BITSAT 2016 Question Paper

BITSAT Question Paper 2016
BITSAT Set 1
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. If C, the velocity of light, g the acceleration due to gravity and P the atmospheric pressure
be the fundamental quantities in MKS system, then the dimensions of length will be same as
that of
(a)
C

g

(b)
C

P

(c) PCg
(d)
2
C

g

2. Seven resistances, each of value 20Ω, are connected to a 2 V battery as shown in the gure.
The ammeter reading will be

(a) 1/10 A
(b) 3/10 A
(c) 4/10A
(d) 7/10 A.

1/2
p
3. The frequency of vibration of string is given by v = [
F

m
] .
2l

Here p is a number of segments in the string and l is the length. The dimensional formula for
m will be
(a) [M LT
0 −1
]

(b) [ML T
0 −1
]

(c) [ML
−1 0
T ]

(d) [M L T ]
0 0 0

4. For the equation A v d , where F is the force, A is the area, v is the velocity and d is the
3 5 c

density, the values of a, b and c are respectively
(a) 1,2,1
(b) 2,1,1
(c) 1,1,2
(d) 0,1,1

5. If the temperature of black body increases from 300 K to 900K, then the rate of energy
radiation increases by how much times?
(a) 81
(b) 3
(c) 9
(d) 2

6. A juggler keeps on moving four balls in the air throwing the balls after intervals. When one
ball leaves his hand (spcod = 20ms ) the position of other balls (height in m) will be (Take
−1

g= 10ms −2
)

(a) 10, 20, 10
(b) 15, 20, 15
(c) 5, 15, 20
(d) 5, 10, 20

7. If a body cools down from 80°C to 60°C in 10 min when the temperature of the surrounding
is 30°C, then the temperature of the body after next 10 min will be
(a) 50°C
(b) 48°C
(c) 30°C
(d) None of these

8. A frictionless wire AB is xed on a sphere of radius R. A very small spherical ball slips on
this wire. The time taken by this ball to slip from A to B is

√2gR

(a)
g cos θ

(b) 2√gR cos θ

g

(c) √ 2
R

g

gR
(d)
√g cos θ

9. A body starts from rest at time t=0, the acceleration time graph is shown in the gure. The
maximum velocity attained by the body will be

(a) 110 m/s
(b) 55 m/s
(c) 650 m/s
(d) 550 m/s

10. A man drives a car from y towards x at speed of 60 km/h. A car leaves station x for station
y every 10 min. The distance between x and y is 60 km. The car travels at the speed of 60
km/h. A man drives a car from y towards x at speed of 60 km/h. If he starts at the moment
when rst car leaves the station y, then how many cars would be meet on the route ?
(a) 20
(b) 7
(c) 10
(d) 2

11. What is the magnetic eld at the centre of arc in the gure below?

μ0
(a) 4π
⋅
2

r
[√2 + π]

μ0
(b) 4π
⋅
2i

r
[ √2 +
π

4
]

μ0
(c)
i
⋅ [√2 + π]
4π r

μ0
(d)
i π
⋅ [ √2 + ]
4π r 4

12. A boy running on a horizontal road at 8 km/h nds the rain falling vertically. He increases
his speed to 12 km/h and nds that the drops makes 30° with the vertical. The speed of rain
with respect to the road is
(a) 4√7km/h
(b) 9√7kmh
(c) 12√7km/h
(d) 15√7km/h

13. One mole of an ideal gas is taken from state A to state B by three different processes,
(i) ACB
(ii) ADB
(iii) AEB
as shown in the P-V diagram. The heat absorbed by the gas is

(a) greater in process (ii) than in (i)
(b) the least in process (ii)
(c) the same in (i) and (iii)
(d) less in (iii) than in (ii)

14. The velocity of a projectile at the initial point A is (2^i + 3^
j) m/s its velocity (in m/s) at

point B is

(a) −2^i + 3^
j

(b) 2^i − 3^
j

(c) 2^i + 3^
j

(d) −2^i − 3^
j

15. A positive charge q is projected in magnetic eld of width mv
with velocity v. Then the
√2qB

time taken by charged particle to emerge from the magnetic eld is
(a) m

√2qB

(b)
πm

4qB

(c)
πm

2qB

(d) πm

√2qB

16. If a stone of mass 0.05 kg is thrown out a window of a train moving at a constant speed of
100 km/h then magnitude of the net force acting on the stone is
(a) 0.5 N
(b) zero
(c) 50 N
(d) 5 N

17. A body of mass M hits normally a rigid wall with velocity V and bounces back with the
same velocity. The impulse experienced by the body is
(a) MV
(b) 1.5 MV
(c) 2 MV
(d) zero

18. At a place, if the earth's horizontal and vertical components of magnetic elds are equal,
then the angle of dip will be
(a) 30°

(b) 90°
(c) 45°
(d) 0°

19. Two equal heavy spheres, each of radius r, are in equilibrium within a smooth cup of
radius 3r. The ratio of reaction between the cup and one sphere and that between the two
sphere is

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

20. Water of volume 2 litre in a container is heated with a coil of 1 kW at 27°C. The lid of the
container is open and energy dissipates at rate of 160 J/s. In how much time temperature will
rise from 27°C to 77°C? [Given speci c heat of water is 4.2 kJ/kg]
(a) 8 min 20 s
(b) 6 min 2 s
(c) 7 min
(d) 14 min

21. A particle of mass moving with velocity v collides with a mass m, at rest, then they get
embedded. Just after collision, velocity of the system
(a) increases
(b) decreases
(c) remains constant
(d) becomes zero

22. A particle of mass m moving in the x direction with speed 2v is hit by another particle of
mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the
percentage loss in the energy during the collision is close to
(a) 56%
(b) 62%

(c) 44%
(d) 50%

23. A conducting circular loop is placed in a uniform magnetic eld, B = 0.025 T with its plane
perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of
1mms
−1
.. The induced e.m.f. when the radius is 2 cm, is
(a) 2πμV
(b) πμV
(c) μV
π

2

(d) 2μV

24. A neutron moving with speed v makes a head on collision with a hydrogen atom in ground
state kept at rest. The minimum kinetic energy of the neutron for which inelastic collision
takes place is
(a) 10.2 eV
(b) 20.4 eV
(c) 12.1 eV
(d) 16.8 eV

25. Two simple pendulums of length 0.5 m and 20 m respectively are given small linear
displacement in one direction at the same time. They will again be in the phase when the
pendulum of shorter length has completed oscillations [nT = (n − 1)T , where T₁ is time
1 2

period of shorter length & T₂ be time period of longer wavelength and n are no. of
oscillations completed]
(a) 5
(b) 1
(c) 2
(d) 3

26. A hoop rolls down an inclined plane. The fraction of its total kinetic energy that is
associated with rotational motion is
(a) 1:2
(b) 1:3
(c) 1:4
(d) 2:3

27. A uniform rod AB of length l, and mass m is free to rotate about point A. The rod is
released from rest in the horizontal position. Given that the moment of inertia of the rod
about A is , the initial angular acceleration of the rod will be
2
mℓ

3

(a)
gℓ

2

(b) 3

2
gℓ

(c)
3g

2ℓ

(d)
2g

3ℓ

28. A whistle of frequency 500 Hz tied to the end of a string of length 1.2 m revolves at 400
rev/min. A listener standing some distance away in the plane of rotation of whistle hears
frequencies in the range. (Speed of sound = 340 m/s)
(a) 436 to 576
(b) 426 to 586
(c) 426 to 576
(d) 436 to 586

29. A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle
between them is 90°. The moment of inertia of the bent rod about an axis passing through the
bending point and perpendicular to the plane de ned by the two halves of the rod is:
2

(a) ML

24
2

(b) ML

12
2

(c) ML

6
2
√2ML
(d) 24

30. A circular disc of radius R and thickness has moment inertia I about an axis passing
through its centre perpendicular to its plane. It is melted and re-casted into a solid sphere.
The moment of inertia of the sphere about its diameter is
(a) I
(b)
2I

8

(c)
I

5

(d) I

10

31. The acceleration due to gravity on the surface of the moon is 1/6 that on the surface of
earth and the diameter of the moon is one-fourth that of earth. The ratio of escape velocities
on earth and moon will be
√6
(a) 2

(b) √24
(c) 3
√3
(d) 2

32. An inductor of inductance L = 400 mH and resistors of resistance R = 2Ω and R = 2Ω
1 2

are connected to a battery of emf 12 V as shown in the gure. The internal resistance of the
battery is negligible. The switch S is closed at t=0. The potential drop across L as a function of
time is

(a) 12

t
e
−3t
V

(6) 6 (1 − e −t/0.2
)V

(c) 12e −5iv

(d) 6e −5t
V

33. A geo-stationary satellite orbits around the earth in a circular orbit of radius 36,000 km.
Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface (
(R = = 6,400km) will approximately be
earth

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

34. In Young's double slit experiment, the slits are 2 mm apart and are illuminated by photons
of two wavelengths λ = 12000A and λ = 10000A. At what minimum distance from the
1 2

common central bright fringe on the screen 2 m from the slit will a bright fringe from one
interference pattern coincide with a bright fringe from the other ?
(a) 6mm

(b) 4mm
(c) 3mm
(d) 8mm

35. A source of sound S emitting waves of frequency 100 Hz and an observer O are located at
some distance from each other. The source is moving with a speed of 19.4 ms at an angle of
−1

60° with the source observer line as shown in the gure. The observer is at rest. The apparent
frequency observed by the observer is (velocity of sound in air 330 ms )−1

(a) 103 Hz
(b) 106 Hz
(c) 97 Hz
(d) 100 Hz

36. A mild steel wire of length 2L and cross-sectional area A is stretched, well within elastic
limit, horizontally between two pillars ( gure). A mass m is suspended from the mid-point of
the wire. Strain in the wire is

(a)
2
x
2
2L

(b) x

L

(c)
2
x

L

(d)
2
x

2L

37. If in a wire of Young's modulus Y, longitudinal strain X is produced, then the value of
potential energy stored in its unit volume will be
(a) Y X 2

(b) 2Y X 2

(c) Y X/2 2

(d) Y X /2 2

38. A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The
separation between the plates is d. The space between the plates is now lled with two
dielectrics constant K = 3 and thickness d/3 while the other one has dielectric constant K, =
1

6 and thickness 2d/3. Capacitance of the capacitor is now
(a) 1.8 pF
(b) 45 pF
(c) 40.5 pF
(d) 20.25 pF

39. A plano convex lens ts exactly into a plano concave lens. Their plane surface are parallel
to each other. If the lenses are made of different materials of refractive indices μ &μ and R
1 2

is the radius of curvature of the curved surface of the lenses, then focal length of combination
is
(a)
R

μ1 −μ2

(b) 2R

μ1 −μ2

(c) R

2(μ1 −μ2 )

(d)
R

2−(μ1 +μ2 )

40. The Young's modulus of a perfectly rigid body is
(a) unity
(b) zero
(c) in nity
(d) some nite non-zero constant

Chemistry

41. The 25 mL of a 0.15 M solution of lead nitrate, Pb(NO ) reacts with all of the aluminium
3 2

sulphate, Al (SO ) , present in 20 mL of a solution. What is the molar concentration of the.
2 4 3

Al2 (SO4 ) ?
3

3Pb(NO3 ) (aq) + Al2 (SO4 ) (aq) ⟶ 3PbSO4 (s) + 2Al(NO3 ) (aq)
2 3 3

(a) 6.25 × 10 M −2

(b) 2.421 × 10 M −2

(c) 0.1875M
(d) None of these

42. Consider the reactions
(A) H O + 2HI → I + 2H O
2 2 2 2

(B) HOCl + H O → H O + Cl + O
+ −
2 2 3 2

Which of the following statements is correct about H O with reference to these reactions?
2 2

Hydrogen peroxide is ?.
(a) an oxidising agent in both (A) and (B)
(b) an oxidising agent in (A) and reducing agent in (B)
(c) a reducing agent in (A) and oxidising agent in (B)
(d) a reducing agent in both (A) and (B)

43. If a 25.0 mL sample of sulfuric acid is titrated with 50.0 mL of 0.025 M sodium hydroxide
to a phenolphthalein endpoint, what is the molarity of the acid?
(a) 0.020M
(b) 0.100M
(c) 0.025M
(d) 0.050M

44. 4g if copper was dissolved in conc. HNO The copper nitrate thus obtained gave 5g of its
3

oxide on strong heating the equivalent weight of copper is
(a) 23
(b) 32
(c) 12
(d) 20

45. The boiling point of water is exceptionally high because
(a) there is a covalent bond between H and O
(b) water molecule is linear
(c) water molecules associate due to hydrogen bonding
(d) water molecules is not linear

46. If the Planck's constant h = 6.6 × 10 Js , the de Broglie wavelength of a particle
−34

having momentum of 3.3 × 10 kgms will be
−24 −1

(a) 0.002A

(b) 0.5A
(c) 2A
(d) 500A

47. The by-product of Solvay-Ammonia process is time to time.
(a) CO 2

(b) NH 3

(c) CaCl 2

(d) CaCO 3

48. The number of radial nodes of 3s and 2p orbitals are respectively
(a) 2,0
(b) 0,2
(c) 1,2
(d) 2,2

49. Which of the following is similar to graphite
(a) B
(b) BN
(c) B H
2 6

(d) B C
4

50. An e has magnetic quantum number as –3, what is its principal quantum number?
−

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

51. Amongst the elements with following electronic con gurations, which one of them may
have the
(a) Ne [3s 3p ] 2 2

(b) Ar[3d 10 2
4s 4p ]
3

(c) Ne[3s 3p ] 2 l

(d) Ne[3s 3p ] 2 3

52. At high pressure, the entire surface gets covered by a monomolecular layer of the gas
follows
(a) three-halved order
(b) second-order
(c) rst-order
(d) zero-order

53. The decreasing order of the ionization potential of the following elements is
(a) Ne > Cl > P > S > Al > Mg
(b) N > Cl > P > S > M g > Al
c

(c) Ne > Cl > S > P > Mg > Al
(d) Ne > Cl > S > P > Al > Mg

54. Electrometallurgical process is used to extract
(a) Fe
(b) Pb
(c) Na
(d) Ag

55. The valency shell of element A contains 3 electrons while the valency shell of element B
contains 6 electrons. If A combines with B, the probable formula of the compound formed will
be
(a) AB 2

(b) A B
2

(c) A B
2 3

(d) A B
3 2

56. Which of the following is the correct and increasing order of lone pair of electrons on the
central atom?
(a) IF < IF < ClF < XCF
7 s 3 2

(b) IF < XeF < ClF < IF
7 2 2 5

(c) IF < ClF < XeF < IF
7 3 2 5

(d) IF < XeF < IF < ClF
7 2 5 3

57. Calcination is used in metallurgy for removal of?

(a) Water and sulphide
(b) Water and CO 2

(c) CO and H S
2 2

(d) H O and H S
2 2

58. Which of the following shows correct order of bond length?
(a) O > O > O > O
+ − 2−

2 2 2 2

(b) O
+ − 2−
< O > O2 < O
2 2 2

(c) O
+ − 2−
> O2 < O > O
2 2 2

(d) O +

2
> O
2

2
< O
2

2
> O
2−

2
.

59. Which of these doesn’t exist?
(a) PH 3

(b) P H 5

(c) LuH 3

(d) PF 5

60. In PO , the formal charge on each oxygen atom and the P- O bond order respectively
3−

4

are
(a) -0.75,0.6
(b) -0.75, 1.0
(c) -0.75, 1.25
(d) -3, 1.25

61. Which of the following shows maximum magnetic moment?
(a) Mg 2+

(b) Ti 3+

(c) V 3+

(d) Fe 2+

62. One moles each of four ideal gases are kept as follows:
I. 1 L of gas (A) at 2 atm pressure
II. 2.5 L of gas (B) at 2 atm pressure
III. 1.25 L of gas (C) at 2 atm pressure
IV. 2.5 of gas (D) at 2.5 atm pressure

Which of the above gases is kept at highest temperature?
(a) Gas (A)
(b) Gas (B)
(c) Gas (C)
(d) Gas (D)

63. At what temperature, the rate of effusion of N , would be 1.625 times than that of SO at
2 2

50°C?
(a) 110K
(b) 173K
(c) 373 K
(d) 273K

64. Which of the following arrangements does not represent the correct order of the property
stated against it ?
(a) V < Cr < Mn < Fe paramagnetic behaviour
2+ 2+ 2+ 2+

(b) Ni < Co < Fe < Mn ionic size
2+ 2+ 2+ 2+

(c) Co < Fe < Cr < Sc stability in aqueous solution
3+ 3+ 3+ 3+

(d) Sc < Ti < Cr < Mn number of oxidation states

65. Increasing order of rms velocities of H , O , N and HBr is
2 2 2

(a) H > O > N > HBr
2 2 2

(b) HBr < O < N < H
2 2 2

(c) H > N < O > HBr
2 2 2

(d) HBr > N < O < H
2 2 2

66. Which one of given elements shows maximum number of different oxidation states in its
compounds?
(a) Am
(b) Fm
(c) La
(d) Gd

67. For the reaction CO(g) + 1

2
O2 (g) → CO2 (g)

Which one of the statement is correct at constant T and P?.
(a) ΔH = ΔE

(b) ΔH < ΔE
(c) ΔH > ΔE
(d) ΔH Is independent of physical state of the reactants.

68. For a given reaction, ΔH = 35.5kJmol and ΔS = 83.6JK mol −1 −1 −1
. The reaction is
spontaneous at : (Assume that and do not vary with temperature)
(a) T > 425K
(b) All temperatures
(c) T > 298 K
(d) T < 425K

69. Chloroform, CHCl, boils at 61.7 °C. If the K for chloroform is 3.63°C/molal, what is the
b

boiling point of a solution of 15 kg of CHCl and 0.616 kg of acenaphthalene C H ?
3 12 10

(a) 61.9
(b) 62.0
(c) 52.2
(d) 62.67

70. Given Reaction Energy Change Li(s) → Li(g) 161 Li(g) → Li
+
(g) 520
1

2
F2 (g) → F(g) T 77 1

2
F2 (g) → F(g) Electron gain enthalpy)
+ 1
Li (g) + F(g) → LiF(s) − 1047 Li(s) + F2 (g) → LiF(s) − 617
2

Based on data provided, the value of electron gain enthalpy of uorine would be:
(a) −300kJmol −1

(b) −350kJmol −1

(c) −328kJmol −1

(d) −228kJmol −1

71. When an aqueous solution of copper (II) sulphate is saturated with ammonia, the blue
compound crystallises on evaporation. The formula of this blue compound is:
(a) [Cu(NH ) ] SO ⋅ H O (square planar)
3 4 4 2

(b) [Cu(NH ) ] SO (Tetrahedral)
3 4 4

(c) [Cu(NH ) SO (Octahedral)
3 6 4

(d) [Cu (SO ) (NH ) ] (Octahedral)
4 3 5

72. The pH of 0.1 M solution of the following salts increases in the order :

(a) NaCl < NH Cl < NaCN < HCl 4

(b) HCl < NH Cl < NaCl < NaCN 4

(c) NaCN < NH Cl < NaCl < HCl 4

(d) HCl < NaCl < NaCN < NH Cl 4

73. The hybridisation of Fe in K Fe(CN) , is 3 6

(a) sp 3

(b) dsp 3

(c) sp d 3 2

(d) d sp
2 3

74. Which of the following can form buffer solution?
(a) aq ⋅ NH + NH OH 3 4

(b) KOH + HNO 3

(c) NaOH + HCl
(d) KI + KOH

75. The boiling point of alkyl halide are higher than those of corresponding alkanes because
of
(a) dipole-dipole interaction
(b) dipole-induced dipole interaction
(c) H-bonding
(d) None of the above

76. The ratio of oxidation states of Cl in potassium chloride to that in potassium chlorate is
(a)
+1

5

(b)
−1

5

(c) −2

5

(d)
+3

5

DMF
77. In a S substitution reaction of the type R − Br + Cl
2

N
−
⟶ R − Cl + Br
−
which one of
the following has the highest relative rate?
(a) CH − CH − CH Br
3 2 2

CH3 − CH − CH2 Br
(b)
CH3

CH3

(c) CH 3 − C − CH2 Br

CH3

(d) CH CH Br
3 2

78. In the reaction
2− − − −
3Br2 + 6CO + 3H2 O → 5Br + BrO + 6HCO
3 3 3

(a) Bromine is oxidised and carbonate is reduced.
(b) Bromine is reduced and water is oxidised
(c) Bromine is neither reduced nor oxidised
(d) Bromine is both reduced and oxidised

79. A gas X at 1 atm is bubbled through a solution containing a mixture of 1MY and 1MZ − −

at 25°C. If the reduction potential is Z>Y>X, then
(a) Y will oxidise X and not Z
(b) Y will oxidise Z and not X
(c) Y will oxidise both X and Z
(d) Y will reduce both X and Z

80. The oxidation states of sulphur in the anions SO follow the order
2− 2− 2−
, S2 O and S2 O
3 4 6

(a) SO
2− 2− 2−
< S2 O < S2 O
3 4 6

(b) S O
2
2−

4
< S2 O
2−

6
< SO
2−

3

(c) S O
2
2−

6
< S2 O
2−

4
< SO
2−

3

(d) S O 2− 2− 2−
2 < SO < S2 O
4 3 6

Mathematics

81. Let A, B, C be nite sets. Suppose that n(A)=10, n(B)=15,n(C)=20, (n(A ∩ B) = 8 and
n(B ∩ C) = 9. Then the possible value of n(AU BU C) is

(a) 26
(b) 27
(c) 28

(d) Can be 26 a 27 or 28

3 −2 4
⎡ ⎤
82. If matrix A = ⎢ 1 2 −1 ⎥ and A −1
=
1

k
adj(A) then k is
⎣ ⎦
0 1 1

(a) 7
(b) -7
(c) 15
(d) -11

83. Two nite sets have m and n elements. The number of subsets of the rst set is 112 more
than that of the second set. The values of m and n respectively are,
(a) 4,7
(b) 7,4
(c) 4,4
(d) 7,7

84. Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is
the circumcentre of this triangle, then the radius of the circle having line segment AC as
diameter, is:
(a) 2√10
(b) 3√ 5

2

3√5
(c) 2

(d) √10

85. The set (A/B) ∪ (B/A) is equal to
(a) [A/(A ∩ B)] ∩ [B/(A ∩ B)]
(b) (A ∪ B)/(A ∩ B)
(c) A/(A ∩ B)
(d) A ∩ B/A ∪ B
¯¯¯¯¯¯¯¯¯¯¯¯¯¯

86. The domain of the function f (x) = √x 2
− [x]
2
where [x] denotes the greatest integer
less than or equal to x, is
(a) (0,x )

(b) ( ∞, 0 )
(c) (−x, x)
(d) None of these

87. The angle between the lines whose intercepts on the axes are a, -b and b, -a respectively,
is
2 2

(a) tan −1 a −b

ab
2 2

(b) tan −1 b −a

2
2 2

(c) tan −1 b −a

2ab

(d) None of these

88. The period of the function f(x)= | sin x| − | cos x|
(a) π/2
(b) π
(c) 2π
(d) none of these

89. The equation of the circle which passes through the point (4, 5) and has its centre at (2, 2)
is
(a) (x - 2)+(y-2)= 13
(b) (x − 2) + (y − 2) = 13
2 2

(c) (x) + (y) = 13
2 2

(d) (x − 4) + (y − 5) = 13
2 2

90. The domain of the functions f (x) = log(− log 1
= (1 +
1

x1.4
) − 1) is
(a) (0,1)
(b) (0,1]
(c) [ 1 , ∞ )
(d) ( 1 , ∞ )

91. If m sin θ = n sin(θ + 2α) then tan(θ + α) is
(a)
m+n
tan α
m−n

(b)
m+n
tan θ
m−n

(c)
m+n
cot α
m−n

(d)
m+n
cot θ
m−n

92. Consider the equation of a parabola y 2
+ 4ax = 0 where a >0 which of the following
is/are correct?

(a) Tangent at the vertex is x=0
(b) Directrix of the parabola is x=0
(c) Vertex of the parabola is not at the origin
(d) Focus of the parabola is at (a,0)

93. The number of roots of equation
cos x + cos 2x + cos 3x = 0 is (0 ≤ x ≤ 2π)

(a) 4
(b) 5
(c) 6
(d) 8

94. The general solution of sin x − 3 sin 2x + sin 3x = cos x − 3 cos 2x + cos 3x is
(a) nπ +
π

8

(b)
nπ π
+
2 8

(c) (−1) n nπ

2
+
π

8

(d) 2nπ + cos −1 3

2

95. lim is equal to
x−sin x
x→0 √ 2
x+sin x

(a) 1
(b) 0
(c) ∞
(d) None of these

n (2n)!
96. If then P(n) is true for
4
<
n+1 (n!)2

(a) n ≥ 1
(b) n > 0
(c) n < 0

(d) n ≥ 2

5
4√2−(cos x+sin x)
97. If lim x→
π
1−sin 2x
then x is equal to
4

(a) √2
(b) 3√2
(c) 5√2
(d) None of the above

98. The greatest positive integer, which divides n(n+1)(n+2)(n+3) for all n ∈ N is
(a) 2
(b) 6
(c) 24
(d) 120

99. Let T(k) be the statement 1 + 3 + 5 + ... + (2k − 1) = k 2
+ 10 .Which of the following is
correct?
(a) T(1) is true
(b) T(k) is true => T(k+1) is true
(c) T(n) is true for all n ∈ N
(d) All above are correct

n
∫ [x]dx
100. The expression in 0

n
where [x] and {x} are integral and fractional part of x and
∫ ⟨x}dx
0

n ∈ N is equal to
(a) n−1
1

(b) 1

n

(c) n
(d) n − 1

101. If the amplitude of z–2=3i is π/4, then the locus of z = x + iy is
(a) x+y-1=0
(b) x-y-1=0
(c) x+y+1=0
(d) x-y+1=0

102. Coef cient of variation of two distributions are 50 and 60, their arithmetic means are 30
and 25, respectively. Difference of their standard deviations is
(a) 0
(b) 1
(c) 1.3
(d) 2.5

103. Roots of equation x 2
+ bx − c = 0(b, c > 0) are
(a) Both positive
(b) Both negative
(c) Of opposite sign
(d) None of these

104. If α and β are the roots of the equations x such that |α − β| = √10 ,
3p
2
+ px + = 0
4

then p belongs to the set :
(a) {2, −5}
(b) {−3, 2}
(c) {−2, 5}
(d) {3, −5}

105. The mean square deviation of a set of n observations x , x , … , , x about a point c is
1 2 n

de ned as . The mean square deviations about - 2 and 2 are 18 and 10
1 n 2
∑ (xi − c)
n i=1

respectively, the standard deviation of this set of observations is
(a) 3
(b) 2
(c) 1
(d) None of these

3−|x|
106. The set of all real x satisfying the inequality 4−|x|
≥ 0 is
(a) [ - 3,3 ] ( - ∞, - 4 ) ( 4 , ∞ )
(b) ( - ∞, - 4 ) ( 4 , ∞ )
(c) ( ∞, -3 ) ( 4, ∞ )
(d) ( ∞, -3 ) ( ∞, 3 )

107. If x satis es |3x − 2| + |3x − 4| + |3x − 6| ≥ 12 then
(a) 0 ≤ x ≥
8

3

(b) x ≥
8 −4
or
3 3

(c) x ≤ 0 or x ≥
8

3

(d) x ≥ 2 only

108. Which of the following is not a vertex of the positive region bounded by the inequalities
2x + 3y ≤ 6, 5x + 3y ≤ 15 and x, y ≥ 0

(a) (0,2)
(b) (0,0)
(c) (3,0)
(d) None of these

109. If then x lies in the interval
2x+3 4x−1
<
5 2

(a) [0, 11

16
)

(b) [
11
, ∞)
16

(c) (0,
11
)
16

(d) ( 11

16
, ∞)

^ → → = y + x^j + (1 + x − y)k →, →b, c]
110. Let a = ^i − k,
¯
¯¯
b = x i + j + (1 − x)k, and c
^ ^ ^
i
^
.Then [a ¯¯

depends on
(a) only y
(b) only x
(c) both x and y
(d) neither x nor y

111. In how many ways can 12 gentlemen sit around a round table so that three speci ed
gentlemen are always together ?
(a) 9 !
(b) 10 !
(c) 3! 10!
(d) 3! 9!

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

2
1−z

|z|
(a) 2

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

113. How many different nine digit numbers can be formed from the number 223355888 by
rearranging its digits so that the odd digits occupy even positions ?
(a) 16
(b) 36
(c) 60
(d) 180

114. Four numbers are multiplied together. Then, the probability that the product will be
divisible by 5 or 10 is
(a) 369/625
(b) 399/625
(c) 123/625
(d) 133/625

115. The ratio in which the join of (2, 1, 5) and (3,4,3) is divided by the plane(x+y+z) = 1/2 is:
(a) 3:5
(b) 5:7
(c) 1:3
(d) 4:5

7

116. The coef cient of x in the expansion of (x −
3 1
)
x

(a) 14
(b) 21
(c) 28
(d) 35

117. The integer just greater than (3 + √5) 2n
is divisible by (n ∈ N) .
(a) 2
n−1

(b) 2 n+1

(c) 2
n+2

(d) Not divisible by 2

y−3 y−4
118. The lines and are coplanar if
x−2 z−4 x−1 z−5
= = = =
1 1 −k k 2 1

(a) k=3 or -3
(b) k=0 or -1
(c) k=1 or -1
(d) k=0 or -3

n 8

119. If ∑ then n =
n r+2 2 −1
Cr =
r=0 r+1 6

(a) 8
(b) 4
(c) 6
(d) 5

120. The coef cient of the middle term in the binomial expansion in power of x, of (1 + ax) 4

and of (1 − ax) is same , if a equals6

(a) 3/5
(b) 10/3
(c) -3/10
(d) -5/3

121. If a, b, c are in GP., then
(a) a , b , c are in GP.
2 2 2

(b) a (b + c), c (a + b), b (a + c) are in GP.
2 2 2

(c) are in GP.
a b c
, ,
b+c c+a a+b

(d) None of these

2
log 2 x (log 2 x)

122. If x>0 ,then 1 +
e e
+ + … =
1! 2!

(a) x
(b) x 2

(c) 2x

(d) √x

123. In a binomial distribution, the mean is 4 and variance is 3. Then its mode is
(a) 5
(b) 6
(c) 4
(d) None of these

124. If ∑ where p, q, t and s are constants,
n 4 3 2
k(k + 1)(k − 1) = pn + qn + tn + sn
k=1

then the value of s is equal to
(a) -1/4
(b) -1/2
(c) 1/2
(d) 1/4

125. If in a frequency distribution, the mean and median are 21 and 22 respectively, then its
mode is approximately
(a) 25.5
(b) 24.0
(c) 22.0
(d) 20.5

Logical Reasoning

126. Neeraj starts walking towards South. After walking 15 m, he turns towards North. After
walking 20 m, he turns towards East and walks 10 m. He then turns towards South and walks 5
m. How far is he from his original position and in which direction?
(a) 10m, East
(b) 10 m, South-East
(c) 10 m, West
(d) 10 m, North-East

127. If 5#6=121 and 10#8=324, then nd the value of 23 # 14=?

(a) 1369
(b) 1349
(c) 1331
(d) 725

128. Shikha is mother-in-law of Ekta who is sister-in law of Ankit. Pankaj is father of Sanjay,
the only brother of Ankit. How is Shikha related to Ankit?
(a) Mother-in-law
(b) Aunt
(c) Wife
(d) Mother

129. Choose the correct alternatives from the given ones that will complete the series.
L_NO__MLLM_00_ML
(a) MNNNO
(b) MONNO
(c) MONON
(d) MONNN

130. In a certain code language, 'SAFER' is written as '5@3#2' and 'RIDE' is written as '2C%#',
how would 'FEDS' be written in that code?
(a) 3#05
(b) 3@%5
(c) 3#%5
(d) 3#%2

131. Which of the following cube in the answer gure cannot be made based on the unfolded
cube in the question gure?

(a)

(b)

(c)

(d)

132. Which one of the following diagram represents the correct relationship among
Professor, Male and Female.

(a)

(b)

(c)

(d)

133. If the rst and second letters in the word DEPRESSION were interchanged, also the third
and fourth letters, the fth and the sixth letters and so on, then which of the following would
be seventh letter from the right.
(a) O
(b) P
(c) R
(d) S

134. Identify the gure that will complete the pattern.

(a)

(b)

(c)

(d)

135. Find out the missing term in the series.. 1, 8, 27, __, 125, 216
(a) 52
(b) 58
(c) 64
(d) 65

English

136. Choose the word which is most similar in meaning to the word 'Optimistic'.
(a) Favourable
(b) Gloomy
(c) Hopeful
(d) Rude

137. Out of the four alternatives, choose the one which express the correct meaning of the
word, AUXILIARY
(a) Chief
(b) Supplemental
(c) Negligible
(d) Separate

138. 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.
He is really feeling under the weather today, he has a terrible cold.
(I) feeling like the weather
(II) feeling over the weather

(III) feeling in the weather
(a) Only (I) is correct
(b) Only (III) is correct
(c) Only (II) is correct
(d) No correction required

139. Choose the word opposite is meaning to the given word, RECOMPENSE
(a) Emolument
(b) Reward
(c) Payment
(d) Penalty

140. 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.
Hey, Nanny, speak about the devil and you are here
(I) speak at the devil
(II) speak on the devil
(III) speak of the devil
(a) Only (I) is correct
(b) Only (II) is correct
(c) Only (III) is correct
(d) No correction required

141. In the following question, out of the four alternatives, choose the one which best
expresses the meaning of the given word, EMBEZZLE
(a) Misappropriate
(b) Balance
(c) Remunerate
(d) Clear

142. 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.
The conclusion regarding the deaths attributed to particulate matter 2.5 micrometers is
considered to be caveated because
(a) Measurement of all aspects of PM2.5 has been done comprehensively
(b) Measurement of all aspects of PM2.5 is not radical
(c) Relation between pollution, disease and death is complete
(d) None of these

143. 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.
They requested me to follow them.
(a) ordered
(b) urged
(c) asked
(d) No improvement

144. 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.
As per the given passage, which of the following is are the measures for lowering particulate
matter in the atmosphere?
(I) Making cleaner fuels available
(II) Landscaping open areas
(III) Providing cooking stoves designed scienti cally
(a) Only (I)
(b) Both (I) And (II)
(c) All of the above
(d) None of these

145. 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.
I am ne, what about you?
(a) your

(b) your's
(c) yours
(d) No improvement

146. In each of the following question choose the alternative which is opposite in meaning to
the word given capital letters GATHER
(a) Separate
(b) Suspend
(c) Glorify
(d) Spend

147. In each of the following questions choose the alternative which is opposite in meaning to
the word given capital letters EXALT
(a) Depreciate
(b) Ennoble
(c) Glorify
(d) Simplify

148. 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.
I am looking after my pen which is missing.
(a) Looking for
(b) Looking in
(c) Looking back
(d) No improvement

149. In each of the following questions choose the alternative which is mostly nearly the same
in meaning to the word given capital letters STUBBORN
(a) Easy
(b) Obstinate
(c) Willing
(d) Pliable

150. Choose the word which is closest to the opposite in meaning of the underlined word in
the sentence.
Hydra is biologically believed to be immortal.

(a) undying
(b) perishable
(c) ancient
(d) eternal