KEAM 2025 Question Paper Engineering with Answers (25 April 2025)

FOR KEAM EXAM PREPARATION

KEAM 2025
Question Paper ·
Engineering
EXAM YEAR TYPE SUBJECT INCLUDES

KEAM 2025 Question Paper Engineering Answers
DATE

25 April 2025

Notes · Sample Papers · Previous Year Papers · Mock Tests

m
m .co

m .co FINAL ANSWER KEY as
e m
se a g l
Question Paper Code: 11/2025/OL
Exam:KEAM 2025 ENGG-2
Date of Test: 25-04-2025

Let U be the universal set and let A and B be any two subsets of U. If 𝑛(𝑈) = 25, 𝑛(𝐴)
1.
= 14 𝑛(𝐴 ∩ 𝐵) = 6 and 𝑛(𝐴 ∪ 𝐵) =20, then 𝑛(𝐵 ) is equal to
A) 12
m
B) 13 m .co
C) 14 .co s e m
D) 15
s em l a
E) 16
g la ag
a

2. 𝑓(𝑥) = , 𝑥 ϵ ℝ . Then the range of 𝑓 is
A) (−8, − 7)
B) [−7, − 4]
m
.co
C)

e m
D)
las
E) , ag

Correct Answer : Option E

3. The domain of the function 𝑓(𝑥) = √7 − 11𝑥 is
A) ( − ∞, − 1]
m
B)
m .co
.co s e m
s emC ) g l a
g la D ) a
a ,1

E)
[−1, 1]

Correct Answer : Option C

Let A and B be two finite sets. If 𝑛(𝐴) = 7 and the number of relations from A into B is
4. 128, then 𝑛(𝐵) = m .
A) 4 .co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 1 of 36

B) 3
C) 2
D) 1
E) 0

Correct Answer : Option D

5. The value of (1 + 𝑖) is equal to
A) 16
B) 16𝑖
C) 32
D) 32𝑖
E) 64

Correct Answer : Option D

6. The value of 𝑖 + 𝑖 + 𝑖 + . . . 𝑖 , where 𝑖 = √−1 , is equal to
A) 𝑖
B) 1
C) −𝑖
D) −1
E) 0

7.

A)

B)

C) 3
D) -3
E)

Correct Answer : Option C

+ 𝑧― ,then ―
√ √
8. Let 𝑧 = +𝑖 and 𝑧 = − −𝑖 .If 𝑤 = 𝑧 𝑤=
A) 1
B) √3
C) 𝑖√3
D) −𝑖√3
E) −√ 3

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m
m .co

m .co s e m
se Correct Answer : Option D
g l a
a
9. Let 𝑎 =2 , 𝑛 = 1, 2, 3. . . . Then the value of the sum 𝑎 is equal to
=

A)

B)
m
.co
√
m
2 −1
.co m
C)

m s e
s e l a
ag
D)

g l a
E)
√ (
a )
Correct Answer : Option C

𝑎 ,𝑎 . . . . . .𝑎 are in G.P., and if 𝑎 + 𝑎 = 6, 𝑎 + 𝑎 = then the common
10.
ratio of the G.P. is equal to
m
.co
A)

e m
B)
las
C) ag
D) 2
E) 3

Three numbers a, b, and c are in G.P. If abc = 27 and 𝑎 + 𝑐 = 10, then 𝑎 +𝑏 +𝑐
11.
o m
m=
. c
A)
c. o81 s e m
e mB ) 82 l a
l as C ) 91 ag
ag DE )) 92 99

Correct Answer : Option C

The positive numbers α and β have geometric mean 6. If α and
12. β are roots of the equation 2𝑥 − 25𝑥 + λ = 0 is equal to then the value of λ is equal to
A) 6
m .
B) 36
.co s e m
C) 12
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 3 of 36

D) 72
E) 48

Correct Answer : Option D

13. Let S be the set of all 5-digit numbers having only the digits 0 and 1. Then n (S) =
A) 16
B) 32
C) 8
D) 64
E) 24

Correct Answer : Option A

14.
A) 4800
B) 3200
C) 5600
D) 5400
E) 6000

Correct Answer : Option E

15. Let A ={a,b,c,d,e,f} Then the number of subsets of A with an odd number of elements is
A) 8
B) 12
C) 16
D) 24
E) 32

Correct Answer : Option E

16.
A) 512
B) 256
C) 511
D) 510
E) 128

17. 𝑃
A) 𝑃

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m
m .co

c. o B ) s e m
m 𝐶
a
se C) 𝑃
ag l
D) 𝑃
E) 𝐶

Correct Answer : Option D

1 − 1⎤ 3 𝑥
18. If 𝑋 = 𝐴 𝐵,Where 𝐴 = ⎡ , 𝐵=⎡ ⎤and 𝑋= ,then 𝑥 + 𝑥 = m
⎣ 2 1 ⎦
m ⎣6⎦ 𝑥
.co
A) 3
m .co s e m
B) 4
s e l a
C) 5
g l a ag
D) 6 a
E) 7

Correct Answer : Option A

The numbers 𝑎 , 𝑎 , 𝑎 , 𝑎 , 𝑎 𝑎𝑛𝑑 a are in G.P. If 𝑎 = 2 and the common ratio 𝑟
19.
m
= , then the value of is equal to
m .co
A) 1
s e
B) 2
g la
C)
a
D) 4
E) 0

Correct Answer : Option E

1 −1
m
20.
.co
If the matrix 𝐴 = is singular, then the value of λ is equal to
o m 4λ 8
m
A .) c -2
s e
m
e B) 2 l a
l as C) 1 ag
ag D ) -1
E) 0

Correct Answer : Option A

21.
m .
.co s e m
A) 5
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 5 of 36

B) 4
C) 6
D) 7
E) 2

Correct Answer : Option A

22. The set of all x satisfying the inequality |3 − 4𝑥 | ≤ 11 is

A)
[−2, 7]

−2,
B)

C)
[−7, 2]

,2
D)

E)
[−2, − 2]

23. If 𝑥 ≠ 11 satisfies the inequality ≥3,then x lies in the interval
A) ( − ∞, 11)
B) (11, 12]
C) (11, 12 )
D) (11, ∞)
E) [12, ∞)

∘ ∘
24. ∘

A) 5
B) 4
C) 2
D) 0
E) 1

Correct Answer : Option E

∘
25. Sin 60 − 𝑆𝑖𝑛80 ∘ + 𝑆𝑖𝑛100 ∘ − 𝑆𝑖𝑛120 ∘ =
A) √3
√
B)

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m
m .co

c. o C ) 2√3 s e m
m a
se D)
√
ag l
E) 0

Correct Answer : Option E

26. If 𝑐𝑜𝑠 𝑥 − 𝑠𝑖𝑛 𝑥= ,then 𝑥 is equal to

m
.co
√
A)
m
B)
m .co s e m
√
s e l a
C)
√
g l a ag
a
D)
√

E)

Correct Answer : Option E

m
.co
27. 𝑐𝑜𝑡 (1) + 𝑐𝑜𝑡 (2) + 𝑐𝑜𝑡 (3 )=
A)
e m
las
B)
ag
C)

D) π
E) 0

m
28. m
If 𝑐𝑜𝑠(2𝑠𝑖𝑛 α)= , where 0 < α < 1 , then the value of α .co
.co s e m
s emA ) g l a
g la B ) a
a
C)

D)

E)

m .
Correct Answer : Option A
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 7 of 36

29. If tan α − = √ , where 0 < α < ,then the value of α is equal to

A)

B)

C)

D)

E)

Correct Answer : Option C

30. 𝑥 = and 𝑦 = , then =

A)

B) 2
C) -2
D)

E) 1

Correct Answer : Option D

The equation of the line passing through the point (-4,2)and the centre of the circle
31. 2𝑥 + 2𝑦 − 8𝑦 = 7 is
A) x+3y=2
B) y=2
C) x=-4
D) x+y=-2
E) y=-2

Let A(-1,2), B(1,-2) and C(-2,-2) be vertices of the triangle ABC. The equation of the line
32. passing through C and parallel to AB is
A) x+2y+6=0
B) 2x-y+6=0
C) 2x+y-6=0
D) 2x-y-6=0
E) 2x+y+6=0

Correct Answer : Option E

33. The area of the triangle bounded by the lines x=4, y=-4 and y=x is

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m
m .co

c. o A ) 28 s e m
m a
se B)
C)
42
24 ag l
D) 32
E) 40

Correct Answer : Option D

The foci of an ellipse are at (-3,0) and (3,0). If the eccentricity of the ellipse is ,then the
34. m
m
equation of the ellipse is
.co
A) + =1
m .co s e m
s e l a
a
+ l= 1 ag
ag
B)

C) + =1

D) + =1

E) + =1

m
Correct Answer : Option E

m .co
s e
la
The coordinates of the focus and the vertex of a parabola, respectively, are (-1,4)
35.
g
and(3,4) Then the equation of the parabola is
a
A) (𝑥 − 3) = 16(𝑦 − 4)
B) (𝑥 − 3) = − 16(𝑦 − 4)
C) (𝑦 − 4) = − 8(𝑥 − 3)
D) (𝑦 − 4) = − 16(𝑥 − 3)
E) (𝑦 − 4) = 1(𝑥 − 3)
m
m
Correct Answer : Option D
.co
.co s e m
m The line segment joining the points (-3,1) and (1,1) is transverselaaxis of a hyperbola. If
s e36. the length of the conjugate axis is 4, then the equation of the g
l a a hyperbola is

ag A ) (𝑥 + 2) − (𝑦 − 1) = 4
B) (𝑥 + 1) − (𝑦 − 1) = 16
C) (𝑥 + 1) − (𝑦 − 1) = 4
D) (𝑥 + 2) − (𝑦 − 1) = 16
E) (𝑥 − 1) − (𝑦 + 1) = 4

m .
.co m
Correct Answer : Option C

s e
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 9 of 36

The line 𝑥 + 𝑦 = 2 touches a circle. If the centre of the circle is at (-4,0) ,then the radius
37. of the circle is
A) 2√2
√
B)

C) √2
√
D)

E) 3√2

Correct Answer : Option E

→ →
^ and 𝐴𝐷
38. Let ABCD be a rectangle. If 𝐴𝐵 = 5𝚤^ + 4𝚥^ − 3𝑘 = 3𝚤^ + 2𝚥^ − ^
𝑘, then the
length of BD is
A) 2√5
B) 3√2
C) 4√3
D) 2√3
E) 3√3

Correct Answer : Option D

39. Let →𝑎 = α ^𝚤 − 3𝚥^ − 2𝑘^ and → ^ . If the projection of →
𝑐 = ^𝚤 − 2𝚥^ + 2𝑘 𝑎 on →
𝑐 is 2,
then the value of α is equal to
A) 2
B) 4
C) 3
D) 5
E) 6

→ → → → → →
40. If |𝑎 | = 8, | 𝑏 | = 5, and |𝑎 − 𝑏 | = 7 then the angle between 𝑎 and 𝑏 is equal
to
A)

B)

C)

D)

E)

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m
m .co

m .co s e m
se Correct Answer : Option E
g l a
→
a
→ →
41. → →
If |𝑎 | = 3, | 𝑏 | = 2, then the value of (2𝑎 + 3𝑏 ). (2𝑎 − 3𝑏 )is equal to
→
A) 6
B) -12
C) 12
D) -6
0
E)
m
m .co
m .co
Correct Answer : Option E
s e m
s e l a
42. The line a =
g l = passes through the point
ag
A) a
(-3,0,-3)
B) (3,0,5)
C) (-3,0,5)
D) (3,4,5)
E) (3,-4,-5)

Correct Answer : Option A

o m
=.
c
43.
If the lines = = and
e m = are coplanar, then the values
of m are
l as
A)
B)
4,1
1,-4
ag
C) 3,1
D) 5,-1
E) 3,-1

m
44.
c o m The angle between the lines = = and = =
m
is
.co
m . cos s e
s e A)
√
g l a
l a a
ag B ) cos
√

C) cos

D) cos √

E) cos √

m .
Correct Answer : Option E
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 11 of 36

45. If the line = = passes through the point (-1,-2,-3) then the value of α is

A) 4
B) -4
C) 3
D) -3
E) -2

Correct Answer : Option D

Let X={a,b} and Y={1,3,4,5} . A subset of 𝑋 × 𝑌 is selected at random. If A is an event of
46. selecting a subset of 𝑋 × 𝑌 containing exactly three elements, then P(A ) =

A)

B)

C)

D)

E)

Correct Answer : Option A

A box contains 8 red balls, 10 white balls and 17 black balls. Two balls are drawn one by
47. one without replacement. The probability, that the first ball drawn is white and the second
ball drawn is black, is
A)

B)

C)

D)

E)

Correct Answer : Option E

Let S={2, 5,8,11,14,17, 20, 23}. Two integers m, n are chosen one by one from S with
48. replacement. Then the probability, that mn is odd, is
A)

B)

C)

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m
m .co

c. o D ) s e m
m a
se ag l
E)

In a class there are n students. The mean of marks obtained by these n students in an
49. exam is 65. If the mark of one student is increased from 50 to 75 and the new mean is
66, then the value of n is equal to
m
.co
A) 10
m
.co m
B) 15
20
m s e
C)

s e l a
a ag
D) 25
30 g l
E)
a
Correct Answer : Option D

50. lim =
→
A) 3
B)
m
C)
m .co
s e
D) 2
g la
E) 0 a
Correct Answer : Option D

/
51. The domain of the function 𝑓(𝑥)= √8𝑥 − 𝑥 − 7 is
A) [1, 7]
B) [−3, 3]
m
.co
C) [−7, − 1]
D ) o[m3, 7] m
c
e mE .) [1, 4] l as e
las ag
ag Correct Answer : Option A

52. lim =
→

A)

B)

m .
.co m
C)

s e
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 13 of 36

D)

E) 0

𝑥+α , if 𝑥 < 0
Let 𝑓(𝑥) = If f is continuous at x = 0, then the value
53. 𝑚𝑎𝑥(2𝑐𝑜𝑠𝑥, 2𝑠𝑖𝑛𝑥), if 𝑥 ≥ 0
of α is equal to
A) 2
B) 3
C) 4
D) 1
E) 0

Correct Answer : Option A

54.

A) 1
B) -1
C) -3
D) 3
E) 0

55. If 𝑦 = 𝑠𝑒𝑐 𝑡𝑎𝑛 𝑥 ,then at 𝑥 = √3 is equal to
√
A)

B)

C) 2
√
D)

E) 2√3

Correct Answer : Option D

56. Let 𝑓(𝑥) = , 𝑥 ≠ 0. Then the value of 𝑓 (27) is equal to

A)

B)

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m
m .co

c. o C ) s e m
m a
se ag l
D)

E)

5𝑥 + 𝑎𝑥 + 16, if 𝑥 < 2
m
.co
Let 𝑓(𝑥) = is differentiable at 𝑥 = 2 , then the value of a
57. 𝑥 , m 𝑖𝑓𝑥 ≥ 2
is equal to
m .co s e m
A) 16
s e l a
B) -18
g l a ag
C) 32 a
D) -32
E) -16

Correct Answer : Option E

58.
m
m .co
A)
s e
g la
B)
a
C)

D)

E)

m
.co
Correct Answer : Option C

o m m
c
. Let 𝑓(𝑥) = s e
e m
59. and let 𝑢 = 𝑓(𝑥)𝑓"(𝑥). then =
l a
s
la A ) -36𝑥 ag
ag B) 36𝑥
C) 42𝑥
D) -42𝑥
E) -30𝑥

Correct Answer : Option A
m .
60. .co
The function 𝑓(𝑥) = 2𝑐𝑜𝑠𝑥 − 𝑥 + 3 is
s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 15 of 36

A) increasing in (0, π )
B) decreasing in (0, π )

C) increasing in (0, ) and decreasing in( π)

D) decreasing in (0, ) and increasing in , ( π)

E) increasing in (0, ) and decreasing in ( π)

61. If 𝑦 = (𝑥 − 1)𝑙𝑜𝑔 (𝑥 − 1), then at 𝑥 = 3 is

A) 𝑒
B) 𝑒
C) 3
D)

E)

Correct Answer : Option D

Let 𝑓(𝑥) = 𝑒 (2𝑥 + 𝑎𝑥 + 2 − 𝑎) . If 𝑓 has a local minimum at x=2. the value of a is
62.
equal to
A) -9
B) -8
C) -6
D) -11
E) 22

Correct Answer : Option A

63. If 𝑒 𝑦 + 2√1 + 𝑥 = 5, then − at (0,3) is

A) 2
B) -2
C) -3
D) 6
E) -6

Correct Answer : Option D

64. ∫ ( )
𝑑𝑥 is equal to

A) 𝑙𝑜𝑔 | | +𝐶

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m
m .co

c. o B ) s e m
m 𝑙𝑜𝑔 | 1 + 𝑥 | + 𝐶
a
se ag l
C) 𝑙𝑜𝑔 | 1 + 𝑥 | + 𝐶

D) 𝑙𝑜𝑔 | | +𝐶

E) 𝑙𝑜𝑔 | | +𝐶

Correct Answer : Option E
m
m .co
65. ∫ 𝑑θ =
m .co s e m
s e l a
ag
+𝐶
A)

g a
l+ 𝐶
B)
a
cos 2θ
2sin 2θ + 𝐶
C)

D) +𝐶
E) sin 2θ + 𝐶

Correct Answer : Option E

m
66. ∫
( )
𝑑𝑥=
m .co
√
s e
A) 2 tan (√2𝑥 + 5) + 𝐶
g la
B) 𝑡𝑎𝑛(√2𝑥 + 5) + 𝐶 a
C) tan (2𝑥 + 5) + 𝐶
D) tan (√2𝑥 + 5) + 𝐶
E) 2 tan (2𝑥 + 5) + 𝐶

Correct Answer : Option D

m
m
67. o∫ 𝑑𝑥 =
m.co
.c s e
s emA ) 𝑙𝑜𝑔 | | +𝐶
g l a
g la a
a B) 𝑙𝑜𝑔 | 5 − 𝑥 | + 𝐶

C) −2𝑙𝑜𝑔 | 5 − 𝑥 | + 𝐶

D) 𝑙𝑜𝑔 | 5 − 𝑥 | + 𝐶

E) 2𝑙𝑜𝑔 | | +𝐶
m .
Correct Answer : Option D .co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 17 of 36

68. ∫ 𝑑𝑥 =

A) 𝑙𝑜𝑔 | 1 + 3𝑒 | +𝐶
B) 𝑙𝑜𝑔 | 𝑒 + 3𝑒 | +𝐶
C) 𝑙𝑜𝑔 | 1 + 3𝑒 | +𝐶

D) 𝑙𝑜𝑔 | 𝑒 + 3𝑒 | +𝐶
E) 𝑙𝑜𝑔 | 1 + 3𝑒 | +𝐶

Correct Answer : Option A

69.
A) 5
B) 6
C) -5
D) -6
E) 0

The area of the region bounded by + = 1 and the line segment joining (0,5) and
70.
(4, 0) in the first quadrant is
A) 10π − 5
B) 5π − 8
C) 4π − 10
D) 4π − 8
E) 5π − 10

Correct Answer : Option E

71. ∫
( )
𝑑𝑥 =
A) 1
B) 2
C) 4
D) 8
E) 0

Correct Answer : Option A

72.

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m
m .co

c. o A ) s e m
m a
se ag l
B)

C) 2
D) -2
E) 1

Correct Answer : Option E

m
73. m
The general solution of the differential equation (1 + 𝑦)𝑑𝑥 − (1 − 𝑥)𝑑𝑦 = 0 is
.co
A) 𝑥 +𝑦 +𝑥−𝑦=𝐶
m .co s e m
s e
𝑥 + 𝑦 − 𝑥𝑦 = 𝐶 l a
ag
B)
C)
g l a
𝑥 − 𝑦 + 𝑥𝑦 = 𝐶
D) a
𝑥 − 𝑦 − 𝑥𝑦 = 𝐶
E) 𝑥 −𝑦 +𝑥+𝑦=𝐶

Correct Answer : Option C

74. The integrating factor of the differential equation (1 + 𝑥 )𝑑𝑦 = (1 − 2𝑥𝑦)𝑑𝑥 is
A) 𝑥 +1 m
B) 𝑙𝑜𝑔 (𝑥 + 1)
m .co
s e
C)
g la
D) 𝑥(𝑥 + 1) a
E) 𝑙𝑜𝑔 | 𝑥|

Correct Answer : Option A

Consider the linear programming problem:
Maximize: 𝑧 = α 𝑥 + 6𝑦
m
.co
Subject to the constraints
m + 2𝑦 ≤ 60
75..co𝑥 + 2𝑦 ≤ 40
3𝑥
s em
s em 𝑥, 𝑦 ≥ 0 la
l a If every point in the line segment joining (20, 0) and (10, 15)aisgoptimal solution of the
ag L.P.P, then the value of α is equal to
A) 3
B) 4
C) 6
D) 8
E) 9

Correct Answer : Option E
m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 19 of 36

The dimensional formula for the product of moment of inertia and the square of angular
76. velocity is
A) 𝑀𝐿𝑇
B) 𝑀𝐿 𝑇
C) 𝑀𝐿 𝑇
D) 𝑀𝐿 𝑇
E) 𝑀𝐿𝑇

Correct Answer : Option D

The ratio of the distance of the sun from the earth to that of the moon from the earth is of
77. the order of
A) 10
B) 10
C) 10
D) 10
E) 10

If a freely falling body from the top of a tower takes 3 s and 5 s to cross the 28 floor
78. and 4 floor respectively, then the height difference between these floors is (g = 10 ms
)
A) 80 m
B) 60 m
C) 100 m
D) 90 m
E) 70 m

Correct Answer : Option A

If θ is the angle of projection of an object for which the horizontal range is equal to the
79. maximum height attained, then the value of tan θ is
A) √2
B) 1
C) 4
D)

E)
√

Correct Answer : Option C

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 20 of 36

m
m .co

.co
m 80. The velocity of a swimmer in the direction of flow of river is 10 𝑘𝑚ℎ s e m
se g l a
and that against
the flow of river is 6 kmh . The velocity of the swimmer in still water in kmh is
A) 6
a
B) 8
C) 7
D) 5
E) 9

m
m .co
81.
m .co
If a ball of mass 0.02 kg bowled by a bowler straight to a batsman is hit back with the
same speed with an impulse of 2 Ns, then the speed of the ball bowled is s e m
s e l a
A) 20 ms
80 ms g
l a ag
B)
a
C) 50 ms
D) 60 ms
E) 40 ms

Correct Answer : Option C

If 𝑓 and 𝑓 o m
represent the coefficeints of static friction and kinetic friction of the relative
82. c
.area A , then
m
motion between two surfaces in contact with
e
A) 𝑓 depends on A
las
𝑓 depends on A a g
B)

C) 𝑓 and 𝑓 are independent of A
𝑓 is greater than the maximum value of 𝑓
D)

E) 𝑓 opposes impending motion
m
m .co
.co
Correct Answer : Option C

e m
e83. a s
m If the kinetic energy of a moving body reduces to 49 %, then itslvelocity is reduced to
l as 49 % a g
ag B ) 70 %
A)

C) 30 %
D) 25 %
E) 51 %

84.
o
The false statement is m m .
c
. good in all inertial frames
Work energy theorem holds
s e
A)
e m l a
l as ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 21 of 36

B) Work energy theorem is not independent of Newton's second law
C) Work done is a scalar quantity
D) Work done by the friction over a closed path is zero
E) Work done by the friction on moving body is negative

Correct Answer : Option D

The ratio between the gravitational potential energies of 1 kg of mass on the surface of
85. two planets having masses and radii in the ratio 1 : 2 and 1 : 3 respectively, is
A) 1:1
B) 2:3
C) 3:2
D) 9:4
E) 4:9

Correct Answer : Option C

86. With usual notations for a rigid body in rotational motion about a fixed axis, its
A) kinetic energy is Iω
B) angular momentum is Iω
C) work done is τ ω
D) power is τ ω

E) angular velocity is

Four identical point masses are placed at the corners of a square ABCD and the centre
87. of mass lies at the centre O of the square. If the mass at B is removed, then the
centre of mass lies at the point
A) O
B) on OB
C) on OA
D) on OD
E) on OC
Correct Answer:-Question Cancelled
If the moment of inertia of a solid sphere of mass M and radius R about its diameter is I,
88. then that of another sphere of mass 2M and radius 2R about its diameter is
A) 2I
B) 4I
C) 8I
D) 16I
E) I

Correct Answer : Option C

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m
m .co

m 89..co s e m
If a satellite of mass M is spinning about its own axis and revolves around the earth in a
se circular orbit, then it does not have
g l a
A) moment of inertia a
B) potential energy
C) rotational kinetic energy
D) vibrational energy
E) angular momentum

Correct Answer : Option D
m
m
If the ultimate strength and fracture points are far apart in a stress – strain curve of a .co
90.
.co
material, then the material is said to be
m s e m
A) ductile
s e l a
B) brittle
g l a ag
C) a
perfectly elastic
D) non malleable
E) very hard

Correct Answer : Option A

∘
Heat is conducted through a uniform rod ABC of length 1 m keeping the end A at 100 C .
m
91. .co
If the temperature at the point B at a distance 0.4m from the end A is 80 C and that at
m
∘
∘
s e
la
the other end is 40 C, then the ratio of heat conducted through AB to that through BC is
A) 3:4
ag
B) 2:1
C) 1:2
D) 2:3
E) 1:1

Correct Answer : Option A

m
m
92.cothen
If a black body at a temperature T radiates the maximum energy at a wavelength λ
m.co
m. s e
to radiate the maximum energy at the wavelength ,its temperature should be

s e A ) increased to 3T g l a
g la B ) increased to 9T a
a C) decreased to 3T
D) decreased to 9T
E) increased to √3T

Correct Answer : Option A

∘ ∘
93. m
The amount of heat to be withdrawn from 3 kg of water at 0 C to obtain 3 kg of ice at 0
.
.co
C in an icemaker is (latent heat of fusion of ice is 80 kcal/kg)
s e m
A) 400 kcal
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 23 of 36

B) 160 kcal
C) 320 kcal
D) 80 kcal
E) 240 kcal

Correct Answer : Option E

If the heat supplied to an ideal gas is used up entirely to do work on the surrounding, then
94. the process is called
A) isothermal compression
B) isothermal expansion
C) adiabatic compression
D) isobaric compression
E) isobaric expansion

The product of the pressure P and volume V of an ideal gas in a container is related to
95. the translational part of the internal energy, E as
A) 𝐸
B) √𝐸
C)

D)

E) 2√𝐸

Correct Answer : Option C

96. The mean free path of a molecule is inversely proportional to
A) its diameter
B) square of its diameter
C) square of the number of molecules
D) square root of the number of molecules
E) square root of its diameter

If the period of the simple pendulum of length 𝑙 is 5 second, then the period of the
97. pendulum of length is

A) 3s
B) 2s
C) 2.5 s
D) 1.5 s
E) 4s

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 24 of 36

m
m .co

m .co s e m
se Correct Answer : Option C
g l a
a
Two particles A and B move in concentric circles with radii in the ratio 2 : 1. If for every
98. completion of one circle of A , B completes 5 circles , then the ratio of their respective
orbital velocities is
A) 1:1
B) 1:2
C) 2:5
D) 5:2
m
E) 1:5
m .co
.co s e m
em C
Correct Answer : Option
s g l a
l a a
ag 3 : 2 and 3 : 1, then the ratio of the velocities of sound in the rods is
If the ratio
99. respectively,
of the Young’s modulii and densities of two rods of different materials are

A) 1:2
B) 2:1
C) √2: 1
D) 1 : √2
E) 1:3
m
Correct Answer : Option D
m .co
s e
la
A conductor with an air core cavity inside, is charged to attain the surface charge density
100. of σ. If E is the magnitude of electric field and V is the potential, then inside the cavity
g
A) E≠0
a
B) V=0
C) E ≠ 0 and V = 0
D) V ≠ 0 and E = 0
E) σ = 0 and E = 0
Correct Answer:-Question Cancelled
If the torque acting on an electric dipole when placed at an angle 30 ∘ with the direction of m
m
101. an uniform electric field is τ, then the torque acting on the same dipole when placed in .co
.co
the same field at an angle 45 ∘ is
s e m
s emA ) 2τ g l a
g la B ) τ a
a
C)
√
τ
D) √2τ
E) τ

Correct Answer : Option D
m .
.co
Two identical isolated capacitors A and B are charged so that each has a charge of 4C .
s e m
em
102. If a charge of -2C is added to A and + 2C to B, then the ratio of respective potentials is
s l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 25 of 36

A) 1:1
B) 1:2
C) 2:1
D) 3:1
E) 1:3

Correct Answer : Option E

If τ is the average time between any two successive collisions for the electrons in a
103. metal wire under the application of an electric field E, then the mobility μ of the electrons
is
A)

B)

C)

D)

E)

Correct Answer : Option E

104. The maximum current drawn from a battery of 12 V with internal resistance of 0.5 Ω is
A) 16 A
B) 12 A
C) 24 A
D) 30 A
E) 4A

Correct Answer : Option C

Three identical resistors are connected in the form of a triangular mesh ABC. If a battery
105. of 12 V is connected across AB, then the ratio of the current flowing through AB to that
through ACB is
A) 2:1
B) 1:1
C) 1:3
D) 3:1
E) 1:2

Correct Answer : Option A

106. According to Biot-Savart’s law, the magnetic field B is
A) inversely proportional to the current
→
B) produced by vector source(𝐼𝑑𝑙)

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m
m .co

c. o C ) of short range s e m
m a
se D)
E)
directly proportional to the square of the distance
independent of the distance ag l

If a rectangular loop carrying a current I and area 𝑎𝑏 is placed such that a uniform
107. magnetic field B is in the plane of the loop, then the magnitude of torque on it is
A) IB ab
IB ab/2 m
.co
B)

m
.co
C) IB
e m
D) IB/2
em l as
E) 2IB ab
l as ag
g
a : Option A
Correct Answer

108. The diamagnetic and paramagnetic materials at 300 K are respectively,
A) Al and Mg
B) Cu and Si
C) Hg and Ca
D) Li and Ag
m
.co
E) Cr and Pb

Correct Answer : Option C
s em
g la
a induced emf is
109. The mismatched pair regarding the
A) Eddy current : Induction furnace
B) Transformer : Laminated core
C) Induced emf : Biot – Savart law
D) Ac generator : Electromagnetic induction
E) Coaxial coils : Mutual inductance

m
.co
Correct Answer : Option C

o m
. c If an electric bulb of resistance 400 Ω is connected to an ac source eofm
m
110.
e V, then the electric power of the bulb is l as peak voltage 282.8

s
la A ) 200 W a g
ag B) 150 W
C) 300 W
D) 100 W
E) 250 W

Correct Answer : Option D

omis c )
The velocity of light in a medium of relative permittivity 2 and relative permeability 4.5 is
111. (velocity of light in free space
.c e m .
A) c
em l as
las ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 27 of 36

B)

C)

D)

E)
√

Correct Answer : Option C

The distance of an object placed in front of a concave mirror of radius of curvature 24 cm
112. that gives its magnification as 3 is
A) 8 cm
B) 16 cm
C) 12 cm
D) 24 cm
E) 32 cm

Correct Answer : Option A

113. The ratio of the speed of light in vacuum to that in a medium is called
A) luminous intensity
B) luminous flux
C) magnification factor
D) refractive index of the medium
E) transparency index

Correct Answer : Option D

In Young’s double slit experiment using a source of wavelength λ interference bands are
114. observed on a screen. If the separation between the slits alone is halved in this
experiment, then the angular separation ω of the fringes on the screen becomes
A) 2ω
B) √2ω
C)

D) ω
E)
√

Correct Answer : Option A

If light waves of wavelengths λ and λ/3 are incident on the surface of a material,
115. photoelectronsare emitted with maximum kinetic energy E and 4E respectively, then the
work function of the material is
A)

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 28 of 36

m
m .co

c. o B ) s e m
m a
se ag l
C)

D)

E)

m
m .co
.co with it is
If 2E is the kinetic energy of a moving particle of mass 𝑚 , then the wavelength of the de
116. Broglie wave associated
e m
em l as
A)
l as ag
B) ag
C)
√

D)
√

E)
√
m
Correct Answer : Option C .co
s em
aaradioactive sample, then the number of atoms
If N is the initial number of atoms in l
g
117. decayed after the five half life periods
a is
A) 𝑁

B) 𝑁

C) 𝑁

D)
m
m .co
m
E)
.co s e m
s e g l a
g la Correct Answer : Option A a
a In a hydrogen atom, the transition of an electron from the energy level,𝑛 = ∞ and 𝑛
118. = 3 is the
A) shortest wavelength of Paschen series
B) longest wavelength of Paschen series
C) shortest wavelength of Balmer series
D) longest wavelength of Balmer series
m .
.co
E) shortest wavelength of Bracket series
e m
em l as
las ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 29 of 36

Correct Answer : Option A

119. Semiconductors are
A) having positive temperature coefficients
B) having forbidden energy gap Eg > 3 eV
C) made to conduct more by adding impurity elements
D) placed in the VI group of elements in periodic table
E) having electrons and ions as charge carriers

Correct Answer : Option C

120. In a full wave rectifier, for an input ac voltage
A) the output voltage appears across the load for positive cycle only
B) both diodes conduct during positive cycle
C) both diodes conduct during negative cycle
D) one diode is always forward biased and the other is always reverse biased
E) a centre tapped transformer is used

Correct Answer : Option E

What is the mass of the substance ‘X’ required to prepare 250 mL of 0.5 molar aqueous
121.
solution? (Molar mass of ‘X ‘is 40 g 𝑚𝑜𝑙 )
A) 2g
B) 4g
C) 5g
D) 10 g
E) 0.5 g

Correct Answer : Option C

A 150 watt bulb emits monochromatic light of wavelength 662 nm. How many number of
122. photons emitted per second by the bulb?
(Planck’s constant, h = 6.62 × 10 J s, c = 3 × 10 m 𝑠 )
A)

B) 3×10 𝑠
C) 6×10 𝑠
D) 5×10 𝑠
E) 1×10 𝑠

Correct Answer : Option D

123. The orbital described by the quantum numbers n=4 and 𝑙 = 2 is
A) 4s
B) 3d

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m
m .co

c. o C ) 2d s e m
m a
se D)
E)
4f
4d ag l
Correct Answer : Option E

124. The correct order of metallic character of the following elements is
A) Na > Mg > Si > P
B) Mg > Na > Si > P
m
.co
C) Na > Mg > P > Si
m
.co m
D) Si > P > Mg > Na
s e
em
P > Si > Mg > Na
E)

s l a
g la : Option A
Correct Answer ag
a
125. Which of the following statement is incorrect about bond order?
A) Bond order is the number of bonds between the two atoms in a molecule.
B) Isoelectronic molecules and ions have identical bond orders.
C) Bond enthalpy decreases with increase in bond order.
D) Bond length decreases with increase in bond order.
Bond enthalpy increases with increase in bond order.
m
E)

.co
em
Correct Answer : Option C
s
la dsp hybridisation?
126. (i) a g
Which of the following molecules have
(ii) 𝐵𝑟𝐹 (iii)[𝐶𝑜(𝑁𝐻 ) ] (iv) [𝐶𝑟𝐹 ] (v) [𝑃𝑡(𝐶𝑙) ]

A) (i) and (ii)
B) (i) and (iii)
C) (ii) and (iii)
D) (i) and (v)
E) (iii) and (v)
m
m .co
.co
Correct Answer : Option D
e m
e m What is the log K of the following reaction, l as
as
l 127. 2N 𝐻 +𝑐𝑜 ( ) ⇌ 𝑁𝐻 𝐶𝑂𝑁𝐻 ( ) + 𝐻 𝑂( ) 𝑎𝑡298𝐾 ag
ag
( )

If ∆rG◦ = - 11.4 kJ 𝑚𝑜𝑙 and 2.303RT = 5.7 kJ 𝑚𝑜𝑙
-1
A) 2.5
B) 1.5
C) 4
D) 3
E) 2

m .
Correct Answer : Option E
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 31 of 36

What is the heat of the following reaction (in kJ 𝑚𝑜𝑙 )?
128. 𝐹𝑒 𝑂 ( ) + 3𝐻 ( ) → 2𝐹𝑒( ) + 3𝐻 𝑂( )

A) -33.29
B) +33.29
C) +3.33
D) -3.33
E) -30.29

Correct Answer : Option A

Which of the following reaction proceeds nearly to completion?
129.
Reaction 𝐾 value
A) 𝑁 ( ) + 𝑂 ( ) ⇌ 2𝑁𝑂( ) at 298 K 4.8 × 10
B) 𝐻 ( ) + 𝐶𝑙 ( ) ⇌ 2𝐻𝐶𝑙( ) at 300 K 4.0 × 10
C) Decomposition of 𝐻 𝑂 into 𝐻 and 𝑂 at 500 K. 4.1 × 10
D) Reaction of 𝐻 with 𝐼 to give HI at 700 K. 57.0
E) Gas phase decomposition of 𝑁 𝑂 to 𝑁𝑂 at 298K. 4.64 × 10

Which of the following solutions of salts are neutral?
130. (i) KBr (ii) 𝑁𝑎𝑁𝑂 (iii) KF (iv) 𝑁𝐻 𝑁𝑂 (v) NaCl
A) (ii) and (iii)
B) (i) and (iv)
C) (i) and (v)
D) (iv) and (v)
E) (iii) and (v)

Correct Answer : Option C

The molar conductivity (Λ ) acetic acid is 78.1 S 𝑐𝑚 𝑚𝑜𝑙 . Its degree of
131. dissociation (α ) is
(Λ ) for acetic acid= 390.5 S 𝑐𝑚 𝑚𝑜𝑙
A) 0.12
B) 0.40
C) 0.02
D) 0.20
E) 0.04

Correct Answer : Option D

132. Which of the following reaction is used to prepare dihydrogen gas in the laboratory?

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m
m .co

c. o A ) 2𝐹𝑒( ) + 3𝐻 𝑂( ) Δ → 𝐹𝑒 𝑂 ( ) + 3𝐻 ( ) s e m
m a
se
―
2𝑁𝑎( ) + 2𝐻 𝑂( ) → 2𝑁𝑎𝑂𝐻( ) + 𝐻 ( ) g l
B)
𝐹𝑒( ) + 2𝐻𝐶𝑙( ) → 𝐹𝑒𝐶𝑙 ( ) + 𝐻 ( )
a
C)

D) 𝑀𝑔( ) + 2𝐻 𝑂( ) ―
Δ → 𝑀𝑔(𝑂𝐻) ( ) + 𝐻 ( )
E) 𝐶𝑎( ) + 2𝐻 𝑂( ) → 𝐶𝑎(𝑂𝐻) ( )
+𝐻 ( )

Correct Answer : Option C

m
m
In which of the following solutions X-Y interactions are weaker than X-X or Y-Y
.co
133. interactions?
m .co s e m
(Where, X and Y are pure components)
s e l a
A)

g l a
Bromoethane and Chloroethane
Carbon disulphide and Acetone ag
B)
C)
a
Chloroform and Acetone
D) Nitric acid and Water
E) Benzene and Toluene.

What is the half life period of the first order reaction whose rate constant is 2.31 ×
134. m
10 𝑠
m .co
A) 3 × 10 𝑠
s e
B) 3 × 10 𝑠
g la
C) 6.3 × 10 𝑠 a
D) 4 × 10 𝑠
E) 3 × 10 𝑠

Correct Answer : Option A

In the Arrhenius equation, 𝑘 = 𝐴𝑒 /
m
.co
, which factor corresponds to the fraction of
m
135. molecules
.co
that have kinetic energy greater than activation energy ?
s e m
s emA ) 𝑒 /
g l a
g la B ) 𝑒 / a
a C) 𝑒 /

D) 𝑒
/
E) 𝐴𝑒

Correct Answer : Option A

m metal does not exhibit variable oxidation state?
136. Which of the following transition .
A) Copper .co s e m
Scandium
s em l a
ag
B)

g la
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 33 of 36

C) Vanadium
D) Nickel
E) Cobalt

The magnetic moment of a divalent ion in aqueous solution is 3.87 BM. The number of
137. unpaired electrons present in it is
A) 4
B) 5
C) 3
D) 2
E) 1

Correct Answer : Option C

138. Chromite ore is
A) 𝐹𝑒𝐶𝑟𝑂
B) 𝐹𝑒𝐶𝑟 𝑂
C) 𝐶𝑟 𝑂
D) 𝐹𝑒𝐶𝑟 𝑂
E) 𝐹𝑒 𝐶𝑟 𝑂

Correct Answer : Option D

139. Which of the following pair of actinoids exhibit maximum oxidation state of +7?
A) Th and Pa
B) Cm and Bk
C) Pa and Fm
D) Pa and U
E) Np and Pu

Correct Answer : Option E

140. The IUPAC name of [𝐶𝑜(𝑒𝑛) ] (𝑆𝑂 ) ) is
A) tris(ethane-1,2-diamine)cobalt(III) sulphate
B) bis(ethane-1,2-diamine)cobalt(III) sulphate
C) bis(ethane-1,2-diamine)cobalt(II) sulphate
D) tris(ethane-1,2-diamine)cobaltate(II) sulphate
E) tris(ethylene-1,2-diamine)cobalt(III) sulphate

Correct Answer : Option A

141. The IUPAC name of the compound 𝐻𝑂𝐶𝐻 (𝐶𝐻 ) 𝐶𝐻 𝐶𝑂𝐶𝐻 is
A) 7-Hydroxyheptan-2-one

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m
m .co

c. o B ) 2-Oxoheptan-7-ol s e m
m a
se C)
D)
1-Hydroxyheptan-2-one
5-Oxoheptan-2-ol ag l
E) 6-Hydroxyheptan-3-one

Correct Answer : Option A

142. Which of the following is a electron donating group?
A) −𝑁𝑂
m
B) −𝐶𝐻
c. o
m m .co
C) −𝐶𝑂𝑂𝐻
m s e
D) −𝐶𝑁
s e l a
E) −𝑂𝐶 𝐻 a
g l ag
a

143. Bromoethane on treatment with sodium metal in dry ethereal solution gives
A) Ethanal
B) Propane
C) n-Butane
m
.co
D) n-Pentane
E) n-Hexane

s em
Correct Answer : Option C
g la
a
The order of reactivity of the following compounds towards SN2 displacement reaction is
144. (i) 𝐶 𝐻 𝐶𝐻(𝐶𝐻 )𝐵𝑟 (ii) 𝐶 𝐻 𝐶𝐻(𝐶 𝐻 )𝐵𝑟 (iii) 𝐶 𝐻 𝐶(𝐶𝐻 )(𝐶 𝐻 )𝐵𝑟 (iv) 𝐶
𝐻 𝐶𝐻 𝐵𝑟
A) (ii) > (i) > (iii) > (iv)
B) (iv) > (ii) > (i) > (iii)
C) (ii) > (iii) > (i) > (iv)
m
.co
D) (i) > (ii) > (iii) > (iv)
m
.co
E) (iv) > (i) .> (ii) > (iii)
e m
em Correct Answer : Option E l as
las a g
ag The major product obtained in the dehydration of ethanol in the presence of 𝐻 𝑆𝑂 at
145.
413 K is
A) Ethanoic acid
B) Ethanal
C) Ethyne
D) Ethoxyethane
E) Ethane
m .
Correct Answer : Option D .co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 35 of 36

The product formed in the following reaction is
146. 𝐶𝐻 − 𝐶𝐻 − 𝐶𝐻(𝐶𝐻 ) − 𝐶𝐻(𝐶𝐻 ) − 𝑂𝑁𝑎 + 𝐶 𝐻 𝐵𝑟 →
A) 2-Ethoxy-3-methylpentane
B) 2-Ethoxy-4-methylpentane
C) 1-Ethoxy-2-methylpentane
D) 2-Ethoxy-2-methylpentane
E) 5-Ethoxy-3-methylpentane

Correct Answer : Option A

147. Which of the following compound has the highest boiling point?
A) n-Butane
B) Propan-1-ol
C) Methoxy methane
D) Propanal
E) Acetone

148. Which of the following acid is highly acidic?
A) Fluoroacetic acid
B) Formic acid
C) Dichloroacetic acid
D) Benzoic acid
E) Acetic acid.

Correct Answer : Option C

149. Which of the following is Hinsberg’s reagent?
A) Nitrous acid
B) Ethanolic potassium hydroxide
C) Benzenesulphonyl chloride
D) 2,4-Dinitrophenyl hydrazine
E) Ammoniacal silver nitrate

Correct Answer : Option C

The activation energy for the hydrolysis of sucrose by the enzyme sucrose is (in kJ 𝑚𝑜
150.
𝑙 )
A) 7.14
B) 6.22
C) 8.60
D) 1.5
E) 2.15
Correct Answer:-Question Cancelled

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