Mahaentrance
Sample Test Paper
Physics
Q.1.
Q.2
Two capacitors of 2µF and 4µF are connected in parallel. A third capacilor of 6µF is
connected in series. The combination is connected across a 12 V battery. The voltage
across 2µF capacitor is
(a) 2 V
(b) 8 V
(c) 6 V
(d) 1 V
Assuming the sun to have a spherical outer surface of radius 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
r 2 (t  273) 4
4r 2 t 4
(b)
R2
4R 2
where  is the Stefan's constant.
(a)
Q.3.
(c)
16 2 r 2 t 4
R2
(d)
r 2 (t  273) 4
R2
Two capacitors of capacitances C1 and C2 are connected in parallel across a battery.
If Q1 and Q2 respectively be the charges on the capacitors, then Q1/Q2 will be equal
to
(a) C2 / C1
(b) C1 / C2
(c)
C 1 2 /C 2 2
(d) C 2 2 /C 1 2
Q.4. The thermo emf of thermocouple is given by e = 2164t - 6.2 t 2 , the neutral temperature
and a temperature of inversion are
(a) 349, 174.5
(b) 174.5, 349
(c) 349, 698
(d) 698, 349
Q.5.
The maximum number of possible interference maxima for slit-separation equal to
twice the wavelength in Young's double-slit experiment, is
(a) infinite
(b) five
(c) three
(d) zero
Q.5.
Q.6
The period of a satellite in circular orbit of radius 12000 km around a planet is 3h.
What is the period of a satellite in circular orbit of radius 48000 km around the same
planet ?
(a) 18 h
(b) 14 h
(c) 24 h
(d) 32 h
Two waves represented by y  a sin (t  kx) and y  a cos(t  kx) are superposed.
The resultant wave will have an amplitude
Q.7
(a) a
(b) 2 a
(c) 2 a
(d) zero
Surface temperature of the sun as estimated is 6032.25 K. The wavelength at which
sun radiates maximum energy is
(Given Wien's constant = 0.2898 cm-K)
0
(a) m  5000A
Q.8
Q10
0
(c) m  3809.5 A
0
(d) m  5000A
A wheel has angular acceleration of 3.0 rad/ s 2 and an initial angular speed of 2.00
rad/s. In a time of 2 s it has rotated through an angle (in radian) of
(a) 6
Q.9.
0
(b) m  4804.2 A
(b) 10
(c) 12
(d) 4
The resistance of an ammeter is 13  and its scale is graduated for a current up to
100 A. After an additional shunt has been connected to this ammeter it becomes
possible to measure currents up to 750 A by this meter. The value of shunt resistance
is
(a) 20 
(b) 2 
(c) 0.2 
(d) 2 k 
What is moment of inertia in terms of angular momentum (L) and kinetic energy (K)?
L
L
L2
L2
(a)
(b)
(c)
(d)
2
2K
K
2K
2K
Q.11. A disc of mass 2 kg and radius 0.2 m is rotating with angular velocity 30 rad/s. What
is angular velocity, if a mass of 0.25 kg is put on periphery of the disc?
(a) 24 rad/s
Q.12
(d) 26 rad/s
(b)
3
mgR
2
(c)
mgR
2
(d)
mgR
4
A piston of cross-section area A is fitted in cylinder in which gas of volume V at
pressure p is enclosed. Gas obeys Boyle's law, what is angular frequency if piston is
displaced slightly?
(a)
Q.14
(c) 15 rad/s
If a body is raised from the surface of the earth upto height R, what is the change in
potential energy?
(a) mgR
Q.13
(b) 36 rad/s
Ag
V
(b) 2
Ag
V
(c)
2 Ag
V
(d)
3 Ag
V
A 50 Hz AC current of crest value 1 A flows through the primary of a transformer. If
the mutual inductance between the primary and secondary be 0.5 H, the crest voltage
induced in the secondary is
(a) 75 V
(b) 150 V
(c) 100 V
(d) None of these
Q.15. If I 1 is the moment of inertia of a thin rad about an axis perpendicular to its length
and passing through its centre of mass and I 2 is the moment inertia of the ring formed
by bending the rod, then
(a) I 2 
I1
4 2
(b) I 2 
I1
(c)
I2
 0.3
I1
(d)
I2  2

I1
3
2
Q.16. The material of a wire has a density of 1.4 g/cm 3 . If it is not wetted by a liquid of
surface tension 44 dyne/cm, then the maximum radius of the wire which can float on
the surface of liquid is
10
12
10
cm
(b)
cm
(c)
cm
(d) 0.7 cm
28
14
7
Q.17. Two concentric spheres of radii R and r have similar charges with equal surface
densities (  ). What is the electric potential at their common centre ?
(a)
(a)
Q.18

0
Q.20

(R  r )
0
(c)

(R  r )
0
(d) None of these
Consider two points 1 and 2 in a region outside a charged sphere. Two points are not
very far away from the sphere. If E and V represent the electric field vector and the
electric potential, which of the following is not possible ?
(a) E1
Q 19
(b)
(b) El # E2,V1#V2
(c) El#E2,V1=V2
(d) Ell=IE2I,Vl#V2
Two spheres of equal masses, one of which is a thin spherical shell and the other a solid,
have the same moment of inertia about their respective diameters. The ratio of their radii
will be
(a) 5 : 7
(b) 3 : 5
(c) 3 : 5
(d) 3 : 7
A material has Poisson's ratio 0.20. If a uniform rod of it suffers a longitudinal strain
of 2  103 , the percentage change in volume is
(a) - 0.28
(b) + 0.28
(c) - 0.12
(d) + 0.12
Q.17 A circular coil of 5 turns and of 10 cm mean diameter is connected to a voltage source.
If the resistance of the coil is 10  , the voltage of the source so as to nullify
the horizontal
component of earth's magnetic field of 30 A turn m 1 at the centre of
the coil should be
Q.20
(a) 6 V, plane of the coil normal to magnetic meridian
(b) 2 V, plane of the coil normal to magnetic meridian
(c) 6 V, plane of the coil along the magnetic meridian
(d) 2 V, plane of the coil along the magnetic meridian
The work function of a surface of a photosensitive material is 6.2 eV. The wavelength
of the incident radiation for which the stopping potential is 5 V lies in the
(a) ultraviolet region
(b) visible region
(c) infrared region
Q.21
The ground state energy of hydrogen atom is -13.6 eV. When its electron is in the first
excited state, its excitation energy is
(a) 3.4 eV
Q.22
Q.25
(b) 2.44 cm
(b) 0.75  108
(c) 3.12 cm
(d) 3.86 cm
(c) 12  108
(d) 14  108
(a) 1 : 30
(b) 30 : 1
(c) 42 : 14
(d) 14 : 42
A slit of size 0.15 cm is placed at 2.1 m from a screen. On illuminated it by a light of
wavelength 5  105 cm. The width of central maxima will be
(b) 0.14 mm
(c) 1.4 mm
(d) 0.14 cm
A thin mica sheet of thickness 2  106 m and refractive index (  = 1.5) is introduced
in the path of the first wave. The wavelength of the wave used is 5000A. The central
bright maximum will shift
(a) 2 fringes upwards
(c) 10 fringes upwards
Q.27
(d) zero
What will be the ratio of temperature of sun and moon, if the wavelength of their
maximum emission radiations rates are 140 A and 4200A respectively ?
(a) 70 mm
Q.26
(c) 10.2 eV
A paramagnetic substance of susceptibility 3  104 is placed in a magnetic field of
4  104 Am 1 . Then, the intensity of magnetization in the units of Am 1 is
(a) 1.33  108
Q.24
(b) 6.8 eV
If the surface tension of water is 0.06 Nm 1 , then the capillary use in a tube of
diameter 1mm (   0 ) is
(a) 1.22 cm
Q.23
(d) X-ray region
(b) 2 fringes downwards
(d) None of these
The photoelectrons emitted from a given cathode, on the incidence of a given
monochromatic beam of light, have
(a) an energy spread with a lower limit
(b) an energy spread with an upper limit
(c) an energy spread with no sharp limit
(d) a definite energy only
Q.28
A transformer has an efficiency of 80%. It is connected to a power input of 5 kW at
200 V. If the secondary voltage is 250 V, the primary and secondary currents are
respectively
Q.29
(a) 25 A, 20 A
(b) 20 A, 16 A
(c) 25 A, 16 A
(d) 40 A, 25 A
A p-n photodiode is made of a material with a band gap of 2.0 eV. The minimum
frequency of the radiation that can be absorbed by the material is nearly
(a) 10  1014 Hz
Q.30
(b) 5  1014 Hz
(c) 1  1014 Hz
(d) 20  1014 Hz
A satellite of mass ms revolving in a circular orbit of radius rs around the earth of
mass M has a total energy E. Then, its angular momentum will be
E
E
(b)
(c) 2Ems rs 2
(d) 2Ems rs
2
2 ms rs 2
ms rs
There is a horizontal film of soap solution. On it a thread is placed in the form of a
loop. The film is pierced inside the loop and the thread becomes a circular loop of
radius R. If the surface tension of the loop be T. Then, what will be the tension in the
thread ?
(a)
Q.31
(a) Rn 2T
Q.32
3
H
16
(b) 4 times
(c) 16 times
(d) 100 times
(b)
16
H
3
(c)
9
H
27
(d)
1
H
16
Two particles of masses m and M are initially at rest and infinitely separated from
each other. Due to mutual interaction they approach each other. Their relative
velocity of approach at a separation of distance d between them, is
2G( M  m)
d
2Gd
 M m
(c)
(d) 2G 

Mm
 d 
A body cools from 50.0°C to 49.9°C in 5 s. How long will it take to cool from 40.0°C
to 39.9°C? Assume the temperature of surroundings to be 30.0°C and Newton's law
of cooling to be valid
(a) [2G(M + m)] 1 / 2
Q.35
(d) 2 RT
A sphere at temperature 600 K is placed in an environment of temperature is 200 K.
Its cooling rate is H. If its temperature reduced to 400 K then cooling rate in same
environment will become
(a)
Q.34
(c) 2 RT
The electric heater, assumed to be black body has a temperature of 727°C. If its
temperature is raised to 1727°C, the amount of energy radiated per unit time now as
compared with that in the first case will be
(a) 2 times
Q.33
(b) R 2T
(b)
(a) 2.5 s
Q.36
(b) 10 s
(c) 20 s
If the radius of the earth were to shrink by 1%, its mass remaining the same, the
acceleration due to gravity on earth surface would
(a) decrease by 2%
(c) increase by 2%
Q.37
(d) 5 s
(b) remain unchanged
(d) increase by 1%
In order to find time, an astronaut orbiting in earth's satellite should use
(a) pendulum clock
(b) a watch having a main string to keep it going
(c) either a pendulum clock or a spring watch
(d) neither a pendulum clock nor a spring watch
Q.38
A particle under the action of an SHM has a period 3 s and under the effect of
another it has a period 4 s. What will be its period under the combined action of both
the two simple harmonic motions in the same direction?
(a) 7 s
Q.39
3
T
8
(b)
5
T
8
(c)
5
T
12
(d)
3
th oscillation is
8
T
3
(b) 8  102 J
(c) 10 3 J
(d) 0.4  103 J
A thin wire of mass M and length L is bent to form a circular ring. The moment of inertia
of this ring about its axis is
(a)
Q.42
(d) 0.4 s
When the load on a wire is increased slowly from 2 kg to 4 kg the elongation
increases from 0.6 mm to 1.0 mm. The work done during the extension of the wire is
(g = 10 m/s 2 )
(a) 14  103 J
Q.41
(c) 2.4 s
A particle undergoes SHM having time period T. The time taken in
(a)
Q.40
(b) 5 s
1
4
2
ML2
(b)
1
ML2
12
(c)
1
3
2
ML2
(d)
1
2
ML2
If g is the acceleration due to gravity on earth's surface, the gain of the potential energy
of an object of mass m raised from the surface of the earth to a height equal to the radius
R of the earth is
(a) 2 mgR
Q.43
(b) mgR
(c)
1
mgR
2
(d)
1
mgR
4
A wave travelling along a string is described by the equation
y  A sin(t  kx)
The maximum particle velocity is
(a) A
(b)  / k
(c) d / dk
(d) x / l
Q.44. Two cells, having the same emf, are connected in series through an external
resistance R. Cells have internal resistances r1 and r2 (rl > r2), respectively. When the
circuit is closed, the potential difference across the first cell is zero. The value of R is
(a) r1 - r2
(b)
r1  r2
2
(c)
r1  r2
2
(d) r1 + r2
Q.45. Which one of the following statements is true?
(a) Both light and sound waves in air are transverse
(b) The sound waves in air are longitudinal while the light waves are transverse
(c) Both light and sound waves in air are longitudinal
(d) Both light and sound waves can travel in vacuum
Q.46. Three objects coloured black, gray and white can with stand hostile conditions at
2800°C. These objects are thrown into furnace where each of them attains a
temperature of 2000°C. Which object will glow brightest?
Q.47
(a) The white object
(b) The black object
(c) All glow with equal brightness
(d) They gray object
A photon and an electron have equal energy E. photon / electron is proportional to
(a) E
(c) 1/E
Q.48
Q.49
(b) 1 / E
(d) does not depend on E
Light from a hydrogen discharge tube is incident on the cathode of a photoelectric
cell the work function of the cathode surface is 4.2 eV. In order to reduce the photocurrent to zero the voltage of the anode relative to the cathode must be made
(a) – 4.2 V
(b) –9.4 V
(c) – 17.8 V
(d) +9.4 V
A solid sphere is rotating in free space. If the radius of sphere is increased keeping
mass same which one of the following will not be affected?
(a) Angular velocity
(c) Moment of inertia
(b) Angular momentum
(d) Rotational kinetic energy
Q.50. The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If
the magnetic flux  linked with the primary coil is given by
  0  4t , where  is in
weber, t is time in second and 0 is a constant, the output voltage across the secondary coil is
(a) 90 V
(b) 120 V
(c) 220 V
(d) 30 V
Chemistry
Q.1
Mark the correct statement
(a) methyl amine is slightly acidic
(b) methyl amine is less basic than ammonia
(c) methyl amine is a stronger base than ammonia
(d) methyl amine forms salts with alkalies
Q.2
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.3
A mixture of 10, 2° and 3° amines can be separated by Hinsberg's reagent which is
(a) benzoyl chloride
(c) benzene sulphonyl chloride
Q.4
(b) acetyl chloride
(d) benzyl chloride
Heroin is an example of
(a) caffeine
(b) cocaine
(c) nicotine
(d) morphine
Q.5.
The solubility of Al(OH)3 is ‘S’ mol/L, its Ksp is
Q.6.
(a) S 2
(b) 27S 4
(c) S 3
(d) 4S 3
An haloalkane is made to react with excess of alcoholic ammonia to give mainly
(a) 1° amine
(b) mixture of 1°, 2°, 3° amines
(c) mixture of 1° and 3° amines
(d) mixture of 1°, 2°, 3° amines and quarternary ammonium salts
Q.7.
The pH of a solution of NaOH having concentration of 0.4 g/L will be
Q.8.
(a) 0
(b) 7
(c) 12
(d) 1
What is the change in internal energy of an ideal gas sample over one complete
(a) Positive
(c) Zero
Q.9.
Q.10
(b) Negative
(d) Depends upon the nature of the path
Which type of thermodynamic process is the heating of water under atmospheric
pressure?
(a) Adiabatic
(b) Isobaric
(c) Isochoric Which of the following is used as an antiseptic?
(a) Phenol
(c) Benzalamine
Q.11
In presence of Na2CO3, the solubility of silver carbonate is expressed by the term
(b) 2[Na  ]
The degree of dissociation of
dissociation of
N
NH4OH ?
2
(a) 0.030
Q.13
(b) 0.015
1
[Ag  ]
2
(d) [Ag  ]
N
NH4OH is 0.03. What would be the degree of
80
(c) 0.035
(d) 0.025
(b) 10 3 M NH4OH
(d) 10 3 M HBr
Solubility product of M(OH)x, is 4  1012 M and the solubility is 10 4 M. Here x would
(a) 1
Q.15
(c)
Solubility of AgBr would be maximum in this solution
(a) 10 3 M NaBr
(c) distilled water
Q.14
be
(d) None of these
(b) Benzaldehyde
(d)Malic anhydride
(a) [Co 3 2  ]
Q.12
cycle?
(b) 3
(c) 2
The first law of thermodynamics confirms the law of
(a) conservation of energy
(b) conservation of momentum of molecules
(c) flow of heat in a particular direction
(d) conservation of heat energy and mechanical energy
(d) 4
Q.16. Enthalpy of formation of ammonia is - 46.0 kJ/mol. The enthalpy for the reaction,
2N2(g) + 6H2(g)  4NH3(g) is equal to
(a) 184.0 kJ
(b) -184.0 kJ
(c) 46.0 kJ
(d) - 46.0 kJ
Q.17. The main product of the reaction CH3CH2Br and AgCN is
(d) H2C=CH2
Q.18
(a) CH3CH2CN
(b) H3CCH2N  C 
(c) CH3CH2CH2Br
Glucose reacts with acetic anhydride to form
(d) hexa-acetate
Q.19
(a) mono-acetate
(b) tetra-acetate
(c) penta-acetate
Which of the following monosaccharide is a pentose ?
(a) Glucose
(d) Fructose
Q.20
(c) Arabinose
The chemical extracted from the plant Rauwolfia serpentina is
(a) aspirin
Q.21
(b) Galactose
(b) quinine
(c) bithional
(d) reserpine
(c) Morphine
(d) Phenacetin
Which of the following is a tranquillizer?
(a) Seconal
(b) Streptomycin
Q.22. The main product of the reaction of an alkyl halide with potassium nitrate is
(a) alkane
(b) alkene
Q.23. The antiseptic action of dettol is due to
(a) chlorobenzene
(c) chloroquine
(c) nitro alkane
(d) alkyl nitrite
(b) chloroxylenol
(d) chloramphenicol
Q.24. The half-life of a first order reaction A  B is 10 min. What % of A remains after
60 min?
(a) 60%
(b) 16.6%
(c) 1.56%
(d) 3.12%
Q.25. Which of the following is used to study kinetics of a reaction?
(a) Dilatometer
(b) Calorimeter
(c) Refractometer
(d) None of these
Q.26. The solubility product of AgCI in water at 20°C is 1  10 20 . Its solubility in g/L will
be
(a) 1.435  10 25
(b) 10 5
(c) 1.435  10 8
(d) 1.435  1010
Q.27. Normal aluminium electrode coupled with normal hydrogen electrode gives an emf
of 1.66 V, so the standard potential of Al is
Q.28
Q.29
(a) -1.66 V
(b) + 1.66 V
(c) -0.83 V
(d) + 0.83 V
Unpleasant smelling carbylamines are formed by heating alkali and chloroform with
(a) any aliphatic amine
(b) any aromatic amine
(c) any amine
(d) any primary amine
Which of the following is an example of the nucleophilic substitution reaction?

(a) CH3Br + (CH3)2NH 

(CH
N HBr
3 ) 33CH
(b)
CH
= CH2 + Br2 
 BrCH2CH =
CH
Ether
2
(c) C H Cl + Na  C H – C H
6
5
(d)
6
5
6
5
OCH3 + HNO3
OCH3
O2N
Q.30
Keratin is the protein present in
(a) muscles
Q.31
(b) hair and nails
(c) stomach
(d) None of these
An organic compound, on treatment with Br2 in CCl4 gives bromo derivative of an
alkene. The compound will be
(a) CH3-CH = CH2
(b) CH3-CH = CH-CH3
(c) HC  CH
(d) H2C = CH2
Q.32. The hydrogen electrode is dipped in a solution of pH = 3.0 at 25°C. The potential of
hydrogen electrode would be
Q.33
(a) 0.177V
(b) -0.177 V
(c) 0.087 V
When dihydroxy acetone reacts with H104, the products is/are
Q.34
(a) HCHO
(c) HCHO and HCOOH
Tear gas is
Q.36
(a) chloretone
(b) ethyl carbonate
(c) chloropicrin
(d) methylene chloride
The fibre of dacron blended with wool is called
(a) terycott
(b) perlon
(d) 0.059 V
(b) HCOOH
(d) HCHO and CO2
(c) tery wool
(d) catswool
Q.37
Which type of bond is formed when amines donate lone pair of electrons to proton?
(a) Covalent bond
(c) Ionic bond
Q.38
(b) Electrovalent bond
(d) Dative bond
For which of the following reactions  H is less than  E .
(a) HCl(aq) + NaOH(aq)  NaCl(aq) + H2O(l)
(b) H2(g)+I2(g)  2HI(g)
(c) C(s) + O2(g)  CO2(g)
(d) N2(g) + 3H2(g)  2NH3(g)
Q.39
Which of the following is not an anodic reaction?
(a) Cu  Cu 2  + 2e 
(c) Fe 2   Fe 3  + e
Q.40
(b) Ag  + e   Ag
(d) 40H   2H2O + O2 + 4e 
Periodic acid oxidises
(a) 1, 4-diols
(c) 1, 3-diols
(b)  -ketone aldehyde
(d) 1, 2-diols
Q.41. When one mole of copper (II) chloride is electrolysed, one mole of chlorine gas will
be liberated at anode by passage of
(a) 1 Faraday of electricity
(c) 35.5 Faraday of electricity
(b) 2 Faraday of electricity
(d) half a faraday of electricity
Q.42. The ionisation constant of NH4OH is 1.8  105 . The degree of ionisation of a 0.02 M
solution will be
(a) 3  102
(b) 0.3
(c) 4.5  103
(d) 6  103
Q.43 Acetamide is
Q.44
(a) feebly basic
(b) feebly acidic
(c) amphoteric
(d) neutral
In the electrolysis of water, one Faraday of electrical energy would evolved
(a) 1 mole of oxygen
(c) 8 g of oxygen
Q.45. Which one/ones will yield 2-propanol?
(b) 1 g atom of oxygen
(d) 22.4 L of oxygen

(ii) CH2 = CH – CH3 + H2O H

MgI
(i) CH3CHO CH
3

H2O
(iii) CH2 = CH – CH3 Neutral


2 H 5 MgI
(iv) CH2O C

(a) (i) and (ii)
(b) (i) and (iv)
(c) (iv) and (ii)
235
92 U
products + neutrons + 3.20  1011 J. The energy released when
KMnO 4
Q.46
1
0 n  fission
235
92 U undergoes
+
1 g of
(a) 12.75  108 kJ
H2O
(d) (iii) and (i)
fission is
(b) 18.60  109 kJ
(c) 8.20  107 kJ
(d) 6.55  106 kJ
Q.47 The half-life period of a radioactive substance is 45 min. The time during which 99.9%
of it will disintef;rate is
(a) 5
Q.48
1
h
2
(b) 6
3
h
4
(c) 7
1
h
2
(d) 7
3
h
4
Highest pH (14) is given by
(a) 0.1 M H2SO4
(b) 0.1 M NaOH
(c) 1 N NaOH
(d) 1 N HCl
Q.49. The heat of formation of C02 is -393.5 kJ. The heat of decomposition of C02 into the
elements, is
(a) 161.7 kJ
Q.50
(b) 196.7 KJ
(c) 203 kJ
(d) 393.5 kJ
(c) H3PO4
(d) PO 34
The conjugate base of H2PO 4 is
(a) HPO 24 
(b) P2O5
MATHEMATICS
Q.1
Angle between the tangents to the curve y  x 2  5x  6 at the points (2, 0) and (3, 0)
is
(a)
Q.2

2
(b)
The value of the integral
(a)
3
2

6

6
3
(b) 2
(c)

4
(d)

3
x
dx is
9x  x
(c) 3
(d) 6
Q.3
The switching function for switching network is
y
x
y'
If y 
(a)
Q.5
Q.6
(b) (x  y  z)  (x  y   z)
(d) None of the above
dy
1  ex
is equal to
, then
x
dx
1e
ex
(1  e x ) 1  e 2 x
(b)
ex
(1  e x ) 1  e 2 x
(c)
ex
(d) 2x2y
1  e 2x
A circle is drawn to cut a chord of length 2 a unit along x-axis and to touch the y-axis.
The locus of the centre of the circle is
(a) x 2  y 2  a 2
(b) x 2  y 2  a 2
(c) x  y  a 2
(d) x 2  y 2  4 a 2




 


The value of [a  b b  c c  a ], where |a| 1,|b| 5 and |c| 3 , is
(a) 0
Q.7
x'
z'
(a) (x  y )  ( y  z)  ( z  x)
(c) (x  y )  ( y  z)  ( z  x)
Q.4
z
(b) 1
(c) 2
(d) 4
The probability that a leap year will have 53 Fridays or 53 Saturdays, is
2
3
4
1
(b)
(c)
(d)
7
7
7
7
The points (5, –4, 2), (4, –3, 1), (7, –6, 4) and (8, –7, 5) are the vertices of
(a)
Q.8
(a) a rectangle
Q.9
Q.10
(b) a square
(c) a parallelogram
(d) None of these
A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius
2. The locus of the centre of the circle is
(a) a parabola
(b) a hyperbola
If
the
interval
difference
(c) a circle
is
1,
then
(d) an ellipse
3 (1  x) (1  2 x)
( 1  3x ) is equal to
(a) 25
Q.11
(b) 32
(c) 40
(d) – 36
The straight line joining the origin to the points of intersection of curves
ax 2  2hxy  by 2  2 gx  0 and ax 2  2 hxy  by 2  2 gx  0 are at right angles, if
(a) g( a  b)  g( a  b)
(c) g( a  b)  g( a  b)
Q.12
The function f ( x ) 
9
17
(a)
Q.16
(b)
5
13
(d) x  2
(c)
(b)
6
13
8
9
(d)
1
9
2
y2
x2
x2 y

 1 and 2  2  1 are equal, then the
169 25
a
b
(c)
13
5
(d)
13
6
If C is the mid point of AB and P is any point outside AB, then

(a) PA  PB  PC  0

(b) PA  PB  2 PC  0
(c) PA  PB  PC
(d) PA  PB  2 PC
The equations of tangents to the ellipse 3x 2  4 y 2  5, which are inclined at 30° to the
x-axis, are
5
2
(b) y 
1
5
x
2
3
(c) y 
1
x1
3
(d) None of these
If the lines x  a  m , y  2 and y  m x are concurrent, the least value of |a|is
(a) 0
Q.18
8
17
a
is
b
(a) y  3 x 
Q.17
(c) x  1
If the eccentricity of the two ellipse
value of
Q.15
(b) x  0
Two persons A and B take turns in throwing a pair of dice. The first person to
through 9 from both dice will be awarded the prize. If A throws first, then the
probability that B wins the game is
(a)
Q.14
(d) None of the above
x 2
 has a local minimum at
2 x
(a) x  2
Q.13
(b) g( a  b)  g ( a  b)
(b)
2
Simpson’s rule for evaluation of
into a
(c) 2 2

b
a
(d) None of these
f ( x ) dx requires the interval ( b  a ) to be divided
Q.19
(a) 3 n intervals
(b) 2n intervals
(c) (2n + 1) intervals
(d) any number of intervals
 1  3  4


4  is nilpotent of index
The matrix A =  1 3
 1  3  4 
(a) 3
Q.20
Q.21
Q.22
(b) 2
(c) 1
(d) 4
2  1
1
 1 1
2  , then det [adj (adj A)] is equal to
If A = 
 2  1 1 
(a) 12 4
(b) 13 4
(c) 14 4
If f (x) is differentiable function and f "(0) = a, then
2 f ( x ) - 3 f (2x )  f (4x)
is equal to
lim
x 0
x2
(d) None of these
(a) 3a
(d) 4a
(b) 2a
The solution of the equation x 2
(c) 5a
d2y
dy
= -1 is
2 = log x when x = 1, y = 0 and
dx
dx
1
1
(log x)z + log x
(b) y = (log x)z - log x
2
2
1
1
(c) y = - (log x)z + log x
(d) y = - (log x)z - log x
2
2
2
If the slope of one of the lines given by ax + 2hxy + by 2 = 0 is 5 times the other, then
(a) y =
Q.23
(a) 5h 2 = ab
(c) 9h 2 = 5ab
Q.24
Area bounded by the curve y 2  16x and line y  m x is
(a) 3
Q.25
(b) 5h 2 = 9ab
(d) h 2 = ab
If ellipse
is
(b) 4
(c) 1
2
, then m is equal to
3
(d) 2
x2 y2

= 1 is rotated 90° about origin, then equation of ellipse after rotation
a2 b2
x2 y2
(a) 2  2 = 1
a
b
(b)
y2
x2

=1
a( a  b ) b( a  b )
Q.26
x2 y2
(c) 2  2 = 1
a
b
Dual of x  (y  x) = x is
(d) None of these
(a) x  (y  x) = x
(c) (x  y)  (x  x) = x
Q.27
If p  (q  r ) is false, then the truth values of p, q , r are respectively
(a) F, T, T
Q.28
(b) x  (y  x) = x
(d) None of the above
(b) T, T, F
(c) T, F, F
The equation of the plane in which the lines
x 5 y 7 z 3
x8 y 4 z5




and
lie, is
4
4
5
7
1
3
(a) 17x - 47y - 24z +152= 0
(c) 17x + 47y + 24z + 172 = 0
Q.29
(d) F, F, F
(b) 17x + 47y - 24z + 172 = 0
(d) 17x - 47y + 24z + 172 = 0
If a , b , c are non-coplanar vectors and  is a real number, then
[  ( a + b ) 2 b  c ] = [ a b + c b ] for
(a) exactly two values of 
(c) no value of 
Q.30
The latusrectum of the parabola y 2 = 4ax whose focal chord is PSQ such that SP = 3
and SQ = 2, is given by
(a)
Q.31
24
5
If f (x) =
(b)
12
5
(c)
6
5
(d)
1
5
x 2 - 10x  25
for x  5 and f is continuous at x = 5, then f (5) is equal to
x 2  7 x  10
(a) 0
Q.32
(b) exactly three values of 
(d) exactly one value of 
(b) 5
(c) 10
(d) 25
Tangent of the angle at which the curves y, = a x and y = b x (a  b > 0) intersect, is
given by a
log ab
(a)
1  log ab
a
log ab
b
(b)
(c)
1  ( log a)( log b )
1  ( log a)( log b)
log
(d) None of these
Q.33
Which of the following is not a proposition ?
(b) 2 is irrational
(d) 5 is an even integer
(a) 3 is a prime
(c) Mathematics is interesting
Q.34
3  3 4


If A  2  3 4  , then adj (adj A) is
0  1 1 
(a) A
Q.35
(b) 2A
The limiting points of the
2 ( x 2  y 2 )   x  9 / 2  0 are
 3 
(a)   , 0 
 2 
(c) 3A
system
9 
(b) (0, 0) and  , 0 
2 
of
circle
(d) None of these
represented
 9 
(c)   , 0 
 2 
by the
equation
(d) ( 3, 0)
Q.36 Three houses are available in a locality. Three persons apply for the houses. Each applies
for one house without consulting others. The probability that all the three apply for the same
house, is
(a)
Q.37
Q.38
(b)
8
9
(c)
1
9
(d)
2
9
 x2  1

If lim  2
 ( ax  b)  2 , then
x  x  1


(a) a  1 and b  1
(b) a  1 and b  1 (c) a  1 and b  2
4
2  x 3
 1
 1 2  is a singular matrix, then x is
If 
 x
1  5
(a)
Q.39
7
9
13
25
Given that
0
x
1
tan x 0.785
(b) 
1
1.107
25
13
2
1.249
(c)
3
1.326
4
1.373
5
13
(d) a  1 and b  2
(d)
25
13
1
Using Simpson's   rd rule, the approximate value of
3
(a) 4.796
Q.40
(b) 3
(b) 2
tan 1 x dx is
(c) 2.796
(d) 5.796
(c) 4
(d) 5
(c) 3
(d)
1
3
For the following linear programming problem minimize Z = 4x + 6y subject to the
constraints 2x + 3y  6, x + y  8, y  1, x  0, the solution is
3 
(b) (0, 2) and  ,1 
2 
(d) (0, 2) and (1, 5)
(a) (0, 2) and (1, 1)
(c) (0, 2) and (1, 6)
Q.43
1
The greatest value of f ( x )  ( x  1)1 / 3  ( x  1)1 / 3 on [0, 1] is
(a) 1
Q.42
5
A coin is tossed n times. The probability of getting head at least once is greater than
0.8, then the least value of n is
(a) 2
Q.41
(b) 3.796

The triangle formed by the tangent to the curve f ( x )  x 2  bx  b at the point (1, 1)
and the coordinate axes, lies in the first quadrant. If its area is 2, then the value of b is
(a) -1
Q.44
(d) 1
(b) F, F
(c) T, T
(d) T, F
Which of following pair of straight lines intersect at right angle ?
(a) 2x 2 = y (x + 2y)
(c) 2y (x + y) = xy
Q.46
(c) -3
If p  (~ p  q) is false, then truth value of p and q are respectively
(a) F, T
Q.45
(b) 3
(b) (x + Y) 2 = x(y + 3x)
(d) y = ± 2x
2
x2 y

 1, which are perpendicular to the line
Equation of tangents to the ellipse
9
4
3x  4 y  7 , are
(a) 4 x  3y   20
Q.47
(b) 4 x  3y   12
(c) 4x  3y   2
(d) 4 x  3 y   1
The coordinates of the foot of perpendicular drawn from point P (1, 0, 3) to the join of
points A ( 4, 7 , 1) and B (3, 5, 3) is
(a) (5, 7, 1)
Q.48
Q.49
 5 7 17 
(b)  , , 
3 3 3 
5 2 7
(d)  , , 
3 3 3
A bag contain 5 black balls, 4 white balls and 3 red balls. If a ball is selected random
wise the probability that it is a black or red ball, is
(a) 1/3
(b) 1/4
(c) 5/12
(d) 2/3
A line with direction cosines proportional to 2,1, 2 meets each of the lines x = y + a = z
and x + a = 2y =2z. The coordinates of each of the points of intersection are given by
(a) (3a, 3a, 3a), (a, a, a)
(c) (3a, 2a, 3a), (a, a, 2a)
Q.50
2 5 7
(c)  , , 
3 3 3
(b) (3a, 2a, 3a), (a, a, a)
(d) (2a, 3a, 3a), (2a, a, a)
The equation of the circumcircle of the triangle formed by the lines x  0 , y  0 and
2 x  3y  5, is
(a) 6 ( x 2  y 2 )  5 ( 3x  2 y )  0
(b) x 2  y 2  2 x  3y  5  0
(c) x 2  y 2  2 x  3y  5  0
(d) 6 ( x 2  y 2 )  5 ( 3x  2 y )  0