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

FOR CUSAT CAT EXAM PREPARATION

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

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

Notes · Sample Papers · Previous Year Papers · Mock Tests

m
m c. o
c. o

e m
em l a s
s ag
B.Tech. (PHYSICS)
SHIFT V

1. Energy stored in the capacitor is

m
.co
1
(A) U = ε 0 E 2 d
m
co m
2

m . s e
la
1
e
U = ε 0 E 2 2d
s
(B)

a a g
2

g l 1
a U = ε 0 E 2 Ad
(C)
2
1
(D) U = ε 0 E 2
2

2. Which magnetic pole does not exist?

m
co
(A) Dipole

.
(B) Quadrupole

em
(C) Octupole

a s
(D) Monopole

g l
3. a
When the source move away from the observer, the frequency as measured by the
observer will be

(A) Larger
(B) Smaller
(C) Infinite
(D) Zero

m
m c. o
c. o m
4. The structural determination of the solids can be obtained by using

s e
s em l a
(A) Ultraviolet rays

la ag
(B) Cosmic rays

ag (C)
(D)
Gamma rays
X-rays

5. In a p-type semiconductor, there is

(A) excess of one electron
(B) a missing of atom
(C) a donor level

m .
co
(D) absence of one electron

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

6. What will be the energy of the photon of red color compared with that of violet color?

(A) Equal
(B) Larger
(C) Smaller
(D) Cannot be compared

7. When a system is at equilibrium, the free energy of the reaction is

(A) positive
(B) negative
(C) zero
(D) can be negative or positive

8. A lead bullet penetrates into a solid object and melts. The initial temperature
of the bullet is 27°C and its melting point is 327°C. Latent heat of fusion of
4
lead = 2.5 × 10 J/kg and specific heat capacity of lead is 125 J/kg/K.
Assuming that 50% of its kinetic energy was used to heat it, then the initial
speed of the bullet is

(A) 200 m/sec
(B) 300 m/sec
(C) 400 m/sec
(D) 500 m/sec

9. If × = × , then the angle between A and B is

(A) π
π
(B)
3
π
(C)
2
π
(D)
4

10. The height up to which water will rise in capillary tube will be

(A) Same at all temperatures
(B) Maximum when the temperature of water is 0°C
(C) Maximum when the temperature of water is 4°C
(D) Minimum when the temperature of water is 4°C

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 2 of 51

m
m c. o
c. o

e m
em l a s
s ag
11. If Young’s double slit experiment is performed in water

(A) The fringe width decreases
(B) The fringe width increases
(C) The fringe width is unchanged
(D) There will be no fringes observed

m
.co
12. If the earth stops rotating about its axis, the acceleration due to gravity will remain

o m m
c
unchanged at

m . s e
se latitude la
(A) Equator

(C)la 60° latitude
(B) 45°
a g
g Poles
a(D)
13. No current flows between two charged bodies when connected, if they have same

(A) capacity
(B) potential
(C) resistance

m
c. o
(D) charges

e mzero, when the frequency of incident
a s
14. Kinetic energy and stopping potential are

l
ag
radiation is

(A) equal to the threshold frequency
(B) very minimum
(C) lower than the threshold frequency
(D) very high

15. What happens during the regulation action of a Zener diode?

m
m c. o
(A) The current and voltage across the Zener diode remains fixed

c. o m
(B) The Zener resistance is constant

s e
em
(C) The resistance offered by the Zener diode changes

s
(D)
g l a
la
The current through the series resistance (R ) does not change

a
s

ag 16. Which of the following electromagnetic radiation has maximum penetrating power?

(A) Radio waves
(B) Microwaves
(C) Ultraviolet rays
(D) Gamma rays

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 3 of 51

17. The lines of forces due to the Earth’s horizontal magnetic field are

(A) elliptical
(B) curved lines
(C) parallel and straight
(D) concentric circles

18. In the transverse waves the direction of vibration in medium of particle is

(A) perpendicular to propagation of wave
(B) parallel to propagation
(C) alternate parallel and perpendicular
(D) in all three directions

19. de Broglie proposed that electron has

(A) dual characters of wave and particle nature
(B) only particle nature
(C) only wave nature
(D) either wave or particle nature

20. The Speed of Light in Vacuum is

µ0
(A)
ε0

(B) µ0ε 0
1
(C)
µ0ε 0
1
(D)
µ0ε 0

21. The working of a scent sprayer is based on

(A) Archimedes' principle
(B) Charles' law
(C) Boyle's law
(D) Bernoulli's principle

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 4 of 51

m
m c. o
c. o

e m
em l a s
s ag
22. A body absorbs all the radiation incident over it is called

(A) perfect black body
(B) perfect white body
(C) emitter
(D) poor absorber

m
m .co
23. The Kα X-ray of molybdenum has wavelength 71 pm. If the energy of a molybdenum

.co e m
atom with a K electron knocked out is 23.32 keV, what will be the energy of this atom

em
when an L electron is knocked out?
las
l a s a g
ag 6.52
(A) 5.82 eV
(B) eV
(C)
8.22 eV
(D) 4.32 eV

24. What is immaterial for an electric fuse wire?

(A) Specific resistance

m
(B) Radius

. co
(C) Length

em
(D) Current flowing through it

l a s
25.
a g
Pressure exerted by a liquid depends upon

(A) density
(B) viscosity
(C) surface tension
(D) buoyancy

26. The temperature coefficient of resistance is positive for

m
m c. o
c. o
(A) Carbon

e m
(B) Germanium

em
(C) Electrolyte
l a s
las ag
(D) Aluminium

ag

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 5 of 51

27. Two coils of self inductances L1 and L2 are placed close together, if mutual
inductance between them is M, then M is proportional to ……………….., where the
proportionality constant is known as ………………..

L1
(A) , coefficient of coupling
L2
(B) L1 L2, coefficient of coupling
2
(C) (L1 L2) , coefficient of coupling

(D) L1L2 , coupling coefficient

28. In a plane electromagnetic wave, if the electric field oscillates sinusoidally with a
10 −1
frequency 2 × 10 Hz and amplitude of 48 Vm , then the wavelength of the wave
and strength of the oscillating magnetic field are

(A) 600 m, 6 × 107 tesla

(B) 3 × 108 m, 24 × 10−10 tesla

(C) 1.5 × 10−2 m, 1. 6 × 10 −7 tesla

(D) 3 × 108 m, 1.6 × 107 tesla

29. A student sets a source at a distance 10 cm away from a double slit which are
separated by 5 cm apart and keeps the micrometer eye piece at 60 cm from the double
slit ϕ, but unable to observe the interference fringes. You must advice him to

(A) increase the distance of the source
(B) decrease the distance between the double slit
(C) replace the light with white light source
(D) replace the micrometer eyepiece with telescope

30. The molecular weights of oxygen and hydrogen are 32 and 2 respectively. The root
mean square velocities of oxygen and hydrogen at NTP are in the ratio

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

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 6 of 51

m
m c. o
c. o

e m
em l a s
s ag
31. What is the unit of self-inductance?

(A) Henry
(B) Weber
(C) Volt
(D) Fermi

m
.co
32. Sparkling of diamond is due to
m
(A)
.co
reflection
s e m
em la
s
(B) diffraction
(C)
l a
total internal reflection
a g
ag
(D) the high refractive index of diamond

33. Magnetic domain formation is the necessary feature of

(A) diamagnetism
(B) ferromagnetism
(C) paramagnetism
(D) superconductivity

m
. co
em
34. The average power consumed in a purely inductive circuit is

l a s
g
(A) Imax × Vmax
(B) zero
a
(C) 1
Imax
(D)
Vmax

m
35. Neutrino is

m c. o
c. o
(A) chargeless, fermion of negligible mass

e m
em s
(B) massless, chargeless

s l a
la ag
1

g
(C) massless, fermion of charge   e

a
3
(D) chargeless, spinless boson

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 7 of 51

36. Which law states that the pressure exerted by a gaseous mixture is equal to the sum of
partial pressure of each component present in the mixture?

(A) Graham's law
(B) Boyle's law
(C) Dalton's law
(D) Charles' law

37. If the intensity of sound is increased three times of its initial intensity, by how many
decibels does the sound level increase?

(A) Remains same
(B) Tripled
(C) 4.77 dB
(D) 6 dB

38. To get output 1 at R for the given logic gate circuit, the input values must be

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

39. Which of the following principle is used in optical fibres?

(A) Diffraction
(B) Scattering
(C) Total internal reflection
(D) Refraction

40. A particle executes simple harmonic motion. The amplitude of oscillation of particle
is 2 cm. The displacement of particle in one time period is

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

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 8 of 51

m
m c. o
c. o

e m
em l a s
s ag
41. In a circuit, if the alternating current is represented by I = 4 cos (ωt +φ), then the r.m.s
value of current is

(A) 2
(B) 4 2
(C) 2 2

m
(D) 1/ 2

co
m m .co
m . s e
la
42. Work function of three metals A, B and C are 4.7 eV, 4.5 eV and 3.5 eV respectively.

s e g
a
If a light of wavelength 3310 A° is incident on the metals, then photoelectrons are

l
g All the metals
emitted by
a
a(A)
(B) C alone
(C) A and B alone
(D) No metals

43. Mirror nuclei are nuclei having

m
co
(A) same mass number but with different atomic number

.
em
(B) same mass number but with proton number and neutron number interchanged

s
(C) equal number of neutrons

l a
(D) mirror images

a g
44. An athlete completes one round of a circular track of radius R in 20 seconds. What
will be his displacement at the end of 2 minutes 20 seconds?

(A) Zero
(B) 2R
(C) 2πR
(D) 7πR

o m
m A marble block of mass 2 kg lying on ice when given a velocity of 6 m c
m/s. is stopped
c. o by friction in 10 s. Then the coefficient of friction is e
45.

em l a s
l as a g
ag
(A) 0.01
(B) 0.02
(C) 0.03
(D) 0.06

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 9 of 51

46. The pair of physical quantities that has the different dimensions is
(A) Reynolds number and coefficient of friction
(B) Curie and frequency of a light wave
(C) Latent heat and gravitational potential
(D) Planck’s constant and torque

2 3
47. The position of a particle varies with time t as x = pt – qt . The acceleration of the
particle will be

(A) 2 pt − 3qt 2
(B) p /q
(C) 2 p − 6qt
(D) zero

48. Which one of the following is the unit of solid angle?

(A) Degree
(B) Radian
(C) Steradian
(D) Second

49. A certain carbon resistor has following colour codes:
I band – Yellow; II band – Violet; III band – Orange; IV band – Gold
Then

(A) the value of the resistance is 4.7 KΩ ±5% tolerance
(B) the value of the resistance is 47 KΩ ±5% tolerance
(C) the value of the resistance is 47 KΩ ±10% tolerance
(D) the value of the resistance is 4.7 KΩ ±10% tolerance

50. A 600 W electric heater is designed to operate from 240 V lines. Then it would draw a
current of

(A) 0.4 A
(B) 2.5 A
(C) 5A
(D) 15 A

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 10 of 51

m
m c. o
c. o

e m
em l a s
s ag
51. Fermi level in the case of intrinsic semiconductor lies

(A) close to the conduction band
(B) close to the valence band
(C) in the middle of the forbidden energy gap
(D) above the conduction band

m
.co
52. A metal wire is first stretched beyond its elastic limit and then released. It
m
(A)
.co
loses its elastic property completely and it will not contract
s e m
em la
s
(B) will contract to its original length
(C)
l a
will contract to its length at elastic limit
a g
ag
(D) will contract but final length will be greater than original length

53. If there were no gravity, which one of the following will not be there for a fluid?

(A) Viscosity
(B) Surface tension
(C) Pressure
(D) Archimedes upthrust or Buoyant force

o m
. c
em constant σ = 5.67 × 10−8 W/m2K4)
4
54. The energy radiated by unit area in unit time of a planet is 5.67 × 10 Watt. Its

la s
g
surface temperature is then (Given Stefan’s

(A) 1273°C a
(B) 1000°C
(C) 727°C
(D) 727 K

55. Bonding in Germanium crystal is

m
c. o
(A) Ionic

m
c. o m
(B) van der Waals’ type

s e
(C) Metallic

s em l a
(D) Covalent

gla ag
a 56. The percentage of U
235
present in natural Uranium is

(A) 100%
(B) 0.714%
(C) 99.28%
(D) 0.006%

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

57. The image formed by the objective of a compound microscope is

(A) virtual and enlarged
(B) virtual and diminished
(C) real and diminished
(D) real and enlarged

58. When the angle of incidence on a certain material is 60°, the reflected light is
completely polarized. The refractive index of the material is then

(A) 1.732
(B) 0.866
(C) 0.577
(D) 1.5

59. In case of a common emitter transistor amplifier, the ratio of the collector current to
the emitter current Ic /Ie is 0.96. The current gain of the amplifier is

(A) 6
(B) 48
(C) 24
(D) 12

60. The decimal equivalent of the binary number 1111 is

(A) 15
(B) 4
(C) 14
(D) 1

61. In Young’s double slit experiment the slits are separated by 0.28 mm and the screen is
placed 1.4 m away. The distance between the central bright fringe and the fourth
fringe is measured to be 1.2 cm. Determine the wavelength of light used in this
experiment.

(A) 650 nm
(B) 400 nm
(C) 500 nm
(D) 600 nm

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 12 of 51

m
m c. o
c. o

e m
em l a s
s ag
62. If an electron and a photon propagate in the form of waves having same wavelength,
it implies that they have same

(A) speed
(B) momentum
(C) energy
(D) All of the above

m
co
m
A book of mass m, placed on an inclined table, making an angle of 30° with the
m .co
.
63.

m s e
e la
g

s
horizontal, slides down with an acceleration of . The frictional force acting on the

a a g
3
l
g 1 mg
a(A)
book is

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

m
6

c o
. of 10 m. It reaches the ground with a
64.
speed of 1.5 m/s. The work done by s
m
e air-friction is
A ball of mass 50 g is dropped from a height

g la
the

(A) 5.056 J a
(B) 4.954 J
(C) −4.954 J
(D) −5.056 J

2
65. A circular disc having a moment of inertia 4 kg m about its axis rotates at 40 rpm.

m
c. o
The torque required to stop the wheel in 2 minutes is

m
c. o m
 2 
  π Nm
s e
em
(A)

a
 45 

s l
gla  1 
ag
a
(B)   π Nm
 45 

 2 
(C)   π Nm
 25 

 1 
(D)   π Nm
 25 

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

66. A particle undergoes simple harmonic motion of time period T. The time taken by the
particle to go directly from the mean position to half the amplitude is

T
(A)
2
T
(B)
3
T
(C)
6
T
(D)
12

2 2
67. A U-shaped tube has areas of cross-sections 2 cm and 20 cm at its two ends. It is
filled with water, and a force of 10 N is applied in the thinner arm using a piston. For
the water to remain in equilibrium the force to be applied in the thicker arm is

(A) 20 N
(B) 40 N
(C) 100 N
(D) 200 N

68. The first overtone frequency of an open organ pipe is equal to the fundamental
frequency of a closed organ pipe. What is the length of the closed pipe, if the length
of open pipe is 80 cm?

(A) 20 cm
(B) 40 cm
(C) 60 cm
(D) 80 cm

69. An ambulance moves away from an observer at a speed of 20.00 m/s. The siren in the
ambulance is detected by the observer and is found to be at a frequency of
2200.00 Hz. Considering the observer to be immobile and speed of sound to be
320.00 m/s, what is the original frequency of the siren?

(A) 2200.00 Hz
(B) 2337.44 Hz
(C) 2557.35 Hz
(D) 3201.23 Hz

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 14 of 51

m
m c. o
c. o

e m
em l a s
s ag
70. The beam from a laser source is incident on a double slit with the distance between
them being 430 micron. A screen is placed at a distance of 2.00 m from the double slit
to observe the fringes. The first bright fringe is observed at 2.2 mm from the central
fringe. The wavelength of the laser source is

(A) 355.05 nm
(B) 423.24 nm

m
.co
(C) 468.09 nm

m
c. o
(D) 532.01 nm

e m
e m beam of light is incident on a glass block at an angle of 60° withlas
a s g
71. A monochromatic

l
g The critical angle for the glass block is
respect
a
to the surface normal. The reflected beam is observed to be completely
apolarised.
(A) 15.77°
(B) 25.34°
(C) 35.27°
(D) 55.71°

m
co
72. A sealed glass container has a volume of 3 liters. It contains 0.5 mole of oxygen and

.
0.3 mole of nitrogen. If the contents of the container are at 300 K, then the pressure in

s em
the chamber is
5

g l a
a
(A) 2.50 × 10 Pa
5
(B) 4.16 × 10 Pa
5
(C) 6.65 × 10 Pa
5
(D) 8.32 × 10 Pa

−5
73. A vertically falling charged liquid droplet of mass 2 × 10 kg is balanced in air by a
5
vertical electric field of magnitude 3.00 × 10 N/C. The charge on the droplet is

m
m
(A) 3.00 × 10−10 C
c. o
c. o s e m
em
(B) 3.57 × 10−10 C

s l a
la ag
(C) 6.67 × 10−10 C

ag (D) 1.60 × 10−19 C

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 15 of 51

74. In a circuit, at a given time, 20 C of charge is passed through a battery, whose plates
are maintained at a potential difference of 20 V. The work done by the battery is

(A) 1J
(B) 10 J
(C) 20 J
(D) 400 J

2
75. A parallel plate capacitor has plates of area 300.00 cm with the separation between
them being 2.00 mm. If a charge of 2 nC is given to the capacitor, what will be the
potential difference that is developed between the plates?

(A) 5.42 V
(B) 15.04 V
(C) 20.12 V
(D 75.00 V

CHEMISTRY UG
(SHIFT V FINAL)

76. In a reversible isothermal process, the change in internal energy

(A) ∆E = 0
(B) ∆E > 0
(C) ∆E < 0
(D) ∆E ≥ 0

77. Which of the following two gases can be cooled from room temperature by the
Joule-Thomson effect?

(A) Hydrogen and oxygen
(B) Helium and nitrogen
(C) Helium and hydrogen
(D) Nitrogen and oxygen

−4
78. A weak acid has a dissociation constant of 1 × 10 . The equilibrium constant for its
reaction with a strong base is

(A) 1.0 × 10−4
(B) 1.0 × 10−10
(C) 1.0 × 1010
14
(D) 1.0 × 10

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 16 of 51

m
m c. o
c. o

e m
em l a s
s ag
79. A plant cell shrinks when it is kept in

(A) Hypertonic solution
(B) Hypotonic solution
(C) Water
(D) Isotonic solution with cell sap

m
.co
80. Two platinum electrodes were immersed in a solution of copper sulphate and electric
m
co m
current was passed till the solution becomes colourless. The colourless solution

m . s e
la
contains

s e sulphate g
a
l Copper hydroxide
(A) Platinum
a
ag Dilute
(B)
(C)
Only water
(D) sulphuric acid

81. To protect iron against corrosion, the most durable metal plating on it is

(A) Tin plating
(B) Copper plating

m
co
(C) Zinc plating

.
(D) Nickel plating

s em
82.
g l a
For a first order reaction, t0.75 is 138.6 sec. Its specific rate constant (in sec) is

(A) 10
−2 a
−4
(B) 10
−5
(C) 10
−6
(D) 10

m
m c. o
2

c. o
83. If the rate law for a reaction is, rate = k[A][B] , the unit for k is

e m
em
−1 −1

l a s
s
(A) mol L s

la ag
−1

g
(B) mol s

a 2
(C) L mol
2
−2 −1

−2 −1
s
(D) mol L s

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

x
84. For a linear plot of log   versus log p in a Freundlich adsorption isotherm, the
m
correct statement is (k and n are constants).

1
(A) Both k and appear in the slope term
n
1
(B) appears as the intercept
n
1
(C) Only appears as the slope
n
1
(D) log   appears as the intercept
n

85. Multilayer adsorption is assumed in

(A) Langmuir equation
(B) Freundlich equation
(C) BET equation
(D) Both Langmuir equation and BET equation

86. The intensive property listed below is

(A) Internal energy
(B) Volume
(C) Mole fraction
(D) Mass

87. When a system releases 10 kJ of energy to the surroundings as work, the internal
energy of the system

(A) decreases by 10 kJ
(B) increases by 5 Kj
(C) reduced 20 kJ
(D) remains constant

88. Quantitative relation between pressure and solubility of a gas in a solvent is given by
…………….. law.

(A) Le Chatelier
(B) Dalton
(C) Henry
(D) Raoult

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 18 of 51

m
m c. o
c. o

e m
em l a s
s ag
89. Which of the following relation is true for Rhombohedral crystal system?

(A) α = β = γ = 90°
(B) α ≠ β = γ = 90°
(C) α = β = 90° γ = 120°
(D) α = β = γ ≠ 90°

m
co
m .co
90. Schottky defect is an example of

. e m
(A)
em
point defect
las
(B)
l a s
metal deficiency
a g
ag
(C) metal excess
(D) electron defect

91. In Ziegler Natta catalyst the commonly used catalyst system is

(A) TiCl4, Al(C2H5)3
(B) 5
(η -cp)2 TiCl2, Al(OEt)3
(C) VO (acac)2 Al2(CH3)6
m
c. o
(D) TiCl4, BF3

m the internal energy of molecules
egas,
92.
la s
In an isothermal expansion of an ideal

(A) may increase or decreasea g
(B) does not change
(C) increase
(D) decrease

93. The combined form of first and second law of thermodynamics is given by
(p = Pressure, V = Volume, T = Temperature, U = Internal energy, S = Entropy,

m
c. o
Q = Quantity of heat)

m
c. o (A) TdS = dU + pdV
s e m
s em l a
(B) dQ = TdS + pdV

la ag
(C) dU = TdS + dQ

ag (D) TdS = dU − pdV

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. In which case rate of diffusion is highest if all are present in the same container at the
same temperature?

(A) 4g H2
(B) 32g O2
(C) 22g CO2
(D) 56g N2

95. One mole of an ideal gas is expanded from 10 L to 20 L at 298 K isothermally and
reversibly. The correct statement describing the entropy change for the above process
is
(A) ∆ = 2
1
(B) ∆ =
2
(C) ∆ = 2
1
(D) ∆ =
2

96. An alkyne on treatment with dilute H2SO4 and HgSO4 gave a mixture of two isomeric
ketones (C5H10O). Identify the structure of the alkyne.

(A)

(B)

(C)

(D)

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 20 of 51

m
m c. o
c. o

e m
em l a s
s ag
97. Propionaldehyde is reduced in presence of sodium borohydride to compound P which
is treated first with thionyl chloride and the resultant compound Q is treated with
magnesium in dry ether to form R. R can react with propionaldehyde to form S. What
product is formed when S is oxidized with potassium dichromate?

(A)

m
co
m m .co
. e
(B)

e m las
(C) as a g
g l
a
(D)

98. Maleic acid (shown below) is a geometrical isomer of fumaric acid. Which of the

m
statements given below is true? (pKa is a measure of acidity)

. co
s em
g l a
a

(A) Both have same pKa (1st and 2nd)
(B) 1st pKa of maleic acid < 1st pKa of fumaric acid
(C) 2nd pKa of maleic acid < 2nd pKa of fumaric acid
m
m c. o
c. o
(D) 1st pKa of maleic and fumaric acids are same,

e m
s
nd nd

em
while 2 pKa of maleic acid < 2 pKa of fumaric acid

s g l a
gla a Gum In Gallon
a
99. An epimer of glucose is (remember, All Altruists Gladly Make
Tanks):

(A) Mannose
(B) Fructose
(C) Allose
(D) Tallose

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

100. Coagulation of blood is promoted by Vitamin

(A) B
(B) C
(C) D
(D) K

101. Which of the following is a polyamide?

(A) Polyurethane
(B) Nylon 6
(C) Polyaniline
(D) Melamine formaldehyde resin

102. A more environmentally friendly alternative to using CFC for refrigeration is:

(A) Tetrafluoroethylene
(B) Hydrofluorocarbons
(C) Bromoflurocarbons
(D) Tetrachloroethylene
103. Cyclohexene can be converted to adipic acid [CO2H(CH2)4CO2H] using

(A) O3, NaBH4
(B) O3, Me2S
(C) O3, H2O
(D) O3, H2O2

104. In which of the following compounds π-delocalization is NOT possible

(A) 1,3-Butadiene
(B) 1,2-Butadiene
(C) 1,3,5-Hexatriene
(D) Benzene

105. The following reaction is best accomplished by

H3CO H3CO
?
+

(A) Treating with strong base
(B) Neat heating at 50 °C
(C) Treating with strong acids like conc. H2SO4
(D) Using free radical initiators

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 22 of 51

m
m c. o
c. o

e m
em l a s
s ag
106. Explain why 2,5-dimethyl-1,4-dioxane (shown below) is not chiral.

O
O

(A) It has an axis of symmetry
(B) It has a plane of symmetry

m
(C) It has no chiral carbons

m .co
(D) It has a centre of symmetry

c o m
107. Which among. the following is a β-lactam antibiotic? s e
s em g la
(A)la Chloramphenicol a
g Penicillin
a(C)
(B)
Vitamin K
(D) Griesofulvin

108. Oximes of benzophenones rearranges on reacting with SOCl2 to form the
corresponding Benzanilides. This rearrangement reaction is an example for

m
co
(A) Hofmann Rearrangment

.
(B) Curtius Rearrangement

em
(C) Wagner-Meerwein Rearrangement
(D) Beckmann Rearrangement
l a s
109. a g
Among the following, the amino acid which has phenolic side chain is?

(A) Aspartic Acid
(B) Asparagine
(C) Leucine
(D) Tyrosine

m
m c. o
110. The principle involved in column chromatography over silica gel is

c. o s e m
em
(A) Absorption

s
(B) Partition
l a
la ag
(C) Adsorption

ag (D) Size exclusion

111. An organic compound which has the ability to exhibit optical activity is

(A) 2–Methylbutane
(B) 3–Methylpentane
(C) Methylcyclopentane
(D) 3–Methylhexane

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

112. Iodoalkane is obtained by the reaction of the corresponding bromoalkane or
chloroalkane with NaI in dry acetone. The reaction is known as

(A) Hunsdiecker reaction
(B) Wurtz reaction
(C) Finkelstein reaction
(D) Iodoform reaction

113. Williamson’s ether synthesis works most efficiently in

(A) acidic medium
(B) basic medium
(C) neutral conditions
(D) neat heating above 50 °C

114. The percent composition of an organic compound was estimated as: 72% C, 12% H.
The molar mass is 100 g/mole. What is the molecular formula of this compound?

(A) C5H8O2
(B) C7H16
(C) C6H12O
(D) C4H4O3

115. SN2 substitution proceeds through

(A) carbocation intermediate
(B) carbanion intermediate
(C) free radical intermediate
(D) no intermediate, only a transition state

116. Which of the following metal cannot be obtained by electrolysis of an aqueous
solution?

(A) Copper
(B) Magnesium
(C) Calcium
(D) Chromium

117. Solubility of the alkaline earth metal sulphates in water decreases in the sequence

(A) Ba > Mg > Sr > Ca
(B) Mg >Ca > Sr > Ba
(C) Ca > Sr > Ba > Mg
(D) Sr >Ca > Mg > Ba

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 24 of 51

m
m c. o
c. o

e m
em l a s
s ag
118. Among the alkali earth metals, which one forms an insoluble sulfide, and what
specific factor contributes to this behavior?

(A) Beryllium (Be); Small size and high lattice energy
(B) Magnesium (Mg); Low ionization energy
(C) 2+
Calcium (Ca); Exceptionally stable Ca ions
(D) Barium (Ba); Increased atomic size

m
co
m m .co
. e
119. Calculate the electron gain enthalpy of sodium ion, whose first ionisation potential is
5.1 eV.
em la s
l a s a g
ag 10.2 eV
(A) −2.55 eV
(B)
5.1 eV
(C)
(D) 2.55 eV

120. Calomel on reaction with NH4OH gives

(A) Hg2O

m
co
(B) HgO

.
(C) HgNH2Cl

s em
(D) NH2Hg2Cl

l a
g and its specific factor which can form
121. Which of the following a elements
superconducting compounds at relatively higher temperatures in comparison to other
d-block elements?

(A) Chromium (Cr); Due to its exceptional hardness
(B) Vanadium (V); Exhibits variable oxidation states
(C) Yttrium (Y); Forms oxygen deficient compounds

m
(D) Manganese (Mn); Displays diverse magnetic properties

m co
. to act both
c. o122. asWhich s e m
among the following catalysts and the unique property made them

em l a
s
homogeneous and heterogeneous catalyst?

l a a g
ag
(A) Platinum (Pt); Due to its high surface area
(B) Iron (Fe); Exhibits redox activity
(C) Palladium (Pd); Forms stable complexes in solution
(D) Zeolites; Possess well-defined porous structures

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 25 of 51

123. Among the following lanthanides, which element is known for exhibiting an unusual
oxidation state, +4, in addition to its more common oxidation states, and what is the
specific compound where this unusual oxidation state is observed?

(A) Europium (Eu); Exhibits +4 oxidation state in europium (IV) oxide
(B) Cerium (Ce); Shows +4 oxidation state in cerium (IV) fluoride
(C) Praseodymium (Pr); Displays +4 oxidation state in praseodymium(IV) sulfide
(D) Gadolinium (Gd); Demonstrates +4 oxidation state in gadolinium(IV) chloride

124. Among the lanthanides, which element is employed in certain medical imaging
applications due to its ability to emit X-rays when exposed to high-energy photons,
and what is the specific medical imaging technique where this element is utilized?

(A) Gadolinium (Gd); Used in magnetic resonance imaging (MRI)
(B) Samarium (Sm); Employed in positron emission tomography (PET)
(C) Lutetium (Lu); Utilized in single-photon emission computed tomography
(SPECT)
(D) Terbium (Tb); Applied in X-ray fluorescence imaging

125. The number of ions per molecule of the complexes CoCl3.5NH3 in aqueous solution will
be

(A) 2
(B) 3
(C) 4
(D) 9

126. The crystal field splitting energy for octahedral (∆o) and tetrahedral (∆t) complexes is
related as

(A) ∆t = 4/9 ∆o
(B) ∆t = 1/2 ∆o
(C) ∆o = 1/2 ∆t
(D) ∆o = 4/9 ∆t

127. The complexes [Co(NH3)5 NO2]Cl2 and [Co(NH3)5 ONO]Cl2 are examples of

(A) Linkage isomers
(B) Ionisation isomers
(C) Geometrical isomers
(D) Co-ordination isomers

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 26 of 51

m
m c. o
c. o

e m
em l a s
s ag
128. Which of the following is hexadentate ligand?

(A) Acetylacetonate
(B) 1,10-phenanthroline
(C) Ethylene diamine
(D) Ethylene diamine tetraacetate

m
m .co
129. The metal atoms present in Haemoglobin and Vitamin B12 respectively is

.co s e m
m
(A) Fe, Mg

s e g la
(B) Fe, Co
(C)
l aCo, Fe
a
ag
(D) Co, Mg

130. The IUPAC name of the compound K4[Fe (CN)6] is

(A) Potassium hexacyanoferrate(II)
(B) Potassium hexacyanoferrate(III)
(C) Hexacyano potassiumferrate(II)

m
(D) Hexacyano potassiumferrate(III)

c o
131. Principal, azimuthal and magnetic quantum. numbers are respectively related to
e m
(A) size, shape and orientation a s
a gl
(B) shape, size and orientation
(C) size, orientation and shape
(D) None of the above

132. To which block do the elements with atomic number 56 belongs?

(A) p

m
(B) f

m c. o
(C) d

c. o e m
(D) s

em 133. The elements with atomic number 35, 53 and 85 are l a s
las ag
ag (A) Noble gas
(B) Halogens
(C) Alkali metals
(D) Alkaline earth metals

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

134. Ionic bonds will be formed more easily between the elements having comparatively

(A) low ionization enthalpy and high electron affinity
(B) high ionization enthalpy and high electron affinity
(C) low ionization enthalpy and low electron affinity
(D) high ionization enthalpy and low electron affinity

135. Which state of matter has the highest kinetic energy?

(A) Solid
(B) Liquid
(C) Gas
(D) Plasma

MATHEMATICS UG
(SHIFT V FINAL)

136. In a group of eight girls, two girls are sisters. The number of ways in which the girls
can sit in a row so that two sisters are not sitting together is
(A) 4820
(B) 1410
(C) 2830
(D) 30240

137. The sum of the factors of 8! which are odd and are the form 3m + 2, where m is a
natural number is

(A) 8
(B) 35
(C) 40
(D) 45

2
 2 x  n(n + 1)  2 x 
138. If x < 1, then 1 + n  +   + ... is equal to
 1+ x  2  1+ x 

n
 2x 
(A)  
 1+ x 
n
 1+ x 
(B)  
 1− x 
n
 1+ x 
(C)  
 2x 
n
 1− x 
(D)  
 1+ x 

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 ag
 1 2 −1
139. If A =  −1 1 2  , then det adj ( adj ( A ) ) =
( )
 2 −1 1 

(A) 14
(B) 142

m
.co
(C) 143

m
co m
(D) 144

m . s e
a s e g la
l a
If the system of equations ax + y = 3, x + 2 y = 3, 3 x + 4 y = 7 is consistent, then the
g of a is equal to
140.

avalue
(A) 0
(B) −1
(C) 1
(D) 2

m
1 2 22

co
141. Sum of the series 1 + + + + ... + ∞ is

.
2! 3! 4!

s em
a
(A) e2

g l
a
1 2
(B)
2
(
e +1 )
1 2
(C)
4
(
e +1 )
(D) e2 − 1

m
c. o
1 − 2 x − x2
The coefficient of x k in the expansion of
m
142. is

c. o
e− x

e m
em
1− k − k 2
l a s
las ag
(A)
k!

ag (B)
2
k +1
k!
1− k
(C)
k!
1
(D)
k!

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

143. A binary relation ρ , defined in R by x ρ y if 1 + xy > 0 for x, y ∈ R, is

(A) reflexive and symmetric
(B) an equivalence relation
(C) symmetric and transitive
(D) only transitive

144. Three natural numbers are taken at random from the set A = { x |1 ≤ x ≤ 100, x ∈ N } .
The probability that the AM of the numbers taken is 15, is
44
C42
(A) 100
C3
15
C2
(B) 100
C3
44
C42
(C) 100
C15
15
C2
(D) 100
C15

145. Probability of getting positive integral roots of the equation x 2 − n = 0 for the integer
n, 1 ≤ n ≤ 40 is

1
(A)
5
1
(B)
10
3
(C)
20
1
(D)
20

π
146. The value of 2 + 2 + 2 + 2 cos8θ where 0 < θ < , is equal to
8

(A) cos θ
(B) 2 cos θ
(C) 2sin θ
(D) −2 cos θ

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 30 of 51

m
m c. o
c. o

e m
em l a s
s a g
147. If f ( x) = cos x ( sin x + sin x + sin θ ) , where θ is a constant, then the maximum
2 2

value of f ( x) is

(A) 1 − cos 2 θ
(B) 1 + sin 2 θ

m
m .co
(C) cos θ
(D) sin θ
.co s e m
e m la
a s
148. If fl( x) = sin x + cos x, then the range of f ( x) is a g
ag
6 6

 5
(A) 1, 4 

1 3
(B)  4 , 4 

3 5
m
co
(C)  4 , 4 

.
em
1 
 4 ,1
a s
(D)

g l
a 1 1 z
149. Let x = cos 55°, y = cos 65° and z = cos175°. Then + + =
x y xy

(A) −1
(B) 1
(C) 0

m
(D) ∞

m If A, B and C are angles of a triangle such that angle A is obtuse, then c o
.tan B ⋅ tan C
c. o150. will s e m
em l a
s g
be less than

l a a
ag
1
(A)
3

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

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 31 of 51

a b π
151. If tan −1   + tan −1   = , then x is equal to
 x  x 2

(A) a 2b
(B) 2ab
(C) 2ab
(D) ab

x2 − 1
152. Let o be the origin and p (α , β ) where α is the least value of and
x2 + 1
1
β =∫ ( x − [ x ]) dx . Then op =
−1

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

153. The equation to the line touching both the parabolas y 2 = 4 x and x 2 = −32 y is

(A) x − 2y + 3 = 0
(B) x − 4y + 2 = 0
(C) x − 2y + 4 = 0
(D) x − 4y + 3 = 0

 1  2   n  dy
154. Let y = 1 +  1 +  ... 1 +  and x ≠ 0. Then at x = −1 is
 x  x   x  dx

(A) (n − 1)!
(B) (−1) n (n − 1)!
(C) (−1) n n !
(D) n!

155. Let f : R → R, be defined by f ( x) = ( x + 1)2 − 1, x ≥ 1. Then f −1 ( x)

(A) does not exists as f is not one-to-one
(B) does not exists as f is not onto
(C) = −1 − x + 1
(D) = −1 + x + 1

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 32 of 51

m
m c. o
c. o

e m
em l a s
s ag
d 1 − cos x
x→0 dx ∫
156. lim dx =
x2

(A) 0
1
(B)
2

m
.co
(C) 1

m
co m
(D) ∞

m . s e
a s e g la
l by a
157. The value of k in order that f ( x) = sin x − cos x − kx + l decreases for all real values, is

g
a(A) k < 1
given

(B) k ≥1
(C) k< 2
(D) k≥ 2

m
co
3

.
158. The value of ∫ ( x − 1)( x − 2)( x − 3)dx is

s em
1

1
g l a
a
(A)
3
9
(B)
4
1
(C)
2
9

m
(D)

c. o
2

m
c. o159. A curve passing through (2,3) and satisfying t y(t ) dt = x y( x), s( xe>m0) is
m a
x

s e ∫
l
2

la a g
g
0

a (A)
x
+
y
=1
2 2

8 18
(B) xy = C

(C) x 2 + y 2 = 13
9
(D) y2 = x

m .
2

.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

160. If a + b + c = 6, then 4a + 1 + 4b + 1 + 4c + 1

(A) ≤9
(B) ≥9
(C) >9
(D) <9

161. For a, b, x, y ∈ R, the correct statement is

(A) a > b ⇒ ax > bx; x ≠ 0

(B) x > y ⇒x> y

1 1
(C) a>b⇒ >
a b
(D) a >b⇒ a+c >b+c

162. If (a + ib)5 = α + i β , then (b + ia )5 is equal to

(A) β + iα
(B) α − iβ
(C) β − iα
(D) −α − i β

5 5
 3 +i   3 −i 
163. If z =   +   , then
 2   2 

(A) Re( z ) = 0
(B) Im( z ) = 0
(C) Re( z ) > 0, Im( z ) > 0
(D) Re( z ) > 0, Im( z ) < 0

164. If z = x + iy and ' a ' is a real number such that z − ai = z + ai , then the locus of z is

(A) x-axis
(B) y-axis
(C) x = y
(D) x2 + y2 = 1

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 34 of 51

m
m c. o
c. o

e m
em l a s
s n a g
165. (
If (1 + x) 1 + x 2
)(1 + x ) ...(1 + x ) = r∑=0
4 128 r
x , then n is

(A) 255
(B) 127
(C) 60
(D) 90

m
co
m m .co
. e
166. If S n denotes the sum of n terms of an A.P., then S n+3 − 3Sn + 2 + 3S n+1 − S n is equal to

(A) 2 em
las
s
(B)la 1 a g
g 1
a(C)
2
(D) 0

167. If x ∈ R , the number of solutions of x + 1 − x − 1 = 1 , is

m
co
(A) 1
.
em
(B) 2

s
(C) 3

l a
(D) 4

a g
168. If roots of x 2 − (k − 3) x + k = 0 are such that both of them are greater than 2, then

(A) k ∈ [7, 9]
(B) k ∈ [ 7, ∞ )
(C) k ∈ [9,10 )

m
c. o
(D) k ∈ [ 7,9 )

m
c. o169. If sin α , cos α are the roots of the equation ax + bx + c = 0, c ≠ 0,sthen
e m
s em l a
2

la a g
ag (A) a + b + 2ac = 02

2
2

2
(B) b − a − 2ac = 0
(C) a 2 − b 2 − 2ac = 0
(D) a 2 − b 2 + 2ac = 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 35 of 51

170. In ∆ABC , let AB = 6 3 cm, AC = 12 cm and BC = 6 cm. Then the angle of B is

(A) 120°
(B) 60°
(C) 90°
(D) 45°

y 2 + 2 y − 11
171. For a real y, the expression takes all real values except those which lie
y −3
between m and n, then m and n are

(A) 1, 2
(B) 4, 12
(C) 4, −12
(D) −1, 4

3 7 15 31
172. The sum of first n terms of the series 1 + + + + + ... is equal to
2 4 8 16

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

173. A common tangent to 9 x 2 − 16 y 2 = 144 and x 2 + y 2 = 9 is

3 x 15
(A) y= +
7 7

2 15
(B) y=3 x+
7 7

3
(C) y=2 x + 15 7
7
2
(D) y =3 x + 15 7
7

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 36 of 51

m
m c. o
c. o

e m
em l a s
s ag
174. Which of the following functions from Z to Z is a bijection?

(A) f ( x) = x3
(B) f ( x) = x + 3
(C) f ( x) = 3x + 1

m
f ( x) = x 2 + 3

.co
(D)

m
.co s e m
e m la
175. The mean and variance of a binomial variable X are 2 and 1 respectively. The

l a s
probability that X takes values greater than 1, is
a g
g 5
a(A) 16
9
(B)
16
11
(C)
16

m
co
2

.
(D)
3

s em
g l a π
a
1
176. If cosec x, 2 cot x, 2 cosec x, where 0 < x < , are in Geometric Progression, then
2 2
x is equal to

(A) 2π
(B) π
π
(C)
2
m
m c. o
π

c. o m
(D)

e
3

em l a s
las ag
ag

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

177. If A and B are two independent events of an experiment such that P( A ∪ B) = 0.6 and
P(A) = 0.3, then P(B) =

1
(A)
10
4
(B)
10
3
(C)
10
2
(D)
10

178. The sum of the focal distances from any point on the ellipse 9 x 2 + 16 y 2 = 144 is

(A) 32
(B) 18
(C) 16
(D) 8

179. The vertex of the parabola whose parametric equations are
x = t 2 + 1, y = t + 1 t ∈ ℝ is

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

4 2
180. For all real numbers of x, the value of cos x + sin x lies in the interval

(A) (1, 2)
(B) [1, 2]
3 
(C)  4 ,1

5 
(D)  4 , 2 

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 38 of 51

m
m c. o
c. o

e m
em l a s
s 20 ag
n
181. Let tn = . Then ∑ tn is equal to
(n + 1)! n =1

20!− 1
(A)
20!
21!− 1

m
(B)

.co
21!

m
co m
1
. s e
(C)

m la
2(n − 1)!

s e1 g
a
l 2(n + 1)! a
ag
(D)

∂z
182. If x x y y z z = a, then is equal to
∂x

 1 + log x 
(A) − 
 1 + log z 

m
. co
 1 + log x 

em
(B)  
 1 + log z 

l a s
g
 1 − log x 

a
(C) − 
 1 − log z 
 1 − log x 
(D)  
 1 − log z 

  x +1  −1  x  
183. The value of lim x  tan −1   − tan    equals
x→∞   x+2  x + 2 
m
m c. o
c. o m
(A) 1

s e
em
(B) −1

s
1
l a
la ag
(C) −

g
2

a
1
(D)
2

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

x x −x
184. The number of real roots of sin(e ) = 5 + 5 is

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

2
185. Let B be a matrix such that B = B and let A = I − B. Then
2
(A) A = A
2
(B) A = I
(C) AB ≠ 0
(D) BA ≠ 0

186. Two dice are thrown n times in succession. The probability of obtaining a double six
at least once is
n
 1 
(A)  
 36 
n
1
(B)  
 12 
n
1
(C) 1−  
 12 
n
 35 
(D) 1 −  
 36 

187. The unit vector in ZOX plane makes an angle 60° and 45° with a = ˆj − kˆ and
b = 2iˆ + 2 ˆj − kˆ respectively. Then the unit vector is

1 ˆ 1 ˆ
(A) i+ k
2 2
1 ˆ 4 ˆ 1 ˆ
(B) i+ j+ k
3 2 3 2 3 2
1 ˆ 1 ˆ
(C) i− k
2 2
1 ˆ 1 ˆ
(D) j− k
2 2

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

m
m c. o
c. o

e m
em l a s
s agare at
z −1
188. The singularities of the analytic function f ( z ) = 2
z +1

(A) i and −i
(B) 1 and −i
(C) 1 and i
(D) 1 and −1

m
co
m m .co
. e
189. A coin is tossed independently four times. The probability of the event “the number of

e m
times head shown up is greater than the number of times tail shown up” is
las
(A)l a s a g
ag 16
5

1
(B)
16
1
(C)
8
1

m
(D)

c. o
4

s emvalue of z + z − 2i is
la
190. For any complex number z, the minimum

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

191. The rank of a 3 × 3 matrix Z = XY, found by multiplying a non-zero column matrix X
of size 3 × 1 and a non-zero row matrix Y of size 1 × 3, is
m
m c. o
c. o
(A) 0

e m
(B) 1

em
(C) 2
l a s
las ag
(D) 3

ag

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

192. A box contains 2 pens, 3 pencils and 4 chocolates. Items are drawn from the box at
random one at a time without replacement. The probability of drawing 2 pens first
followed by 3 pencils and subsequently the 4 chocolates is

2
(A)
315
1
(B)
630
1
(C)
1260
1
(D)
2520

193. A mapping is selected at random from the set of all the mappings of the set
A = {1, 2,..., n} into itself. The probability that the mapping selected is an injection is

1
(A)
nn
1
(B)
n!
(n − 1)!
(C)
n n−1
n!
(D)
n n−1

194. If the graph of the function f ( x) has a unique tangent at the point (a, 0), then

lim log
(1 + 6 f ( x) ) is
x →a 3 f ( x)

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

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 42 of 51

m
m c. o
c. o

e m
em l a s
s ag
195. If a and b are roots of the equation y 2 − 2 y + 4 = 0 . Then a 6 + b3 =

A) 60
(B) 56
(C) 128
(D) 256

m
m .co
196. If the equation sin 4 x + a sin 4 x + 1 = 0 has a solution, then a lies in

( −∞, −.2c)o e m
em, 2) las
(A)

s g
(C)la ( 2, ∞ ) a
(B) ( −∞

g
a(D) ( −2, ∞ )

197. Let ω be the cube root of unity. The number of complex numbers satisfying the
system of equations z 3 + ω 7 = 0 and z 5 + ω11 = 1 is

m
(A) 2

. co
(B) 1

em
(C) 0

s
(D) 4

g l a
198. a
Let f ( x) =  x3 − 3 , where [.] denotes the greatest integer function. Then the number

of points in the interval (1, 2) where f ( x ) is discontinuous, is

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

m
(D) 5

m c. o
c. o199. If ∫ f ( x)dx = f ( x), then ∫ ( f ( x) ) dx is equal to
2

s e m
s em l a
gl a 1
ag
a
2
(A) ( f ( x) )
2
2
(B) ( f ( x) )
1 3
(C) ( f ( x) )
3
(D) 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 43 of 51

200. If the sum of the distance of a point to two perpendicular lines in a plane is 1, then its
locus is

(A) square
(B) circle
(C) straight line
(D) two intersecting lines

x2 y2
201. Equation + = 1 represents an ellipse if
k k −1

(A) 0<k<1
(B) k>1
(C) k < 0 or k > 1
(D) 1<k<2

202. The least value of cosec 2θ + 36sec2 θ is

(A) 36
(B) 40
(C) 49
(D) 72

203. If f ( x) is an odd periodic function with period 2, then f (4) equals

(A) −4
(B) 4
(C) 2
(D) 0

204. If A is symmetric as well as skew symmetric matrix, then A is

(A) diagonal
(B) null
(C) upper triangular
(D) lower triangular

205. The number of divisors of 9600 including 1 and 9600 are

(A) 60
(B) 58
(C) 48
(D) 46

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 44 of 51

m
m c. o
c. o

e m
em l a s
s 2 2 ag
206. The minimum value of 4sin x + 4cos x is

(A) 4
(B) 5
(C) 1
(D) 8

m
m .co
If A = { x is a prime number and < 30} , then the number of rational numbers whose

co
207.

. e m
s
numerator and denominator belong to A is

eP m la
(A)
l a s
10

a g
ag
2
10
(B) P2 + 1
10
(C) P2 − 1
10
(D) P2 + 2

208. The number of non negative integer solutions of x + y + z = 10 is

m
co
12
(A) C2
.
em
12
(B) C4

l a s
g
10
(C) C3
(D) 11
C3 a
209. There are two bags one of which contains 3 black and 4 white balls while the other
contains 4 black and 3 white balls. A die is cast. If the face 1 or 3 turns up with, a ball
is taken from the first bag and if any other face turn up with, a ball is chosen from the
second bag. The probability of choosing a black ball is

m
m c. o
13

c. o m
(A)

e
21

em l a s
s
11

la ag
(B)

g
31

a (C)
11
21
16
(D)
21

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

210. If a = 99100 and b = 10099 , then

(A) a>b
(B) a=b
(C) a<b
100
(D) a + 2b = 101

211. The points A(2, 3), B(3, 5), C(7, 7) and D(4, 5) are such that

(A) ABCD is a parallelogram
(B) A, B, C, D are colinear
(C) D lies inside the triangle ABC
(D) D lies on the boundary of the triangle ABC

212. The value of log ( tan1) ⋅ log ( tan 2 ) ⋅⋅⋅ log ( tan 89 ) =

(A) 0
(B) −1
(C) 2
(D) −2

213. If a is an integer lying in [−5, 30] , then the probability that the graph of
y = x 2 + 2(a + 4) x − 5a + 64 is strictly above the x-axis is

1
(A)
6
7
(B)
36
2
(C)
9
3
(D)
5

214. Equation of the tangent to the circle with centre (2, −1) is 3x + y = 0 . The square of
the length of the tangent to the circle from the point (23, 17) is

(A) 1354
(B) 1452
(C) 1320
(D) 1525

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

m
m c. o
c. o

em
em l a s
s 2 ag
215. If p and q are distinct primes and x − px + q = 0 has distinct positive integral roots,
then p + q equals,

(A) 5
(B) 7
(C) 19
(D) 40

m
c o m = m .co
2 + 2 + 2. + 2 cos 4x e
2

em s
216.

s g la
g la sec  x  a
a(A)
2
(B) sec x
(C) cosec x
(D) 1

om
−1  1 + x
2

c
π

.
217. The number of solutions of the equation sin   = ( sec( x − 1) ) is

em
 2x  2

l a s
g
(A) 0

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

218. If the system of linear equations x + y + z = 6, x + 2 y + 3 z = 14 and
2 x + 5 y + λ z = µ , (λ , µ ∈ ℝ ) has a unique solution, then

m
(A) λ ≠8

m c. o
(B) λ = 8, µ ≠ 36

c. o e m
(C) λ = 8, µ = 36

em
(D) λ ≠ 8, µ = 36
l a s
las a g
ag 1 3cos x 1
219. If f ( x) = sin x 1 3cos x , the maximum value of f ( x) is
1 sin x 1

(A) 10
(B) 11
(C) 6

m .
(D) 7

.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

220. If A is a 3 × 3 matrix such that A ' A = I and A = 1, then the value of A − I is

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

221. Let p be a prime number such that p ≥ 23. Let n = p! + 1. The number of primes in the
list n + 1, n + 2, n + 3,..., n + p − 1 is

(A) p − 1
(B) 2
(C) 1
(D) 0

222. If a = b, c ∈ ℝ and b 2 > c, then zz + az + bz + c = 0 represents

(A) a circle
(B) a parabola
(C) a straight line
(D) a hyperbola

223. If the slope of one of the lines given by 36 x 2 + 2hxy + 72 y 2 = 0 is four times the
other, then the value of h 2 is equal to

(A) 4050
(B) 4020
(C) 3040
(D) 3050

224. If F1 = (3, 0), F2 = (−3, 0) and P is any point on the curve 16 x 2 + 25 y 2 = 400, then
PF1 + PF2 equals

(A) 8
(B) 6
(C) 10
(D) 12

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
225. If α and β are the roots of x 2 + x + 1 = 0 , then α 2020 + β 2020 is

(A) −2
(B) −1
(C) 1
(D) 2

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

Subject Name: 101 B TECH 12 MAY 2024 - S2 Subject Name: 101 B TECH 12 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 C 31 A 61 D 91 A 121 C 151 D 181 B 211 C
2 D 32 C 62 B 92 B 122 C 152 C 182 A 212 A
3 B 33 B 63 D 93 A 123 B 153 C 183 D 213 C
4 D 34 B 64 C 94 A 124 D 154 B 184 A 214 D
5 D 35 A 65 A 95 C 125 B 155 D 185 A 215 A
6 C 36 C 66 D 96 B 126 A 156 B 186 D 216 A
7 C 37 C 67 C 97 C 127 A 157 D 187 C 217 B
8 D 38 C 68 A 98 B 128 D 158 C 188 A 218 A
9 A 39 C 69 B 99 A 129 B 159 B 189 A 219 A
10 D 40 D 70 C 100 D 130 A 160 A 190 A 220 C
11 A 41 C 71 C 101 B 131 A 161 D 191 B 221 D
12 D 42 B 72 C 102 B 132 D 162 A 192 C 222 A
13 B 43 B 73 C 103 D 133 B 163 B 193 C 223 A
14 A 44 A 74 D 104 B 134 A 164 A 194 C 224 C
15 C 45 D 75 B 105 C 135 D 165 A 195 B 225 B
16 D 46 D 76 A 106 D 136 D 166 D 196 A

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
17 B 47 C 77 D 107 B 137 C 167 A 197 A
18 A 48 C 78 C 108 D 138 B 168 C 198 C
m199
om . co
19 A 49 B 79 A 109 D 139 D 169 D A
20om .c 110 Cem
s
c m a
m. se l
C 50 B 80 D C 140 D 170 200 A
la g B
l a se 21 D 51 C 81
a gC 111 D 141 C 171 a 201 B
ag 22 A 52 D 82 A 112 C 142 A 172 D 202 C
23 A 53 D 83 C 113 B 143 A 173 B 203 D

m
24 C 54 C 84 C 114 C 144 A 174 B 204 B
o
m
o145 C m.c
om .c se
25 A 55 D 85 C 115 D C 175 C 205
. c C se
m l a
em56
s la ag
26 D B 86 C 116 146 B 176 D 206 A
g
D gla 57 a
27
a D 87 A 117 B 147 B 177 C 207 B
28 C 58 A 88 C 118 A 148 D 178 D 208 A
29 B 59 C 89 D 119 B 149 C 179 C 209 C
m
om co
m.
30 D 60 A 90 A 120 C 150 C 180 C 210 A
m . c e
.co s em l as
s em g la ag
l a a
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