CUSAT CAT 2025 Question Paper with Answer Key B.Tech Shift II

FOR CUSAT CAT EXAM PREPARATION

CUSAT CAT 2025
Question Paper ·
B.Tech Shift II
EXAM YEAR TYPE SUBJECT INCLUDES

CUSAT CAT 2025 Question Paper B.Tech Shift II Answer Key

Notes · Sample Papers · Previous Year Papers · Mock Tests

m
m .co

m .co s em
se g la
1. a constant G are respectively
The dimensional formula of latent heat and gravitational

(A) ML2T−2 and M2L1T−1
(B) ML−2T−2 and M2L3T−1
(C) ML2T−1 and M2L0T−1
(D) M0L2T−2 and M−1L3T−2

m
m .co
.co
2. The period of oscillation of a simple pendulum of length l is about 0.5sec. The time of
e m
100 oscillations has been measured with a stop watch of 1 sec resolution. The length l
em l as
las
is 10cm measured with the accuracy of 1mm. Then the percentage error in the g
measurement is ag
g
a(A) 1%
(B) 2%
(C) 3%
(D) 5%

3. The radius of a planet is double that of the earth but their average densities are the

m
same. If the escape velocities at the planet and the earth are v p and ve respectively,
then
m .co
s e
(A) v p = 2ve
g la
(B) 2v p = ve a
(C) v p = ve
1
(D) v p = ve
4

4. A particle is projected at 60° to the horizontal with a kinetic energy K. The kinetic
m
m energy at highest point is
.co
m .co (A) Zero s e m
s e g l a
la a
K
(B)
ag 4
K
(C)
2
(D) K

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 1 of 51

5. What is the angle between the frictional force and the instantaneous velocity of a
vehicle plying on a rough road?

(A) 0°
(B) 45°
(C) 90°
(D) 180°

6. When the kinetic energy of a body increases by 4 times,then its momentum increases
by

(A) 2 times
(B) 16 times
(C) 2 times
(D) 4 times

7. The radius of the earth is approximately 6000km, the weight of the object 6000km
above the surface of the earth is

(A) 4g
(B) g
g
(C)
2
g
(D)
4

8. The acceleration due to gravity on the moon's surface is 1.7m/sec2 and acceleration
due to gravity on earth is 9.8m/sec2 . If time period of a simple pendulum on the earth
is 3.5sec, its time period on the moon is

(A) 7sec
(B) 8.4sec
(C) 10.2sec
(D) 11.8sec

9. According to Stefan’s law the total radiant energy emitted per second per unit surface
area of a black body is proportional to

(A) T−1
(B) T
(C) T−4
(D) T4

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m
m .co

m .co s em
se g la
10. a At a distance of 5cm from the
An electric current passes through a long straight wire.
wire, the magnetic field is B. The magnetic field at 20cm from the straight wire would
be

B
(A)
6
B
(B)
m
.co
4
m
.co m
B
(C)
m s e
3
s e l a
(D)l a B
ag
ag 2
Cp
11. The ratio of specific heats = γ in terms of degrees of freedom (f) is given by
Cv

 f 
(A) 1 + 
 3
m
(B)
 2
1 + 
m .co
 f 
s e
 f 
1 +  g la
(C)
 2 a
 1
(D) 1 + 
 f 

12. What is the wavelength of a television station which transmits vision on 500 MHz?

(A) 0.6m
m
.co
(B) 0.8m
m
.co em
(C) 1m

e m (D) 1.1m
la s
las a g
ag 13. A source of sound of frequency 600Hz is placed inside water. The speed of the sound
in water is 1500m/sec and in air is 300m/sec. The frequency of sound detected in air
is

(A) 200Hz
(B) 600Hz
(C) 750Hz
(D) 3000Hz

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 3 of 51

14. Two capacitors have a capacitance of 5µF when connected in parallel and 1.2µF when
connected in series. Then the capacitances are

(A) 2µF and 3µF
(B) 3µF and 5µF
(C) 2µF and 4µF
(D) 1µF and 2µF

15. In the capacitor of capacitance C, charge Q and energy W is stored. If charge is
increased upto 2Q, the energy stored will be

W
(A)
4
W
(B)
2
(C) 2W
(D) 4W

16. At room temperature (27°C), the resistance of a heating element is 100Ω. At
temperature T°C, the resistance is found to be 117Ω. Given that temperature
coefficient of the resistor material is 1.7 × 10−4/°C,then the temperature T is

(A) 1027°C
(B) 820°C
(C) 527°C
(D) 1232°C

17. An ideal gas is filled in a closed rigid and thermally insulated container. A coil of
100Ω resistor carrying current 1A for 5minutes supplies heat to the gas. The change
in internal energy of the gas is

(A) 10kJ
(B) 20kJ
(C) 30kJ
(D) 0 kJ

18. Si and Cu are cooled from 300K to a temperature of 60K. Then resistivity

(A) for Si increases and for Cu decreases
(B) for Cu increases and for Si decreases
(C) decreases for both Si and Cu
(D) increases for both Si and Cu

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m
m .co

m .co s em
se g la
19. The magnetic field near a current carrying conductorais given by

(A) Coulomb’s law
(B) Lenz’s law
(C) Biot-Savart’s law
(D) Kirchhoff’s law

20. A positive charge is moving upward in a magnetic field directed towards north. The
m
m
particle will be deflected towards
co m .co
(A) east . s e
s em l a
ag
(B) west
(C)la north
g south
a(D)
21. In a common base mode of a transistor, the collector current is 5.488mA for an
emitter current of 5.6mA. The value of the base current amplification factor (β ) will
be

(A) 49
(B) 50
m
.co
(C) 51

em
(D) 48

las
How does the focal length of a g
22.
instead of violet light?
a convex lens change if monochromatic red light is used

(A) Focal length is increased
(B) Focal length is decreased
(C) Focal length remains same
(D) Focal length does not depend on colour of light used

23. An electron of mass m and charge e is accelerated from rest through a potential
m
.co
difference V in vacuum. Its final velocity will be
m
m .co 2 s e m
s e (A)
g l a
g la a
a
(B)

(C)

(D) 2
m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 5 of 51

24. Which of the following is wrongly matched?

(A) Raman effect- Scattering of light
(B) Thomson effect- Thermoelectricity
(C) Hall effect- Work function
(D) Photoelectric effect- Quantum nature of light

25. The speed of light in the medium is

(A) maximum on the axis of the beam
(B) minimum on the axis of the beam
(C) the same everywhere in the beam
(D) directly proportional to the intensity I

26. In an ac circuit, the voltage applied is E = E0 sin ω t . The resulting current in the
 π
circuit is I = I 0 sin  ωt −  . The power consumption in the circuit is given by
 2

(A) P = 2 E0 I 0

E I
(B) P= 0 0
2
(C) =0
E I
(D) P= 0 0
2

27. When a long spring is stretched by 2 cm, its potential energy is V. If the spring is
stretched by 10 cm, the potential energy in it will be

(A) 10V
(B) 25V
V
(C)
5
(D) 5V

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m
m .co

m .co s em
se g la
28. The centripetal force in a circular motion is given byathe relation

mv 2
(A)
r
mv3
(B)
r
mv3 m
.co
(C)
r3
o m m
mv . c s e
(D)
re
m l a
l as ag
29.
aAgdiesel engine pumps 40 kg of water in 1 second. The water comes out vertically
upwards with a velocity of 3 m/s. What is the power of the engine in kilo watt ?

(A) 12 kW
(B) 1.2 kW
(C) 120 kW
(D) 1 kW

o m
30. . c
Two objects of mass 10 kg and 20 kg respectively are connected to the two ends of a
m
rigid rod of length 10m with negligiblee mass. The distance of the center of mass of the
system from the 10 kg mass is la
s
a g
(A) 5 m
10
(B) m
3
20
(C) m
3
(D) 10 m
m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 7 of 51

31. Sphere A with radius a and sphere B with radius b are at same electric potential.
Then the ratio of the surface charge densities of A and B is

a
(A)
b
b
(B)
a
a2
(C)
b2
b2
(D)
a2

32. An electron enters a higher potential region V2 from a lower potential region V1. Then
what happens to its velocity?

(A) Its velocity decreases
(B) Its velocity increases
(C) There is no change in magnitude of the velocity but its direction changes
(D) Its velocity reduces to zero

33. If a magnetic material is having magnetic susceptibility (χ) = − 1, then the relative
magnetic permeability (µr) and type of magnetic material are

(A) 0, diamagnetic
(B) 2, ferromagnetic
(C) 1, paramagnetic
(D) −1, diamagnetic

34. In an LCR circuit, the capacitance is changed from C to 2C. For the resonant
frequency to remain unchanged, the inductance should be changed from L to

(A) 4L
(B) 2L
L
(C)
2
L
(D)
4

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m
m .co

m .co s em
se g la
35. a days how much quantity of
The half-life of radioactive sample is 4 days. After 16
matter remain undecayed?

1
(A)
16
1
(B)
32
m
.co
1
(C) m
.co m
4
m s e
s
1
e l a
ag
(D)

g l a 2

a
36. The colour of the light emitted by the light emitting diode (LED) depends on

(A) the magnitude of the current injected into the diode junction
(B) semiconductor material used in the making of LED
(C) doping concentration on either side of the diode junction
(D) forward bias voltage

m
37.
.co
In the circuit given below, the value of the current is
m
s e
g la
a

(A) Zero
(B) 10−2 A
(C) 10−3 A
(D) 102 A

o m
m A strip of Copper and another of Germanium are cooled to a temperature c
. of 80 K. The
c. o resistance of m
38.

m s e
s e g l a
l a (A) each of these decreases
a
ag (B) each of these increases
(C) Copper strip decreases and that of Germanium increases
(D) Copper strip increases and that of Germanium decreases

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 9 of 51

39. An explosion breaks a rock into three parts in a horizontal plane. Two of them go
off at right angles to each other. The first part of mass 1 kg moves with a speed of
12 ms−1 and the second part of mass 2 kg moves with 8 ms−1 speed. If the third part
flies off with 4 ms−1 speed, then its mass is

(A) 3 kg
(B) 5 kg
(C) 7 kg
(D) 17 kg

40. Which one of the following statements is INCORRECT?

(A) Frictional force opposes the relative motion
(B) Limiting value of static friction is directly proportional to normal reaction
(C) Rolling friction is smaller than sliding friction
(D) Coefficient of sliding friction has dimensions of length

41. A child is swinging a swing. Minimum and maximum heights of swing from the
earth's surface are 0.75 m and 2 m respectively. The maximum velocity of this swing
is

(A) 5 m/s
(B) 10 m/s
(C) 15 m/s
(D) 20 m/s

42. A piece of iron is heated in a flame. If first becomes dull red, then becomes reddish
yellow and finally turns to white hot. The correct explanation for the above
observation is possible by using

(A) Stefan’s law
(B) Wien’s displacement law
(C) Kirchhoff’s law
(D) Newton’s law of cooling

43. Two cylinders A and B of equal capacity are connected to each other via a stop cock.
A contains an ideal gas at standard temperature and pressure. B is completely
evacuated. The entire system is thermally insulated. The stop cock is suddenly
opened. The process is

(A) adiabatic
(B) isochoric
(C) isobaric
(D) isothermal

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m
m .co

m .co s em
se g la
44. a the freezing point and boiling
The efficiency of an ideal heat engine working between
point of water, is

(A) 6.25%
(B) 20%
(C) 26.8%
(D) 12.5%

m
45.
m
Nickel shows ferromagnetic property at room temperature. If the temperature is
.co
.co
increased beyond Curie temperature, then it will show
s e m
s em l a
laanti-ferromagnetism ag
(A) Paramagnetism
g
(B)
a nodiamagnetism
(C) magnetic property
(D)

46. A magnetic field of 2 × 10−2 T acts at right angles to a coil of area 100 cm2, with 50
turns. The average emf induced in the coil is 0.1 V, when it is removed from the field
in t second. The value of t is

(A) 10 s
m
(B) 0.1 s
.co
em
(C) 0.01 s
(D) 1s
la s
a g
47. Pick the WRONG statement in the context of rainbow formation.

(A) The order of colours is reversed in the secondary rainbow
(B) An observer can see a rainbow when his front is towards the sun
(C) Rainbow is a combined effect of dispersion, refraction and reflection of
sunlight
(D) When the light rays undergo total internal reflections in a water drop, a
secondary rainbow is formed
m
m
c. o48. The Brewster’s angle i for an interface should be m.co
m s e
a
b

s e g l
la a
(A) 30° <ib< 45°

ag (B) 45° <ib< 90°
(C) ib = 90°
(D) 0° <ib< 30°

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 11 of 51

49. The number of beta particles emitted by a radioactive substance is twice the number
of alpha particles emitted by it. The resulting daughter is an

(A) isobar of parent
(B) isomer of parent
(C) isotone of parent
(D) isotope of parent

236
50. In a fission reaction, 92 U →117 X +117 Y + n + n the binding energy per nucleon of

X and Y is 8.5 MeV whereas of 236U is 7.6 MeV. The total energy liberated will be
about

(A) 2000 MeV
(B) 200 MeV
(C) 2 MeV
(D) 1 keV

51. A uniform rod of length 2 m is pivoted at one end. If the rod is in equilibrium under
its own weight, what is the distance of its center of mass from the pivot point?

(A) 1.0 m
(B) 0.5 m
(C) 0.75 m
(D) 0.25 m

52. The gravitational potential energy of a two-particle system is negative. What does this
indicate about the system?

(A) The particles are repelling each other
(B) The particles are moving away from each other
(C) The particles are bound to each other
(D) None of the above

53. The rise of a liquid in a capillary tube depends on

(A) Mass of the liquid
(B) Radius of the capillary tube
(C) Density of the solid
(D) Bulk modulus of liquid

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m .co

m .co s em
se g la
54. a volume of 5 m at a constant
A gas expands from an initial volume of 2 m to a final 3 3

pressure of 100 Pa. Calculate the work done by the gas.

(A) 100 J
(B) 200 J
(C) 300 J
(D) 400 J

m
55.
m
An electromagnetic wave is represented by the electric field
.co
.co
E = E0 n sin ω t + ( 6 y − 8 z )  . Taking unit vectors in x, y and z directions to be l, j, k ,
s e m
s em l a
ag
the direction of propagation s is

g la 4 j − 3k
a(A) s = 5
3i − 4 j
(B) s=
5
−3 j + 3k
(C) s=
5
−4 k + 3 j
m
.co
(D) s=
5

s em
56. Two objects A and B are placedlaat 15 cm and 25 cm from the pole in front of a
a
concave mirror having radius gof curvature 40 cm . The distance between images
formed by the mirror is

(A) 40 cm
(B) 60 cm
(C) 160 cm
(D) 100 cm

m
.co
57. In an electron microscope, the resolution that can be achieved is of the order of the
m
.co m
wavelength of electrons used. To resolve a width of 7.5 × 10−12 m, the minimum
m s e
s e
electron energy required is close to
g l a
g la (A) 100 KeV a
a (B)
(C)
500 KeV
25 KeV
(D) 1 KeV

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 13 of 51

58. An excited He+ ion emits two photons in succession, with wavelengths 108.5 nm and
30.4 nm, in making a transition to ground state. The quantum number n, corresponding

λ( )
to its initial excited state is ( for photon of wavelength λ, energy E = ).

(A) n=5
(B) n=4
(C) n=6
(D) n=7

59. If a semiconductor photodiode can detect a phonon with a maximum wavelength of
400 nm, then its band gap energy is

Plank’s constant h = 6.63 × 10−34 J s
Speed constant c = 3 × 108 m/s

(A) 2.0 eV
(B) 1.5 eV
(C) 3.1 eV
(D) 1.1 eV

60. The modulation frequency of an AM radio station is 250 kHz, which is 10% of the
carrier wave. If another AM station approaches you for license what broadcast
frequency will you allot ?

(A) 2750 kHz
(B) 2000 kHz
(C) 2250 kHz
(D) 2900 kHz

61. A wire of 1 Ω has a length of 1 m. It is stretched till its length increases by 25%. The
percentage change in resistance to the nearest integer is

(A) 56%
(B) 25%
(C) 12.5%
(D) 76%

62. The number of turns of the coil of a moving coil galvanometer is increased in order to
increase current sensitivity by 50%. The percentage change in voltage sensitivity of
the galvanometer will be

(A) 100%
(B) 50%
(C) 75%
(D) 0%

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m
m .co

m .co s em
se g la
63. A proton and an αparticle ( with their masses in thearatio of 1 : 4 and charges in the
ratio of 1: 2) are accelerated from rest through a potential difference V. If a uniform
magnetic field (B) is set up perpendicular to their velocities, the ratio of their radii
rp: rα of the circular paths described by them will be

(A) 1 : √2
(B) 1:2
(C) 1:3
1 : √3 m
.co
(D)
m
.co
m connected to a coil of resistance 6 Ω through a switch, drives alas e m
A 12 V ebattery
64.
l as
constant a g
current in the circuit. The switch is opened in 1 ms.Theemf induced across
athegcoil is 20 V. The inductance of the coil is
(A) 5 mH
(B) 12 mH
(C) 8 mH
(D) 10 mH

.The
om
65. For an RLC circuit driven with voltage of amplitude vmand frequency ω0 =
√
quality factor, Q is given by
. c
e m
(A)
ω las
ω L ag
(B)

ω R
(C)

R
ω
(D)

m
m
66. A child of mass 5 kg is going to round a merry-go-round that makes 1 rotation in
.co
m .co 3.14 s. The radius of the merry-go-round is 2 m. The centrifugal force on the child
s e m
s e will be
g l a
g la (A) 80 N a
a (B)
(C)
50 N
100 N
(D) 40 N

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 15 of 51

67. What percentage of kinetic energy is transferred to a stationary particle when a
moving particle strikes a stationary particle of 5 times its mass? (Assume the collision
to be head-on elastic collision )

(A) 50.0%
(B) 66.6%
(C) 55.5%
(D) 33.3%

68. Two satellites A and B of masses 200 kg and 400 kg are revolving around the earth at
height of 600 km and 1600 km respectively. If TA and TB are the time periods of A and
Brespectively then the value of TB−TA

[ Given: radius of earth = 6400 km, mass of earth = 6 × 1024 kg ]

(A) 1.33 × 103 s
(B) 3.33 × 102 s
(C) 4.24 × 103 s
(D) 4.24 × 102 s

69. A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage
change in the length of the side of the cube is close to ( Given bulk modulus of metal
B = 8 × 1010 Pa )

(A) 0.6
(B) 1.67
(C) 5
(D) 20

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m .co

m .co s em
se g la
70. The root mean squaree sspeed of molecules of nitrogenagas at 27°C is approximately
rogen molecule = 4.6×10−26 kg and take Boltzm
( given mass of a nitrog zmann constant
−13 −1
KB = 1.4 × 10 JK )

(A) 523 m/s
(B) 1260 m/s
(C) 91 m/s
(D) 27.4 m/s
m
m .co
71. .co
A granite rod of 60 cm length is clamped at its middle point and is set into latitudinal
s e m
em nsity of granite is 2.7 × 103 and its Yooung’s modulus is
vibrations. The densi
s l a
g la
9.27 × 1010 Pa. Whatt will
w be the fundamental frequency of the latit
titudinal vibrations?
ag
a(A) 7.5 kHz
(B) 5 kHz
(C) 2.5 kHz
(D) 10 kHz

72. A rod of length 50 cm
m is pivoted at one end. It is raised such that it makes an angle of
30° from the horizont
ntal as shown and released from rest. Its angungular speed when it
m
.co
−1 −2
passes through the hori
orizontal ( in rad s ) will be ( g = 10 m/s )

e m
las
ag

(A) 30

30
(B)
2
m
m .co
.co
30
(C)
e m
e m
2
l as
las (D)
20
ag
ag 2

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 17 of 51

73. Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on
the same inclined plane without slipping. Assume that they start rolling from rest and
having identical diameter. The correct statement for this situation is

(A) The sphere has the greatest and the ring has the least velocity of the centre of
mass at the bottom of the inclined plane
(B) The ring has the greatest and the cylinder has the least velocity of the centre of
mass at the bottom of the inclined plane
(C) All of them will have same velocity
(D) The cylinder has the greatest, and the sphere has the least velocity of the centre
of mass at the bottom of inclined plane

74. If the size of an atom (~ 1Å) is enlarged to the size of the earth (~ 107) what would be
the size of the nucleus (10−15 m)?

(A) 10 m
(B) 100 m
(C) 1000 m
(D) 1m

75. If the errors in the measurement of l and g are 2% and 4% respectively, the percentage
of error in the time period of pendulum is

(A) 3
(B) 4
(C) 6
(D) 5

76. Which of the following fuel has the highest calorific value?
(A) Coal
(B) Gasoline
(C) Kerosine
(D) Hydrogen

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m .co

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77. Palmitic acid (Molecular weight = 256.42 g/mol)ais one of the major sources of
energy in our diet as shown in the chemical reaction provided below

C16H32O2(s)+23O2(g)→16CO2(g)+16H2O(l)

The energy released by the combustion of 1 g of palmitic acid is………. kJ/g

(∆H0f (CO2) = -393.5 kJ/mol; ∆H0f (H2O) = -285.8 kJ/mol; ∆H0f (C16H32O2) =
−891.5kJ/mol; ∆H0f (O2) = 0 kJ/mol) m
m .co
(A)
.co
– 19 kJ/g
m s e m
(B)
s
– 29 kJ/g
e l a
ag
(C) – 39 kJ/g

g l
(D) a – 49 kJ/g
a
78. A chemical reaction having higher equilibrium constant suggests

(A) Rate of forward reaction is faster
(B) Rate of backward reaction is faster
(C) Rate of both backward and forward reactions are equal
(D) None of the above

m
79. .co
For a general chemical equilibria AX3 (g)⇌ AX2 (g) + ½ X2 (g), the equilibrium
m
constant is Kc; The equilibrium constant for the reaction 2AX2 (g) + X2 (g) ⇌ 2 AX3
e
(g) will be ……..
las
ag
(A) 2Kc
(B) Kc/2
(C) Kc2
(D) 1/Kc2

80. For the Haber Process, N2 (g) + 3H2 (g) ⇌ 2NH3 (g), the value of Kc at 300 oCis 9.60.
The value of Kp at same temperature will be
(The value of R, is 0.08206 L-atm. mol-1.K-1) m
m .co
m .co (A)
(B)
4.34 x 10-3
2.17 x 104 s e m
s e (C) 1.6 x 10-2
g l a
g la (D) 5.8 x 103 a
a
81. The standard EMF for the cell reaction Zn + Cu2+→ Cu + Zn2+ is 1.10 V at 25 oC. The
EMF of the cell when 0.1M Zn2+ and 0.1M Cu2+ solutions are used at 25 oC is

(A) 1.10 V
(B) 0.55 V
(C) 0.275 V
(D) 0.11 V
m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 19 of 51

82. The equilibrium constant for a cell reaction, Cu(s) + 2Ag+(aq) → Cu2+(aq) + 2Ag (s)
is 4× 1016. E0(cell) for the cell reaction is

(A) 0.63 V
(B) 0.49 V
(C) 0.77 V
(D) 0.89 V

83. The chemical reactions of high molecularity are rare because

(A) Activation energy for many body collisions is very high
(B) Many body collisions are energetically less favorable
(C) Many body collisions have a low probability
(D) All of the above

84. The shape of orbital with the value of l = 2, m = 0 is
(A) Spherical
(B) Double dumb-bell
(C) Trigonal planar
(D) Square planar

85. The vapour pressure of water at 300 K in a closed container is 0.4 atm. If the volume
of container is doubled, its vapour pressure at 300 K will be

(A) 0.8 atm
(B) 0.2 atm
(C) 0.4 atm
(D) 0.6 atm

86. Internal energy does not include

(A) Rotational energy
(B) Vibrational energy
(C) Nuclear energy
(D) Gravitational energy pull

87. Precipitation takes place when

(A) Ionic product < Ksp
(B) Ionic product > Ksp
(C) [Ionic product]2 = Ksp
(D) [Ionic product]2 > Ksp

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m
m .co

m .co s em
se g la
88. a A is doubled and that of B is
In the reaction 2A + B → A B, if the concentration of
2
halved, then the rate of the reaction will

(A) increase 2 times
(B) increase 4 times
(C) decrease 2 times
(D) remain the same

m
89.
m
Hess’ law is applicable for the determination of heat of
.co
(A) .co
Transition
m s e m
(B)
s e
Formation
l a
l
(C)
g a Reaction
ag
a(D) All of the above

90. Which of the following is an example of a fractional order reaction?

(A) NH4NO2 → N2 + 2H2O
(B) NO + O3 → NO2 + O2
(C) 2NO + Br2 → 2NOBr
(D) CH3CHO → CH4 + CO
m
91.
m .co
The E0M3+/M2+ values for Cr, Mn, Fe and Co are −0.41, + 1.57, + 0.77 and +1.97 V

s e
respectively. For which one of the metals, the change in oxidation state from +2 to +3
is easiest?
g la
(A) Cr
a
(B) Mn
(C) Fe
(D) Co

92. Glucose of 18 g was dissolved in 170 g of water. The vapour pressure of water for this
aqueous solution at 37°C is [ Given : vapour pressure of water as solvent is 760 torr]
m
m .co
.co
(A) 652 torr
e m
e m
(B)
(C)
752 torr
756 torr
l as
las (D) 854 torr
ag
ag

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 21 of 51

93. A mixed oxide has ccp arrangement in which the cations 'X' occupy 1/3rd of
octahedral voids and the cations 'Y' occupy 1/3rd of tetrahedral voids. The formula of
oxide is

(A) X2Y3O2
(B) XY3O
(C) X2YO3
(D) XY O3

94. Calculate the energy associated with the second orbital of Li2+. What is the radius of
this orbit?

(A) −3.27 × 10−18 J, 0.0793 nm
(B) −4.905 × 10−18 J, 0.0705 nm
(C) −9.81 × 10−18 J, 0.1190 nm
(D) 1.635 × 10−18 J, 0.0352 nm

95. P, F, B represents Primitive, Face - centered, Body centered cubic structures
respectively. The crystal structure types of CsCl and NaCl are

(A) B, F
(B) F, C
(C) P, F
(D) F, P

96. Arrange (i) 3- nitrophenol, (ii) 3-chlorophenol, (iii) 4-nitrophenol and (iv) phenol in
decreasing order of acidity

(A) (i) > (ii) > (iii) > (iv)
(B) (iii) >(i) > (ii) > (iv)
(C) (iv) >(i) > (ii) > (iii)
(D) (iv) > (iii) > (ii) > (i)

97. is named as

(A) 1,1-dimethyl-3-cycloheptene
(B) 4,4-dimethyl-cycloheptene
(C) 3,3-dimethyl-cycloheptene
(D) 6,6-dimethyl-cycloheptene

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m
m .co

m .co s e m
se g l a
a
98. In E2 elimination, some compounds follow Hofmann’s rule which means

(A) the double bond goes to the most substituted position
(B) newly formed double bond will be in conjugation with double bond already
present in the molecule
(C) when strong bases are used double bond goes to the less substituted carbon,
and when weak bases are used double bond goes to the less substituted carbon
m
.co
(D) the double bond goes mainly towards the least substituted carbon
o m m
. c s e
99.
s em
When pent-2-yne is treated with dil. H SO and2HgSO , major
4 product4formed is
g l a
(A)la pentan-2-ol a
g pentan-3-ol
a(B)
(C) pentan-3-one
(D) pentane-2,3-diol

100. To which of the following molecules will ammonia (a nucleophile) add in a 1,4-
fashion?

(A)
m
trans-but-2-ene

.co
(B) butenone
(C) 4-penten-2-one
(D) cyclopentanone e m
las
101. Phenol fails to ag
(A) release carbon dioxide from aqueous sodium bicarbonate solution
(B) decolorize bromine water
(C) give a violet color with neutral FeCl3 solution
(D) dissolve in cold dilute sodium hydroxide solution

102. Most reactive compound among the following towards sulphonation is
m
m (A) toluene .co
m .co (B) chlorobenzene
s e m
s e (C) nitrobenzene
g l a
la
(D) thiophene
g a
a 103. Which among the following amino acids has an aromatic ring residue?

(A) Tryptophan
(B) Valine
(C) Isoleucine
(D) Aspartic Acid

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 23 of 51

104. Which one of the following does not have sp2 hybridized carbon?

(A) Acetonitrile
(B) Acetic acid
(C) Acetone
(D) Acetamide

105. Which among the following fails to give a positive test for nitrogen in Lassaigne’s
test?

(A) RNA
(B) Nicotine
(C) Insulin
(D) Cholesterol

106. Which of the following is not an addition polymer?

(A) Teflon
(B) Plexiglass
(C) Orlon
(D) Kevlar

107. Among the following saccharides, identify the one that does not form silver mirror
with Tollen’s reagent

(A) Lactose
(B) Maltose
(C) Galactose
(D) Sucrose

108. Selective reduction of PhCH=CHCO2Et to PhCH=CHCH2OH is performed using

(A) Zn/Hg, HCl
(B) H2/Pd-C
(C) NH2NH2, NaOH
(D) LiAlH4 in dry ether

109. Listed below are one each of olefin, carbanion, carbocation and carbon centered radical.
Stability of one among the following species cannot be explained on the basis of
hyperconjugation. Identify it.

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m
m .co

m .co s e m
se g l a
110. Pyrethrins are well-known as a
(A) Anti-oxidants
(B) Insecticides
(C) Flavouring agent
(D) Drugs

111. In Wolff-Kishner reduction, in the first step ketones (or aldehydes) are converted to
m
the corresponding
c o m m .co
(A) imine . s e
s em l a
ag
(B) hydrazone
(C)la semicarbazone
g cyanohydrin
a(D)
112. Which reagent can be used to efficiently convert carboxylic acid to acid chloride
derivative?

(A) SOCl2
(B) Cl2 in the presence of light
(C) Interhalogen compound bromine monochloride (Br-Cl) in the presence of
m
.co
peroxides

em
(D) Sodium hypochlorite (NaOCl)
s
la hydrogenation of the following optically active
ag
113. Major product formed in the catalytic
eneyne compound in the presence of poisoned palladium catalyst is

(A) an optically active compound
(B) an optically inactive compound
m
m (C) a racemic mixture of two optical isomers
.co
.co m
(D) a mixture of several optically active compounds
s e
s em 114. Aniline is successively treated with i) excess bromine ii) gNaNO
l a
l a a , HCl iii) H PO .
ag
2 3 2
Major product formed is

(A) 2,4,6-tribromoaniline
(B) 2,4-dibromoaniline
(C) 1,3,5-tribromobenzene
(D) 2,4-dibromobenzene

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 25 of 51

115. Ozonolysis of an organic compound 'A' gave a 1:1 mixture of propanone and
propanal. Identify 'A' from the following compounds

(A) hex-1-ene
(B) hex-2-ene
(C) 2-methylpent-2-ene
(D) 2-methylpent-1-ene

116. Which of the following statements about lithium compounds is untrue?

(A) The hydroxides, carbonates, nitrate, decompose, to give oxides on heating
(B) It is the most electronegative among alkali metals
(C) The hydrogen carbonates cannot be isolate as stable solid
(D) It forms a peroxide but not superoxide

117. Upon heating sodium hydrogen carbonate, the products formed are

(A) Na2O + CO2 + H2O
(B) Na2CO3 + CO2
(C) Na2CO3 + CO2 + H2O
(D) NaCO3 + H2O

118. Metallic magnesium is prepared by

(A) Displacement of magnesium by iron from magnesium sulphate solution
(B) Electrolysis of an aqueous solution of Mg(NO3)
(C) Electrolysis of molten MgCl2
(D) Reduction of MgO by aluminium

119. The sodium is made by the electrolysis of a molten mixture of about 40% NaCl and
60% CaCl2 because

(A) Ca2+ can displace Na from NaCl
(B) This mixture has a lower melting point than NaCl
(C) CaCl2 helps in conduction of electricity
(D) Ca2+ can reduce NaCl to Na

120. S and O both are non-metals in the oxygen family, but their melting points are largely
different O = 90K and S = 718K this is because

(A) S is larger in size than O
S exhibit more oxidation state +2, +4, +6 whereas O exhibit −2 and +2
(B)
oxidation state
(C) O exist as diatomic molecule whereas S exhibit polyatomic molecule (S8)
(D) S has more allotropes than O

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m
m .co

m .co s e m
se g l a
121. Of the following, which one isn't a reducing oxide? a

(A) SO2
(B) SeO2
(C) TeO
(D) SO3

122. The compound insoluble in aqueous NH3 is
m
m .co
.co
(A) AgI
e m
(B)
(C)
em
AgCl
ZnSO4
l as
las
(D) HgCl2
ag
ag
123. Which one of the following anions is present in the chain structure of silicates?

(A) SiO44−
(B) (Si2O7)6−
(C) (SiO3)2−
(D) (Si2O5)2−

m
.co
124. In borax bead test which compound is formed?

(A) Orthoborate e m
(B) Metaborate
las
(C)
(D)
Double oxide
Tetraborate ag
125. Carbon and silicon belong to (IV) group. The maximum coordination number of
carbon in commonly occurring compounds is 4, whereas that of silicon is 6. This is
due to

(A) Availability of low lying d-orbitals in Silicon
(B) Large size of Silicon m
m (C) More electropositive nature of Silicon
.co
.co (D) None of the above
s e m
s em 126. Nitrogen forms N , but phosphorus does not form P , However,
g l ait forms P reason is
g la 2
a 2 4,

a (A) Triple bond present between phosphorus atom
(B) pπ-pπ bonding is weak
(C) pπ-pπ bonding is strong
(D) Multiple bonds form easily

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 27 of 51

127. Transuranic elements start with

(A) Np
(B) Cm
(C) Pu
(D) U

128. The number of moles of KMnO4 required to reduce one mole of KI in alkaline
medium is

(A) 1/4
(B) 5
(C) 1
(D) 2

129. Which of the following is diamagnetic complex?

(A) [Fe(H2O)6]3+
(B) [Fe(H2O)6]2+
(C) [Fe(CN)6]3-
(D) [Fe(CN)6]4-

130. A magnetic moment of 1.73 BM will be shown by which one among the following?

(A) [Ni(CN)4]2-
(B) TiCl4
(C) [CoCl6]4-
(D) [Cu(NH)3]2+

131. Which of the following complex ion is not expected to absorb visible light?

(A) [Ni(CN)4]2-
(B) [Cr(NH)6]3+
(C) [Fe(H2O)6]2+
(D) [Ni(H2O)6]2+

132. The colorless species are

(A) Cu2Cl2 and [NiCl4]2-
(B) [TiF6]2- and Cu2Cl2
(C) [CoF6]3-and [NiCl4]2-
(D) [TiF6]2-and [CoF6]3-

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m
m .co

m .co s em
se g la
133. The number of unpaired electrons in the complex iona[CoF ] is 6
3-

(A) 1
(B) 6
(C) 4
(D) 2

134. Which of the following electronic configuration has associated magnetic moment of
m
4.89 B.M.?
m .co
(A) .co
[Ar] 3d5
m s e m
(B)
s e
[Ar] 3d6
l a
l
(C)
g a [Ar] 3d7
ag
a(D) [Ar] 3d8

135. What is the number of electrons in all the completely filled subshells of n = 4 ?
(A) 30
(B) 32
(C) 34
(D) 36

o m
c
The function f : ℝ → ℝ, defined by f ( x). = sin x + cos x, is
em
136.

(A) one-one la s
(B) onto a g
(C) one-one and onto
(D) neither one-one nor onto

137. The value of y = sec −1 (−2) is

π
(A)
3 m
m .co
.co
2π
(B)
e m
e m 3
l as
las (C)
5π
ag
ag 3
7π
(D)
3

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 29 of 51

 cos θ sin θ  2025 π
138. If A =   , then the matrix A at θ = is
 − sin θ cos θ  3

0 0
(A)  
0 0
1 0
(B)  
0 1
 −1 0 
(C)  
 0 1
 −1 0 
(D)  
 0 −1

 1 −3 2 
 
139. The value of x for which the matrix A =  4 −1 x  is singular, is
 3 5 2
 

31
(A)
7
32
(B)
7
33
(C)
7
34
(D)
7

140. Let f and g be continuous functions at a point x0 . Then which of the following is
NOT necessarily true?

(A) f + g is continuous at x0

(B) f − g is continuous at x0

(C) f ⋅ g is continuous at x0

f
(D) is continuous at x0
g

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m
m .co

m .co s e m
se g l a
141. The function f ( x) = x − 3 at x = 3 is a
(A) not defined
(B) differentiable
(C) not continuous
(D) not differentiable

m
.co
 x + 1, x < 2
142. If f ( x) = 
m , then f is
.co
2 x − 1, x ≥ 2
s e m
s em except x ≠ 2 l a
ag
(A) continuous

g lacontinuous only at ( −∞, 2]
(B)
a discontinuous in ℝ
(C)
(D) continuous in ℝ

143. The number of points at which sin x attains its minimum in ℝ , is

(A) 1
(B) 2
(C) 0
m
(D) infinitely many
m .co
144. The value of cosec(−1080°) is la
se
a g
(A) 2
1
(B)
2
(C) 0
(D) ∞

m
m
145. A function f satisfies f ( x) + 2 f (6 − x) = x for all real numbers x. Then the value of
.co
m .co f (1) is
s e m
s e g l a
g la (A) 1
a
a (B)
(C)
2
3
(D) 4

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 31 of 51

146. If a line of slope π is reflected over y-axis, then the slope of the reflected line is

(A) π
(B) −π
π
(C)
2
π
(D) −
2

4 − x2
147. The largest possible domain of the real valued function f ( x) = is
x2 − 9

(A) [3, 4]
(B) (3, 4]
(C) [3, 4)
(D) (3, 4)

148. There are 7 bulbs in a room. Then the number of ways in which the room can be
illuminated is

(A) 127
(B) 128
(C) 63
(D) 64

149. cosec cosec−1x = x holds if x belongs to
( )
(A) ℝ
 −π π 
(B)  2 , 2 
(C) ℝ − (−1,1)
(D) [ −1,1]

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m
m .co

m .co s e m
se g l a
150. Sum of n terms of the series 3 + 27 + 75 + 147a+ ... is

n( n + 1)(2n + 1)
(A)
2 3

3n(n + 1)
(B)
2
( n + 1) m
.co
(C)
3
o m m
c
. n − 1) s e
(D) m
n( n − 1)(2
e 23 l a
l as ag
a g
P( n)
151. Let P ( x) be a polynomial in real variable x of degree 5. Then lim is
n→∞ 2n

(A) 5
(B) 1
(C) 0
(D) ∞

o m
c
152. Subject to the conditions 0 ≤ x ≤ 10; 0 ≤ y .≤ 5, the minimum value of the function
s em
la
4 x − 5 y + 10 = 0 is

(A) 5 a g
(B) −15
(C) 10
(D) −2

1 1 1 1
153. lim + + + ... + n =
n→∞ 2 4 8 2
m
m (A) 0
.co
m .co (B) 1
s e m
s e
(C) 2
(D) ∞
g l a
g la a
a 154. Let f (n) defined to be the sum of all prime factors of n, where n is any composite
positive integer. Then the range of f is the set of all

(A) positive integers
(B) composite positive integers
(C) integers greater than 3
(D) integers greater than 4
m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 33 of 51

∞ π
155. ∑ cosn 6 =
n =0

2
(A)
2− 3

3
(B)
2
(C) 2
(D) ∞

 cos x − sin x  T
156. Consider A =   . Let S be set of all real x satisfying A ⋅ A = I 2 . Then
 sin x cos x 
S is equal to

(A) {0}
(B) {2π }
(C) ℤ
(D) ℝ

157. An onto function f :{1, 2,3, 4,5} → {{1, 2,3, 6, 7} is

(A) one-to-one in some cases
(B) always one-to-one
(C) not one-to-one in some cases
(D) one-to-one if f is the identity

158. If p ( x) is a polynomial such that the sum of co-efficients of p (− x) is zero, then one
of the roots of p ( x) = 0 is

(A) −1
(B) 0
(C) 1
(D) 2

159. The area enclosed within the curve x + y = 2 is

(A) 16 sq units
(B) 8 sq units
(C) 6 sq units
(D) 4 sq units

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m
m .co

m .co s em
se g la
a to a circle, then the radius of
160. If 3 x − 6 y + 10 = 0 and 12 y − 6 x + 16 = 0 are two tangents
the circle is

3
(A)
2 5
3
(B)
5
m
3
m .co
.co m
(C)
4 5
m s e
s3e l a
la 2
(D)
g ag
a
161. Three normals are drawn to the parabola y 2 = x through the point (a, 0). Then

1
(A) a=
2
1
(B) a=
4
m
(C)
1
m .co
e
a>
2
las
(D) a<
1
4 ag

162. If a, b, c are elements of a group (G ,*) , then the solution of the equation c * y * a = b
in G is

(A) b * a −1 * c −1
(B) b * c −1 * a −1
m
m (C) a −1 * b * c −1
.co
m .co (D) c −1 * b * a −1
s e m
s e g l a
g la 163. The equation z + 3 − 2i = z + 2i − 3 represents a
a
(A) a pair of straight lines
(B) two points
(C) a circle
(D) an ellipse

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 35 of 51

z −i
164. The radius of the circle = 5 is
z +i

20
(A)
81
40
(B)
81
(C) 4
(D) 484

1 2
165. The maximum sum of the series 30 + 29 + 28 + 28 + ... is
3 3

(A) 690
(B) 560
(C) 430
(D) 360

166. The positive integer n for which 2 × 2 2 + 3 × 23 + 4 × 2 4 + ... + n × 2 n = 2 n +6 , is

(A) 17
(B) 21
(C) 31
(D) 33

167. The number of points (a, b, c) in space, whose each coordinate is a negative integer
such that a + b + c + 12 = 0 is

(A) 162
(B) 18
(C) 136
(D) 153

168. The roots of the equation 4 2 x +1 + 4 2 = 4 x +3 + 4 x are

(A) 1, −2
(B) 1, 2
(C) −1, 2
(D) −1, −2

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m
m .co

m .co s e m
se g l a
10  a
 
The value of   , when the numerator and the denominator take their greatest
r
169.
11
 
r
value, is

6
(A) m
.co
11
m
(B)
5
m .co s e m
s e
11
l a
g
(C)
a
l 610 ag
a
10
(D)
5

170. The coefficient of x 6 in (1 + x)6 + (1 + x)7 + ... + (1 + x)15 is
{ }
m
.co
(A) 16 C9

(B) 16
C5 −6 C5
e m
las
(C) 16
C6 − 1
ag
(D) 16 C6 −6 C5

 λ 1 6
171. If the matrix  −3 0 4  is not invertible, then
 −1 1 2 
m
m .co
.co
(A) 10
(B) e m
e m (C)
−10
−4
l as
las (D) 4
ag
ag

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 37 of 51

 cos 2 α cos α sin α   cos 2 β cos β sin β 
172. If A =   and B =   are two matrices
 cos α sin α sin 2 α  cos β sin α
2
sin β 
such that AB is a null matrix, then α − β is

(A) 0
π
(B) an odd multiple of
2
π
(C) an even multiple of
2
(D) α = β

1 1 1
173. The sum of the series cos x − cos 2 x + cos3 x − cos 4 x + ... is
2 3 4

x
(A) log 2 + log cos  
2

x
(B) log 2 − 2 log cos  
2

 x
(C) log 2 − log cos  
2

x
(D) log 2 + 2 log cos  
2

174. Let N be the set of all natural numbers. If aN = {an : n ∈ N } and bN ∩ cN = dN ,
where a, b, c ∈ N and b, c are coprimes, then

(A) b = cd
(B) c = bd
(C) d = bc
(D) a = bc

175. Two finite sets X and Y have p and q elements respectively. If the total number of
subsets of X is 56 more than the total number of subsets of Y. Then the value of q is

(A) 2
(B) 3
(C) 6
(D) 28

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m
m .co

m .co s em
se g la
a The probability that an even
176. A fair die is tossed until a number greater than 4 appears.
number of tosses shall be required, is

1
(A)
2
1
(B)
5
m
.co
3
(C) m
.co m
5
m s e
s
2
e l a
ag
(D)

g l a 3

a
177. Seven balls are drawn simultaneously from a bag containing 5 white and 6 green
balls. The probability of drawing 3 white and 4 green balls is

7
(A) 11
C7
5
C3 + 6 C4
m
.co
(B) 11
C7

e m
(C)
5
C3 + 6 C2
las
11
C7
ag
6
C3 + 5 C4
(D) 11
C7

178. The maximum value of 5cos x + 5sin x + 5 is

(A) 5
m
m (B) 10
.co
.co m
(C) 10 + 2
m s e
s e (D) 5(1 + 2)
g l a
g la a
a 179. The equation 4 sin x + 5 cos x = 7 has

(A) only one solution
(B) two solutions
(C) infinitely many solutions
(D) no solution

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 39 of 51

3
180. In a triangle ABC, b = 3, c = 2 and sin B = , then C is equal to
4

(A) 30°
(B) 60°
(C) 90°
(D) 120°

181. The equation of the straight line which is parallel to x-axis and crosses the curve
y = x at an angle of 45° , is

1
(A) x=
2
1
(B) y=
4
1
(C) y=
2
(D) y =1

y dy
182. If x y x = 100, then is equal to
dx

y ( x + y ) log x
(A) −
x( x log y + y )
y ( y + x log x)
(B) −
x( y log x + x )
y
(C) −
x
x
(D) −
y

1
183. If f : ℝ → ℝ is defined by f ( x) = x − [ x] − for x ∈ ℝ where [ x] is the greatest
4
 3
integer not exceeding x , then  x ∈ ℝ : f ( x) =  is equal to
 4

(A) ℤ, the set of all integers
(B) ℕ , the set of all natural numbers
(C) φ , the empty set
(D) ℝ, the set of all real numbers

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 40 of 51

m
m .co

m .co s e m
se g l a
5 x − 5− x a
184. The value of lim is
x →0 2x

(A) log 5
(B) 0
(C) 1
(D) 2 log 5

m
m
c. o 1!1 + 1 2!+ 2 + 1 + 3!2 + 3 + ... + ∞ equals m .co
185. The sum of series
m s e
e l a
(A) as ag
g l e
a(B) e
2
3e
(C)
2
e
(D) 1 +
2

m
2
m .co
186. ∫ [ x] dx is equal to
s e
la
−2

(A) 1 ag
(B) 2
(C) 4
(D) 5

187. A curve through (1, 0) and satisfying the differential equation 1 + y 2 dx − xydy = 0
( )
represents a/an
m
m .co
.co m
(A) circle

m (B) parabola
s e
s e (C) ellipse
g l a
g la (D) hyperbola a
a
188. If a , b , c are three non-coplanar mutually perpendicular unit vectors, then  a b c
 
is

(A) 2
(B) 0
(C) 1
(D) 3
m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 41 of 51

2
189. The maximum value of z when z satisfies the condition z + = 2 is
z

(A) 3 −1
(B) 3 +1
(C) 3
(D) 2+ 3

190. If a1, a2 ,...an are n distinct odd natural numbers not divisible by any prime greater
1 1 1
than 5, then + + ... + is less than
a1 a2 an

15
(A)
8
16
(B)
8
8
(C)
15
15
(D)
4

191. The number of real solutions of the equation e x = x is

(A) 0
(B) 1
(C) 2
(D) infinite

x+λ x x
192. If f ( x) = x x+λ x , then f (3 x) − f ( x) is equal to
x x x+λ

(A) 3xλ 2
(B) 6xλ 2
(C) xλ 2
(D) 4xλ 2

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m
m .co

m .co s em
se g la
193. If α and β are solutions of sin 2 x + a sin x + b = 0 asawell that of
cos 2 x + c cos x + d = 0, then α + β is equal to

2bd
(A)
b + d2
2

a 2 + c2
(B)
m
.co
2ac
m
(C)
b2 + d 2
m .co s e m
s e2ac
2bd
l a
(D)la 2 2 ag
ag a + c
194. The minimum number of terms of the series 1 + 3 + 9 + 27 + ... so that the sum may
exceed 1000 is

(A) 7
(B) 5
(C) 3
m
.co
(D) 8

s em
195. If f ( x) = a + b x + c x , where al,a
4

at x = 0 if ag b, c are real constants, then f ( x) is differentiable

(A) a=0
(B) b=0
(C) c=0
(D) a =b=c

m
.co
196. If 3a − 2b + 5c = 0, the family of lines ax + by + c = 0 are always concurrent at a point
m whose coordinates are
m .co s e m
s e  −3 2 
 ,  g l a
la
(A)
g
 5 5 a
a  3 −2 
(B)  , 
5 5 
3 2
(C)  , 
5 5
 −3 −2 
(D)  , 
 5 5 
m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 43 of 51

197. For each n ∈ ℕ, 23n − 1 is divisible by

(A) 6
(B) 16
(C) 8
(D) 7

198. The sum of all possible values of k for which the polynomials x2 − 3x + 2 and
x2 5x + k have a root in common is
−
(A) 7
(B) 8
(C) 9
(D) 10

199. If a, b, c ∈ ℝ and quadratic equation x2 + (a + b)x + c = 0 has no real roots, then

(A) c(a + b + c) > 0
(B) c + c(a + b + c) > 0
(C) c + c(a + b c) > 0
−
(D) c(a + b c) > 0
− π 
200. If f ( x) = cos x cos 2 x cos 4 x cos8 x, then f '   is
4

(A) 1 −
(B) 2
(C) 2
(D) 2 2

2n 2n
201. If ∑ cos−1 xi = 0 then ∑ xi is
i =1 i =1

(A) n
(B) 2n
n(n + 1)
(C)
2
n(n − 1)
(D)
2

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m
m .co

m .co s em
se g la
202. There is a positive integer n such that (n + 1)! + (n +a2)! = n! 440 . The sum of the
·
digits of n is

(A) 3
(B) 8
(C) 10
(D) 11

m
c o m
If an = 7 + 7 + 7 + ... having n radical signs, then by methods of mathematical
m .co
203.
induction m
. s e
s e which is true
l a
a
(A)l an > 7, ∀n ≥ 1
g a < 2, ∀n ≥ 1 ag
a(B) n
(C) an < 7, ∀n ≥ 1
(D) an > 13, ∀n ≥ 1

204. The number of solutions of the equation 4esin x − 3e−sin x + 4 = 0 in [0, 2π ] is

m
.co
(A) 1
(B) 2
(C) 3
e m
(D) 4
las
ag
205. In 4 × 4 matrix, sum of each row, column and both the main diagonal is α, then the
sum of four diagonal corner elements

(A) α
(B) may not be α
(C) its never equal to α
(D) α 2
m
m
c. o206. The image of the point (−1, 3, 4) in the plane x − 2 y = 0 is m.co
m s e
s e g l a
g la  9 −13  a
a (A)  ,
5 5
,4

 −17 −19 
(B)  , ,1
 3 3 
(C) (8, 4, 4)

 −17 −19 
(D)  , ,4
 3 3 
m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 45 of 51

π   3π  3π   3π 
207. The value of cos3   cos   + sin   sin   is
8  8  8  8 

1
(A)
2
1
(B)
2 2
1
(C)
2
1
(D)
4

 1+ i 3 
208. If a and b are real numbers such that (2 + α )4 = a + bα , where α =  , then
 2 
 
a+b =

(A) 9
(B) 24
(C) 33
(D) 57

209. If the sum of the coefficients of all even powers of x in the product
(1 + x + x2 + ...x2n )(1 − x + x2 − x3 + ... + x2n ) is 61, then n is equal to
(A) 30
(B) 60
(C) 61
(D) 122

x2 y2 x2 y2 1
210. If the foci of the ellipse + 2 = 1 and the hyperbola − = coincide, then
16 b 144 81 25
the value of b 2 is

(A) 9
(B) 1
(C) 5
(D) 7

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 46 of 51

m
m .co

m .co s em
se g la
a ω 0 
211. If ω ≠ 1 is the complex cube root of unity and matrix H =   , then H 70 is
 0 ω
equal to

(A) 0
(B) −H
(C) H 2
m
.co
(D) H
m
.co s e m
em a
1
212.
s
Let f : R → R be a differential function with f (2) = 6 and f '(2) = . Then
l
g laf ( x) 4t 3
48
ag
axlim
→2 ∫ x − 2
dt =
0

(A) 24
(B) 36
(C) 12
(D) 18

m
213. tan x is not defined when x is
m .co
(A) 0
s e
nπ
g la
(B)
2 a
(2n + 1)π
(C)
2
(D) nπ

214. If −2 < 2 x − 1 < 2, then the value of x lies in the interval
m
m .co
.co
1 3
(A)  , 
e m
e m 2 2
l as
las  −1 3 
 ,  ag
ag (B)
 2 2
3 1
(C)  , 
2 2
 3 −1 
(D)  , 
2 2 

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 47 of 51

2
215. If the slope of a line is , then the slope of the line perpendicular to that line is
3

3
(A) −
2
3
(B)
2
2
(C)
3
2
(D) −
3

sin 2 x
216. The value of lim is
x→0 x2

(A) 2
(B) 1
(C) 4
(D) limit does not exist

 13π 
217. The principal value of cos −1  cos  is
 6 

13π
(A)
6
π
(B)
2
π
(C)
3
π
(D)
6

π
3
218. The value of ∫ ( x + sin x ) dx is
−π

(A) 0
(B) π
(C) 2π
(D) π3

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 48 of 51

m
m .co

m .co s e m
se g l a
219. The direction cosines of the y-axis are respectively a

(A) 1, 0, 0
(B) 1,1, 0
(C) 0,1, 0
(D) 0, 0,1

m
.co
2
220.
m
The principal argument of z = − is
.co m
1 + 3i
m s e
sπe l a
(A)
g la 3 ag
a(B) 2π
3
π
(C)
6
π
(D)
4

o m
c
. number z = 12 − 5i is
m
221. The multiplicative inverse of the given complex
e
(A) −12 + 5i
la s
12 5 a g
(B) + i
169 169
12 5
(C) + i
13 13
(D) 12 + 5i

m
.co
1
tan −1 x
m
222. The value of definite integral ∫ dx is
.co m
2
0 1+ x

m s e
s e π3
g l a
g la (A)
72 a
a π2
(B)
32
π3
(C)
4
π3
(D)
8
m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 49 of 51

223. There is an equilateral triangle with each side of length 24 cm. The mid-point of its
sides is joined to form another triangle. This process is going continuously infinitely
many times. Then the sum of perimeter of first 6 triangles (in cm) is

(A) 144
(B) 120
(C) 139.5
(D) 141.75

224. If C be the centroid of the triangle having vertices (3, −1), (1,3) and (2, 4) . Let A be
the point of intersection of the lines x + 3 y − 1 = 0 and 3 x − y + 1 = 0, then the line
passing through the points C and A also pass through the point

(A) (−9, −7)
(B) (−9, −6)
(C) (7, 6)
(D) (9, 7)

y +e y +...∞ dy
225. If x = e y + e , then is
dx

1
(A)
x +1
1− x
(B)
x
x −1
(C)
x +1
1
(D)
x

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 50 of 51

m
m .co

m .co s e m
se g l a
KEY (PROVISIONAL) a
SI SI SI SI SI SI SI SI
No Key No Key No Key No Key No Key No Key No Key No Key
1 D 31 B 61 A 91 A 121 D 151 C 181 C 211 D
2 D 32 B 62 D 92 B 122 A 152 B 182 B 212 D
3 A 33 A 63 A 93 D 123 D 153 B 183 D 213 C
4 B 34 C 64 D 94 B 124 B 154 C 184 A 214 B
5 D 35 A 65 B 95 C 125 A 155 A 185 C 215 A
m
6 A 36 B 66
m D 96 B 126 B 156 D 186 C 216 B
.co
7 D 37 B
m .co
67 C 97 B 127 A 157 B 187 D 217 D
s e m
8 B 38
s
C
e 68 A 98 D 128 D 158 A 188 C 218
l aA

a ag
D B B C D B B C
l
9 39 69 99 129 159 189 219
10
11
B
B ag
40
41
D
A
70
71
A
B
100
101
B
A
130
131
D
A
160
161
A
B
190
191
A
A
220
221
B
B
12 A 42 B 72 A 102 D 132 B 162 D 192 B 222 B
13 B 43 A 73 A 103 A 133 C 163 A 193 D 223 D
14 A 44 C 74 B 104 A 134 B 164 B 194 A 224 B
15 D 45 A 75 A 105 D 135 B 165 A 195 B 225 B
16 A 46 B 76 D 106 D 136 D 166 D 196 B
17 C 47 B 77 C 107 D 137 B 167 C 197 D
m
.co
18 A 48 B 78 A 108 D 138 C 168 C 198 D
19 C 49 D 79 D 109 B 139 D 169 A 199 B
B B A
e
B m D A C
s
20 50 80 110 140 170 200
21 A 51 A 81 A 111
g la B 141 D 171 C 201 B
22
23
A
A
52
53
C
B
82
83
B
C
112
113
a A
B
142
143
D
D
172
173
B
D
202
203
C
C
24 C 54 C 84 B 114 C 144 A 174 C 204 B
25 B 55 C 85 C 115 C 145 C 175 B 205 A
26 C 56 C 86 D 116 D 146 B 176 C 206 A
27 B 57 C 87 B 117 C 147 B 177 C 207 B
28 A 58 A 88 A 118 C 148 A 178 D 208 A
29 B 59 C 89 D 119 B 149 C 179 D 209 A
m
.co
30 C 60 B 90 D 120 C 150 A 180 B 210 D
m
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 51 of 51