KEAM 2025 Question Paper Engineering with Answers (29 April 2025, Additional)

FOR KEAM EXAM PREPARATION

KEAM 2025
Question Paper ·
Engineering
EXAM YEAR TYPE SUBJECT INCLUDES

KEAM 2025 Question Paper Engineering Answers
DATE

29 April 2025, Additional

Notes · Sample Papers · Previous Year Papers · Mock Tests

m
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m .co FINAL ANSWER KEY s e m
se g l
Question Paper Code: 15/2025/OL a
Exam:KEAM 2025 ENGG-ADL a
Date of Test: 29-04-2025

Two finite sets A and B have 𝑚 and 𝑛 elements, respectively. The total number of subsets
1. of A is 48 more than the number of subsets of B. The values of 𝑚 and 𝑛, respectively, are
A) 6,3
B) 6,4
m
C) 5,6
m .co
D) 2,6
.co s e m
E) 7,1
s em l a
g la: Option B ag
a
Correct Answer

Let A and B be subsets of universal set 𝑈 such that 𝑛(𝑈)
800,𝑛(𝐴) = 300, 𝑛(𝐵) =
2. and
𝑛(𝐴 ∩ 𝐵). Then the number of elements in the set A' ∩ 𝐵'is
A) 50
B) 100
C) 700
m
D) 400
200
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e
E)

las
Correct Answer:-Question Cancelled

3. If 𝑓(𝑥) =
𝑥
then
𝑓(𝑎) g
isaequal to
𝑥−1 𝑓(𝑎 + 1)
A) 𝑓 𝑎2
B) 𝑓 −𝑎
C) 𝑓 −𝑎2
D)
m
m .co
E) .co s e m
s em g l a
g la Correct Answer : Option A a
a
If 𝑓: 𝑅 → 𝑅 satisfies the relation 𝑓(𝑥 + 𝑦) = 𝑓(𝑥) + 𝑓(𝑦), ∀𝑥, 𝑦ϵ 𝑅 and 𝑓(1) = 3
4. then
𝑓(0) + 𝑓(1) + 𝑓(2 )+ 𝑓(3) is equal to
A) 12
B) 14
C) 16
D) 18
m .
E) 22 .co s e m
s em l a
g la ag
a
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2
5. If 𝑧 = 2 + 𝑖, 𝑖 = − 1 , then the value of 𝑧2 − 4𝑧 + 15
A) 2
B) 6
C) 15
D) 12
E) 10

Correct Answer : Option E

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

Correct Answer : Option E

If the complex number z varies so that the real and imaginary parts of 𝑧 − 2 − 3𝑖 are
7. equal, then the locus of 𝑧 is
A) a circle
B) a straight line
C) a parabola
D) an ellipse
E) a hyperbola

Correct Answer : Option B

8. If 𝑘 = 4𝑛 + 3, where 𝑛 is an integer and 𝑖
2
= − 1 then 𝑖𝑘 is equal to
A) 0
B) 1
C) -1
D) 𝑖
E) −𝑖

Correct Answer : Option E

The sum of first three terms of a G.P. is 14 and the sum of next three terms is 112. Then 100
9. 𝑡ℎ
term of the G.P. is
A) 299
B) 2101
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c. oC ) 2100 s e m
m D ) 298 − 1 a
se ag l
E) 299 + 1

The product of first four terms of a G.P. is 324 and the product of first three terms of the G.P.
10. is 216. Then the first term is
A) 3
B) 6
m
C) 9
m .co
D) 16 .co s e m
E) 12
s em l a
g la: Option E ag
a
Correct Answer

1
The product of first four terms of a G.P. is . Then the product of second and third terms
11. 1024
is,
1
A)
28
1
B)
16
m
.co
1
C)
64
1
e m
D)
32
las
E)
1
128 ag

12. If the A.M. of 𝑎 and 𝑐 is 16 and if 𝑎 = 8 , then the G.M. of 𝑎 and 𝑐 is
A) 8 √3
B) 6 √3
m
.co
C) 5 √3
o m m
. c
D) 4 √3
s e
e m
E) 2 √3
l a
s
la Correct Answer : Option A ag
ag
𝑛
13. If𝑛 𝑃5 = 42 𝑃3 then 𝑛 is equal to
A) 3
B) 5
C) 7
D) 12
E) 10
m .
. co s e m
em
Correct Answer : Option E

s l a
g la ag
a
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The number of arrangements of the letters of the word INDEPENDENCE such that the first
14. letter is I and the last letter is P, is
A) 12400
B) 12420
C) 12440
D) 12600
E) 12620

15. If four coins are tossed, then the number of possible ways of getting 2 or 3 heads, is
A) 12
B) 10
C) 8
D) 6
E) 4

Correct Answer : Option B

5𝐶
16. The value of 6
𝑟
when the numerator and denominator take their greatest value, is
𝐶𝑟
A) 2
1
B)
2
C) 1
5
D)
6
6
E)
5

Correct Answer : Option B

6
17. If 1 + 𝑥 − 2𝑥2 = 1 + 𝑎1 𝑥 + 𝑎2 𝑥2 + . . . . . + 𝑎12 𝑥12 then the sum
𝑎2 + 𝑎4 + 𝑎6 + . . . . + 𝑎12 has the value
A) 31
B) 32
C) 33
D) 63
E) 64

Correct Answer : Option A

18.
A) 4,2,3
B) 4,2,-3
C) 4,2,-7
D) 2,4,-7
E) 4,3,2
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c. o Correct Answer : Option B s e m
m a
se ag l
0 16 0 2
19. If 𝐴 = and 𝐵 = and if 𝐴 = 𝐵 then the value X is equal to
1 1 5 1
A) 2
B) 3
C) 4
D) 5
E) 6
m
m .co
m .co s e m
s e l a
g l a ag
20.
a

A) 𝑒−1
B) 𝑒
C) 𝑒2
𝑒3 m
.co
D)
E) 0
e m
Correct Answer : Option E
la s
ag
21. If the points (2,-3),(x,1) and (0,5) are collinear, then the value of 𝑥 is
A) 2
B) -2
C) -1
D) 1
E) 0
m
m
.co
.co s e m
em a
𝑥−3
s22. If x satisfies the inequality > 3 then 𝑥 lies in the interval
g l
la A ) (3,8)
𝑥−5

g a
a B) (0,5)
C) (5,6)
D) ( − ∞, 3)
E) (5,8)

m .
23.
.co s e m
s em l a
g la ag
a
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A)

B)

C)

D)

E) ( − ∞, − ∞)

Correct Answer : Option A

24.
1
A)
√10
−1
B)
√10
3
C)
√10
D)
√3
1
−3
E)
√10

5π π
25. The value of sin 𝑠𝑖𝑛 is equal to
12 12
A) 1
1
B)
4
1
C)
2
√3
D)
2
E) 0

Correct Answer : Option B

1 − 𝑠𝑖𝑛6 θ − 𝑐o𝑠6 θ
26. =
𝑐𝑜𝑠2 2θ
1
A) 𝑡𝑎𝑛2 2θ
4
1
B) 𝑡𝑎𝑛2 2θ
2
3
C) 𝑡𝑎𝑛2 2θ
2
3
D) 𝑡𝑎𝑛2 2θ
4
E) 𝑡𝑎𝑛2 2θ
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c. o Correct Answer : Option D s e m
m a
se 𝑐𝑜𝑠𝐴 α +1 ag l
27. If
𝑐𝑜𝑠𝐵
= α , then
α −1
is equal to

A)

B)

C)
m
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D)
m .co s e m
s e l a
g l a ag
E)
a

π
28. If 𝑡𝑎𝑛−1 2𝑥 + 𝑡𝑎𝑛−1 3𝑥 = , then the value of 𝑥 is equal to
4
1
A)
6
1
m
.co
B)
4
C)
1
e m
3
1
las
D)
2 ag
E) 1

Correct Answer : Option A

The domain of the function 𝑓(𝑥) = 𝑐𝑜𝑠−1 𝑥 (where[𝑥 ] denotes the greatest
29.
integer function) is
m
.co
A) [-1,2]
o m
[-1,2)
m
C ) .c
B)
(-2,2)
s e
s eDm) (-2,1)
g l a
g la E ) (-1,1) a
a
Correct Answer : Option B

30.
A) 3
B) 6
C) 4
m .
D) 1 .co s e m
E) 5
s em l a
g la ag
a
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Correct Answer : Option E

π 1
If the angle between two lines is and the slope of one of the lines is , then the slope of
31. 4 2
other line is
−1
A) 3 𝑜𝑟
3
−1
B) 2 𝑜𝑟 2
C) 1 or -1
D) -3 or 2
1
E) 3 𝑜𝑟
2

Correct Answer : Option A

32.
A) 4
B) 3
C) -4
−4
D) 3

4
E) 3

Correct Answer : Option E

If the base of an equilateral triangle is along the straight line 2𝑥 − 𝑦 = 1 and the opposite
33. vertex is (-1,2) , then the length of the side of the triangle is
20
A) 𝑢𝑛𝑖𝑡𝑠
3
5
B) 2 units
3
√20
C) units
3
2
D) units
√15
3
E) units
20

Correct Answer : Option B

34. A circle passes through (4,0) and (0,2) with centre on the y-axis. The radius of the circle is
A) 5
B) 10
C) 15
D) 20
E) 25

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c. o Correct Answer : Option A s e m
m la
se g
a of minor axis, then its eccentricity
If the length of major axis of an ellipse is twice the length
35. is equal to
A)
√2
3
√3
B)
2
1
C)
√2
m
.co
2
m
.co
D) 3
e m
2√2
em l as
E)
3
las ag
g
a : Option B
Correct Answer

𝑥2 𝑦2
36. The lengths of the transverse axis and conjugate axis of the hyperbola − =1
9 25
respectively, are
A) 3,5
B) 4,5
C) 6,10
m
D) 9,25
m .co
E) 6,5
s e
g la
a
2
37. The equation of the directrix of the parabola (𝑥 − 1) = 2(𝑦 − 2) is
A) 2𝑦 − 3 = 0
B) 2𝑦 + 3 = 0
C) 3𝑦 − 2 = 0
D) 3𝑦 + 2 = 0
E) 2𝑥 − 1 = 0
m
m .co
.co
Correct Answer : Option A
s e m
s em The vectors−^𝑖 + 1 ^𝑗 + 2𝑘^ and^𝑖 + 1 ^𝑗 + 2^𝑘 ,are the adjacentglsides
a
l a 38. a of a parallelogram.
ag
4 4
The area of the parallelogram is
√65
A)
4
B) √65
65
C)
2

√65
D)
m .
.co m
2
√65
s e
em a
E)
3
s l
g la ag
a
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→ → → → 2 → →
Let the vectors 𝑎 and 𝑏 be such that |𝑎| = 3 and |𝑏| = √ .If 𝑎 × 𝑏 is a unit vector, then the
39. → →
3
angle between a 𝑎 and 𝑏
π
A)
3
π
B)
4
π
C)
6
π
D)
2
3π
E)
4
Correct Answer:-Question Cancelled
→ ^ ^ ^ → ^ ^ ^
40. The projection of the vector 𝑎 = 3 𝑖 − 𝑗 − 2𝑘 on 𝑏 = 𝑖 + 2 𝑗 − 3𝑘 is
√14
A)
2
14
B)
√2
C) √14
D) 14√2
E) 2√14

Correct Answer : Option A

41.
A) [1,4]
B) [1,3]
C) [4,14)
D) (3,12)
E) [4,12]
Correct Answer:-Question Cancelled

42.

A)

B)

C)

D)

E)

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m .co iss
The equation of line joining the points (-3,4,11) and (1,-2,7) a
e m
se A ) 𝑥 + 3 = 𝑦 − 4 = 𝑧 − 11
43.
g l
2 3 4
a
𝑥+3 𝑦−4 𝑧 − 11
B) = =
−2 3 2
𝑥+3 𝑦+4 𝑧 + 11
C)
−2
= 3 = 4
𝑥+3 𝑦+4 𝑧 + 11
D) = =
2 −3 2
𝑥+3 𝑦−4 𝑧 − 11
= −3 = −4
E)
m
.co
−2
m
Correct Answer : Option B
.co s e m
s em𝑦 + 1 𝑧 + 10 𝑥 − 4 𝑦 + 3 𝑧 + 1 l a
gvalue of
The lines la =
𝑥−1
= and = = a
are coplanar. Then the
ag
44. 2 −3 8 1 𝑘 7
k is
A) 0
B) -2
C) 2
D) 4
E) -4

Correct Answer : Option E
m
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s e
45.
g la
A) (9,12,-15)
a
B) (9,15,12)
C) (12,9,-17)
D) (9,12,-17)
E) (-9,-12,17)

o m
othe c
m mean of 12 + 𝑥 , 17 + 𝑥 , 25 + 𝑥 , 34 + 𝑥 is 22 then themmean
. of
46. .cIf38 e
e m + 𝑥 , 42 + 𝑥, 52 + 𝑥 , 60 + 𝑥 is
l as
as A)
l B ) 22
42
a g
ag C ) 48
D) 46
E) 50

The standard deviation of 3, 8, 6, 10, 12, 9, 11, 10, 12, 7 is 2.71 . The standard deviation of
47.
m
30, 80, 60, 100, 120, 90, 110, 100, 120, 70 is
.
A) 2.17
.co s e m
B) 0.271
s em l a
g la ag
a
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C) 27.1
D) 271
E) 2.71√10

1 13
If A and B are mutually exclusive events and 𝑃(𝐵) , 𝑃(𝐴 ∪ 𝐵) = ,then 𝑃(𝐴) is equal
48. 5 35
to
1
A)
35
3
B)
35
1
C)
7
6
D)
35
1
E)
5

′
49. If A and B are two independent events and 𝑃(𝐴 ) = 0.8, 𝑃(𝐵) = 0.6, then 𝑃(𝐴 ∪ 𝐵) is
equal to
A) 0.86
B) 0.8
C) 0.68
D) 0.52
E) 0.48

(𝑥 + 𝑥2 + 𝑥3 + 𝑥4 + 𝑥5 ) − 5
50. 𝑙𝑖𝑚 𝑥−1
=
𝑥→1
A) 5
B) 12
C) 14
D) 0
E) 15

Correct Answer : Option E

𝑠𝑖𝑛2𝑥 + 3𝑥
51. 𝑥𝑙𝑖𝑚 =
→ 0 4𝑥 + 𝑠𝑖𝑛6𝑥
A) 1
1
B)
4
1
C)
2
D) 2
E) 3

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c. o Correct Answer : Option C s e m
m a
se g l
52. The domain of 𝑓(𝑥) = |𝑥 | − 1 + 4 − | 𝑥| is a
A) [ − 4, − 1] ∪ (1, 4)
B) ( − 4, − 1) ∪ (1, 4)
C) [ − 4, − 1]
D) [ − 4, − 1) ∪ (1, 4)
E) [ − 4, − 1] ∪ [1, 4]
m
c o m
Correct Answer : Option E

m .co
53. The range of 𝑓(𝑥) m .= 𝑠𝑖𝑛𝑥 + 𝑐𝑜𝑠𝑥 + 3 s e
s e l a
A) −1 + √
g a
l 3 , 1 + √3 ag
a
B) −√2 + 3, √2 + 3

C) −√3 + 3, 3 + √3

D) −√2 − 3, 2 + √3

m
.co
E) −2 + √3 , 2 + √3

s em
la
Correct Answer : Option B

g
a (𝑥) − (1) = is equal to
54. If 𝐹(𝑥) = − √9 − 𝑥2 , then 𝑙𝑖𝑚 𝑥→1 𝑥−1
1
A)
2
1
B)
√2
−1
C)
2√2
m
.co
1
m
D)

.co1
2√2
E)
e m
emCorrect Answer : Option D l as
las ag
g
a 55. If 𝑙𝑜𝑔 𝑦 = 𝑥, then 𝑑𝑦 is equal to
2 𝑑𝑥
𝑥
A) 2 𝑙𝑜𝑔𝑒 2
B) 2𝑥
C) 𝑥2
D) 2𝑥
2𝑥
m .
.co
E)
𝑙𝑜𝑔𝑒 𝑦
e m
em l as
la
Correct Answer : Option A s ag
ag
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5/9/25, 4:18 PM FINAL ANSWER KEY

1
56. The derivative of 𝑦 = (𝑥 − 1)(2𝑥 − 1)(3 − 𝑥)(4 − 𝑥) at 𝑥 =
2
is equal to
A) 35
−35
B)
4
−35
C)
2
35
D)
4
35
E)
2

Correct Answer : Option B

57.
−(√3 + 1)
A)
2
(√3 + 1)
B)
2
√3
C)
2
2
D)
√3
2
E)
√3 + 1

Correct Answer : Option A

𝑥
58. Let 𝑓: (0, ∞) → 𝑅 and 𝐹(𝑥) = ∫0 𝑓(𝑡)𝑑𝑡 . If 𝐹(𝑥) = 𝑥2 (1 + 𝑥),then 𝑓(2) is
equal to
A) -4
B) 4
C) -16
D) 16
E) 12

59.
A) 3
B) 1
C) 4
3
D)
2
E) 2

Correct Answer : Option A

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m
om A critical point of the function 𝑓(𝑥) = 𝑥 + 3𝑥2 − 7𝑥,is em .co

c. 60. s
3

e m 3
l a
s A) ag
B) (0,0)

C)

D)

E)
m
m .co
Correct Answer : Option A
m .co s e m
s e l a
l
61. The function a𝑓(𝑥) = 2𝑥3 + 9𝑥2 + 12𝑥 − 1 is decreasing in the interval is ag
A) (-1,1) ag
B) (-3,1)
C) (-2,-1)
D) [-2,1]
E) (-1,3)

m
62. m .co
The radius of a right circular cylinder is increasing at the rate of 2 cm/s and its height is
decreasing at the rate of 3 cm/s. The rate of change of volume when radius is 4 cm and
height 6 cm, is (in cm3 /s) s e
A) 24π g la
B) 28π a
C) 42π
D) 44π
E) 48π

Correct Answer : Option E

m
.co
The sum of two positive numbers is 12. If the sum of whose square is minimum, then the
63.
m
numbers are
A) .co3,9
s e m
s eBCm)) 4,8
g l a
g la D ) 5,7 a
a 6,6
E) 2,10

𝑑𝑥
64. ∫ 𝑥 + 𝑥 − 2 is equal to
√ √
1 3/2
𝑥3 / 2 − (𝑥 − 1) +𝐶
A)
2
o m m .
3 ./c2 e
B)
1
𝑥3 / 2 − (𝑥 − 2)m
e +𝐶
l as
3
l as ag
ag
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1
C)
3
𝑥2 / 3 − (1 − 𝑥)2 / 3 +𝐶
1
D)
2
𝑥2 / 3 − (1 − 𝑥)2 / 3 +𝐶
1
E)
3
𝑥2 / 3 − (𝑥 − 2)2 / 3 +𝐶

Correct Answer : Option B

𝑑𝑥
65. ∫ 𝑐𝑜𝑠𝑥 2𝑠𝑖𝑛2𝑥 =
√
1
A) 𝑡𝑎𝑛𝑥 + 𝐶
2√
B) √𝑡𝑎𝑛𝑥 + 𝐶
C) 2√𝑡𝑎𝑛𝑥 + 𝐶
D) 4√𝑡𝑎𝑛𝑥 + 𝐶
E) 3√𝑡𝑎𝑛𝑥 + 𝐶

Correct Answer : Option B

′ 2
66. If 𝑓 (𝑥) = 3𝑥 2 − and 𝑓(1) = 0, then 𝑓(𝑥) =
𝑥3
1
A) 𝑥2 + 3 + 1
𝑥
1
B) 𝑥 3 + 𝑥2 + 1
3 1
C) 𝑥 + 2+2
𝑥
13
D) 𝑥 + 𝑥2 − 2
3 1
E) 𝑥 + 2−1
𝑥

1 1
67. ∫ − 𝑑𝑥=
𝑙𝑜𝑔𝑥 (𝑙𝑜𝑔𝑥)2

A) 𝑙𝑜𝑔𝑥 + 𝐶
B) x 𝑙𝑜𝑔𝑥 + 𝐶
𝑙𝑜𝑔𝑥
C) +𝐶
𝑥
𝑥
D) +𝐶
𝑙𝑜𝑔𝑥
E) 𝑥 + 𝑙𝑜𝑔𝑥 + 𝐶

68. ∫ 𝑥2 + 2𝑥 + 3 d𝑥 =
A)

B)

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m
m .co

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

69.
m
m .co
.co
5
A)
e m
B) 1
e m l as
C) 2
l as ag
D)
E)
3
0 ag
Correct Answer : Option B

70.
A) 2a
m
.co
B) 3a
C) 4a
e m
D) 6a
las
E) a
ag

71. The area bounded by the curve 𝑦 = 3𝑥 − 𝑥 2 and the 𝑥 - axis is
21
A) sq.units
2
B) 18 sq.units
27
m
.co
C) sq.units
2
m
D)
c. o99 sq.units s e m
s em 2 sq.units
E)
g l a
g la Correct Answer : Option E a
a
72. Area of the region bounded by 𝑦 = | 𝑥| and 𝑥 = 4 is
A) 4 sq.units
B) 6 sq.units
C) 8 sq.units
D) 12 sq.units
E) 13 sq.units m .
.co s e m
s em l a
g la ag
a
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73.

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

Correct Answer : Option B

𝑑𝑦
74. The order and degree of differential equation 𝑥
𝑑𝑥
+ 𝑦 = 𝑒𝑥 is
𝑒𝑥
A) 𝑦 = + 𝐶𝑥
𝑥
B) 𝑦 = 𝑥𝑒𝑥 + 𝐶𝑥
𝑒𝑥
C) 𝑦= +𝐶
𝑥
𝑒𝑥 𝐶
D) 𝑦= +
𝑥 𝑥
1
E) 𝑦 = 𝑥 + 𝐶𝑥𝑒𝑥
Correct Answer:-Question Cancelled
Let 𝑧 = 𝑎𝑥 + 𝑏𝑦 , where 𝑎, 𝑏 > 0 .The corner points of the feasible region determined by
75. the system of linear constraints are(0,10), ( 5, 5) , (15,15) , (0, 20) . Condition on 𝑎 and 𝑏 so
that the minimum of 𝑧 occurs at both the points (15,15) and (0, 20) , is
A) 𝑎=𝑏
B) 2𝑎 = 𝑏
C) 𝑎 = 2𝑏
D) 3𝑎 = 𝑏
E) 𝑎 = 3𝑏

A distance of 50 cm is measured using a metre stick with the smallest division 1 mm. The
76. percentage error involved in the measurement is
A) 2%
B) 0.5%
C) 0.2%
D) 0.1%
E) 5%

77. The value of (200 𝑚 + 200 𝑚𝑚) with regard to significant figures is
A) 200.2 𝑚
B) 200 𝑚
C) 202 𝑚
D) 200.200 𝑚
E) 202.2 𝑚
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m
m .co

c. o Correct Answer : Option B s e m
m la
se → a g
78. The angle subtended by the vector 𝐴 = ^𝑖 + ^𝑗 + 𝑘^ with the 𝑦-axis is
A)

B)

m
.co
C)

m
D)
m .co s e m
s e l a
ag
π
E)
2
g la
a

When a body with its initial velocity non-zero, moves with constant retardation, the velocity-
79. time graph is
A) an oblique straight line with positive slope
B) a straight line parallel to time axis
C) a straight line parallel to velocity axis
m
.co
D) an oblique straight line with negative slope
E) a curve with bend upwards
e m
las
ag
If two bodies are projected with angles of projection θ and (90 - θ ) with the same speed,
80. then the ratio between their times of flight 𝑇1 and 𝑇2 is
A) cot θ
B) cos θ
C) sec θ
D) sin θ
tan θ m
.co
E)
m
.co
Correct Answer : Option E
s e m
s em A machine gun having mass 5 kg fires 40 gram bullet at the rateglofa 25 bullets per minute at a
g la 81. speed of 300 ms−1 . The force required to keep the gun in position
a is
a A) 7N
B) 4N
C) 2.5 N
D) 10 N
E) 5N

Correct Answer : Option E
m .
.co s e m
s em l a
g la ag
a
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→ ^ ^ ^
82. A force 𝐹 = 𝑖 + 2 𝑗 −2 𝑘 applied on a body, accelerates the body with 2 ms−2 . Then the
mass of the body is
A) 0.5 kg
B) 10 kg
C) 5 kg
D) 1.5 kg
E) 7 kg

A body moving with kinetic energy E is stopped by applying a stopping force F. The stopping
83. distance is
A) 𝐹𝐸
𝐹
B)
𝐸
𝐸
C)
𝐹
D) 𝐹2 𝐸
E) 𝐹𝐸2

The work done by the applied force in changing the elongation of a spring of spring constant
84. K, from 𝑥 1 to 𝑥 2 is
1
A) 𝐾(𝑥22 − 𝑥21 )
2
1
B) 𝐾𝑥1 𝑥2
2
1
C) 𝐾(𝑥21 − 𝑥22 )
4
1
D) 𝐾𝑥1 𝑥2
4
1
E) 𝐾(𝑥21 𝑥22 )
2

Correct Answer : Option A

In the uniform circular motion of a particle, the point about which the angular momentum of
85. the particle is conserved is
A) on the circumference of the circle
B) inside the circle
C) outside the circle
D) the centre of the circle
E) anywhere on the rotation axis

−3
86. A wheel of moment of inertia 4 × 10 𝑘𝑔𝑚2 rotates with an angular speed of 25 rev. s−1 .
The torque (in Nm) required to stop it in 10s is
A) 4π × 10−4
B) 2π × 10−2
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m
m .co

c. oC ) 6π × 10−3 s e m
m D ) π × 10−1 a
se ag l
E) 3π × 10−5

Correct Answer : Option B

→ → →
A force 𝐹 acting on a particle, having position vector 𝑟 exerts a torque τ about the origin
87. → →
on the particle. Then the angle between 𝑟 and τ is
60°
A)
m
B) 45°
m .co
C) 0°
.co s e m
D) 90°
s em l a
E) 180°
g la ag
a : Option D
Correct Answer

The gravitational potential energy between two bodies each of mass 1 kg kept at a distance
88. of 1 m is (G - Gravitational constant)
A) 𝐺
B) −𝐺
−𝐺
C)
2
m
.co
𝐺
D)
2
e m
E)
−𝐺
las
4
ag
Correct Answer : Option B

If the acceleration due to gravity on the surface of a planet of mass m and radius r is g, then
89. the escape velocity of a body from the surface of the planet is
A) 2𝑔𝑟
2𝑔
B)
𝑟
m
C)
c √m
o 𝑔𝑟
m.co
D ) . 𝑔𝑟 2 e
eEm) 2𝑔𝑟2 l as
las ag
ag Correct Answer : Option A

The wall between two thermal systems that allows the flow of heat from one to another to
90. bring thermal equilibrium is called
A) adiabatic wall
B) insulated wall
C) diathermic wall
semiconducting wall m .
.co
D)
non-conducting wall e m
E)

em l as
las ag
ag
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If 𝑑𝑉 is the change in volume of a liquid of density ρ under the pressure P, then the
91. pressure energy per unit mass of the liquid is
A) 𝑃𝑑𝑉
𝑃𝑑𝑉
B)
ρ
𝑃𝑑𝑉
C)
ρ2
𝑃
D)
ρ
E) 𝑃ρ

If 𝐹1 is the force exerted by air on a small piston of area of cross-section 𝐴 1 in a car lift ,
92. then the force 𝐹2 realised on the second piston of area of cross-section 𝐴 2 due to the
transfer of pressure is
𝐴
A) 𝐹1 1
𝐴2
𝐴
B) 𝐹1 2
𝐴1
C) 𝐹1 (𝐴1 𝐴2 )
𝐴1
D) 𝐹1
𝐴2

𝐴1
E)
𝐴2

Correct Answer : Option B

93. Find the mismatch pair in the thermodynamic process
A) Isothermal : Absorption or emission of heat
B) Isobaric : Pressure constant
C) Isochoric : Volume constant
D) Irreversible : Loss of heat
E) Adiabatic : Heat exchange

Correct Answer : Option E

In a Carnot engine if the ratio of the heat rejected to the sink to the heat absorbed from the
94. source is 1 : 4, then the efficiency of the engine is
A) 75 %
B) 60 %
C) 50 %
D) 25 %
E) 45 %

Correct Answer : Option A

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m
om The mean free path of a gas is directly proportional to its em .co

c. 95. s
e m A ) pressure l a
s B) density ag
C) molecular diameter
D) absolute temperature
E) square of molecular diameter

The condition for real gases to obey the ideal gas equation PV = RT is that the gases should
96. m
.co
be at
m
.co m
A) high pressure
low temperature
m s e
B)
s e l a
a ag
C) low pressure and low temperature
g l
high pressure and low temperature
a
D)
E) low pressure and high temperature

Correct Answer : Option E

A particle is executing simple harmonic motion with A and B as its extreme positions and O
97. as its mean position. If 𝑎 and 𝑣 represent the acceleration and velocity, then
A) at A , 𝑎 = 0
at B, 𝑎 = 0 m
.co
B)
C) at O, 𝑎 is maximum
at O, 𝑎 and 𝑣 are maximum e m
D)
E) at O, 𝑎 = 0
las
ag
Correct Answer : Option E

The equation for the displacement 𝑥 (in 𝑚) of a particle executing simple harmonic motion
98. in SI unit is 𝑥(𝑡) = 5𝑐𝑜𝑠4 πt Its displacement after 3 s is
A) 2m
B) 5m
C) 3m
m
.co
D) 4m
m
.co m
E) 10 m
s e
s emCorrect Answer : Option B g l a
g la a
a 99. Two sound sources produce 24 beats in 3 s . The difference between the two frequencies of
the sources is
A) 2
B) 4
C) 8
D) 12
E) 3
m .
.co s e m
s em l a
g la ag
a
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Electric potential due to an electric dipole on its axis at a distance r from its centre is
100. inversely proportional to
A) 𝑟
B) 𝑟3
C) 𝑟2
D) 𝑟 −2
E) 𝑟 −1

If the potential difference between two conductors separated by a distance of 2 cm is
101. 4 × 103 V then the electric field between them (in 𝑉𝑚−1 ) is
A) 8 × 103 𝑉𝑚−1
B) 4 × 105 𝑉𝑚−1
C) 8 × 105 𝑉𝑚−1
D) 2 × 103 𝑉𝑚−1
E) 2 × 105 𝑉𝑚−1

Correct Answer : Option E

102. The electrostatic energy density of the electric field E in a capacitor is directly proportional to
A) 𝐸2
B) 𝐸
C) √𝐸
D) 𝐸3
E) 𝐸−2

Correct Answer : Option A

103. In an electrolyte, the mobile charge carriers are
A) electrons only
B) negative ions only
C) positive ions only
D) negative and positive ions
E) electrons and positive ions

If both the length and area of cross-section of a linear conductor are halved, its resistance
104. would
A) be doubled
B) remain unchanged
C) be halved
D) be tripled
E) be quadrupled

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m
m .co

c. o Correct Answer : Option B s e m
m la
se g
The power dissipated in the transmission cables of 0.03aΩ resistance, when 11 kW of power
105. is transmitted at 220 V is
A) 0.025 kW
B) 0.050 kW
C) 0.075 kW
D) 1.075 kW
E) 1.025 kW
m
m .co
.co
e m
s
m the vertical component of earth’s magnetic field are, respectively,l0.26
a
106. G and (0.26) se3 𝐺, then the dip angle is
If the horizontal and

l a√ ag
A) 0⁰
a g
B) 30⁰
C) 45⁰
D) 60⁰
E) 90⁰

m
.
107. a uniform magnetic field B is (𝑙- length; A - area cofo cross-section)
The maximum torque experienced by a rectangular coil carrying a steady current I placed in

A) 𝐼𝐵𝐴 s em
B) 𝐼𝑙𝐵
g la
C) 𝐼𝐵𝐴2 a
D) 𝐼𝑙𝐵2
2
E) 𝐼𝑙 𝐵

Correct Answer : Option A

108. In a television, the required magnetic field is produced by a/an
m
A)
m
toroid
.co
B)
.coelectromagnet
s e m
s eCDm)) permanent magnet
g l a
g la E ) circular coil a
a solenoid
Correct Answer:-Question Cancelled
2
If the flux linked with the coil of area of cross-section 0.5 m placed in a magnetic field of
109. 16 𝑇 is 4 Wb, then the angle between the magnetic field and the area vector of the coil is
A) 0⁰
B) 30⁰
C) 45⁰
D) 60⁰
m .
E) 90⁰ .co s e m
s em l a
g la ag
a
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110. The self-inductance of a coil does not depend on
A) its radius
B) its number of turns
C) its area of cross-section
D) the current through it
E) permeability of the medium

111. Which one of the following proves the transverse nature of electromagnetic waves?
A) Interference of light
B) Dispersion of light
C) Polarization of light
D) Photoelectric effect
E) Diffraction of light

If the angle of a prism 𝐴 is equal to the angle of minimum deviation, then the refractive
112. index of the material of the prism is
𝐴
A) 2𝑐𝑜𝑠 2
𝐴
B) 𝑐𝑜𝑠
2
C) 2𝑐𝑜𝑠𝐴
D) 𝑐𝑜𝑠𝐴
𝐴
E) 𝑠𝑖𝑛 2

Correct Answer : Option A

113. According to Huygens Principle, a wavefront is
A) a single ray of light
B) a surface of constant phase
C) a surface of varying phase
D) a random arrangement of waves
E) a region where crests and troughs overlap

Correct Answer : Option B

In Young’s experiment, the wavelength of light is 600 𝑛𝑚, the slit separation is 0.5 𝑚𝑚,
114. and the screen is 2 𝑚 away. The fringe width of the interference pattern with the same set
up becomes 3 times if the wavelength of light used is
A) tripled
B) doubled
C) halved
D) made one-third

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m
m .co

c. oE ) made one-sixth s e m
m a
se Correct Answer : Option A
ag l
If the frequency of the incident radiation 𝑓 increases above the threshold frequency 𝑓0 of a
115. photo-sensitive material, then the stopping potential
A) increases linearly with 𝑓
B) decreases linearly with 𝑓
C) is independent of 𝑓
D) increases with intensity of light
m
.co
E) decreases with intensity of light
m
Correct Answer : Option A .co s e m
s em g l a
l a
116. The emission a
of electrons from a metal by applying a very strong electric field is called
A) ag emission
photoelectric
B) field emission
C) thermionic emission
D) beta emission
E) gamma emission

Correct Answer : Option B

m
117. The size of a nucleus is of the order of . co
A) 10−15 𝑚 s em
B) 10−10 𝑚 g la
C) 10−5 𝑚
a
D) 10−6 𝑚
E) 1010 𝑚
Correct Answer:-Question Cancelled
118. The radiations of extremely short wavelength are
A) alpha rays
m
.co
B) beta rays
o m m
D).
c
C) gamma rays
s e
eEm)
X rays
s ultra-violet rays
g l a
g la a
a Correct Answer : Option C

119. The naturally occurring crystal which was used as a detector of radio waves is
A) Ruby
B) Galena
C) silicon
D) germanium
m .
.co
zinc selenide
E)
e m
em l as
Correct Answer : Option B
las ag
ag
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If n and n represent the concentrations of holes and electrons, respectively, then in a p-
120. typeℎ semiconductor,
𝑒

A) 𝑛𝑒 = 𝑛ℎ
B) 𝑛𝑒 ≫ 𝑛ℎ
C) 𝑛ℎ ≫ 𝑛𝑒
D) 𝑛𝑒 = 2𝑛ℎ
E) 𝑛ℎ + 𝑛𝑒 = 𝑛ℎ 𝑛𝑒

149 g of 𝐾𝐶𝑙 is dissolved in 10 litres of an aqueous solution. The molarity of the solution is
121. (molar mass of 𝐾𝐶𝑙 = 74.5)
A) 1M
B) 0.1M
C) 2M
D) 0.2M
E) 0.002 M

122. Which of the following statement is NOT true?
The energies of the orbitals in the same subshell increases with increase in the atomic
A)
number
B) The probability density function is zero on the plane where the two lobes touch each other.
C) The lower the value of (𝑛 + 𝑙) for an orbital, the lower is its energy.
D) The total number of nodes is given by (𝑛 − 1).
The maximum number of electrons in the shell with principal quantum number ‘𝑛′ is equal
E)
to '𝑛2 '

Correct Answer : Option E

123. Which of the following quantum numbers determines the orientation of the orbital?
A) 𝑛
B) 𝑙
C) 𝑚𝑙
D) 𝑚𝑠
both 𝑛
E) and
𝑙

124. Which of the following statement is INCORRECT regarding f-block elements?
A) The elements of the periodic table in which the last electron gets filled up in the f-orbital.
B) The f-block elements are from atomic number 58 to 71 and from 90 to 103.
C) Actinoid elements are radioactive.
D) There are 28 f-block elements in the periodic table.

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o m
m c
c. oE ) The outer electronic configuration of Actinoids is (𝑛 − 1)𝑓1 s−e14m(𝑛. − 1)𝑑0 − 1𝑛𝑠2 .

m la
se Correct Answer : Option E
a g
125. The H-C-H bond angle in ethene is
A) 117.6°
B) 121°
C) 110°
D) 105°
E) 119°
m
m .co
Correct Answer : Option A
m .co s e m
s e l a
ΔT = 0 g
l a
126. For the process to occur under adiabatic conditions, the correct condition is
ag
A)
B) ΔP = 0
a
C) q=0
D) w=0
E) ΔU = 0

m
.co
For the following gas phase decomposition, the magnitude of ΔH and ΔS is
127.
e m
las
A) ΔH< 0 and ΔS < 0
ag
B) ΔH > 0 and ΔS > 0
C) ΔH > 0 and ΔS < 0
D) ΔH < 0 and ΔS > 0
E) ΔH = 0 and ΔS = 0

Correct Answer : Option B

m
.co
What is the value of Kc for the following equilibrium, if the value of Kp for the reaction at
m
.co
128. 1000 K is 8.21 × 10−2 ? (R = 0.0821)
e m
2𝑁𝑂𝐶𝑙(𝑔) ⇌ 2𝑁𝑂(𝑔) + 𝐶𝑙2 (𝑔) at 1000 K.
eAm) 10−3 l as
s
la B ) 10−8 ag
ag
C) 10−9
D) 10−10
E) 10−5

Correct Answer : Option A

m is true for the effect of catalyst in equilibrium?
129. Which of the following statement .
A)
.co
Lowers activation energy for forward reaction only.
s e m
B)
em
Lowers activation energy for reverse reaction only.
s l a
g la ag
a
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C) When K is small catalyst has greater effect.
D) It effects to equilibrium composition of reaction mixture.
E) Lowers activation energy for forward and reverse reaction by same amount.

Correct Answer : Option E

130. Which of the following is INCORRECT for the concept of reduction?
A) Removal of oxygen
B) Addition of hydrogen
C) Addition of electron
D) Decrease in oxidation number
E) Removal of an electron

Correct Answer : Option E

The conductivity (𝑘) of a decinormal solution of KCl is 0.012 ohm−1 cm−1 . The
131. resistance of a cell containing this solution was found to be 50 ohm at 298 K. The cell
constant value is
A) 0.02 cm−1
B) 0.5 cm−1
C) 0.8 cm−1
D) 0.1 cm−1
E) 0.6 cm−1

Correct Answer : Option E

When 1 g of a non-electrolyte solute dissolved in 50 g of benzene lowered the freezing point
132. of benzene by 0.20 K. The freezing point depression constant of benzene is 5 K kg mol−1 .
The molar mass (g /mol) of the solute is
A) 500
B) 400
C) 300
D) 200
E) 100

Correct Answer : Option A

133. The pre-exponential factor in the Arrhenius equation is called as
A) probability factor
B) activation energy
C) collision frequency
D) reaction coordinate
E) frequency factor

Correct Answer : Option E

In a first order reaction, A→ Products, the half-life period is found to be 10 minutes. The rate
134. of the reaction in mol lit−1 min−1 at [A] = 0.1 mol lit−1 is

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m
m .co

c. oA ) 0.693 × 10−3−3 mol lit−1−1 min−1−1 s e m
m B ) 6.93 × 10 a
se C) 69.3 × 10 −3
mol lit
mol lit −1
min
min−1 ag l
D) 693.3 × 10−3 mol lit−1 min−1
E) 6932 × 10−3 mol lit−1 min−1

Correct Answer : Option B

The correct statement/s about Cr2 + and Mn3 + is/are
[Atomic numbers of Cr = 24 and Mn = 25] m
(i) Cr2 + is a reducing agent m .co
7+
135. (ii) Mn is2an .co
oxidising agent in acidic medium
m s e m
(iii) Both Cr +
s e
and Mn3 + exhibit d4 electronic configuration
l a
l a
(iv) The highest oxide of Mn is Mn3 O4 .
g ag
a
(v) Cr2 + and Mn3 + have the same magnetic moment as both have four unpaired
electrons.
A) Only (i)
B) (i), (ii) and (iii)
C) (i), (iv) and (v)
D) (i) and (v) only
E) (i), (ii), (iii) and (v)

m
.co
Correct Answer : Option E

m
se
136. Which of the following metal ion is diamagnetic?
la
A) Zn2 +
ag
B) Ni2 +
C) Co2 +
D) Cu2 +
E) Mn2 +

Correct Answer : Option A
m
m
Match the Column-I with Column-II. .co
.co s e m
s em
137.
g l a
g la a
a
A) (a)-(iii), (b)-(iv), (c)-(v), (d)-(ii), (e)-(i)
B) (a)-(ii), (b)-(iv), (c)-(v), (d)-(iii), (e)-(i)
C) (a)-(iii), (b)-(ii), (c)-(v), (d)-(iv), (e)-(i)
D) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii), (e)-(v)
E) (a)-(iii), (b)-(v), (c)-(iv), (d)-(ii), (e)-(i)

Correct Answer : Option A
m .
.co s e m
emstate of the elements of lanthanoid series is
138. The common oxidation
s l a
l a ag
ag
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A) +1
B) +2
C) +3
D) +4
E) +5

The complex ions [NiCl4 ]2 − and [Ni(CN)4 ]2 − differ by
139. (i) Magnetic moment (ii) Geometry
(iii) Hybridisation of central metal ion (iv) Oxidation state of nickel
A) (i), (ii) and (iv)
B) (i), (ii) and (iii)
C) (ii), (iii) and (iv)
D) (ii) and (iii)
E) (i), (ii), (iii) and (iv)

Correct Answer : Option B

Four complex ions are given in Column I and the colours of light absorbed are given in
Column II. Match the correct answer from the codes given below.

140.

A) (a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)
B) (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)
C) (a)-(iii), (b)-(ii), (c)-(iv), (d)-(i)
D) (a)-(i), (b)-(iv), (c)-(ii), (d)-(iii)
E) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)

Correct Answer : Option A

The number of α -hydrogens in tertiary butyl chloride, isopropyl chloride, ethyl chloride and
141. methyl chloride are respectively
A) 0, 1, 2 and 3
B) 0, 3, 6 and 9
C) 1, 3, 6 and 9
D) 9, 6, 3 and 0
E) 3, 6, 9 and 12

Correct Answer : Option A

142. The correct order of the rate of β-elimination reaction among the alkyl halides is
A) Secondary > Tertiary > Primary
B) Tertiary > Primary > Secondary
C) Tertiary > Secondary > Primary
D) Primary > Tertiary > Secondary
E) Primary > Secondary > Tertiary
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m
m .co

c. o Correct Answer : Option C s e m
m a
se a g l
Alkyl iodides are normally prepared by the following reaction:
143. CH3 CH2 Cl + NaI → CH3 CH2 I+ NaCl
This reaction is known as
A) Wurtz reaction
B) Wurtz-Fittig reaction
C) Williamson synthesis
D) Finkelstein reaction
Etard reaction m
.co
E)

m
m .co s e m
s e l a
144. Which of theafollowing is most reactive towards nucleophilic aromatic substitution?ag
g l
a
A)

B)

m
m .co
s e
C)
g la
a
D)

E)

m
c o m m.co
m . Answer : Option E
Correct
s e
e
s What is the major product of the following reaction? g l a
l a a
ag 145.

A)

m .
B)
.co s e m
s em l a
g la ag
a
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C)

D)

E)

146. Benzophenone and Acetophenone are distinguished by treating with
A) Fehling’s reagent
B) Lucas reagent
C) Iodine and alkali
D) Aqueous CrO3
E) Tollens’ reagent

The product of the following reaction is
147.
A) C6 H5 CH = CHCOC6 H5
B) C6 H5 COCH2C6 H5
C) C6 H5 CH = CHC6 H5
D) C6 H5 CH(OH)COC6 H5
E) C6 H5 COCOC6 H5

Correct Answer : Option A

148. Which of the following is the strongest acid?
A) FCH2 COOH
B) CF3 COOH
C) NC-CH2 COOH
D) Br-CH2 COOH
E) CH3 COOH

Correct Answer : Option B

Choose the correct combinations for the column I with column II.

149.

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m
m .co

c. oA ) (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii) s e m
m B ) (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv) a
se C) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
ag l
D) (a)-(i), (b)-(iii), (c)-(ii), (d)-(iv)
E) (a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)

150. Peptide on hydrolysis gives
glucose
A)
m
B) fatty acids
m .co
C) amino acids
m .co s e m
D)
s e
ribose sugar, H3 PO4 and base
l a
E)
la
heterocyclic base and sugar
g ag
a : Option C
Correct Answer

m
m .co
s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
g la ag
a
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