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

FOR CUSAT CAT EXAM PREPARATION

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

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

Notes · Sample Papers · Previous Year Papers · Mock Tests

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1. The intensity of radiation emitted by sun is maximum for the wavelength of 560 nm
and that emitted by a star is maximum for the wavelength of 350 nm. If the average
temperature of the sun is 2 × 107 K, the temperature of the star is

(A) 3.2 × 107K
(B) 4.3 × 106K
m
(C) 3.2 × 106K
m .co
(D) 5.4 × 107K .co s e m
s em l a
2. Agmass ag
la m is suspended from a spring of negligible mass and the system oscillates
awith a frequency f1 . The frequency of oscillations is f2 when a mass 16 m is
f
suspended from the same spring. The value of 1 is
f2

(A) 1 :16
(B) 1:4
(C) 4:1
m
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(D) 1 : 32

e m
3.
las
A capacitor of capacitance C has reactance Xc. If capacitance and frequency become

ag
double, then the capacitive reactance will be

(A) 2Xc
(B) 4Xc
Xc
(C)
2
Xc
(D)
4
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a

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4. A solid sphere of radius R and mass M is rotating about its diameter. A solid cylinder
of same mass and same radius is also rotating about its geometrical axis with an
angular speed twice that of the sphere. The ratio of their kinetic energies of rotation
KE sphere
will be
KE cylinder

(A) 3:1
(B) 2:3
(C) 1:5
(D) 1:4

5. Two particles of the same mass are revolving with the same speed on circular paths of
radii r1 and r2. The ratio of their centripetal forces will be

r1
(A)
r2

r2
(B)
r1
2
 r1 
(C)  
 r2 
2
 r2 
(D)  
 r1 

6. A child stands at the centre of a turntable with two arms outstretched. The turntable is
set rotating with an angular speed of 40 rev/min. If he holds his hand back and
2
thereby reduces his moment of inertia to times the initial value, and the turntable
5
rotates without the friction, the angular speed of the child is

(A) 100 rev/min
(B) 80 rev/min
(C) 40 rev/min
(D) 16 rev/min

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7. a to uniform pressure P,
The bulk modulus of a spherical object is B. If it is subjected
the fractional decrease in radius is

P
(A)
B
B
(B)
3P
m
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3P
(C)
o m m
B
Pm
. c s e
s e l a
ag
(D)

g l a 3B

a
8. The dimension and unit of coefficient of viscosity is

(A) [ML−1T −1] and poise
(B) [ML−1T −2] and poise
(C) [ML−2T −2] and newton
(D) [ML−1T −2] and newton

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9.
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A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If
m
e
the radius were halved and the temperature doubled, the power radiated in watt would
s
be
g la
(A) 450 a
(B) 900
(C) 1800
(D) 225

10. The number of degrees of freedom of a rigid diatomic molecule is

(A) 2
m
m (B) 3
.co
m .co (C)
(D)
4
5 s e m
s e g l a
g la a
a

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11. Two springs of force constant k1 and k2 are attached to mass m as shown. The time
period of the oscillation is

1 m
(A)
2π k
m(k1 + k2 )
(B) 2π
k1 + k2

m
(C) 2π
k1 + k2

1 m(k1 + k2 )
(D)
2π k1 + k2

π
12. In a circuit the current lags behind the voltage by a phase difference of . The circuit
2
contains which of the following?

(A) only R
(B) only L
(C) only C
(D) R and C

13. Four metal conductors having different shapes: (i) a sphere, (ii) a cylinder (iii) a
pear (iv) a lightning conductor are mounted on an insulating stands and charged.
The one which is best suited to retain the charges for a longer time is

(A) sphere
(B) cylinder
(C) pear
(D) lightning conductor

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14. a are raised to the same potential.
A solid sphere and a hollow sphere of equal diameters
Then

(A) hollow sphere has more charge
(B) both have equal charge
(C) only hollow sphere has charge
(D) solid sphere has more charge

m
15.
m
The free electrons of a copper wire of cross sectional area 10−6m2 acquire a drift
.co
.co
velocity of 10−4 m/sec when a certain potential difference is applied across the wire. If
s e m
em
the density of free electrons in copper is 8.5 × 1028 electrons/m3, then current flowing
s l a
la
in the wire is
g ag
a(A) 1.36 A
(B) 2.45 A
(C) 3.65 A
(D) 13.6 A

16. If two identical heaters each rated as 1000 W, 220 V are connected in parallel to
220 V, then the total power consumed is
m
(A) 200 W
m .co
(B) 250 W
s e
la
(C) 2000 W
(D) 2500 W
ag
17. The emf E (in volts) of a certain thermocouple is found to vary with
θ2
θ (in °C) according to the equation E = 20θ − , where θ is the temperature of the
20
hot function, the cold function being kept at 0°C. Then, the neutral temperature of the
thermocouple is
m
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(A) 300°C
m
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(B) 100°C

m (C) 340°C
s e
s e (D) 200°C
g l a
g la a
a

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18. A solenoid coil of 300 turns/m is carrying a current of 5 A. The length of the solenoid
is 0.5 m and has a radius of 1 cm. The magnitude of the magnetic field inside the
solenoid is

(A) 1.9 × 10−3 T
(B) 4.5 × 10−3 T
(C) 2.3 × 10−3 T
(D) 3.2 × 10−3 T

19. Magnetic field at the centre of a current carrying circular loop having 1 A current and
number of turns one (radius of the loop is 1 m) will be

2
(A)

(B) 2µ o

4
(C)

(D) 4µ o

20. A substance has a critical angle of 45° for yellow light. Then its refractive index is

(A) 2
1
(B)
2

3
(C)
2
1
(D)
2

21. The β particle is emitted from the nucleus of mass number A with velocity v, then the
recoil speed of nucleus will be

−
(A)

4
+4
(B)

(C)
4
(D) −4

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22. a was first established by
The existence of positively charged nucleus in an atom

(A) Bohr’s theory of hydrogen atom
(B) Positive rays analysis
(C) α-particle scattering experiment
(D) Thomson’s model of atom

23. A photocell is illuminated by a small bright source placed 1 m away. When the source
m
m
of light is placed 0.5 m away, the number of electrons emitted by photo cathode
.co
would
.co s e m
s em by a factor of 4 l a
laincrease ag
(A) decrease
g
(B) by a factor of 4
a increase byby aa factor
(C) decrease factor of 2
(D) of 2

24. Which of the phenomena is not common to sound and light waves?

(A) Interference
(B) Diffraction
(C) Coherence
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(D) Polarisation

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25.
las
Suppose the number of turns in a coil be tripled, the value of magnetic flux linked
with it
ag
(A) remains unchanged
1
(B) becomes
3
(C) is tripled
(D) None of the above

o m
m c
. of 1 cm
c. o26. Two m
−10
equal and opposite charges of 2 × 10 C are placed at a distance
m forming a dipole and are placed in an electric field of 2 × 10 s e The maximum 5

s e g l a N/C.

l a torque on dipole is
a
ag (A) 2 2 × 10−6 Nm
(B) 4 × 10−9 Nm
(C) 8 × 108 Nm
(D) 4 × 10−7 Nm

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27. Three vessels A, B and C of different shapes contain a water up to the same height as
shown in the figure. PA, PB and PC be the pressures exerted by the water at the
bottom of the vessels A, B and C respectively. Then

(A) PA > PB > PC
(B) PB > PC > PA
(C) PC > PB > PA
(D) PA = PB = PC

28. The length of a metallic rod is 5 m at 0°C and becomes 5.01 m, on heating up to
100°C. The linear expansion of the metal will be

(A) 2.33 × 10−5/∘C
(B) 6.0 × 10−5/∘C
(C) 4.0 × 10−5/∘C
(D) 2.0 × 10−5/∘C

29. A Carnot engine absorbs 750 J of heat energy from a reservoir at 137°C and rejects
500 J of heat during each cycle, then the temperature of sink is

(A) 0.25°C
(B) 0.34°C
(C) 0.44°C
(D) 0.54°C
30. An alternating voltage E (in V) = 200 2 sin (100 t) is applied to a 1 µ F capacitor
through an AC ammeter. Then the ammeter will read a current of

(A) 10 mA
(B) 20 mA
(C) 40 mA
(D) 80 mA

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31. To establish an instantaneous current of 2 A through a
a 1 µF capacitor; the potential
difference across the capacitor plates should be changed at the rate of

(A) 2 × 104 V/s
(B) 4 × 106 V/s
(C) 2 × 106 V/s
(D) 4 × 104 V/s
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32. .co
A 90 pF capacitor is connected to a 12 V battery. How many electrons are transferred
s e m
s em
from one plate to another?
l a
g la1.1 × 109 ag
a(B)
(A)
9
6.7 × 10
(C) 4 × 1019
(D) 5 × 1019

33. A small angle prism (µ = 1.62) gives a deviation of 4.8°. The angle of prism is

m
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(A) 5°
(B) 6.36°
e m
(C)
(D)
3°
las
7.74°
ag
34. A proton, a neutron, an electron and an α -particle have same energy. Then their de-
Broglie wavelengths compare as

(A) λp = λn > λe > λα
(B) λα < λp = λn < λe
(C) λe < λp = λn > λα
m
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(D) λe = λp > λn > λα
m
m .co s e m
s e g l a
g la 35. According to wave theory, time required for photo emissionais
a
(A) less than 10s
(B) around 10−9s
(C) around 1s
(D) around few hours

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36. A black body is at a temperature of 300 K. It radiates energy at a rate proportional to

(A) 300
(B) (300)2
(C) (300)3
(D) (300)4

37. Range of frequencies allotted for commercial FM radio broadcast is

(A) 88 to 108 MHz
(B) 88 to 108 KHz
(C) 8 to 88 MHz
(D) 88 to 108 GHz

38. For an AM wave, the maximum voltage was found to be 10V and minimum voltage
was 4V. The modulation index of the wave is

(A) 0.33
(B) 0.43
(C) 0.56
(D) 0.64

39. A disc is rotating with angular velocity ω. If a child sits on it, what is conserved ?

(A) Linear momentum
(B) Angular momentum
(C) Kinetic energy
(D) Moment of inertia

40. Two astronauts are floating in gravitational free space after having lost contact with
their spaceship. The two will

(A) keep floating at the same distance between them
(B) move towards each other
(C) move away from each other
(D) will become stationary

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41. The acceleration duee to gravity on the planet A isa9 times the acceleration
a due to
gravity on the planet B. A man jumps to a height of 2 m on the sur
surface of A. What is
the height of jump byy the
t same person on the planet B?

(A) 6 m
2
(B) m
3
m
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2
(C) m
o m m
9
. c s e
(D) 18 m
s em g l a
l a a
42. aInga guitar, two stringngs A and B made of same material are slighthtly out of tune and
produce beats of frequ
quency 6 Hz. When tension in B is slightlyy decreased,
d the beat
frequency increases to 7 Hz. If the frequency of A is 530 Hz, the or
original frequency of
B will be

(A) 524 Hz
(B) 536 Hz
(C) 537 Hz
(D) 523 Hz m
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s e
la
43. The variation of elect
ctrostatic potential with radial distance r from
fro the centre of a
positively charged met
g
etallic thin shell of radius R is given by the gra
a
raph

(A)

(B)
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m .co s e m
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g la (C) a
a

(D)

m .
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g la ag
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44. A capacitor of 2 µF is charged
c as shown in the figure. When the sw
witch S is turned to
position 2, the percenta
ntage of its stored energy dissipated is

(A) 20%
(B) 75%
(C) 80%
(D) 0%

45. Energy in a current car
arrying coil is stored in the form of

(A) electric field
(B) magnetic field
(C) dielectric streng
ngth
(D) heat

46. A step down transformormer connected to an AC mains supply off 220 V is made to
operate at 11 V, 44 W lamp. Ignoring power losses in the transf
sformer, what is the
current in the primaryy circuit?

(A) 0.2 A
(B) 0.4 A
(C) 2A
(D) 4A

47. An electron is accelera
erated from rest through a potential difference
ce of V volt. If the
−2
de-Broglie wavelengthth of the electron is 1.227 ×10 nm, the potent
ntial difference is

(A) 102 V
(B) 103 V
(C) 104 V
(D) 10 V

48. The spectrum obtained
ed from a sodium vapour lamp is an example of
o

(A) band spectrum
(B) continuous spec
ectrum
(C) emission spectru
trum
(D) absorption spect
ectrum

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49. A solenoid of inductance = 2H is connected to a
a battery. If the current changes
uniformly at the rate of 5 A/s, what is the EMF induced in the solenoid?

(A) 2V
(B) 5V
(C) 10 V
(D) 20 V

m
50.
m
A plane electromagnetic wave has an electric field amplitude E0 = 300 V/m and
.co
.co
propagates in free space. What is the amplitude of the magnetic field (B0) associated
s e m
em
with the wave?
s l a
(A)la 0.5 × 10 T
g 1 × 10 T
−6 ag
a(B) −6

(C) 1.5 × 10−6 T
(D) 2 × 10−6 T

51. Which of the following phenomena cannot be explained by the wave theory of light?

(A) Diffraction
(B) Interference
m
(C) Polarization
.co
em
(D) Photoelectric effect

la s
The work function of a metal isg4.5 eV. When monochromatic light with a wavelength
52.
a
of 200 nm strikes the metal surface, what is the maximum kinetic energy of the
emitted photoelectrons?

(A) 1.1 eV
(B) 1.7 eV
(C) 2.1 eV
(D) 2.7 eV

o m
m What prevents protons in a nucleus from collapsing together despite the c
.short-range
c. o nuclear attraction?
53.
e m
e m l as
l as (A) Pauli exclusion principle
a g
ag (B) Coulomb repulsion
(C) Quantum mechanical zero-point energy
(D) Shell model of the nucleus

m .
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g la ag
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54. What is the main purpose of doping a semiconductor material?

(A) Increase its resistance
(B) Enhance its conductivity
(C) Reduce its melting point
(D) Increase its hardness

55. A signal is transmitted through an optical fiber with a refractive index of n = 1. If the
length of the fiber is 10 km, what is the time taken for the signal to travel through it?

(A) 33.3 µs
(B) 51.3 µs
(C) 63.3 µs
(D) 70 µs

56. The electromagnetic waves travel in a medium at a speed of 2.0 × 108 m/s. The
relative permeability of the medium is 1.0. The relative permittivity of the medium
will be

(A) 2.25
(B) 4.25
(C) 6.25
(D) 8.25

57. A microscope is focused on an object at the bottom of a bucket. If liquid with
refractive index is poured inside the bucket, the microscope have to raised by 30 cm
to focus the object again. The height of the liquid in the bucket is

(A) 75 cm
(B) 50 cm
(C) 18 cm
(D) 12 cm

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58. a V has a de-Broglie wavelength
An electron accelerated through a potential difference 1
of λ. When the potential is changed to V2, its de-Broglie wavelength increases by
V 
50%. The value of  1  is equal to
V 
 2

(A) 3
9
m
.co
(B)
4
m
3
m .co s e m
(C)
s2e l a
a
(D)l 4 ag
ag
59. Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes,
respectively. Initially, the samples have equal number to nuclei. After 80 minutes, the
ratio of decayed numbers of A and B nuclei will be

(A) 1 : 16
(B) 4:1
(C) 1:4
m
(D) 5:4
.co
s em
60.
l
If an emitter current is changed by
g a 4 mA, the collector current changes by 3.5 mA.
The value of β will be a
(A) 7
(B) 0.5
(C) 0.875
(D) 3.5

61. In a cuboid of dimension 2L × 2L × L, a charge q is placed at the centre of the surface
m
.co
‘S’ having area of 4 L2. The flux through the opposite surface to ‘S’ is given by
m
m .co 12ɛ s e m
s e
(A)
g l a
g la (B)
3ɛ
a
a
2ɛ
(C)

6ɛ
(D)

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

62. A galvanometer havin ing a coil resistance 100 Ω gives a full- scale
le deflection when a
current of mA is pas assed through it. What is the value of the resistance
res which can
convert this galvanome
meter into a voltmeter giving full-scale deflec
ection for a potential
difference of 10 V ?

(A) 9.9 kΩ
(B) 8.9 kΩ
(C) 7.9 kΩ
(D) 10 kΩ

63. The resistive networkk shown
s below is connected to a D.C source pf 16 V. The power
consumed by the netwowork is 4 Watt. The value of R is

(A) 8Ω
(B) 6Ω
(C) 1Ω
(D) 16 Ω

64. A magnetic needle of magnetic moment 6.7 × 10−2 Am2 and moment mo of inertia
−6 2
7.5×10 kg m is perf erforming simple harmonic oscillations in a m
magnetic field of
0.01 T. Time taken for
or 10 complete associations is

(A) 6.98 s
(B) 8.76 s
(C) 6.65 s
(D) 8.89 s

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65. The AC current is given by I = I sin ωt + cos ωt. Aahot wire ammeter will give a
1
reading

−
2
(A)

+
(B)
2 m
+
m .co
.co s e m
e√2+m
(C)
s l a
g
(D)la 2√2 ag
a
66. Which of the following physical quantities have the same dimensions?

(A) Electronic displacement (D) and surface charge density
(B) Displacement current and electric field
(C) Current density and surface charge density
(D) Electric potential and energy
m
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67.
e
A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by
s
la
a distance of 80 cm with a constant velocity. Calculate the work done by the porter in
g
a
lowering the suitcase. ( take g = 9.8 ms−2 )

(A) -62720.0 J
(B) -627.2 J
(C) +627.2 J
(D) +784.0 J

68. Moment of inertia of square plate of side l about the axis passing through one of the
m
.co
corner and perpendicular to the plane of square plate is given by
m
m .co Ml 2
s e m
s e
(A)
6
g l a
g la 2 2 a
a (B)
3
Ml

(C) Ml 2
Ml 2
(D)
12

m .
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s em l a
g la ag
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69. The time period of satellite, revolving above earth’s surface at a height equal to R will
be ( given G = π2m/s2, R = radius of earth )

(A) √4
(B) √8
(C) √32
(D) √2

70. A hydraulic automobile lift is designed to lift vehicles of mass 5000 kg. The area of
cross section of the cylinder carrying the Load is 250 cm2. The maximum pressure the
smaller piston would have to bear is [ Assuming g = 10 m/s2 ]

(A) 2 × 105 Pa
(B) 200 × 106 Pa
(C) 20 × 106 Pa
(D) 2 × 106 Pa

71. If two similar springs each of spring constant K are joined in series, the new spring
constant and time period (T) would be changed by a factor

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

72. A certain charge Q is divided into two parts q and (Q – q). How should the charges Q
and q be divided so that q and (Q – q) placed at a certain distance apart experience
maximum electrostatic repulsion ?

q
(A) Q =
2
(B) Q = 2q
(C) Q = 4q
(D) Q = 3q

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73. a 5 m/s along the curve from
A particle of mass 20 g is released with an initial velocity
the point A as shown in the figure. The point A is at height h from the point B. The
particle slides along the frictionless surface. When the particle reaches point B, its
angular momentum about O will be

m
m .co
.co s e m
s em l a
g la8 kg-m /s ag
a(B) 6 kg-m /s
2
(A)
2

(C) 3 kg-m2/s
(D) 2 kg-m2/s

1 th
74. A body sliding down on a smooth inclined plane, slides of its distance in 2 s. The
4
time required for sliding the complete plane is
m
(A) 4s
m .co
(B) 2s
s e
(C) 5s
g la
(D) 3s
a
75. The ratio of magnitude of displacement to distance for a moving object is always

(A) equal to 1
(B) greater than 1
(C) less than 1
(D) less than or equal to 1

o m
m thermochemical process, 500 J of heat is absorbed by a system and c
.250 J of work
c. o76. isIn adone s
m
e entire process is
e m a
by the system. The change in internal energy during the
l
l as ……..
a g
ag (A) +750 J
(B) +250 J
(C) -250 J
(D) -750 J

m .
.co s e m
s em l a
g la ag
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77. Spontaneous adsorption of gas molecules on solid surfaces is an exothermic process
because of …………………

(A) Increase in enthalpy
(B) Increase in entropy
(C) Decrease in entropy
(D) Decrease in enthalpy

78. Which of the following condition favors formation of ammonia in Haber Process?

(A) High Temperature and High Pressure
(B) Low Temperature and Low Pressure
(C) Low Temperature and High Pressure
(D) High Temperature and Low Pressure

79. The exhaust of a car shows a carbonmonoxide (CO) emission of 400 ppm. The
concentration of CO per Liter of exhaust is ………….

(A) 0.004 mL
(B) 0.04 mL
(C) 0.4 mL
(D) 4.0 mL

80. During an experiment on observing depression in freezing point of an organic solvent
(5g) by the addition of an non-volatile, non-electrolytic miscible solute (weight = 0.5
g), depression of freezing point 5 oC was observed. Molal depression constant of the
pure solvent is 7.0 K. Kg.mol-1. The molecular weight of the solute is ………….g/mol

(A) 280
(B) 210
(C) 140
(D) 70

81. The mass of Cu deposited on cathode during electrolysis when 268 milli-amperes
(268 mA) of current was passed through a Faradaic cell containing a Cu cathode in
saturated CuSO4 solution for 1 hour is ……….. (atomic weight of Cu is 63.546 u)

(A) 415 mg
(B) 315 mg
(C) 215 mg
(D) 115 mg

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m
m .co

m .co s em
se g la
82. a equation for a second order
Which of the following graph represents integrated rate
reaction? [A is the reactant]
The image cannot be display ed. Your computer may not hav e enough memory to open the image, or the image may hav e been corrupted. Restart y our computer, and then open the file again. If the red x still appears, y ou may hav e to delete the image and then insert it again.

m
m .co
(A) (I)
m .co s e m
(B)
s e
(II) l a
l
(C)
g a (III)
ag
a(D) None of the above

83. Radioactive decay follows ……….. order kinetics

(A) Zero
(B) First
(C) Second
(D) Third

o m
c
. of filling the electrons in different
84.
e m
Which of the following explains the sequence
shells?
la s
(A) Aufbau principle a g
(B) Octet rule
(C) Hund’s rule
(D) All of the above

85. For the reaction H2(g) + I2(g) → 2HI(g) the change in enthalpy (∆H) will be

(A) = ∆U
m
.co
(B) > ∆U
m
.co em
(C) < ∆U

e m (D) zero
las
las g
a state the value of the
ag 86. When a catalyst is added to a reversible reaction in equilibrium
equilibrium constant

(A) increases
(B) decreases
(C) does not change
(D) becomes zero

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

87. How many gram of CaC2O4 will dissolve in one litre of saturated solution? Ksp of
CaC2O4 is 2.5 × 10–9 mol–2 and its molecular weight is 128

(A) 0.0064 g
(B) 0.0128 g
(C) 0.0032 g
(D) 0.0640 g

88. During the decomposition of H2O2 to give dioxygen, 48 g O2 is formed per minute at
certain point of time. The rate of formation of water at this point is

(A) 0.75 mol min−1
(B) 1.5 mol min−1
(C) 2.25 mol min−1
(D) 3.0 mol min−1

89. For which one of the following equilibria, Kp= Kc?

(A) 2SO2(g)+O2(g)⇌2SO3(g)
(B) C2H6(g) ⇌ C2H4(g) + H2(g)
(C) 2HI(g) ⇌ H2(g) + I2(g)
(D) N2(g) + 3H2(g)⇌ 2NH3(g)

90. The standard reduction potentials of X, Y, Z metals are 0.52, −3.03, −1.18
respectively. The order of reducing power of the corresponding metals is

(A) Y>Z>X
(B) X>Y>Z
(C) Z>Y>X
(D) Z>X>Y

91. Which of the following solutions shows positive deviation from Raoult’s law?

(A) Acetone + Aniline
(B) Acetone + Ethanol
(C) Water + Nitric acid
(D) Chloroform + Benzene

92. An element with atomic mass 100 has a bcc structure and edge length 400 pm. The
density of element is

(A) 10.37 g cm−3
(B) 5.19 g cm−3
(C) 7.29 g cm−3
(D) 2.14 g cm−3

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m
m .co

m .co s em
se g la
93. a Calculate the radius (r) of the
An element possesses cubic close packing structure.
atom in the unit cell. (The edge length of unit cell is a = 252 nm)

(A) 89.36 nm
(B) 126 nm
(C) 152 nm
(D) 109.1 nm

m
94.
m
Which of the following relationship is correct?
c o m .co
(A) 1 poise. = 1 g cm s s e
m = 10 kg m s
–1 –1

(B) 1 e
s l a
ag
–2 –1 –1
poise
(C)la 1 poise = 10 kg m s
–1 –1 –2

g 1 poise = 1 g cm s
a(D) –1 –2

95. An ideal gas is allowed to expand from 1 l to 10 l at 300 K against constant external
pressure of 1 atm. The work done is

(A) 6 kJ
(B) 6 l atm.
(C) 9 l atm.
m
(D) 9 kJ
.co
s em
96.
g la One of the two contributing structures (canonical
Formate ion is resonance stabilized.
a below. Consider other contributing structure and
forms) of formate anion is shown
answer the following question on C-O bonds marked A and B. Which C–O bond is
longer?

(A) A
m
m (B) B
.co
m .co (C) Both A and B are of equal length
s e m
s e
(D) Depends on the nature of the counter ion
g l a
g la a
a 97. The IUPAC name of the following compound is:

(A) (E)-1-cyclohexyl-2-hexene
(B) (E)-2-cyclohexyl-2-hexene
(C) (Z)-1-cyclohexyl-1-hexene
(D)
m
(Z)-2-cyclohexyl-2-hexene
.
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 23 of 51

98. Major product formed when 2-bromo-2-methylpentane is treated with NaOEt in
ethanol is (Note: under these conditions Zaitsev elimination predominates):

(A) 2-methylpent-1-ene
(B) 2-methylpent-2-ene
(C) (E)-4-methylpent-2-ene
(D) (Z)-4-methylpent-2-ene

99. Which sets of reagents would selectively give the expected product?

(A) Hg(CF3CO2)2
(B) Hg(OAc)2 in THF/H2O, NaBH4
(C) BH3, NaOH/H2O2
(D) BH3, H2O2/HO-, NaH, CH3I

100. Which among the following organic halide/halides on reaction with sodium metal
(Wurtz coupling reaction) will give n-hexane as the only product?

(A) 1:1 mixture of chloroethane and 1-chlororobutane
(B) 1:1 mixture of bromomethane and 1-bromopentane
(C) 1-bromopropane only
(D) 1-bromopropane and propene

101. Which of the following does not give a yellow precipitate with I2+NaOH?

(A) CH3CH2OH
(B) CH3OH
(C) CH3CHO
(D) CH3COCH3

102. Cyclohexanol (I), 2,4,6-trichlorophenol (II), 2,4,6-trinitrophenol (III) and 2,4,6-
trimethoxyphenol (IV) are given. In these, the order of decreasing acidic character
will be:
OH OH OH OH
Cl Cl O2N NO2 MeO OMe

Cl NO2 OMe
I II III IV

(A) III > II > IV > I
(B) II > III > I > IV
(C) II > III > IV > I
(D) III > IV > II > I

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m
m .co

m .co s e m
se g l a
a
103. Which of the following amino acid has a –CH OH residue? 2

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

104. Pick the correct statement on C-H bond distance in ethane, ethene and ethyne.
m
m .co
.co m
(A) C-H bond distance is equal in all the three compounds

m
(B) C-H bond distance in ethene is shorter than that in ethane but longer than that
s e
s e
in ethyne l a
l a
(C) C-H bond distance is shortest in ethyne and highest in ethane
g ag
a(D) C-H bond distance is shortest in ethane and highest in ethyne

105. Peptide bonds are formed by what type of linkages?

(A) ester
(B) amide
(C) urethane
(D) disulfide
o m
c
. in the industrial production of which
e m
106. Styrene (PhCH=CH ) is not used as a monomer
s
2
among the following polymers?
g la
(A) ABS a
(B) PPS
(C) SAN
(D) SBR

107. Preservative used widely in processed food is:

(A) Saccharin
m
m (B) Menthol
.co
.co m
(C) Corn starch
s e
em
(D) Sodium benzoate
s g l a
g la a
a 108. Which among the following carboxylic acid derivatives is least reactive towards
dilute NaOH solution in water?

(A) Amide
(B) Ester
(C) Acid chloride
(D) Anhydride

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

109. Arrange following carbanions in decreasing stability order.

(i) (CH3)3C-
(ii) CH3-
(iii) Benzyl anion (C6H5CH2-)
(iv) CH3COCH2-

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

110. Which among the following vitamins is considered as a steroid?

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

111. What is common for both Cannizzaro reaction and Meerwein-Pondroff-Verley
reduction?

(A) Aluminium triisopropoxide is used in both reactions
(B) Cannot be performed successfully with aromatic aldehydes
(C) Both reactions give a 1:1 mixture of the corresponding alcohol and carboxylic
acid from aliphatic aldehydes
(D) Both reactions involve hydride (H−) transfer in a key step.

112. The compound formed as a result of oxidation of ethylbenzene with alkaline KMnO4
followed by acidification is:

(A) benzyl alcohol
(B) benzophenone
(C) acetophenone
(D) benzoic acid

113. The Catalyst used for stereoregular polymerization of propene is:

(A) Ziegler-Natta catalyst
(B) Wilkinson’s catalyst
(C) Lindlar catalyst
(D) Zeise’s salt complex

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m
m .co

m .co s e m
se g l a
114. Name of following Nobel Prize winning reaction. a

(A) Claisen Condensation
(B) Diel’s Alder reaction
(C) Dieckmann cyclisation
m
.co
(D) Michael addition reaction
o m m
c
. from DNA because RNA contains s e
m
115. RNA is different
e l a
(A) as ag
g l Ribose sugar and uracil
Ribose sugar and thymine
a(C) Deoxyribose sugar and thymine
(B)

(D) Deoxyribose sugar and uracil

116. Which of the following complex ions shows geometrical isomerism?

(A) [Cr(H2O)4Cl2]+
(B) [Pt(NH3)3Cl]2─
m
.co
(C) [Co(NH3)6]3─
(D) [Co(CN)5(NC)]3─

s em
117. Which is the reason for the purplela
ag
colour of KMnO ? 4

(A) Ligand to metal charge transfer
(B) Metal to ligand charge transfer
(C) d-d transition
(D) p-d transition

118. Which of the following is a hexadentate ligand?
m
.co
(A) Ethylene diamine
m
.co m
(B) Ethylene diamine tetraacetic acid

m
(C) 1,10-phenanthroline
s e
s e (D) Acetyl acetonato
g l a
g la a
a 119. How many atoms are present in hexagonal close-packed unit cell?

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

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

120. Identify the product in the nuclear reaction 12Mg24 + 2He4 = 0n1 + …………….?
27
(A) 13Al
27
(B) 14Si
28
(C) 13Al
25
(D) 12Mg

121. What is the n/p ratio of a stable nuclides?

(A) n/p =1
(B) n/p = 2
(C) n/p > 1
(D) n/p < 1

122. Which of the following is a π-acid ligand?

(A) NH3
(B) CO
(C) F─
(D) H2O

123. Which of the following shows +7 oxidation state?

(A) Co
(B) Cr
(C) V
(D) Mn

124. A compound having molecular mass of 99 has face-centred cubic structure. Its `
density is 3.4g cm-3. The length of unit cell in Å (in Angstroms) is
(A) 6.783
(B) 5.783
(C) 7.783
(D) 8.683

125. Which of the following statements is not true?
(A) Si, Ga can be purified by zone refining
(B) Zone refining is carried out in an inert atmosphere
(C) Zinc can be refined by distillation
(D) Principle of zone refining is different from fractional crystallization

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m
m .co

m .co s e m
se g l a
126. The essential element for nitrogen fixation is a
(A) Zn
(B) Cu
(C) Co
(D) Mo

127. The ligand system present in Vitamin B12 is
m
m .co
.co m
(A) Porphyrine
(B)
m
Corrin
s e
(C)
s e
Crown ether l a
l
(D)
g a Chlorin ag
a
128. The hybridization and geometry in SF4 is

(A) sp3 - Tetrahedral
(B) dsp2 - Square planar
(C) sp3d - See-saw
(D) sp3d2 - Octahedral

m
.co
129. Which of the following has highest magnetic moment?

(A) Fe2+ e m
(B) Cr2+
las
(C)
(D)
Mn2+
Co2+ ag
130. Volume of O2 liberated from 0.96g of H2O2 at STP is

(A) 316.2 ml
(B) 224. 6 ml
(C) 613.2 ml
(D) 449.2 ml
m
m
c. o131. In the reaction 2[K Fe(CN) ] +2 KOH + H O → 2[K Fe(CN) ] +2H mO +O , H O .co
s e
em
3 6 2 2 4 6 2 2 2 2

s
acts as
g l a
la a
ag
(A) Oxidizing agent
(B) Reducing agent
(C) Bleaching agent
(D) Both oxidizing agent and bleaching agent

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

132. Shape of CIO4− ion is

(A) Tetrahedral
(B) Square planar
(C) Square Pyramidal
(D) Trigonal bipyramidal

133. Appearance of colour in solid alkali metal halides is generally due to

(A) F-centres
(B) Frenkel defects
(C) Schottky defects
(D) Interstitial positions

134. Bell metal is an alloy of

(A) Sn and Pb
(B) Cu and Sn
(C) Sn and Sb
(D) Cu and Pb

135. The bond order of O2+ is

(A) 1
(B) 1.5
(C) 2
(D) 2.5

136. Which of the following is the equation of a circle?

2
(A) x 2 + ( y + 3) + 27 = 0

(B) x2 + y 2 − x + 2 y + 3 = 0

(C) x2 + y 2 + x = 9

(D) x2 + y2 + y + 3 = 0

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m
m .co

m .co s e m
se g l a
137. The minimum value of cosec−1x is
a
(A) 0
π
(B)
2
π
(C) −
2
m
(D) π m .co
m .co s e m
s e l a
a ag
2025 2024 0
g l
138.
a 2020 2019 0 =
2027 2026 1

(A) −5
(B) 5
(C) −3
(D) 3

m
139. Which of the following equation is satisfied by A = 
m .co
 2 3
?
s e 1 2

(A) A2 − I = 2 A g la
a
(B) A2 − 2 A + I = 0
(C) A2 − I = 0
(D) A2 − 4 A + I = 0

140. When m ≤ 4 is a positive integer, the probability of getting real roots for
m
m 2 x 2 + 2mx + 1 = 0 is
.co
m .co 3
s e m
s e (A)
5
g l a
g la 1 a
a (B)
2
3
(C)
4
2
(D)
5

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

141. Let f : [ −1,1] → B be defined by f ( x) = x 2 . Then the set B for which f is onto, is

(A) (0, 1)
(B) [−1,1]
(C) ( −1,1]
(D) [0,1]

142. The absolute maximum value of the function f ( x) = 4 x5 + 5 x 4 on [1, 2] is

(A) −1
(B) 2
(C) 0
(D) 1

143. The least value of n such that n! is a multiple of 2025 is

(A) 10
(B) 25
(C) 81
(D) 9

 π
144. The area bounded by the curve cos x and the x-axis in 0,  is
 2

(A) 0
1
(B)
2
(C) 1
(D) 2
145. The minimum value of f ( x) = (19 − x)e19− x is

(A) e
1
(B)
e
1
(C) −
e
1
(D) − 2
e

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m
m .co

m .co s em
se g la
a
146. If f , g : ℝ → ℝ are defined by f ( x) = x , g ( x) = x 2 , then g f is

(A) x

(B) x2
(C) x
(D) 1
m
c o m m .co
147. The function . f defined by f ( x) = x 2 is a bijection if the domain and the range are s e
s em g l a
l a
respectively
g ℝ, ℝ a
a(A)
(B) ℝ, (0, ∞)
(C) (0, ∞), ℝ
(D) [0, ∞),[0, ∞)

148. The number of arrangements of alphabets α , α , α , α , β , γ , δ such that no two α ' s are
adjacent is
m
(A) 3!
m .co
(B) 4!
s e
(C) 5!
g la
(D) 6!
a
149. How many five digit even numbers can be formed using the digits 3, 4, 5, 6, 7 in all
possible ways?

(A) 120
(B) 240
(C) 10
(D) 24
o m
m The polynomial f ( x) = x + ax + bx + cx + d has real coefficients, and.c
co f (3i) = f (3 + i) = 0. Then the value of a + b + c + d is equal to sem
4 3 2
150.
.
s em g l a
la a
ag
(A) 16
(B) 25
(C) 36
(D) 49

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

n
 1 
151. lim  1 − 2  equals
n→∞  n 

(A) 1
−1
(B)
e2
(C) e −2
(D) e−1

4
152. The value of 1 + ω − 2ω 2
( ) , where ω is the cube root of unity is
(A) −81
(B) 81ω 2
(C) −81ω 2
(D) 81

5π
153. The number of ‘x’ satisfying cos 2 x > sin is
2

(A) 0
(B) 1
(C) 2
(D) ∞

154. Which of the following function is onto?

(A) f : ℕ → ℕ defined by f (n) = n + 2
1
(B) f : ℝ − {0} → ℝ defined by f ( x) =
x
(C) f :[0, ∞) → ℝ defined by f ( x) = x

(D) f : ℕ ∪ {0} → ℕ defined by f (n) = n + 1

155. The 5th and 6th term of an arithmetic progression are 20 and 17. Then which term of
the arithmetic progression lies between −1127 and −1125?

(A) 375
(B) 376
(C) 377
(D) 378

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m
m .co

m .co s e m
se g l a
x −1 a
156. One of possible values of lim
x →1 x − 1

(A) −1
(B) 0
1
(C)
2
m
(D) 1
m .co
m .co s e m
s e l a
ag
157. The total number of proper factors of 2025 is

g a
l 13
a(B) 14
(A)

(C) 15
(D) 2

dy
158. The solution of the differential equation 2 x − y = 5 represents
dx
m
.co
(A) circles
(B) straight lines
e m
(C)
(D)
ellipses
parabolas
las
ag
159. Let A(2, −1) and B(6, 5) be two points. The ratio in which the foot of the
perpendicular from (4, 1) divides AB is

(A) 8 : 15
(B) 5:8
(C) −5 : 8
(D) −8 : 5
m
m
c. o160. A circle touches both the axes. Then the locus of its center is givensebym .co
s em g l a
la a
(A) 2 2
x − y = 0
ag (B) x2 + y 2 = 0

(C) x2 − y 2 = 1

(D) x2 + y 2 = 1

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

161. With respect to multiplication, the set {0,1, −1} does not form a group,
since it fails to satisfy

(A) associativity
(B) existence of inverse
(C) existence of identity
(D) closure law

162. {
The generators of the cyclic group G = 8n | n ∈ Z are }
1
(A) 2 and
2
1
(B) 4 and
4
1
(C) 6 and
6
1
(D) 8 and
8

 a − ib 
163. cos  i log  is equal to
 a + ib 

(A) ab
a2 − b2
(B)
a 2 + b2
a 2 − b2
(C)
2ab
2ab
(D)
a + b2
2

3
164. The product of all values of (cos α + i sin α ) 5 is

(A) 1
(B) cos α + i sin α
(C) cos 3α + i sin 3α
(D) cos 5α + i sin 5α

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m
m .co

m .co s e m
se g l a
165.
1 1
The product 16 (16 ) 3 (16 ) 9 . . . ∞ is equal to
a
(A) 16
(B) 32
(C) 64
(D) 0

m
166.
m
The sum of 25 terms of the series
o
2 + 8 + 18 + 32 + ... is
m .co
(A) 325 2.c e
em2
(B) s225 l as
(C)la 265 2
g 125 2 ag
a(D)
167. If x 2 − 3x + 2 be one of the factors of the expression x 4 − px 2 + q, then

(A) p = 4, q = 5
(B) p = −5, q = −4
(C) p = 5, q = 4
m
(D) p = −5, q = 4
.co
s em
g a butof digits
168. How many numbers greater than l2000,
the digits 0, 1, 2 and 3, wherearepetition
not greater than 3000 can be formed with
being allowed?
(A) 128
(B) 64
(C) 65
(D) 52

169. The sides PQ, QR, RP of a triangle PQR have 3,4,5 interior points on them. Total
m
.co
number of triangles that can be formed using these points as vertices is equal to
m
m .co (A) 135
s e m
s e (B) 145
g l a
la
(C) 178
g (D) 205 a
a

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

2 3 x 
 
170. The solution set of the equation  2 1 x 2  = 0 is
6 7 3 
 

(A) φ
(B) {0,1}
(C) {1, −1}
(D) {1, −3}

log e log e2 log e3
171. log e2 log e3 log e4 is equal to
log e3 log e4 log e5

(A) 0
(B) 1
(C) 4 log e
(D) 5log e

9 27 81
172. If a = 1 + 3 + + + + ..., then a −1 is
2! 3! 4!

(A) e−3
(B) e3
1
(C)
e3
−1
(D)
e3

173. LetR be the relation over the set all real numbers as x and y are related under R if
xy ≥ 0. Then R is

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

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m
m .co

m .co s em
se g la
a } to the set Y = {1, 2} is
174. The number of onto mappings from the set X = {1, 2,...,11

(A) 211 − 2
(B) 211
(C) 210 − 2
(D) 22

m
m 4
.co
.co m
175. The probability that a man will live 10 more years, is and the probability that his

m
9
s e
s e 3
l a
ag
wife will live 10 more years, is . Then the probability that none of them will be

g l a 5
a
alive after 10 years is

2
(A)
5
2
(B)
9
3
(C)
m
.co
7

em
5
(D)
9
la s
ag
176. A committee of 5 is to be chosen from a group of 10 people. The probability that a
certain married couple will either serve together or not at all is

1
(A)
2
5
(B)
9
m
m 4
.co
.co
(C)
9
e m
e m l as
las (D)
2
3 ag
ag

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

177. A coin with probability p , 0 < p< 1 for getting a head is tossed until a head appears
2
for the first time. If the probability that the number of tosses required is odd is ,
5
then p equals

1
(A)
3
2
(B)
3
2
(C)
5
3
(D)
5

1 1 r
178. If p = cos 55°, q = cos 65° and r = cos175° , then the value of + + is
p q pq

(A) 0
(B) −1
(C) 1
(D) 2

179. Given that the sides of a triangle ABC are in AP. If c < b < a, then cosA is equal to

3c − 4b
(A)
2b
3c − 4b
(B)
2c
4c − 3b
(C)
2b
4c − 3b
(D)
2c

180. The equation x 2 + 4 y 2 − 4 xy + 4 + x − 2 y = 1 represents

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

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m
m .co

m .co s em
se g la
a
181. The number of points on the circle 2 x 2 + 2 y 2 − 5 x = 0 which are at distance 2 from
the point (1, −3) is

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

m
m .co
.co m
 1+ x 
e
dy
182. If sec−1   = a, then is
em
 1− y  dx
l as
s
la y − 1 ag
g
a x +1
(A)

y +1
(B)
x −1
x −1
(C)
y −1
x −1
(D)
m
.co
y +1

e m
183. lim log e (sin x) tan x
is
las
x→0
ag
(A) 1
(B) −1
(C) 0
(D) ∞

184. Angle of intersection of the curves r = sin θ + cos θ and r = 2sin θ is equal to
m
m .co
π

.co
(A)
2
e m
e m π
l as
las (B)
3
ag
ag (C)
π
4
π
(D)
6

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

1
185. If L = lim n , then
n→∞ n !

(A) L=0
(B) L =1
(C) 0 < L <1
(D) L=∞

π
186. The solution of the differential equation cos x dyy = y (sin x − y )dx, 0 < x < is
2

(A) sec x = tan x + c
(B) y sec x = tan x + c
(C) y (tan x + c) = sec x
(D) tan x = (sec x + c) y

187. If a = b = a + b = 1, then a − b is equal to

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

188. If a + b + c = 0 and a = 3, b = 4 and c = 37, then the angle between a and b is

π
(A)
4
π
(B)
2
π
(C)
6
π
(D)
3

3 2
189. If = a + ib, then ( a − 2 ) + b 2 is equal to
2 + cos θ + i sin θ

(A) 0
(B) 1
(C) −1
(D) 2

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m
m .co

m .co s em
se g la
a
190. If x > 0 and log 2 x + log 2 ( x ) + log 2 ( 4 x ) + log 2 ( 8 x ) + log 2 (16 x ) + ... = 4 then x
equals

(A) 2
(B) 3
(C) 4
(D) 5
m
m .co
.co m
191. In a polygon no three diagonals are concurrent. If the total number of points of
m s e
intersection of diagonals interior to the polygon be 70, then the number of diagonals
s e l a
a ag
of the polygon is
g l 20
a(B) 10
(A)

(C) 28
(D) 8

192. An integer is chosen at random from first two hundred numbers. Then the probability
that the integer chosen is divisible by 6 or 8 is
m
.co
1
(A)
4
e m
2
las
(B)
4
ag
3
(C)
4
1
(D)
3

193. In a set of (2n + 1) elements, the number of subsets which contain at most n elements
m
m is
.co
m .co (A) 2n
s e m
s e 2n+1 g l a
la
(B)
g a
a (C) 2n−1
(D) 22 n

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

1
194. If 3 f ( x) − 2 f   = x, then f '(2) =
x

2
(A)
7
1
(B)
2
(C) 2
7
(D)
2

1
2
195. The value of ∫ e x dx
0

(A) >e
(B) <e
(C) >2
(D) <1

196. In a deck of 52 cards, two cards are drawn without replacement. Then the probability
that both cards are aces is

2
(A)
211
2
(B)
221
1
(C)
211
1
(D)
221

197. Which of the following is not divisible by any prime number less than 10 ?

(A) 2606 1 −
606
(B) 2 +1
(C) 2607 1 −
(D) 2607 + 1

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m
m .co

m .co s em
se g la
198. If a + b + c = 0 and a, b, c are rational, then the rootsaof the equation
(b + c a)x2+ (c + a
− − b)x + (a + b − c) = 0 are

(A) rational
(B) irrational
(C) imaginary
(D) equal

m
) o= m .co
n
199. If 1 − x + x 2
( a0 + a1x + a2 x 2 + ... + a2n x 2n , then a0 + a2 + a4 + ... + a2n is equal to
c m
3ne2 +
m. l as e
(A) s
la 2
1
ag
g
a(B) 1 − 3n
2
3n − 1
(C)
2
3n + 1
(D)
2
m
c. o 2
x2
e y m
200. If the ellipse
4
las
+ y 2 = 1 meets the ellipse x 2 + 2 = 1 in four distinct points and
a
a = b2 − 5b + 7, then b does not lie in ag
(A) [4, 5]
(B) ( , 2)
−∞−∞ ∪ ∞ (3, )
(C) ( , 0)
(D) [2, 3]

201. The ratio of w to x is 4 : 3 , the ratio of y to z is 3 : 2 , and the ratio of z to x is
m
.co
1 : 6 . Then the ratio of w to y is
m
m .co (A) 4:3
s e m
s e (B) 3:2
g l a
g la (C) 8:3
a
a (D) 16 : 3

202. The largest term common to the sequences, 1, 11, 21, 31, …..to 100 terms and 31, 36,
41, ….. to 100 terms is
(A) 281
(B) 381
(C) 471
(D) 521
m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 45 of 51

a x − xa
203. If a > 0 and lim x = −1 then a =
x →a x − a a

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

204. 12 seats in a row are to be occupied by 4 boys the number of possible arrangement of
there should be at least two empty seats between any two boys is

(A) 4! × 6C4

(B) (12C4 − 5C3 ) × 3!
12 P4 × 4!
(C)
3!
8 P4 × 4!
(D)
2!

205. The median of a set of 9 distinct observations is 20.5. If each of the largest 4
observations of the set is increased by 2, then the median of the new set

(A) is increased by 2
(B) is decreased by 2
(C) is two times the original median
(D) remains the same as the that of the original set

1
206. If f ( x) + 2 f   = 3 x, x ≠ 0 andSs = { x ∈ R : f ( x) = f (− x)} then the set S
 x

(A) contains exactly two elements
(B) contains more than two elements
(C) is an empty set
(D) contains exactly one element

4
207. If Z − = 2, then the maximum value of z is equal to
z

(A) 5 +1
(B) 2
(C) 2 + 2
(D) 3 +1

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m
m .co

m .co s e m
se g l a
a
x x
3  4
208. If f ( x) =   +   − 1, x ∈ R then the equation f ( x ) = 0 has
5 5

(A) no solution
(B) one solution
(C) two solutions
m
.co
(D) more than two solutions
m
.co s e m
209. em
The shortest distance between the line y − x = 1 and the curve x = y 2 is
s l a
g la 2 3 ag
a(A)
8
3 2
(B)
5
3
(C)
4
m
.co
3 2
(D)

em
8

las
g
a xlim
210. Let f : R → [ 0, α ) be such that f ( x) exists and lim
f ( x) 2 − 9
= 0 , then
→5 x→5 x−5
lim f ( x) =
x→5

(A) 0
(B) 1
(C) 2
(D) 3
m
m .co
.co
m 211.
 1 ω n ω 2n 
s e m
s e

If 1, ω, ω 2 are the cube roots of unity, then ∆ =  ω n ω 2 n 1 =

g l a
g la  2n
1

ω n  a
a ω

(A) ω2
(B) 0
(C) 1
(D) ω

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

212. The number of real values of l for which the system of linear equations
2 x + 4 y − λ z = 0, 4 x + λ y + 2 z = 0, λ x + 2 y + 2 z = 0 has infinitely many solutions, is

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

213. The polar form of the complex number −1 + i is

 5π 
(A)  2, 
 4 
 3π 
(B)  2, 
 4 
 π
(C)  − 2, 
 4
 π
(D)  2, 
 4

214. If the general term of an A.P. is3n, then the common difference is

(A) 2
(B) 3
(C) 5
(D) 6

215. The three points A(1, 2,3), B(3,1, 2), C (2,3,1) form

(A) an equilateral triangle
(B) a right angled triangle
(C) an isosceles triangle
(D) a right angled isosceles triangle

216. The variance of the first 10 natural numbers is

(A) 7.25
(B) 7
(C) 8.25
(D) 8

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m
m .co

m .co s e m
se g l a
217. If A2 − A + I = 0, then the inverse of the matrix A is
a
(A) A+ I
(B) A
(C) A− I
(D) I−A

m
.co
218. The value of λ for which the vectors 3iˆ − 6 ˆj + kˆ and 2iˆ − 4 ˆj + λ kˆ are parallel is
m
3
m .co s e m
(A)
s e l a
ag
2

g a
l 2
a 3
(B)

2
(C)
5
5
(D)
2

m
.co
219. If P( A) = 0.4, P( B) = 0.8, P( B | A) = 0.6 then P ( A ∪ B) is

e m
(A)
(B)
0.24
0.30
las
(C) 0.48
ag
(D) 0.96

 z −i 
220. If S =  z ∈ ℂ : ∈ ℝ  , then
 z + 2i 

(A) S contains exactly two elements
(B) contains only one element
m
.co
(C) S is a circle in the complex plane
m
.co m
(D) S is a straight line in the complex plane

m s e
s e g l a
la a
n
 5
ag 221. lim 1 +  is equal to
n→∞  n

(A) 5 log e
(B) e5
(C) 5e
(D) log e

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

1 1+ 2 1+ 2 + 3
222. The sum of the series + + + ... to ∞equals
1! 2! 3!

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

dy
223. If x = a (cos t + t sin t ) and y = a (sin t − t cos t ), then =
dx

(A) tan t
(B) cot t
(C) − tan t
(D) − cot t

224. The number of tangents that can be drawn from (1, 2) to x2 + y 2 = 5 is

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

225. If cos−1 x + cos−1 y + cos−1 z = 3π ; then the value of xy + yz + zx is

(A) 3
(B) 1
(C) −1
(D) 0

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

m
m .co

m .co s e m
se g l a
ANSWER BOOK
a
SI SI SI SI SI SI SI SI
No Key No Key No Key No Key No Key No Key No Key No Key
1 A 31 C 61 D 91 B 121 A 151 A 181 A 211 B
2 C 32 B 62 A 92 A 122 B 152 B 182 A 212 B
3 D 33 D 63 A 93 A 123 D 153 A 183 C 213 B
4 C 34 B 64 C 94 C 124 B 154 D 184 C 214 B
B D B C D D A A
m
.co
5 35 65 95 125 155 185 215
A D
m A B D C C C

.co
6 36 66 96 126 156 186 216
D A B B B A C D
e m
s
7 37 67 97 127 157 187 217
A B
em B C C D D
l aB
s
8 38 68 98 128 158 188 218
9 C 39
g l a B 69 C 99 D 129 C 159 B 189 B
ag
219 D
10
11
D
C
a
40
41
B
D
70
71
D
A
100
101
C
B
130
131
A
B
160
161
A
B
190
191
C
A
220
221
D
B
12 B 42 A 72 B 102 A 132 A 162 D 192 A 222 C
13 A 43 B 73 B 103 B 133 A 163 B 193 D 223 A
14 B 44 C 74 A 104 C 134 B 164 C 194 B 224 B
15 A 45 B 75 D 105 B 135 D 165 C 195 B 225 A
16 C 46 A 76 B 106 B 136 C 166 A 196 D
17 D 47 C 77 C 107 D 137 C 167 C 197 C
m
.co
18 A 48 C 78 C 108 A 138 A 168 B 198 A
A C C B D D D
19 49 79 109
e m139 169 199
20 A
A
50 B
D
80 C
B
110
las C
D
140 C
D
170 D
A
200 D
D
21
22 C
51
52 B
81
82 A
111
112ag D
141
142 D
171
172 A
201
202 D
23 B 53 B 83 B 113 A 143 A 173 D 203 B
24 D 54 B 84 A 114 B 144 C 174 A 204 A
25 C 55 A 85 A 115 B 145 C 175 B 205 D
26 D 56 A 86 C 116 A 146 B 176 C 206 A
27 D 57 A 87 A 117 A 147 D 177 A 207 A
28 D 58 B 88 D 118 B 148 A 178 B 208 B
B D A D B D D
29 59 89 119 149 179 209
m
.co
B A B B D A D
30
m 60 90 120 150 180 210

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

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