of the satellite
above the earth's surface will be
(a) 6000 km
(b) 5800 km
(c) 7500 km
(d) 6400 km
1
A train is moving at 30 ms in still air. The frequency of the locomotive whistle is
500 Hz and the speed of sound is 345 ms 1 . The apparent wavelength of sound in
front of and behind the locomotive are respectively
(a) 0.80 m, 0.63 m
Q.20
(b)  / 4
(b) 0.63 m, 0.80 m
(c) 0.50 m, 0.85 m
(d) 0.63 m, 0.75 m
A strong argument for the particle nature of cathode rays is that they
(a) produce fluorescence
(b) travel through vacuum
(c) get deflected by electric and magnetic fields
(d) cast shadow
Q.21
Digital circuit can be made by repetitive use of this gate
(a) AND
(b) OR
(c) NOT
(d) NAND
Q.22
When the two inputs of a NAND gate are shorted, the resulting gate is
Q.23
(a) NOR
(b) OR
(c) NOT
(d) AND
Which polaroid is formed when the stretched film is impregnated with iodine?
(a) K-polaroid
(c) Both polaroids can be formed
Q.24
(b) H-polaroid
(d) None of the above
The nature of the communication system used in the present time is
(a) electrical only
(b) optical only
(c) electronic only
(d) All of these
Q.25 In moving coil galnvnometer a current of 2A for radial magnetic field of 4  10 3 Wb/m
2
produces some deflection. If the field is doubled by keeping all other
quantities same, the
current for the same deflection will be
(a) 0.5 A
Q.26
(b) 1 A
(c) 3 A
(d) 1.5 A
A long hollow copper tube carries a current I. Then, which of the following will be
true?
(a) The magnetic field B will be zero at all points inside the tube
(b) The magnetic field B will be zero only at points on the axis of the tube
(c) The magnetic field B will be maximum at points on the axis of the tube
(d) The magnetic field will be zero at any point outside the tube
Q.27
Find the magnetic potential at a point and distance of 1 m from the centre of short
magnetic dipole of moment 100 Am 2 if line joining point to the centre of dipole makes
anige 60° with the dipole moment vector.
Q.28
(a) 10  6 J/Am
(b) 2.5  106 J/Am
(c) 5  106 J/Am
(d) 0.5  106 J/Am
The plates of a parallel plate capacitor with air as medium are separated by a
distance of 8 mm. A medium of dielectric constant 2 and thickness 4 mm having the
same area is introduced between the plates. For the capacit2.nce to remain the same,
the distance between the plates is
(a) 8 mm
Q.29
(d) 10 mm
(b) 144 yr
(c) 72 yr
(d) 36 yr
An inductance L and a resistance R are connected in series with a battery of emf  .
The maximum rate at which the energy is stored in the magnetic field is
(a)
Q.31
(c) 4 mm
Taking the earth revolves round the sun in a circular orbit of 15  10 10 m, with a time
period of 1 yr, the time taken by another planet, which is at distance of 540  10 10 ml
to revolve round the sun in circular orbit once, will be
(a) 216 yr
Q.30
(b) 6 mm
2
4R
(b)
2
2R
(c)
2R

(d)
4R

A wire 3m in length and 1 mm in diameter at 30°C is kept in a low temperature at
-170°C and is stretched by hanging a weight of 10 kg at one end. The change in length
of the wire is [Y = 2  1011 N/m 2 ,g = 10m/s 2 and  = 1.2 10 5 /°C]
Q.32
(a) 5.2 mm
(b) 2.5 mm
(c) 52 mm
(d) 25 mm
Two beams of light of intensity Il and I2 interfere to give an interference pattern. If
I
25
the ratio of maximum intensity to that of minimum intensity is
, then 1 is
I2
9
(a)
Q.33
5
3
(b) 4
(c)
81
625
(d) 16
When the forward bias voltage of a diode is changed from 0.6 V to 0.7 V, the current
changes from 5 mA to 15 mA. Then, its forward bias resistance is
(a) 0.01 
(b) 0.1 
(c) 10 
(d) 100 
Q.34 In common emitter amplifier, the current gain is 62. The collector resistance and input
resistance are 5 k  and 500  respectively. If the input voltage is 0.01 V, the
output voltage
is
(a) 0.62 V
Q.35
(b) 6.2 V
(c) 62 V
(d) 620 V
The current gain of a transistor in common base mode is 0.995. The current gain of
the same transistor ir, common emitter mode is
(a) 197
(b) 201
(c) 198
(d) 199
Q.36. A tank is filled with water of density 1 g/cm 3 and oil of density 0.9 g/cm 3 . The height
of water layer is 100 cm and of the oil layer is 400 cm. If g = 980 cm/s 2 , then
the velocity of
efflux from an opening in the bottom of the tank is
(a) 900 980 cm/s
(b) 1000 980 cm/s
Q.37
(c) 920 980 cm/s
(d) 950 980 cm/s
A mass m is moving with a constant velocity along a line parallel to axis. Its angular
momentum with respect to origin of z-axis is
(a) zero
(c) goes on increasing
Q.38
One end of a wire 2m long and diameter 2 mm, is fixed in a ceiling. A naughty boy of
mass 10 kg jumps to catch the free end and stays there. The change is length of wire
is (Take g  10 m/s 2 , Y  2  1011 N/m 2 )
(a) 31.85  105 m
Q.39
(b) remains constant
(d) goes on decreasing
(b) 2 mm
(c) 3 mm
(d) 4 mm
In a surface tension experiment with a capillary tul e water rises upto 0.1 m. If the
same experiment is repeated on an artificial satellite, which is revolving around the
earth, water will rise in the capillary, tube upto a height of
(a) 0.1 m
(c) 0.98 m
Q.40
Q.41
(b) 0.2 m
(d) full length of the capillary tube
A capillary tube of radius R is immersed in water and water rises in it to a height H.
Mass of water in the capillary tube is M. If the radius of the tube is doubled, mass of
water that will rise in the capillary tube will now be
(a) M
(b) 2M
(c) M/2
(d) 4M
In steel, the Young's modulus and strain at the breaking point are 2  1011 N/m 2 and
0.15 respectively. The stress at the breaking point for steel is
(a) 1.33  1011 N/m 2
(c) 7.5  1013 N/m 2
Q.42
Two periodic waves of intensities Il and I2 pass through a region at the same time in
the same direction. The sum of the maximum and minimum intensities is
(a) Il + I2
Q.43
Q.45
(b)

I1  I2


I1  I2

2
(d)2(Il + I2)
(b)
(a) 18
(b) 12
(c) 36
The attenuation in optical fiber is mainly due to
(d) 48
(b) scattering
(d) Both (a) and (b)
When a ceiling fan is switched off, its angular velocity falls to half while it makes 36
rotations. How many more rotations will it make before coming to rest?
(a) 24
Q.47
(c)
2

(c) 
(d)
3
3
6
When a ceiling fan is switched off its angular velocity reduces to 50% while it makes
36 rotations. How many more rotation will it make before coming to rest ? (Assume
uniform angular retardation)

(a) absorption
(c) neither absorption nor scattering
Q.46
2
Two points are located at a distance of 10 m and 15 m from the source of oscillation.
The period of oscillation is 0.05 s and the velocity of the wave is 300 m/s. What is the
phase difference between the oscillations of two points?
(a)
Q.44
(b) 1.33  1012 N/m 2
(d) 3  1010 N/m 2
(b) 36
(c) 18
Which of the following is not the property of the photons?
(d) 12
(a) Momentum
Q.48
(d) Velocity
(b) 0.0021 kg-wt
(c) 0.036 kg-wt
(d) 0.0029 kg-wt
In Millikan oil drop experiment, an oil drop of radius r and charge q is held in
equilibrium between the plai:es of a parallel plate capacitor when the potential
difference is V. To keep a drop of radius 2r with charge 2q in equilibrium between
the plates the potential difference required is
(a) V
Q.50
(c) Charge
In Melde's experiment, the string vibrates in 4 loops when a 50 g weight is placed in
the pan of weight 15 g. To make the string to vibrates in 6 loops the weight that has
to be removed from the pan is
(a) 0.0007 kg-wt
Q.49
(b) Energy
(b) 2V
(c) 4V
(d) 8V
The momentum of a photon of energy 1 MeV in kg-m/s, will be
(a) 0.33  106
(b) 7  1024
(c) 10 22
(d) 5  1022
Chemistry
Q.1.
Q.2
The precipitate of CaF2(Ksp = 1.7  1010 ) is obtained, when equal volumes of the
following are mixed
(a) 10 4 M Ca 2  + 10 4 M F 
(b) 10 2 M Ca 2  +10 3 M F 
(c) 10 5 M Ca 2  +10 3 M F 
(d) 10 3 M Ca 2  + 10 5 M F 
The dissociation energies of H2 and O2 are 104 and 118 kcal mol 1 respectively. The
heat of reaction
1
1
 O – H(g)
H2 (g) + O2(g) 
2
2
is 10 kcal. The bond energy of O–H bond is
(a) 111 kcal/mol
(b) 11.1 kcal/mol
(c) 10.1 kcal/mol
(d) 101 kcal/mol
Q.3.
Reaction of ethyl formate with excess of CH3MgI followed by hydrolysis gives
Q.4
(a) n-propyl alcohol
(b) iso-propyl alcohol
(c) acetaldehyde
(d) acetone
5
If Ka = 10 for a weak acid, pKb value of its conjugate base is
(a) 5
(b) 6
(c) 7
(d) 9
Q.5.
The solubility of Mg3(PO4)2 is `S' mol L1 . The solubility product is given by the
relation
(a) S 5
Q.6
(b) 36 S 5
Q.9
(c) 6.023  1013
(d) 1  1016
(a) Hell-Volhard Zelinsky reaction
(b) Kolbe's reaction
(c) Claisen reaction
(d) Hunsdiecker reaction
 N2(g) + 3H2(g) which of the following statements is
For a reaction, 2NH3(g) 
correct?
(b) H  E
(c) H  E
(d) H  0
 H2O + 13.7 kcal, then heat of complete neutralisation of 1 g mole
If H  + OH  
of H2SO4 with a base will be
(a) 13.7 kcal
Q.11
(b) 1  1013
The reaction of Br2/P or Cl2/P with carboxylic acid to form a-halogenated acid is called
(a) H  E
Q.10
(b) chemical energy to internal energy
(d) chemical energy to electrical energy
The number of H  in 1 cc of a solution of pH = 13 is
(a) 6.023  107
Q.8.
(d) 108 S 5
In a galvanic cell, the energy change is
(a) chemical energy to heat energy
(c) internal energy to heat energy
Q.7.
(c) 6 S 5
(b) 27.4 kcal
(c) 6.85 kcal
(d) 3.42 kcal
An aqueous solution of CuSO4 is stirred with a silver spoon. The following will
happen
(a) Ag  will be formed
(c) Cu will be formed
(b) Cu  will be formed
(d) Nothing will happen
Q.12. The refluxing of silver salt of the carboxylic acid in CCl4 to form haloalkane or
haloalkene is called
(a) Friedel-Craft reaction
(c) Hofmann bromamide reaction
(b) Wittig reaction
(d) Hunsdiecker reaction
Q.13
Cyclic amides are called
(a) lactones
(b) lactams
(c) both (a) & (b)
(d) None of these
Q.14. Acetic acid has molecular weight of 120 in benzene solution. This is due to
(a) ion-dipole attraction
(b) dipole-dipole attraction
(c) van der Waals' forces
(d) None of the above
Q.15. What is the main reason for the fact that carboxylic acids can undergo ionisation ?
(a) Resonance stabilisation of carboxylate ion
(b) Hydrogen bonding
(c) High reactivity of a-hydrogen
(d) Absence of a-hydrogen
Q.16. Heat exchanged in a chemical reaction at constant temperature and constant pressure
is called
(a) internal energy
(b) enthalpy
(c) entropy
(d) free energy
Q.17. In thermodynamics, a process is called reversible when
(a) surroundings and system changes into each other
(b) the surroundings are always in equilibrium with the system
(c) there is no boundary between the system and surroundings
(d) the system changes into surroundings spontaneously
Q.18. When CH3MgBr reacts with C2H5OH, the product is
(a) CH4
(b) C2H6
(c) C3H8
(d) C4H10
Q.19. Westrosol is
Q.20
Q.21
(a) ClCH = CCl2
(b) Cl2CF2
(c) CHCl2 – CHCl2
(d) Cl3CNO2
Which of the following can possibly be used as analgesic without causing addiction
and any modification?
(a) Morphine
(b) N-acetyl-para-aminophenol
(c) Diazepan
(d) Tetrahydrocatinal
Arrange the following in the order of their increasing electrode potentials. Mg, K Ba
and Ca
(a) K, Ba, Ca, Mg
Q.22
(b) Ba, Ca, K, Mg
(c) Ca, Mg, K, Ba
(d) Mg, Ca, Ba, K
When zinc reacts with very dilute nitric acid, it produces
(a) NO
(b) NH4NO3
(c) NO2
(d) H2
Q.23
Melting of zinc metal and then, pouring it into cold water gives
(a) zinc dust
Q.24
(c) hard zinc metal
(d) soft zinc metal

The radius of La 3 (atomic number = 57) is 1.06 A . Which one of the following given
values will be closest to the radius of Lu 3 (atomic number = 71) ?

(a) 1.60 A
Q.25
(b) granulated zinc

(b) 1.40 A

(c) 1.06 A

(d) 0.85 A
The pH of solution obtained on mixing 50 mL 0.1 M NaOH ( K b  1.8  105 ) and 50
mL 0.1 M CH3COOH ( K a  1.8  105 ) is
(a) 8.72
Q26
Q.27
(b) 5.28
(c) 0.872
(d) 10
The pOH of solution obtained on mixing 50 mL 0.1 M NH4OH ( K b  1.8  105 ) with
50 mL 0.05 M HCl is
(a) 4.74
(b) 1.6
(c) 7.8
(d) 10.5
The reaction of C6H5O  Na  and CO2 at 6 atm 400 K followed by addition of aqueous
acid is called
(a) Kolbe reaction
(c) Cannizaro's reaction
(b) Wurtz reaction
(d) Reimer-Tiemann reaction
Q.28
The synthesis of PhOH from PhCl is called (
Q.74
a) Dow's process
(b) Cumene process
(c) Williamson's synthesis
(d) Kolbe-Schmidt process
d-block elements form coloured ion because
(a) they absorb some energy for d-s transition
(b) they absorb some energy for d-p transition
(c) they absorb some energy for d-d transition
(d) they do not absorb any energy
Q.29
One of the characteristic of transition metals to form the complex ion is
Q.30
(a) having unpaired electrons in d-subshell
(b) having paired electrons in d-subshell
(c) providing empty d-orbitals
(d) having small charge/size ratio
Methyl ketones are usually characterised through
(a) the Tollen's reagent
(b) the iodoform test
(c) the Schiff s test
Q.31
(d) the Benedict's reagent
If the activation energy of a reaction is zero, then the rate constant of this reaction
(a) increases with rise in temperature
(b) decreases with rise in temperature
(c) decreases with decrease in temperature (d) is independent of temperature
Q.32
Which of the following oxides is capable of reacting with HCl and NaOH ?
(a) CaO
Q.33
(b) ZnO
(b) ethers
(d) aldehydes and ketones
In 3d-transition series with increase in nuclear charge, the screening effect
(a) increases
(c) first decreases and then increases
Q.36
(b) formaldehyde oxirne
(d) acetoxime
Mono carboxylic acids are functional isomers of
(a) alcohols
(c) esters
Q.35
(d) CO2
The end product ‘C’ in the following sequence of chemical reactions is
2 OH

3  A Heat
 B NH

 C
CH3COOH CaCO
(a) acetaldehyde oxime
(c) methyl nitrate
Q.34
(c) N2O5
(b) decreases
(d) first increases and then decreases
Oxidation of acetaldehyde with selenium dioxide produces
(a) ethanoic acid
(b) methanoic acid
(c) glyoxal
(d) oxalic acid
Q.37
The half-life period of a radioactive substance if 87.5% of it disintegrates in 40 min, is
Q.38
(a) 160 min
(b) 10 min
(c) 20 min
(d) 13 min 20 s
How many grams of NaOH will be required to neutralize 12.2 g of benzoic acid?
(a) 40 g
(b) 4 g
(c) 16 g
(d) 12.2 g
Q.39
Which of the following is not a state function?
(c) W
(d)  H
Q.40
(a)  G
(b)  E
Amino acids are building blocks of
(a) carbohydrates
(b) vitamins
The standard emf for the cell reaction,
Zn + Cu 2   Zn 2  + Cu
(c) fats
(d) proteins
Q.31
is 1.1 Volt at 25°C. The emf of 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
Q.42
(b) 0.10V
(b) x < y
(c) x = y
(d) x  y
(c) 73 Li
(d) 84 Be
In the nuclear reaction 94 Be ( p, ) X , the X is
(a) 24 He
Q.45
(b) nucleoside linkage
(d) peptide linkage
Enthalpy change of CH4 + 1/2O2  CH3OH is negative. If enthalpy of combustion
of CH4 and CH3OH are x and y respectively, then which relation is correct?
(a) x > y
Q.44
(d) -0.110V
In polysaccharides, the linkage connecting mop asaccharide units is called
(a) glycoside linkage
(c) glycogen linkage
Q.43
(c) -1.10 V
(b) 63 Li
The hydrolysis of 1 mole of chloroform requires
(a) 1 mole of KOH
(c) 3 moles of KOH
(b) 2 moles of KOH
(d) 4 moles of KOH
Q.46
Aqueous solution of acetic acid contains
Q.47
(a) CH3COO  and H 
(b) CH3COO  , H3O  and CH3COOH
(c) CH3COO  , H3O  and H 
(d) CH3COOH, CH3COO and H 
Which of the following oxides of chromium is amphoteric in nature ?
Q.48
Q.49
Q.50
(a) CrO
(b) Cr2O3
Heat
 4K2CrO4 + 3O2 + X,
4K2Cr2O7 
In the above reaction, X is
(c) CrO3
(d) CrO5
(a) CrO3
(c) Cr2O3
(d) CrO5
(b) Cr2O7
Which one of the following forms a colourless solution in aqueous medium?
[Atomic numbers : Sc = 21, Ti = 22, V = 23, Cr = 24]
(a) Cr 3 
(b) Ti 3 
(C) Sc 3 
(d) V 3 
The reduction of which of the following compounds would yield secondary amine?
(a) Alkyl nitrile
(c) Primary amine
(b) Carbyl amine
(d) Secondary nitro compound
MATHEMATICS
Q.1
x2
If f ( x ) 
. Then
2x  3

 f (x) 
 2 
 x 
1/2
dx is equal to
 1  2 f (x) 
 3 f (x)  2 
  2 h
  c where
g
3  3 f ( x )  2 
2  1  2 f ( x) 
1
Q.2
(a) g( x )  tan 1 x , h ( x )  log|x|
(b) g( x )  log|x|, h ( x )  tan 1 x
(c) g( x)  h( x)  tan 1 x
(d) g(x)  log|x|, h(x)  log|x|
The function
f (x) |px  q| r|x|, x (, ) where
minimum value only of one point is
(a) p  q
Q.3
(b) r  q
The
area
of
the
feasible
3y  x  3, x  3, x  0 , y  0 will be
(a) bounded
Q.4
(b) unbounded
the
(c) convex
following
constraints
(d) concave
(b) on x-axis
(d) corner points of the feasible region
(b) -1
(c) 0
(d)
1
2
A function y = f(x) has a second order derivative f "(x) = 6(x - 1). If its graph passes
through the point (2, 1) and at that point the tangent to graph is y = 3x - 5,
then the function is
Let f(x) =
e
(a) (-  ,- 2)
Q.8
for

(a) (x - 1) 2
Q.7
region
(d) p  q  r
If f(x) = x log x and f (0) = 0, then the value of  for which Rolle's theorem can be
applied in [0, 1], is
(a) -2
Q.6
(c) r  p
its
The optimal value of the objective function is attained at the points
(a) on y-axis
(c) both the axes
Q.5
p  0 , q  0 , r  0 assume
(b) (x - 1) 3
x
(c) (x + 1) 3
(d) (x + 1) 2
(x - 1) (x - 2)dx. Then of decreases in the interval
(c) (1, 2)
(d) (2,  )
 A 1
B 1
For two events A and B, if P(A) = P    and P    , then
B 4
 A 2
(b) (-2, - 1)
Q.9
(a) A and B are independent
 A'  3
(b) P   
B 4
 B'  1
(c) P   
 A'  2
(d) All of the above
Let f : R  R be a differentiable function and f (1) = 4, then the value of

lim
4
x-1
f (x)
2t dt
x1
, if f ‘(1) = 2 is
(a) 16
Q.10
Q.13
(d) 2
(b) (–2, 0)
(c) (4, 0)
(d) (–4, 0)
If the parabola y 2  4ax passes through (–3, 2), then length of its latusrectum is
(a) 2/3
Q.12
(c) 4
If (2, 0) is the vertex andy-axis the directrix of a parabola, then its focus is
(a) (2, 0)
Q.11
(b) 8
(b) 1/3
(c) 4/3
(d) 4
If f ( x )  xe x( 1 x ) , then f (x) is
 1 
(a) increasing on   , 1
 2 
(b) decreasing on R
(c) increasing on R
 1 
(d) decreasing on   , 1
 2 
If a , b , c are the pth, qth, rth terms of an HP and u = (q - r) î + ( r – p ) ĵ + ( p - q) k̂
 iˆ ˆj kˆ
and v    , then
a b c
 
(a) u, v , are parallel vectors
 
(c) u .v =1
 
(b) u, v are orthogonal vectors

 
(d) u  v = î  ĵ  k
Q.14 A line through (0, 0) cuts the circle x 2 + y 2 - 2ax = 0 at A and B, then locus of the centre
of the circle drawn AB as diameter is
(a) x 2 + y 2 - 2ay = 0
(c) x 2 + y 2 + ax = 0
Q.15
(b) x 2 + y 2 + ay = 0
(d) x 2 + y 2 - ax = 0
If the chord y = mx + 1 of the circle x 2 + y 2 =1 subtends an angle of measure 45° at the
major segment of the circle, then value of m is
(a) 2
(b) -2
(c) -1
(d) None of these
Q.16 Let AB be a chord of the circle x 2 + y 2 = r 2 subtending a right angle at the centre. Then
the locus of the centroid of the  PAB as P moves on the circle is
Q.17
(a) a parabola
(b) a circle
(c) an ellipse
(d) a pair of straight lines
Two persons A and B throw a die alternately till one of them gets a 3 and wins the
game, the respective probabilities of winning, if A begins are
(a)
Q.18
Q.19
7 4
,
11 11
(b)
Q.21
(b)  / 3
(d)  / 6
(c)  / 4
If y 
a  bx 3 /2
and y  0 at x  5, then the ratio a : b is equal to
x 5 /4
(a)
5 :1
(b) 5 : 2
(c) 3 : 5
(d) 1 : 2
The area which does not represent a hyperbola, is
(b) x 2  y 2  5
The maximum value
x  y  10 , x , y  0 is
(a) 36
Q.23
4 3
(d) ,
7 7
(a) first and second quadrant
(b) second and third quadrant
(c) first and third quadrant
(d) third and fourth quadrant
If the direction ratios of two lines are given by 3lm – 4ln + mn = 0 and
l  2m  3n  0, then the angle between the lines is
(a) xy  1
Q.22
5 1
(c) ,
6 6
The graph of x  2 and y  2 will be situated in the
(a)  / 2
Q.20
6 5
,
11 11
of
(c) (x  1) ( y  3)  3
z  4x  2 y subject
(b) 40
to
the
(c) 20
(d) x 2  y 2  0
constraints
2 x  3 y  18 ,
(d) None of these
dx
 x (log x) (log log x)...(log log ...x) is equal to

 

8 times
(a) (log log ...x )  c

 

8 times
(b) (log log ...x )

 

7 times
(c) (log log ...x )  c

 

9 times
(d) None of these
Q.24
The straight lines 2 x  11 y  5  0 , 24 x  7 y  20  0 and 4x  3y  2  0
(a) form a right angled triangle
(c) form an equilateral triangle
Q.25
(b) form an isosceles triangle
(d) are concurrent
The probability of India wining a test match against West Indies is 1/2. Assuming
independence from match to match the probability that in a 5 match series India's
second win occurs at the third test, is
1
1
1
(b)
(c)
8
4
2
The angle between the pair of straight lines
y sin 2  - xy sin 2  + x 2 (cos 2  - 1) = 0 is
(a)
Q.26

(a)
Q.27
3

4
(c)

6
2
3
(b)
1
5
(c)
3
5
Q.30

2
(d)
2
5
The normal to the curve x = a(cos  +  sin  ), y = a(sin  -  cos  ) at any point
`  ' is such that
(a) it is at a constant distance from the origin
 

(b) it passes through  a ,a 
 2


(c) it makes angle   with the x-axis
2
(d) it passes through the origin
Q.29
(d)
2
3
A line makes the same angle  , with each of the x and z axes. If the angle  , which
it makes withy-axis is such that,
sin 2  R = 3 sin 2  , then cos 2  equals
(a)
Q.28
(b)
(d)
The solution of the differential equation x dy  y dx  x 2  y 2 dx is
(a) x  x 2  y 2  cx 2
(b) y  x 2  y 2  cx
(c) x  x 2  y 2  cx
(d) y  x 2  y 2  cx 2
If
 1 
t 2 f (t ) dt  1  sin x , x  [0 ,  / 2 ], then f 
 is
sin x
 3

1
Q.31
1
3
3
2
2
3
The two curves x  3xy  2  0 and 3x y  y  2  0
Q.32
(a) cut at right angles
(b) touch each other


(c) cut at an angle
(d) cut at an angle
3
4
If the slopes of the lines 3x 2 + 2hxy + 4y 2 = 0 are in the ratio 3 : 1, then h equals
(a) 3
(b)
(c)
3
1
1
(b) 
(c) 4
4
4
The eccentricity of the hyperbola 5x 2  4y 2  20x  8y  4 is
(a)
Q.33
(a)
Q.34
2
(d) 3
(c) non-coplanar
(d) non-collinear
(b) 1, 1, 2
5
4

x
0
(c) 1, 1, 2
(d)
2 , 1, 1
f (t ) dt . If F(x 2 )  x 2 (1  x), then f ( 4) equals
(b) 7
(c) 4
(d) 2
x 2 , x  0
Area of the region bounded by the curve y  
and the line y  4 is
 x, x  0
(a)
Q.38
(b) coplanar,
Let f : (0, )  R and F( x ) 
(a)
Q.37
(c) 2
The direction ratio of normal to the plane through (1, 0, 0), (0, 1, 0), which makes an

angle with plane x  y  3 , are
4
(a) 1, 2 , 1
Q.36
3
2
(d) None of these
The points A(4, 5, 1),B(O,-1,-1),C(3,9,4) and D(-4,4,4) are
(a) collinear
Q.35
(b)
(d) None of these
10
sq unit
3
(b)
20
sq unit
3
(c)
40
sq unit
3
1
1
1
1
is equal to


 ... 
n n
n2  n
n2  2 n
n 2  (n  1) n
lim
(d) None of these
(a) 2  2 2
Q.39
(d) 2
1 ˆ ˆ
( i  j)
2
(b)
1 ˆ ˆ
( i  j)
2
(c)
(d) None of these
A box contains 24 identical balls of which 12 are white and 12 are black. The balls are
drawn at random from the box one at a time with replacement. The probability that a
white ball is drawn for the 4th time on the 7th draw is
(a)
Q.41
(c) 2 2
A unit vector in xy-plane that makes an angle 45° with the vector ( iˆ  ˆj) and an angle
of 60° with the vector (3 iˆ  4 ˆj) is
(a) î
Q.40
(b) 2 2  2
5
64
If the function
(b)
27
32
(c)
5
32
(d)
1
2
f ( x )  2 x 3  9 ax 2  12a 2 x  1, where a  0 attains its maximum and
minimum at p and q respectively such that p 2  q , then a equals
(a) 3
(b) 1
(c) 2
Q.42
If P ( A  B)  0.8 and P ( A  B)  0.3, then P ( A)  P (B) equals to
Q.43
(a) 0.3
(b) 0.5
(c) 0.7
2
2
The equation x  2xy  y  3x  2  0 represents
Q.44
1
2
(d) 0.9
(a) a parabola
(b) an ellipse
(c) a hyperbola
(d) a circle
 x1 
1  1 2
3




Let X  x2  , A  2 0 1  and B   1  . If AX  B, then X is equal to
 x3 
 3 2 1 
 4 
1
(a) 2 
 3 
Q.45
(d)
  1
(b)   2 
 3 
  1
(c)   2 
  3 
  1
(d)  2 
 3 
Tangent at the vertex divides the distance between directrix and latusrectum in the
ratio
(a) 1 : 1
(b) 1 : 2
(c) depends on directrix and focus
Q.46
(d) None of the above
 e1 / x  1 x  0

For the function f ( x )   e1 / x  1 ,
, which of the following is correct?
 0 , x  0
(a) lim f ( x ) does not exist
x0
(b) lim f ( x )  1
x 0
(c) lim f ( x ) exist but f (x) is not continuous at x  0
x0
(d) f (x) is continuous at x  0
Q.47
The shaded region for the inequality x  5 y  6 is
(a) at the non-origin side of x  5y  6
(c) to the either side of x  5y  6
Q.48
Q.49
(b) to the origin side of x  5y  6
(d) to the neither side of x  5y  6
The set of all values of the parameters a for which the points of minimum of the
x2  x  2
 0 is
function y  1  a 2 x  x 3 satisfy the inequality 2
x  5x  6
(a) an empty set
(b) ( 3 3 ,  2 3 )
(c) ( 2 3 , 3 3 )
(d) ( 3 3 ,  2 3 )  ( 2 3 , 3 3 )
If tangents at A and B on the parabola y 2  4 ax intersect at point C, then ordinates of
A, C and B are
(a) always in AP
(b) always in GP
(c) always in HP
(d) None of these
2
2
Q.50 The parabolas y  4x and x  4 y divide the square region bounded by the lines
x  4 , y  4 and the coordinate axes of S1 , S2 , S3 are respectively the areas of these parts
numbered from top to bottom, then S1 : S2 : S3 is
(a) 1 : 1 : 1
(b) 2 : 1 : 2
(c) 1 : 2 : 3
(d) 1 : 2 : 1