BITSAT 2018 Question Paper

BITSAT Question Paper 2018
BITSAT Set 3
Duration : 3 : 00 Hrs

Exam Total Questions
BITSAT 180
Marks for
Negative Logical
Correct Physics Chemistry Mathematics English
Marks Reasoning
Answer 40 40 45 15
1 10
3

Physics

1. A capillary tube of radius R is immersed in water and water rises in it to a height H. Mass of
water in the capillary tube is M. If the radius of the tube is doubled, mass of water that will
rise in the capillary tube will now be:
(a) M
(b) 2M
(c) M/2
(d) 4M

2. A 10V battery with internal resistance 1Ω and a 15V battery with internal resistance 0.6Ω
are connected in parallel to a voltmeter (see gure). The reading in the voltmeter will be close
to :

(a) 12.5 V
(b) 24.5V
(c) 13.1 V
(d) 11.9 V

3. If the edge lengths of a cuboid are measured to be 1.2 cm, 1.5 cm and 1.8 cm, then the
volume of the cuboid is

(a) 3.240 cm 3

(b) 3.24 cm 3

(c) 3.2 cm 3

(d) 3.0 cm 3

4. In the circuit shown in the gure, nd the current through

(a) the 3Ω is 0.50 A
(b) the 3Ω is 0.25 A
(c) the 4Ω is 0.50 A
(d) the 4Ω is 0.25 A

Correct: d

5. The resistance of the wire at 20⁰C is 20 Ω and 500⁰C is 60 Ω. At which temperature its
resistance will be 25 Ω ?
(a) 50⁰C
(b) 60⁰C
(c) 70⁰C
(d) 80⁰C

Correct: d

6. A particle moving along x-axis has acceleration f, at time t, given by f = f (1 − , where
t
0 )
T

f0, and T are constants. The particle at t = 0 has zero velocity. In the time interval between t =
0 and the instant when f = 0, the particle's velocity (v ) is
x

(a) 1

2
f0 T
2

(b) f T
0
2

(c) f T
1
0
2

(d) f T 0

7. A charged particle enters in a uniform magnetic eld with a certain velocity. The power
delivered to the particle by the magnetic eld depends on
(a) force exerted by magnetic eld and velocity of the particle.
(b) angular speed ω and radius r of the circular path.
(c) angular speed ω and acceleration of the particle.

(d) None of these

Correct: d

→ = 2^i − 3^j + 4k
8. Given P ^ → ^
and Q = j − 2k. The magnitude of their resultant is
^

(a) √3
(b) 2√3
(c) 3√3
(d) 4√3

9. Two projectiles A and B thrown with speeds in the ratio 1 : √2 acquired the same heights.
If A is thrown at an angle of 45° with the horizontal, the angle of projection of B will be
(a) 0°
(b) 60°
(c) 30°
(d) 450

10. A wire carrying current I has the shape as shown in adjoining gure. Linear parts of the
wire are very long and parallel to X-axis while semicircular portion of radius R is lying in Y-Z
plane. Magnetic eld at point O is:

→ =−
(a) B
μ0 1 ^ ^
(μ i × 2k)
4π R

→=−
(b) B
μ0 1
^^
(n
^
i + 2k)
4π R

→=
(c) B
μ0 I ^ ^
(π i − 2k)
4π R

→=
(d) B
μ0 1 ^
(ni + 2k)
4π R

11. 0.5 mole of an ideal gas at constant temperature 27°C kept inside a cylinder of length L
and cross section area A closed by a massless piston.

The cylinder is attached with a conducting rod of length I, cross-section area (1/9) m2 and
thermal conductivity k, whose other end is maintained at 0°C. If piston is moved such that
rate of heat ow through the conducing rod is constant then velocity of piston when it is at
height L/2 from the bottom of cylinder is : (Neglect any kind of heat loss from system)
(a) ( k

R
) m/sec

(b) ( 10R
k
) m/sec

(c) (
k
) m/sec
100R

(d) ( k
) m/sec
1000R

12. A block of mass m= 2 kg is placed on a plank of mass M = 10 kg which is placed on a
smooth horizontal plane. The coef cient of friction between the block and the plank is μ = 1

3

. If a horizontal force F is applied on the plank, then nd the maximum value of F for which
the block and the plank move together. (Take g= 10m/s )2

(a) 30 N
(b) 40 N
(c) 120 N
(d) None of these

13. The susceptibility of a magnetism at 300 K is 1.2 × 10 . The temperature at which the
−5

susceptibility increases to 1.8 × 10
−5

(a) 150K
(b) 200K
(c) 250K
(d) 20K

14. Magnetic moment of bar magnet is M. The work done to turn the magnet by 90° of magnet
in direction of magnetic eld B will be
(a) zero
(b) M B
1

2

(c) 2MB
(d) MB

Correct: d

15. If M is magnetic moment and B is the magnetic eld, then the torque is given by
¯
→
(a) M. B
¯¯¯¯

¯
¯¯¯¯
|M|
(b) →
|B|

→ ×B
(c) M →
→ |B|
(d) |M →

16. A copper rod of length l rotates about its end with angular velocity ω in uniform magnetic
eld B. The emf developed between the ends of the rod if the eld is normal to the plane of
rotation is
(a) Bωℓ 2

(b) Bωℓ1 2

2

(c) 2Bωℓ 2

(d) Bωℓ1

4
2

17. Consider elastic collision of a particle of mass m moving with a velocity u with another
particle of the same mass at rest. After the collision the projectile and the struck particle
move in directions making angles , and , respectively with the initial direction of motion. The
sum of the angles θ + θ , is: 1 2

(a) 45°
(b) 90°
(c) 135°
(d) 180°

18. A particle of mass m executes simple harmonic motion with amplitude a and frequency v.
The average kinetic energy during its motion from the position of equilibrium to the end is
(a) 2π ma v 2 2 2

(b) π ma v 2 2 2

(c) mu v
1

4
2 2

(d) 4π ma v 2 2 2

19. An elastic string of unstretched length L and force constant k is stretched by a small
length x. It is further stretched by another small length y. The work done in the second
stretching is

(a) 1/2Ky 2

(b) 1/2Ky(2x + y)
(c) 1/2K (x + y )2 2

(d) 1/2k(x + y) 2

20. A coil 10 turns and a resistance of 20Ω is connected in series with B.G of resistance 30Ω.
The coil is placed with its plane perpendicular to the direction of a uniform magnetic eld of
induction 10 T. If it is now turned through an angle of 60° about an axis in its plane. Find
−2

the charge in duced in the coil. (Area of a coil = 10 m ))
−2 2

(a) 2 × 10 C −5

(b) 3.2 × 10 C −5

(c) 1 × 10 C −5

(d) 5.5 × 10 C −5

21. A thin but rigid semicircular wire frame of radius r is hinged at O and can rotate in its own
vertical plane. A smooth peg P starts from O and moves horizontally with constant speed v , 0

lifting the frame upwards as shown in the gure.

Find the angular velocity of the frame when its diameter makes an angle of 60 with the
∘

vertical:
(a) v /r
0

(b) v /2r
0

(c) 2v /r
0

(d) v r
0

22. A resistor and an inductor are connected to an ac supply of 120 V and 50 Hz. The current
in the circuit is 3 A. If the power consumed in the circuit is 108 W, then the resistance in the
circuit is
(a) 12Ω
(b) 40Ω
(c) √(52 × 25)Ω
(d) 360Ω

23. In nite number of masses, each 1 kg are placed along the x-axis at
x = ±1m, ±2m, ±4m, ±8m ±16m …… the magnitude of the resultant gravitational

potential in terms of gravitational constant G at the origin (x=0) is
(a) G/2
(b) G
(c) 2G
(d) 4G

24. A resistor of resistance R, capacitor of capacitance C and inductor of inductance L are
connected in parallel to AC power source of voltage εₒ, sin ωt. The maximum current through
the resistance is half of the maximum current through the power source. The value of R is
√3
(a) ∣ωC− 1 ∣
∣ ωL
∣

(b) √3 ∣∣ 1

ωC
− ωL∣
∣

(c) √5 ∣∣
1
− ωL
ωC

(d) None of these

25. A direct current of 5A is superposed on an alternating current I = 10sinωt owing through
the wire. The effective value of the resulting current will be
(a) (15A/2)
(b) 5√3A
(c) 5√5A
(d) 15A

26. The electric and the magnetic eld associated with an E.M. wave, propagating along
the+z-axis, can be represented by
→ = E ^i ⋅ B
(a) [E → = B ^j ]
0 0

→ = E k,
(b) [E → B = B ^i ]
0
¯
¯¯¯
¯

0

→ = E ^i, B
(c) [E → = B i]
0 0

→ = E ^j , B
(d) [E → = B k]
0
^
0

27. Two concentric conducting thin spherical shells A, and B having radii
rA and r ((r
B > r ) are charged to Q
B A A and − Q B (Q | > |Q ]. The electric eld along a
B A

line passing through the centre is

(a)

(b)

(c)

(d)

28. An electromagnetic wave passes through space and its equation is given by
E = E sin(ωt − kx) where E is electric eld. Energy density of electromagnetic wave in
0

space is
(a) ε E
1

2
0
2

0

(b) 1

4
ε 0 E0
2

(c) ε E
0
2

0

(d) 2ε E 0
2
0

29. The magnetic eld in a travelling electromagnetic wave has a peak value of 20 nT. The
peak value of electric eld strength is
(a) 3V/m
(6) 6V/m
(c) 9V/m
(d) 12V/m

30. Four point charges -Q, -q, 2q and 2Q are placed, one at each corner of the square. The

relation between Q and q for which the potential at the centre of the square is zero is :
(a) Q = -q
(b) Q = − 1

q

(c) Q = q
(d) Q = 1

q

31. A point object O is placed in front of a glass rod having spherical end of radius of
curvature 30 cm. The image would be formed at

(a) 30 cm left
(b) ∞
(c) 1 cm to the right
(d) 18 cm to the left

32. A cube is subjected to a uniform volume compression. If the side of the cube decreases by
2% the bulk strain is
(a) 0.02
(b) 0.03
(c) 0.04
(d) 0.06

Correct: d

33. The focal length of thin convex lens for blue rays are 100 cm and 96.8 cm respectively.
Then, the dispersive power of the material of the lens is
(a) 0.968
(b) 0.98
(c) 0.0325
(d) 0.325

34. A biconvex lens has a radius of curvature of magnitude 20 cm. Which one of the following
options best describe the image formed of an object of height 2 cm placed 30 cm from the
lens?
(a) Virtual, upright, height=1 cm
(b) Virtual, upright, height=0.5 cm

(c) Real, inverted, height=4 cm
(d) Real, inverted, height = 1cm

35. A thin plano-convex lens of focal length f is split into two halves: one of the halves is
shifted along the optical axis. The separation between object and image planes is 1.8 m. The
magni cation of the image formed by one of the half-lenses is 2. If f and d be the focal length
of the lens and separation between the two halves respectively then,

(a) f=0.4 m
(b) f=0.6 m
(c) d=0.5 m
(d) d=0.9 m

36. In Young's double slit experiment, λ = 500nm, d=1mm, D=1m. Minimum distance from
the central maximum for which intensity is half of the maximum intensity is
(a) 2.5 × 10 m−4

(b) 1.25 × 10 m−4

(c) 0.625 × 10 m −4

(d) 0.3125 × 10 m −4

37. The gure shows the interference pattern obtained in a double-slit experiment using light
of wavelength 600 nm. 1, 2, 3, 4 and 5 are marked on ve fringes. The third order bright fringe
is

(a) 2
(b) 3
(c) 4
(d) 5

Correct: d

38. What is the minimum energy required to launch a satellite of mass m from the surface of a
planet of mass M and radius R in a circular orbit at an altitude of 2R?
(a) 5GmM

6R

(b) 2GmM

3R

(c) GmM

2R

(d) GmM

2R

39. There are two sources kept at distances 2λ. A large screen is perpendicular to line joining
the sources. Number of maximas on the screen in this case is ( \lambda \) = wavelength of
light)

(a) 1
(b) 3
(c) 5
(d) 7

40. An interference pattern the position of zeroth order maxima is 4.8 mm from a certain
point P on the screen. The fringe width is 0.2 mm. The position of second order minima from
point P is
(a) 5.1 mm
(b) 5 mm
(c) 40 mm
(d) 5.2 mm

Chemistry

41. On passing a current of 1.0 ampere for 16 min and 5 sec through one litre solution of
CuCl all copper of the solution was deposited at cathode. The strength of CuCl , solution
2 2

was (Molar mass of Cu=63.5; Faraday constant=96,500 Cmol ) −1

(a) 0.01 N
(b) 0.01 M

(c) 0.02 M
(d) 0.2 N

42. A 100.0 mL dilute solution of Ag⁺ is electrolysed for 15.0 minutes with a current of 1.25
mA and the silver is removed completely. What was the initial [Ag⁺]?
(a) 2.32 × 10 −1

(b) 2.32 × 10 −4

(c) 2.32 × 10
−3

(d) 1.16 × 10 −4

Correct: d

43. On electrolysis of water, a total of 1 mole of gases is evolved. The amount of water
decomposed is
(a) 1 mol
(b) 2 mol
(c) ⅓ mol
(d) ⅔ mol

Correct: d

44. What is the freezing point of a 10% (by weight) solution of CH OH in water?
3

[K of CH OH = -1.86°C/m]
f 3

(a) 90°C
(b) 10°C
(c) 6.45°C
(d) -6.45°C

Correct: d

45. Which one the following removes temporary hardness of water?
(a) Slaked lime
(b) Plaster of Paris
(c) Epsom
(d) Hydrolith

46. The accompanying gure depicts a change in concentration of species A and B for the
reaction A → B, as a function of time. The point of intersection of the two curves represents

(a) t 1/2

(b) t 3/4

(c) t 2/3

(d) Data insuf cient to predict

47. The rate constant of a reaction is 1.5 × 10 −3
at 25°C and 2.1 × 10
−2
at 60°C. The
activation energy is:
−2

(a) 35

333
R log
e
2.1×10

−2
1.5×10

(b) 298×333

35
R log
e
21

1.5

(c) 298×333

35
R log
e
2.1

(d) 298×333

35
R log
e
2.1

1.5

48. Beryllium shows diagonal relationship with aluminium. Which of the following similarity
is incorrect?
(a) Be forms beryllates and Al forms aluminates
(b) Be(OH) , like Al(OH) is basic.
2 3

(c) Be like Al is rendered passive by HNO 3

(d) Be C like Al C yields methane on white due to formation of
2 4 3

49. A graph is ploted between log K virsus 1/T for calculation of activation energy (E ). The
a

correct plot is

(a)

(b)

(c)

(d)

50. Clathrates are
(a) non-stoichiometric compounds
(b) complex compounds
(c) interstitial compounds
(d) ionic compounds

51. Freundlich equation for adsorption of gases (in amount of x g) on a solid (in amount of m
g) at constant temperature can be expressed as
(a) log x

m
= log p + log K
1

n

(b) log m
x
= log K +
1

n
log p

(c) x

m
∝ p
n

(d) x

m
= log p +
1

n
log K

52. Which of the following feature of catalysts is described in reactions given below?
Cu/ZnO−C2 O3
(i) CO(g) + 2H (g) 2 ⟶
CH3 OH(g)

Cu

(ii) CO(g) + H (g) ⟶ HCHO(g)
2

Ni

(iii) CO(g) + 3H (g) ⟶ CH (g) + H O(g)
2 4 2

(a) Activity
(b) Selectivity
(c) Catalytic promoter
(d) Catalytic poison

53. The IUPAC name of the compound is

(a) 3,3-dimethyl - 1- cyclohexanol
(b) 1, 1-dimethyl-3-hydroxy cyclohexane
(c) 3,3-dimethyl-1-hydroxy cyclohexane
(d) 1, 1-dimethyl-3-cyclohexanol

54. The isoelectric-point of a colloidially dispersed material is the pH value at which
(a) the dispersed phase migrate in an electric eld.
(b) the dispersed phase does not migrate in an electric eld.
(c) the dispersed phase has pH equal to 7.
(d) the dispersed phase has pH equal to zero.

55. Which of the following contain plane of symmetry?
(a) trans-1,3 dichloro cyclohexane
(b) trans-1,2 dichloro cyclohexane
(c) cis-1,2 dichloro cyclohexane
(d) trans-1,3 cyclopentane

56. Which of the following metal is leached by cyanide proces
(a) Ag
(b) Na
(c) Al
(d) Cu

57. In the following structures, which two forms are staggered conformations of ethane ?

(a) 1 and 4
(b) 2 and 3
(c) 1 and 2

(d) 1 and 3

58. Metal which can be extracted from all three dolomite, magnesite and carnallite is
(a) Na
(b) K
(c) Mg
(d) Ca

59. Semiconductor materials like Si and Ge are usually puri ed by
(a) distillation
(b) zone re ning
(c) liquation
(d) electrolytic re ning

60. Give the possible structure of X in the following reaction :
D2 O

C6 H6 + D, SO4 ⟶ x

(a)

(b)

(c)

(d)

Correct: d

61. Which of the following is not a member of chalcogens?
(a) O
(b) S
(c) Se
(d) Po

Correct: d

62. Pick out the wrong statement.
(a) Nitrogen has the ability to form pt-pt bonds with itself
(b) Bismuth forms metallic bonds in elemental
(c) Catenation tendency is higher in nitrogen when compared with other elements of the
same group.
(d) Nitrogen has higher rst ionisation enthalpy when compared with other
elements of the same group.

63. Which of the following shows nitrogen with its increasing order of oxidation number?
(a) NO < N O < NO < NO − < NH
2 2 3
+

4

(b) NH < N O < NO < NO < NO
+

4 2 2
−

3

(c) NH + −
< N2 O < NO < NO2 < NO
4 3

(d) NH +

4
< NO < N2 O < NO2 < NO
−

3

64. Two elements A and B have electronegativities 1.2 and 3.0 respectively. The nature of
bond between A and B would be
(a) ionic
(b) covalent
(c) co-ordinate
(d) metallic

65. Laughing gas is
(a) nitrogen pentoxide
(b) nitrous oxide
(c) nitrogen trioxide
(d) nitric oxide

66. Which of the following is not involved in the formation of photochemical smog?

(a) Hydrocarbon
(b) NO
(c) so
2

(d) O3

67. The colour of 62 Sm
3+
is yellow. The expected colour of 66 Dy
3+
is
(a) Yellow
(b) Red
(c) Blue
(d) Green

68. Identify the wrong statement in the following:
(a) Chloro uorocarbons are responsible for ozone layer depletion.
(b) Greenhouse effect is responsible for global warming
(c) Acid rain is mostly because of oxides of nitrogen and sulphur.
(d) Ozone layer does not permit infrared radiation from the sun to reach the earth.

Correct: d

69. The number of elements present in the d-block of the periodic table is
(a) 40
(b) 41
(c) 45
(d) 46

70. Al (at. wt 27) crystallizes in the cubic system with a cell edge of 4.05 Å. Its density is 2.7 g
per cm . Determine the unit cell type & calculate the radius of the Al atom.
3

(a) fcc, 2.432 Å
(b) bcc, 2.432 Å
(c) bcc, 1.432 Å
(d) fcc, 1.432 Å

Correct: d

71. Which of the following element do not form complex with EDTA?
(a) Ca
(b) Mg
(c) Be
(d) Sr

72. Which one of the following cyano complexes would exhibit the lowest value of
paramagnetic behaviour ?
(a) [Co(CN) ]
3−
6

(b) [Fe(CN) ]
3−
6

(c) [Mn(CN) ]
3−
6

(d) [Cr(CN) ]
3−
6

(At. Nos : Cr=24, Mn=25, Fe=26, Co=27)

73. Equal weights of NaCl and KCl are dissolved separately in equal volumes of solutions
Molarity of the two solutions will be
(a) Equal
(b) That of NaCl will be less than that of KCI
(c) That of NaCl will be more than that of KCI
(d) That of NaCl will be about half of that of KCl solution

74. Which of the following complexes has square planar structure?
(a) Ni(CO) 4

(b) [Ni(CN) ]
−2
4

(c) [Ni(Cl) ]
−2
4

(d) [Zn(NH ) ]
+2

3 4

75. When N O is heated at certain temperature, it dissociates as
2 5

N2 O5 (g) ⇌ N2 O3 g (+O2 )(g); Kc = 2.5

At the same time also decomposes as:
N2 O3 (g) ⇌ N2 O g (+O2 ) (g)

If initially 4.0 moles of N O are taken in 1.0 litre ask and allowed to dissociate.
2 3

Concentration of O fata equilibrium is 2.5 M. Equilibrium concentration of N O is:
2 2 5

(a) 1.0M
(b) 1.5M
(c) 2.166M
(d) 1.846M

Correct: d

76. An aromatic compound has molecular formula C H Br .Give the possible isomers and the
7 7

appropriate method to distinguish them.

(a) 3 isomers; by heating with AgNO solution
3

(b) 4 isomers; by treating with AgNO solution
3

(c) 4 isomers; by oxidation
(d) 5 isomers, by oxidation

77. Which of the following can act as both Bronsted acid and Bronsted base?
(a) Na CO
2 3

(b) OH
(c) HCO
−

3

(d) NH 3

78. The number of double bonds in gammexane is :
(a) 0
(b) 1
(c) 2
(d) 3

79. Which of the following is less acidic among the given halogen compounds?
(a) CHF 3

(b) CHI 3

(c) CHCl 3

(d) CHBr 3

80. The oxidation state of sulphur in is
(a) +6
(b) +3/2
(c) +5/2
(d) -2

Mathematics

81. The points represented by the complex numbers 1 + i, −2 + 3i, 5

3
i on the argand plane
are

(a) vertices of an equilateral triangle
(b) vertices of an isosceles triangle
(c) collinear
(d) None of these

82. A and B are any two non-empty sets and A is proper subset of B. If n(A) = 5, then nd the
minimum possible value of n(AΔB).
(a) 1
(b) 5
(c) Cannot be determined
(d) none of these

∣ 0 −y −2 ∣
∣ ∣
83. If x, y, z are complex numbers, and Δ = ∣¯¯
y
¯
0 −x ∣ then Δ is
∣ ∣
∣¯¯
¯
z
¯
¯¯
x 0 ∣

(a) purely real
(b) purely imaginary
(c) complex
(d) 0

84. Let A and B be two sets such that A ∩ X = B ∩ X = ϕ and A ∪ X = B ∪ X for same set
X. Then
(a) A = B
(b) A = X
(c) B = X
(d) A ∪ B = X

∣ p q − y r − z∣
p q
85. If ∣ p − x q r − z
∣
= 0 then the value of x
+
y
+
r

z
is
∣ ∣
∣p − x q − y r ∣

(a) 0
(b) 1
(c) 2
(d) 4pqr

86. If x is real number, then 2
x

x −5x+9
must lie between
(a) 1/11 and 1
(b) 1 and 1/11
(c) -11 and 1
(d) -1/11 and 1

Correct: d

3π
1, when 0 < x ≤
87. If f (x) = {
4

2 3π
2 sin x, when < x < π
9 4

(a) f(x) is continuous at x = 0
(b) f(x) is continuous at x = π
(c) f(x) is continuous at x = 3π

4

(d) f(x) is discontinuous at x =
3π

4

88. The value of c in (0, 2) satisfying the mean value theorem for the function
f (x) = x(x − 1) , x ∈ [0, 2] is equal to
2

(a) 3/4
(b) 7/8
(c) 1/4
(d) -7/8

89. If e + e
x f (x)
= e then the domain of f(x) is
(a) ( -∞ , 1 )
(b) ( - ∞, 0 )
(c) ( 1, ∞ )
(d) None

2

90. Let y = e .Then ( is
d y 2
2x d x
)( 2
)
2
dx dy

(a) 1
(b) e−2x

(c) 2e2x

(d) −2e −2x

Correct: d

91. A ball is dropped from a platform 19.6m high. Its position function is –
(a) x = −4.9t + 19.6(0 ≤ t ≤ 1)
2

(b) x = −4.9t 2
+ 19.6(0 ≤ t ≤ 2)

(c) x = −9.8t + 19.6(0 ≤ t ≤ 2)
2

(d) x = −4.9t − 19.6(0 ≤ t ≤ 2)
2

92. Number of solutions of equation sin 9θ = sin θ in the interval [0, 2π] is
(a) 16
(b) 17
(c) 18
(d) 15

93. A cylindrical gas container is closed at the top and open at the bottom. if the iron plate of
the top is 5/4 time as thick as the plate forming the cylindrical sides. The ratio of the radius to
the height of the cylinder using minimum material for the same capacity is
(a) 2/3
(b) 1/2
(c) 4/5
(d) 1/3

94. If A and B are positive acute angles satisfying
2 2 3 sin A 2 cos B
3 cos A + 2 cos B = 4 and =
sin B cos A

Then the value of A + 2B is equal to
(a) π/6
(b) π/2
(c) π/3
(d) π/4

95. The set of all values of a for which the function
does not possess critical
2 2 2
f (x) = (a − 3a + 2) (cos x/4 − sin x/4) + (a − 1)x + sin 1

points is
(a) [ 1 , ∞)
(b) (0, 1) ∪ (1, 4)
(c) (−2, 4)
(d) (1, 3) ∪ (3, 5)

96. 2 3x
− 7n − 1 is divisible by

(a) 64
(b) 36
(c) 49
(d) 25

2
x 3
e (2x+x )

97. ∫ 2
dx is equal to
(3+x2 )

2

(a)
x
e
+ k
2
(3+x )
2
x

(b) 1

2
e

2
2
+ k
(3+x )
2

(c)
x
1 e
+ k
2
4 (3+x2 )

2

(d)
x
1 e
+ k
2
2 (3+x )

Correct: d

98. If :p Raju is tall and q: Raju is intelligent, then the symbolic statement −p ∨ q means
(a) Raju is not tall or he is intelligent.
(b) Raju is tall or he is intelligent
(c) Raju is not tall and he is intelligent .
(d) Raju is not tall implies he is intelligent

99. If ∫ is equal to
cos x−1 x
e dx
sin x+1
x

(a)
e cos x
+ C
1+sin x

(b) C −
x
e sin x

1+sin x
x

(c) C − 1+sin x
e

x

(d) C −
e cos x

1+sin x

100. For n ∈ N , x n+1
+ (x + 1)
2n−1
is divisible by
(a) x
(b) x+1
(c) x + x + 1
2

(d) x − x + 1
2

101. The area enclosed by the curves y = x and y = √x is 3

(a) 5/3 sq units

(b) 5/4 sq units
(c) 5/12 sq units
(d) 12/5 sq units

1±5√−3
102. The roots of the equation 5, −4, 2
are:
1±5√−3
(a) 5, −4,
2

−1±5√−3
(b) −5, 4, 2

−1±5√−3
(c) 5, 4, 2

(d) −5, −4,
1±5√−3

2

103. Let the straight line x = b divide the area enclosed by y = (1 − x) , y = 0 and x=0 into
2

two parts R (0 ≤ x ≤ b) and R (b ≤ x ≤ 1) such that R (b ≤ x ≤ 1) Then b equals
1 2 2

(a) 3/4
(b) 1/2
(c) 1/3
(d) 1/4

104. If f (z) = where z=1+2i then |f (z)| is
7−z

1−z 2

|z|
(a) 2

(b) |z|
(c) 2|z|
(d) None of these

105. The area of the region bounded by the x-axis the curve y=f(x) and the lines x=1,x=b, is
equal to for all b>1 ,then f(x) is
(a) √x − 1
(b) √x + 1
(c) √x + 1 2

(d) x

√1+x2

Correct: d

dy
106. An integrating factor of the differential equation sin x dx
+ 2y cos x = 1 is
(a) sin x 2

(b)
2

sin x

(c) log | sin x|
(d) 1
2
sin x

dy
107. The expression satisfying the differential equation (x 2
− 1)
dx
+ 2xy = 1 is
(a) x y − xy = c
2 2

(b) (y − 1) x = y + c
2

(c) (x 2
− 1) y = x + c

(d) none of these

dy
108. The solution of dx
= cos(x + y) + sin(x + y) is
x+y
(a) log[1 + tan( 2
)] + C = 0

x+y
(b) log[1 + tan( 2
)] = x + C

x+y
(c) [1 − tan( 2
)] = x + C

(d) none of these

109. Let f : (1∞) → (2∞) be differentiable function such that f (1) = 2 . If
for all x ≥ 1 then the value of f(2) is
x
3
6∫ f (t)dt = 3xf (x) − x
1

(a) 3
(b) 4
(c) 5
(d) 6

Correct: d

110. If ϕ(x) is a differential function then the solution of the differential equation
′
dy + {yϕ(x) − ϕ(x)ϕ (x)} dx = 0

(a) y = {ϕ(x) − 1} + Ce −ϕ(x)

(b) yϕ(x) = {ϕ(x)} + C 2

(c) ye ϕ(x)
= ϕ(x)e
ϕ(x)
+ C

(d) y − ϕ(x) = ϕ(x); −ϕ(x)

111. The area of the region R = {(x, y); |x| ≤ b| and x 2
+ y
2
≤ 1} is

(a) sq units
3π

8

(b) 5π

8
sq units
(c) π

2
sq units
(d) sq units
π

8

112. If ^i + ^
j, ^
j + k̇, ^ ^ are the position vector of the vertices of triangle ABC taken in
i + k

order then ∠A is equal to
(a)
π

2

(b)
π

5

(c) π

6

(d)
π

3

Correct: d

113. Let a, →
b&c be non-coplanar unit vectors equally inclined to one another at an acute
¯
¯¯ ¯¯

→→b c]| in terms of θ is equal to
angle θ . Then |[a ¯¯

(a) (1 + cos θ)√cos 2θ
(b) (1 + cos θ)√1 − 2 cos 2θ
(c) (1 − cos θ)√1 + 2 cos 2θ
(d) None of these

114. Let a
^ and ^
b be two non -collinear unit vector .If \(u = a a − ^
^ − (^ b , \) and v = a
b)^ ^ × ^
b

then |v| is equal to
(a) |u|
(b) |u| + |(v + a
^ )|

(c) 2|v|
(d) |v| + u. (a
^ + ^
b)

115. The number of times the digit 5 will be written when listing the integers from 1 to 1000,
is
(a) 271
(b) 272
(c) 300
(d) None of these

116. The projection of line joining (3, 4, 5) and (4,6,3) on the line joining (-1,2,4) and (1,0,5) is
(a) 4

3

(b)
2

3

(c)
8

3

(d) 1/3

117. Let f (x) = then fof (x) , provided that:
ax+b

cx+d

(a) d=-a
(b) d=a
(c) a=b=1
(d) a=b=c=d=1

118. The distance of the point (1, -5,9) from the plane x + y + z = 5 measured along a straight
line x = y − z is 2√3k then the value of k is
(a) 5
(b) 6
(c) √3
(d) 4

119. The coef cient of x in the expansion of (1 + x)
5 21
+ (1 + x)
22
+ … + (1 + x)
30
is
(a) C 51
5

(b) C 9
5

(c) 31 −21
C C6
6

(d) 30
C5 −
20
C5

120. The equation of the plan through the interaction of the planes x + y + z = 1 and
2x + 3y − z + 4 = 0 parallel to x axis, is

(a) y - 3z + 6 = 0
(b) 3y - 2+ 6 = 0
(c) y + 3z + 6 = 0
(d) 3y - 2z + 6 =0

121. Let R= {(3,3), (6,6), (9,9), (12, 12),(6,12), (3,9),(3, 12), (3,6)} be a relation on the set A=
{3,6,9,12). Then, the relation is
(a) an equivalence relation

(b) re exive and symmetric
(c) re exive and transitive
(d) only re exive

122. One mapping is selected at random from all mappings of the set S= {1, 2, 3, .......} into
itself. The probability that it is one-one is 3/32 . Then the value of n is
(a) 3
(b) 4
(c) 5
(d) 6

123. A random variable X has the probability distribution
X 1 2 3 4 5 6 7 8

p(X) 0.15 0.23 0.12 0.10 0.20 0.08 0.07 0.05

For the events E={ X is a prime number} and F={X<4},then P (E ∪ F )
(a) 0.50
(b) 0.77
(c) 0.35
(d) 0.87

124. A man takes a step forward
5 5

(a)
2 ⋅3
10
5
5

(b) 462 × ( 25
6
)

5

(c) 231 ×
3
10
5

(d) None of these

125. Let X denote the number of times head occur in n tosses of a fair coin, If P (X = 6) are
in AP, then the value of n is
(a) 7,14
(b) 10,14
(c) 12,7
(d) 14, 12

English

126. In each ot the following questions, out of the four alternatives, choose the one which can
be substituted for the given words/sentence.
A person who believes that pleasure is the chief good.
(a) Stoic
(b) Hedonist
(c) Epicure
(d) Sensual

127. Choose the word opposite in meaning to the given word, METICULOUS
(a) Forgetful
(b) Destructive
(c) Careless
(d) Flagrant

128. Out of the four alternatives, choose the one which express the correct meaning of the
word, CONSOLATION
(a) Comfort
(b) Problem
(c) Sadness
(d) Solution

129. Choose the word opposite in meaning to the given word, FLAGITIOUS
(a) Innocent
(b) Vapid
(c) Ignorant
(d) Frivolous

130. A person who is incharge of museum.
(a) caretaker
(b) warden
(c) supervisor
(d) curator

Correct: d

131. Choose the word opposite is meaning to the given word, AUSPICIOUS
(a) Prosperous
(b) Unfavourable
(c) Improper
(d) New

132. Which of the following phrases (I), (II), and (III) given below each sentence should
replace the phrase printed in bold letters to make the sentence grammatically correct?
Choose the best option among the ve given alternatives that re ect the correct use of phrase
in the context of the grammatically correct sentence. If the sentence is correct as it is, mark
(d) ie., "No correction required" as the answer.
By working part-time and looking after his old mother, he managed to get the best for both
worlds.
(I) the best at both worlds
(II) the best of both worlds
(III) the best on both worlds
(a) Only (I) is correct
(b) Only (II) is correct
(c) Only (III) is correct
(d) No correction required

133. Choose the word opposite is meaning to the given word, IMPEDE
(a) Block
(b) Delay
(c) Push
(d) Freeze

134. Read the following passage carefully and answer the questions given below it.
The likelihood of at least 600,000 deaths being caused annually in India by ne particulate
matter pollution in the air is cause for worry, even if the data released by the World Health
Organisation are only a modelled estimate. The conclusion that so many deaths could be
attributed to particulate matter 2.5 micrometres a or less in size is, of course, caveated,
sincero comprehensive measurement of PM2.5 is not yet being n done and the linkages
between pollution, disease and in deaths need further study. What is not in doubt is that 1
residents in many urban areas are forced to breathe unhealthy levels of particulates, and the
smallest of these - PM10 and less - can penetrate and get lodged deep in the lungs. The WHO
Global Burden of Disease study has been working to estimate pollution-linked health impacts,
such as stroke and ischaemic heart disease, acute lower respiratory infection and chronic
obstructive pulmonary disease. Data on ne particulates in India show that in several

locations the pollutants come from burning of biomass, such as coal, fuel wood, farm litter
and cow dung cakes. In highly built-up areas, construction debris, road dust and vehicular
exhaust add to the problem. The Prime Minister launched an Air Quality Index last year
aimed at improving pollution control. The new data, which the WHO says provide the best
evidence available on the terrible toll taken by particulates, should lead to intensi ed action.
A neglected aspect of urban air pollution control is the virtual discarding of the Construction
and Demolition 3 Waste Management Rules, noti ed to sustainably manage debris that is
dumped in the cities, creating ·severe particulate pollution.
The Environment Ministry has highlighted the role that debris can play as a resource.
Municipal and government contracts are, under the rules, required to utilise up to 20 per cent
materials made from construction and demolition waste, and local authorities must place
containers to hold debris. This is is dumped in the cities ,creating severe particulate pollution.
must be implemented without delay. Providing cleaner fuels and scienti cally designed
cookstoves to those who have no option but to burn biomass, would have a big impact on
reducing particulate matter in the northern and eastern States, which are the worst-hit during
winter, when biomass is also used for heating. Greening the cities could be made a mission,
involving civil society, with a focus on landscaping open spaces and paving all public areas to
reduce dust. These measures can result in lower PM10 and PM2.5 levels. measurement of
these particulates is currently absent in many cities, a lacuna that needs to be addressed.
Which of the following is/are not true in the context of the passage?
(a) Eastern and Southern states are worst hit in winter by burning of biomass.
(b) The smallest particulate matter PM2.5 penetrates and gets lodged in lungs.
(c) Data on ne particulates in India show that in several locations the pollutants come from
the smoke emitted by vehicles.
(d) None is true

Correct: d

135. A part of sentence is underlined. Balance are given alternatives to the underlined part a,
b, c and d which may improve the sentence. Choose the correct alternative.
She did not believe me.
(a) believing
(b) believe to
(c) believe
(d) No improvement

Correct: d

136. Choose the correct alternative option out of four
China is big country ,in area it is bigger than any other country ______________ Russia?
(a) accept
(b) except
(c) expect
(d) access

137. Out of the four alternatives, choose the one which express the correct meaning of the
word, SAGACIOUS
(a) Shameless
(b) Wise
(c) Powerless
(d) Foolish

138. A part of sentence is underlined. Below are given alternatives to the underlined part (a),
(b), (c) and (d) which may improve the sentence. Choose the correct alternative.
It was not possible to drag any conclusion so he left the case.
(a) Fetch
(b) Find
(c) Draw
(d) No improvement

139. In each of the following questions choose the alternative which is mostly nearly the same
in meaning to the word given capital letters
EMPHERIAL
(a) Uneral
(b) Mythical
(c) Short-living
(d) Pliable

140. A part of sentence is underlined. Below are given alternatives to the underlined part (a),
(b), (c) and (d) which may improve the sentence. Choose the correct alternative.
"Mind your language !" he shouted.
(a) change
(b) inspect
(c) hold
(d) No improvement

Correct: d

Logical Reasoning

141. In a code language, if REGAINS is coded as QDFZHMR, then the word PERIODS will be

coded as
(a) ODQNHCR
(b) ODDOHCR
(c) ODQHNCR
(d) ODQHNRC

142. The average age of 8 men is increased by 2 yr when one of them whose age is 20 yr is
replaced by a new man. What is the age of the new man
(a) 28 yr
(b) 36 yr
(c) 34 yr
(d) 35 yr

143. Select the related letter/word/ number from the given alternatives. Distance: Odometer ::
?: Barometer
(a) Humidity
(b) Pressure
(c) Thickness
(d) Wind

144. In a queue of children, Arun is fth from the left and Suresh is sixth from the right.
When they interchange their places among themselves, Arun becomes thirteenth from the
left. Then, what will be Suresh's position from the right?
(a) 8th
(b) 14th
(c) 15th
(d) 16th

145. Choose the correct alternatives from the given ones that will complete the series.
22,26,53,69, 194, ?
(a) 230
(b) 260
(c) 250
(d) 245

Correct: d

146. Which of the following will ll the series?

2, 9, 28, __ , 126
(a) 64
(b) 65
(c) 72
(d) 56

147. Select the missing number from the given responses.

(a) 888
(b) 788
(c) 848
(d) 842

148. Today is Thursday. The day after 59 days will be
(a) Sunday
(b) Monday
(c) Tuesday
(d) Wednesday

149. Which answer gure complete the form in question gure ?
Question gure :

Answer Figure:

(a)

(b)

(c)

(d)

Correct: d

150. In a code language, if SUMMER is coded as SDNLVR, then the word WINTER will be
coded as:
(a) SDUMJV
(b) SDMUJV
(c) SUUMVJ
(d) VJMUDS