BITSAT 2027 Sample Paper

SAMPLE PAPER

S A M P L E Q U E S T I O N P A P E R

BITSAT 2027
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME MARKING

130 390 180 Min +3 / −1

GENERAL INSTRUCTIONS

1. This paper contains 130 multiple-choice questions. All questions are compulsory.

2. Each question has four options — (A), (B), (C) and (D) — of which only one is correct.

3. Each correct answer carries 3 marks; 1 mark is deducted for each wrong answer.

4. Total time allowed is 180 minutes. Manage your time across all sections.

5. Use of calculators, mobile phones or any electronic device is not permitted.

6. Attempt the paper first, then check your answers against the Answer Key at the end.

Candidate Name: Roll No.: Date:

SAMPLE PAPER

BITSAT 2027
SAMPLE QUESTION PAPER

Questions 130 Max Marks 390 Time 180 Min Marking +3 / −1

Attempt all questions. Choose the one correct option for each.

PHYSICS

1. A resistor and an inductor are connected to an ac 2. In Young's double slit experiment, the slits are 2 mm
supply of 120 V and 50 Hz. The current in the circuit is 3 apart and are illuminated by photons of two wavelengths
A. If the power consumed in the circuit is 108 W, then the λ _ 1 = 12000 A and λ _ 2 = 10000 A . At what minimum
resistance in the circuit is distance from the common central bright fringe on the
screen 2 m from the slit will a bright fringe from one
(A) 12 Ω
interference pattern coincide with a bright fringe from
(B) 40 Ω
the other ?
(C) √( ( 52 × 25 ) ) Ω
(A) 6mm
(D) 360 Ω
(B) 4mm

(C) 3mm

(D) 8mm

3. The approximate depth of an ocean is 2700 m. The 4. In the circuit shown in the figure, find the current
compressibility of water is 4 x 10-11 Pa-l and density of through
water is 103 kg/m2.What fractional compression of water
(A) the 3 Ω is 0.50 A
will be obtained at the bottom of the ocean ?
(B) the 3 Ω is 0.25 A
(A) 1.0 x 102
(C) the 4 Ω is 0.50 A
(B) 1.2 x 102
(D) the 4 Ω is 0.25 A
(C) 1.4 x 10 -2

(D) 0.8 x 10-2

5. If in a wire of Young's modulus Y, longitudinal strain X 6. Consider elastic collision of a particle of mass m
is produced, then the value of potential energy stored in moving with a velocity u with another particle of the
its unit volume will be same mass at rest. After the collision the projectile and
the struck particle move in directions making angles ,
(A) Y X ^ 2
and , respectively with the initial direction of motion. The
(B) 2 Y X ^ 2
sum of the angles θ _ 1 + θ _ 2 , is:
(C) Y ^ 2 X / 2
(A) 45°
(D) Y X ^ 2 / 2
(B) 90°

(C) 135°

(D) 180°

7. If the series limit wavelength of Lyman series for the 8. A plano convex lens fits exactly into a plano concave
hydrogen atom is 912 Å, then the series limit wavelength lens. Their plane surface are parallel to each other. If the
for Balmer series of hydrogen atoms lenses are made of different materials of refractive
indices μ _ 1 \& μ _ 2 and R is the radius of curvature of
(A) 912 Å
the curved surface of the lenses, then focal length of
(B) 912 * 2 Å
combination is
(C) 912 * 4 Å
(A) R μ _ 1 - μ _ 2
(D) 912 Å / 2
(B) 2 R μ _ 1 - μ _ 2

(C) R 2 ( μ _ 1 - μ _ 2 )

(D) R 2 - ( μ _ 1 + μ _ 2 )

9. In the circuit shown, the symbols have their usual 10. A circular disc of radius R and thickness R/6 has
meanings. The cell has emf E. X is initially joined to Y for moment inertia I about an axis passing through its centre
a long time. Then, X is joined to Z. The maximum charge perpendicular to its plane. It is melted and re-casted into
on C at any later time will be a solid sphere. The moment of inertia of the sphere about
its diameter is
(A) E R √( L C )

(B) E R 2 √( L C ) (A) I

(C) E √( L C ) 2 R (B) ( 2 I )/( 8 )

(D) E √( L C ) R (C) ( I )/( 5 )

(D) ( I )/( 10 )

11. Figure below shows two paths that may be taken by 12. A thin rod of length L and mass M is bent at its
a gas to go from a state A to a state C In process AB, 400 midpoint into two halves so that the angle between them
J of heat is added to the system and in process BC, 100 J is 90°. The moment of inertia of the bent rod about an
of heat is added to the system. The heat absorbed by the axis passing through the bending point and
system in the process AC will be perpendicular to the plane defined by the two halves of
the rod is:
(A) 500 J

(B) 460J (A) ML ^ 2 24

(C) 300J (B) ML ^ 2 12

(D) 380J 0.5 (C) ML ^ 2 6

(D) √( 2 ) ML ^ 2 24

13. There are two sources kept at distances 2 λ . A large 14. A test charge qₒ is placed at the centre of a spherical
screen is perpendicular to line joining the sources. conductor of radius R. A charge Q is placed on the
Number of maximas on the screen in this case is ( λ = spherical conductor. What will be the electrostatic force
wavelength of light) on the charge Q due to qₒ?

(A) 1 (A) zero

(B) 3 (B) 1 4 π ε _ 0 · Q q _ 0 R ^ 2

(C) 5 (C) 1 4 π ε _ 0 · Q q _ 0 2 R ^ 2

(D) 7 (D) 1 4 π ε _ 0 · Q q _ 0 4 R ^ 2

15. A coil 10 turns and a resistance of 20Ω is connected in 16. The acceleration due to gravity on the surface of the
series with B.G of resistance 30Ω. The coil is placed with moon is 1/6 that on the surface of earth and the diameter
its plane perpendicular to the direction of a uniform of the moon is one-fourth that of earth. The ratio of
magnetic field of induction 10 ^ - 2 T . If it is now turned escape velocities on earth and moon will be
through an angle of 60° about an axis in its plane. Find
(A) √( 6 ) 2
the charge in duced in the coil. (Area of a coil = 10 ^ - 2
(B) √( 24 )
m^2)
(C) 3
(A) 2 × 10 ^ - 5 C
(D) √( 3 ) 2
(B) 3.2 × 10 ^ - 5 C

(C) 1 × 10 ^ - 5 C

(D) 5.5 × 10 ^ - 5 C

17. For the equation F = A ^ a v ^ b d ^ c , where F is the 18. In hydrogen atom spectrum λ _ 3 - 1 and λ _ 2 - 1
force, A is the area, v is the velocity and d is the density, represent the wavelengths emitted due to transition from
the values of a, b and c are respectively second and first excited states to the ground state
respectively. The value of λ _ 3 - 1 λ _ 2 - 1 is
(A) 1,2,1

(B) 2,1,1 (A) 27/32

(C) 1,1,2 (B) 32/27

(D) 0,1,1 (C) 4/9

(D) 9/4

19. The frequency of vibration of string is given by v = ( 20. A mild steel wire of length 2L and cross-sectional
p )/( 2 l ) [ ( F )/( m ) ] ^ 1 / 2 . Here p is a number of area A is stretched, well within elastic limit, horizontally
segments in the string and l is the length. The between two pillars (figure). A mass m is suspended from
dimensional formula for m will be the mid-point of the wire. Strain in the wire is

(A) [ M ^ 0 LT ^ - 1 ] (A) x ^ 2 2 L ^ 2

(B) [ ML ^ 0 T ^ - 1 ] (B) ( x )/( L )

(C) [ ML ^ - 1 T ^ 0 ] (C) x ^ 2 L

(D) [ M ^ 0 L ^ 0 T ^ 0 ] (D) x ^ 2 2 L

21. A thin but rigid semicircular wire frame of radius r is 22. An elastic string of unstretched length L and force
hinged at O and can rotate in its own vertical plane. A constant k is stretched by a small length x. It is further
smooth peg P starts from O and moves horizontally with stretched by another small length y. The work done in
constant speed v _ 0 , lifting the frame upwards as shown the second stretching is
in the figure. Find the angular velocity of the frame when
(A) 1 / 2 Ky ^ 2
its diameter makes an angle of 60 ^ ° with the vertical:
(B) 1 / 2 Ky ( 2 x + y )
(A) v _ 0 / r
(C) 1 / 2 K ( x ^ 2 + y ^ 2 )
(B) v _ 0 / 2 r
(D) 1 / 2 k ( x + y ) ^ 2
(C) 2 v _ 0 / r

(D) v _ 0 r

23. A plane electromagnetic wave is incident on a 24. A cyclic process ABCD is shown in the figure P-V
material surface. If the wave delivers momentum p and diagram. Which of the following curves represent the
energy E, then same process?

(A) p=0, E=0 (A)

(B) p ≠ 0, E ≠ 0 (B)

(C) p≠ 0, E = 0 (C)

(D) p = 0, E ≠ 0 (D)

25. ABC is an equilateral triangle. Charges +q are placed 26. A cube is subjected to a uniform volume
at each corner as shown in fig. The electric field intensity compression. If the side of the cube decreases by 2% the
at centre O will be bulk strain is

(A) 1 4 π ε _ 0 ( q )/( r ) (A) 0.02

(B) 1 4 π ε _ 0 q r ^ 2 (B) 0.03

(C) 1 4 π ε _ 0 3 q r ^ 2 (C) 0.04

(D) zero (D) 0.06

27. A common emitter amplifier has a voltage gain of 50, 28. In the circuit given below, V(t) is the sinusoidal
an input impedance of 100 Ω and an output impedance of voltage source, voltage drop V _ A B ( t ) across the
200 Ω. The power gain of the amplifier is resistance R is

(A) 500 (A) is half wave rectified

(B) 1000 (B) is full wave rectified

(C) 1250 (C) has the same peak value in the positive and negative

(D) 50 half cycles

(D) has different peak values during positive and negative
half cycle

29. Two oscillators are started simultaneously in same 30. A body starts from rest at time t=0, the acceleration
phase. After 50 oscillations of one, they get out of phase time graph is shown in the figure. The maximum velocity
by ⊼, that is half oscillation. The percentage difference of attained by the body will be
frequencies of the two oscillators is nearest to
(A) 110 m/s
(A) 2% (B) 55 m/s
(B) 1% (C) 650 m/s
(C) 0.5% (D) 550 m/s
(D) 0.25%

CHEMISTRY

31. Identify the incorrect statement from the following: 32. Pick out the wrong statement.

(A) Ozone absorbs the intense ultraviolet radiation of the (A) Nitrogen has the ability to form pt-pt bonds with itself
sun. (B) Bismuth forms metallic bonds in elemental
(B) Depletion of ozone layer is because of its chemical (C) Catenation tendency is higher in nitrogen when
reactions with chlorofluoro alkanes. compared with other elements of the same group.
(C) Ozone absorbs infrared radiation atmosphere. (D) Nitrogen has higher first ionisation enthalpy when
(D) Oxides of nitrogen in the atmosphere can cause the compared with other elements of the same group.
depletion of ozone layer.

33. Which of the following ions can be separated by aq. 34. When an aqueous solution of copper (II) sulphate is
NH _ 4 OH in presence of NH _ + Cl saturated with ammonia, the blue compound crystallises
on evaporation. The formula of this blue compound is:
(A) Al ^ 3 + and Fe ^ 3 +

(B) Cr ^ 3 · and Al ^ 3 (A) [ Cu ( NH _ 3 ) _ 4 ] SO _ 4 · H _ 2 O (square planar)

(C) Cu ^ 2 + and Al ^ 3 + (B) [ Cu ( NH _ 3 ) _ 4 ] SO _ 4 (Tetrahedral)

(D) None of these (C) [ Cu ( NH _ 3 ) _ 6 SO _ 4 . (Octahedral)

(D) [ Cu ( SO _ 4 ) ( NH _ 3 ) _ 5 ] (Octahedral)

35. In PO _ 4 ^ 3 - , the formal charge on each oxygen 36. Maximum p K _ a value is of
atom and the P- O bond order respectively are
(A)
(A) -0.75,0.6 (B) ( CH _ 3 CH _ 2 ) _ 2 NH
(B) -0.75, 1.0 (C) ( CH _ 3 ) _ 2 NH
(C) -0.75, 1.25 (D)
(D) -3, 1.25

37. The colour of _ 62 Sm ^ 3 + is yellow. The expected 38. The most reactive amine towards reactions with dil.
colour of _ 66 Dy ^ 3 + is HCl is

(A) Yellow (A) CH _ 3 - NH _ 2

(B) Red (B)

(C) Blue (C) ( CH _ 3 ) _ 3 N

(D) Green (D)

39. A graph is ploted between log K virsus 1/T for 40. Which of the following is a diamine?
calculation of activation energy ( E _ a ) . The correct plot
(A) Dopamine
is
(B) Histamine
(A)
(C) Meprobamate
(B)
(D) Chlorphenamine
(C)

(D)

41. Which of the following pollutants is main product of 42. In a set of reactions, ethylbenzene yielded a product
automobiles exhaust? D.

(A) CO (A)

(B) CO _ 2 (B)

(C) NO (C)

(D) Hydrocarbons (D)

43. The reaction, is known as: 44. Consider the reactions (A) H _ 2 O _ 2 + 2 HI arrow I _
2 + 2 H _ 2 O (B) HOCl + H _ 2 O _ 2 arrow H _ 3 O ^ + + Cl
(A) Wurtz reaction
^ - + O _ 2 Which of the following statements is correct
(B) Koch reaction
about H _ 2 O _ 2 with reference to these reactions?
(C) Clemmensen reduction . Hydrogen peroxide is ?.
(D) Kolbe's reaction
(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)

45. 3.92 g of ferrous ammonium sulphate react 46. For the reaction CO ( g ) + ( 1 )/( 2 ) O _ 2 ( g ) arrow
completely with 50 ml ( N )/( 10 ) KMnO _ 4 solution. The CO _ 2 ( g ) Which one of the statement is correct at
percentage purity of the sample is constant T and P?.

(A) 50 (A) Δ H = Δ E

(B) 78.4 (B) Δ H Δ E

(C) 80 (C) Δ H > Δ E

(D) 39.2 (D) Δ H Is independent of physical state of the reactants.

47. A 100.0 mL dilute solution of Ag⁺ is electrolysed for 48. The average kinetic energy of an ideal gas per
15.0 minutes with a current of 1.25 mA and the silver is molecule in SI unit at 25° C will be
removed completely. What was the initial [Ag⁺]?
(A) 6.17 × 10 ^ - 21 kJ
(A) 2.32 × 10 ^ - 1 (B) 6.17 × 10 ^ - 21 J
(B) 2.32 × 10 ^ - 4 (C) 6.17 × 10 ^ - 20 J
(C) 2.32 × 10 ^ - 3 (D) 7.16 × 10 ^ - 20 J
(D) 1.16 × 10 ^ - 4

49. The decreasing order of the ionization potential of 50. Following are colours shown by some alkaline earth
the following elements is metals in flame test. Which of the following are not
correctly matched ? Metal Colour (i) Calcium - (i) Apple
(A) Ne > Cl > P > S > Al > Mg
green (ii) Strontium - (ii) Crimson (iii) Barium - (ii) Brick
(B) N _ c > C l > P > S > M g > A l
Red
(C) Ne > Cl > S > P > Mg > Al
(A) (i) and (iii)
(D) Ne > Cl > S > P > Al > Mg
(B) (i) only

(C) (ii) and (iv)

(D) (ii) and (iii)

51. Formation of polyethylene from calcium carbide 52. Which of the following element do not form complex
takes place as follows CaC _ 2 + 2 H _ 2 O Ca ( OH ) _ 2 + C with EDTA?
_ 2 H _ 2 C _ 2 H _ 2 + H _ 2 C _ 2 H _ 4 nC _ 2 H _ 4 + CH _ 2
(A) Ca
- CH _ 2 + _ n The amount of polyethylene obtained from
(B) Mg
64.1 kg of CaC _ 2 is
(C) Be
(A) 7 kg
(D) Sr
(B) 14 kg

(C) 21 kg

(D) 28 kg

53. If V is the volume of one molecule of gas under given 54. An organic compound A ( C _ 4 H _ 9 Cl ) on reaction
conditions, the van der Waal's constant b is with Na/diethyl ether gives a hydrocarbon which on
monochlorination gives only one chloro derivative then A
(A) 4 V
is
(B) 4 V N _ 0
(A) tert-butyl chloride
(C) N _ 0 4 V
(B) sec-butyl chloride
(D) 4 VN _ 0
(C) isobutyl chloride

(D) n-butyl chloride

55. Graphite is a 56. Which of the following can act as both Bronsted acid
and Bronsted base?
(A) molecular solid

(B) covalent solid (A) Na _ 2 CO _ 3

(C) ionic solid (B) OH

(D) metallic solid (C) HCO _ 3 ^ -

(D) NH _ 3

57. Identify the wrong statement in the following: 58. Semiconductor materials like Si and Ge are usually
purified by
(A) Chlorofluorocarbons are responsible for ozone layer
depletion. (A) distillation

(B) Greenhouse effect is responsible for global warming (B) zone refining

(C) Acid rain is mostly because of oxides of nitrogen and (C) liquation
sulphur. (D) electrolytic refining
(D) Ozone layer does not permit infrared radiation from the
sun to reach the earth.

59. The number of radial nodes of 3s and 2p orbitals are 60. Following compounds are given Which of the above
respectively compound(s), on being warmed with iodine solution and
NaOH, will give iodoform?
(A) 2,0

(B) 0,2 (A) (1) and (2)

(C) 1,2 (B) (1), (3) and (4)

(D) 2,2 (C) only (2)

(D) (1), (2) and (3)

MATHEMATICS

61. The lines ( x - 2 )/( 1 ) = ( y - 3 )/( 1 ) = ( z - 4 )/( - k ) 62. The set ( A B ) ( B A ) is equal to
and ( x - 1 )/( k ) = ( y - 4 )/( 2 ) = ( z - 5 )/( 1 ) are
(A) [ A ( A B ) ] [ B ( A B ) ]
coplanar if
(B) ( A B ) ( A B )
(A) k=3 or -3
(C) A ( A B )
(B) k=0 or -1
(D) A B A B
(C) k=1 or -1

(D) k=0 or -3

63. If A and B are positive acute angles satisfying 3 ^ 2 A 64. Let R= {(3,3), (6,6), (9,9), (12, 12),(6,12), (3,9),(3,
+ 2 ^ 2 B = 4 and ( 3 A )/( B ) = ( 2 B )/( A ) Then the value 12), (3,6)} be a relation on the set A={3,6,9,12). Then,
of A + 2B is equal to the relation is

(A) π/6 (A) an equivalence relation

(B) π/2 (B) reflexive and symmetric

(C) π/3 (C) reflexive and transitive

(D) π/4 (D) only reflexive

65. The coefficient of x ^ 5 in the expansion of ( 1 + x ) ^ 66. Roots of equation x ^ 2 + b x - c = 0 ( b , c > 0 ) are
21 + ( 1 + x ) ^ 22 + … + ( 1 + x ) ^ 30 is
(A) Both positive
(A) ^ 51 C _ 5 (B) Both negative
(B) ^ 9 C _ 5 (C) Of opposite sign
(C) ^ 31 C _ 6 ^ - 21 C _ 6 (D) None of these
(D) ^ 30 C _ 5 - ^ 20 C _ 5

67. If x, y, z are complex numbers, and Δ = | array c c c 0 68. Minimise Z = Σ _ j = 1 ^ n Σ _ i = 1 ^ m c _ i j x _ i j
& - y & - 2 \ y & 0 & - x \ z & x & 0 array | then Δ is subject to Σ _ i = 1 ^ m x _ i j = b _ j , j = 1,2 , … , n Σ _ j =
1 ^ n x _ i j = b _ j , i = 1,2 , … , m is a LLP with number of
(A) purely real
constraints
(B) purely imaginary
(A) m-n
(C) complex
(B) mn
(D) 0
(C) m+n

(D) m/n

69. In a Δ ABC, the lengths of the two larger sides are 10 70. The probability of getting 10 in a single throw of
and 9 units, respectively. If the angles are in AP, then the three fair dice is :
length of the third side can be
(A) 1/6
(A) 5 ± √( 6 ) (B) 1/8
(B) 3 √( 3 ) (C) 1/9
(C) 5 (D) 1/5
(D) None of these

71. The ratio in which the join of (2, 1, 5) and (3,4,3) is 72. If Σ _ r = 0 ^ n ( - 1 ) ^ r ^ n C _ r r + 3 C _ r = ( 3 )/( a
divided by the plane(x+y+z) = 1/2 is: + 3 ) then a-n is equal to

(A) 3:5 (A) 0

(B) 5:7 (B) 1

(C) 1:3 (C) 2

(D) 4:5 (D) None of these

73. Four numbers are multiplied together. Then, the 74. If the amplitude of z–2=3i is π/4, then the locus of z =
probability that the product will be divisible by 5 or 10 is x + i y is

(A) 369/625 (A) x+y-1=0

(B) 399/625 (B) x-y-1=0

(C) 123/625 (C) x+y+1=0

(D) 133/625 (D) x-y+1=0

75. Which of the following statements is correct? 76. If A = ( 1 )/( 3 ) [ array c c c 1 & 2 & 2 \ 2 & 1 & - 2 \ a
& 2 & b array ] is an orthogonal matrix, then
(A) Every L.P.P. admits an optimal solution.

(B) A L.P.P. admits a unique optimal solution. (A) a=-2,b=-1

(C) If a L.P.P. admits two optimal solutions, it has an infinite (B) a=2, b= 1

number of optimal solutions. (C) a=2,b=-1

(D) The set of all feasible solutions of a L.P.P. is not a convex (D) a=-2, b=1
set.

77. If m θ = n ( θ + 2 α ) then ( θ + α ) is 78. If ∫ ( x - 1 )/( x + 1 ) e ^ x d x is equal to

(A) ( m + n )/( m - n ) α (A) e ^ x x 1 + x + C

(B) ( m + n )/( m - n ) θ (B) C - e ^ x x 1 + x

(C) ( m + n )/( m - n ) α (C) C - e ^ x 1 + x

(D) ( m + n )/( m - n ) θ (D) C - e ^ x x 1 + x

79. The coefficient of the middle term in the binomial 80. Line joining the points (0, 3) and (5, - 2) is a tangent
expansion in power of x, of ( 1 + a x ) ^ 4 and of ( 1 - a x ) to the curve y = ( a x )/( 1 + x ) , then a =
^ 6 is same , if a equals
(A) a = 1 ± √( 3 )
(A) 3/5 (B) a φ
(B) 10/3 (C) a = - 1 ± √( 3 )
(C) -3/10 (D) a = - 2 ± 2 √( 3 )
(D) -5/3

81. A random variable X has the probability distribution 82. A ball is dropped from a platform 19.6m high. Its
array | c | c | c | c | c | c | c | X & 1 & 2 & 3 & 4 & 5 & 6 & 7 position function is –
& 8 \ p ( X ) & 0.15 & 0.23 & 0.12 & 0.10 & 0.20 & 0.08 &
(A) x = - 4.9 t ^ 2 + 19.6 ( 0 ≤ t ≤ 1 )
0.07 & 0.05 \ array For the events E= X is a prime number
(B) x = - 4.9 t ^ 2 + 19.6 ( 0 ≤ t ≤ 2 )
and F=X4,then P ( E F )
(C) x = - 9.8 t ^ 2 + 19.6 ( 0 ≤ t ≤ 2 )
(A) 0.50
(D) x = - 4.9 t ^ 2 - 19.6 ( 0 ≤ t ≤ 2 )
(B) 0.77

(C) 0.35

(D) 0.87

83. Two finite sets have m and n elements. The number 84. Let a , b \& c be non-coplanar unit vectors equally
of subsets of the first set is 112 more than that of the inclined to one another at an acute angle θ . Then | [ a b c
second set. The values of m and n respectively are, ] | in terms of θ is equal to

(A) 4,7 (A) ( 1 + θ ) √( 2 θ )

(B) 7,4 (B) ( 1 + θ ) √( 1 - 2 2 θ )

(C) 4,4 (C) ( 1 - θ ) √( 1 + 2 2 θ )

(D) 7,7 (D) None of these

85. Let a = i - k , b = x i + j + ( 1 - x ) k , and c = y _ i + x j 86. If x is real number, then x x ^ 2 - 5 x + 9 must lie
+ ( 1 + x - y ) k .Then [ a , b , c ] depends on between

(A) only y (A) 1/11 and 1

(B) only x (B) 1 and 1/11

(C) both x and y (C) -11 and 1

(D) neither x nor y (D) -1/11 and 1

87. The area enclosed by the curves y = x ^ 3 and y = √( 88. Consider the equation of a parabola y ^ 2 + 4 a x = 0
x ) is where a >0 which of the following is/are correct?

(A) 5/3 sq units (A) Tangent at the vertex is x=0

(B) 5/4 sq units (B) Directrix of the parabola is x=0

(C) 5/12 sq units (C) Vertex of the parabola is not at the origin

(D) 12/5 sq units (D) Focus of the parabola is at (a,0)

89. Let A, B, and C are the angles of a plain triangle and 90. The number of times the digit 5 will be written when
tan(A/2)=1/3,tan(B/2) =2/3. Then tan(C/2) is equal to listing the integers from 1 to 1000, is

(A) 7/9 (A) 271

(B) 2/9 (B) 272

(C) 1/3 (C) 300

(D) 2/3 (D) None of these

91. Let f and g be functions from R to R defined as f ( x ) 92. _ x arrow 0 √ x - x x + ^ 2 x is equal to
= \ array c 7 x ^ 2 + x - 8 , x ≤ 1 \ 4 x + 5,1 x ≤ 7 , g ( x )
(A) 1
= \ array l 0 , - 3 ≤ x 2 \ x ^ 2 + 4 , x ≥ 2 array . array .
(B) 0
Then
(C) ∞
(A) (fog) (-3)=8
(D) None of these
(B) (fog)(9)=683

(C) (gof)(0)=-8

(D) (gof) (6)=427

93. Number of solution for the system of inequalities \ 94. The area of the region bounded by the x-axis the
array l 2 x + 1 x + 2 \ x - 1 > 2 x array . curve y=f(x) and the lines x=1,x=b, is equal to √b2+1-
√(2) for all b>1 ,then f(x) is
(A) 1

(B) 2 (A) √( x - 1 )

(C) 3 (B) √( x + 1 )

(D) 0 (C) √ x ^ 2 + 1

(D) x √ 1 + x ^ 2

95. Two equal sides of an isosceles triangle are 7x-y+3 = 96. If Σ _ k = 1 ^ n k ( k + 1 ) ( k - 1 ) = p n ^ 4 + q n ^ 3 +
0 and x+y-3=0 and its third side passes through the point t n ^ 2 + s n where p, q, t and s are constants, then the
(1,-10). find the equation of the third side value of s is equal to

(A) x-3y=-31 (A) -1/4

(B) x-3y- 31=0 (B) -1/2

(C) x+3y= 31 (C) 1/2

(D) x+3y=-31 (D) 1/4

97. If a variable takes value 0, 1, 2, ...,n with frequencies 98. If a, b, c are in GP., then
q^n,^nC_1q^n-1p,^nC_2q^n-2p^2,….
(A) a ^ 2 , b ^ 2 , c ^ 2 are in GP.
^ n C _ n p ^ n +6 where p+q=1, then the mean is
(B) a ^ 2 ( b + c ) , c ^ 2 ( a + b ) , b ^ 2 ( a + c ) are in GP.
(A) np
(C) ( a )/( b + c ) , ( b )/( c + a ) , ( c )/( a + b ) are in GP.
(B) nq
(D) None of these
(C) n(p+q)

(D) None of these

99. n arrow ∞ ( π √ n ^ 2 + 1 ] is equal to 100. Which of the following is not a vertex of the positive
region bounded by the inequalities 2 x + 3 y ≤ 6,5 x + 3 y
(A) ∞
≤ 15 and x , y ≥ 0
(B) 0
(A) (0,2)
(C) does not exist
(B) (0,0)
(D) none of these
(C) (3,0)

(D) None of these

101. If x satisfies | 3 x - 2 | + | 3 x - 4 | + | 3 x - 6 | ≥ 12 102. Let a, b and c be three vectors satisfying the All
then conditions , then equals a × b=(a × c),|a|=|c|=1,|b|=4 and
|b × c|=√(5) . If b-2 c=λ a
(A) 0 ≤ x ≥ ( 8 )/( 3 )

(B) x ≥ ( 8 )/( 3 ) or ( - 4 )/( 3 ) (A) 1

(C) x ≤ 0 or x ≥ ( 8 )/( 3 ) (B) -1

(D) x ≥ 2 only (C) 2

(D) -4

103. Coefficient of variation of two distributions are 50 104. ^ - 1 ( 2 a 1 + a ^ 2 ) - ^ - 1 ( 1 - b ^ 2 1 + b ^ 2 ) =
and 60, their arithmetic means are 30 and 25, ^ - 1 ( 2 x 1 - x ^ 2 ) then what is the value of x?
respectively. Difference of their standard deviations is
(A) a/b
(A) 0 (B) ab.
(B) 1 (C) b/a
(C) 1.3 (D) ( a - b )/( 1 + a b )
(D) 2.5

105. If the constraints in a linear programming problem
are changed then

(A) The problem is to be re-evaluated.

(B) Solution is not defined.

(C) The objective function has to be modified.

(D) The change in constraints is ignored.

ENGLISH PROFICIENCY

106. Which of the following phrases (I), (II), and (III) 107. The miser gazed ____________________ at the pile of gold
given below each sentence should replace the phrase coins in front of him.
printed in bold letters to make the sentence
(A) avidly
grammatically correct? Choose the best option among the
(B) admiringly
five given alternatives that reflect the correct use of
phrase in the context of the grammatically correct (C) thoughtfully

sentence. If the sentence is correct as it is, mark (d) ie., (D) earnestly
"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

108. The treasure was hidden ____________________ a big 109. Select the pair wherein the words have closest
shore. relationship to the original pair. WATER : SWIM ::

(A) on (A) Ground : Play

(B) underneath (B) Plan : Implement

(C) toward (C) Graze : Grass

(D) off (D) Knot : Tie

110. His speech was disappointing it __________ all the 111. Choose the word which is most opposite in meaning
major issues. to the word 'Drowsy'.

(A) projected (A) Sleepy

(B) revealed (B) Nodding

(C) skirted (C) Yawning

(D) analysed (D) Wakeful

112. Select the pair wherein the words have closest 113. Read the following passage carefully and answer
relationship to the original pair. DRIVER : DRIVING :: the questions given below it. The likelihood of at least
600,000 deaths being caused annually in India by fine
(A) Carpenter : Wood
particulate matter pollution in the air is cause for worry,
(B) Counsellor : Counselling
even if the data released by the World Health
(C) Garden : Plants Organisation are only a modelled estimate. The
(D) Psychologist : Teaching 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 fine 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
intensified action. A neglected aspect of urban air
pollution control is the virtual discarding of the
Construction and Demolition 3 Waste Management Rules,
notified 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
scientifically 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. According to the WHO Global

Get Free Sample Papers, Question Papers, MockBurden of Disease
Tests & Study Material atstudy which of the following is/are

pollution linked health impacts? (I) Infection of the lower
respiratory system (II) Chronic obstructive pulmonary
disease (III) Stroke and ischaemic heart disease

114. 115. I saw a __________________ of cows in the field.

Which of the following phrases (I), (II), and (III) given (A) group

below each sentence should replace the phrase printed in (B) herd
bold letters to make the sentence grammatically correct? (C) swarm
Choose the best option among the five given alternatives
(D) flock
that reflect the correct use of phrase in the context of
the grammatically correct sentence. If the sentence is
correct as it is, mark (d) i.e. "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

LOGICAL REASONING

116. If 5#6=121 and 10#8=324, then find the value nd of 117. Identify the figure that will complete the pattern.
23 # 14=?
(A)
(A) 1369 (B)
(B) 1349 (C)
(C) 1331 (D)
(D) 725

118. Find the next term 3,4,7,7,13, 13, 21, 22, 31, 34, ? 119. When Rahul was born, his father was 32 years older
than his brother and his mother was 25 years older than
(A) 42
his sister. If Rahul's brother is 6 years older than him and
(B) 43
his mother is 3 years younger than his father, how old
(C) 51 was Rahul's sister when he was born?
(D) 52
(A) 7 years

(B) 10 years

(C) 14 years

(D) 19 years

120. Select the missing number from the given 121. Select the related letter/word/ number from the
responses. given alternatives. Distance: Odometer :: ?: Barometer

(A) 888 (A) Humidity

(B) 788 (B) Pressure

(C) 848 (C) Thickness

(D) 842 (D) Wind

122. Which answer figure complete the form in question 123. Deepak said to Nitin, "That boy playing with the
figure ? Question figure : Answer Figure football is the younger of the two brothers of the
daughter of my father's wife." How is the boy playing
(A)
football related to Deepak?
(B)
(A) Son
(C)
(B) Brother
(D)
(C) Cousin

(D) Brother-in-law

124. Look at this series: J14, L16,____,P20, R22, ... What 125. If A x B means A is to the south of B; A + B means A
number should fill the blank? is to the north of B; A % B means A is to the east of B; A -
B means A is to the west of B; then in P % Q + R - S, S is
(A) S24
in which direction with respect to Q?
(B) N18
(A) South-West
(C) M18
(B) South-East
(D) T24
(C) North-East

(D) North-West

126. Which of the following cube in the answer figure 127. Choose the correct alternatives from the given ones
cannot be made based on the unfolded cube in the that will complete the series. 22,26,53, 69, 194, ?
question figure?
(A) 230
(A) (B) 260
(B) (C) 250
(C) (D) 245
(D)

128. Choose the correct alternatives from the given ones 129. Choose the correct alternatives from the given ones
that will complete the series. 22,26,53,69, 194, ? that will complete the series. L O_ LLM 0 L
N M 0 M

(A) 230 (A) MNNNO

(B) 260 (B) MONNO

(C) 250 (C) MONON

(D) 245 (D) MONNN

130. Look at this series: 36, 34, 30, 28, 24, … What
number should come next?

(A) 22

(B) 24

(C) 26

(D) 28

ANSWER KEY

1. (A) 2. (A) 3. (B) 4. (D) 5. (D) 6. (B) 7. (C)

8. (A) 9. (D) 10. (C) 11. (B) 12. (B) 13. (B) 14. (A)

15. (C) 16. (B) 17. (A) 18. (A) 19. (C) 20. (A) 21. (A)

22. (B) 23. (B) 24. (A) 25. (D) 26. (D) 27. (C) 28. (D)

29. (B) 30. (B) 31. (C) 32. (C) 33. (C) 34. (A) 35. (C)

36. (D) 37. (A) 38. (B) 39. (B) 40. (C) 41. (C) 42. (D)

43. (B) 44. (B) 45. (A) 46. (B) 47. (D) 48. (B) 49. (B)

50. (A) 51. (D) 52. (C) 53. (D) 54. (A) 55. (B) 56. (C)

57. (D) 58. (B) 59. (A) 60. (D) 61. (D) 62. (B) 63. (B)

64. (C) 65. (C) 66. (C) 67. (B) 68. (C) 69. (A) 70. (B)

71. (B) 72. (A) 73. (A) 74. (D) 75. (C) 76. (A) 77. (A)

78. (A) 79. (C) 80. (B) 81. (B) 82. (B) 83. (B) 84. (C)

85. (D) 86. (D) 87. (C) 88. (A) 89. (A) 90. (C) 91. (B)

92. (B) 93. (D) 94. (D) 95. (B) 96. (B) 97. (A) 98. (A)

99. (B) 100. (D) 101. (C) 102. (D) 103. (A) 104. (D) 105. (A)

106. (C) 107. (A) 108. (D) 109. (A) 110. (C) 111. (D) 112. (B)

113. (D) 114. (D) 115. (B) 116. (A) 117. (D) 118. (B) 119. (B)

120. (B) 121. (B) 122. (B) 123. (B) 124. (B) 125. (B) 126. (C)

127. (A) 128. (A) 129. (D) 130. (A)