CUSAT CAT 2024 Question Paper with Answer Key B.Tech Shift II

FOR CUSAT CAT EXAM PREPARATION

CUSAT CAT 2024
Question Paper ·
B.Tech Shift II
EXAM YEAR TYPE SUBJECT INCLUDES

CUSAT CAT 2024 Question Paper B.Tech Shift II Answer Key

Notes · Sample Papers · Previous Year Papers · Mock Tests

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B.TECH. (PHYSICS) – SHIFT II

1. In measurements of physical quantities, the standard deviation σ and the probable
error ‘r’ are related by

(A) r = ± 0.6745 σ

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(B) r = σ

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(C) σ = ± 0.6745 r
(D) σ = r
m . s e
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Twola a
2.
g
aof linear momentum of B to A is
bodies having masses in the ratio of 3 : 1 possess same kinetic energy. The ratio

(A) 1: 3
(B) 3 :1
(C) 1: 3
(D) 3 :1

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3.
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A diesel engine pumps 40 kg of water in 1 second. The water comes out vertically

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upwards with a velocity of 3 m/s. What is the power of the engine in kilo watt?

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

4. The ratio of specific heats (Cp/Cv) for monoatomic gas is about

(A) 1.5
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(B) 1.33

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(C) 1.4
(D) 1.67
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em 5. A Carnot engine is working between steam point and ice point.glThen
a its efficiency
las a
ag will be

(A) 24.9%
(B) 25.7%
(C) 26.8%
(D) 28.8%

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6. The angular momentum of the electron results in

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(A) Zeeman effect
(B) Magnetic moment
(C) Stark effect
(D) Emission of light and emission spectrum

7. If g is the acceleration due to gravity at a place on the surface of the earth and g' is
the acceleration due to gravity at a depth h below the surface of the earth (h < R,
the radius of the earth), then

h
(A) g'= g−
R
R
(B) g'= g−
h
(C) g'= g

 h
(D) g ' = g 1 − 
 R

−5
8. Coefficient of surfacial expansion of a solid is 2 × 10 / °C . Then the coefficient of
linear expansion is

(A) 4 ×10−5 / °C
(B) 3 × 10−5 / °C
(C) 2 ×10−5 / °C
(D) 1× 10−5 / °C

9. Which one of the following is not a green house gas?

(A) Water vapour
(B) Carbon dioxide
(C) Methane
(D) Nitrogen

10. An inductor of inductance 30 mH is connected to a 220 V, 100 Hz AC source. It
offers an inductive reactance of

(A) 10.58 Ω
(B) 12.64 Ω
(C) 18.85 Ω
(D) 22.67 Ω

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11. A step down transformer with a primary winding of 1,74,000 turns and secondary
windings of 1000 turns operates from a 40,000 V high tension line and supplies a load
of 60 A. Assuming 100% efficiency, the power output of the transformer is

(A) 2400 KW
(B) 13.8 KW
(C) 24,000 KW
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(D) 40,000 KW

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12. The parallel combination of inductor and capacitor is called

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ag aa filter
(A) a rectifier circuit
(B) circuit
(C) tank circuit
(D) an acceptor circuit

13. A closed organ pipe has a frequency ‘n’. If its length is doubled, its frequency nearly
becomes

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(A) Halved

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(B) Doubled

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(C) Three times

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(D) Four times

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14. a
Two slits are made one millimeter apart and the screen is placed one meter away.
What is the fringe separation when the blue-green light of wavelength 500 nm is
used?

(A) 0.05 mm
(B) 0.01 mm
(C) 0.5 mm

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(D) 0.1 mm

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c. o15. What is the ratio of output frequency of a full wave rectifier to halfsewave
m rectifier fed
s em g l a
la
with a input signal of frequency 50 Hz?

g a
a
(A) 1 : 2
(B) 1 : 4
(C) 2 : 1
(D) 4 : 1

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16. An amplitude modulated wave varies from 10 V to 4 V. Its percentage modulation is

(A) 36%
(B) 42.8%
(C) 54%
(D) 68%

17. Which of the following is fundamental quantity?

(A) Velocity
(B) Time
(C) Volume
(D) Force

18. In a p-type semiconductor, the majority and minority charge carriers are, respectively,

(A) Protons and Neutrons
(B) Electrons and Holes
(C) Electrons and Protons
(D) Holes and Electrons

19. Speed of electromagnetic waves in vacuum is equal to

1
(A)
µ0ε 0

(B) µ0ε 0

(C) µ0ε 0

1
(D)
µ0ε 0

20. The displacement of a particle in SHM is always measured from

(A) Mean position
(B) Extreme position
(C) Mid-point of mean and extreme position
(D) Initial position

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21. Two resistances R1 = 10.0 Ω ± 0.1 Ω and R2 = 5.0 ± 0.1 Ω are connected in parallel.
Then % of error in the resultant value of R is
(A) 4.3%
(B) 1.393%
(C) 3.83%
(D) 0.0133%

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22.
co
m
If earth shrinks to half its radius without changing its mass then the length of the day
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will be
m . s e
a
6e
s g la
l 12 hours a
(A) hours

ag 824hours
(B)
(C)
(D) hours

23. σ1 and σ2 are the electrical conductivities of Ge and Na respectively. If these
substances are heated then

(A) σ1 and σ2 increases

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(B) σ1 increases and σ2 decreases

.
(C) σ1 decreases and σ2 increases

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(D) σ1 and σ2 decreases

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24.
a g is not explained by Huygen’s construction of
Which one of the following phenomena
wavefront?

(A) Refraction
(B) Reflection
(C) Diffraction
(D) Origin of spectra

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25. The frequency of X-rays, ϒ-rays and ultraviolet rays are respectively a, b and c. Then

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(A)
a
a > b, b < c

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(B) a < b, b > c

la
(C)
g
a < b, b < c

a
(D) a > b, b > c

26. When a source of sound moves towards an observer

(A) the frequency of the source is increased
(B) the velocity of sound in the medium is increased
(C) the wavelength of the sound in the medium towards the observer is decreased
(D) the amplitude of vibration of the particles is increased

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27. If the angle between two nonzero vectors A and B is 120°, its resultant C

(A) must be equal to A − B
(B) must be greater than A − B
(C) may be equal to A − B
(D) must be less than A − B

28. Two mercury drops of same radius merge to form a bigger drop. Then the released
surface energy is

(A) 1.65 πr2S
2
(B) 3.3 πr S
(C) 2.56 πr3S
(D) 2.56 πr2S

29. The temperature of a hypothetical gas increases to 2 times when compressed
adiabatically to half the volume. Its equation can be written as

(A) PV = constant
1
(B)
PV 2 =constant
3
(C)
PV 2 =constant
5
(D)
PV 2 =constant

30. Bernoulli theorem is based on conservation of

(A) momentum
(B) mass
(C) energy
(D) angular momentum

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31. Two bodies A and B of equal masses are suspended from two separate massless
springs of spring constant k1 and k2 respectively. If the bodies oscillate vertically such
that their maximum velocities are equal, the ratio of the amplitude of A to that of B is

k1
(A)
k2

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k2

m
(B)

.c o m
k1

m s e
s e g la
k1

la a
(C)

g
k2

a(D) k2
k1

32. A particle of mass m is observed from an inertial frame of reference and is found to
move in a circle of radius r with a uniform speed v. The centrifugal force on it is

m
co
mv 2
.
(A) towards the centre

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r
mv 2
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(B) away from centre

a
r
mv 2
(C) along the tangent through the particle
r
(D) zero

33. Two radioactive materials A and B have decay constants 10λ and λ, respectively. If

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initially they have the same number of nuclei, then the ratio of the number of nuclei of

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1

c. o m
A to that of B will be after a time

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e

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1
(A)
g
9λ
a (B)
11
10λ
1
(C)
10λ
1
(D)
11λ

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34. As an electron makes a transition from an excited state to the ground state of a
hydrogen like atom/ion

(A) Kinetic energy decreases, potential energy increases but total energy remains
same
(B) Kinetic energy and total energy decrease but potential energy increases
(C) Kinetic energy increases but potential energy and total energy decreases
(D) Kinetic energy, potential energy and total energy decreases

35. Which of the following is best method to reduce eddy currents?

(A) Laminating core
(B) Using thick wires
(C) Reducing hysteresis loss
(D) Using thin wires

36. A bar magnet of magnetic moment M and moment of inertia I is freely suspended
such that the magnetic axial line is in the direction of the magnetic meridian. If the
magnetic induction of earth’s horizontal field is BH and the magnet is displaced by a
very small angle θ, angular acceleration is

MBH θ
(A)
I
IBH θ
(B)
M
Mθ
(C)
IBH
Iθ
(D)
MBH

37. For which of the following dependences of drift velocity vd on electric field E, is
Ohm’s law obeyed?

(A) vd ∝ E

(B) vd ∝ E 2

(C) vd ∝ E

1
(D) vd ∝
E

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38. The freezer in a refrigerator is located at the top section so that

(A) the entire chamber of the refrigerator is cooled quickly due to convection
(B) the motor is not heated
(C) the heat gained from the environment is high
(D) the heat gained from the environment is low

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39. Two rods of same length and area of cross section and Young’s modulii Y1 and Y2 are

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joined end to end. The equivalent Young’s modulus for the composite rod is

(A) 1em2 las
a s g
Y +Y

l
g Y1 + Y2
2
a
a(B)
Y1Y2

2Y1Y2
(C)
Y1 + Y2

(D) Y1 + Y2

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40. A prism can produce a minimum deviation δ in a light beam. If three such prisms are

a s
combined, the minimum deviation that can be produced in this beam is

g l
a
(A) 0
δ
(B)
3
(C) δ
(D) 3δ

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41. Light year is used to measure the

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(A) Time

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(B) Distance

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(C) Energy

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(D) Mass

a
42. The motion of a rocket is based on the principle of conservation of

(A) linear momentum
(B) angular momentum
(C) kinetic energy
(D) mass

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43. According to Hook’s law, if stress is increased, the ratio of stress to strain

(A) decreases
(B) increases
(C) remains constant
(D) zero

44. Convection does not take place in

(A) Boiling of water
(B) Sea and land breeze
(C) Heating air around a furnace
(D) Warming of glass of the bulb due to filament

45. The number of degrees of freedom of a triatomic gas is

(A) 1
(B) 2
(C) 6
(D) 8

46. A stone tied to a string is rotated in a circle with the other end of the string as the
centre. If the string breaks the stone will

(A) move towards the centre
(B) move away from the centre
(C) move along the tangent
(D) stop

47. In a parallel plate capacitor, the capacity increases if

(A) area of the plate is increased
(B) distance between the plates increases
(C) area of the plate is decreased
(D) dielectric constant decreases

48. If an ammeter is used in the place of a voltmeter, then we must connect the ammeter with

(A) a low resistance in parallel
(B) a high resistance in parallel
(C) a high resistance in series
(D) a low resistance in series

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49. At magnetic poles the angle of dip is

(A) 45°
(B) 90°
(C) 30°
(D) 5°

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50. In a step-down transformer with 20 turns in the secondary coil and 100 turns in the
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primary coil, if the voltage applied to the primary coil is 120 V, the voltage output

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from the secondary coil is
s e
a 24eV
s g la
l 12 V a
(A)

ag 618VV
(B)
(C)
(D)

51. Ratio of the angle subtended at the eye by the image to the angle subtended at the eye
by the object is called

(A) Magnifying power of a simple microscope

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(B) Magnifying power of a telescope

.
(C) Magnifying power of a electron microscope

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(D) Astigmatism

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If the diameter of the objective g
52.
increased to
a of a telescope is doubled, the intensity of the image is

(A) Two times
(B) Four times
(C) Eight times
(D) Sixteen times

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53. The time taken for a radio signal to travel 150 km from the transmitter to receiving

c. o e m
antenna is

em l a s
s ag
−4

la
(A) 5 × 10 s

g
(B) 4.5 × 10−3 s
a (C) 5 × 10−8 s
(D) 4.5 × 10−6 s

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54. In uniformly accelerated motion, how many variables are required to fully describe
the system?

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

55. 1 Joule is equal to

(A) 10 ergs
(B) 4
10 ergs
(C) 7
10 ergs
(D) 9
10 ergs

56. Two satellites of mass m, and 10 m, are put in the same orbit around the sun. If T1 and
T
T2 are their time periods, then 1 =
T2

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

57. What is the number of molecules in 2.24 L of SO2 at STP?

(A) 23
6.023 × 10
(B) 22
6.023 × 10
(C) 20
6.023 × 10
(D) 2
6.023 × 10

58. A 250-turn rectangular coil of length 2.1 cm and width 1.25 cm carries a steady
current of 85 µA and is subjected to a magnetic field of strength 0.85 T. The work
done for rotating the coil by 180° against the torque is

(A) 1.5 pJ
(B) 4.55 pJ
(C) 9.5 pJ
(D) 2.3 pJ

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59. What is the de Broglie wavelength of a ball of mass 150 g moving at a speed of 50 m/s?

(A) 8.8 × 10−34 m
(B) 8.8 × 10−30 m
(C) 8.8 × 10−25 m
(D) 8.8 × 10−35 m

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m
In the common emitter amplifier, the phase difference between the input voltage and
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m . s e
la
output voltage signal across the collector and emitter is

s e g
l a
(A) 0
g π2 a
a(B)
(C) π
π
(D)
4

61. Which of the following is a dimensionless quantity?

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co
(A) Meter (m)
.
em
(B) Kilogram (kg)

s
(C) Radian (rad)
(D) Second (s)
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62.
a
A projectile is launched with a speed of 20 m/s at an angle θ from the ground. At what
point in its trajectory does the projectile have the maximum kinetic energy?

(A) At the apex of its trajectory
(B) At the initial point
(C) Upon reaching the ground
(D) Halfway between the initial and final points

o m
c
m A rocket of mass 1000 kg is initially at rest in space. The rocket engines
. are turned
c. o63. on, s
m
eWhat is the final
em l
and a constant thrust of 5000 N is exerted for 20 seconds.
a
l as velocity of the rocket?
a g
ag (A) 50 m/s
(B) 100 m/s
(C) 150 m/s
(D) 200 m/s

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64. An object is thrown vertically upwards with an initial velocity of 20 m/s. Considering
the gravitational force acting on the object during its ascent, what is the net work done
by the gravitational force?

(A) Zero
(B) Negative
(C) Positive
(D) Cannot be determined

65. A fluid with viscosity η flows through a horizontal pipe of radius r and length L The
pressure difference between the two ends of the pipe is P. What is the flow rate of the
fluid?

π r 4P
(A)
8η L

π r 4P
(B)
4η L

π r 4P
(C)
2η L

π r 3P
(D)
8η L

66. According to kinetic theory, the pressure exerted by an ideal gas on the walls of its
container is due to

(A) Collisions between gas molecules
(B) Gravitational attraction between gas molecules
(C) Magnetic forces between gas molecules
(D) Electrostatic repulsion between gas molecules

67. What is the speed of a wave with a frequency of 50 Hz and a wavelength of 2 m?

(A) 25 m/s
(B) 50 m/s
(C) 100 m/s
(D) 200 m/s

68. Identify the incorrect statement from the following.

(A) The direction of momentum and the velocity of an object is the same
(B) Momentum is a scalar quantity
(C) The object has a large momentum if either mass or velocity is large
(D) Momentum describes the motion of an object

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69. The average number of atoms per unit cell in a body centered cubic structure is

(A) 6
(B) 4
(C) 2
(D) 8

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70. The work done against electrostatic force gets stored in the ……….……… form
m
(A)
.co
Thermal energy
s e m
(B)
em
Potential energy
la
(C)
l a s
Kinetic energy
a g
ag
(D) Gravitational energy

71. The energy difference between the ground state and the first excited state of an
electron in a box of length 1.0Å is

(A) 1.81 × 10−17 eV
(B) 1.81 × 10−17 Cal

m
(C) 1.81 × 10−17 J
(D) 1.81 × 10−17 KCal
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s em
g l a
a
72 A measure of the repeatability of measurement of a quantity is
(A) error
(B) precision
(C) accuracy
(D) sensitivity

73. Ratio of absolute viscosity to the density of the fluid is called

m
c. o
(A) relative viscosity
m
c. o m
(B) viscosity index

s e
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(C) kinematic viscosity

s
(D) fluidity
g l a
gla a
a 74. Just before striking the ground, a 2.0 kg mass has 400 J of KE. If friction can be
ignored, from what height was it dropped?

(A) 200 m
(B) 20 m
(C) 40.8 m
(D) 40 m

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75. Inversion temperature of a gas is the temperature above which

(A) the gas shows cooling effect while passing through a narrow orifice
(B) the temperature of the gas remains unaltered while passing through narrow
orifice
(C) the gas shows heating effect while passing through a narrow orifice
(D) the gas can be liquefied

CHEMISTRY UG
(SHIFT II - FINAL)

76. The heat of formation of sulphur dioxide is ∆Hf = −297 kJ. The heat liberated on
burning 8 g of sulphur in oxygen is
(A) −148.5 kJ
(B) −74.25 kJ
(C) 148.5 kJ
(D) 74.25 kJ

77. The efficiency of a heat engine is given by

W T2 − T1
(A) =
q2 T2

W T1 − T2
(B) =
q2 T2

W T2 − T1
(C) =
q2 T1

W T1 − T2
(D) =
q2 T1

78. The pH of the blood is maintained by buffer system given by

(A) NaCl and HCl
(B) NH4Cl and NH4OH
(C) Sodium citrate and Citric acid
−
(D) HCO3 and H2CO3

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79. In which of the following reactions, increase in the volume at constant temperature
does not affect the number of moles at equilibrium?

(A) 2NH3 → N2 + 3H2
(B) C (g) + ½ O2 (g) → CO (g)
(C) H2 (g) + O2 (g) → H2O2 (g)
(D) None of the above
m
co
m m .co
. s e
80. An azeotropic solution of two liquids has the boiling point lower than either of them,

e m la
(A)las
when it

a g
g shows no deviation from Raoul’s law
a(B)
shows negative deviation from Raoult’s law

(C) shows positive deviation from Raoult’s law
(D) contains non-volatile solute

81. In a H2-O2 fuel cell, combustion of hydrogen occurs to

(A) Remove adsorbed oxygen from electrode surface

m
co
(B) Create potential difference between the two electrodes

.
(C) Produce high purity water

em
(D) Generate heat

l a s
82.
ag which can displace all others from salt solution is
Out of Cu, Ag, Fe and Zn, the metal

(A) Ag
(B) Cu
(C) Zn
(D) Fe

m
83. According to Arrhenius theory, the activation energy (Ea) for a reaction with rate constant k

m c. o
at a temperature T is ………… (R is gas constant)

c. o s e m
em l a
=
(A)

las ag
ag (B) =−

=
(C)

(D) =−

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84. The presence of double layer in colloids accounts for

(A) kinetic properties
(B) electrokinetic properties
(C) optical properties
(D) tyndal effect

85. Which of the following is an example of isobar?

(A) 14 15
6 C and 6 C
14 14
(B) 6 C and 7 N
15 14
(C) 7 N and 7 C
6 7
(D) 14 C and 14 C

86. Among the given equations, the correct one representing a closed system is
(A) ∆ = −
(B) ∆ =
(C) ∆ =−
(D) ∆ =∆ +∆

87. If in a nearly saturated solution, the dissolution process is endothermic, then the
solubility should

(A) decrease with rise in temperature
(B) increase with rise in temperature
(C) increase with reduce in temperature
(D) decrease with reduce in temperature

88. A 2 (g) + 2B(g) ⇌ C(g) + 2D(s) , the K c for the given reaction will be

[C][D]2
(A) Kc =
[A 2 ][B]2

[C]
(B) Kc =
[A 2 ][B]2

[A 2 ][B]2
(C) Kc =
[C][D]2

[A 2 ][B]2
(D) Kc =
[C]

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89. If the initial concentration of the reactants in a reaction increases then the equilibrium
constant

(A) also increases
(B) decreases
(C) remain constant

m
(D) may increase or decrease

m .co
90. The enthalpy of unit mass for any system is

.co s e m
m
(A) H = U + pV + S
(B)
a s e
H = U + pV − S
g la
l a
ag
(C) H = U + pV
(D) H = U − pV + S

2
91. Within an atom, the probability density ψ is always

(A) zero
(B) negative

m
(C) ±1

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(D) positive

According to Ostwald’s dilution lawse
m
la
92.

ka a g
(A) α =
C
1
(B) k  2
α = a 
C 
ka
(C) α=
m
c. o
V

m
c. o m
k

e
(D) α = a

em a s
V

s g l
gla The fuel cell reaction generates electricity directly from 2Ha + O →2H O. What
a
93. 2 2 2
potential should the battery generate (under standard conditions)?

(A) 0.40
(B) 0.43
(C) 0.68
(D) 1.23

m .
.co se m
e m l a
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 19 of 51

94. For a second order reaction, the time required for half change is

(A) Directly proportional to the initial concentration
(B) Independent of the initial concentration
(C) Inversely proportional to the initial concentration
(D) Inversely proportional to the square of the initial concentration

95. Arrhenius equation is k = A e− Ea RT . Choose the correct statement.

(A) A depends on temperature
(B) Ea depends on temperature
(C) Both Ea and A are independent of temperature
(D) Both Ea and A depend on temperature

96. Overall 3D structure of a simple protein is called
(A) Quaternary structure
(B) Tertiary structure
(C) Secondary structure
(D) Primary structure

97. The reactive intermediate involved when HBr is added to propene in the presence of
peroxide is

(A)

(B)

(C)

(D)

98. Reagents used in Wolff-Kishner reduction of cyclohexanone to give cyclohexane
is/are

(A) LiAlH4
(B) Na, liq NH3
(C) Zn, HCl
(D) NH2NH2, NaOH

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m
m c. o
c. o

e m
em l a s
s ag
99. Benzene diazonium chloride can be converted to chlorobenzene by treating with

(A) PCl5
(B) Cl2, FeCl3
(C) CuCl2
(D) CuCl

m
c o m m .co
.
100. Which is the reserve carbohydrate in animals?

s e
(B) s em
(A) Starch
g la
(C)la Glycogen a
Pectin
g Inulin
a(D)
101. Nitration of phenol is much faster than nitration of benzene due to ………. of OH group

(A) +I effect
(B) +M effect
(C) –I effect

m
c. o
(D) Hydrogen bonding with the incoming nitronium ion electrophile

mhave been used to poison a famous historic
102. Which among the following is allegedeto
la s
a g
figure?

(A) Mg
(B) Si
(C) Al
(D) As

103. AZT is the azido derivative of a DNA nucleoside based anti-AIDS drug. The nitrogen

m
base present in AZT is not present in RNA. Which among the following nucleic acid

m c. o
c. o
base does AZT contain?

e m
em
(A) Uracil
l a s
las ag
(B) Cytosine

g
(C) Thymine

a (D) Guanine

104. There are two different isomeric compounds with molecular formula C2H6O. One of
these isomers has a much higher boiling point than the other. Explain why?
(A) Due to difference in their ability to form strong intermolecular hydrogen bonds
(B) Due to large difference in their dipole moments
(C) Due to difference in the number of carbon-carbon bonds in the two isomers
m .
co m
(D) Due to difference in carbon oxygen bonds in the two isomers

m . se
se g l a
l a a
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 21 of 51

105. How to accomplish the following transformation?

(A) Anhydrous AlCl3 catalyzed rearrangement
(B) Markovnikov addition of HBr followed by base catalyzed E1 elimination of
HBr
(C) Anti-Markovnikov addition of HBr followed by base catalyzed E2 elimination
of HBr
(D) Base catalysed equilibration

106. Trans addition of Br2 to Compound X gave meso-2,3-dibromobutane. What is the
identity of compound X?

(A) 1-butene
(B) cis-but-2-ene
(C) trans-but-2-ene
(D) 1,3-butadiene

HOOC COOH
107. Glutaric acid can be written as n with n equals to (remember, Oh,
My Such Good Apples)

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

108. Which of the following, in aqueous solutions of equal concentration, has the lowest pH?

(A) ClCH2CO2H
(B) CH3CO2H
(C) Cl2CHCO2H
(D) C2H5OH

109. Nucleic acids are biopolymers. The monomer units present in them

(A) Pyrimidine and purine bases
(B) Sugars
(C) Nucleosides
(D) Nucleotides

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m
m c. o
c. o

e m
em l a s
s ag
110. Shown below is Cholesterol, which is the most abundant compound from steroids in
animals. (Note: Thick solid wedge indicates a bond coming above the plane, while
broken wedge indicates a bond below the plane)

m
co
m m .co
m . s e
a s e g la
l
g many chiral carbons are present in Cholesterol? a
aHow
(A) 10
(B) 8
(C) 6
(D) 4

o m
c
111. Picric acid is

m . rich aromatic compounds
s e of polyester PET
(A) Strong acid that can protonate electron

(C) 2,4,6-trinitrobenzoic acid la
(B) Monomer used in the preparation

(D) 2,4,6-trinitrophenol ag

112. According to rules for drawing Fischer projection, the groups on the horizontal line
are

(A) Above the plane of the paper
(B) Below the plane of the paper

m
c. o
(C) In the plane of paper

m
c. o
(D) Group appearing on the right side is above and group appearing on the left is
below the plane of the paper
e m
em 113. Reaction of silver salts of carboxylic acids with halogen to form
l s
aorganic halides with
las a g
ag one carbon less (Hunsdiecker reaction) proceeds through

(A) Carbocation intermediate
(B) Carbanion intermediate
(C) Radical intermediate
(D) Carbene intermediate

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

114. Aspirin is an acetylation product of

(A) Aspartic acid
(B) o-Hydroxybenzoic acid
(C) Asparagine
(D) m-Hydroxybenzoic acid

115. Resonance energy of benzene is

(A) 152 kJ/mol
(B) 36 kJ/mol
(C) 36 eV/mol
(D) 36 cal/mol

116. The number of unpaired electrons in the complexes [Cu(en)2(H2O)2]Cl2 and K3[CrI6] are

(A) 0 and 1
(B) 1 and 2
(C) 1 and 3
(D) 2 and 3

117. The number of geometric and optical isomers of the complex [Co(en)3]Cl3 are

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

118. Which of the following pairs does not represent an acid and its conjugate base?

(A) HNO3 and NO3¯
(B) H2SO4 and HSO4¯
2
(C) H2SO4 and SO4 ¯
2
(D) HSO4¯ and SO4 ¯

119. Which is the most acidic compound?

(A) CH4
(B) NH3
(C) H2O
(D) H2S

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m
m c. o
c. o

e m
em l a s
s ag
120. What type of bond, a hydrogen atom need have for hydrogen bonding to occur?

(A) An ionic bond
(B) A polar covalent bond
(C) A non-polar covalent bond
(D) An alkaline bond

m
.co
121. Which of the following compounds cannot act as a Lewis base?
m
(A) NF3
.co s e m
em la
s
(B)
g
PCl5

l a a
ag
(C) SF4
(D) ClF3

122. Given below are two statements, one is labelled as Assertion A and the other is
labelled as Reason R

Assertion A : The H–O–H bond angle in water molecule is 104.5°.
Reason R : The lone pair - lone pair repulsion of electrons is higher than the bond

m
co
pair - bond pair repulsion.

.
em
Choose the correct alternative from given below.
(A) A is false but R is true
l a s
g
(B) Both A and R are true, but R is not the correct explanation of A
(C)
(D)
A is true but R is false
a
Both A and R are true, and R is the correct explanation of A

123. The incorrect statement regarding the structure of C60 is

(A) The six-membered rings are fused to both six and five-membered rings
(B) Each carbon atom forms three sigma bonds

m
(C) The five-membered rings are fused only to six-membered rings

m c. o
(D) It contains 12 six-membered rings and 24 five-membered rings

c. o124. The oxidation states of X in H X O , H X O and H X O , respectively,
s e m
em l a
s g
are
a
4 2 7 4 2 5 4 2 6

l a
ag
(A) 7, 5 and 6
(B) 5, 4 and 3
(C) 5, 3 and 4
(D) 6, 4 and 5

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

x
125. The interaction energy of London forces between two particles is proportional to r ,
where r is the distance between the particles. The value of x is

(A) 3
(B) −3
(C) −6
(D) 6

−
126. The bond order and magnetic behaviour of O2 ion are

(A) 1.5 and paramagnetic
(B) 1.5 and diamagnetic
(C) 2 and diamagnetic
(D) 1 and paramagnetic

127. Strongest back donation of an electron pair from halide to boron is expected in

(A) BCl3
(B) BF3
(C) BBr3
(D) BI3

128. Which among the following is NOT isostructural?

(A) SO3
−
(B) NO3
(C) PCl3
2−
(D) CO3

129. According to molecular orbital theory, the species among the following that does not
exist is
+
(A) He2
–
(B) He2
(C) Be2
2–
(D) O2

130. The correct statement about B2H6 is

(A) Terminal B–H bonds have less p-character when compared to bridging bonds
(B) The two B–H–B bonds are not of same length
(C) All B–H–B angles are of 120°
(D) Its fragment, BH3, behaves as a Lewis base

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m
m c. o
c. o

e m
em l a s
s ag
131. Which among the following species has unequal bond lengths?
–
(A) BF4
(B) XeF4
(C) SF4
(D) SiF4

m
132.
o m
Identify the ion having the 'spin only' magnetic moment equal to 4.9 BM
m .co
(A) Ni .c e
m las
Cre
2+

(B) s
(C)la V a g
2+

g
a(D)
2+
2+
Mn

133. The number of bonds between the two Mn in Mn2(CO)10 is

(A) 0
(B) 1

m
co
(C) 2

.
(D) 3

s em
134. Select the correct option
g l a
(A) a2-
[Ni(CO)4] and [NiCl4] both are diamagnetic
2-
(B) [Ni(CO)4] is paramagnetic and [NiCl4] is diamagnetic
2-
(C) [Ni(CO)4] is diamagnetic and [NiCl4] is paramagnetic
2-
(D) [Ni(CO)4] and [NiCl4] both are paramagnetic

m
135. The Cr compounds that is not involved in the reaction sequence of chromyl chloride

m c. o
test for confirmation of Cl¯ ion is

c. o s e m
em
(A) K2Cr2O7

s l a
ag
(B)

la
CrO2Cl2

g
(C) Cr2O3
a (D) CrO3

MATHEMATICS UG – SHIFT II
(FINAL)

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

1 ω3 ω 2
136. The value of ω 3 1 ω is
ω2 ω 1

(A) 0
(B) 1
(C) 2
(D) 3

1 1 1 1
137. The series + + + + ... is
1 2 3 4

(A) divergent
(B) convergent
(C) oscillatory
(D) constant

x − sin x
138. The value of lim =
x→0 x3

1
(A)
3
1
(B)
4
1
(C)
5
1
(D)
6

139. A missile fixed from ground level rises x meters vertically upwards in t seconds and
25
x = 100t − t 2 . The maximum height reached is
2

(A) 100 m
(B) 300 m
(C) 150 m
(D) 200 m

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 28 of 51

m
m c. o
c. o

e m
em l a s
s 6 4 ag
140. ∫ sin θ cos θ dθ =
3π
(A)
512
π
(B)
512

m
.co
5π

o m
(C)

7π . c m
512

s e
(D)
s em g l a
l a a
512

a g
141. If the first 2 moments of a distribution about the value 5 are 2 and 20, then the
standard deviation of the distribution is

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

o m
c
142. In a group of employed persons, 30% are. women. 65% of the men and 40% of the

s em that a randomly chosen person is not
la
women pay income tax. The probability
a income tax payer is
a g
(A) 0.575
(B) 0.525
(C) 0.475
(D) 0.425

143. The function f : R → R defined by f (x) = x + 1 is

m
m c. o
(A) surjective only

c. o m
(B) injective only

s e
em
(C) both surjective and injective

s
(D) neither surjective nor injective
g l a
gla a
a 144. The area bounded by the curve y = sin x between x = 0 and x = π is

(A) 2 sq.unit
(B) 4 sq.unit
(C) 8 sq.unit
(D) 16 sq.unit

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

3
145. The equation of the tangent to the curve y = x at the point (1, 1) is

(A) y = 3x
(B) y = 3x – 1
(C) y = 3x – 3
(D) y = 3x – 2

146. The number of common terms in the two sequences 15, 19, 23, 27, …., 415 and
14, 19, 24, 29, …, 464 is

(A) 18
(B) 21
(C) 20
(D) 19

147. Let A be non singular square matrix of order 5 × 5 . Then |adj A| is equal to

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

148. The differentiation of log(cos x) is

(A) cot x
− cos x
(B)
sin x
(C) − cot 2 x
(D) − tan 2 x

149. Which of the functions have maxima?

(A) f ( x) = e x
1
(B) f ( x) =
x
(C) f ( x) = tan x
(D) f ( x) = sin x

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m
m c. o
c. o

e m
em l a s
s ag
150. If log( xy 3 ) = 1, log( x 2 y ) = 1, then log( xy ) is equal to

(A) 1
3
(B)
5
4

m
(C)

.co
5
m
.co m
(D) 2

m s e
a s e g la
l a
151. Area bounded by the function f ( x) = [ x] , where [x] is the greatest integer less than or
g to x , in the interval [2, 3] is
aequal
(A) 1
(B) 2
(C) 3
(D) 4

152. Consider the system of linear equations x + 2y + z = 7 ; x + y + λz = 3 ;
m
co
x + 3y − 5z = 5. This system has unique solution for
.
em
(A)
s
any real number λ

l a
(B) λ=7
(C)
(D)
any real number except λ = 7
no value of λ a g
4C1 4C2 4C3
153. 5C1 5C2 5C3 =
6C1 6C2 6C3

m
c. o
(A) 18

m
c. o
(B) 19

e m
s
(C) 20

em l a
(D) 21

las a g
ag 154. Which of the following statement is false about inverse sine function?

(A) Domain is [−1, 1]
 −π π 
(B) Range is  , 
 2 2
(C) An even function

m .
(D) An odd function

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

1 2
155. tan −1   + tan −1   =
4 9

 3
(A) cos −1  
5
 2 
(B) cos −1  
 5
2
(C) cos −1  
 11 
4
(D) cos −1  
5

t3 2
156. The distance covered by the particle is given by s (t ) = − t + 3. After starts
3
moving, the velocity and acceleration are zero respectively at

(A) t = 1, t = 2
(B) t = 0, t = 3
(C) t = 2, t = 1
(D) t = 0, t = 1

dy
157. The general solution of differential equation log = x + y is
dx

(A) ex + e y = C
(B) e x + e− y = C
(C) e− x + e y = C
(D) e− x + e − y = C

158. Let A and B be any two events. Which of the following is not true?

(A) P ( B − A) = P ( A ∩ B )
(B) P ( A ∪ B ) = P ( A) + P ( B − A)
(C) P( A − B) = P( A ∪ B )
(D) P( A ∪ B) = P( B) + P( A ∩ B )

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m
m c. o
c. o

e m
em l a s
s ag
 x x  
159. Let M =   : x ∈ ℝ − {0} . If X , E ∈ M such that X ⋅ E = X for all X ∈ M ,
 x x  
where ⋅ is matrix multiplication. Then E is

1 1
(A)  
1 1

m
.co
1 0
(B)  
o m m
0 1
. c
 2 m2  s e
(C) s e la
1 1

a
l 2 2

a g
g
1 1

a(D)  0 1 
 
1 0

160. In a multiple choice examination with four multiple options (out of which, only one is
correct), for each of five questions, the probability that a candidate would get four

m
correct answers by just guessing is

. co
em
15
(A)

s
256
3
g l a
a
(B)
1024
405
(C)
1024
15
(D)
1024

m
c. o
161. Kiran ride a bicycle for 30 minutes at a speed of 16 km/hr, then walked for 90 minutes
m
c. o m
at speed of 4 km/hr. The overall average speed is

s e
s em l a
(A) 7

la ag
(B) 9

ag (C)
(D)
10
12

m .
.co se m
e m l a
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 33 of 51

2 2
162. If the line y = x + a passes through the vertex of the parabola y = x + a , then the
number of possible values of ' a ' is

(A) 0
(B) 1
(C) 2
(D) ∞

163. The cost function of certain commodity is c(x) = 30x + 250 and the price of the
commodity is fixed at `55. Then the break even point is

(A) 5
(B) 10
(C) 15
(D) 20

164. In four throws with pair of dice, the chance of throwing doublets at least twice is

5
(A)
432
7
(B)
432
11
(C)
432
13
(D)
432

165. Which of the following is true?

(A) sin θ + i cos θ = i (cos θ − i sin θ )

(B) (cos θ − i sin θ )− n = cos nθ − i sin nθ

(C) (cos θ + i sin θ )− n = − cos nθ − i sin nθ
1 cos nθ
(D) zn + n = , where z = cos θ + i sin θ
z 2

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m
m c. o
c. o

e m
em l a s
s ag
 2 3
166. The matrix A =   satisfies the equation
1 2
2
(A) A − I = 2A
2
(B) A − 2A + I = 0
2
(C) A − 2I = 0

m
2

.co
(D) A − 4A + I = 0

m
.co s e m
em = la
1

s
−1

g
167. ∫ x tan xdx

g la a
0

a(A) 0
(B) π −1
π 1
(C) −
4 2
π
(D)
e

o m
c
.120 − x is an integer, is
e m
s
168. The number of real values of x for which

g la
a
(A) 6
(B) 9
(C) 10
(D) 11

2
169. For a positive integer n, let n − 3n + 2 be prime. Then number of possible values of n is

(A) 0
m
c. o
(B) 1
m
c. o m
(C) 3

s e
(D) infinitely many

s em 170. The product of three consecutive positive integers is 8 times gtheir
l a
l a a
ag
sum. Then the sum
of their squares is

(A) 50
(B) 77
(C) 110
(D) 194

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

171. Let S (n) equal the sum of the digits of positive integer n. For a particular integer n ,
let S (n) = 1274 . Then the possible value of S(n + 1) is

(A) 1
(B) 3
(C) 1239
(D) 1265

172. Let f (x) be differentiable function for all x with f '(x) ≤ 17 and f (2) = 7 . Then the
maximum value of f (7) is
(A) 82
(B) 92
(C) 102
(D) 112

173. The sum of three whole numbers taken in pairs are 12, 17 and 19 . The middle
number is
(A) 4
(B) 5
(C) 6
(D) 7

1
 n!  n
174. lim  n  equals
n→∞  n 

(A) e
1
(B)
e
π
(C)
4
4
(D)
π

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m
m c. o
c. o

e m
em l a s
s ag
175. The value of x satisfying the condition |x + 3| > |2x − 1| lies in the interval

 2 
(A)  − ,4
 3 
 2
(B)  −∞, 
 3

m
.co
(C) (0, 2)

m
co m
(D) (0, ∞)

m . s e
a s e g la
l a
1 1 1

ag
176. For a, b, c > 0, the equations a(1 − b) > , b(1 − c) > and c(1 − a ) > are
4 4 4

(A) consistent for some values
(B) inconsistent
(C) consistent
(D) inconsistent for some values

m
b+c c+a a+b
177. For real positive numbers a, b, c, the minimum value of is

co
+ +

.
a b c

s em
(A) 1

l a
(B) 2
(C)
(D)
4
6 a g
5 2
2  1 
178. If x − x + 1 = 0, then the value of ∑  x n + n  is
n =1  x 

(A) 8

m
(B) 10

m c. o
(C) 12

c. o e m
(D) 16

em l a s
l as ag
g
 z + 2i 

a
179. If Im   = 0, then z lies on the curve
 z+2 
2 2
(A) x + y + 2x + 2y = 0
(B) x2 + y2 − 2x = 0
(C) x + y + 2 = 0
(D) x2 + y2 + 2x = 0

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

180. In an AP, the notation Sr denotes the sum of first r terms, Sp = q and Sq = p. Then
Sp + q is equal to

(A) 0
(B) −(p + q)
(C) p+q
(D) pq

m n p
181. Assume that m, n, p are in Harmonic Progression. Then , , are in
n+ p p+m m+n

(A) Harmonic Progression
(B) Geometric Progression
(C) Arithmetic Progression
(D) Standard Progression

2 3
182. The sum of the series 1 + 2x + 3x + 4x +. . . up to infinity is

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

x 2 − bx k − 1
183. If the sum of the roots of the equation = , then the value of k is
ax − c k + 1

a −b
(A)
a+b
a+b
(B)
a −b
1
(C)
c
(D) c

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m
m c. o
c. o

e m
em l a s
s 2 4 3 ag
184. If x − 1 is a factor of x + ax + 3x − b, then

(A) a = 3, b = −1
(B) a = −3, b = 1
(C) a = 3, b = 1
(D) a = 4, b = 3

m
.co
2

m
185. If α is a root of the equation 4x + 2x − 1 = 0, then the other root of the

.co e m
equation is

(A) 3α m− 4α
la s
se g
2

(B)la 4α − 3α a
g 3α + 4α
3

a(C) 2

(D) 4α 3 + 3α

3
 1 1
186. The number of real roots of the equation  x +  + x + = 0 is
 x x

m
. co
(A) 0

em
(B) 2

s
(C) 4
(D) 6
g l a
a
187. Numbers greater than 1000, but not greater than 4000 that can be formed with the
digits 0, 1, 2, 3, 4 (repetition of digits being allowed) is

(A) 375
(B) 385
(C) 396
(D) 456

o m
m . c
c. o188. If the coefficient of the p term in the expansion of (2x + 3) is 1440,e m
th 6

s
then p is

em l a
l as (A) 2
a g
ag
(B) 3
(C) 4
(D) 5

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

n  10  20   p
189. Let S = ∑    where   = 0 when p < q . The value of m, for
i =0  i  m − i  q
which the value of the sum S is maximum, is

(A) 5
(B) 10
(C) 15
(D) 20

190. The number of positive integral solutions of x + y + z = n, n ∈ ℕ is

n −1
(A) P2

(n + 1)(n + 2)(n + 3)
(B)
6
n −1
(C) Cn−4
n −1
(D) C2

191. Let [x] be the greatest integer less than or equal to x. If the set of
equations x − 3y = 4; 5x + y = 2; [2π]x − [e]y = [2a] are consistent,
then a should lie in

 7
(A) 3, 2 
 
 7
(B)  3, 
 3
 7
(C) 3, 3 
 
(D) [3, ∞ )

 1 −1 x 
192. If x is real and A =  1 x 1  has no inverse, then x is equal to
 x −1 1 

(A) 2
(B) 3
(C) 0
(D) 1

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m
m c. o
c. o

e m
em l a s
s ag
1 1 1
193. The sum of the series cos x − cos 2 x + cos3 x − cos 4 x + ...
2 3 4

x
(A) log 2 + 2 log cos  
2

 x

m
(B) 2 log 2 − 2 log cos  

.co
2
m
.co x
s e m
m
(C) log 2 + log cos  

e la
2

a s
(D)l 2 log 2 + 2 log cos   a g
ag
x
2

23 33 43
194. The sum of the series 1 + + + + ... is
2! 3! 4!

(A) 2e
(B) 3e
m
co
(C) 5e
.
em
(D) 6e

l a s
195.
a g
4 gentlemen and 4 ladies take seats at random, round a table. The probability that they
are sitting alternatively is

4
(A)
35
1
(B)
70

m
1

c. o
(C)

m
35

c. o 2
s e m
em a
(D)

s l
35

gla ag
a

m .
.co se m
e m l a
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 41 of 51

10 x − 10− x
196. The inverse of the function f ( x) = , is
10 x + 10− x

x
(A) f −1 ( x) = log10
2− x
1 x
(B) f −1 ( x) = log10
2 2− x
1 x
(C) f −1 ( x ) = log10
2 1− x
x
(D) f −1 ( x) = log10
2+ x

197. The number of onto mappings from the set A = {1, 2, . . . , 100} to
set B = {1, 2} is

(A) 2100
(B) 2100 − 2
99
(C) 2 −2
99
(D) 2

2
198. If A is a matrix such that A + A + 2I = 0, then

(A) A is non-singular
(B) A ≠ 0
(C) A is symmetric
1
(D) A−1 = − ( A + I )
2

199. If sin α, sin β and cos α are in Geometric Progression, then the roots of the equation
2
x + 2x cot β + 1 = 0 are always

(A) equal
(B) real
(C) imaginary
(D) greater than 1

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m
m c. o
c. o

e m
em l a s
s ag
200. An example for a rational number is

(A) sin 15°
(B) cos 15°
(C) sin 15° cos 15°
(D) sin 15° cos 75°

m
m .co
201. The solution of the equation 4sin 4 x + cos 4 x = 1 is

.co s e m
m la
(A) x = 2nπ
xe= nπ + 1
l
(B)
a s a g
ag
(C) x = (n + 2)π
 2
(D) x = 2nπ or nπ ± sin −1  
 5

π
202. In a ∆ABC, a = 2b and A − B = , the ∠C is equal to
3

m
π
. co
em
(A)
4
π
l a s
g
(B)

a
3
π
(C)
6
π
(D)
8

 4 2
203. tan cos −1 + tan −1  is equal to
m
c. o
 5 3

m
c. o 13
s e m
em
(A)

l a
6

las 13
ag
ag
(B) −
6
17
(C)
6
17
(D) −
6

m .
.co se m
e m l a
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 43 of 51

204. The lines x + 2y + 3 = 0, x + 2y − 7 = 0 and 2x − y − 4 = 0 are the sides of
a square. Equation of a remaining side of the square can be

(A) 2x − y − 14 = 0
(B) 2x − y + 8 = 0
(C) 2x − y − 10 = 0
(D) 2x − y − 6 = 0

2
e x − cos x
205. lim is equal to
x →0 x2

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

π
2
cos x − sin x
206. ∫0 1 + cos x sin x is equal to
(A) 0
π
(B)
2
π
(C)
4
π
(D)
6

2
 dy  dy
207. A solution of the differential equation   − x + y = 0 is
 dx  dx

(A) y=0
(B) y = 2x
(C) y = 2x – 4
(D) 2
y = 2x – 4

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m
m c. o
c. o

e m
em l a s
s ag
208. The number of solutions of the equation sin ( e x ) = 3x + 3− x is

(A) 0
(B) 2
(C) 1
(D) Infinitely many

m
m .co
2

co
209. The tangent to the parabola y = 16x, which is perpendicular to a line

.
y − 3x − 1 = 0 is
e m
xe m las
(A)
s
la − x − 36 = 0
− y + 36 = 0
a g
ag x3y++yx−+3636==00
(B) 3 y
(C)
(D)

dy
210. The solution of the differential equation x = 2 y + x3e x , where y = 0 when x = 1, is
dx

(A) y = x2 ( e x − e )

m
(B) y = x3 ( e − e x )
. co
y = x2 ( e − e x )
s em
a
(C)

g l
a
(D) tan x = (sec x + c) y

211. The points A, B, C with position vectors 2i − j − k , i − 3 j − 5k and 3i − 4 j − 5k
are the vertices of

(A) a triangle but not a right angled triangle
(B) a right angled triangle

m
(C) an equilateral triangle

m c. o
(D) an isosceles triangle

c. o212. If (2n + 1) + (2n + 3) + (2n+ 5) +…+ (2n + 47) = 5280, then the value
s e mof
s em g l a
gla 1 + 2 + 3 + …+ n is
a
a (A) 1854
(B) 1485
(C) 5148
(D) 4851

m .
.co se m
e m l a
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 45 of 51

213. Let f ( x) = 10 − 4 x − x 2 and the range of f ( x) be (−∞, b]. Then b + 2 is equal to

(A) 0
(B) 4
(C) 14
(D) 16

214. If log10 2, log10 ( 2 x + 1) and log10 ( 2 x + 3) are in A.P, then the value of x is

(A) log 2 5
(B) log 5 2
(C) log10 2
(D) 1

215. If 1, ω and ω 2 are the cube roots of unity, then

(1 − ω + ω 2 )(1 − ω 2 + ω 4 )(1 − ω 4 + ω8 )(1 − ω8 + ω16 ) ...upto 2n factors are
(A) 2n
(B) 22 n
(C) 1
(D) −2 2 n

680
 1 1

216. The number of integral terms in the expansion of  5 2 + 5 4  is equal to
 

(A) 170
(B) 171
(C) 136
(D) 137

217. The equation of a tangent to the parabola x 2 = 8 y , which makes an angle θ with the
positive direction of x-axis, is:

(A) y = y tan θ + 2 cot θ
(B) y = y tan θ − 2 cot θ
(C) x = y cot θ + 2 tan θ
(D) x = y cot θ − 2 tan θ

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m
m c. o
c. o

e m
em l a s
s ag
218. The negation of ( p ∧ (~ q) ) ∨ (~ p ) is equivalent to

(A) p ∧ ( q ∧ (~ p) )
(B) p ∧ (~ q)
(C) p ∧ ( q ∨ (~ p) )
(D) p∧q

m
co
m m .co
. e
219. Given E ( X + c) = 12 and E ( X − c) = 8 then the value of c is

4e m las
s
la2
(A)
a g
ag −02
(B)
(C)
(D)

a *b
220. Let * be the binary operation defined on R by a * b = , for every a, b ∈ R, then
4
the operation * is

m
co
(A) Commutative and Associative

.
(B) Commutative but not Associative

em
(C) Associative but not Commutative
(D)
l
Neither Associative nor Commutative
a s
a g
 1+ 3   
−1  8 + 4 3 
221. tan −1   + sec is equal to
 3 + 3   6 + 3 3 
 

π
(A)
4

m
π

c. o
(B)

m
2

c. o π
s e m
em a
(C)

s l
6

gla π
ag
a
(D)
3

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

222. Let A =  aij  , where aij ≠ 0 for all i, j and A2 = I . Let a be the sum of all
  2×2
diagonal elements of A and b = A . Then, 4a 2 + 3b 2 is equal to

(A) 4
(B) 3
(C) 7
(D) 14

51 −1
223. ∫ x ( tan x + cot −1 x dx equals to
)
x52
(A) tan −1 x − cot −1 x + c
( )
52
π x52 π
(B) + +c
104 2
x52
(C) tan −1 x + cot −1 x + c
( )
52
π x52 π
(D) + +c
52 2

224. The value of k for which the image of (5,1, −3) by reflection in 2 x + y − 3 z + k = 0 is
the point (1, −1, 3) is

(A) 3
(B) 1
(C) −6
(D) 2

225. If B = 2iˆ + ˆj − kˆ and C = iˆ + 3kˆ . If A is a unit vector, then the maximum value of the
scalar triple product  ABC  is

(A) −1
(B) 10 + 6
(C) 60
(D) 59

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

m
m c. o
c. o

e m
em l a s
s ag

m
co
m m .co
m . s e
a s e g la
l a
ag

m
. co
s em
g l a
a

m
m c. o
c. o s e m
s em l a
gla ag
a

m .
.co se m
e m l a
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 49 of 51

FINAL ANSWER KEY
Subject Name: 101 B TECH 10 MAY 2024 - S2

SI No. Key SI No. Key SI No. Key SI No. Key SI No. Key SI No. Key SI No. Key SI No. Key
1 A 31 D 61 C 91 D 121 B 151 B 181 A 211 B
2 C 32 D 62 B 92 B 122 D 152 C 182 D 212 D
3 B 33 A 63 B 93 D 123 D 153 C 183 B 213 B
4 D 34 C 64 B 94 C 124 C 154 C 184 B 214 A
5 C 35 A 65 A 95 C 125 C 155 B 185 B 215 B
6 B 36 A 66 A 96 B 126 A 156 C 186 A 216 B
7 D 37 A 67 C 97 A 127 B 157 B 187 A 217 C
8 D 38 A 68 B 98 D 128 C 158 C 188 A 218 D
9 D 39 C 69 C 99 D 129 C 159 C 189 C 219 B
10 C 40 C 70 B 100 C 130 A 160 D 190 D 220 B
11 B 41 B 71 C 101 B 131 C 161 A 191 A 221 D
12 C 42 A 72 A 102 D 132 B 162 C 192 D 222 B
13 A 43 C 73 C 103 C 133 B 163 B 193 A 223 B
14 C 44 D 74 B 104 A 134 C 164 B 194 C 224 C
15 C 45 C 75 C 105 C 135 C 165 A 195 C 225 D

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

co
m m.co
m . e
co s

. e m la
s em las ag
gla ag
a
16 B 46 C 76 D 106 C 136 D 166 D 196 A
17 B 47 A 77 A 107 C 137 A 167 C 197 B
m 198
om co
18 D 48 C 78 D 108 C 138 D 168 D D
.
19om
c m.
c 109 seBm
a
m. e
A 49 B 79 D D 139 D 169 199 B
s
lCa gl B
l a se 20 A 50 A 80
a g 110 B 140 A 170 a 200 C
ag 21 A 51 B 81 B 111 D 141 D 171 C 201 D
22 A 52 B 82 C 112 A 142 D 172 B 202 B

m
23 B 53 A 83 A 113 C 143 C 173 D 203 C
o
m
o144 Am.c
m .c se
24 D 54 B 84 B 114 B A 174 B 204
co
.55 A se
m l
205 g C a
25 B
s em C 85 B 115
ga
l
145 D 175 A
a
C gl a a C
26
a 56 A 86 A 116 146 C 176 B 206 A
27 D 57 B 87 B 117 B 147 D 177 D 207 C
28 A 58 C 88 B 118 C 148 B 178 A 208 A
m
om co
m.
29 C 59 D 89 C 119 D 149 D 179 C 209 D

co
m m .c 180 se
a
m. e l
30 C 60 C 90 C 120 B 150 B B 210 A
e la s ag
la s a g
ag

m
om . co
co
m m.c sem
. se l a
em la ag
las ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 51 of 51