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

FOR CUSAT CAT EXAM PREPARATION

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

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

Notes · Sample Papers · Previous Year Papers · Mock Tests

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1. The acceleration due to gravity on the earth's surfaceais g. If the diameter of the earth
reduces to half of its original value and mass remains constant, then acceleration due
to gravity on the surface of earth would be

(A) 2g
(B) 4g
g
(C)
m
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2
m
(D)
g
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4
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2. aA particle of unit mass−undergoes
2n
one dimensional motion such that its velocity varies
according to v( x) = bx where b and n are constants and x is the position of the
particle. The acceleration of the particle as a function of x is given by

(A) −2nb 2 x −4n−1
(B) −2nb 2 x −2n−1
(C) −2nb 2 x −2n+1 m
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em
(D) −2nbx −4n+1
s
3. gla in the same direction
When two parallel wires carryacurrents

(A) they attract each other
(B) they repel each other
(C) magnetic forces on two wires are perpendicular to each other
(D) they do not experience any magnetic force

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4. A rigid ball of mass m strikes a rigid wall and gets reflected without loss of speed as
shown in figure. The value of impulse imparted by the wall to the ball will be

v

60o
60o

v

mv
(A)
3
(B) mv
(C) 2mv
mv
(D)
2

5. A refrigerator works between 4°C and 30°C. It is required to remove 600 calories of
heat every second in order to keep the temperature of the refrigerated space constant.
The power required is (Take 1 cal = 4.2 J)

(A) 2.365 W
(B) 23.65 W
(C) 236.5 W
(D) 2365 W

6. The distance between the centres of carbon and oxygen atoms in CO molecule is
0.12 nm. The distance of the centre of the mass of the molecule from the carbon
atom is

(A) 0.03 nm
(B) 0.05 nm
(C) 0.06 nm
(D) 0.07 nm

7. Kepler’s second law is based on which one of the following physical quantity?

(A) Energy
(B) Mass
(C) Linear momentum
(D) Angular momentum

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8.
a 2
The moment of inertia of a sphere about a diameter of a sphere is MR 2 , M is the
5
mass and R is the radius, then the moment of inertia of a sphere about a tangent to the
sphere is

2
(A) MR 2
7
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2
MR 2
(B)
3
o m m
. c s e
(C)
3
e m 2
l a
s5
MR
l a
g 7 MR2 ag
a(D) 5

9. The wettability of a surface by a liquid depends primarily on

(A) viscosity
(B) surface tension
(C) angle of contact between the surface and the liquid
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(D) density

e m
10.
las
Cp and Cv are specific heat at constant pressure and constant volume respectively. It is

ag
observed that Cp – Cv = a for hydrogen gas and Cp – Cv = b for nitrogen gas. The
correct relation between a and b is

(A) a = 28b
1
(B) a = b
14
(C) a = b
(D) a = 14b
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a

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11. An ideal gas undergoes a quasi static reversible process in which its molar heat
capacity C remains constant. If during this the relation of pressure P and volume V is
given by PV n = constant, then n is given by

C −Cp
(A) n=
C − Cv

Cp − C
(B) n=
C − Cv
C − Cv
(C) n=
C −Cp

Cp
(D) n=
Cv

12. The displacement equation of a progressive wave is y = 3sin (2000t – 5x), where the
distance x and y are in metre and time in second the speed of the wave is

(A) 200 m/sec
(B) 400 m/sec
(C) 600 m/sec
(D) 800 m/sec

13. The extension in a string, obeying Hook’s law is x. The speed of sound in the
stretched string is v. If the extension in the string is increased to 1.5x, the speed of
sound will be

(A) 1.22 v
(B) 0.61 v
(C) 1.50 v
(D) 0.75 v

14. A parallel plate condenser with oil between the plates (dielectric constant of oil k = 2)
has a capacitance C. If the oil is removed, then capacitance of the capacitor becomes

(A) 2C
C
(B)
2
(C) 2 C
C
(D)
2

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15. a of length 3 m, area of cross
The electrical conductivity of the material of a conductor
section 0.02 mm2 having a resistance of 2 Ω is

(A) 75 × 106/ Ω-m
(B) 85 × 105/Ω-m
(C) 75 × 105/ Ω-m
(D) 85 ×106/ Ω-m
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16. .co
A carbon resistance is having a following coding: green, orange, black, gold. The
s e m
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resistance of the resistor is
s l a
g
(A)la53 × 10 ± 5%
0 ag
a(B) 53 × 10 ± 5%1

(C) 53 × 100 ± 10%
(D) 53 × 101 ± 10%

17. A heater coil is cut into two equal parts and only one part is now used in the heater.
The heat generated will be
m
(A) doubled
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(B) four times
s e
(C) one fourth
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(D) one third
a
18. Which of the following statement is FALSE?

(A) Wheatstone bridge is most sensitive when all the four resistances are of the
same order of magnitude
(B) In a balanced Wheatstone bridge if the cell and the galvanometer are
exchanged, the null point is disturbed
(C) A rheostat can be used as a potential divider
m
m (D) Kirchhoff’s second law represents energy conservation
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m 19. s em
e A boy standing on a stationary lift (open from above) throws laaball upwards with the
las ag time does the ball take
ag maximum initial speed he can, equal to 49 m/sec. How much
to return to his hands?

(A) 5 secs
(B) 10 secs
(C) 15 secs
(D) 30 secs

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20. The most penetrating radiation out of the following is

(A) β- rays
(B) γ-rays
(C) X-rays
(D) α-rays

21. The half life of radium is 1600 years. The fraction of a sample of radium that would
remain after 6400 years

1
(A)
4
1
(B)
2
1
(C)
8
1
(D)
16

22. What is the ratio of Bohr magneton to the nuclear magneton?

mp
(A)
me
(B) 1
2
mp
(C) 2
me

(D)

23. The energy of a photon whose wavelength 6840 Å is

(A) 1.81 eV
(B) 3.6 eV
(C) 12.1 eV
(D) 13.2 eV

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24. a the electric and magnetic
In Thomson’s experiment to measure e/m of electrons,
fields are

(A) in the same direction
(B) in the opposite direction
(C) at an angle of 45° with each other
(D) perpendicular to each other

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Two thin lenses, one of focal length 60 cm and the other of focal length −20 cm are .co
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put in contact, the combined focal length is
m s e m
15ecm
s l a
la−15 cm ag
(A)
g
(B)
a −30 cm
(C)
(D) 30 cm

26. An ideal fluid is flowing in a non-uniform cross-sectional tube XY (as shown in the
figure) from end X to end Y. If K1 and K2 are the kinetic energy per unit volume of the
fluid at X and Y respectively, then the correct option is

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a
K2
(A) K1 =
2
(B) K1 = K 2

(C) K1 < K 2

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(D) K1 > K 2
m
c. o27. If a body moves in such a way that its linear momentum is constant,sethen
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la a
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(A) its kinetic energy is zero
(B) the net force acting on it must be zero
(C) its acceleration must be non-zero and constant
(D) its center of mass must remain at rest

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28. Two spheres of masses m and M are situated in air and the gravitational force between
them is F. The space around the masses is now filled with a liquid of specific gravity
5. The gravitational force will now be

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

29. Within the limit of elasticity, which of the following graphs obey Hooke's law?

(A)

(B)

(C)

(D)

30. The current density is a

A
(A) Scalar with SI units
m
A
(B) Vector with SI units
m2
A
(C) Scalar with SI units
m2
A
(D) Vector with SI units
m

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31. a uniformly over its cross-
A long, straight wire of radius R carries a current distributed
section. The magnitude of the magnetic field is

(A) maximum at the axis of the wire
(B) minimum at the axis of the wire
(C) maximum at the surface of the wire
(D) minimum at the surface of the wire

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32.
m
The equation ϕ = 3t2 + 4t + 9 represents the magnetic flux (in Weber) linked with a
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coil. Then the magnitude of the emf induced after t = 2s will be
m s e m
2e
s l a
la4 V ag
(A) V
g
(B)
a 8V
(C)
(D) 16 V

33. When light is incident normally on an air-glass interface, what percentage of light is
reflected back, if the refractive index of the glass is 1.5?

(A) 80%
(B) 50%
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(C) 10%
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(D) 4%
s
laby a lens. If half of the lens is covered with black
34.
a g
An image of an object is formed
paper, how will the image change?

(A) Size of the image will be reduced to one half
(B) Brightness of the image will be reduced
(C) The image will disappear
(D) An inverted image will be formed

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35. In Young’s double slit experiment, when two light waves interfere to produce a
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interference pattern of maxima and minima, at the third minima, the two waves have

m s e
s e (A) phase difference of 3π
g l a
g la 5π a
a (B) phase difference of
2
(C) path difference of 3λ
5λ
(D) path difference of
2

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36. Which one of the following statements is NOT correct?

(A) A diode does not obey Ohm's law.
(B) A p-n junction diode symbol shows an arrow identifying the direction of
current (forward) flow
(C) An ideal diode is an open switch
(D) An ideal diode is an ideal one way conductor

37. To get output 1for the following circuit, the correct choice for the input is

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

38. The combination of gates as shown in the figure forms the

(A) AND gate
(B) OR gate
(C) NOR gate
(D) NOT gate

39. A position dependent force F = (7 − 2x + 3x2) N, acts on a small body of mass 2 kg
and displaces it from x =0 to x = 5 m. Work done is

(A) 35 J
(B) 70 J
(C) 135 J
(D) 270 J

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40. a to operate a turbine. The losses
Water falls from a height of 60 m at the rate of 15 kg/s
due to frictional force are 10% of the input energy. How much power is generated by
the turbine? (g = 10 m/s2)

(A) 10.2 kW
(B) 8.1 kW
(C) 12.3 kW
(D) 7.0 kW
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41.
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In a carbon monoxide molecule, the carbon and the oxygen atoms are separated by a
s e m
em
distance 1.12 × 10−10 m. The distance of the centre of mass from the carbon atom is
s l a
(A)la 0.64 × 10 m
g
−10
ag
a(B) −10
0.56 × 10 m
(C) 0.51 × 10−10 m
(D) 0.48 × 10−10 m

42. A cylinder contains hydrogen gas at pressure of 249 kPa and temperature 27°C. Its
density is (R = 83 Jmol−1K−1)
m
(A) 0.2 kg/m3
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(B) 0.1 kg/m3
s e
(C) 0.02 kg/m3
g la
(D) 0.5 kg/m3 a
43. Three containers of the same volume contain three different gases. The masses of the
molecules are m1, m2 and m3 and the number of molecules in their respective
containers are N1, N 2 and N3 . The gas pressure in the containers are p1, p2 and p3
respectively. All the gases are now mixed and put in one of these containers. The
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pressure p of the mixture will be
m
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s e m
s e g l a
g la (B)
p + p2 + p3
p= 1 a
a 3
(C) p = p1 + p2 + p3

(D) p > ( p1 + p2 + p3 )

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44. For hydrogen gas C p − Cv = a and for oxygen gas C p − Cv = b , so the relation
between a and b is given by

(A) a = 16b
(B) 16b = a
(C) a = 4b
(D) a=b

45. In which of the following devices, the eddy current effect is NOT used?

(A) Magnetic braking in train
(B) Electromagnet
(C) Electric heater
(D) Induction furnace

46. The magnetic potential energy stored in a certain inductor is 25 mJ, when the current
in the inductor is 60 mA. This inductor is of inductance

(A) 1.389 H
(B) 138.88 H
(C) 0.138 H
(D) 13.89 H

47. The cathode of a photoelectric cell is changed such that the work function changes
from W1 to W2 ( W1 > W2 ). If the current before and after changes are I1 and I 2 , all
other conditions remaining unchanged, then (assuming hν > W2 )

(A) I1 = I 2
(B) I1 < I 2
(C) I1 > I 2
(D) None of the above

48. The 21 cm radio wave emitted by hydrogen in interstellar space is due to the
interaction called the hyperfine interaction in atomic hydrogen. The energy of the
emitted wave is nearly

(A) 10−17 J
(B) 1J
(C) 7 × 10−6 J
(D) 10−24 J

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49. a configuratiation (see figure) in
An n-p-n transistor is connected in common emitter
age drop across load resistance (800 Ω) connec
which collector voltage ected to the collector
circuit is 0.8 V. The co
collector current is

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m .co s e m
s e l a
(A) a 2 mA
g l 0.1 mA ag
a(C) 1 mA
(B)

(D) 0.2 mA

50. The voltage gain of an amplifier with 9% negative feedback is 10.. T
The voltage gain
without feedback will
ll bbe

(A) 90
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(B) 10
(C) 1.25
(D) 100
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51. The figure shows a log a with two inputs A and B and the output
ogic circuit ou C. The
voltage wave forms ac
across A, B and C are as given. The logic circui
uit gate is

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g la a
a (A)
(B)
OR gate
NOR gate
(C) AND gate
(D) NAND gate

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52. If the tension in a stretched string is increased, what happens to the velocity of a wave
traveling through the string?

(A) Increases
(B) Decreases
(C) Remains the same
(D) Becomes zero

53. A parallel-plate capacitor initially has a capacitance of 10 µF and is charged to 100 V.
If the plate separation is reduced by half while maintaining the same charge on the
capacitor, what is the resulting capacitance?

(A) 5 µF
(B) 10 µF
(C) 20 µF
(D) 40 µF

54. A steady current of 5A flows through a copper wire for 10 s. Calculate the total
charge that passes through the wire during this time.

(A) 2C
(B) 5C
(C) 15 C
(D) 50 C

55. The magnetic dipole moment of a current-carrying circular coil is doubled by

(A) Doubling the radius of the loop
(B) Doubling the current through the loop
(C) Doubling the number of turns
(D) Doubling the current through the loop and the number of turns

56. The electric field of a plane electromagnetic wave is given by
E = E0 (x + y) sin (kx – ωt), its magnetic field will be given by

E0
(A) (x – y) cos (kx – ωt)
C
E0
(B) (−x + y) sin(kz – ωt)
C
E0
(C) (x – y) sin(kz – ωt)
C
E0
(D) (x + y) sin(kz - ωt)
C

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57. Find the critical angle of a medium for a specificawavelength, if the medium has
4
relative permittivity 3 and relative permeability for this wavelength.
3

(A) 60°
(B) 15°
(C) 45°
(D) 30°
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58. .co
The de-Broglie wavelength of a molecule in a gas at room temperature ( 300 K ) is λ1.
m s e m
s e
If the temperature of the gas is increased to 600 K, then the de Broglie wavelength of l a
l a
the same gas molecule becomes
g ag
a 1
(A) λ1
2
(B) 2 λ1
1
(C) λ1
2
(D) 2 λ1
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59.
s e
An electron having de-Broglie wavelength λ is incident on a target in an X- ray tube.
Cut-off wavelength of emitted X-ray is
g la
(A) 0 a
2 λ
(B)
ℎ
2 λ
(C)
ℎ
ℎ
(D)
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m
c. o60. An NPN transistor is used in common emitter configuration as ansamplifier
m with 1 kΩ .co
e
s em a base-emitter. This
load resistance. Signal voltage of 10 mV is applied acrosslthe
g
la a in the base current of the
ag
produces a 3 mA change in the collector and 15 µA change
amplifier. The input resistance and voltage gain are

(A) 0.033 kΩ, 1.5
(B) 0.67 kΩ, 200
(C) 0.33 kΩ, 300
(D) 0.67 kΩ, 300

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61. The modulation index for an A.M. wave having maximum and minimum peak to peak
voltages of 14 mV and 6 mV respectively is

(A) 1.4
(B) 0.4
(C) 0.2
(D) 0.6

62. A capacitor of capacitance C = 1 µF is suddenly connected to a battery of 100 volt
through a resistance R = 100 Ω. The time taken for the capacitor to be charged to get
50 V is Take ln 2 = 0.69

(A) 1.44 × 10−4 S
(B) 3.33 × 10−4 S
(C) 0.69 × 10−4 S
(D) 0.30 × 10−4 S

63. A potentiometer wire PQ of 1 m length is connected to a standard cell E1. Another
cell E2 of emf 1.02 V is connected with a resistance ‘r’ and switch S (as shown in
figure ). With switch S open, the null position is obtained at a distance of 49 cm from
Q. The potential gradient in the potentiometer wire is

(A) 0.02 V/cm
(B) 0.04 V/cm
(C) 0.01 V/cm
(D) 0.03 V/cm

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64. 5a magnetic field of 0.3 T at
−1
A beam of protons with speed 4 × 10 ms enters a uniform
an angle of 60o to the magnetic field. Then the pitch of the resulting helical path of
protons is close to

[Mass of the proton =1.67 × 10−27 kg, charge of the proton =1.69×10−19 C]

(A) 12 cm
(B) 4 cm
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(C) 5 cm
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(D) 2 cm
e m
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65.
a
In an LC
l s gits
oscillator, if values of inductance and capacitance become twice and eight
a
g resonance frequency ω . The value of ‘x’ is
times,
ainitial
respectively, then the resonant frequency of oscillator becomes ‘x’ times
0

1
(A)
4
(B) 4
(C) 16
1
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(D)
6

s em
66.
g l aif we change the resistance only, from a lower to
In a series, LCR Resonance circuit,
higher value then a
(A) the bandwidth of resonance circuit will increase
(B) the resonance frequency will increase
(C) the quality factor will increase
(D) the quality factor and the residence frequency will remain constant

67. A uniform cable of mass ‘M’ and length ‘L’ is placed on a horizontal surface that is
m
m cable up to the surface, the work done should be .co
th
part is hanging below the edge of the surface. To lift the hanging part of the

m .co s e m
s e g l a
la a
(A) MgL

ag n2
(B) MgL
2n 2
(C) 2MgL
n2
(D) nMgL

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68. A fly wheel is accelerated uniformly from the rest and rotates through 5 rad in the first
second. The angle rotated by fly wheel in the next second, will be

(A) 7.5 rad
(B) 15 rad
(C) 20 rad
(D) 30 rad

69. The time period of satellite revolving around earth in a given orbit is 7 hours. If the
radius of orbit is increased to 3 times its previous value, then approximate new time
period of the satellite will be

(A) 40 hours
(B) 36 hours
(C) 30 hours
(D) 25 hours

70. The elastic limit of brass is 379 MPa. What should be the minimum diameter of brass
rod if it is to support a 400 N load without exceeding its elastic limit?

(A) 1.16 mm
(B) 0.90 mm
(C) 1.36 mm
(D) 1.00 mm

71. A gas has n degrees of freedom. The ratio of specific heat of gas at constant volume to
the specific heat of gas at constant pressure will be

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

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72. A string of length 1m and mass 5 kg is fixed at bothaends. The tension in the string is
8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz.
The separation between successive nodes and the string is close to

(A) 16.6 cm
(B) 20.0 cm
(C) 10.0 cm
(D) 33.3 cm
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73.
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Moment of inertia of a body about a given axis is 1.5 kg m2. Initially the body is at
m s e m
e
rest. In order to produce rotational kinetic energy of 1200 J, the angular acceleration
s l a
a
of 20 rad /s2 must be applied about the axis for a duration of
g l ag
a(A) 2 s
(B) 5 s
(C) 2.5 s
(D) 3 s

74. 105 Fermi is equal to

(A) 1 meter
m
(B) 100 micron
.co
em
(C) 1 Angstrom
(D) 1 mm
las
a g
75. Which of the following have same dimensions?

(A) Planck’s constant and momentum
(B) Torque and force
(C) Potential energy and force
(D) Torque and potential energy

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76. According to the first law of thermodynamics, for an isolated system, ∆U =
m
m .co (A) Negative
s e m
s e (B) Zero
g l a
la
(C) Positive
g (D) The value of ∆U cannot be predicted by using first law a
a
77. The ionization of water (H2O(l) ⇌ H+(aq) + OH-(aq)) has an equilibrium constant of
1 x 10-14 at 298 K. The ∆G0 of the reaction is ……..kJ/mol

(A) – 79.8 kJ/mol
(B) +79.8 kJ/mol
(C) +39.9 kJ/mol
(D) – 39.9 kJ/mol
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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 19 of 52

78. Yellow and Red phosphorous are two important allotropes of Phosphorous. Heat of
combustion of red and yellow phosphorous are –8.78 kJ and – 9.91 kJ respectively.
The heat of transition of yellow to Red phosphorous is

(A) –18.69 kJ
(B) +1.13 kJ
(C) +18.69 kJ
(D) –1.13 kJ

79. pOH of a 1 × 10−9 M aqueous solution of hydronium ion in room temperature will be

(A) 9
(B) 7.9
(C) 5
(D) 10.9

80. A solution containing equimolar concentration of SnCl2, NiCl2, MgCl2, AgNO3,
AuCl3 is being electrolyzed by using inert electrodes. The standard electrode
potentials (in Volts) for each metal ions is
Sn2+/Sn = −0.14V, Ni2+/Ni = −0.25 V, Mg2+/Mg= −2.36 V, Ag+/Ag = 0.80 V
and Au3+/Au = 1.40V

With an increasing voltage, the order of metal deposition on the cathode will be

(A) Sn, Ni, Ag, Au, Mg
(B) Au, Ag, Sn, Ni, Mg
(C) Mg, Ni, Sn, Ag, Au
(D) Mg, Au, Ag, Ni, Sn

81. The amount of O2 dissolved in one liter of water at 25°C under a partial pressure of
oxygen 0.75 atm is ……………. (Henry’s law constant kH = 1.4 × 10−3 mol/L/atm)

(A) 33.6 mg
(B) 3.36 mg
(C) 33.6 g
(D) 3.36 g

82. ………… gets deposited on both anodic and cathodic plates of a discharged lead-acid
battery

(A) Pb
(B) PbO2
(C) Pb2O4
(D) PbSO4

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m
m .co

m .co s em
se g la
83. a relationship?
Which of the following expression gives the de Broglie

h
(A) λ=
mp
h
(B) p=
mv
ε = mc 2
(C)
m
m .co
.co
h
(D) λ=
e m
em
mv
l as
a s
lenthalpies ag
84. g
The
a of all elements in their standard states are

(A) Unity
(B) Zero
(C) <0
(D) Different for each element

85. Half-life of 10 g of radioactive substance is 10 days. The half-life of 20 g is
m
(A)
(B)
10 days
20 days
m .co
(C) 40 days
s e
(D) 15 days
g la
a
86. Ksp for AgCl (mol wt 143.5) is 17 × 10−11 at 298 K. The molar solubility of AgCl at
298 K is

(A) 18.7 × 10−5
(B) 2.3 × 10−3
(C) 9.90 × 10−3
(D) 1.3 × 10−5
m
m
c. o87. What is the activation energy for a reaction if its rate doubles whensethemtemperature is .co
s em raised from 200 K to 400 K? (R = 8.314 JK mol ) −1

g l a
−1

la a
ag (A)
(B)
234.65 kJ mol−1
434.65 kJ mol−1
(C) 229.1 J mol−1
(D) 334.65 J mol−1

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 52

88. DDT on exposure to water decomposes. Half-life = 10 years. How much time will it
take for its 90% decomposition?

(A) 50 years
(B) 33.3 years
(C) 70 years
(D) 80 years

89. Which of the following is used as an electrolyte in an H2-O2 fuel cell?

(A) KOH
(B) NH4OH
(C) Fe(OH)2
(D) Cu(OH)2

90. If Zn2+/Zn electrode is diluted 100 times, then the change in emf is

(A) increase of 59 mV
(B) decrease of 59 mV
(C) increase of 29.5 mV
(D) decrease of 29.5 mV

91. In Zinc blende structure

(A) zinc ions occupy half of the tetrahedral sites
(B) each Zn2− ion is surrounded by six sulphide ions
(C) each S2− ion is surrounded by six Zn2+ ions
(D) it has fcc structure

92. A + 2B → C + D. If −d[A]/dt = 5 × 10−4 mol L−1 s−1, then −d[B]/dt is

(A) 2.5 × 10−4 mol L−1 s−1
(B) 5.0 × 10−4 mol L−1 s−1
(C) 2.5 × 10−3 mol L−1 s−1
(D) 1.0 × 10−3 mol L−1 s−1

93. A metal crystallizes into two cubic phases, body centered cubic and face centered
cubic whose unit cell length are 2.5 and 2.0 Aº respectively. The ratio of densities of
body centered cubic and face centered cubic is

(A) 0.24
(B) 0.25
(C) 0.26
(D) 0.23

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m
m .co

m .co s em
se g la
94. a and 40 mm Hg respectively. If
The vapour pressure of A and B at 27°C are 60 mm Hg
A and B are mixed such that the mole fraction of A in the mixture is 0.8, then the mole
of B in the vapour phase is Z × 10−1. The value of Z is

(A) 1.0
(B) 1.2
(C) 1.4
(D) 1.6
m
m .co
95. .co
A buffer solution was prepared by mixing equal concentration of acid (ionization
s e m
em
constant Ka) and a salt. The pH of the buffer is
s l a
g
(A)la14 – pKa ag
a(B) pKa + 1
(C) pKa
(D) pKa – 14

96. When the hybridization state of carbon atom changes from sp3 to sp2 and finally to sp,
the angle between the hybridized orbitals

(A) decreases gradually
m
hybridization state changes from sp2 to sp m .co
(B) decreases when hybridization state changes from sp3 to sp2 and increases when

s e
la
(C) remains unchanged
(D) increases progressively
ag
97. IUPAC name of (CH3)2CHCH=CHCH3 is

(A) 2-methylpent-3-ene
(B) 4-methylpent-2-ene
(C) 1,1-dimethylbut-2-ene
(D) 4,4,-dimethylbut-2-ene

o m
c
m Major product formed when 2,2-dibromobutane is heated at 200 °Cmin. presence of
c. o molten KOH is (note: reaction is carried out under thermodynamically
98.

m s e controlled
s e conditions)
g l a
g la a
a (A) 1-bromo-but-1-yne
(B) 1-bromo-but-2-yne
(C) but-1-yne
(D) but-2-yne

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 52

99. Pick the major product formed in the following reaction sequence.

(A)

(B)

(C)

(D)

100. Which of the following does not give a white precipitate with ammoniacal AgNO3
solution?

(A) propyne
(B) but-1-yne
(C) but-2-yne
(D) ethyne

101. Benzoic acid is treated with thionyl chloride to give compound Q which is converted
to benzaldehyde as shown below. What reagent is required to convert
Q to benzaldehyde?

PhCOOH → Q → PhCHO

(A) NH4Cl
(B) H2/Pd-C
(C) H2, Pd/BaSO4
(D) O2, Pt

102. Which of the following reactions will not result in the formation of new
carbon-carbon bonds?

(A) Reimer-Tieman reaction
(B) Cannizaro reaction
(C) Wurtz reaction
(D) Friedel-Crafts acylation

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m
m .co

m .co s em
se g la
a a primary amino (NH )
103. Which among the following amino acids does not have 2
group?

(A) Serine
(B) Proline
(C) Tyrosine
(D) Lysine

m
104.
m
Pick the correct statement about allene (propa-1,2-diene):
.co
.co s e m
em a
H H

s l
ag
C C C

g la H H

a(A) only sp hybridized carbons are present in allene
2

(B) both sp2 and sp hybridized carbons are present in allene
(C) all four hydrogens in allene lie in the same plane
(D) C-C-C bond angle in allene is about 120 ± 5 degrees

105. An example of a polar protic solvent is:

(A) Acetonitrile
m
(B) Methanol
.co
(C) Acetone
s em
la
(D) Dimethyl formamide

ag
106. The exterior surface of a soap micelle in water is:

(A) hydrophobic
(B) hydrophilic
(C) amphiphilic
(D) lipophilic

m
.co
107. The term invert sugar refers to an equimolar mixture of:
m
m .co (A) D-glucose and D-galactose
s e m
s e (B) D-glucose and D-fructose
g l a
la a
(C) D-glucose and D-mannose

ag (D) D-glucose and D-ribose

108. SN1 substitution on a chiral carbon of an optically active compound proceeds with:

(A) retention in configuration
(B) inversion in configuration
(C) racemization
(D) inversion at higher temperature and retention at lower temperature
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 52

109. Formal charge of nitrogen atom in nitric acid (HNO3) and nitrous acid (HNO2) is

(A) +1 and 0 respectively
(B) 0 and +1 respectively
(C) +1 and -1 respectively
(D) +1 and +1 respectively

110. Additive that was used as an anti-knock agent in petrol that has now been banned due
to environmental and health concerns is:

(A) Ethyl acetate
(B) Lead tetrachloride
(C) Lead acetate
(D) Tetraethyllead [(C2H5)4Pb]

111. Which among the following name reactions is best suited to convert acetic acid to
bromoacetic acid?

CH3CO2H → Br-CH2CO2H

(A) Hell-Volhard-Zelinsky reaction
(B) Hunsdiecker reaction
(C) Reformatsky raction
(D) Hoffmann bromamide reaction

112. Which one of the following bases is not present in DNA?
(A) Adenine
(B) Guanine
(C) Cytosine
(D) Uracil

113. Which of the following halides can undergo nucleophilic substitution under mild
conditions?

(i) 3-chloroprop-1-ene
(ii) 1-chloropropane
(iii) Benzyl chloride
(iv) Chloroethene (Vinyl Chloride)

(A) (i), (ii), and (iii)
(B) (i) and (ii)
(C) (ii) and (iv)
(D) (i) and (iii)

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m
m .co

m .co s em
se g la
a NH is:
114. Major product formed when hex-3-yne reacts with Na/liq. 3

(A) cis-hex-3-ene
(B) trans-hex-3-ene
(C) 3-aminohexane
(D) 3,4-diaminohexane

115. Which among the following reactions is best suited to convert benzyl bromide to
m
c o m
benzylamine with minimal side product formation?
m .co
. s e
em with KCN followed by reduction with LiAlH a
(A) Reaction with liquid ammonia
s
(B) Reaction
g
(C)la Reaction with potassium phthalimide followed by hydrolysis with strong base
l
a
4

g Reaction with sodium nitrite (NaNO )followed by reduction with LiAlH
a(D) 2 4

116. What is the correct set of four quantum numbers for the valence electron of an atom
with Z = 37 ?

1
(A) 5, 0,1, +
2
1
m
.co
(B) 5,1, 0, −
2
1
e m
(C) 5, 0, 0, +
2
las
(D) 5,1,1, −
1
ag
2

117. What is the number of radial nodes for 3p orbital ?

(A) 1
(B) 2
(C) 3
m
.co
(D) 4
m
.co
m 118. The wave function ( ) of 2s is given by
"
s em
e 2 −la &
# %
s
'%∕
= . Find the
ag
!

la
√ ! !

ag value of r where radial node is formed

(A) 0
(B) )*
(C) 2)*
(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 27 of 52

119. Which transition in the hydrogen atom spectrum would have the same wavelength as
the Balmer type transition from n = 4 to n = 2 of He+ spectrum

(A) n = 2 to n = 1
(B) n = 3 to n = 1
(C) n = 2 to n = 4
(D) n = 3 to n = 4

120. Which of the following represents isoelectronic species?

(A) Li+, Na+, Mg2+, Ca2+
(B) Ba2+, Sr2+, K+, Ca2+
(C) O2─, F─, S2─, Ca2+
(D) Ar, K+, Cl─, Sc3+

121 Which among the atomic orbitals 6s, 7s, 7p, 8p and 8d have 5 radial nodes?

(A) 7s, 7p, 8d
(B) 6s, 7s, 8p
(C) 6s, 7p, 8d
(D) 7s, 7p, 8p

122. Statement I: 5f electrons can participate in bonding to a far greater extent than 4f
electrons
Statement II: 5f orbitals are not as buried as 4f orbitals

Choose the correct option

(A) Both the Statements are true
(B) Statement I is true but Statement II is false
(C) Statement I is false and Statement II is true
(D) Both the Statements are false

123. Which of the following have highest bond dissociation energy?

(A) F2
(B) Cl2
(C) Br2
(D) I2

124. Which among the following is the most basic oxide?

(A) Ga2O3
(B) Al2O3
(C) B2O3
(D) In2O3

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m
m .co

m .co s e m
se g l a
125. Identify the correct order of electronegativity a
(A) Br > O > P > C
(B) C > P > O > Br
(C) O > Br > C > P
(D) P > C > O > Br

126. What is the spin only magnetic moment value of [Pt(NH3)2Cl(NH2CH3)]Cl?
m
m .co
.co m
(A) 0
(B) 2.6
m s e
(C)
s e
3.4 l a
l
(D)
g a 4.9 ag
a
127. Which of the following has square pyramidal shape?

(A) [Ni(CN)4]2─
(B) PCl5
(C) BrF5
(D) PF5

m
128.
.co
Which of the following transition metal has the highest third ionization enthalpy?
m
s e
la
(A) Cr
(B)
(C)
Mn
V ag
(D) Fe

129. What is the change of oxidation state of Cr in potassium dichromate as a strong
oxidising agent in acidic solution?

(A) +3 to +1
(B) +6 to 0
m
m (C) +6 to +3
.co
.co m
(D) +3 to +2

m s e
s e l a
a 130. Why boric acid is solid and BF is gas at room temperature? g
l a
ag
3

(A) Strong ionic bond in boric acid
(B) Strong covalent bond in BF3
(C) Strong van der Waal’s interaction in boric acid
(D) Strong hydrogen bond in boric acid

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 52

131. What is the geometry of B in BF3 and BF3NMe3?

(A) Trigonal planar and tetrahedral
(B) Trigonal planar and pentagonal bipyramidal
(C) Tetrahedral and pentagonal bipyramidal
(D) Tetrahedral and trigonal planar

132. Identify the correct statement about B2H6.

(A) All B─H─B angles are 120°
(B) The two B─H─B bonds have different length
(C) Terminal B─H bonds have less p-character than the bridging B─H bonds
(D) Its fragment BH3 is a Lewis base

133. How many geometrical isomers are possible for the square planar complex
[Pd(py)(Cl)(Br)(NH3)], py = pyridine?

(A) 2
(B) 4
(C) 5
(D) 3

134. Why is cuprous ion colourless while cupric ion is coloured?

(A) Both have half-filled p- and d-orbitals
(B) Cuprous ion has incomplete d-orbital and cupric ion has a complete d-orbital
(C) Both have unpaired electrons in the d-orbitals
(D) Cuprous ion has complete d-orbital and cupric ion has an incomplete d-orbital

135. Identify the correct geometry and magnetic property of [Ni(CO)4] complex.

(A) Square planar and diamagnetic
(B) Tetrahedral and diamagnetic
(C) Tetrahedral and paramagnetic
(D) Square planar and paramagnetic

136. The number of one-one functions from A to A , where A = {1, 2,3} , is

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

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m
m .co

m .co s em
se g la
137. If the directional cosines of a straight line are 0, 0, 1,athen the equation of the straight
line is

(A) x = 0, y = 0
(B) y = 0, z = 0
(C) x = 0, z = 0
(D) x+ y+ z =0

m
c o m
If a non zero matrix A of order 5 × 5 satisfies the equation A2 − 5 A = 0, then the m .co
138.
matrix A ism
. s e
s e l a
g a
l A =  5 5  ag
a(A)
 5 5
5 0
(B) A= 
0 5
5 0
(C) A= 
0 0

m
.co
0 5
(D) A= 
5 0
s em
g l=a0, az + y = 0, ax + z = 0 has infinite number of
a
139. If the system of equations x + ay
solutions, then the value of a is

(A) 0
(B) −1
(C) 1
(D) z

m
.co
sin x
m
140. The function f ( x) = is continuous in the interval
.co m
x

m s e
s e (A) (0, ∞)
g l a
g la (B) (−∞, 0) a
a (C) [ −1,1]
(D) (−∞, ∞)

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 52

141. Let S be the set of points at which the function f : ℝ → ℝ defined by f ( x) = cos x
is not differentiable. Then S is equal to

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

142. Let f be a continuous function on [0, 4]. If f ( x) takes rational values for all x and
f (4) = 2025 , then f (π ) is

(A) 0
(B) 2025
(C) π
(D) 1

143. The sum of three numbers is 96. The first number is 6 times the third number, and the
third number is 40 less than the second number. Then the absolute value of the
difference between the first and second numbers is

(A) 2
(B) 3
(C) 4
(D) 5

5
144. If sin a + sin b = and cos a + cos b = 1, then cos(a − b) is equal to
3

1
(A)
3
2
(B)
3
3
(C)
4
(D) 1

145. The equation 3 x13 + 5 x5 − 7 = 0 has

(A) exactly one real root
(B) more than one real root
(C) exactly 13 real roots
(D) no real root

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m
m .co

m .co s e m
se g l a
146. The mapping f :[−2, 2] → ℝ , defined by f ( x) = x xa, is

(A) bijective
(B) not one-one but onto
(C) not onto
(D) not a function

m
.co
147. The number of constant functions from a set containing m elements to a set containing
m
.co
n elements is
e m
mn m as
me l
(A)
a
(B)s
ln ag
g
(C)
a m+n
(D)

 −π π 
148. The mapping f :  ,  → ℝ, defined by f ( x) = tan x , is
 2 2

(A) one-one
(B) onto
m
.co
(C) bijective
(D) not a function
e m
las
g
149. The value of cos −1 x + sin −1 x is
a
(A) 0
(B) 1
π
(C)
2
(D) π
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 33 of 52

150. Let a, b, c and d be distinct integers such that (6 − a )(6 − b)(6 − c)(6 − d ) = 36 . Then
a + b + c + d is equal to

(A) 23
(B) 24
(C) 13
(D) 14

151. Let f : X → X be a mapping such that f ( f ( x) ) = x for all x ∈ X . Then

(A) f is one-to-one and onto
(B) f is one-to-one but not onto
(C) f is onto but not one-to-one
(D) f is neither one-to-one nor onto

152. The number of transition points for the function f ( x) = e −2 x is

(A) ∞
(B) 2
(C) 1
(D) 0

153. The least number of positive integers ‘n’ satisfying n n n... = n is

(A) 0
(B) 1
(C) 2
(D) ∞

154. Let G = {(a, b) / a ∈ ℝ*, b ∈ ℝ} and be defined as (a, b) ♦ (c, d ) = (ac, bc, d ). Then
which of the property that G does not satisfy under the operation ♦?

(A) Associative
(B) Existence of identity
(C) Existence of inverse
(D) Commutative

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m
m .co

m .co s em
se g la
155. The question paper in a test consists of 15 questions.aIn how many ways the test can
be attempted if each question has four choices?

(A) 154
(B) 15
(C) 415
(D) 1
m
m .co
156. .co
The derivative of f ( x) = x exists in
m s e m
s e l a
(A) a ℝ
g l ℝ − {0} ag
a(C) (0, ∞)
(B)

(D) [0, ∞)

157. Let M be the set of all n × n matrices such that each matrix is both symmetric and
skew symmetric. Then M is

m
.co
(A) n
(B) 1
e m
(C) n2
las
(D) ∞
ag
158. Which of the following function has maxima?

(A) f ( x) = e2 x , x ∈ ℝ
1
(B) f ( x) = 2 , x ∈ ℝ
x
m
.co
(C) f ( x) = cot( x) , x ∈ ℝ
m
.co (D) f ( x) = cos( x) , x ∈ ℝ
s e m
s em g l a
g la a to the line y = x, then
159. If the point P(4,5) is shifted by a distance 2 2 units parallel
a the coordinates of P in new position is

(A) (6, 7)
(B)
( 4 + 2, 5 + 2 )
(C) 4 + 2,5 − 2
( )
(D) (5, 4)
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 52

160. The solution set of log3 9 − 5 x > 2 is

 18 
(A)  ,∞
5 
 3 18 
(B)  , 
5 5 
18
(C) ( −∞, 0 ) ∪  
, +∞ 
5 
 18 
(D)  −∞, − 
 5

161. The angle between the tangents drawn from the point (1, 4) to the parabola y 2 = 4 x is

π
(A)
6
π
(B)
4
π
(C)
3
π
(D)
2

162. A set of matrices of same order under matrix multiplication can never be

(A) a monoid
(B) a non abelian group
(C) a semi group
(D) an abelian group

3n
4π 4π  1+ a 
163. If a = cos + i sin , then the value of   is
3 3  2 

(A) (−1) n

(−1) n
(B)
23n
1
(C)
23n
(D) (−1) n + 1

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m
m .co

m .co s em
se g la
164. Locus of the point z satisfying the equation iz − 1 + a
z − i = 2 is

(A) an ellipse
(B) a parabola
(C) a circle
(D) a straight line

m
.co
1
165.
m
Sum of all terms of an infinite GP is times the sum of odd terms. The common

.co m
7
ratio is
m s e
s e l a
(A)l a 6
ag
ag 7
−1
(B)
7
−6
(C)
7
1
(D)
7
m
m .co
166.
s e
The number of solutions of the equation log 0.5 sin x = 1 − log 0.5 cos x , in∈ [−2π , 2π ] ,
is
g la
(A) 1
a
(B) 2
(C) 3
(D) 4

167. If x 2 − 1 is a factor of x 4 + mx3 + 4 x − nk , then
m
m (A) m = 4, n = −1
.co
m .co (B) m = −4, n = 1
s e m
s e (C) m = 4, n = 1
g l a
la a
(D) m = −4, n = −1

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 52

n n n
Pr −1 Pr P
168. If = = r +1 , then
x y z

1
(A) ∑ x =1
(B) xyz = 1

(C) y 2 = x( y + z )

(D) x2 = z ( x + y)

169. The number of triangles which can be formed by using the vertices of a regular
polygon of n + 3 sides is 220. Then n is equal to

(A) 8
(B) 9
(C) 10
(D) 11

18
 1
170. The middle term in the expansion of  x −  is
 x

(A) 18 C9

(B) −18 C9
18
(C) C10

(D) −18 C10

a b  1 0 
171. If the matrix   commutes with the matrix   , then
c d  1 1 

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

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m
m .co

m .co s e m
se g l a
− x x 2 a
172. The values of x for which the matrix  2 x − x  will be invertible are
 x −2 − x 

(A) −2 ≤ x ≤ 2
(B) x ≠ 2 and x ≠ −2
(C) x≥2
m
.co
(D) x ≤ −2
m
.c2 o s e m
173.
e{m
Let X = a : a = 1 and a is a complex value and
s } l a
a
Y g=l{b : b 4 = 1 and b is a complex value} . Then the set X ∆Y is equal to ag
a
(A) {i, −i}
(B) {1, −1, i, −i}
(C) {1, −1}
(D) φ

m
174.
1 x
m .co 
If g ( x) = cos(log x), then g ( x) g ( y ) −  g  + g ( xy )   is equal to
s e 2  y 

g la
(A) 1
1
a
(B)
2
(C) −2
(D) 0

175. Let A = {1, 2,3, 4} and r = {(2, 2), (3,3), (4, 4), (1, 2)} . Then this relation R is m
m .co
m .co (A) reflexive
s e m
s e (B) symmetric
g l a
la
(C) transitive
g (D) anti-symmetric 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 39 of 52

176. The probability density function of a continuous random variate is given by

0, x<2
 (3 + 2 x)

f ( x) =  , 2≤ x≤4
 18
0, x>4

Then, the probability that x will lie between 2 ≤ x ≤ 3 is

4
(A)
9
2
(B)
9
5
(C)
9
−2
(D)
9

177. An urn contains 3 red and 5 blue balls. The probability that two balls are drawn in
which the second ball drawn is blue without replacement is

5
(A)
16
5
(B)
56
5
(C)
8
20
(D)
56

178. The number of integral values of k for which the equation 7 cos x + 5 sin x = 2k + 1
has a solution is
(A) 4
(B) 8
(C) 10
(D) 12

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m
m .co

m .co s em
se g la
a B
179. In a triangle, sides are a, b, c and angles are A, B, C. If b + c = 3a, then cot cot
C
2 2
is equal to

(A) 3
(B) 1
(C) 4
(D) 2
m
m .co
180. .co
The lines x + 2 y + 3 = 0, x + 2 y − 7 = 0 and 2 x − y − 4 = 0 are the sides of a square.
s e m
s em
The equation of the remaining side of the square can be
l a
g la 2 x − y + 6 = 0 ag
a(B) 2 x − y + 8 = 0
(A)

(C) 2 x − y − 10 = 0
(D) 2x − y − 6 = 0

181. The four straight lines given by 12 x 2 + 7 xy − 12 y 2 = 0 and
−12 x 2 + 7 xy − 12 y 2 − x + 7 y − 1 = 0 lie along the sides of a
m
(A) square
m .co
(B) parallelogram
s e
(C) rectangle
g la
(D) rhombus
a
π dy
182. If sin −1 x + sin −1 y = , then is equal to
2 dx

x
(A)
y
m
.co
x
m (B) −
.co m
y

m s e
s e (C)
y
g l a
g la x
a
a (D) −
y
x

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 52

e3 x −9 + 7
183. The value of lim is equal to
x→3 cos(3 − x)

3
(A)
7
(B) ∞
(C) 3
(D) 0

184. If f ( x ) = 2 x3 + 9 x 2 + λ x + 20 is a decreasing function of x in the interval (−2, −1) ,
then λ is equal to

(A) 12
(B) −12
(C) 6
(D) −6

185. A polynomial of odd degree with real coefficients must have

(A) at least one real root
(B) no real root
(C) only real roots
(D) at least one root which is not real

186. The solution of the differential equation xdy − ydx = 0 represents a

(A) parabola whose vertex is at origin
(B) circle whose center is at origin
(C) rectangular hyperbola
(D) straight line passing through origin

187. The integrating factor of the differential equation ( y log y )dx = (log y − x)dy is

1
(A)
log y
(B) log(log y )
(C) 1 + log y
(D) log y

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m
m .co

m .co s em
se g la
a
188. If the vectors a = iˆ + ajˆ + a 2 kˆ, b = iˆ + bjˆ + b2 kˆ, c = iˆ + cjˆ + c 2 kˆ are three non-coplanar
a a 2 1 + a3
vectors and b b 2 1 + b3 = 0, then the value of abc is
c c 2 1 + c3

(A) 0
m
.co
(B) 1
m
.co m
(C) 2
(D)
s e
em
−1

s g l a
l a a
aforg
189. The complex numbers sin x + i cos 2 x and cos x − i sin 2 x are conjugate to each other

(A) x = nπ
 1
(B) x =  n +  π
 2
(C) x = 0
(D) no value of x
m
190. The sum of n terms of the series
m .co
s e
la
1 2 1 2 1
tan −1 + tan −1 + tan −1 + tan −1 + tan −1 + ... is
2 5 8 25
ag 18

(A) tan −1 (−3)

1
(B) cot −1  
3
1
(C) tan −1  
3
m
m 2
cot −1   .co
.co
(D)
3
e m
em l as
las g
191. An urn contains 3 red pens, 4 green pens and 6 yellow pens.aThe number of ways of
ag drawing 4 pens from the urn if at least one red pen is to be included in the draw is

(A) 500
(B) 505
(C) 510
(D) 520

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 52

192. There are 12 white and 12 red balls in a bag. Balls are drawn one by one with
replacement from the bag. The probability that 7th drawn ball is 4th white is

1
(A)
4
1
(B)
8
1
(C)
2
1
(D)
3

193. The sum of the digits in the unit place of all the numbers formed by 3, 4, 5, 8 taken all
at a time is

(A) 432
(B) 108
(C) 36
(D) 18

194. Let f be a continuous function on [2, 5] . If f ( x) takes rational values for all x and
f (4) = 8 then f (3.6) =

(A) 0
(B) 8
(C) 1 −
(D) 5

195. The number of ways of choosing 10 balls from infinite white, red, blue and green
balls is
(A) 70
(B) 84
(C) 286
(D) 86

196. The tangents to the hyperbola x 2 − y 2 = 3 are parallel to the straight line
2 x + y + 8 = 0 at the points

(A) (2, 1) or (1, 2)
(B) (2, 1) or ( 2, 1)
−− − −
(C) ( 1, 2)
(D) ( 2, 1)
−−
For more Question Papers, Sample Papers, Notes & Syllabus visit Page 44 of 52

m
m .co

m .co s em
se g la
a 10 through 30, inclusive. Let N
197. Let M be the least common multiple of all the integers
be the least common multiple of M, 32, 33, 34, 35, 36, 37, 38, 39, and 40. What is the
N
value of ?
M

(A) 1
(B) 2
(C) 37
m
.co
(D) 74
o m m
. c s e
em a
3 2
198. The number of ordered pairs ( , ) of integers that the polynomial + + + 6
have 3 sdistinct integer roots is
a
a b x ax bx
g l
l
g 4 a
a(A)
(B) 5
(C) 6
(D) 7

199. Which of the following is correct?

(A) Skew symmetric matrix of even order is always singular
m
.co
(B) Skew symmetric matrix of odd order is always non-singular
(C) Skew symmetric matrix of odd order is always singular
(D) None of the above
s em
g la
b a
200. If lim (1 + ax ) x = e4 , where a and b are natural numbers, then
x→0

(A) a = 4, b = 2
(B) a = 8, b = 4
(C) a = 16, b = 8
(D) None of the above

m
m
201. If AB = A and BA = B , then B2 is equal to
.co
m .co (A) B
s e m
s e (B) A
g l a
g la (C) 1 a
a (D) 0

202. The number of complex numbers that satisfy the equation z5 = z is

(A) 2
(B) 3
(C) 5
(D) 7
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 52

1
203. The maximum or minimum value of on R is
4 x2 + 2 x + 1

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

204. The equation of the plane which is parallel to Y- axis and making intercepts of length
3 and 4 on X-axis and Z-axis respectively is

(A) 2 x + 2 z = 20
(B) 4 x + 3z = 12
(C) 4 x − 3z = 12
(D) 46 x + 13z = 15

205. A plane passes through the point (1, −2, 3) and is parallel to the plane 2 x − 2 y + z = 0 .
The distance of the point (−1, 2, 0) from the plane is

(A) 2
(B) 3
(C) 4
(D) 5

206. Nine digit numbers are formed using 1, 2, 3,…. ,9 without repetition. The probability
that a number so formed is divisible by 4 is

2
(A)
7
3
(B)
8
1
(C)
9
2
(D)
9

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m
m .co

m .co s e m
se g l a
 −1 + i 3 
30 a
207. The value of   is
 1− i 

(A) −215
(B) 215 i
(C) −215 i
m
m .co
.co
(D) 5
6
e m
e m l as
208. If A a s
l= {x ∈ R, x < 2} and B = {x ∈ R, x − 2 ≥ 3} , then ag
g
a(A) A ∩ B = (−2, −1)
(B) B − A = R − ( −2,5)
(C) A ∪ B = R − ( −2, 5)
(D) A − B = [ −1, 2]

209. A point on the straight line, 3x + 5y = 15 which is equidistant from the coordinate
m
.co
axes will lie only in

(A) 4th quadrant
e m
st
(B) 1 quadrant
l as
(C) 1 and 2 quadrant a
st nd g
(D) 1st , 2nd and 4th quadrant

210. The slope of the line touching both the parabolas y 2 = 4 x and x 2 = −32 y is

1
(A)
8
m
m .co
.co
2
(B)
e m
e m
3
l as
las (C)
1
ag
ag 2
3
(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 47 of 52

 −4 −1
211. If A =   , the determinant of the matrix A2016 − 2 A2015 − A2014 is
( )
3 1

(A) −175
(B) 2014
(C) 2016
(D) −25

212. At present, a firm is manufacturing 2000 items. It is estimated that the rate of change
dP
of production P w.r.t. additional number of workers x is given by = 100 − 12 x . If
dx
the firm employs 25 more workers, then the new level of production of items is

(A) 2500
(B) 3000
(C) 3500
(D) 4500

1
213. If cos x = then cos 2 x is
2

(A) 0
(B) −1
1
(C)
2
(D) 1

214. In how many ways 2 red balls, 3 blue balls and 4 black balls can be arranged if same
colour balls are indistinguishable?

(A) 362880
(B) 1260
(C) 24
(D) 105680

215. The number of tangents that can be drawn from (1, 2) to the circle x 2 + y 2 = 5 is

(A) 0
(B) 1
(C) 2
(D) more than 2

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m
m .co

m .co s e m
se g l a
a
x2 − 1
216. What are the critical points of the function f ( x) = ?
x2

(A) 0,1
(B) 0, −1
(C) 1, −1
(D) 0,1, −1
m
m .co
217. .co
If the matrix A is both symmetric and skew-symmetric, then
m s e m
Aeis a diagonal matrix
s l a
laA is a zero matrix
(A)
g
(B) ag
a A is a square matrix
(C)
(D) None of the above

218. Area of the region bounded by the curve y 2 = 4 x, y-axis and the line y = 1 is

1
(A)
3
m
(B)
1
m .co
4
s e
(C)
1
g la
12 a
3
(D)
4

x − 2 y −3 z + 2 x − 2 y −3 z + 2
219. If the lines = = and = = are parallel, then the value
k 3 −1 8 6 −2
of k is
m
m .co
.co
(A) −2
e m
e m 1
l as
las (B)
2
ag
ag (C) 2
(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 49 of 52

220. ( ) (
The value of sin log i i + cos log ii is )
(A) −1
(B) 1
(C) 0
(D) −i

2n
 1− i 
221. The smallest positive integer for which   = −1 where i = −1 is
 1+ i 

(A) 1
(B) 2
(C) 3
(D) 4

dx
222. The integral of partial fraction ∫ is
( x + 1)( x + 2)

x +1
(A) log +c
x+2
x+2
(B) log +c
x +1
x −1
(C) log +c
x+2
x +1
(D) log +c
x−2

1 1 1
223. If a , b, c are in G.P., and a = b y = c z , then
x

(A) y = x+ z

(B) y 2 = xz
(C) x+ y+ z =0
(D) 2y = x + z

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m
m .co

m .co s e m
se g l a
a 0 1  a
224. If A =  0 a 1  , then the value of Adj A is
 0 0 a 

(A) a3
(B) a9
m
(C) a6
m .co
(D) 2
.co s e m
em a
a
s l
g la ag
a 3
 d 2 y   dy  2
225. The degree of the differential equation 
1

 = 1 +  is
 dx 2   dx 
 

(A) 2
(B) 3
1
(C)
2
m
(D) 6
m .co
s e
g la
a

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 51 of 52

KEY (PROVISIONAL)
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 B 31 A 61 B 91 C 121 C 151 A 181 A 211 D
2 A 32 D 62 C 92 D 122 A 152 D 182 B 212 C
3 A 33 D 63 A 93 B 123 B 153 D 183 B 213 B
4 B 34 B 64 B 94 C 124 D 154 D 184 A 214 B
5 C 35 D 65 A 95 C 125 C 155 C 185 A 215 B
6 D 36 C 66 A 96 D 126 A 156 C 186 D 216 C
7 D 37 D 67 B 97 B 127 C 157 B 187 D 217 B
8 D 38 A 68 B 98 D 128 B 158 D 188 D 218 C
9 C 39 C 69 B 99 D 129 C 159 A 189 D 219 D
10 D 40 B 70 A 100 C 130 D 160 C 190 B 220 A
11 A 41 A 71 A 101 C 131 A 161 C 191 B 221 A
12 B 42 A 72 B 102 B 132 C 162 D 192 C 222 A
13 A 43 C 73 A 103 B 133 D 163 B 193 B 223 D
14 D 44 D 74 C 104 B 134 D 164 D 194 B 224 C
15 A 45 C 75 D 105 B 135 B 165 C 195 C 225 D
16 A 46 D 76 B 106 B 136 D 166 B 196 B
17 A 47 A 77 B 107 B 137 A 167 B 197 D
18 B 48 D 78 D 108 C 138 B 168 C 198 B
19 B 49 C 79 C 109 A 139 B 169 B 199 C
20 B 50 D 80 B 110 D 140 D 170 B 200 D
21 D 51 A 81 A 111 A 141 D 171 C 201 A
22 A 52 A 82 D 112 D 142 B 172 B 202 D
23 A 53 C 83 D 113 A 143 D 173 A 203 A
24 D 54 D 84 B 114 B 144 A 174 D 204 B
25 C 55 D 85 A 115 C 145 A 175 C 205 D
26 D 56 B 86 D 116 C 146 C 176 A 206 D
27 B 57 D 87 C 117 A 147 C 177 C 207 C
28 B 58 A 88 B 118 C 148 C 178 B 208 B
29 C 59 C 89 A 119 A 149 C 179 D 209 C
30 B 60 D 90 B 120 D 150 B 180 A 210 C

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