CUSAT CAT 2022 Question Paper PCM Shift 2

Test in Physics Chemistry and Mathematics for B Tech (Second Shift)

1. Galvanometer is used to

(A) measure amount of current flowing
(B) measure direction of current flow
(C) check whether current is flowing or not
(D) measure potential difference

2. Which one is true for super conducting behavior?

(A) Large conductivity
(B) Paramagnetism
(C) Ferromagnetism
(D) Perfect conduction and perfect diamagnetism

3. What is the critical angle of incidence for water?

(A) 49.75°
(B) 47.75°
(C) 48.75°
(D) 46.75°

4. Sunlight incident on prism is split into several colours due to

(A) diffraction
(B) reflection
(C) incident
(D) dispersion

5. 10 cm is a wavelength corresponding to the spectrum of

(A) Radio waves
(B) Infrared waves
(C) Microwaves
(D) X-rays

6. The particle nature of light is proved by which of the following?

(A) Polarization
(B) Diffraction
(C) Photoelectric effect
(D) Interference

7. A doped semiconductor is also known as

(A) intrinsic semiconductor
(B) extrinsic semiconductor
(C) diffused semiconductor
(D) compound semiconductor

8. Which one of the following has highest mobility?

(A) Neutron
(B) Electron
(C) Positive ions
(D) Holes

9. Photoelectric effect is based on the law of conservation of

(A) Mass
(B) Energy
(C) Momentum
(D) Angular velocity

10. The main origin of the magnetism is based on the

(A) polar nature of the materials
(B) Pauli’s exclusion principle
(C) intrinsic spin of the electron
(D) charge of the electron

11. Electromagnetic waves are produced due to

(A) uniformly moving charge
(B) constantly circulating charge
(C) rest charge
(D) accelerated charge

12. An equivalent representation for the Boolean expression A' + 1 is

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

13. Ohms law says

(A) R = VI
(B) V = IR
(C) V = I 2R
(D) R = V 2I

14. The reason why metals are so shiny is

(A) their hardness makes them easy to polish
(B) the electric field of the photon is forced to go to zero at the surface of the
metal, generating a wave in the opposite direction
(C) because metals are so hard, photons undergo completely elastic collisions
which gives them an equal and opposite momentum
(D) metals carry a large static charge at their surface that repels the photons

15. Two identical objects having mass ‘m’ are released from rest and they move
towards each other under the influence of mutual gravitational force.
Gravitational potential energy of the two particle system

(A) is zero
(B) is constant (≠0)
(C) decreases as the separation decreases
(D) increases as the separation decreases

16. Expression of Brewster's law is

(A) µ = tan ip
(B) µ = tan r
(C) µ = cos r
(D) µ = sin r

17. What is the focal length of the combination of the two lens having
power +14D and –4D respectively are placed in contact coaxially?

(A) 100 cm
(B) 10 cm
(C) 10 m
(D) 100 m

18. Two electric bulbs having resistance in the ratio of 1 : 3 are connected in
parallel to a constant voltage source. The power dissipated in them has the ratio
of

(A) 1:6
(B) 1:3
(C) 3:1
(D) 6:1

19. The value of Young’s modulus for a perfect rigid body is

(A) zero
(B) infinity
(C) one
(D) less than one

20. A body of mass of 10 kg is placed at the centre of the earth. Now, the weight of
the body will be

(A) Infinite
(B) 10 kg
(C) Zero
(D) 20 kg

21. At a given temperature, the pressure of an ideal gas is

(A) directly proportional to its density
(B) inversely proportional to its density
(C) inversely proportional to square of its density
(D) independent of its density

22. Which one of the below given frequency is audible to human ears?

(A) 2 Hz
(B) 25 kHz
(C) 2000 Hz
(D) 200 kHz

23. Which of these crystal defects occurs due to the interstitial position of atoms?

(A) Schottky defect
(B) Frenkel defect
(C) Metal ion defect
(D) Screw dislocation

24. As the accelerating potential used in a Coolidge tube to produce X-rays is
increased, the cut-off wavelength

(A) increases
(B) decreases
(C) first increases, then decreases
(D) remain unchanged

25. For a P-N junction diode

(A) forward current is in mA and reverse current is in µA
(B) forward current is in A and reverse current is in mA
(C) both forward and reverse currents are in µA
(D) both forward and reverse currents are in mA

26. When a light frequency n is shined on the metal surface, the maximum velocity
of the photoelectrons emitted from the surface is v. If the incident frequency is
increased to 4n, the maximum velocity of the ejected photoelectrons will be

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

27. A time dependent force F = 8t acts on a particle of mass 1 kg. If the particle
starts from rest, the work done by the force during the first 2 second will be
(A) 16 J
(B) 256 J
(C) 128 J
(D) 64 J

28. Copper of fixed volume V is drawn into wire of length l. When this wire is
subjected to a constant force F, the extension produced in the wire is ∆l. Which
of the following graph is a straight line?

1
(A) ∆l versus
l
(B) ∆l versus l 2
1
(C) ∆l versus 2
l
(D) ∆l versus l

29. Seven capacitors each of capacitance 4 µF are to be connected to obtain a
20
capacitance of µ F , which of the following combination is possible?
11

(A) 4 in parallel 3 in series
(B) 5 in parallel 2 in series
(C) 3 in parallel 4 in series
(D) 2 in parallel 5 in series

30. If the source of light used in a Young’s double slit experiment is changed from red to
violet,

(A) the fringes will become brighter
(B) the intensity of minima will increase
(C) consecutive fringes will come closer
(D) the consecutive fringes moves apart

1
31. The SI unit of is
ε 0 µ0

(A) F/m
(B) m/sec
(C) H-F
(D) m/HF

32. The permanent magnetic moment of the atoms of a material is zero. The
material

(A) must be paramagnetic
(B) must be diamagnetic
(C) must be ferromagnetic
(D) must be ferrimagnetic

33. A coil of inductance 300 mH and resistance 2 Ω is connected to a 2 V voltage
source. The current reaches half of its steady state value in

(A) 0.05 sec
(B) 0.1 sec
(C) 0.15 sec
(D) 0.3 sec

34. A stone of mass m tied to a string of length l is rotated in a circle with the other
end of the string as the centre. The speed of the stone is v. If the string breaks,
the stone will

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

35. A sphere, a cube and a thin circular plate all of same material having same mass
are initially heated to 200°C. Which of these will cool faster?

(A) Circular plate
(B) Sphere
(C) Cube
(D) Both the circular plate and sphere

36. The image formed by an objective of a compound microscope is

(A) Virtual and diminished
(B) Real and diminished
(C) Real and enlarged
(D) Virtual and enlarged

37. The shortest height of a vertical mirror required to see the entire image of a man
will be

(A) one third of man’s height
(B) half of the man’s height
(C) two third of man’s height
(D) one fourth of the man’s height

38. A cell supplies a current of 0.9 A through a 2 Ω resistor and a current of 0.3 A
through a 7 Ω resistor. What is the internal resistance of the cell?

(A) 0.5 Ω
(B) 1Ω
(C) 1.2 Ω
(D) 2Ω

39. A spring of force constant k is cut into two pieces such that one piece is double
the length of the other. Then the longer piece will have a force constant of

(A) 2k/3
(B) 3k/2
(C) 3k
(D) 6k

40. A body of mass 10 kg is moving on a horizontal surface by applying a force of
10 N in forward direction. If body moves with constant velocity, the work done
by applied force for a displacement of 2 m is

(A) 20 J
(B) 10 J
(C) 30 J
(D) 40 J

41. Out of gravitational, electromagnetic, van der Waal’s, electrostatic and nuclear
forces, which of the following provides an attractive force between neutrons?
(A) gravitational and van der Waal’s
(B) electrostatic and gravitational
(C) electrostatic and nuclear
(D) nuclear

42. A condenser of capacity 10 µF is charged to a potential difference of 100 V. It
is now connected in parallel to another uncharged condenser. The common
potential now is 40 V. The capacitance of the other condenser is

(A) 25 µF
(B) 20 µF
(C) 15 µF
(D) 10 µF

43. For ferromagnetic substances the permeability is ………………..
and susceptibility is ………………..

(A) very large; positive and large
(B) very large; negative and small
(C) very small; positive and large
(D) very low; negative and small

44. The magnetic flux linked with a coil changes from 1 Weber to 0.1 Weber in 0.1
sec. The induced e.m.f is

(A) 9 Volts
(B) 10 Volts
(C) 0.009 Volts
(D) 0.1 Volts

45. A step down transformer transforms supply line voltage of 2200 V into 220 V.
The primary coil has 5000 turns. The efficiency and power transmitted by
the transformer are 90% and 8 kW respectively. Then the number of turns in the
secondary and the power supplied are

(A) 50 turns, 9.89 kW
(B) 500 turns, 9.89 kW
(C) 500 turns, 8.89 kW
(D) 100 turns, 8.89 kW

46. On a glass plate a light ray is incident at an angle of 60°. If the reflected and
refracted rays are mutually perpendicular, the refractive index of the material is

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

47. If the least distance for clear vision is 25 cm, power of objective and the
eyepiece are 25 dioptre and 5 dioptre lenses respectively, with separation
between them is 30 cm, the maximum magnifying power of the compound
microscope is

(A) 8.4
(B) 7.4
(C) 9.4
(D) 10.4

48. A proton and an α particle are accelerated by the same potential difference.
Their ratio of the de Broglie wavelengths (λp, λα) is

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

49. A photon and an electron have same kinetic energy. If λp and λe are the
wavelengths of them respectively, then

(A) λp < λe

(B) λp > λe

(C) λp = λe

(D) λp = λe = 0

50. Ratio of wavelengths of first line of Lyman series and the first line of Balmer
series is

(A) 1:3
(B) 27 : 5
(C) 5 : 27
(D) 4:9

23
51. If Avogadro’s number is 6 × 10 then the number of protons, neutrons and
14
electrons in 14 gm of 6C are respectively

(A) 36 × 1023, 48 × 1023, 36 × 1023

(B) 36 × 1023, 36 × 1023, 36 × 1023

(C) 48 × 1023, 36 × 1023, 48 × 1023

(D) 48 × 1023, 48 × 1023, 36 × 1023

2
52. The binding energy per nucleus of deuteron (1H ) and helium nucleus
4
(2He ) is 1.1 MeV and 7 MeV respectively. If two deuteron nuclei react to
form a single helium nucleus, then the energy released is

(A) 13.9 MeV
(B) 25.8 MeV
(C) 23.6 MeV
(D) 19.2 MeV

2
53. An aluminium rod of length 3.14 m is of square cross-section 3.14 × 3.14 mm .
What should be the radius of 1 m length of another rod of same material to have
equal (same) resistance?

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

54. The resistance across AB in the circuit is

(A) 2.8 Ω
(B) 14/3 Ω
(C) 3/14 Ω
(D) 5/14 Ω

55. The energy band gap in conductors, semiconductors and insulators are EG1,
EG2 and EG3 respectively. Then the relation among them is

(A) EG1 = EG2 = EG3

(B) EG1 > EG2 > EG3

(C) EG1 < EG2 < EG3

(D) EG1 < EG2 > EG3

56. The magnitude of average velocity is equal to the average speed when a particle
moves

(A) on a curved path
(B) in a straight line
(C) with the constant acceleration
(D) with constant retardation

57. If F is the force between two point charges submerged in a medium of dielectric
constant K, then on withdrawing the medium, the force between the charges
becomes

(A) F√
(B) FK
(C) F/√
(D) F/K

58. Resistances n, each of r ohm, when connected in parallel give an equivalent
resistance of R ohm. If these resistances were connected in series, the
combination would have resistance in ohm, equal to

(A) R/n2
(B) R/n
(C) nR
(D) n2R

59. A stationary particle explodes into two particles of masses m1 and m2 which
move in opposite directions with velocities v1 and v2. The ratio of their kinetic
energies E1/E2 is

(A) m2/m1

(B) m1/m2
(C) 1
(D) m1v2/m2v1

60. A ray of light is incident normally on one of the faces of a prism of angle 30°
and refractive index √2. The angle of deviation of the ray is

(A) 0°
(B) 12.5°
(C) 15°
(D) 22.5°

61. Matter wave duality is associated with

(A) Pauli’s principle
(B) De Broglie relation
(C) Schrodinger wave equation
(D) Plank’s equation

62. If energy of a photon of 3 eV strikes a metal surface and resulting work function
on the metal is 2 eV, calculate the kinetic energy of the emitted photon.

(A) 5 eV
(B) 2.5 eV
(C) 1.5 eV
(D) 1 eV

63. According to Graham’s law of diffusion, the rate of diffusion of a gas at
constant pressure is

(A) directly proportional to density of the gas
(B) inversely proportional to density of the gas
(C) directly proportional to square root of density of the gas
(D) inversely proportional to square root of density of the gas

64. In a cyclic process

(A) work done is zero
work done by the system is equal to the quantity of heat given to the
(B)
system
(C) work done does not depend on the quantity of heat given to the system
(D) the internal energy of the system increases

65. If solute-solvent interaction are weaker than those
between solute-solute and solvent-solvent
interactions, then

(A) ∆Hmix = 0
(B) ∆Hmix = +ve
(C) ∆Hmix = –ve
(D) ∆Hmix = T∆S

66. When a catalyst is added to a reversible reaction in equilibrium state, the value
of the equilibrium constant

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

67. What is the relation between Kp and Kc?

(A) Kp = ∆n Kc RT
(B) Kp = –∆n Kc RT
(C) Kp = Kc (RT)∆n
(D) Kp = Kc (RT)–∆n

68. Henderson–Hasselbalch equation for a buffer solution is

 [Salt] 
(A) pH = pKa + log  
 [Acid] 
 [Salt] 
(B) pH = pKa – log  
 [Acid] 
 [Salt] 
(C) pH = pKb + log  
 [Acid] 
 [Salt] 
(D) pH = pKb – log  
 [Acid] 

−1
69. Solubility product for a M2S salt having solubility ‘s’ mol lit is

(A) Ksp = 2s2
2
(B) Ksp = 4s
(C) Ksp = 2s3
(D) Ksp = 4s3

70. If half life time of a reaction is independent of initial concentration of reactant,
what is the order of reaction?

(A) Zero order
1
(B) order
2
(C) First order
(D) Second order

71. For the reaction, 4NH3 + 5O2 → 4NO + 6 H2O

d  NH3 
(A) Rate = 0.25 
dt
d  NH3 
(B) Rate = −0.25 
dt
d  NH3 
(C) Rate = 4 
dt
d  NH3 
(D) Rate = −4 
dt

2+ 2+
72. The reaction Zn + Cu → Zn + Cu is

(The reduction potentials of Zn and Cu are −0.76 V and +0.34 V respectively)
(A) non-spontaneous process
(B) spontaneous process
(C) spontaneous at high temperature
(D) spontaneous at lower temperature

73. Considering the formation, breaking and strength of hydrogen bond, predict
which of the following mixtures will show a negative deviation from Raoult’s
law?

(A) Methanol and acetone
(B) Chloroform and acetone
(C) Nitric acid and water
(D) Phenol and aniline

74. The physical adsorption of gases on the solid is due to

(A) Covalent bond
(B) Hydrogen bond
(C) Ionic bond
(D) van der Waal’s forces

75. Which among the following is NOT a facile reaction for primary amides
(RCONH2)?

(A) Dehydration to give the corresponding nitriles
(B) Reaction with bromine in the presence of sodium hydroxide to give
primary amines with one carbon less
(C) Reaction with alkyl halides to give the corresponding secondary and
tertiary amides
(D) Reaction with lithium aluminum hydride to give primary amines having
the same number of carbon atoms

76. In amylopectin, branching occurs by

(A) C1-C4 glycosidic linkage
(B) C6-C6 linkage
(C) C1-C3 glycosidic linkage
(D) C1-C6 glycosidic linkage

77. Which among the following name reactions is suitable for the conversion of
ethanoic acid to 2-bromoethanoic acid?

(A) Hell-Volhard-Zelinsky reaction
(B) Hunsdiecker reaction
(C) Reformatsky reaction
(D) Favorskii reaction

78. Methyl cinnamate can be prepared as shown

COOH COCl COOCH3

H H H
H H H

Step 1 Step 2

Which reagents should be used?

(A) Step 1 - HCl, Step 2 - CH3OH
(B) Step 1 - HCl, Step 2 - CH3CO2H
(C) Step 1 - PCl5, Step 2 - CH3OH
(D) Step 1 - PCl5, Step 2 - CH3CO2H

79. C60 (Fullerene) also known as buckminsterfullerene has

(A) 14 pentagons and 18 hexagons
(B) 12 pentagons and 20 hexagons
(C) 10 pentagons and 20 hexagons
(D) 20 pentagons and 12 hexagons

80. Among formaldehyde, trichloroacetaldehyde (CCl3CHO) and benzaldehyde, the
aldehydes that undergo Cannizzaro reaction are

(A) all the three aldehydes
(B) formaldehyde and trichloroacetaldehyde
(C) trichloroacetaldehyde and benzaldehyde
(D) formaldehyde and benzaldehyde

81. Which nitrogenous base is NOT present in Ribonucleic Acids (RNA)?

(A) Adenine
(B) Thymine
(C) Guanine
(D) Cytosine

82. Which among the following is NOT a reducing sugar?

(A) 2-deoxyribose
(B) fructose
(C) glucose
(D) sucrose

83. Which of the following is formed by the dimerization of 1,3-butadiene by Diels-
Alder reaction?

(A)

(B)

(C)

(D)

84. IUPAC name of the following compound is

O

O

(A) Dodecyl benzoate
(B) Benzyl dodeconate
(C) Benzoyl oxy dodecane
(D) Phenyl dodeconate

85. Which hydrogen is most easily abstracted from the below mentioned compound
to give the corresponding radical intermediate?

H CH3
1
CH3
H3C
H
4 H 3
2

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

86. Which among the following aromatic compounds is most reactive towards
sulfonation reaction?

(A) Benzene
(B) Toluene
(C) Ethylbenzane
(D) t-Butylbenzene

87. Pick the statement that is NOT true for SN1 substitutions.

(A) Carbocation intermediate is involved
(B) EI elimination is a possible side reaction
Reaction rate is doubled when the concentration of nucleophile is
(C)
doubled
(D) Primary alkyl halides seldom undergo SN1 substitutions

88. Arrange the elements in the order of increase in ionization energy?

(A) H, Li, Na, K, Rb, Cs
(B) K, Rb, Cs, H, Li, Na
(C) Cs, H, Li, K, Rb, Na
(D) Cs, Rb, K, Na, Li, H

89. Cobalt and Nickel are

(A) diamagnetic
(B) paramagnetic
(C) ferromagnetic
(D) antiferromagnetic

90. Chlorine exists in two isotopic forms Cl-37 and Cl-35, but its atomic mass is
35.5. What would be the approximate ratio of Cl-37 and Cl-35?

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

91. Which one is the example for linkage isomerism?

(A) [Co(NH3)5(NO2)]2+
(B) [Pd(NH3)4]
(C) [Co(NH3)4ClBr]Br
(D) [Cr(NH3)5CN]

92. The packing fraction (%) of simple cubic unit cell is

(A) 74
(B) 68
(C) 52
(D) 39

93. Calculate de Broglie wavelength for an electron moving at the speed of 6.0 ×
6 −31 −34
10 m/s. (m = 9.1 × 10 Kg, h = 6.627 × 10 Js)

(A) 1.46 ×10−10 m

(B) 1.21×10−9 m

(C) 1.46 ×10−9 m

(D) 1.21 × 10−10 m

94. Physical properties of the elements in the periodic table depends upon the

(A) size of atom
(B) size of proton
(C) number of electrons
(D) size of neutron

95. ……………….. is a polar molecule.

(A) BF6
(B) XeF4
(C) SF4
(D) SiF4

96. Which type of radioactive decay causes the atomic number of a nucleus to
increase by one unit?

(A) Electron capture
(B) α - particle emission
(C) β - particle emission
(D) γ - ray emission

97. The maximum temperature that can be achieved in blast furnace is

(A) up to 1200 K
(B) up to 2200 K
(C) up to 1900 K
(D) up to 5000 K

98. The structures of beryllium chloride in solid state and vapour phase are

(A) chain and dimer, respectively
(B) linear in both phases
(C) dimer and linear, respectively
(D) chain in both phases

99. Match the following.

List I List II
(a) PCl (i) Square pyramidal
5
(b) SF (ii) Trigonal planar
6
(c) BrF (iii) Octahedral
5
(d) BF (iv) Trigonal bipyramidal
3

(A) (a)-(iv), (b)-(iii), (c)-(i), (d)-(ii)
(B) (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)
(C) (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)
(D) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

100. What is the correct electronic configuration of the central atom in K4[Fe(CN)6]
based on crystal field theory?
4 2
(A) t2g eg
6 0
(B) t2g eg
3 3
(C) t2g eg
4 2
(D) e t2

101. If the non-zero numbers x, y , z are in A.P, and tan −1 x, tan −1 y, tan −1 z are
also in A.P, then
(A) x = y = z
(B) xy = yz
(C) x 2 = yz

(D) z 2 = xy

102. Let f ( x) be a polynomial of second degree. If f ( 1) = f ( −1) and a, b, c are in
A.P, then f '(a ), f '(b) and f '(c) are

(A) in A.P
(B) in G.P
(C) in H.P
(D) equal

103. How many 5 letter words, with or without meaning can be formed out of the
letters of the word ′EQUATIONS′ if repetition of letters is not allowed?

(A) 126
(B) 59
(C) 95
(D) 15120

1
104. If lim (cos x + a sin bx) x = e 2 , then
x→0

(A) a = 1, b = −2

(B) a = 2 2, b = 2
1
(C) a = 2 2, b =
2
(D) a = −2, b = 1

105. If the point (a, − a ) lies inside the circle
x 2 + y 2 − 4 x + 2 y − 8 = 0, then ‘a’ lies in the interval

(A) (−1, 4)
(B) (−∞, −1)
(C) (4, ∞)
(D) [ −1, 4]

106. ( )
If (n − 1)Cr = k 2 − 3 nCr +1, then k lies in the interval

(A)  − 3, 3 
 
(B) (−∞, −2)
(C) (2, ∞)
(D) ( 3, 2

107. The remainder when 1! + 2! + 3! + ... + 100! is divided by 240, is

(A) 187
(B) 33
(C) 73
(D) 153

1
108. The solution set of f '( x) > g '( x) where f ( x) = 52 x +1 and
2
x
g ( x ) = 5 + 4 x log e 5 is

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

109. Let f be the greatest integer function defined by f ( x) = [ x] and g be the
 −1 
modulus function defined by g ( x ) = x . Then the value of ( g o f )   is
 3 

(A) 1
(B) −1
(C) 0
1
(D)
3

110. The probability of obtaining an even prime number on
each die, when a pair of dice is rolled, is

(A) 0
1
(B)
6
1
(C)
12
1
(D)
36

111. The product of three consecutive numbers is always divisible by

(A) 6
(B) 10
(C) 15
(D) 8

112. In the group of quarternions Q8 = {±1, ±i, ± j , ± k} , the order of −j is

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

1 1
113. If P + = 1 and Q + = 1, then the product of P, Q and R is
Q R

(A) −1
(B) 2
(C) −2
(D) 3

114. The sum of mean and variance of a binomial distribution of 5 trails is
4.8. Then the probability of success is

(A) 0.2
(B) 1.2
(C) 0.8
(D) 0.5
115. The set of all points of discontinuity of the greatest integer function f ( x) = [ x]
is

(A) the set of all integers
(B) the set of all real numbers
(C) the set of all natural numbers
(D) the set of all rational numbers

r r
116. If a and b are two non-zero vectors such that
r r r r r r
a × b = a ⋅ b , then the angle between a and b is

π
(A)
3
π
(B)
4
π
(C)
6
π
(D)
2

117. Let the roots of bt 2 + ct + a = 0 be imaginary. For all real values of t, the
expression 3b 2t 2 + 6bct + 2c 2 is

(A) less than −4ab
(B) greater than −4ab
(C) less than 4ab
(D) greater than 4ab

ab
118. In a triangle ABC, if sin A sin B = 2 , then the triangle is
c

(A) equilateral
(B) isosceles
(C) right angled
(D) obtuse angled

119. Let f (t ) = 2t 2 + 5t + 1. If f (t ) = a(t + 1)(t − 2) + b(t − 2)(t − 1) + c(t − 1)(t + 1) for
real numbers a, b, c, then

(A) there are infinite number of choices for a, b, c
(B) only one choice for a but infinite number of choices for b and c
(C) exactly one choice for each of a, b, c
(D) more than one but finite number of choices for a, b, c

 π π  1 
 cos 4 − sin  
Let M =  4  and Y =  2  . Then M 3Y =
120. 
 sin π π  1 
 cos   
 4 4   2

 −1
(A)  
0
1
(B)  
0
 −1 
 2
(C)  
 1 
 
 2
 −1 
 2
(D)  
 −1 
 
 2

7 5 3
121. The number of real solutions of the equation x + 14x + 16x + 30x − 560 = 0
is

(A) 7
(B) 1
(C) 3
(D) 5

r r r r r r r
122. The vector a = α i + 2 j + β k lies in the plane of the vectors b = i + j and
r r r r r
c = j + k and bisects the angle between b and c . Then

(A) α = 1, β = 1
(B) α = 2, β = 2
(C) α = 1, β = 2
(D) α = 2, β = 1

123. Which of the following function is not one to one?

(A) g :  →  , g ( x) = 2 x + 5
(B) g :[0, π ] → [−1,1], g ( x) = cos x

 −π π 
(C) g: , → [1, 7], g ( x) = 3sin x + 4
 2 2 
(D) g :  → [−1,1], g ( x) = sin x

6− x x
124. The number of real solutions of the equation 2
= 2+ is
x −4 x+2

(A) 0
(B) 1
(C) 2
(D) 4

..x1
x.
125. If xn > xn−1 > ... > x2 > x1, then the value of log x log x log x ...log xn xnn−1 is
1 2 3
equal to

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

3 1
126. If tan x = and tan y = , then x + y is equal to
4 7

(A) π
(B) 2π
π
(C)
4
π
(D)
2

2
127. If α and β are roots of both the equations cos x + a cos x + b =
2
0 and sin x + p sin x + q = 0, then
2 2
(A) 1 + b + a = p − q
(B) a2 + b2 = p2 + q2
(C) b + q = a2 + p2 − 2
2 2
(D) b + q = a + p + 2

z1
128. If z1 and z2 are complex numbers satisfying = 1 and arg ( z1z2 ) = 0, then
z2

(A) z1 = z2

(B) z22 = z1z2

(C) z1z2 = 1
(D) z1.z2 = 1

129. 2 + 2 + 2 + ...∞ is equal to

(A) 2i
(B) i
(C) −i
(D) −1

130. The complex numbers sin x + i cos 2x and cos x − i sin 2x are conjugate to each
other for

(A) x = nπ
 1
(B) x =  n +  π
 2
(C) all values of x
(D) no value of x

a b c
131. Let a, b, c be in Harmonic Progression. Then , , are
b+c a+c a+b

(A) in Harmonic Progression
(B) in Geometric Progression
(C) in Arithmetic Progression
(D) equal

132. The sum of all two digit odd numbers is

(A) 2475
(B) 2530
(C) 4095
(D) 5049

1 1 3 5 2n − 1
133. If H n = 1 + + ... + , then the value of 1 + + + ... is
2 n 2 3 n

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

134. A person read common difference of an Arithmetic Progression as −4 instead
of 4 and obtained the sum of first eight terms as 48. The correct sum of first
eight terms is

(A) 212
(B) 272
(C) 312
(D) 342

 1  1  1
dy
135. Let y = 1 + x  1 + x  1 − x 4  . Then
4 2 is equal to
    dx
   

(A) 1
(B) −1
(C) x
(D) x

136. Let f ( x) be a polynomial in x. Then, the second order derivative of f ( e x )
with respect to x is

(A) f '' ( e x ) .e x + f ' ( e x )

(B) ( )
f '' ( e x ) .e 2 x + f ' e 2 x .e2 x

(C) f '' ( e x ) .e2 x

(D) f '' ( e x ) .e2 x + f ' ( e x ) .e x

dy π
137. Let y = xsin x . Then the value of at x = is
dx 2

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

138. If f ( x) = e x sin x, then f (6) ( x) is equal to

(A) e6 x sin 6 x
(B) −8e x cos x
(C) 8e x sin x
(D) 8e x cos x

139. ( )
Let P(−1, 0), Q(0, 0) and R 3, 3 3 be three points. Then the equation of the
bisector of the ∠PQR is

3
(A) x+ y =0
2
(B) x − 3y = 0

(C) 3x + y = 0

3
(D) x+ y=0
2

2 2 2 2 2
140. The circles x + y − 12x + 20 = 0 and x + y = k intersect at two distinct
points, if

(A) k<2
(B) 2 < k < 10
(C) k>8
(D) k=2

1 1
141. Given f1 ( x) = x1, f 2 ( x) = − x, f3 ( x) = and f 4 ( x) = − and o stands for
x x
composition of function. Then ( f 4 o f 2 ) ( x) is

(A) f1 ( x)

(B) f 2 ( x)

(C) f3 ( x)

(D) f 4 ( x)

2
142. Locus of the midpoint of any focal chord of y = 4ax is

(A) y2 = a(x − 2a)
(B) y2 = 2a(x − 2a)
2
(C) y = 2a(x − a)
(D) y2 = a(x − a)

2
143. The latus rectum of the parabola y = 4ax whose focal chord is PSQ such that
SP = 3 and SQ = 2 is given by

24
(A)
5
12
(B)
5
6
(C)
5
1
(D)
5

144. The number of values of c such that the line y = 4x + c touches the curve
x2
+ y 2 = 1, is
4

(A) 1
(B) 2
(C) ∞
(D) 0

2 2
145. The diameter of 16x − 9y = 144 which is conjugate to x = 2y, is

16 x
(A) y=
9
32 x
(B) y=
9
16 y
(C) y=
9
32 y
(D) y=
9

sin nx
146. The value of n ∈ I, for which the function f ( x) = has 4π as its period,
 x
sin  
n
is

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

x+4
 x+6
147. lim  is equal to
x→∞  x + 1 

(A) e−5
(B) e5
(C) 0
(D) e−1

148. The points of discontinuity of the function given below is/are

1
 5 ( 2 x + 3) x ≤ 1
2


f ( x ) = 6 − 5 x 1< x < 3
x − 3 x≥3



(A) x=1
(B) x=3
(C) x = 1, 3
(D) x=4

x − sin x
149. If f ( x) = , then lim f ( x) is
x + cos 2 x x→∞

(A) 0
(B) ∞
(C) 1
(D) −1

2
150. The point of the curve y = 2(x − 3) at which the normal is parallel to
the line y − 2x + 1 = 0 is

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

x  1 − sin x 
151. ∫ e  1 − cos x  dx is equal to
 x
(A) −e x tan   + c
2
x
(B) −e x cot   + c
2
1 x
(C) − e x tan   + c
2 2
1 x x
(D) e cot   + c
2 2

152. The differential equation
dy x 1 + y
=
2
( )
represents a family of
dx y 1 + x 2 ( )
(A) parabola
(B) hyperbola
(C) circle
(D) ellipse

dy
153. The solution of + 1 = e x+ y is
dx

(A) e−( x + y ) + x + c = 0
(B) e−( x + y ) − x + c = 0
(C) e( x + y ) + x + c = 0
(D) e( x + y ) − x + c = 0

r r 2 r r 2
154. The value of
( a × b ) + (a ⋅b )
r is
r
2a 2 ⋅ b 2
r r
(A) a ⋅b
(B) 1
(C) 0
1
(D)
2

155. The points (5, −4, 2), (4, −3, 1), (7, −6, 4) and (8, −7, 5) are the vertices of a

(A) rectangle
(B) square
(C) parallelogram
(D) trapezium

156. The inverse of the mapping f : R → R defined by f ( x) = 7 x − 8 for all x ∈ R,
is

y −7
(A) g ( y) = for all y ∈ R
8
y+7
(B) g ( y) = for all y ∈ R
8
y +8
(C) g ( y) = for all y ∈ R
7
y −8
(D) g ( y) = for all y ∈ R
7

 2 −2 x 
157. If  2 x 2  has no inverse, then the real value of x is
 x −2 2 

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

158. If the sum of two unit vectors is a unit vector then the magnitude of their
difference is

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

1− i
159. If is a root of the equation ax 2 + bx + 1 = 0, where a, b are real, then (a, b)
1+ i
is

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

160. Pipe A can fill a cistern in 36 minutes and pipe B in 48 minutes. If both the
pipes are opened together, when should pipe B be closed so that the cistern may
be just full in 24 minutes?

(A) 8 minutes
(B) 9 minutes
(C) 12 minutes
(D) 16 minutes

161. If f : R → R is defined by f ( x ) = cos x and g : R → R is defined by
g ( x) = x 2 , then f o g is

(A) x 2 cos x
(B) (cos x)2
(C) cos x 2
cos x
(D)
x2

1 1
  dy 2  4  d 3 y  3
162. The order and degree of the differential equation  3 +    =  3  are
  dx    dx 
   

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

e2
163. The value of ∫ log e x dx is
e

(A) 2e2
(B) 2e2 − e
(C) e
(D) e2

x3
164. The values of x for which the graph of f ( x) = − x 2 + 3 has a horizontal
3
tangent, are

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

100
165. ( )
The value of ∑ i n + i n+2 is
n=1

(A) i
(B) 1 + i
(C) 0
(D) −i

166. If Z = 7 −1 and Z is non-real, then Z 86 + Z 175 + Z 289 equals

(A) Z
(B) −1
(C) Z2
(D) (2 Z − 3)3

1
167. The area of the region satisfying < (1 + i ) z + i < 2 is
2

(A) 3π
3π
(B)
2
3π
(C)
4
1
(D) −
3

168. A man from the top of a 100 meter high tower sees a car moving towards the
tower at an angle of depression of 30°. After some time, the angle of depression
becomes 60°. The distance (in meters) travelled by the car during this time is

(A) 200 3
3
(B) 100 3
100 3
(C)
3
(D) 200 3

169. On the interval [0, 1], the function x 25 (1 − x)75 takes its maximum value at the
point

(A) 0
1
(B)
4
1
(C)
2
1
(D)
3

170. The solution set of x 2 − 5 x < 6 is

(A) (−1, 2) ∪ (3,6)
(B) 0≤ x≤5
(C) x≥6

(D) −5 ≤ x ≤ 5
171. A balloon which always remains spherical is being inflated by pumping in 1000
cubic centimetres of gas per second. Then the rate at which the radius of the
balloon is increasing when its radius is 5 cm, is

10 2
(A) cm /sec
π
10
(B) cm/sec
3π
π
(C) cm/sec
10
10
(D) cm/sec
π

172. The function f ( x) =
x3 + x2 −16 x + 20 is not defined at x = 2. In order to
x−2
make f ( x) continuous at x = 2, f(2) should be

(A) 1
(B) 4
(C) 0
(D) −4

d  esin x  4
3 3
173. Let f ( x) =   , x > 0. If ∫ esin x dx = f ( k ) − f (1), then one of the
dx  x 
  1x
possible values of k, is

(A) 15
(B) 16
(C) 63
(D) 64

174. For a value of k, the area bounded by the curve y = − x5 + 8x2 , the straight

lines x = 1 and x = k and the x-axis is equal to
16 . Such a value of k is
3

(A) 3 8 − 17

(B) −1
(C) 2
(D) 3

7x x
175. The value of ∫ 77 77 7 x dx is equal to

7x
77
(A) +c
(log 7)3
7x
77
(B) +c
(log 7)2
7x
(C) 77 (log 7)3 + c
7x
(D) 77 + c

176. If * is a binary operation defined by a * b = 3a + 4b – 2, then 4 * 5 is

(A) 48
(B) 31
(C) 29
(D) 30

177. If R = {(x, y) : x + 2y =8} is a relation on the set of all natural numbers N, then
the range of R is

(A) {1, 2, 3}
(B) {1}
(C) {2, 5}
(D) {4, 3, 1}

2
178. If b, k are intercepts of a focal chord of the parabola y = 4ax, then k is equal to

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

179. The equation of the tangent to the hyperbola
x 2 − y 2 = 1 , parallel to the
4 3
line y = x + 2, is

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

x2 y2
180. If θ is the angle between the asymptotes of the hyperbola − = 1 with
a2 b2
θ 
eccentricity e, then sec   is
2

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

1
181. If X follows binomial distribution with parameters n = 8 and p = , then
2
(
P X − 4 ≤ 2 is )
117
(A)
128
116
(B)
128
29
(C)
128
119
(D)
128

182. A monoid becomes a group if it also satisfies the

(A) closure axiom
(B) associative axiom
(C) identity axiom
(D) inverse axiom

183. An example for a tautology is

(A) p∨q
(B) p∧q
(C) p ∨ ∼p
(D) p∧∼p

184. The Arithmetic Mean of n observations is M. If the sum of n – 4 observations is
a, then the mean of remaining 4 observations is

nM − a
(A)
4
nM + a
(B)
4
(C) nM − a
nM − a
(D)
2

185. If the equation hxy + gx + fy + c = 0, h ≠ 0 represents two straight lines, then

(A) 2 fgh = c 2
(B) 2 fg = ch

(C) fgh = c 2
(D) fg = ch

10
 k 
186. If the absolute term in the expansion of  x − 2  is 405, then ‘k’ is equal to
 x 

(A) ±2
(B) ±1
(C) ±3
(D) 0

187. ( )
The range of the function f ( x) = log e 3x 2 − 4 x + 5 is

 11 
(A)  −∞, log e 
 3
 11 
(B) log e 3 , ∞ 

 11 11 
(C)  − log e 3 , log e 3 

 11 
(D)  −∞, − log e 
 3

13
188. ( )
The value of the sum ∑ n=1 i n + i n+1 , where i = −1, equals

(A) 1 − i
(B) i − 1
(C) −i
(D) 0

189. The locus represented by z − 1 = z + i is

(A) a circle of radius 1
(B) an ellipse with foci at 1 and −i
(C) a line through the origin
(D) a circle on the join of 1 and −i as diameter

 0 2b c 
190. Let A =  a b −c  be an orthogonal matrix. Then
 a −b c 

1 1
(A) b=± , c=±
6 3
1 1
(B) a=± , c=±
2 6
1 1
(C) a=± , b=±
2 6
1 1 1
(D) a=± , b=± , c=±
2 6 3

α −β 0
191. If 0 α β = 0 then
β 0 α

(A) α β is one of the cube roots of unity
(B) α is one of the cube roots of unity
(C) β is one of the cube roots of unity
(D) α + β is one of the cube roots of unity

192. The value of λ for which the equations x + y − 3 = 0,
(1 + λ ) x + (2 + λ ) y − 8 = 0, x − (1 + λ ) y + (2 + λ ) = 0 are consistent is

(A) −1
5
(B)
3

(C) −5
3
3
(D)
5

193. The sum to n terms of the sequence log a, log ar , log ar 2 , ... is

n
(A) log a 2 r n−1
2
(B) n log a 2 r n−1
3n
(C) log a 2 r n −1
2
(D) 3n log ar n−1

194. If a, b, c are positive, then the minimum value of
a log b−log c + blog c −log a + c log a −log b is

(A) 1
(B) 3
(C) 9
(D) 16

195. Let f ( x) and g ( x) be two differentiable functions and f (1) = g (1) = 2. Then
f (1) g ( x) − f ( x) g (1) − f (1) + g (1)
lim x→1 is equal to
g ( x) − f ( x)

(A) 0
(B) 1
(C) 2
(D) −1

f ( x) − 5
196. ( )
If g ( x) = x 2 + 2 x + 3 f ( x), f (0) = 5 and lim
x→0 x
= 4, then g '(0) is equal

to

(A) 22
(B) 20
(C) 18
(D) 12

197. If the sum of distances of a point from two perpendicular lines in a plane
is 1, then its locus is

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

198. The distance between the planes 3 x + 2 y − 6 z − 14 = 0 and
3 x + 2 y − 6 z + 21 = 0 is

(A) 1
(B) 5
(C) 7
(D) 35

 A
199. If A and B are two events such that P ( A) = 0.7, P ( B ) = 0.3 and P   = 0.5 ,
B
 A' 
then P   is
 B'

3
(A)
8
3
(B)
12
3
(C)
14
3
(D)
16

200. Two cards are drawn from a well shuffled pack of 52 cards with replacement.
The probability that both cards are aces is

1 1
(A) ×
13 13
1 1
(B) +
13 13
1 1
(C) ×
13 17
1 4
(D) ×
13 51

KEY
SI SI SI SI SI SI SI
No. Key No. Key No. Key No. Key No. Key No. Key No. Key
1 A 31 B 61 B 91 A 121 B 151 B 181 D
2 D 32 B 62 D 92 C 122 A 152 B 182 D
3 C 33 B 63 D 93 D 123 D 153 A 183 C
4 D 34 C 64 B 94 A 124 B 154 D 184 A
5 C 35 A 65 B 95 C 125 B 155 C 185 D
6 C 36 C 66 C 96 C 126 C 156 C 186 C
7 B 37 B 67 C 97 B 127 C 157 C 187 B
8 B 38 A 68 A 98 A 128 B 158 B 188 B
9 B 39 B 69 D 99 A 129 D 159 D 189 C
10 C 40 A 70 C 100 B 130 D 160 D 190 D
11 D 41 D 71 B 101 A 131 A 161 C 191 A
12 C 42 C 72 A 102 A 132 A 162 C 192 C
13 B 43 A 73 B 103 D 133 C 163 D 193 A
14 B 44 A 74 D 104 C 134 B 164 B 194 B
15 C 45 C 75 C 105 A 135 B 165 C 195 C
16 B 46 B 76 D 106 D 136 D 166 B 196 A
17 B 47 C 77 A 107 D 137 B 167 C 197 A
18 C 48 C 78 C 108 D 138 B 168 A 198 B
19 B 49 A 79 B 109 A 139 C 169 B 199 C
20 C 50 C 80 D 110 D 140 B 170 A 200 A
21 A 51 A 81 B 111 A 141 C 171 D
22 C 52 C 82 D 112 B 142 C 172 C
23 B 53 C 83 A 113 A 143 A 173 D
24 B 54 A 84 A 114 C 144 B 174 A
25 A 55 C 85 C 115 A 145 B 175 A
26 B 56 B 86 B 116 B 146 A 176 D
27 C 57 B 87 C 117 B 147 B 177 A
28 B 58 D 88 D 118 C 148 B 178 A
29 B 59 A 89 C 119 C 149 C 179 B
30 C 60 C 90 D 120 A 150 C 180 A