KEAM 2025 Question Paper Engineering with Answers (27 April 2025)

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KEAM 2025
Question Paper ·
Engineering
EXAM YEAR TYPE SUBJECT INCLUDES

KEAM 2025 Question Paper Engineering Answers
DATE

27 April 2025

Notes · Sample Papers · Previous Year Papers · Mock Tests

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m .co FINAL ANSWER KEY as
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Question Paper Code: 13/2025/OL
Exam:KEAM 2025 ENGG-4
Date of Test: 27-04-2025

The relation
𝑅 = {(4, 4)(4, 5), (5, 7), (4, 8), (5, 5), (7, 8), (7, 7), (7, 5), (8, 8), (8, 7), (8, 5), (9, 9)}on the set
1. A={4, 5, 7, 8, 9 } is
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transitive
A)
e m
B) symmetric
e m l as
C) reflexive
l as ag
D)
E) ag
equivalence relation
a function

Let 𝐴 ={ 1, 2, 3, 4} 𝑎𝑛𝑑 B ={ 7, 8, 3, 4} Then the number of elements common to
2. both 𝐴 × 𝐵 and
𝐵 × 𝐴 is
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A) 8
B) 6
e m
C) 12
4 las
D)
E) 2 ag
Correct Answer : Option D

3. The range of the function 𝑓(𝑥) = 𝑙𝑜𝑔 4𝑥 − 4𝑥 + 1 , where 𝑥 ≠ is
A) ( − ∞, 0)
[0, ∞)
B)
m
C) (0, ∞)
m .co
D)
.co ( − ∞, 0)
s e m
s emE ) ( − ∞, ∞)
g l a
g la Correct Answer : Option E a
a
4. The domain of the function 𝑓(𝑥) = √𝑥 + 2𝑥 − 15 is
A) ( − ∞, − 5) ∪ (3, ∞)
B) ( − ∞, − 5) ∪ [3, ∞)
C) ( − ∞, − 5] ∪ (3, ∞)
D) ( − ∞, − 5] ∪ [3, ∞)
m .
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[ − 5, 3]
E)
e m
em l as
las ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 1 of 36

Correct Answer : Option D

5. All the points in 𝐴 = ; λ ϵ ℝ lie on
A) a circle with radius √2
B) a circle with radius 2
C) a circle with radius

D) a circle with radius 1
E) a straight line with slope 1

Correct Answer : Option D

6. ,is equal to
=
A) 𝑖+1
B) 𝑖−1
C) −𝑖 − 1
D) −𝑖 + 1
E) −𝑖

Correct Answer : Option B

7. If 𝑥, 𝑦 ϵ ℝ and 𝑥 + 𝑖𝑦 = − (6 + 𝑖) , 𝑖 = − 1, then 𝑥 − 𝑦 is equal to
A) 93
B) -93
C) 91
D) -91
E) -107

Correct Answer : Option D

8. Let 𝑧 = 𝑥 + 𝑖𝑦, where 𝑥, 𝑦 ϵ ℝ and 𝑖 = − 1. If|𝑧 − 𝑖 | = | 𝑧 − 1|, then 𝑦 =
A) −𝑥
B) 𝑥+1
C) −𝑥 − 1
D) 𝑥+2
E) 𝑥

Correct Answer : Option E

9. If a, b, c are real numbers such that (𝑎 − 2) + (𝑏 − 2) + (𝑐 − 2) = 0
A) 𝑎, 𝑏, 𝑐 are in G.P. and 𝑎 + 𝑏 + 𝑐 = 6

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c. o B ) 𝑎, 𝑏, 𝑐 are in G.P. and 𝑎 + 𝑏 + 𝑐 = 4 s e m
m a
se C) 𝑎, 𝑏, 𝑐 are not in G.P.
ag l
D) 𝑎, 𝑏, 𝑐 are in G.P. and 𝑎 + 𝑏 + 𝑐 = 8
E) 𝑎, 𝑏, 𝑐 are not in G.P. and 𝑎 + 𝑏 + 𝑐 = 16

Correct Answer : Option A

Let 𝑎, , 𝑎𝑟 , 𝑎𝑟 , . . . be in G.P. where r > 0 If the product of first four terms of the
10.
m
G.P. is then 𝑎 is equal to
m .co
m .co s e m
A)

s e l a
B)
g l a ag
a
C)

D)

E) 1

Correct Answer : Option D
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Let 𝑎 , 𝑎 , . . . . , 𝑎 be positive non-zero real numbers. If 𝑎 , 𝑎 , . . . . , 𝑎 = 𝑘 then
the minimum value of 𝑎 + 𝑎 + . . . . + 𝑎 is
s e
𝑛(𝑘) / g la
A)
a
B) 𝑛(𝑘) /
C) (𝑘) /
D) (𝑘) /
E) 2𝑛(𝑘) /
Correct Answer:-Question Cancelled
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Let λ be the A.M. between and and also G.M. between and . Then α +
βm =
12.
c o
. 3α β e m
e m
A)
l as
l as B) αβ ag
ag C ) α β
D) 4α β
E) 2α β

Correct Answer : Option E

13. The number of integers greater than 7000 using 2,4,6,7,8 without repetition, is
m .
A) 168
.co s e m
B) 336
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 3 of 36

C) 196
D) 256
E) 512

Correct Answer : Option A

14.
A) − 𝐶 (4) (3)
B) 𝐶 (4) (3)
C) 𝐶 (4) (3)
D) 𝐶 (4) (3)
E) 0

Correct Answer : Option E

Five digit number is formed using the digits 0,1,2,3,4 and 5 without repetitions. Number of
15. five digit numbers which are divisible by 10 is
A) 360
B) 240
C) 120
D) 480
E) 520

16.
A) -160
B) 160
C) -180
D) 180
E) 0

Correct Answer : Option A

17.

A) 18
B) 16
C) 17
D) 21
E) 19

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m .co s e m
se Correct Answer : Option A
g l a
a
Let 𝐴 = 𝑎 ,𝐵 = 𝑏 and 𝐶 = 𝑐 .Which one of the following
18. × × ×
products, is not defined ?
A) 𝐶 𝐴𝐵
B) 𝐴 𝐴𝐵
C) (𝐴𝐵) 𝐶
m
D) (𝐴𝐵)𝐶
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E) 𝐵 𝐶
m .co s e m
s e l a
l
Correct Answer
g a : Option D
ag
a
19. Let A be a square matrix of order 3 and |𝐴 | = 9 Then |𝑎𝑑𝑗(𝑎𝑑𝑗𝐴) | =
A) 6561
B) 6564
C) 6569
D) 8187
E) 8164
m
Correct Answer : Option A
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s e
g la
20. a
A) 2,3
B) -2,3
C) -2,-3
D) 1,2,3
-1,2,-3
E)
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s e
s em g l a
g la 21. a
a
A) 14
B) -14
C) 12
D) -12
E) 15

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Correct Answer : Option B
e m
em l as
las ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 5 of 36

22. The solution set for −12𝑥 > 38, where 𝑥 is a natural number, is
A) {1,2,3}
B) {1,2}
C) {1}
D) empty set
E) {-1,-2,-3}

Correct Answer : Option D

23. Let 𝑥 be a real number such that 𝑥 + + < 13 .Then the solution set is

A)

B)

C)

D)

E)

Correct Answer : Option A

24. 𝑐𝑜𝑠75 ∘𝑐𝑜𝑠45 ∘𝑐𝑜𝑠15 ∘=
A)
√

B)
√

C)
√

D)
√

E)
√

25. If α + β + ν = 2π , then tan + 𝑡𝑎𝑛 + 𝑡𝑎𝑛 =

A)

B) -tan 𝑡𝑎𝑛 𝑡𝑎𝑛

C) 2 tan 𝑡𝑎𝑛 𝑡𝑎𝑛

D) 3 tan 𝑡𝑎𝑛 𝑡𝑎𝑛

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c. o E ) 4 tan 𝑡𝑎𝑛 𝑡𝑎𝑛 s e m
m a
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Correct Answer : Option A

26. ∘ ∘
tan (315 ) cot (-405 ) =
A) -1
B) 1
C)
√
m
√
m .co
.co m
D)

s e
s em l a
ag
E)

g la
a : Option B
Correct Answer

27. =

A) 𝑐𝑜𝑡

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B) 𝑐𝑜𝑠

1 + 𝑠𝑖𝑛 e m
C)

las
D) 1 + 𝑐𝑜𝑠 ag
E) 𝑡𝑎𝑛

Correct Answer : Option E

28.
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A)
.co s e m
s emB ) g l a
g la a
a C)

D)

E)

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

29.
A) -2
B) -4
C) 2
D) 4
E) -1
Correct Answer:-Question Cancelled

30.

A)

B) π
C) 1
D)

E)

Correct Answer : Option E

Let 𝑎 ≠ 1 be non-zero real number. If the lines 2𝑥 + 𝑎𝑦 = 1 and 𝑥 + 2𝑦 = 1 are
31. perpendicular, then the value of 𝑎 is equal to
A) 1
B) -2
C) 2
D) -1
E) −

Correct Answer : Option D

Let 𝑃(1, 2), 𝑄(𝑎, 𝑏), 𝑅(5, 7)𝑎𝑛𝑑 S(2, 3
32. ) be the vertices of a parallelogram PQRS . Then
A) 𝑎 = 4, 𝑏 = 2
B) 𝑎 = 6, 𝑏 = 2
C) 𝑎 = 6, 𝑏 = 4
D) 𝑎 = 3, 𝑏 = 2
E) 𝑎 = 4, 𝑏 = 6

Correct Answer : Option E

Which one of the following lines, passes through the point of intersection of
33. 𝑥 + 𝑦 = 5 𝑎𝑛𝑑 2𝑥 + 𝑦 = 7 ?
A) 4𝑥 + 3𝑦 = − 1
B) 3𝑥 + 2𝑦 = 7

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c. o C ) 4𝑥 − 3𝑦 = − 1 s e m
m a
se D) 4𝑥 + 3𝑦 − 2 = 0
ag l
E) 4𝑥 + 3𝑦 + 3 = 0

The axis of a parabola is 𝑥 = 0 . If the vertex is at a distance 3 from the origin above the
34. 𝑥 -axis. The vertex of the parabola is at
A) (3,0)
m
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B) (-3,0)
m
.co m
C) (3,-3)
s e
em
(3,3)
D)

s l a
ag
(0,3)
la
E)

g
a : Option E
Correct Answer

35. Length of the Latus rectum of the ellipse + = 1 is

A)

B) 8
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C)

D) 2
e m
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E)
ag

36. The centre of the ellipse 4𝑥 + 24𝑥 + 9𝑦 − 18𝑦 + 9 = 0 is
A) (1, 3)
B) (1, − 3)
C) (3, − 1) m
D)
o m
( − 3, 1)
m.co
E .) c (3, − 3) e
em l as
l as Correct Answer : Option D ag
ag
37. The line 𝑥 − 𝑦 + 4 = 0 touches the ellipse 𝑥 + 3𝑦 = 12 at
A) (1,3)
B) (3,1)
C) (0,2)
D) (0,-2)
E) (-3,1)
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 9 of 36

→ ^ → ^ →
^ + 3𝚥^ − 5𝑘, 𝑂𝐵 = 3𝚤^ + ^𝚥 − 2𝑘; 𝑂𝐶 = 6𝚤^ − 5𝚥^ + 7k be the ^
38. Let 𝑂𝐴 = 2𝚤
position vectors of the points ,A B and C. Then
→ →
A) 𝐴𝐶 = 3𝐴𝐵
→ →
B) 𝐴𝐵 = 3𝐵𝐶
→ →
C) 𝐴𝐶 = 2𝐴𝐵
→ →
D) 𝐴𝐵 = 3𝐵𝐶
→ →
E) 𝐴𝐶 = 4𝐴𝐵

Correct Answer : Option E

→ →
^ and 𝐴𝐶 ^ .If θ is the angle between
39. Let 𝐴𝐵 = 2𝚤^ + 10𝚥^ + 11𝑘 = − ^𝚤 + 2𝚥^ + 2𝑘
→ →
𝐴𝐵 and 𝐴𝐶 then sinθ=
√
A)

√
B)

√
C)

√
D)

E)

Correct Answer : Option D

Let → ^ ×→
^ = 2𝚤^ + 3𝚥^ + 4𝑘
𝑎 × 2𝚤^ + 3𝚥^ + 4𝑘 →+→
𝑏 . If |𝑎 𝑏 | = √29 ,then →
→
𝑎+𝑏
40.
=
A) ^
2𝚤^ + 3𝚥^ − 4𝑘
B) − 2𝚤^ + 3𝚥^ − 4𝑘^
C) ^
± 2𝚤^ + 3𝚥^ + 4𝑘
D) ^
± 2𝚤^ − 3𝚥^ + 4𝑘
E) ^
±√29 2𝚤^ + 3𝚥^ + 4𝑘

41. Let →
𝑎 = ^𝚤 + 2𝚥^ + 4𝑘
→
^ ,𝑏 ^ and →
= 2𝚤^ + 4𝚥^ + 8𝑘 ^ .Then
𝑐 = 2𝚤^ + 4𝚥^ + 3𝑘
→
.𝑐 =

A) 4
B) 6
C) 8
D) 2

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c. o E ) 0 s e m
m a
se Correct Answer : Option E ag l

42. The point of intersection of the lines = = and = = is

A)

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

Correct Answer:-Question Cancelled
43. The equation of the line passing through (0, 0, 1) and (1,1,0) is
→ ^ + λ ^ ^ ^ ,λ ϵℝ
𝑟 =𝑘 m
.co
A) 𝚤+ 𝚥−𝑘
→
𝑟 = ^𝚥 + λ ^𝚤 − ^𝚥 + ^
B) 𝑘 ,λ ϵ ℝ
e m
→
𝑟 = ^𝚤 + λ ^𝚤 + ^𝚥 + ^
𝑘 ,λ ϵℝ las
C)
→ ag
D) 𝑟 = ^𝚤 + ^𝚥 + λ ^𝚤 − ^𝚥 − ^
𝑘 ,λ ϵ ℝ
E)
→
𝑟 = ^𝚤 + ^𝚥 + ^ ^ ,λ ϵ ℝ
𝑘 + λ ^𝚤 + ^𝚥 − 𝑘

Correct Answer : Option A

Which one of the following is a vector parallel to the straight line
44. → ^ + λ 3𝚤^ − 5𝚥^ + 2𝑘
^ ,λ ϵℝ m
.co
𝑟 = ^𝚤 − 11𝚥^ + 101𝑘
m ^ + 5𝚥^ − 2𝑘^
A ) co−3𝚤 m
m . s e
s e B ) 3𝚤^ + 5𝚥^ + 2𝑘^ g l a
l a a
ag C ) ^𝚤 − 11𝚥^ + 101𝑘^
D) ^
−𝚤^ + 11𝚥^ + 101𝑘
E) −4𝚤^ − 16𝚥^ + 103𝑘^

Correct Answer : Option A

m
A straight line through the point (1,-1,0) meets the line = = at right angle .
45.
c. o s e m
em
. It's equation is
s l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 11 of 36

A) = =

B) = =

C) = =

D) = =

E) = =

Correct Answer : Option A

The mean deviation about the mean for the following data

46.

A) 2
B) 2.5
C) 4
D) 6
E) 5

Correct Answer : Option B

47. If 𝑃(𝐴) = 0.7, 𝑃(𝐵) = 0.5 and 𝑃(𝐴 ∪ 𝐵) = 0.9 . Then 𝑃(𝐴 / 𝐵 ) is
A) 0.3
B) 0.4
C) 0.5
D) 0.6
E) 0.7

Correct Answer : Option D

48. The variance of 240, 260, 270, 280 is

A)

B)

C)

D)

E)

Correct Answer : Option E

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 12 of 36

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m 49..co s e
Four unbiased coins are tossed simultaneously. Probability of getting atmost two heads, m
se is
g l a
A)
a
B)

C)

D)

m
E)
m .co
.co s e m
s em l a
ag

gl( a )
50. 𝑙𝑖𝑚 a =
→

A)

B) π
C) 2π
D) π
m
E)
m .co
s e
Correct Answer : Option B
g la
a [ ]
51. If [𝑥] is the greatest integer less than or equal to 𝑥, then 𝑙𝑖𝑚 is equal to
→ [ ]
A) 1
B) sin 1
C) -1
D) 0
m
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E) -sin 1
m
.co Correct Answer : Option B
s e m
s em g l a
l a ( ) ( )
a
ag 52. 𝑙𝑖𝑚 is equal to
→
A) 4
B) 8
C) 12
D) -8
E) -12

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e m
em l as
las ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 13 of 36

53. 𝑙𝑖𝑚 is equal to
→
A) 4
B) 2
C) -2
D) 0
E) 1

Correct Answer : Option E

54.
A) 2
B) 1
C) 3
D) 0
E) 4

55. If 𝑓(𝑥) = 𝑠𝑖𝑛( | 𝑥 | ) − | 𝑥 | , 𝑥 ϵ ℝ, then 𝑓 is

A) not differentiable at 𝑥 =

B) not differentiable at 𝑥 =

C) not differentiable at 𝑥 =

D) not differentiable at 𝑥 = π
E) not differentiable at 𝑥 = 0
Correct Answer:-Question Cancelled
56. The function 𝑓(𝑥) = | 𝑥 − 3𝑥 + 2| ,xϵ ℝ is not differentiable at
A) 𝑥 = 1 and 𝑥 = 3
B) 𝑥 = 1 and 𝑥 = 2
C) 𝑥 = 2 and 𝑥 = 4
D) 𝑥 = 4 and 𝑥 = 5
E) 𝑥 = − 1 and 𝑥 = − 2

Correct Answer : Option B

57. If 𝑒 + 𝑥 𝑦 + 𝑥𝑦 = 𝑒 , then at (0,1) is equal to

A)

B) 𝑒
C) −𝑒
D)

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 14 of 36

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c. o E ) s e m
m a
se ag l
Correct Answer : Option E

58. If 𝑓(𝑥) = 𝑥 | 𝑥|, then 𝑓 ( − 10)=
A) -20
B) -10
C) -40
m
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D) 20
m
E) 40
.co s e m
s em l a
la ag
Correct Answer : Option D

g
59. If 𝑦 =a(tan 𝑥) , then =

A) 𝑙𝑜𝑔(tan 𝑥) + 2𝑥 𝑐𝑜𝑠𝑒𝑐(2𝑥)
B) 𝑙𝑜𝑔(𝑡𝑎𝑛𝑥) +𝑥 𝑐𝑜𝑠𝑒𝑐(2𝑥)
C) x 𝑙𝑜𝑔(tan 𝑥) + 2𝑥𝑐𝑜𝑠𝑒𝑐(2𝑥)
D) 𝑥𝑙𝑜𝑔(tan 𝑥) + 𝑥 𝑐𝑜𝑠𝑒𝑐(2𝑥)
m
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E) 𝑙𝑜𝑔(𝑡𝑎𝑛𝑥) + 𝑐𝑜𝑠𝑒𝑐(2𝑥)

s em
la
Correct Answer : Option A
g
60. The minimum of 𝑓(𝑥) = | 𝑥 + a2 | , 𝑥 ϵ ℝ occurs at
A) 𝑥=0
B) 𝑥=2
C) 𝑥=1
D) 𝑥= −2
E) 𝑥= −1
m
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.co
Correct Answer : Option D

e m
m If 𝑔(𝑥) = 𝑥 − 𝑥, 𝑥 ϵ ℝ, then 𝑔(𝑥) is increasing in
e61. l as
s
la A ) ( − ∞, ∞) ag
ag B) ( − ∞, 0)
C) (0, − ∞)
D) (-5,5)

E)

Correct Answer : Option E
m .
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s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 15 of 36

The distance travelled by a moving particle is given by 𝑠 = 𝑡 − 6𝑡 + 10 , where is
62.
the time in seconds. The particle is at rest when =
A) 1
B) 4
C) 6
D) 3
E) 8

Correct Answer : Option D

63. The maximum value of the function 𝑓(𝑥) = 𝑥√4𝑥 − 𝑥 is
A) √3
B) 4√3
C) 5√3
D) 3√3
E) 6√3

Correct Answer : Option D

64. ∫ 𝑑𝑥 =
A) 𝑠𝑖𝑛𝑥 + 𝐶
B) 2𝑐𝑜𝑠𝑥 + 𝐶
C) −𝑐𝑜𝑠𝑥 + 𝐶
D) −𝑠𝑖𝑛𝑥 + 𝐶
E) 2𝑠𝑖𝑛𝑥 + 𝐶

Correct Answer : Option E

( )
65. ∫ ( )
𝑑𝑥 =

A) 𝑙𝑜𝑔(1 + 𝑥) + 𝐶

B) [𝑙𝑜𝑔(1 + 𝑥)] + 𝐶
C) [𝑙𝑜𝑔(1 + 𝑥)] + 𝐶
D) 𝑙𝑜𝑔(1 + 𝑥) + 𝐶
E) x 𝑙𝑜𝑔(1 + 𝑥) + 𝐶

Correct Answer : Option B

66. ∫ 𝑑θ =

A)

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m
m .co

m .co s e m
se
B)
g l a
a
C)

D)

E)

m
m .co
.co
Correct Answer : Option E
e m
m𝑐𝑜𝑠 √𝑥 𝑑𝑥 =
67. ∫ 𝑠𝑖𝑛 √s𝑥e+ l as
g la ag
A) +𝐶
a
B) +𝐶

C) +𝐶

D) +𝐶

+𝐶 m
.co
E)

e m
Correct Answer : Option D
las
ag
68. ∫ 𝑒 −
( )
𝑑𝑥 =

A) +𝐶

B) +𝐶
C) 𝑒 (1 + 𝑥) + 𝐶
m
m
c. o( )
D) +𝐶
m.co
s e
s emE ) +𝐶
g l a
g la a
a Correct Answer : Option A

69.

A)

B) 𝑙𝑜𝑔(5)
m .
C) 𝑙𝑜𝑔(2) .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

D)

E)

Correct Answer : Option A

70.
A) -3
B) -6
C) -4
D) -2
E) 0

Correct Answer : Option A

71.

A)

B) π
C)

D)

E) 0

Correct Answer : Option E

72.

A) 3
B) 6
C) 4
D) 8
E) 0

73. The integrating factor of the differential equation − 2𝑦 = 2𝑥 − 3 is
A) 𝑒
B) 𝑒

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m
m .co

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

Correct Answer : Option E

The elimination of arbitrary constants 𝑐 , 𝑐 , 𝑐 , 𝑐 from 𝑦 = (𝑐 + 𝑐 )𝑠𝑖𝑛(2𝑥 + 𝑐 )
74.
+𝑐 𝑒 gives a differential equation of order m
m .co
.co
2
A)
e m
B) 4
e m l as
C) 3
l as ag
D)
E)
1
5 ag

Consider the linear programming problem.
Minimize z=𝑥+𝑦
75. Subject to the constraint
2𝑥 + 3𝑦 ≥ 6, 𝑥 ≥ 0, 𝑦 ≥ 0
m
Then the solution of L.P.P. is
m .co
A) 0
s e
B) 2
g la
C)
D)
3
5
a
E) 6

Correct Answer : Option B

The dimensions of where m is the magnetic moment, B, the magnetic flux density, k,
76.
Boltzmann constant and T, the absolute temperature are: m
A) m
c. o𝑀𝐿 𝑇 m.co
s e
s emB ) 𝑀𝐿 𝑇 g l a
g la C ) 𝑀𝐿𝑇 a
a D) 𝑀𝐿 𝑇
E) 𝑀 𝐿 𝑇

Correct Answer : Option E

77. The SI unit of surface tension is
m .
A) 𝑁𝑚
.co s e m
B) 𝑁𝑚
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 19 of 36

C) 𝑁𝑚
D) 𝑁𝑚
E) N

Correct Answer : Option A

A car starting from rest moves such that its acceleration varies with time as a = 6t (ms )
78.
. Its velocity (in ms and displacement (in m) after 4 seconds, respectively, are
A) 48, 64
B) 16, 24
C) 16, 38
D) 24, 32
E) 32, 24

Correct Answer : Option A

For the graph shown below between time t and velocity v of the motion of a body, the
correct statement is:

79.

A) The body comes to rest at infinite time
B) At t = 0, acceleration is positive
C) At t = 0, acceleration is negative
D) At t = 0, the body has maximum velocity
E) The displacement of the particle is zero.

Correct Answer : Option D

80. The coefficient of friction is defined as the ratio of
A) frictional force to applied force
B) frictional force to normal force
C) normal force to frictional force
D) weight of the object to frictional force
E) applied force to frictional force

Correct Answer : Option B

A tennis ball of mass 150 g is moving at 20 ms . A racket strikes it, reversing its
81. direction with a final speed of 30 ms . If the contact time is 0.02 s, then the magnitude
of the force (in N) exerted by the racket is

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m
m .co

c. o A ) 1.5 N s e m
m a
se B)
C)
3.75 N
15 N ag l
D) 150 N
E) 375 N

Correct Answer : Option E

A traffic light of mass 10 √3 kg is suspended by two cables making 30° with the vertical.
82.
m
.co
The tension in each cable is:
m
.co
10 N
A)
e m
B) 9.8 N
e m l as
C) 98 N
l as ag
D)
E)
19.6 N
20 N ag

A car moves at a speed of 20 ms under a force of 500 N. The power output of the car
83.
is
A) 9.8 kW
m
.co
B) 980 kW
98 kW
C)
e m
D) 10 kW
las
E) 100 kW
ag
Correct Answer : Option D

A spring is stretched twice its initial extension. Compared to its initial value, the potential
84. energy
A) becomes four times
B) is doubled
is halved m
.co
C)
D)
o m
remains the same
m
E .) c e
em
becomes zero
l as
l as Correct Answer : Option A ag
ag
85. If a spinning object contracts, its angular velocity
A) remains the same
B) becomes zero
C) becomes negative
D) increases
E) decreases
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 21 of 36

A boy whirls a ball on a string along a horizontal circle of radius 98 cm. The angular
86. velocity (in rad s ) with which the ball has to be whirled so that its acceleration towards
the centre of the circle has the same magnitude as acceleration due to gravity is
A) √10
B)
√
C) 10
D) 0.1
E) 100

Correct Answer : Option A

87. The centre of mass of a thin uniform rod of length L lies at a distance (from one end)

A)

B)

C)

D)

E)

88. The ratio of the escape velocity to the orbital velocity of the earth is
A) 2
B) √2
C)
√

D)

E) √3

Correct Answer : Option B

The gravitational potential energy of a body of mass m on the surface of earth of mass M
89. and radius R is (G - Gravitational constant)
A)

B)

C) mgR
D) -mgR
E) Zero
Correct Answer:-Question Cancelled
90. In a liquid medium, if the depth increases, the pressure at that place

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m
m .co

c. o A ) decreases s e m
m a
se B)
C)
increases
remains constant ag l
D) depends on the shape of the container
E) is zero

Correct Answer : Option B

91. The angle of contact is the angle between
m
.co
A) the normals to the liquid surface and the container wall
m
.co m
B) the liquid surface and the container wall

m
the tangent to the liquid surface and solid surface within the liquid at the point of contact s e
C)

s e l a
a ag
D) the liquid surface and solid surface outside the liquid
g l
the line joining the centres of curvature of the liquid meniscus
E)
a

Water flows at 3 ms in a horizontal pipe under a pressure of 2 × 10 Nm The pipe
92. narrows to half its original diameter at one end. The speed of water (in ms ) in this
narrow section is
A) 3
m
.co
B) 4
C) 6
e m
D) 12
las
E) 24
ag
Correct Answer : Option D

A Carnot engine is working between 127 °C and 27 °C. Keeping the sink temperature
93. unaltered, the temperature at which the source has to be kept so as to double its
efficiency is
A) 400°C
273 °C m
.co
B)
C)
o m
327°C
m
D .) c e
emE )
525 °C
l as
l as 600°C
ag
ag Correct Answer : Option C

The ratio of specific heat capacities of a diatomic gas at constant pressure and constant
94. volume is
A) 1.4
B) 1.6
C) 1.7
1.8 m .
.co
D)
1.5 e m
E)

em l as
las ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 23 of 36

Correct Answer : Option A

The translational kinetic energy of an ideal gas containing N molecules at temperature T
95. is (k - Boltzmann constant)
A) 𝑁𝑘𝑇

B) 𝑁𝑘𝑇

C) 𝑁𝑘𝑇

D) 𝑁𝑘𝑇

E) 𝑁𝑘𝑇

For an ideal gas of molar mass M, the slope of the plot between the rms velocity (v
96.
along the y-axis) and the square root of absolute temperature ( √𝑇 along the x-axis) is

A)

B)

C)

D)

E)

Correct Answer : Option B

97. In a simple harmonic motion,
A) the velocity is constant
B) the motion is periodic
C) the acceleration is directly proportional to velocity
D) the acceleration is along the direction of displacement
E) the motion must be along a straight line

Correct Answer : Option B

98. The principle of superposition in wave motion states that
A) the net displacement is the vector sum of individual displacements
B) waves interfere with each other and lose energy
C) waves cannot occupy the same space at the same time
D) it is applicable to sound waves only

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m
m .co

c. o E ) it is applicable to standing waves only s e m
m a
se Correct Answer : Option A ag l
99. The number of nodes and antinodes in a guitar string vibrating in the third harmonic is:
A) 5 nodes, 4 antinodes
B) 4 nodes, 3 antinodes
C) 3 nodes, 2 antinodes
D) 2 nodes, 3 antinodes
m
.co
E) 1 node, 2 antinodes
o m m
c
. B s e
e m
Correct Answer : Option
l a
as
l field inside a uniformly charged spherical shell of radius R is:
100. The electric ag
A) directly
g
a proportional to the charge within the shell
B) inversely proportional to R
C) same as that outside the shell
D) zero
E) maximum at the centre

Correct Answer : Option D
o m
c
The torque on an electric dipole consisting of. charges q and -q of dipole moment P in a
101. uniform electric field E is
s em
A) qE
g la
B) -qE a
C) Zero
D) P.E
E) P×E

Correct Answer : Option E

m
.co
102. The direction of the electric field due to a positive charge is:
o m around the charge m
A)
B .)
c circular
s e
m radially inwards towards the charge
e C ) radially outwards away from the charge l a
l as ag
ag DE )) along a fixed straight line away from the charge
along a fixed straight line towards the charge

103. A Wheatstone bridge is used to measure
A) unknown resistances
direct current
B)
m .
C) alternating current
.co s e m
D) electric power
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 25 of 36

E) voltage

Correct Answer : Option A

The current carrying rail of a subway track is made of steel and has a cross-sectional
104. area of about 20 cm . The resistance of 2 km of the track is (in ohm) as a multiple of the
specific resistance of steel, ρ is:
A) 10 ρ
B) 10 ρ
C) 10 ρ
D) 10 ρ
E) 10 ρ

Correct Answer : Option E

If n identical cells each of emf E and internal resistance r are connected in parallel, the
105. total EMF and total internal resistance of the combination, respectively, are
A) nE, nr
B) E, nr
C) 𝐸,
D) nE, 2nr
E) 𝑛𝐸,

106. The line integral of the magnetic field around a closed loop is directly proportional to the:
A) current enclosed
B) charge enclosed
C) voltage across the loop
D) length of the loop
E) electric field around the loop

Correct Answer : Option A

The magnetic dipole moment of a current loop carrying current I and of area A with n
107. turns is
A)

B)

C)

D) nIA
E) IA

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m
m .co

m .co s e m
se Correct Answer : Option D
g l a
a
108. A galvanometer is converted into a voltmeter by connecting
A) a high resistance in series
B) a low resistance in series
C) a high resistance in parallel
D) a low resistance in parallel
E) an inductance in series
m
m .co
.co
Correct Answer : Option A
e m
m as
se of a semiconductor
109. The resistance
la ag
l
A)
B) ag
increases with increase in temperature
decreases with increase in temperature
C) is independent of temperature
D) becomes infinite at high temperature
E) becomes zero at high temperature

Correct Answer : Option B

m
.co
A metal rod of length 0.5 m moves with its length perpendicular to a uniform magnetic
110. field of 0.2 T with a velocity of 3 ms . The induced emf in the rod is
e m
A) 0.1 V
las
B)
C)
0.2 V
0.3 V ag
D) 0.4 V
E) 0.6 V

111. The speed of electromagnetic waves in a medium depends on the
m
.co
A) intensity of the wave
m
B)
C .)
co initial phase of the wave
s e m
emD )
permittivity and permeability of the medium
s g l a
l a energy it carries
a
ag E ) reflectivity of the medium

112. When a beam of white light enters into an optical prism, the most deviated colour is
A) green
B) violet
yellow
m .
C)
D) red
.co s e m
E) blue
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 27 of 36

Correct Answer : Option B

113. The phenomenon of diffraction is most significant when the slit width is
A) much larger than the wavelength
B) much smaller than the wavelength
C) comparable to the wavelength
D) equal to the screen distance
E) independent of the wavelength

114. In Huygens construction, the secondary wavelets move
A) in all directions
B) only radially outward
C) only radially inward
D) only in the backward direction of the incident light
E) in a direction perpendicular to the direction of the incident light

Correct Answer : Option A

The plot of maximum kinetic energy of photo-electrons to the energy of the incident
115. photon above its threshold frequency on a photo-sensitive material of work function φ is
A) an oblique straight line with a positive slope.
B) an oblique straight line with a negative slope.
C) an oblique straight line passing through the origin.
D) an exponential curve.
E) a polynomial curve of order 2.

Correct Answer : Option A

The ratio of the respective de Broglie wavelengths of two particles with kinetic energy of
116. 0.02 eV and 2 eV, respectively, is
A) 1:1
B) 10 : 1
C) 1 : 10
D) 1 : √10
E) √10 : 1

Correct Answer : Option B

In the following nuclear reaction, Z is a/an
117.
𝑋→ 𝑌+𝑍+𝑣
A) α particle
B) β particle

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m
m .co

c. o C ) β particle s e m
m a
se D) proton
ag l
E) neutron

Correct Answer : Option B

If a radioactive element disintegrates for a period of time equal to its mean life, then the
118. fraction of the original amount remaining undisintegrated is
A) 𝑒-
m
.co
B) 1-𝑒
m
C) 1-
m .co s e m
s e l a
D)
l a ag
E) 2𝑒 ag

Correct Answer : Option D

In a Germanium crystal containing N atoms, the total number of outer electrons in the
119. crystal is
A) N
B) 2N
m
C) 3N
m .co
D) 6N
s e
E) 4N
g la
Correct Answer : Option E
a
120. The donor level in an n-type semiconductor lies
A) just below the conduction band
B) exactly at the middle of the band gap
C) just below the valence band
D) just above the conduction band m
m
on the valence band .co
.co
E)

e m
em Correct Answer : Option A l as
las a g
ag Ten grams of calcium carbonate which is only 90% pure is treated with excess
121. hydrochloric acid. What is the mass of 𝐶𝑂 gas liberated? (Atomic mass: Ca=40, C=12
& O=16)
A) 4.4g
B) 3.96g
C) 2.2g
D) 0.44g
E) 0.22g
m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 29 of 36

Correct Answer : Option B

For any sub-shell defined by ‘𝑙 value how many values of magnetic quantum number (m
122. ) are possible?
A) (2𝑙)
B) (2𝑙 -1)
C) (2𝑙 +1)
D) (𝑙 +1)
E) (𝑙-1)

123. What is the total number of orbitals associated with the principal quantum number n=3?
A) 3
B) 6
C) 9
D) 10
E) 14

124. The alkali metal with the highest first enthalpy of ionization is
A) Cs
B) Rb
C) K
D) Na
E) Li

Correct Answer : Option E

125. Which one of the following molecules contains two 'sigma' bonds and two 'pi' bonds?
A) O
B) N
C) C H
D) CO
E) CO

Correct Answer : Option D

12g of pure graphite is burnt completely in a bomb calorimeter in excess of oxygen at 298
K at 1 atm. pressure. During combustion, the temperature rises from 298 K to 308 K. The
126. heat capacity of the bomb calorimeter is 20.7 kJ K . What is the enthalpy change for
combustion of 1 mole of graphite
(in kJ mol ) at 298 K and 1 atm. pressure? (R=8.3 JK mol )

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m
m .co

c. o A ) -2070 s e m
m a
se B)
C)
-207
+2070 ag l
D) +207
E) +2.07

Correct Answer : Option B

If water vapour is assumed to be a perfect gas, molar enthalpy change for vapourisation
m
.co
of 1 mol of water at 1bar and 100°C is 41kJ mol . Calculate the internal energy change
127. m
.co m
(in kJ mol ) when 1 mole of water is vaporized at 100°C at 1 bar assuming water

m
vapour as an ideal gas. (R=8.3 JK mol ) s e
s e l a
A) 43.1
37.9 g l a ag
B)
C) -43.1
a
D) -37.9
E) 41.0

Correct Answer : Option B

If “S” is the solubility of X Y in pure water, assuming that neither kind of ion reacts with
128. water, then, the solubility product, K m
.co
is
A) 27 S
e m
B) 108 S las
C) 108 S ag
D) 27 S
E) 27 S

Correct Answer : Option B

129. In which of the following equilibrium K =K ?
m
A)
m ( ) ⇋ 𝐶𝑎𝑂( ) + 𝐶𝑂 ( )
𝐶𝑎𝐶𝑂
co2SO ( ) + O ( ) ⇋ 2SO ( ) m.co
m .
B)
s e
s e C ) PCl ( ) ⇋ PCl ( ) + Cl ( ) g l a
g la D ) H ( ) + I ( ) ⇋ 2HI( ) a
a
E) N2O ( ) ⇋ 2NO ( )

Correct Answer : Option D

In the following cell reaction,

Zn + Cu (0.1 M) ⇋ Zn (0.001 M) + Cu , at 298 K,
130. m .
Calculate the E .co
at 298 K if E at this temperature is 1.1V. (2.303 RT/F = 0.059 V
s e m
at 298 K)
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 31 of 36

A) 1.218 V
B) 1.118 V
C) 1.159 V
D) 1.041 V
E) 0.982 V

For which of the following electrode reactions the standard electrode potential is the
131. highest at 298 K? The ions are present in aqueous solution.
A) 𝐶𝑜 + e → Co
B) Cl ( ) + 2e → 2Cl
C) MnO ( ) + 4H + 2e → Mn + 2H O
D) F ( ) + 2e → 2F
AgCl( ) + e → Ag( ) + Cl
E)

Correct Answer : Option D

The vapour pressure of pure benzene (molar mass=78 g mol ) at a certain
temperature is 0.85 bar. When 0.5 g of a non-volatile, non-electrolyte is added to 39 g of
132.
benzene, the vapour pressure was found to be 0.845 bar at the same temperature. What
is the molar mass of the substance?
A) 85 g mol
B) 127.5 g mol
C) 170 g mol
D) 210 g mol
E) 145 g mol

A first order reaction is 75% completed in 6000 s at 300 K. What is its half life period at
133. the same temperature? (log 2 = 0.3010)
A) 15 min
B) 25 min
C) 75 min
D) 50 min
E) 60 min

Correct Answer : Option D

134. Ammonium ion (NH ) reacts with nitrite ion (NO ) according to the following equation:

NH + NO N ( ) + 2H O(l)
The following initial rates of reaction have been measured for the given reactant

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m
m .co

m .co concentrations.
s e m
se g l a
a

Which of the following is the rate law (rate equation) for this reaction?
A) Rate = k[NH ] / [NO ]

Rate = k[NH ] [NO ]
B)
m
C)
c o m
Rate = k[NH ] [NO ]
m .co
Rate = k[NH m . ]/ s e
D)
s e ] [NO
l a
E) a
l ] [NO ]
Rate = k[NH
g ag
a
Correct Answer : Option E

135. Acidified potassium dichromate cannot oxidize
A) Iodides to iodine
B) Iron (II) salt to iron (III) salt
C) Tin (II) salt to tin (IV) salt
m
.co
D) H S to sulphur
E) Fluoride to fluorine
e m
las
Correct Answer : Option E
ag
136. Which of the following is a basic oxide?
A) CrO
B) CrO
C) Mn O
D) Cr O
m
.co
E) V O
om
c.Correct e m
e m Answer : Option A
l as
as g
l 137. The transistion metal ion with the highest magnetic momentais
ag A ) Fe
B) Mn
C) Ni
D) Co
E) Cr

m .
Correct Answer : Option B
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 33 of 36

138. The transition metal with the highest melting point is
A) Mo
B) Mn
C) W
D) Cr
E) Au

139. Which of the following complex has the least conductivity?
A) [Co(NH ) Cl]Cl
B) Cis-[Co(NH ) Cl ]Cl
C) [Co(NH ) ]Cl
D) [Co(NH ) Cl ]
E) trans-[Co(NH ) Cl ]Cl

Correct Answer : Option D

140. Which one of the following is an ambidentate ligand?
A) Oxalate
B) Carbon monoxide
C) Ethylene diamine
D) Ammonia
E) Nitrite

Correct Answer : Option E

The empirical formula of an organic compound is CH . The molar mass of the
141.
compound is 56g mol . The organic compound is
A) n-Butane
B) Propene
C) Propane
D) 2-Methylpropane
E) Cyclobutane

Correct Answer : Option E

Which of the following finely divided metals can be used as catalyst in the hydrogenation
142. of alkenes and alkynes?
(i) Pt (ii) Fe (iii) Ni (iv) Pd
A) (i), (ii) & (iii)
B) (ii), (iii) & (iv)
C) (i), (iii) & (iv)
D) (ii) & (iii)
E) (i), (ii), (iii) & (iv)

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m
m .co

m .co s e m
se Correct Answer : Option C
g l a
a
143. The solvent used in Wurtz reaction is
A) Water
B) Methanol
C) Ethanol
D) Dry ether
E) Aqueous ethanol
m
m .co
.co
Correct Answer : Option D
e m
em is treated with Cl in the presence of anhydrous FeCl catalyst l as
l as
When chlorobenzene
144. gives a mixture g
of 1,2-dichlorobenzene and 1,4-dichlorobenzene. This reaction isaan
agof
example
A) Nucleophilic substitution reaction
B) Electrophilic substitution reaction
C) Free radical substitution reaction
D) Nucleophilic addition reaction
E) Electrophilic addition reaction

m
.co
Correct Answer : Option B

e m
Which of the following compound contains two primary alcoholic and one secondary
145. alcoholic groups?
las
A) Ethylene glycol
ag
B) Isopropyl alcohol
C) 3° Butyl alcohol
D) Glycerol
E) 2° Butyl alcohol

Correct Answer : Option D

m
m on hydroboration-oxidation gives
146. Propene
co1-propanol m.co
m .
A)
s e
s e B ) 2-propanol g l a
l a C) propanal a
ag D ) propanone
E) etanoic acid

Correct Answer : Option A

When propanone is treated with Zn/Hg and Con.HCl propane is formed. This reaction is
147. known as
A) Wolf-Kishner reaction
m .
B) Clemmensen reaction
.co s e m
C) Hoffman reaction
s em l a
g la ag
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D) Kolbe’s reaction
E) Cannizzaro reaction

Correct Answer : Option B

148. Benzoyl chloride can be converted to benzaldehyde by
A) Rosenmund reduction
B) Etard reaction
C) Stephen reaction
D) Gatterman reaction
E) Gatterman-Koch reaction

Correct Answer : Option A

149. The amine with the highest pK value is
A) Methanamine
B) N-methylmethanamine
C) Benzeneamine
D) N-Methylaniline
E) Ethanamine

150. The base that is not present in DNA is
A) uracil
B) adenine
C) guanine
D) thymine
E) cytosine

Correct Answer : Option A

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