KEAM 2025: KEAM Engineering entrance (Mathematics, Physics and Chemistry), session 3
Text of page 1
FINAL ANSWER KEY
Question Paper Code: 12/2025/OL
Exam:KEAM 2025 ENGG-3
Date of Test: 26-04-2025
1. The relation R={(1,3),(2,3),(2,4),(3,1)(4,4)(4,1)} on the set X={1,2,3,4} is
A) a1-1function
B) reflexive
C) transitive
D) not symmetric
E) an onto function
Correct Answer : Option D
If two sets A and B are having 11 elements in common, then the number of elements
2. common to A × B and B × A
A) 121
B) 22
C) 99
D) 11
E) 33
Correct Answer : Option A
3. The domain of the function f(x) = √x + x − 2 is
A) (- ∞ ,- 2) ∪ [1, ∞)
B) ( − ∞, − 2] ∪ (1, ∞)
C) ( − ∞, − 2) ∪ (1, ∞)
D) ( − ∞, − 2] ∪ [1, ∞)
E)
Correct Answer : Option D
4. The range of the function f(x) = x + 4x + 4 is
A) [0, ∞)
B) [1, ∞)
C) [3, ∞)
D) [2, ∞)
E) [4, ∞)
Correct Answer : Option A
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Let s, t, r be non-zero distinct positive real numbers. If the complex number z = x + iy
5. satisfies
sz + tz― + r = 0 , then z lies on
A) imaginary axis
B) real axis
C) y=x
D) y = 2x
E) x+y =0
Correct Answer : Option B
Let z = x + iy be a complex number, where i = √−1 is the complex unit. Then z − 1 + i
6. = 5 is a circle with
A) centre at (-1,1) and radius 5
B) centre at (1,1) and radius √5
C) centre at (-1,-1) and radius √5
D) centre at (1,1) and radius 25
E) centre at (1,-1) and radius 5
Correct Answer : Option E
7. Let z be a complex number such that z + iz − iz + 1 = 0 where i = − 1. Then |z| =
A) 2
B)
C) 1
D)
E) 3
Correct Answer : Option C
8. Real part of is equal to
A) cos
B) sin
C) 1 + sin
D) 1 + cos
E) sin + cos
Correct Answer : Option B
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9. The 25th term of 9,3,1, , ,...is
A)
B)
C)
D)
E)
Correct Answer : Option D
10. The first three terms in a G.P. are , a, b and c where a ≠ b Then the fifth term is
A)
B)
C)
D)
E)
Correct Answer : Option C
The sum of first n terms of a G.P. is 1023. If the first term is 1 and the common ratio is 2,
11. then the value of n is
A) 12
B) 11
C) 10
D) 9
E) 8
Correct Answer : Option C
Let G , G , G be geometric means between l and n, where l and n are positive real
12. numbers.Then the common ratio is
A)
B)
C)
D)
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E)
Correct Answer : Option D
25 distinct objects are divided into 5 groups and each group consists of exactly 5 objects.
13. Then the number of ways of forming such groups, is
!
A)
( !)
!
B)
!
!
C)
( !)
!
D)
( !)
!
E)
( !)
Correct Answer : Option C
14. 1+ C + C +...+ C +1 =
A) 2
B)
C)
D) 2
E) 100
Correct Answer : Option D
15. The coefficient of x in (1 − x )(1 − x ) is
A) C
B) − C
C) − C
D)
E) 0
Correct Answer : Option E
16. C + C +...+ C =
A) 2
B) 2
C) 2 −1
D) 2 −2
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E) 2 −1
Correct Answer : Option E
17.
A)
B)
C)
D)
E) 0
Correct Answer : Option C
Let B be a matrix of order 3 × 2 and C be a matrix of order 3 × 3 . If A is a matrix such that
18. BA = C, then the order of A is
A) 2×2
B) 2×3
C) 3×2
D) 3×4
E) 3×3
Correct Answer : Option B
19.
A) 12
B) 8
C) 48
D) 24
E) 6
Correct Answer : Option E
20.
A) P =P
B) P = −P
C) P = 2P
D) P = − 2P
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E) P = 3P
Correct Answer : Option A
21. sec x + cosec x − sec xcosec x =
A) sec x
B)
C) cot x
D) 1
E) 0
Correct Answer : Option E
Let x be a real number such that 7x + 4 < 9x + 8 . Then the solution set of the inequality
22. is
A) ( − ∞, − 2)
B) ( − ∞, − 4)
C) ( − 2, ∞)
D) [ − 2, ∞)
E) [ − 1, ∞)
Correct Answer : Option C
( ) ( )
Let x be a real number such that ≤ Then the solution set of
23.
the inequality is
A)
B)
C)
D)
E)
Correct Answer : Option C
24. sin15 ∘sin45 ∘sin75 ∘ =
A)
√
B)
√
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C)
√
D)
√
E)
√
Correct Answer : Option B
25. If sin θ = and the angle θ is in the second quadrant, then sec θ is equal to
A)
√
√
B)
√
C)
√
D)
E)
√
Correct Answer : Option E
26.
A) sin2x
B) sinx
C) cos2x
D) cos x
E) sin
Correct Answer : Option B
∘ ∘
27. ∘ ∘
A)
√
B)
√
C)
√
D)
√
E) √3
Text of page 8
Correct Answer : Option A
( )( )
28. ( )( )
A) tan α
B)
C) 1
D) 2
E)
Correct Answer : Option C
29.
A)
B) 2
C) 3
D) 1
E)
Correct Answer : Option D
30. If tan x = tan (3) − , then x is equal to
A)
B)
C) 1
D) 3
E) 2
Correct Answer : Option A
If the distance of the line 4x − 3y + k = 0 from the point (1, 2) is 5 units, then the values
31. of k are
A) 27,-23
B) -27,23
C) 29,-24
D) -29,24
E) -28,-25
Correct Answer : Option A
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Two sides of a parallelogram are along the lines x + y = 5 and x − y = -5. If the
32. diagonals of the parallelogram intersects at (3, 6 ) then one of its vertices, is at
A) (6,5)
B) (7,6)
C) (7,5)
D) (6,7)
E) (5,7)
Correct Answer : Option D
Let ax + by + c = 0 the equation of a straight line such that 3a + 2b + 4c = 0 . Which one
33. of the following points, lies on the line?
A)
B)
C)
D)
E) (2,4)
Correct Answer : Option A
If two diameters of a circle are along the lines 2x − 3y = 5 and 3x − 4y = 7 , then the
34. centre is at
A) (1,1)
B) (-1,1)
C) (-1,-1)
D) (1,-1)
E) (1,-2)
Correct Answer : Option D
Let y = 8x be the equation of a parabola. Which one of the following is an arbitrary point
35. on the parabola?
A) (2t, 4t ), t ϵ ℝ
B) (2t , 4t ), t ϵ ℝ
C) (2t , 2t ), t ϵ ℝ
D) (2t, 2t ), t ϵ ℝ
E) (2t , 4t), t ϵ ℝ
Correct Answer : Option E
Let P be any point on the ellipse 4(x + 2) + 9(y − 4) = 144. If F and F are the Foci of
36. the ellipse, then F P + F P=
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A) 8
B) 12
C) 16
D) 6
E) 10
Correct Answer : Option B
( ) ( )
37. The eccentricity of the hyperbola - =1 is
A)
B)
C)
D)
E)
Correct Answer : Option C
→
Let →a, b, →
c be any three vectors and m, n be scalars. Which one of the following is not
38.
true?
→ → → → →
A) a + b + c = a + b +→ c
→ → → →
B) m →a + b +→
c = ma + mb + m c
C) (m + n)→ → + na
a = ma →
m → → →
→ . mb
D) a . b = ma
m → → →×→
E) a × b = ma b
Correct Answer : Option D
→ →
39. If → →) . (3b
a . b = 12, then (3a )is equal to
A) 36
B) 4
C) 108
D) 16
E) 144
Correct Answer : Option C
40. Leta ^, →
→ = 3ı^ + 2ȷ^ + 2k b = ^ı + 2ȷ^ − 2k →+→
^ .Then (a →−→
b ) .(a b) =
A) 6
Text of page 11
B) 7
C) 8
D) 9
E) 10
Correct Answer : Option C
→ → → → → → →
41.a, b,→
c , d be non-zero vectors such that →
a×b =→
c × d and →
a ×→
c = b × d .Then
→ → →
A) a − d is parallel to b − →
c
→ → →
B) a − b is parallel to b − →
c
→ → →
C) b − c is parallel to b + →
c
→ → → →
D) a − c is parallel to b − c
→ → →
E) a +→
c is parallel to b + d
Correct Answer : Option A
→
Let OP = 2ȷ^ be the position vector a point P. Let →
r = ^ȷ + λ (ı^ + ^ȷ)be a straight line. The
42.
distance of the point P from the line is
√
A)
√
B)
√
C)
√
D)
√
E)
Correct Answer : Option A
The Cartesian equation of the line → ^ +λ
r = 2ı^ − 7ȷ^ + 11k
43. ^ is
3ı^ + 7ȷ^ − 13k
A) = =
−
B) = =
−
C) = =
D) = =
E) = =
Correct Answer : Option A
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Which one of the following is a point on the straight line
44. →
r = 13ı^ − 14ȷ^ + 23k^ + λ 5ı^ − 7ȷ^ − 9k
^ ,λ ϵ ℝ
A) (13,-14,-23)
B) (5,-7,-9)
C) (23,-28,7)
D) (23,-28,5)
E) (13,14,23)
Correct Answer : Option D
45. The point at which the line = = meets the zx -plane is
A) (19,2,5)
B) (19,0,5)
C) (0,2,-1)
D) (-3,2,0)
E) (0,2,-1)
Correct Answer : Option B
46. The mean deviation about the mean from the data 400,410, 420,430,440 is
A) 14
B) 10
C)
D)
E)
Correct Answer : Option D
47. An unbiased die is thrown and B is an event showing an odd number on top. Then P(B)
A)
B)
C)
D)
E)
Correct Answer : Option D
48. The standard deviation of 1,2,3,...,100 is
A) √ 3333
B) √ 3333
Text of page 13
C) √ 3333
D) √ 3333
E) √ 1111
Correct Answer : Option A
Consider the random experiment that an integer is chosen from the first 100 positive
49. integers. Probability that the chosen number is a multiple of 11, is
A)
B)
C)
D)
E)
Correct Answer : Option C
50.
A) √2
B) 2√2
C)
√
D) √
E)
Correct Answer : Option E
51. lim
→
A) 1
B)
C) -1
D)
E) 0
Text of page 14
Correct Answer : Option A
52. The function f(x) = x √x + 2 + √x + 1 is continuous on
A) ( − ∞, 1]
B) [4, ∞)
C) [-3,∞)
D) [-1,∞)
E) (−∞,∞)
Correct Answer : Option D
53. lim
→
=
A) -1
B) 1
C) 4
D) 2
E) 0
Correct Answer : Option B
Let f(x) = [x], x ϵ (0, 6), where[x] is the greatest integer function. Then the number of
54. discontinuities of f(x)
A) 1
B) 2
C) 3
D) 4
E) 5
Correct Answer : Option E
55. Let f(x) = 10 − | x − 5 | , x ϵ ℝ , Then f(x ) is not differentiable at
A) x=10
B) x=15
C) x=-5
D) x=5
E) x=-15
Correct Answer : Option D
56. For x ϵ ℝ,let f(x) = log3 − sinx and g(x) = f(f(x))Then g'(0)=
A) sin(log3)
B) ( )
C) −cos(log3)
D) 2cos(log3)
Text of page 15
E) cos(log3)
Correct Answer : Option E
57.
A)
B)
C)
D)
E)
Correct Answer : Option A
58. Let f: ℝ → ℝ be a function such that f(x) = x + x f (1) + xf"(2) + f (3) , then f (3)=
A) 3
B) 6
C) 9
D) -2
E) f"(2)
Correct Answer : Option B
59. If u = sec ( − sec2θ ) and v = cos θ , then at θ = ,is equal to
A) √2
B) 2√ 2
C)
√
D)
√
E) −√2
Correct Answer : Option B
60. The functionf(x) = e − x is increasing in the interval
A) (0, 4)
B) ( − ∞ ,0 )
C) ( − 1, 1)
D) ( − 1, 0)
E) (0, ∞)
Text of page 16
Correct Answer : Option E
61. Let f(x) = 10 − | x − 3 | , x ϵ ℝ The maximum of f(x) occurs at
A) x=0
B) x=3
C) x=-3
D) x=10
E) x=1
Correct Answer : Option B
The distance travelled by a moving particle is given by s = − 6t + 8,where t denotes
62.
the time in seconds. The velocity becomes zero when t is equal to
A) 1
B) 4
C) 3
D) 6
E) 8
Correct Answer : Option D
63. If a + b = 10 and ab is maximum, then the value of a is
A) 5
B) 3
C) 6
D) 25
E) 10
Correct Answer : Option A
64.
A)
B)
C)
Text of page 17
D)
E)
Correct Answer : Option B
sec
65. ∫ (sec tan )
dx =
A)
B)
C)
D) (secx + tanx) +C
E)
Correct Answer : Option C
66.
A) 9e − 4e + C
B) log|9e + 4e |+ C
C) 4e − 9e + C
D) log |4e − 9e |+ C
E) log |9e − 4e |+ C
Correct Answer : Option E
67.
A) e cos θ + C
B) e sin2θ + C
C) 2e cos θ + C
D) e sinθ + C
E) e co s2θ + C
Correct Answer : Option A
68.
Text of page 18
A)
B)
C)
D)
E)
Correct Answer : Option B
69. The area bounded by y = x − 1, 1 ≤ x ≤ 2, y = 0 (in sq.units) is
A) 2
B) 1
C)
D) 4
E)
Correct Answer : Option C
70.
A) − log2
B) − log3
C) + log2
D) + log2
E) − log2
Correct Answer : Option E
71.
A) 2
B)
C)
D) 1
Text of page 19
E) 0
Correct Answer : Option D
72.
A) 14
B) 16
C) 8
D) 10
E) 12
Correct Answer : Option E
73.
A) 16 + 25 + √x + C
B) 16 + 25 + √x +x+ C
C) 16 + 25 + √x + x + C
D) x 16 + 25 + √x + C
E) x 16 + 25 + √x + C
Correct Answer : Option A
The elimination of arbitrary constants c , c , c and c from y = (c + c ) sin (x + c ) − c
74. e gives a differential equation of order
A) 1
B) 2
C) 3
D) 4
E) 5
Correct Answer : Option C
The maximum value of the objective function z = 2x + 3y , when the corner points of the
75. feasible region are (0, 0), (5, 0) , (4, 1) and (0, 2), is
A) 0
B) 6
C) 10
Text of page 20
D) 11
E) 16
Correct Answer : Option D
The dimension of X in the equation, F = 6π η X is
76. ( F – Force; η -Coefficient of viscosity)
A) M L T
B) ML T
C) M L T
D) M L T
E) ML T
Correct Answer : Option A
77. One torr is
A) 1 mm of Hg
B) 1 cm of Hg
C) 76 mm of Hg
D) 100 mm of Hg
E) 76 cm of Hg
Correct Answer : Option A
A particle moving with an initial velocity of 1 ms has an uniform acceleration of 2 m
78. s . The distances travelled by the particle in the first two intervals of 5 s are
respectively
A) 30 m and 110 m
B) 50 m and 110 m
C) 40 m and 80 m
D) 30 m and 80 m
E) 60 m and 160 m
Correct Answer : Option D
When a cricketer hits a ball at an angle of 45⁰ with an initial velocity of 40 ms ,the ball
79. falls on the ground at a distance of 160 m. If he hits the ball at the same angle with an
initial velocity of 50 ms the ball will fall at a distance of
A) 480 m
B) 180 m
C) 280 m
D) 300 m
Text of page 21
E) 250 m
Correct Answer : Option E
A ball moves in a circle of radius 0.5 m from A to B in √2 s. The average velocity of the
ball is (in ms )
80.
A) 0.25
B) 0.5
C) 0.75
D) 1.5
E) 1.25
Correct Answer : Option B
A block of mass m suspended from the ceiling of a lift by an inextensible string of
81. negligible mass. When the lift moves in the upward direction with an acceleration of 0.2
ms , the tension acting on the wire is 80 N. Then the mass of the block is
A) 1 kg
B) 2 kg
C) 8 kg
D) 6 kg
E) 4 kg
Correct Answer : Option C
The force to be applied to a body of mass 200 g to change its velocity by 25 ms in 5 s
82.
is
A) 2.5 N
B) 50 N
C) 3N
D) 30 N
E) 1N
Correct Answer : Option E
Two bodies having masses in the ratio 1:3 have equal linear momentum. Their respective
83. kinetic energies are in the ratio
A) 3:1
B) 1:2
C) 1:3
Text of page 22
D) 4:1
E) 2:1
Correct Answer : Option A
A particle moving in a horizontal circle of radius 0.5 m completes half rotation. The work
84. done by the centripetal force of 5 N on the particle (in J) is
A) 2
B) 5
C) 2.5
D) 3
E) 1
Correct Answer:-Question Cancelled
The moment of inertia and rotational kinetic energy of a rigid body about an axis are
85. respectively 4 kgm and 50 J. The angular velocity of the body (in rad s ) is
A) 10
B) 20
C) 25
D) 5
E) 15
Correct Answer : Option D
If a torque of 1.25 Nm acts on a circular ring for a duration of 4 s, then its angular
86. momentum changes by (kgm s )
A) 25
B) 50
C) 15
D) 5
E) 10
Correct Answer : Option D
If the angular displacement made by a rotating wheel in 10 s is 150π radian, then the
87. number of revolutions made by it is
A) 75
B) 100
C) 300
D) 150
E) 50
Correct Answer : Option A
Two satellites A and B are orbiting the earth at a height of 2.5R and 7.5R respectively
88. from the centre of the earth. The ratio of time periods of A and B is
A) √3: 1
Text of page 23
B) 1: 3√3
C) 1: √3
D) 1: 2√3
E) 3√3: 1
Correct Answer : Option B
The orbital velocity v of an artificial satellite revolving around the earth at a height R
89. from the surface of the earth in terms of escape velocity v from the earth is (R - radius
of the earth)
A)
B)
C)
√
D) v
E) √2v
Correct Answer : Option A
P is the atmospheric pressure and P is the absolute pressure at a depth ℎ in an ocean.
90. The gauge pressure at the depth ℎ is
A) P+P
B)
C) 2P − P
D)
E) P−P
Correct Answer : Option E
91. The principle behind the function of Bunsen burner is
A) Pascal’s law
B) law of flotation
C) venturimeter
D) Toricelli’s law
E) Archemedes’ principle
Correct Answer : Option C
92. Bernoulli’s principle is applicable to
A) non-viscous, incompressible fluids in streamline flow
B) viscous, compressible fluids in streamline flow
Text of page 24
C) viscous, incompressible fluids in streamline flow
D) non-viscous, incompressible fluids in turbulent flow
E) non-viscous, compressible fluids in turbulent flow
Correct Answer : Option A
93. Specific heat capacity of a substance depends on the
A) material of the substance only
B) volume of the substance only
C) mass of the substance only
D) material and temperature of the substance
E) mass and volume of the substance
Correct Answer : Option D
94. Which one is INCORRECT statement?
A) In an isochoric process, volume remains constant
B) In an adiabatic process, there is a heat exchange with the surrounding
C) In an isobaric process, pressure remains constant
D) In an isothermal process, temperature remains constant
E) In a cyclic process, the change in internal energy is zero
Correct Answer : Option B
The number of molecules contained in the gas of mass M is
95. (M - molar mass, N - Avogadro’s number)
A)
B)
C)
D)
E)
Correct Answer : Option E
If the mean free path of a gas molecule at 27 ⁰C is 10 x 10 m. Its mean free path at 87
96.
⁰C is
A) 12 x10 m
B) 8 x10 m
C) 6 x10 m
D) 10 x10 m
E) 14 x10 m
Text of page 25
Correct Answer : Option A
If the speed of the transverse wave in a wire under certain tension is v , then its speed
97.
under tension 2 (in ms ) is
A)
√
B) 2v
C) √2v
D)
√
E)
Correct Answer : Option C
98. A musician hits a drum 90 times in a minute. The time period of hit is
A) 1.34 s
B) 1.5 s
C) 0.33 s
D) 0.75 s
E) 0.67 s
Correct Answer : Option E
If the time period of a particle executing SHM is 8 s, then the time period of the potential
99. energy of this particle is
A) 16 s
B) 4s
C) 2s
D) 8s
E) 32 s
Correct Answer : Option B
Which one of the following pairs of charges separated by the same distance r will
100. experience a maximum force?
A) 0.3 C and 0.7 C
B) 0.1 C and 0.9 C
C) 0.2 C and 0.8 C
D) 0.5 C and 0.5 C
E) 0.4 C and 0.6 C
Correct Answer : Option D
A charge of 5 C is moved from a point P to another point Q by doing a work of 10 J. If the
101. potential at P is 0.5 V, then the potential at Q is
Text of page 26
A) 1.0V
B) 2.0V
C) 2.5 V
D) 1.5V
E) 3.0V
Correct Answer : Option C
The equivalent capacitance of n capacitors of equal capacitance when connected in
102. series and parallel are respectively 0.4 μF and 10 μF. The capacitance of each capacitor
is
A) 2μF
B) 4μF
C) 5 μF
D) 6 μF
E) 1μF
Correct Answer : Option A
The value of R in the given circuit is
103.
A) 0.4 Ω
B) 8Ω
C) 2Ω
D) 0.8 Ω
E) 4Ω
Correct Answer : Option E
The resistance of a wire at 30⁰C and 40⁰C are respectively 5 Ω and 6 Ω. The temperature
104. coefficient of resistance of the material of the wire (in per degree Celcius) is
A) 0.04
B) 0.05
C) 0.02
D) 0.03
E) 0.01
Correct Answer : Option B
A wire of 25 Ω resistance is cut into n pieces of equal length. If these pieces of wires are
105. connected in parallel, their equivalent resistance is 1 Ω , then the value of is
Text of page 27
A) 3
B) 6
C) 8
D) 5
E) 4
Correct Answer : Option D
A coil having 100 turns and an area of 0.02 m is placed with its plane perpendicular to
106.
the magnetic field of 1 Wbm . The magnetic flux linked with the coil is
A) zero
B) 1 Wb
C) 2 Wb
D) 3 Wb
E) 5 Wb
Correct Answer : Option C
Two charged particles of same mass but having charges in the ratio 1: 4 enter a uniform
107. perpendicular magnetic field. The ratio of their time period in their respective circular path
is
A) 1: 4
B) 1: 8
C) 8: 1
D) 4: 1
E) 2: 1
Correct Answer : Option D
108. Which one is not a ferromagnetic material?
A) cobalt
B) tungsten
C) nickel
D) gadolinium
E) iron
Correct Answer : Option B
If an inductor coil of self-inductance 2 H stores 25 J of magnetic energy, then the current I
109. passing through it is
A) 25 A
B) 10A
C) 15A
D) 2A
E) 5A
Text of page 28
Correct Answer : Option E
110. When a current passing through a coil changes at the rate of 30 As , the emf induced
in the coil is 12 V. The self-inductance of the coil is
A) 0.4 H
B) 0.2 H
C) 0.6 H
D) 0.3 H
E) 0.1 H
Correct Answer : Option A
An electromagnetic wave travelling in vacuum has its electric field component,
111. E = 15 sin [1.57y + 5.4t]ȷ^ The wavelength of the wave is
A) 4.0 m
B) 3.0 m
C) 2.5 m
D) 2.0 m
E) 1.0 m
Correct Answer : Option A
112. Chromatic aberration arises in thick lenses due to
A) scattering of light
B) refraction of light
C) interference of light
D) reflection of light
E) dispersion of light
Correct Answer : Option E
An unpolarized light incident on a plane glass surface gets totally polarized on reflection.
113. If the refractive index of glass is tan 57 ∘, then the angle of refraction is
A) 90⁰
B) 33⁰
C) 13⁰
D) 37⁰
E) 45⁰
Correct Answer : Option B
114. Light energy is redistributed in
A) diffraction and interference
B) reflection and diffraction
C) refraction and interference
Text of page 29
D) reflection and polarisation
E) polarization and refraction
Correct Answer : Option A
Which one of the following statements is INCORRECT?
115.
In photoelectric effect
A) Threshold frequency is different for different metals
B) The same metal gives same response to light of different wavelengths
C) The emission of photoelectrons is an instantaneous process
Above the threshold frequency the number of photoelectrons emitted per sec is
D)
directlyproportional to the intensity of incident radiation
The maximum K.E. of the photoelectrons is independent of the intensity of incident
E)
radiation
Correct Answer : Option B
When an electron is accelerated from rest by a potential of 480 V, the wavelength
116. associated with it is λ. If the electron at rest is accelerated by a potential of 120 V, then
the wavelength associated with it is
A) 5λ
B) 4λ
C) 2λ
D) 3λ
E) 6λ
Correct Answer : Option C
In hydrogen spectrum, the shortest wavelength of Bracket series is produced during the
117. transition between the states
A) n = 5 and n = 4
B) n = 4 and n = 1
C) n = 4 and n = 3
D) n = ∞ and n = 4
E) n = 4 and n = 2
Correct Answer : Option D
118. A radioactive element having 6 x 10 atoms initially decays and is left with 0.75 x 10
undecayed atoms in 48 years. The half-life time of this radioactive element is
A) 16 years
B) 24 years
C) 12 years
D) 6 years
E) 18 years
Text of page 30
Correct Answer : Option A
119. The possible number of energy states in a Ge crystal containing 5 x 10 atoms is
A) 2 x 10
B) 4 x 10
C) 4 x 10
D) 3 x 10
E) 5 x 10
Correct Answer : Option B
120. A pn junction diode without any voltage biasing acts as a
A) rectifier
B) resistor
C) ac generator
D) voltage regulator
E) transformer
Correct Answer : Option B
How many moles of methane are required to produce 11 g CO ( ) after combustion?
121.
(Molar mass of CO = 44 g mol )
A) 0.25
B) 0.5
C) 1.5
D) 2.0
E) 2.5
Correct Answer : Option A
A sub-atomic particle of mass 6.63 × 10 kg is moving with a velocity of 1 × 10 ms
122.
. What is the de Broglie wave length (in nm) associated with it (h = 6.63 × 10 Js)?
A) 10.0
B) 1.0
C) 0.10
D) 5.0
E) 0.50
Correct Answer : Option B
For hydrogen atom, the orbitals with the lowest energy among the given orbitals are
123. (i) 4s (ii) 2p (iii) 3d 2 (iv) 2p
A) (i) & (iii)
B) (ii) & (iv)
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C) (ii) & (iii)
D) (ii) only
E) (i) only
Correct Answer : Option B
Which of the following species will have the largest and the smallest sizes respectively?
124.
Na, Mg, Na , Mg
A) Mg and Na
B) Mg and Mg
C) Na and Mg
D) Na and Mg
E) Na and Mg
Correct Answer : Option C
125. Which of the following statement is INCORRECT?
A) The dipole moment of BF is zero.
B) The bond order of CO molecule is the same as the bond order in NO ion.
C) In ozone molecule, the two O-O bond lengths are equal.
D) The dipole moment of NF is much greater than that in NH
E) Carbonate ion has three canonical forms.
Correct Answer : Option D
In which of following reactions entropy decreases?
(i) 2Pb(NO ) ( ) → 2PbO( ) + 4NO ( ) + O ( )
126. (ii) H O( ) → H O( )
(iii) Br ( ) → 2Br( )
(iv) C H ( ) → C H ( )
A) (ii), (iii) and (iv)
B) (i) and (iii)
C) (i) and (iii)
D) (i) and (iv)
E) (ii) and (iv)
Correct Answer : Option E
The enthalpy of combustion values of C H ( ) , C(graphite,s) and H ( ) are
127. respectively -1411kJ mol , -394 kJ mol and -286 kJ mo . What is the value of
enthalpy of formation of C H ( ) in kJ mol ?
A) -102
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B) -51
C) +102
D) +153
E) +51
Correct Answer : Option E
The following concentrations were obtained in the formation of NH ( ) from N ( ) and
H ( ) at equilibrium at 500 K:
[NH ] =1.5 × 10 M, [N ] = 5 × 10 M and [H ] = 0.10 M
128.
Calculate the equilibrium constant for the reaction (in dm mol ) at 500 K.
N ( ) + 3H ( ) ⇋ 2NH ( )
A) 0.45
B) 4.5
C) 45.0
D) 4.5 × 10
E) 4.5 × 10
Correct Answer : Option C
129. Which of the following is a Lewis acid?
A) HCl
B) HO
C) H O
D) Co
E) NH
Correct Answer : Option D
The EMF of the following cell at 298K is
130. Mg( ) │Mg (aq) (0.10M) ││ Ag (aq)(0.001M)│Ag( )
(Given: E =3.17V and 2.303RT/F = 0.06 V)
A) 3.32V
B) 2.96V
C) 3.02V
D) 3.17V
E) 3.47V
Correct Answer : Option C
131. The electrolyte used in lead storage battery is
A) 10% H SO aqueous solution
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B) 60% H SO aqueous solution
C) 38% H SO aqueous solution
D) 38% HCl aqueous solution
E) 60% HCl aqueous solution
Correct Answer : Option C
132. The binary liquid mixture that has positive deviation from Raoult’s law is
A) Chloroform-Acetone
B) Chloroethane-Bromoethane
C) Phenol-Aniline
D) Benzene-Toluene
E) Ethanol-Acetone
Correct Answer : Option E
133. A first order reaction has a rate constant of 6.93 × 10 s at 300 K. What is the half
life period of the reaction in seconds at the same temperature?
A) 693
B) 6930
C) 10000
D) 1000
E) 500
Correct Answer : Option D
134. Which of the following is true in respect of a zero order reaction?
A) Plot of [Reactant] against time is a straight line with slope equal to k
B) Plot of [Reactant] against time is a straight line with slope equal to -k
C) Plot of [Reactant] against time is a straight line with slope equal to 2.303 k
D) Plot of [Reactant] against time is a straight line with slope equal to -2.303 k
E) Plot of [Reactant] against time is a straight line with slope equal to -k/2.303
Correct Answer : Option B
135. Which of the following 3d transition metal has +5 state as the more stable state?
A) Titanium
B) Vanadium
C) Manganese
D) Nickel
E) Silver
Correct Answer : Option B
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In acidic medium, dichromate behaves as an oxidizing agent which can be represented
as
136. Cr2O + xH + ye → 2Cr + zH O
The values of x, y and z are respectively
A) 6, 7 and 14
B) 7, 6 and 14
C) 14, 6 and 7
D) 14, 7 and 6
E) 6,12 and 7
Correct Answer : Option C
137. Which of the following is not an interstitial compound?
A) Sc O
B) TiC
C) Mn N
D) TiH .
E) Fe H
Correct Answer : Option A
138. Which of the following transition metal has the highest magnetic moment?
A) Sc
B) Ti
C) Cr
D) Fe
E) Mn
Correct Answer : Option E
139. Which of the following complex is optically active?
A) trans − [CrCl (ox) ]
B) trans − [PtCl (en) ]
C) cis − [Pt(NH ) ]Cl
D) trans − [Pt(NH ) ]Cl
E) cis − [PtCl (en) ]
Correct Answer : Option E
140. The number of bridging carbonyl groups in [Mn (CO) ] is
Text of page 35
A) 2
B) 0
C) 4
D) 3
E) 1
Correct Answer : Option B
On complete combustion 0.12g of an organic compound gives 0.11g of CO . What is the
141. percentage of carbon in the organic compound?
A) 15%
B) 20%
C) 25%
D) 17.5%
E) 21.5%
Correct Answer : Option C
One mole of an alkene reacts with acidic KMnO to give two moles of ethanoic acid.
142. What is the alkene?
A) 2-Methylpropene
B) 1-Butene
C) 2-Pentene
D) 2-Butene
E) 2-Methyl-2-butene
Correct Answer : Option D
143. Which of the following is a vicinal dihalide?
A) 1,1-Dibromopropane
B) 1,2-Dibromopropane
C) 1,3-Dibromopropane
D) Benzal dibromide
E) 1,3-Dibromobutane
Correct Answer : Option B
144. S 1 reaction is most favoured by
A) Ethyl bromide
B) 2-methyl-2-bromopropane
C) 2-bromopropane
D) 1-bromopropane
E) 1-bromobutane
Correct Answer : Option B
Text of page 36
Phenol is treated with Con.H SO to gives a product ‘X” which on treatment with Con.H
145. NO gives compound ‘Y’. The compounds ‘X’ and ‘Y’ are respectively
A) Phenol-2- sulphonic acid and 2-nitrophenol
B) Phenol-2-sulphonic acid and 4-nitrophenol
C) Phenol-2-sulphonic acid, mixture of 2-nitrophenol and 4-nitrophenol
D) Phenol-2,4-disulphonic acid, mixture of 2-nitrophenol and 4-nitrophenol
E) Phenol-2,4-disulphonic acid and picric acid
Correct Answer : Option E
146. Denatured alcohol with colour and foul smell is made now a days by mixing ethanol with
A) Methanol
B) ZnSO and thiophene
C) CuSO and pyridine
D) FeSO and furan
E) Fe (SO ) and hexane
Correct Answer : Option C
147. Benzoyl chloride is converted to benzaldehyde by
A) Etard reaction
B) Stephen reaction
C) Gatterman reaction
D) Gatterman – Koch reaction
E) Rosenmund reaction
Correct Answer : Option E
148. In which of the following liquid inter molecular hydrogen bonding does not exist?
A) CH COOH
B) C H OH
C) Phenol
D) Diethylether
E) Ethylamine
Correct Answer : Option D
149. The IUPAC name of allylamine is
A) But-2-en-1-amine
B) But-1-en-2-amine
C) Prop-2-en-1-amine
D) Prop-1-en-2-amine
E) 2-Amino 1-propene
Text of page 37
Correct Answer : Option C
150. The carbohydrate found in yeast is
A) lactose
B) starch
C) cellulose
D) maltose
E) glycogen
Correct Answer : Option E
Official key not published for this paper.
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Source: Commissioner for Entrance Examinations. Question paper published by Commissioner for Entrance Examinations.