KEAM 2025 Question Paper Engineering with Answers

Entrance Exam
2025

QUESTION
PAPER

FINAL ANSWER KEY
Question Paper Code: 8/2025/OL
Exam:KEAM 2025 ENGG-1
Date of Test: 23-04-2025

Let A, B, C be any three finite sets.
1. If 𝑛(𝐴 × 𝐵) = 160, 𝑛(𝐵 × 𝐶) = 80 and 𝑛(𝐶 × 𝐴) = 200, then 𝑛(𝐴) =
A) 10
B) 18
C) 16
D) 12
E) 20

Correct Answer : Option E

2. Let 𝑓(𝑥) = 𝑥 − 10𝑥 − 19, 𝑥 ϵ ℝ .Then the inverse image of 5, 𝑓 (5) =
A) {−2, − 12}
B) {−2, 12}
C) {2, − 12}
D) {2, 12}
E) ϕ

Correct Answer : Option B

Let 𝑓(𝑥) = 𝑐𝑜𝑠𝑥. Then the value of [𝑓(𝑥 + 𝑦) + 𝑓(𝑦 − 𝑥)] − 𝑓(𝑥)𝑓(𝑦) is equal
3.
to
A) 2
B) -2
C) 1
D) -1
E) 0

Correct Answer : Option E

4. Let f(x)=log x(x>0) and g(x)=cos x(−1≤x≤1). Then the domain of g∘f is
A) (0,1]
B) [−1,α)
C) [0,α)

D) ,5
E) [−1, 5]

Correct Answer : Option D

1
5. Let 𝑧 = 1 + .Then the value of 𝑧 is equal to

A) 4
B) -4
C) 1−𝑖
D) 1+𝑖
E) 𝑖

Correct Answer : Option B

6. The modulus of the complex number 2√2 + 𝑖2√2 is equal to
A) 64
B) 4
C) 32
D) 8
E) 16

Correct Answer : Option E

7. If 𝑧 + 𝑧¯ = 6 and 𝑧 − 𝑧¯ = 4𝑖 , then 𝑧 =
A) 36
B) 16
C) 15
D) 13
E) 9

Correct Answer : Option D

8. Let z= , where is a real number. If 4𝑅𝑒(𝑧) = 3𝐼𝑚(𝑧¯) then the value of is

A) 5
B) -5
C) 3
D) 2
E) -2

Correct Answer : Option D

9. In a G.P., the first and third terms are 4 and 8 respectively. Then the 21 term is
A) 4012
B) 4064
C) 4098

D) 2048
E) 4096

Correct Answer : Option E

Let 𝑎 , 𝑎 , 𝑎 , . . . be in G.P. If 𝑎 . 𝑎 . 𝑎 = 64 and 𝑎 . 𝑎 . 𝑎 . 𝑎 . 𝑎 = 32 ,
10. then common ratio is
A)

B)

C)

D)

E)

Correct Answer : Option D

( )
The general term of a sequence is 𝑡 = ,n= 1, 2, 3, . . . . If 𝑡 = 5, then the
11.
value of 𝑛 is
A) 2
B) 3
C) 4
D) 5
E) 6

Correct Answer : Option C

The product of first 5 terms of a G.P., whose terms are increasing, is 32. The third term of
12. the G.P. is
A) 2
B)

C) 4
D)

E) 8

13. Let α = 𝐶 and β = 𝐶 .Then α − β is equal to
= =
A) 32
B) 64

C) 128
D) 256
E) 0

Correct Answer : Option E

14. If α = 𝐶 and β = 𝐶 , then 1 + is equal to

A)

B)

C)

D)

E)

Correct Answer : Option B

15. If 𝑃 = 7920 , then the value of 𝑟 is equal to
A) 7
B) 6
C) 5
D) 4
E) 3

Correct Answer : Option D

In the binomial expansion of (2𝑥 + α ) , the co-efficients of 𝑥 and 𝑥 are equal. Then
16.
the value of α is equal to
A) 2
B)

C) 4
D)

E) 3

Correct Answer : Option C

Let 𝐴 = {0, 2, 4, 6, 8}. The number of 5-digit numbers that can be formed using the
17. digits in 𝐴 without replacement, is
A) 120
B) 96
C) 88
D) 64

E) 32

Correct Answer : Option B

| |
18. Let 𝐴 be a 3×3 matrix and let B=3𝐴 . If |A|=5 , then the value of
| |
is equal to

A) 27
B) 125
C) 25
D) 135
E) 81

Correct Answer : Option D

19.

A) -18
B) 18
C) 21
D) -21
E) -2

Correct Answer : Option E

20.
A) 6
B) 5
C) 4
D) 3
E) 2

The following system of equations

𝑥+𝑦+𝑧=1
21. 2𝑥 + 3𝑦 − 𝑚𝑧 = 2
3𝑥 + 5𝑦 + 3𝑧 = 3
has no unique solution. Then the value of 𝑚 is equal to
A) 3
B) 5
C) 2
D) -2
E) -3

Correct Answer : Option D

22. The set of all x satisfying the inequalities −4 ≤ 2 − 3𝑥 < 7 is

A)

B)

C)

D)

E)

Correct Answer : Option D

23. −5 < 𝑥 ≤ − 1 implies −21 < 5𝑥 + 4 ≤ b, the least value of 𝑏 is
A) 5
B) -5
C) -4
D) 4
E) -1

Correct Answer : Option E

24. 𝑡𝑎𝑛15 ∘ + 𝑡𝑎𝑛75 ∘=
A) √5 + 1
B) 2
C) √7 − 1
D) 4
E) 0

Correct Answer : Option D

25. If 𝑥 + 𝑧 = 2𝑦 and 𝑦 = ,then tan 𝑥 tan 𝑦 tan 𝑧=

A) 1
B) 𝑡𝑎𝑛(𝑥 − 𝑦)
C) 𝑡𝑎𝑛(𝑧 − 𝑦)
D)

E) 0

If sin 𝑥 + sin 𝑦 = 𝑎 ,cos 𝑥 + cos 𝑦 = 𝑏 and 𝑥 + 𝑦 = , then the value of is equal
26.
to
√
A)

B) 2√3
C) √3
D) 4√3
√
E)

Correct Answer : Option C

27. If sin α = , where <α < then the value of tan α is equal to

A)

B)

C)

D)

E)

Correct Answer : Option C

28.

A)

B)

C)

D)

E) 0

Correct Answer : Option C

29. if 5 𝑠𝑖𝑛 α + 3𝑐𝑜𝑠 α = π ,then α is equal to
A)
√
B) 1
C)
√
D) -1

E) 0

Correct Answer : Option C

30. If θ=𝑐𝑜𝑡 , then s 𝑒𝑐 θ

A)

B)

C)

D) 𝑥
E) 2𝑥

Correct Answer : Option C

The straight line 𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0 passes through the point ( − 10, 7).If the line is
31. perpendicular to 11𝑥 − 7𝑦 = 13, then the value of c is equal to
A) 8
B) -7
C) 13
D) -13
E) 5
Correct Answer:-Question Cancelled
Let 𝐴𝐵𝐶 be an equilateral triangle. If the coordinates of 𝐴 are ( − 2, 2) and the side BC
32. is along the line 𝑥 + 𝑦 = 6, then the length of the side of the triangle is
A) 2√3
B) 3√2
C) 4√6
D) 6√6
E) 2√6

Correct Answer : Option E

33. The focus of the parabola 𝑥 − 4𝑥 + 8𝑦 + 4 = 0 is
A) ( − 2, − 2)
B) (1, 1)
C) (2, 1)
D) (2, − 2)
E) (1, 2)

Correct Answer : Option D

A circle touches the 𝑥 − axis at (9, 0). If it also touches the straight line 𝑦 = 14 , then
34. the equation of the circle is
A) (𝑥 − 9) + (𝑦 − 7) = 49
B) 𝑥 + (𝑦 − 7) = 49
C) (𝑥 − 9) + 𝑦 = 49
D) (𝑥 − 9) + (𝑦 − 7) = 81
E) (𝑥 − 7) + (𝑦 − 9) = 49

The length of major axis and minor axis of an ellipse are, respectively, 𝑚 and 𝑛. If 𝑚 −
35. √
𝑛 =45 and the eccentricity of the ellipse is , then the length of the major axis is

A) 13
B) 6
C) 12
D) 18
E) 9

Correct Answer : Option E

36. The vertex of the parabola 4𝑦 = 𝑥 − 6𝑥 + 17 is
A) (3, 2)
B) (4, 3)
C) (4, 2)
D) (3, 7)
E) (7, 2)

( ) ( )
37. The eccentricity of the hyperbola - = 1 is
A) √5
√
B)

C) √3
D) √10
√
E)

Correct Answer : Option C

→ → ^ → → ^ → →
Let 𝑎 + 𝑏 = λ ^
𝚤 + 16𝚥^ − 18𝑘 and 𝑎 − 𝑏 = 2𝚤^ + 8𝚥^ + λ 𝑘. If 𝑎 + 𝑏 is
38. → → →
perpendicular to 𝑎 − 𝑏 ,then |𝑎 |=
A) 5√13
B) √174
C) √184
D) 13√5
E) √194

Correct Answer : Option E

→ →
39. → |=12 and the projection of →
If |𝑎 𝑎 on 𝑏 is 6 3, then the angle between →
𝑎 and 𝑏 is

A)

B)

C)

D)

E)

Correct Answer : Option B

→ ^ + 2𝚥^ + 3𝑘. If ^ → →
40. Let 𝑎 = 6𝚤 is parallel to and . 𝑏= , then |𝑏 |=

A) 49
B) 7
C) 14
D) 7√2

E)

Correct Answer : Option E

→ → √ → → → →
If |𝑎 + 𝑏 | = where 𝑎 and 𝑏 are unit vectors, then the value of |𝑎 + 𝑏 | −
41. →
|→
𝑎 − 𝑏 | is equal to
A) 3
B) 4
C) √5
D) √7
E) 7

Let α , β and γ be the angles made by a straight line with the x-axis, y-axis and z-axis
42. respectively. If 𝑐𝑜𝑠 α + 𝑐𝑜𝑠 β + 𝑐𝑜𝑠 γ = ,then the value of 𝑐𝑜𝑠 α 𝑐𝑜𝑠 β + 𝑐𝑜𝑠 β
𝑐𝑜𝑠 γ + 𝑐𝑜𝑠 γ 𝑐𝑜𝑠 α is equal to
A)

B)

C)

D)

E)

Correct Answer : Option B

A straight line passing through (6,1,3) meets the line = = at Q. If the lines are
43.
perpendicular to each other, then the coordinates of 𝑄 are
A) (2,1,3)
B) (1,2,3)
C) (3,1,5)
D) (2,-1,3)
E) (-1,2,3)

Correct Answer : Option C

44. The angle between the lines = = and = = is

A)

B)

C)

D)

E)

Correct Answer : Option D

A straight line passes through the points (10,8, 6) and (13,9, 4) . A unit vector parallel to
45. this line is

A)
^)
(3𝚤^ + 2𝚥^ + 2𝑘
√

B) (𝚤 ^)
^ + ^𝚥 − 2𝑘
√

C)
^)
(3𝚤^ + ^𝚥 + 2𝑘
√

D)
^)
(3𝚤^ + ^𝚥 + 2𝑘
√

E)
^)
(3𝚤^ + ^𝚥 − 2𝑘
√

Correct Answer : Option E

A box contains 4 red and 6 white marbles. Two successive draws of 3 balls are made
46. without replacement. The probability that in the first draw, all the 3 balls are white and in
the second draw, all the 3 balls are red, is
A)

B)

C)

D)

E)

Let 𝐴 and 𝐵 be two events. If 𝑃(𝐴 | 𝐵) = 0.4, P ( A | B ')= 0.7 and 𝑃(𝐵) = 0.7, then 𝑃(
47. 𝐴) =
A) 0.44
B) 0.54
C) 0.49
D) 0.5
E) 0.65

Correct Answer : Option C

48. The standard deviation of the numbers -3, 0, 3, 8 is
√
A)

√
B)

√
C)

√
D)

√
E)

Correct Answer : Option D

An unbiased die is tossed until 5 appears. If 𝑋 denotes the number of tosses required,
49. ( = )
then ( = ) =

A)

B)

C)

D)

E)

Correct Answer : Option C

50. lim √ √
is equal to
→
A) 4√2
B) 4
C) 2√2
D) √2
E) 0

51.

A) 2
B) 3
C) 4
D) 5
E) 6

Correct Answer : Option C

52. The domain of the function 𝑓(𝑥) = √𝑥 − 3 + 4√5 − 𝑥 is
A) [1,2]
B) [2,4]
C) [3,5]

D) [3,20]
E) [12,20]

Correct Answer : Option C

53. If 𝑓(𝑥) =
√
, then 𝑓(𝑥) + 𝑓(1 − 𝑥) is equal to

A) √3
B)
√
C) 2√3
D) 1
E) 0

Correct Answer : Option D

54. lim =
→

A)

B)

C)

D)

E) -1

Correct Answer : Option B

55. If 𝑓(𝑥) = | 𝑥 + 𝑥 − 6| is not differentiable at 𝑥 = 𝑎 and 𝑥 = 𝑏, then 𝑎 + 𝑏 =
A) 11
B) 14
C) 12
D) 13
E) 16

Correct Answer : Option D

56.
A) −3√2
B) 3√2
C)
√

D)
√

E) 0

57. Let ℎ(𝑥) = 𝑓 𝑔(𝑥) . If 𝑓 (3) = 6, 𝑔 (3) = 3 and 𝑔(3) = 9, then the value of ℎ
(3) is equal to
A) 1
B) 3
C) 6
D) 9
E) 18

Correct Answer : Option B

58. Let 𝑓(𝑥) = 𝑐𝑜𝑠 𝑥 (𝑎 + cos 𝑥).If 𝑓 =0 then the value of 𝑎 is equal to
√
A)

B)

C)

D)

E) -1

Correct Answer : Option C

59. If 𝑦 = 𝑡𝑎𝑛 𝑥 − 𝑥 , then =

A)

B)

C)

D)

E) (2𝑥 − 1) 1 + (𝑥 − 𝑥)

Correct Answer : Option B

60. The function 𝑓(𝑥) = 𝑥 (𝑥 − 2) is strictly decreasing in
A) (1,2)
B) (-1.1)

C)

D) (-1,0)

E)

Correct Answer : Option E

The surface area of a solid hemisphere is increasing at the rate of 8 c 𝑚 / sec
61. (retaining its shape). Then the rate of change of its volume (in 𝑐𝑚 / sec ), when the
radius is 5𝑐𝑚, is
A)

B)

C)

D)

E)

Correct Answer : Option C

62. The function 𝑓(𝑥) = 2𝑥 − 3𝑥 − 36𝑥 + 28 is increasing in
A) ( − ∞, − 1] ∪ [3, ∞)
B) ( − ∞, − 2] ∪ [3, ∞)
C) ( − ∞, − 2] ∪ [5, ∞)
D) ( − ∞, − 5] ∪ [3, ∞)
E) ( − ∞, − 2] ∪ [8, ∞)

Correct Answer : Option B

63. Let 𝑓(𝑥) = 𝑥 + 𝛼𝑥 + β . If has a local minimum at (2, 6), then (0) is equal to
A) 10
B) -6
C) 8
D) -8
E) 6

64. ∫ 𝑑𝑥 =
A) 2𝑙𝑜𝑔 | 𝑥 + 𝑥 + 1 | + 𝐶
B) 2𝑥𝑙𝑜𝑔 | 𝑥 + 𝑥 + 1 | + 𝐶
C) 𝑙𝑜𝑔 | 𝑥 + 𝑥 + 1 | + 𝐶

D) 2𝑥 + 𝑙𝑜𝑔 | 𝑥 + 𝑥 + 1 | + 𝐶
E) 𝑥 + 2𝑙𝑜𝑔 | 𝑥 + 𝑥 + 1 | + 𝐶

Correct Answer : Option D

65. ∫ 𝑑𝑥 =

A) (𝑠𝑖𝑛 𝑥) + 𝐶
B) −(𝑠𝑖𝑛 𝑥)√1 − 𝑥 + 𝐶
C) (𝑠𝑖𝑛 𝑥)√1 − 𝑥 + 𝑥 + 𝐶
D) (𝑠𝑖𝑛 𝑥)√1 − 𝑥 − 𝑥 + 𝐶
E) (𝑠𝑖𝑛 𝑥) + 𝐶

/
66. ∫ 𝑥 𝑥 + 1 𝑑𝑥 =
/
A) 1+ +𝐶
/
B) 4 1+ +𝐶
/
C) 𝑥 +1 +𝐶
/
D) 4 𝑥 +1 +𝐶
/
E) 𝑥 +1 +𝐶

Correct Answer : Option E

67. ∫ 𝑒 sec 𝑥(1 + 𝑡𝑎𝑛𝑥)𝑑𝑥
A) 𝑒 𝑠𝑒𝑐 𝑥 + 𝐶
B) 𝑒 𝑡𝑎𝑛𝑥 + 𝐶
C) 𝑒 sec 𝑥 + 𝐶
D) 𝑒 𝑡𝑎𝑛 𝑥 + 𝐶
E) 𝑒 𝑠 ec 𝑥 𝑡𝑎𝑛𝑥 + 𝐶

Correct Answer : Option C

68. ∫ 𝑒 (𝑥 − 2)𝑐𝑜𝑠 𝑒 (𝑥 − 2𝑥) dx=
A) 𝑠𝑖𝑛 𝑒 (𝑥 − 2𝑥) + 𝐶
B) 𝑠𝑖𝑛 𝑒 (𝑥 − 2) + 𝐶

C) 𝑥 𝑒 𝑠𝑖𝑛 𝑒 (𝑥 − 2) + 𝐶
D) 𝑒 𝑠𝑖𝑛 𝑒 (𝑥 − 2) + 𝐶
E) 𝑒 𝑠𝑖𝑛 𝑥 𝑒 − 2𝑥𝑒 + 𝐶

If

69. ( − 6𝑥 + 18)𝑑𝑥 = α + β √3
√
then the value of α +
β is equal to
A) 12
B) 18
C) 24
D) 28
E) 32

Correct Answer : Option D

The value of

/
𝑐𝑜𝑡 𝑥
70. 𝑑𝑥
1 + 𝑐𝑜𝑡 𝑥
/
is equal
to
A)

B)

C)

D)

E)

Correct Answer : Option C

71. The area of the region bounded by 𝑦 = 𝑥 / and 𝑦 = 𝑥 (in square units) is

A)

B)

C)

D)

E)

Correct Answer : Option C

72.

A)

B)

C)

D)

E)

73. If 𝑦(𝑥) = 2𝑦 (𝑥), 𝑦(𝑥) ≥ 0 and 𝑦(0) = 𝑒 then 𝑦(𝑥) =
A) 𝑒 /2 + 2
B) 𝑒
C) 𝑒 /2
D) 𝑒 𝑒 /2
E) 𝑒 +2

Correct Answer : Option D

The integrating factor of the differential equation 𝑠𝑖𝑛x 𝑑𝑦 = (𝑠𝑖𝑛2𝑥 + 2y 𝑐𝑜𝑠𝑥)𝑑𝑥
74.
is
A) sec x
B) sin x
C) tan x
D) cos x
E) cosec x

Correct Answer : Option E

75. In the graphical method of a linear programming problem, the optimal solution lies
A) at the centre of the feasible region
B) at a corner point of the feasible region

C) at a point on the x-axis
D) at the origin
E) at the point where the objective function is zero

Correct Answer : Option B

– –
If 2.7×10 is added to 4.3×10 , giving due regard to significant figures, the result
76.
will be
A) 4.57×10 –
B) 4.6×10 –
C) 4.5×10 –
D) 7.0×10 –
E) 4.57×10 –

Correct Answer : Option B

77. [𝐿 𝑀 𝑇 ] is the dimensional formula for
A) angular velocity
B) activity of radioactive substance
C) time period of oscillation
D) half life period of a radioactive substance
E) impulse of the force
Correct Answer:-Question Cancelled
^ + 3.0𝑡𝚥^ then the
If the velocity (in 𝑚𝑠 – ) of a particle at any instant 𝑡 is given by 2.0𝚤
78. –
magnitude of its acceleration (in 𝑚𝑠 ) is
A) 5
B) 3
C) 2
D) 4
E) 6

Correct Answer : Option B

Among the following pairs of vectors, if the resultant of two vectors can never have
79. magnitude 4 units, then the magnitudes of the vectors are
A) 2 units and 2 units
B) 1 unit and 3 units
C) 5 units and 1 unit
D) 7 units and 2 units
E) 5 units and 8 units

Correct Answer : Option D

80. The ratio of angular speeds of the minute hand and second hand of a watch is

A) 1 : 12
B) 1:6
C) 1 : 60
D) 12 : 1
E) 60 : 1

Correct Answer : Option C

When a body is thrown vertically upwards, from the ground, the time of ascent is and
81.
the time of descent is 𝑡 in the absence of air resistance. Then is equal to
A) 2𝑡
B) 0.5𝑡
C) 0.25𝑡
D) 𝑡
E) 4𝑡

Correct Answer : Option D

When a person of mass m climbs up or down a rope with uniform speed 𝑣 , the tension in
82. the rope is (g = acceleration due to gravity)
A) 𝑚𝑔
B) 𝑚(𝑔 + 𝑣)
C) 𝑚(𝑔 − 𝑣)
D) 𝑚𝑔𝑣
E) 𝑚( )

A body of mass 0.2 kg travels along a straight line path with velocity 𝑣 = (2𝑥 + 2)𝑚
83. 𝑠 . The net work done by the driving force during its displacement from 𝑥 = 0 to 𝑥 =
2𝑚 is
A) 5.4 J
B) 4.8 J
C) 9.6 J
D) 10.8 J
E) 6.5 J

Correct Answer : Option C

84. Two colliding particles after collision move together. Then the collision is
A) partial elastic collision
B) perfectly inelastic collision
C) perfectly elastic collision
D) partial inelastic collision

E) collision without any transfer of energy

Correct Answer : Option B

A solid cylinder, a solid sphere, a disc and a ring are released from the top of an inclined
85. plane (frictionless) so that they slide down the plane without rolling. The maximum
acceleration down the plane is
A) for the disc
B) for the solid cylinder
C) for the solid sphere
D) for the ring
E) the same for all

Correct Answer : Option E

86. When a particle is rotating with constant angular momentum, then
A) torque acting on it is constant
B) force acting on it is constant
C) linear momentum is constant
D) torque acting on it is zero
E) linear velocity is constant

Correct Answer : Option D

Two objects of masses 1 kg and 2 kg are moving towards each other with accelerations 2
87. 𝑚𝑠 – and 3 𝑚𝑠 – respectively on a smooth horizontal surface. The acceleration of
centre of mass of the system is

A) 𝑚𝑠 – in in the direction of acceleration of 2 kg mass

B) 𝑚𝑠 – in in the direction of acceleration of 1 kg mass

C) 𝑚𝑠 – in in the direction of acceleration of 2 kg mass

D) 𝑚𝑠 – in in the direction of acceleration of 1 kg mass
E) zero

There is a mine of depth about 3.0 km. Conditions prevailing in this mine as compared to
88. those at the surface of earth are
A) higher air pressure, lower acceleration due to gravity
B) higher air pressure, higher acceleration due to gravity
C) lower air pressure, higher acceleration due to gravity
D) lower air pressure, lower acceleration due to gravity
E) same air pressure and acceleration due to gravity

The period of revolution of the planet around the sun is 27 times that of another planet
89. . If the distance of from the sun is times greater than that of from the sun, then
the value of is
A) 8
B) 4
C) 9
D) 3
E) 12

Correct Answer : Option C

The work done in splitting a spherical liquid drop of radius ‘𝑎 into eight liquid droplets of
90.
the same size is (surface tension of the liquid = S)
A) 8π 𝑆𝑎
B) π 𝑆𝑎
C) 2π 𝑆𝑎
D) 4π 𝑆𝑎
E) 16π 𝑆𝑎

Correct Answer : Option D

vessel containing a liquid of density 𝑑 moves down with an acceleration 𝑎(𝑎 < 𝑔 ). The
91. pressure due to the liquid at a depth of ℎ below the free surface of the liquid is
A) ℎ𝑔𝑑
B) ℎ(𝑔 − 𝑎)𝑑
C) ℎ(𝑔 + 𝑎)𝑑
D) ℎ 𝑑

E) ℎ 𝑑

Correct Answer : Option B

An incompressible liquid flows through a horizontal pipe having cross-sectional areas 𝐴
at one end and 2𝐴 at the other end. If the pressure and velocity of the liquid at the lower
92. cross- sectional end are P and v, then those values at the other end are (density of the
liquid =ρ )

A) ,𝑃 + ρ 𝑣

B) 𝑣, 𝑃 + ρ 𝑣

C) ,𝑃 + ρ 𝑣

D) 𝑣, 𝑃 + ρ 𝑣
E) 2𝑃 + ρ 𝑣

93. Efficiency of a Carnot engine
A) depends on the nature of the working substance
B) does not depend on the nature of the working substance
C) depends only on the temperature of the source 𝑇
D) depends only on the temperature of the sink 𝑇
E) does not depend on both temperature of the source 𝑇 and temperature of the sink 𝑇

Correct Answer : Option B

A cylindrical vessel contains 16 kg of gas at a pressure of 1 atmosphere. A certain
94. amount of gas is taken out and the pressure of gas in the vessel becomes 0.75
atmosphere. The amount of gas taken out is
A) 2.5 kg
B) 4 kg
C) 7.5 kg
D) 8.25 kg
E) 10 kg

Correct Answer : Option B

95. The number of degrees of freedom for monoatomic gas molecule is
A) 3
B) 4
C) 5
D) 7
E) 1

96. Pick out the INCORRECT STATEMENT
A) Internal energy of an ideal gas depends only on its temperature
B) Change in the internal energy in a cyclic process is not zero
C) Change in the internal energy of a gas depends only on its initial and final states
D) Internal energy depends upon state of matter
E) Change in the internal energy in a cyclic process is zero

Correct Answer : Option B

The distance travelled by a particle executing linear S.H.M. from its mean position in 2s is
97. equal to times its amplitude. Then its time period in seconds is
√
A) 10
B) 8
C) 9
D) 12
E) 16

Correct Answer : Option E

Time periods of pendulums A and B are T and . If they start executing S.H.M. at the
98. same time from the mean position, the phase difference between them after the bigger
pendulum has completed one oscillation is
A) π /4
B) (π / 2)
C) π /8
D) π / 16
E) π

Correct Answer : Option E

string of length 𝑙 is divided into three segments of lengths 𝑙 , 𝑙 and 𝑙 with the
fundamental frequencies 𝑛 , 𝑛 and 𝑛 respectively. The original fundamental frequency
99.
of
the string 𝑛 is given by
A) 𝑛=𝑛 +𝑛 +𝑛
B) = + +

C)

D)

E) 𝑛=𝑛 𝑛 𝑛

Correct Answer : Option B

The inward and outward electric flux from a closed surface are 6 × 10 𝑁𝑀 𝐶 and
100.
3 × 10 𝑁𝑀 𝐶 . Then the net charge (in coulomb) inside the closed surface is
A) −6 × 10 𝜀
B) 6 × 10 𝜀
C) 3 × 10 𝜀
D) 9 × 10 𝜀

E) −3 × 10 𝜀

Correct Answer : Option E

In a circuit, the capacitance C is connected. The effective capacitance of the circuit can
101. be reduced by
A) introducing a metal plate between the plates of the capacitor
B) introducing a dielectric slab between the plates
C) reducing the potential difference between the plates
D) connecting another capacitor in series with it
E) connecting another capacitor in parallel with it

Correct Answer : Option D

A given charge Q is divided into two parts which are then kept at a distance ‘d’ apart.
102. The electrostatic force between them will be maximum if the two parts are

A) and

B) and

C) and

D) and

E) each

Correct Answer : Option E

The dependence of drift velocity 𝑣 on the electric field E, for which Ohm’s law is obeyed
103.
is
A) 𝑣 ∝𝐸
B) 𝑣 ∝𝐸
C) 𝑣 ∝ √𝐸
D) 𝑣 ∝

E) 𝑣 ∝

Correct Answer : Option B

If an equilateral triangle is made of a uniform wire of resistance R, then the equivalent
104. resistance between the ends of a side is
A)

B)

C)

D)

E)

Correct Answer : Option D

105. When ‘𝑛 identical cells are connected in parallel,
A) net voltage increases
B) net current increases
C) net voltage decreases
D) net current decreases
E) total internal resistance increases

Correct Answer : Option B

In a cyclotron, if the frequency of the accelerating field is doubled, then the radius of the
106. charged particle moving in a circular path will be
A) doubled
B) quadrupled
C) the same
D) halved
E) reduced to one fourth of the original radius

Correct Answer : Option C

A galvanometer of resistance 100Ω gives a full scale deflection for a current of 1mA
107. through it. The resistance required to convert it into a voltmeter which can read upto 2 V
is
A) 1175 Ω
B) 1200 Ω
C) 1525 Ω
D) 1900 Ω
E) 2025 Ω

Correct Answer : Option D

If a magnetic material has magnetic susceptibility χ = − 0.5 , then its relative
108. magnetic permeability μ and the type of material is
A) 0, diamagnetic
B) 2, ferromagnetic
C) 1, paramagnetic
D) –1, ferromagnetic
E) 0.5, diamagnetic

Correct Answer : Option E

The self-inductance of an air core solenoid is L. If the number of turns in the solenoid is
109. doubled, keeping all other factors constant, then its self-inductance will be
A) 𝐿
B)

C) 2𝐿
D) 4𝐿
E) 8𝐿

Correct Answer : Option D

110. An alternating current having the peak value 10 2𝐴 is used to heat a metal wire. To
√
produce the same heating effect, the constant current required is
A) 10√2𝐴
B) 5A
C) 14A
D) 7A
E) 10A

Correct Answer : Option E

If 𝑣 , 𝑣 𝑎𝑛𝑑 v are the speeds of gamma rays, X-rays and visible light respectively in
111. vacuum, then
A) 𝑣 >𝑣 >𝑣
B) 𝑣 <𝑣 <𝑣
C) 𝑣 =𝑣 =𝑣
D) 𝑣 >𝑣 <𝑣
E) 𝑣 <𝑣 <𝑣
Correct Answer:-Question Cancelled
112. When a ray of light moves from one medium to another medium,
A) its frequency remains unchanged
B) its frequency alone changes
C) its wavelength remains unchanged
D) both its frequency and wavelength change
E) its velocity remains constant

113. The Brewster’s angle 𝑖 for any interface should lie between
A) 30 ∘ and 45 ∘
B) 45 ∘ and 90 ∘

C) 0 ∘ and 30 ∘
D) 0 ∘ and 90 ∘
E) 30 ∘ and 60 ∘

Correct Answer : Option B

In an Young’s double slit experiment, the band width of the fringes observed is β , when
114. light of wave length λ is used. With same experimental set up, to double the band width
of the fringes, the wave length of light required is
A) λ
B)

C) 2λ
D)

E)

Correct Answer : Option C

Pick out the INCORRECT statement from the following :
115. In photoelectric phenomenon,
A) the value of stopping potential is the same for radiations of all frequencies
B) the stopping potential is more negative for the incident radiation of higher frequency
C) the value of saturation current depends on the intensity of incident radiation
D) the value of saturation current is independent of frequency of incident radiation
E) the emission of electrons is instantaneous

If λ be the wavelength of any electromagnetic radiation, the de-Broglie wavelength of its
116. quantum (photon) is

A)

B) λ
C)

D) 2λ
E)

Correct Answer : Option B

The half-life periods of two radioactive materials A and B are 1500 years and 1200 years
respectively. If their mean life periods are τ and τ respectively, then the value of the
117.
ratio

A)

B)

C)

D)

E)

118. The greatest wavelength of the radiation that will ionize unexcited hydrogen atom is
A) 1820 Å
B) 450 Å
C) 910 Å
D) 700 Å
E) 1400 Å

Correct Answer : Option C

An alternating voltage of 250 V, 50 Hz is applied to a full wave rectifier. If the internal
119. resistance of each diode is 10Ω and the load resistance is 5𝑘 Ω , the peak value of
output current is
A) 0.05 A
B) 0.07 A
C) 0.02 A
D) 0.03 A
E) 0.04 A

Correct Answer : Option B

120. The reverse biasing in a junction diode,
A) increases the number of majority charge carriers
B) increases the number of minority charge carriers
C) reduces the number of minority charge carriers
D) decreases the potential barrier
E) increases the potential barrier

Correct Answer : Option E

The density of 3 M aqueous solution of a solute ‘X’ is 1.86 g . The molality of the
121.
solution is (Molar mass of solute ‘X’ is 120 g 𝑚𝑜𝑙 )
A) 3m
B) 4m
C) 2m

D) 5m
E) 1m

Correct Answer : Option C

The Vividh Bharati station of All India Radio, Kozhikode, broadcasts on a frequency of
122. 1500 kHz. What is the wavelength of the electromagnetic radiation emitted by
transmitter?( c = 3 × 10 𝑚𝑠 )
A) 200 m
B) 300 m
C) 100 m
D) 250 m
E) 150 m

Which of the following experimental phenomenon is explained by the wave nature of
123. electromagnetic radiation?
A) Black-body radiation
B) Photoelectric effect
C) Diffraction
D) Variation of heat capacity of solids as a function of temperature
E) Line spectra of atoms with reference to hydrogen

Correct Answer : Option C

124. Which of the following pair of oxides is neutral?
A) 𝐴𝑙 𝑂 and 𝑁𝑎 𝑂
B) 𝐴𝑙 𝑂 and 𝐴𝑠 𝑂
C) 𝐶𝑙 𝑂 and 𝑁𝑎 𝑂
D) 𝐶𝑙 𝑂 and 𝐴𝑙 𝑂
E) CO and 𝑁 𝑂

Correct Answer : Option E

The correct increasing order of dipole moment of 𝑁𝐹 , 𝐻 𝑆, 𝐶𝐻𝐶𝑙 and 𝑁𝐻
125.
molecules is
A) 𝑁𝐹 < 𝐻 𝑆 < 𝐶𝐻𝐶𝑙 < 𝑁𝐻
B) 𝑁𝐻 < 𝐻 𝑆 < 𝐶𝐻𝐶𝑙 < 𝑁𝐹
C) 𝑁𝐹 < 𝐶𝐻𝐶𝑙 < 𝐻 𝑆 < 𝑁𝐻
D) 𝑁𝐻 < 𝐶𝐻𝐶𝑙 < 𝐻 𝑆 < 𝑁𝐹
E) 𝐶𝐻𝐶𝑙 < 𝐻 𝑆 < 𝑁𝐹 < 𝑁𝐻

126. Choose the INCORRECT pair of MOLECULE and its SHAPE among the following:
A) 𝑆𝐹 Seesaw
B) 𝐵𝑟𝐹 Trigonal bipyramidal
C) 𝑁𝐻 Trigonal pyramidal
D) 𝑋𝑒𝐹 Square planar
E) 𝐶𝑙𝐹 T-shape

Correct Answer : Option B

In the reaction 3/2 𝑂 ( ) → 𝑂 ( ) , the value of at 298 K is approximately (𝐾
127.
= 10 and 2.303𝑅𝑇 = 5.7𝑘𝐽𝑚𝑜𝑙 )
A) 171 kJ 𝑚𝑜𝑙
B) 191 kJ 𝑚𝑜𝑙
C) -171 kJ 𝑚𝑜𝑙
D) -191 kJ 𝑚𝑜𝑙
E) 100 kJ 𝑚𝑜𝑙

128. Which of the following has least mean multiple bond enthalpy (in kJ 𝑚𝑜𝑙 ) at 298 K?
A) 𝑁≡𝑁
B) 𝐶≡𝑁
C) C=C
D) 𝐶≡𝑂
E) C=N

Correct Answer : Option C

129. Which of the following can act as Lewis acid?
A) 𝐻 𝑂
B) 𝐻𝑂
C) 𝐹
D) 𝑁𝐻
E) 𝐴𝑙𝐶𝑙

Correct Answer : Option E

130. The concentration of hydrogen ions in a sample of soft drink is 2×10 mol 𝑙𝑖𝑡 . Its
pH value is (log 2 = 0.3010)
A) 4.369
B) 3.699

C) 2.369
D) 5.301
E) 3.301

Correct Answer : Option B

131. Which of the following is the correct order of conductivity (in S 𝑚 )?
A) Fe < Na < Cu < Ag
B) Fe < Cu < Na < Ag
C) Ag < Na < Cu < Fe
D) Ag < Cu < Na < Fe
E) Na < Fe < Cu < Ag

132. ‘Layer Test’ is used to identify
A) Bromide
B) Fluoride
C) Potassium
D) Water
E) Chloride

133. Which of the following solvent has highest value of Molal elevation constant, K ?
A) Cyclohexane
B) Carbon disulphide
C) Carbon tetrachloride
D) Acetic acid
E) Chloroform

Correct Answer : Option C

The initial concentration of 𝑁 𝑂 in the first order reaction, 𝑁 𝑂 ( ) → 2𝑁𝑂 ( ) +
½ 𝑂 ( ) , was 1.68×10 mol 𝐿 at 310 K. The concentration of 𝑁 𝑂 after 10
134.
minutes was 0.84×10 mol 𝐿 . What is the rate constant of the reaction at 310 K ?
(log 2 = 0.3010)
A) 0.0693
B) 0.693 𝑚𝑖𝑛
C) 6.93
D) 0.0639
E) 0.0963

135. Which of the following statement is not true about a catalyst?
A) It catalyses the spontaneous reactions
B) A small amount of the catalyst can catalyse the large amount of reactants.
C) It does not alter the Gibbs energy of a reaction.
D) It catalyses the non-spontaneous reactions.
E) It does not change the equilibrium constant of a reaction.

Correct Answer : Option D

136. The most common oxidation states of chromium are
A) +2,+7
B) +3,+6
C) +2,+4
D) +2,+5
E) +3,+5

Correct Answer : Option B

137. Which of the following statement is true about potassium permanganate?
A) It is isostructural with 𝐾𝐶𝑙𝑂 .
B) It is paramagnetic in nature.
C) It oxidizes oxalates to carbon monoxide.
D) The structure of permanganate ion is square planar.
E) It is prepared by fusion of 𝑀𝑛𝑂 with an alkali metal hydroxide and an oxidising agent.

Correct Answer : Option E

138. The type of sulphide formed by Lanthanoids is
A) 𝐿𝑛𝑆
B) 𝐿𝑛𝑆
C) 𝐿𝑛𝑆
D) 𝐿𝑛 𝑆
E) 𝐿𝑛 𝑆

Correct Answer : Option D

139. In which of the following compound, Mn has +7 oxidation state?
A) 𝑀𝑛𝑂𝐹
B) 𝑀𝑛𝑂 𝐹
C) 𝑀𝑛𝑂 𝐹
D) 𝑀𝑛𝑂𝐹

E) 𝑀𝑛𝑂 𝐹

Correct Answer : Option E

140. Which of the following is a heteroleptic complex?
A) [𝐶𝑜(𝑁𝐻 ) ]
B) [𝐹𝑒(𝐶𝑁) ]
C) [𝐶𝑜(𝑆𝐶𝑁) ]
D) [𝐶𝑜(𝑁𝐻 ) 𝐶𝑙 ]
E) [𝐶𝑜(𝐶𝑁) ]

Correct Answer : Option D

141. Which of the following technique is used to separate chloroform and aniline?
A) Fractional distillation
B) Distillation under reduced pressure
C) Steam distillation
D) Continuous extraction
E) Distillation

Correct Answer : Option E

In Kolbe’s electrolytic method, when sodium acetate is electrolysed, the gases generated
142. at anode are
A) ethane and 𝐻
B) 𝐻 and 𝐶𝑂
C) methane and ethane
D) ethane and 𝐶𝑂
E) methane and 𝐻

Correct Answer : Option D

143. The number of sigma (σ) and pi (π ) bonds present in 3-Methylbut-1-ene are respectively
A) 1 and 14
B) 18 and 2
C) 16 and 2
D) 17 and 1
E) 14 and 1

Correct Answer : Option E

The order of reactivity of the following compounds towards 𝑆 2 displacement reaction is
144. (i) 2-Bromo-2-methylbutane (ii) 1-Bromopentane (iii) 2-Bromopentane

A) (ii) > (i) > (iii)
B) (iii) > (i) > (ii)
C) (ii) > (iii)> (i)
D) (i) > (ii) > (iii)
E) (iii) > (ii) > (i)

Correct Answer : Option C

145. The IUPAC name of phenyl isopentyl ether is
A) 3-Methtylbutoxybenzene
B) 2-Methylbutoxybenzene
C) 2-Methylphenoxybutane
D) 4-Methylbutoxybenzene
E) 1-Methylbutoxybenzene

Phenol on treatment with chloroform in the presence of NaOH, a -CHO group is
146. introduced at ortho position of benzene ring. The reaction is known as
A) Kolbe’s reaction
B) Reimer-Tiemann reaction
C) Gattermann-Koch reaction
D) Stephen reaction
E) Sandmeyer reaction

Correct Answer : Option B

Toluene on treatment with chromic oxide in presence of acetic anhydride at 273 - 283 K
147. gives compound(X). Compound(X) on hydrolysis with aqueous acid gives compound(Y).
The compounds (X) and (Y) are respectively
A) Benzylidene diacetate and phenol
B) Benzylalcohol and benzene
C) Benzylidene diacetate and benzaldehyde
D) Benzene and phenol
E) Benzaldehyde and phenol

Correct Answer : Option C

148. Fehling’s reagent is a mixture of
A) aqueous 𝐶𝑢𝑆𝑂 and ammonical 𝐴𝑔𝑁𝑂 solution
B) aqueous 𝐶𝑢𝑆𝑂 and 2,4-DNP
C) aqueous KOH and ammonical 𝐴𝑔𝑁𝑂 solution
D) aqueous 𝐶𝑢𝑆𝑂 and alkaline sodium potassium tatarate
E) aqueous KOH and alkaline sodium potassium tatarate

Correct Answer : Option D

The order of basic strength of following amines is
149. (i) 𝐶𝐻 𝑁𝐻 (ii) (𝐶 𝐻 ) 𝑁 H (iii)𝐶 𝐻 𝑁𝐻 (iv)𝐶 𝐻 𝑁𝐻𝐶𝐻
A) (ii) < (i) < (iv) < (iii)
B) (iii) < (iv) < (ii) < (i)
C) (ii) < (iii) < (iv) < (i)
D) (i) < (ii) < (iii) < (iv)
E) (iii) < (iv) < (i) < (ii)

Correct Answer : Option E

150. The disease caused by the deficiency of riboflavin is
A) Cheilosis
B) Rickets
C) Beri beri
D) Scurvy
E) Xerophthalmia

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