KEAM 2025 Question Paper Engineering with Answers (26 April 2025)

FOR KEAM EXAM PREPARATION

KEAM 2025
Question Paper ·
Engineering
EXAM YEAR TYPE SUBJECT INCLUDES

KEAM 2025 Question Paper Engineering Answers
DATE

26 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: 12/2025/OL
Exam:KEAM 2025 ENGG-3
Date of Test: 26-04-2025

1. The relation R={(1,3),(2,3),(2,4),(3,1)(4,4)(4,1)} on the set X={1,2,3,4} is
A) a1-1function
B) reflexive
m
transitive m .co
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C)
not symmetric e m
D)

em
an onto function
l as
E)

l as ag
g
a : Option D
Correct Answer

If two sets 𝐴 and 𝐵 are having 11 elements in common, then the number of elements
2. common to 𝐴 × 𝐵 and 𝐵 × 𝐴
A) 121
B) 22
C) 99
m
D) 11
m .co
E) 33
s e
g la
Correct Answer : Option A
a
3. The domain of the function 𝑓(𝑥) = √𝑥 + 𝑥 − 2 is
A) (- ∞ ,- 2) ∪ [1, ∞)
B) ( − ∞, − 2] ∪ (1, ∞)
C) ( − ∞, − 2) ∪ (1, ∞)
( − ∞, − 2] ∪ [1, ∞)
D)
m
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E)
e m
em Correct Answer : Option D l as
las ag
ag 4. The range of the function 𝑓(𝑥) = 𝑥 + 4𝑥 + 4 is
A) [0, ∞)
B) [1, ∞)
C) [3, ∞)
D) [2, ∞)
E) [4, ∞)
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 1 of 37

Let s, t, r be non-zero distinct positive real numbers. If the complex number 𝑧 = 𝑥 + 𝑖𝑦
5. satisfies
𝑠𝑧 + 𝑡𝑧― + 𝑟 = 0 , then z lies on
A) imaginary axis
B) real axis
C) 𝑦=𝑥
D) 𝑦 = 2𝑥
E) 𝑥+𝑦=0

Let 𝑧 = 𝑥 + 𝑖𝑦 be a complex number, where 𝑖 = √−1 is the complex unit. Then 𝑧 − 1 + 𝑖
6. = 5 is a circle with
A) centre at (-1,1) and radius 5
B) centre at (1,1) and radius √5
C) centre at (-1,-1) and radius √5
D) centre at (1,1) and radius 25
E) centre at (1,-1) and radius 5

7. Let 𝑧 be a complex number such that 𝑧 + 𝑖𝑧 − 𝑖𝑧 + 1 = 0 where 𝑖 = − 1. Then |z| =
A) 2
B)

C) 1
D)

E) 3

8. Real part of is equal to

A) 𝑐𝑜𝑠

B) 𝑠𝑖𝑛

C) 1 + 𝑠𝑖𝑛

D) 1 + 𝑐𝑜𝑠

E) 𝑠𝑖𝑛 + 𝑐𝑜𝑠

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 2 of 37

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c. o9. The 25th term of 9,3,1, , ,...is s e m
m a
se A) ag l
B)

C)

D)

m
.co
E)
m
.co s e m
em D
Correct Answer : Option
s g l a
l a a
agthree terms in a G.P. are , 𝑎, b and 𝑐 where 𝑎 ≠ 𝑏 Then the fifth term is
10. The first
A)

B)

C)

D)
m
E)
.co
s em
g la
a
The sum of first n terms of a G.P. is 1023. If the first term is 1 and the common ratio is 2,
11. then the value of n is
A) 12
B) 11
C) 10
D) 9
E) 8
m
m .co
.coCorrect Answer : Option C
s e m
s em Let 𝐺 , 𝐺 , 𝐺 be geometric means between 𝑙 and 𝑛, where 𝑙 and
g l a𝑛 are positive real
g la 12. numbers.Then the common ratio is a
a
A)

B)

C)

m .
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D)
e m
em l as
las ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 3 of 37

E)

Correct Answer : Option D

25 distinct objects are divided into 5 groups and each group consists of exactly 5 objects.
13. Then the number of ways of forming such groups, is
!
A)
( !)
!
B)
!
!
C)
( !)
!
D)
( !)
!
E)
( !)

14. 1+ 𝐶 + 𝐶 +...+ 𝐶 +1 =
A) 2
B)

C)

D) 2
E) 100

Correct Answer : Option D

15. The coefficient of 𝑥 in (1 − 𝑥 )(1 − 𝑥 ) 𝑖𝑠
A) 𝐶
B) − 𝐶
C) − 𝐶
D)

E) 0

16. 𝐶 + 𝐶 +...+ 𝐶 =
A) 2
B) 2
C) 2 −1
D) 2 −2

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c. o E ) 2 − 1 s e m
m a
se ag l

17.

A)

B)
m
m .co
C)
m .co s e m
s e l a
D)
g l a ag
E) 0 a

Let B be a matrix of order 3 × 2 and C be a matrix of order 3 × 3 . If A is a matrix such that
18. 𝐵𝐴 = 𝐶, then the order of A is
A) 2×2
2×3 m
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B)
3×2
C)
e m
D) 3×4
las
E) 3×3
ag

19.
A) 12
B) 8
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C) 48
m
D)
E .)
co 24
s e m
em
6
s g l a
l a a
ag

20.

A) 𝑃 =𝑃
B) 𝑃 = −𝑃
𝑃 = 2𝑃 m .
.co
C)

e m
D) 𝑃 = − 2𝑃
em l as
las ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 5 of 37

E) 𝑃 = 3𝑃

Correct Answer : Option A

21. 𝑠𝑒𝑐 𝑥 + 𝑐𝑜𝑠𝑒𝑐 𝑥 − 𝑠𝑒𝑐 𝑥𝑐𝑜𝑠𝑒𝑐 𝑥 =
A) 𝑠𝑒𝑐 𝑥
B)

C) 𝑐𝑜𝑡 𝑥
D) 1
E) 0

Let 𝑥 be a real number such that 7𝑥 + 4 < 9𝑥 + 8 . Then the solution set of the inequality
22. is
A) ( − ∞, − 2)
B) ( − ∞, − 4)
C) ( − 2, ∞)
D) [ − 2, ∞)
E) [ − 1, ∞)

( ) ( )
Let x be a real number such that ≤ Then the solution set of
23.
the inequality is
A)

B)

C)

D)

E)

24. 𝑠𝑖𝑛15 ∘𝑠𝑖𝑛45 ∘𝑠𝑖𝑛75 ∘ =

A)
√

B)
√

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 6 of 37

m
m .co

m .co s e m
se
C)
√
g l a
D)
a
√

E)
√

25. If 𝑠𝑖𝑛 θ = and the angle θ is in the second quadrant, then sec θ is equal to m
m .co
A)
m.co s e m
√
s e l a
B)
g
√
l a ag
√
a
C)

√
D)

E)
√
m
m .co
s e
26. g la
a
A) 𝑠𝑖𝑛2𝑥
B) 𝑠𝑖𝑛𝑥
C) 𝑐𝑜𝑠2𝑥
D) 𝑐𝑜𝑠 𝑥
E) 𝑠𝑖𝑛
m
m .co
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e m
m
e27. l as
s
∘ ∘

la ∘ ∘
ag
ag
A)
√

B)
√

C)
√

D)
√
m .
E) √3
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 7 of 37

Correct Answer : Option A

( )( )
28. ( )( )
A) 𝑡𝑎𝑛 α
B)

C) 1
D) 2
E)

29.

A)

B) 2
C) 3
D) 1
E)

Correct Answer : Option D

30. If 𝑡𝑎𝑛 𝑥 = 𝑡𝑎𝑛 (3) − , then x is equal to

A)

B)

C) 1
D) 3
E) 2

Correct Answer : Option A

If the distance of the line 4𝑥 − 3𝑦 + 𝑘 = 0 from the point (1, 2) is 5 units, then the values
31. of 𝑘 are
A) 27,-23
B) -27,23
C) 29,-24
D) -29,24
E) -28,-25

Correct Answer : Option A

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m .co

m 32..co Two sides of a parallelogram are along the lines 𝑥 + 𝑦 = 5 and 𝑥 − 𝑦 = -5. If the
s e m
se l a
diagonals of the parallelogram intersects at (3, 6 ) then one of its vertices, is at
g
A) (6,5) a
B) (7,6)
C) (7,5)
D) (6,7)
E) (5,7)

Correct Answer : Option D
m
m
Let 𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0 the equation of a straight line such that 3𝑎 + 2𝑏 + 4𝑐 = 0 . Which one .co
33.
.co
of the following points, lies on the line?
m s e m
s e l a
a ag
A)

g l
B)
a
C)

D)

E) (2,4)
m
Correct Answer : Option A
m .co
s e
34. centre is at g la lines 2𝑥 − 3𝑦 = 5 and 3𝑥 − 4𝑦 = 7 , then the
If two diameters of a circle are along the

A) (1,1)
a
B) (-1,1)
C) (-1,-1)
D) (1,-1)
E) (1,-2)

m
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Correct Answer : Option D

o m mis an arbitrary point
. c s e
Let 𝑦 = 8𝑥 be the equation of a parabola. Which one of the following

s em on the parabola?
35.
g l a
la A ) (2𝑡, 4𝑡 ), 𝑡 ϵ ℝ a
ag B) (2𝑡 , 4𝑡 ), 𝑡 ϵ ℝ
C) (2𝑡 , 2𝑡 ), 𝑡 ϵ ℝ
D) (2𝑡, 2𝑡 ), 𝑡 ϵ ℝ
E) (2𝑡 , 4𝑡), 𝑡 ϵ ℝ

m
Let 𝑃 be any point on the ellipse 4(𝑥 + 2) + 9(𝑦 − 4) = 144. If 𝐹 and 𝐹 are the Foci of .
36. the ellipse, then 𝐹 𝑃 + 𝐹 P= .co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 9 of 37

A) 8
B) 12
C) 16
D) 6
E) 10

( ) ( )
37. The eccentricity of the hyperbola - =1 is

A)

B)

C)

D)

E)

→
Let →𝑎, 𝑏, →
𝑐 be any three vectors and m, n be scalars. Which one of the following is not
38.
true?
→ → → → →
A) 𝑎 + 𝑏 + 𝑐 = 𝑎 + 𝑏 +→ 𝑐
→ → → →
B) 𝑚 →𝑎 + 𝑏 +→
𝑐 = 𝑚𝑎 + 𝑚𝑏 + 𝑚 𝑐
C) (𝑚 + 𝑛)→ → + 𝑛𝑎
𝑎 = 𝑚𝑎 →

𝑚 → → →
→ . 𝑚𝑏
D) 𝑎 . 𝑏 = 𝑚𝑎
𝑚 → → →×→
E) 𝑎 × 𝑏 = 𝑚𝑎 𝑏

Correct Answer : Option D

→ →
39. If → →) . (3𝑏
𝑎 . 𝑏 = 12, then (3𝑎 )is equal to
A) 36
B) 4
C) 108
D) 16
E) 144

40. Let𝑎 ^, →
→ = 3𝚤^ + 2𝚥^ + 2𝑘 𝑏 = ^𝚤 + 2𝚥^ − 2𝑘 →+→
^ .Then (𝑎 →−→
𝑏 ) .(𝑎 𝑏) =
A) 6

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 10 of 37

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m .co

c. o B ) 7 s e m
m a
se C) 8
ag l
D) 9
E) 10

→ → → → → → →
41. 𝑎, 𝑏,→
𝑐 , 𝑑 be non-zero vectors such that →
𝑎×𝑏 =→
𝑐 × 𝑑 and →
𝑎 ×→
𝑐 = 𝑏 × 𝑑 .Then
→ → →
𝑎 − 𝑑 is parallel to 𝑏 − → m
.co
A) 𝑐
→ → m
.co
→𝑎 − 𝑏 is parallel to 𝑏 − →
B) 𝑐
e m
C)
→ →
e m →
𝑏 − 𝑐 is parallel to 𝑏 + →
𝑐
l as
D) → →
l as → →
𝑎 − 𝑐 is parallel to 𝑏 − 𝑐 ag
E) →
𝑎 +→
g
a𝑐 is parallel to →𝑏 + →𝑑
Correct Answer : Option A

→
Let 𝑂𝑃 = 2𝚥^ be the position vector a point P. Let →
𝑟 = ^𝚥 + λ (𝚤^ + ^𝚥)be a straight line. The
42.
distance of the point P from the line is
√
m
.co
A)

√
e m
B)

las
C)
√
ag
√
D)

√
E)

Correct Answer : Option A
o m
m . c
.
43.
coThe Cartesian equation of the line 𝑟 = 2𝚤^ − 7𝚥^ + 11𝑘sem+ λ
→ ^

s em 3𝚤^ + 7𝚥^ − 13𝑘^ is g l a
la a
ag A) = =
−
B) = =
−
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 11 of 37

Which one of the following is a point on the straight line
44. →
𝑟 = 13𝚤^ − 14𝚥^ + 23𝑘^ + λ 5𝚤^ − 7𝚥^ − 9𝑘
^ ,λ ϵ ℝ
A) (13,-14,-23)
B) (5,-7,-9)
C) (23,-28,7)
D) (23,-28,5)
E) (13,14,23)

Correct Answer : Option D

45. The point at which the line = = meets the 𝑧𝑥 -plane is
A) (19,2,5)
B) (19,0,5)
C) (0,2,-1)
D) (-3,2,0)
E) (0,2,-1)

46. The mean deviation about the mean from the data 400,410, 420,430,440 is
A) 14
B) 10
C)
D)
E)

Correct Answer : Option D

47. An unbiased die is thrown and B is an event showing an odd number on top. Then 𝑃(𝐵)

A)

B)

C)

D)

E)

Correct Answer : Option D

48. The standard deviation of 1,2,3,...,100 is

A) √ 3333

B) √ 3333

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m
m .co

c. o C ) s e m
m √ 3333
a
se ag l
D) √ 3333

E) √ 1111

Correct Answer : Option A

Consider the random experiment that an integer is chosen from the first 100 positive
49. m
.co
integers. Probability that the chosen number is a multiple of 11, is
m
A)
m .co s e m
s e l a
B)

g l a ag
C) a
D)

E)

m
m .co
50. s e
g la
A) √2
a
B) 2√2
C)
√

D) √

E)
m
m .co
.co Correct Answer : Option E
s e m
s em 𝑙𝑖𝑚 g l a
g la 51. a
a
→

A) 1
B)

C) -1
D)

0 m .
.co
E)

e m
em l as
las ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 13 of 37

Correct Answer : Option A

52. The function 𝑓(𝑥) = 𝑥 √𝑥 + 2 + √𝑥 + 1 is continuous on
A) ( − ∞, 1]
B) [4, ∞)
C) [-3,∞)
D) [-1,∞)
E) (−∞,∞)

Correct Answer : Option D

53. 𝑙𝑖𝑚
→
=

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

Let 𝑓(𝑥) = [𝑥], 𝑥 ϵ (0, 6), where[x] is the greatest integer function. Then the number of
54. discontinuities of 𝑓(𝑥)
A) 1
B) 2
C) 3
D) 4
E) 5

55. Let 𝑓(𝑥) = 10 − | 𝑥 − 5 | , 𝑥 ϵ ℝ , Then 𝑓(𝑥 ) is not differentiable at
A) x=10
B) x=15
C) x=-5
D) x=5
E) x=-15

Correct Answer : Option D

56. For 𝑥 ϵ ℝ,let 𝑓(𝑥) = 𝑙𝑜𝑔3 − 𝑠𝑖𝑛𝑥 and 𝑔(𝑥) = 𝑓(𝑓(𝑥))Then g'(0)=
A) 𝑠𝑖𝑛(𝑙𝑜𝑔3)
B) ( )
C) −𝑐𝑜𝑠(𝑙𝑜𝑔3)
D) 2𝑐𝑜𝑠(𝑙𝑜𝑔3)

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 14 of 37

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c. o E ) 𝑐𝑜𝑠(𝑙𝑜𝑔3) s e m
m a
se Correct Answer : Option E ag l

57.

A)

B)
m
m .co
.co m
C)

m s e
s e l a
ag
D)

g l a
E) a
Correct Answer : Option A

58. Let 𝑓: ℝ → ℝ be a function such that 𝑓(𝑥) = 𝑥 + 𝑥 𝑓 (1) + 𝑥𝑓"(2) + 𝑓 (3) , then 𝑓 (3)=
A) 3
6
B)
m
C) 9
m .co
D) -2
s e
E) 𝑓"(2)
g la
a
59. If 𝑢 = 𝑠𝑒𝑐 ( − 𝑠𝑒𝑐2θ ) and 𝑣 = 𝑐𝑜𝑠 θ , then at θ = ,is equal to

A) √2
B) 2√ 2
m
.co
C)

o m
√

m
D .)
c s e
e m √
l a
l as E ) −√2 ag
ag

60. The function𝑓(𝑥) = 𝑒 − 𝑥 is increasing in the interval
A) (0, 4)
B) ( − ∞ ,0 )
( − 1, 1)
C)
m .
D) ( − 1, 0) c. o s e m
E) (0, ∞) m e l a
l as ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 15 of 37

61. Let f(𝑥) = 10 − | 𝑥 − 3 | , 𝑥 ϵ ℝ The maximum of 𝑓(𝑥) occurs at
A) x=0
B) x=3
C) x=-3
D) x=10
E) x=1

The distance travelled by a moving particle is given by 𝑠 = − 6𝑡 + 8,where 𝑡 denotes
62.
the time in seconds. The velocity becomes zero when 𝑡 is equal to
A) 1
B) 4
C) 3
D) 6
E) 8

Correct Answer : Option D

63. If 𝑎 + 𝑏 = 10 and 𝑎b is maximum, then the value of 𝑎 is
A) 5
B) 3
C) 6
D) 25
E) 10

Correct Answer : Option A

64.

A)

B)

C)

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 16 of 37

m
m .co

m .co s e m
se D)
g l a
a
E)

sec
65. ∫ (sec 𝑑𝑥 = m
.co
tan )
m
A)
m.co s e m
s e l a
B)
g l a ag
a
C)

D) (𝑠𝑒𝑐𝑥 + 𝑡𝑎𝑛𝑥) +𝐶
E)

m

m .co
s e
66.
g la
a
A) 9𝑒 − 4𝑒 + 𝐶
B) log|9𝑒 + 4𝑒 |+ 𝐶
C) 4𝑒 − 9𝑒 + 𝐶
D) log |4𝑒 − 9𝑒 |+ 𝐶
E) log |9𝑒 − 4𝑒 |+ 𝐶
m
m .co
.co
e m
m
e67. l as
s
la A ) 𝑒 𝑐𝑜𝑠 θ + 𝐶 ag
ag
B) 𝑒 sin2θ + 𝐶
C) 2e 𝑐𝑜𝑠 θ + 𝐶
D) 𝑒 sinθ + 𝐶
E) 𝑒 𝑐𝑜 s2θ + 𝐶

Correct Answer : Option A

m .
68. .co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 17 of 37

A)

B)

C)

D)

E)

69. The area bounded by 𝑦 = 𝑥 − 1, 1 ≤ 𝑥 ≤ 2, 𝑦 = 0 (in sq.units) is
A) 2
B) 1
C)

D) 4
E)

70.
A) − 𝑙𝑜𝑔2

B) − 𝑙𝑜𝑔3

C) + 𝑙𝑜𝑔2
D) + 𝑙𝑜𝑔2

E) − 𝑙𝑜𝑔2

71.
A) 2
B)

C)

D) 1

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 18 of 37

m
m .co

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

72.

A) 14
B) 16
C) 8 m
10 m .co
.co
D)

e m
E) 12
em l as
s
la : Option E ag
g
Correct Answer
a
73.

A) 16 + 25 + √𝑥 + 𝐶

B) 16 + 25 + √𝑥 +x+ 𝐶
m
16 + 25 + √𝑥 + 𝑥 + 𝐶
m .co
C)
s e
g la
D) 𝑥 16 + 25 + √𝑥 + 𝐶
a
E) 𝑥 16 + 25 + √𝑥 + 𝐶

Correct Answer : Option A

The elimination of arbitrary constants 𝑐 , 𝑐 , 𝑐 and 𝑐 from 𝑦 = (𝑐 + 𝑐 ) sin (𝑥 + 𝑐 ) − 𝑐
74. m
c o
𝑒 gives a differential equation of order
m m.co
.
A) 1
s e
s C)emB ) 2
g l a
l a 3
a
ag DE )) 4
5

The maximum value of the objective function 𝑧 = 2𝑥 + 3𝑦 , when the corner points of the
75. feasible region are (0, 0), (5, 0) , (4, 1) and (0, 2), is
A) 0
m .
.co m
B) 6
s e
em
10
C)
s l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 19 of 37

D) 11
E) 16

Correct Answer : Option D

The dimension of X in the equation, 𝐹 = 6π η 𝑋 is
76. ( F – Force; η -Coefficient of viscosity)
A) 𝑀 𝐿 𝑇
B) 𝑀𝐿 𝑇
C) 𝑀 𝐿 𝑇
D) 𝑀 𝐿 𝑇
E) 𝑀𝐿 𝑇

Correct Answer : Option A

77. One torr is
A) 1 mm of Hg
B) 1 cm of Hg
C) 76 mm of Hg
D) 100 mm of Hg
E) 76 cm of Hg

Correct Answer : Option A

A particle moving with an initial velocity of 1 𝑚𝑠 has an uniform acceleration of 2 𝑚
78. 𝑠 . The distances travelled by the particle in the first two intervals of 5 s are
respectively
A) 30 m and 110 m
B) 50 m and 110 m
C) 40 m and 80 m
D) 30 m and 80 m
E) 60 m and 160 m

Correct Answer : Option D

When a cricketer hits a ball at an angle of 45⁰ with an initial velocity of 40 𝑚𝑠 ,the ball
79. falls on the ground at a distance of 160 m. If he hits the ball at the same angle with an
initial velocity of 50 ms the ball will fall at a distance of
A) 480 m
B) 180 m
C) 280 m
D) 300 m

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m
m .co

c. o E ) 250 m s e m
m a
se Correct Answer : Option E ag l
A ball moves in a circle of radius 0.5 m from A to B in √2 s. The average velocity of the
ball is (in 𝑚𝑠 )

80.
m
m .co
m .co s e m
s e l a
A) 0.25
g l a ag
B) 0.5 a
C) 0.75
D) 1.5
E) 1.25

m
A block of mass 𝑚 suspended from the ceiling of a lift by an inextensible string of
81. .co
negligible mass. When the lift moves in the upward direction with an acceleration of 0.2
m
e
ms , the tension acting on the wire is 80 N. Then the mass of the block is
s
A) 1 kg
g la
B) 2 kg a
C) 8 kg
D) 6 kg
E) 4 kg

The force to be applied to a body of mass 200 g to change its velocity by 25 𝑚𝑠 m
.co
in 5 s
82.
o m
is
m
A .) c 2.5 N e
emB ) l as
l as C) 50 N
3N ag
ag D ) 30 N
E) 1N

Two bodies having masses in the ratio 1:3 have equal linear momentum. Their respective
83. kinetic energies are in the ratio
A) 3:1
m .
B) 1:2
.co s e m
C) 1:3
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 21 of 37

D) 4:1
E) 2:1

Correct Answer : Option A

A particle moving in a horizontal circle of radius 0.5 m completes half rotation. The work
84. done by the centripetal force of 5 N on the particle (in J) is
A) 2
B) 5
C) 2.5
D) 3
E) 1
Correct Answer:-Question Cancelled
The moment of inertia and rotational kinetic energy of a rigid body about an axis are
85. respectively 4 𝑘𝑔𝑚 and 50 J. The angular velocity of the body (in rad 𝑠 ) is
A) 10
B) 20
C) 25
D) 5
E) 15

Correct Answer : Option D

If a torque of 1.25 Nm acts on a circular ring for a duration of 4 s, then its angular
86. momentum changes by (kgm 𝑠 )
A) 25
B) 50
C) 15
D) 5
E) 10

Correct Answer : Option D

If the angular displacement made by a rotating wheel in 10 s is 150π radian, then the
87. number of revolutions made by it is
A) 75
B) 100
C) 300
D) 150
E) 50

Correct Answer : Option A

Two satellites A and B are orbiting the earth at a height of 2.5R and 7.5R respectively
88. from the centre of the earth. The ratio of time periods of A and B is
A) √3: 1

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m
m .co

c. o B ) 1: 3√3 s e m
m a
se C) 1: √3
ag l
D) 1: 2√3
E) 3√3: 1

The orbital velocity 𝑣 of an artificial satellite revolving around the earth at a height R
89. from the surface of the earth in terms of escape velocity 𝑣 from the earth is (R - radius m
of the earth) m .co
m .co s e m
A)

s e l a
B)
g l a ag
a
C)
√
D) 𝑣
E) √2𝑣

Correct Answer : Option A

m
90.
m .co
P is the atmospheric pressure and P is the absolute pressure at a depth ℎ in an ocean.
The gauge pressure at the depth ℎ is
s e
A) 𝑃+𝑃
g la
B) a
C) 2𝑃 − 𝑃
D)

E) 𝑃−𝑃

m
.co

o m m
91..c The principle behind the function of Bunsen burner is
s e
s emA ) Pascal’s law g l a
g la B ) law of flotation a
a C) venturimeter
D) Toricelli’s law
E) Archemedes’ principle

92. Bernoulli’s principle is applicable to
m .
.co
non-viscous, incompressible fluids in streamline flow
A)
e m
B) viscous, compressible fluids in streamline flow
em l as
las ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 23 of 37

C) viscous, incompressible fluids in streamline flow
D) non-viscous, incompressible fluids in turbulent flow
E) non-viscous, compressible fluids in turbulent flow

Correct Answer : Option A

93. Specific heat capacity of a substance depends on the
A) material of the substance only
B) volume of the substance only
C) mass of the substance only
D) material and temperature of the substance
E) mass and volume of the substance

Correct Answer : Option D

94. Which one is INCORRECT statement?
A) In an isochoric process, volume remains constant
B) In an adiabatic process, there is a heat exchange with the surrounding
C) In an isobaric process, pressure remains constant
D) In an isothermal process, temperature remains constant
E) In a cyclic process, the change in internal energy is zero

The number of molecules contained in the gas of mass M is
95. (𝑀 - molar mass, 𝑁 - Avogadro’s number)

A)

B)

C)

D)

E)

If the mean free path of a gas molecule at 27 ⁰C is 10 x 10 m. Its mean free path at 87
96.
⁰C is
A) 12 x10 m
B) 8 x10 m
C) 6 x10 m
D) 10 x10 m
E) 14 x10 m

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m
m .co

m .co s e m
se Correct Answer : Option A
g l a
a
If the speed of the transverse wave in a wire under certain tension is 𝑣 , then its speed
97.
under tension 2 (in ms ) is

A)
√
B) 2𝑣
C) √2𝑣
m
D)
m .co
.co m
√

s e
E)
s em l a
g l a ag
a : Option C
Correct Answer

98. A musician hits a drum 90 times in a minute. The time period of hit is
A) 1.34 s
B) 1.5 s
C) 0.33 s
D) 0.75 s
m
.co
E) 0.67 s

s em
g la SHM is 8 s, then the time period of the potential
a
If the time period of a particle executing
99. energy of this particle is
A) 16 s
B) 4s
C) 2s
D) 8s
E) 32 s
m
m
.co
.co
m Which one of the following pairs of charges separated by the sames e m
s e100. g l a distance 𝑟 will

l a experience a maximum force?
a
ag AB )) 0.3 C and 0.7 C
0.1 C and 0.9 C
C) 0.2 C and 0.8 C
D) 0.5 C and 0.5 C
E) 0.4 C and 0.6 C

Correct Answer : Option D

om
.c the potential at Q is
A charge of 5 C is moved from a point P to another point Q by doing a work of 10 J. If the
101. potential at P is 0.5 V, then e m .
em l as
las ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 25 of 37

A) 1.0V
B) 2.0V
C) 2.5 V
D) 1.5V
E) 3.0V

The equivalent capacitance of n capacitors of equal capacitance when connected in
102. series and parallel are respectively 0.4 μF and 10 μF. The capacitance of each capacitor
is
A) 2μF
B) 4μF
C) 5 μF
D) 6 μF
E) 1μF

Correct Answer : Option A

The value of R in the given circuit is

103.

A) 0.4 Ω
B) 8Ω
C) 2Ω
D) 0.8 Ω
E) 4Ω

The resistance of a wire at 30⁰C and 40⁰C are respectively 5 Ω and 6 Ω. The temperature
104. coefficient of resistance of the material of the wire (in per degree Celcius) is
A) 0.04
B) 0.05
C) 0.02
D) 0.03
E) 0.01

A wire of 25 Ω resistance is cut into 𝑛 pieces of equal length. If these pieces of wires are
105. connected in parallel, their equivalent resistance is 1 Ω , then the value of is

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m
m .co

c. o A ) 3 s e m
m a
se B)
C)
6
8 ag l
D) 5
E) 4

Correct Answer : Option D

A coil having 100 turns and an area of 0.02 𝑚 is placed with its plane perpendicular to
106.
m
.co
the magnetic field of 1 Wb𝑚 . The magnetic flux linked with the coil is
m
.co m
A) zero
1 Wb
m s e
B)
s e l a
a ag
C) 2 Wb
3 Wb g l
D)
E) 5 Wb
a

Two charged particles of same mass but having charges in the ratio 1: 4 enter a uniform
107. perpendicular magnetic field. The ratio of their time period in their respective circular path
is
m
.co
A) 1: 4
B) 1: 8
e m
C) 8: 1
4: 1 las
D)
E) 2: 1 ag
Correct Answer : Option D

108. Which one is not a ferromagnetic material?
A) cobalt
B) tungsten
m
.co
C) nickel
m
D)
E .)
co gadolinium
s e m
em
iron
s g l a
l a a
ag

If an inductor coil of self-inductance 2 H stores 25 J of magnetic energy, then the current I
109. passing through it is
A) 25 A
B) 10A
C) 15A
D) 2A
m .
.co
E) 5A
e m
em l as
las ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 27 of 37

110. When a current passing through a coil changes at the rate of 30 𝐴𝑠 , the emf induced
in the coil is 12 V. The self-inductance of the coil is
A) 0.4 H
B) 0.2 H
C) 0.6 H
D) 0.3 H
E) 0.1 H

Correct Answer : Option A

An electromagnetic wave travelling in vacuum has its electric field component,
111. E = 15 sin [1.57𝑦 + 5.4𝑡]𝚥^ The wavelength of the wave is
A) 4.0 m
B) 3.0 m
C) 2.5 m
D) 2.0 m
E) 1.0 m

Correct Answer : Option A

112. Chromatic aberration arises in thick lenses due to
A) scattering of light
B) refraction of light
C) interference of light
D) reflection of light
E) dispersion of light

An unpolarized light incident on a plane glass surface gets totally polarized on reflection.
113. If the refractive index of glass is tan 57 ∘, then the angle of refraction is
A) 90⁰
B) 33⁰
C) 13⁰
D) 37⁰
E) 45⁰

114. Light energy is redistributed in
A) diffraction and interference
B) reflection and diffraction
C) refraction and interference

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m
m .co

c. o D ) reflection and polarisation s e m
m a
se E) polarization and refraction
ag l
Correct Answer : Option A

Which one of the following statements is INCORRECT?
115.
In photoelectric effect
A) Threshold frequency is different for different metals
B) The same metal gives same response to light of different wavelengths
m
C)
m
The emission of photoelectrons is an instantaneous process
.co
D) .co
Above the threshold frequency the number of photoelectrons emitted per sec is
m s e m
e
directlyproportional to the intensity of incident radiation
s l a
E) l a
The maximum K.E. of the photoelectrons is independent of the intensity of incident
g ag
a
radiation

When an electron is accelerated from rest by a potential of 480 V, the wavelength
116. associated with it is λ. If the electron at rest is accelerated by a potential of 120 V, then
the wavelength associated with it is
A) 5λ
m
.co
B) 4λ
2λ
C)
e m
D) 3λ
las
E) 6λ
ag

In hydrogen spectrum, the shortest wavelength of Bracket series is produced during the
117. transition between the states
A) 𝑛 = 5 and 𝑛 = 4
B) 𝑛 = 4 and 𝑛 = 1
m
.co
C) 𝑛 = 4 and 𝑛 = 3
m
D)
.co
mE )
𝑛 = ∞ and 𝑛 = 4
s e m
s e 𝑛 = 4 and 𝑛 = 2
g l a
g la a
a Correct Answer : Option D

118. A radioactive element having 6 x 10 atoms initially decays and is left with 0.75 x 10
undecayed atoms in 48 years. The half-life time of this radioactive element is
A) 16 years
B) 24 years
C) 12 years
D) 6 years m .
E) 18 years .co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 29 of 37

Correct Answer : Option A

119. The possible number of energy states in a Ge crystal containing 5 x 10 atoms is
A) 2 x 10
B) 4 x 10
C) 4 x 10
D) 3 x 10
E) 5 x 10

120. A 𝑝𝑛 junction diode without any voltage biasing acts as a
A) rectifier
B) resistor
C) ac generator
D) voltage regulator
E) transformer

How many moles of methane are required to produce 11 g CO ( ) after combustion?
121.
(Molar mass of CO = 44 g mol )
A) 0.25
B) 0.5
C) 1.5
D) 2.0
E) 2.5

Correct Answer : Option A

A sub-atomic particle of mass 6.63 × 10 kg is moving with a velocity of 1 × 10 ms
122.
. What is the de Broglie wave length (in nm) associated with it (h = 6.63 × 10 Js)?
A) 10.0
B) 1.0
C) 0.10
D) 5.0
E) 0.50

For hydrogen atom, the orbitals with the lowest energy among the given orbitals are
123. (i) 4s (ii) 2p (iii) 3d 2 (iv) 2p
A) (i) & (iii)
B) (ii) & (iv)

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m
m .co

c. o C ) (ii) & (iii) s e m
m a
se D)
E)
(ii) only
(i) only ag l

Which of the following species will have the largest and the smallest sizes respectively?
124.
Na, Mg, Na , Mg
m
.co
A) Mg and Na
m
.co m
B) Mg and Mg

m s e
C)
s e
Na and Mg
l a
D)
g a
lMg
Na and Mg
ag
E)
a
Na and

125. Which of the following statement is INCORRECT?
A) The dipole moment of BF is zero.
B) The bond order of CO molecule is the same as the bond order in NO ion.
m
.co
C) In ozone molecule, the two O-O bond lengths are equal.
D) The dipole moment of 𝑁𝐹 is much greater than that in 𝑁𝐻
e m
E) Carbonate ion has three canonical forms.
las
ag
Correct Answer : Option D

In which of following reactions entropy decreases?

(i) 2Pb(NO ) ( ) → 2PbO( ) + 4NO ( ) + O ( )
126. (ii) H O( ) → H O( )
(iii) Br ( ) → 2Br( )
(iv) C H ( ) → C H ( ) m
A)
c o m(ii), (iii) and (iv) m.co
B .) e
m (i) and (iii)
e C ) (i) and (iii) l as
l as D ) (i) and (iv) ag
ag E ) (ii) and (iv)

The enthalpy of combustion values of C H ( ) , C(graphite,s) and H ( ) are

127. respectively -1411kJ mol , -394 kJ mol and -286 kJ mo . What is the value of
m .
.co
enthalpy of formation of C H ( ) in kJ mol ?
s e m
A) -102
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 31 of 37

B) -51
C) +102
D) +153
E) +51

The following concentrations were obtained in the formation of NH ( ) from N ( ) and
H ( ) at equilibrium at 500 K:
[NH ] =1.5 × 10 M, [N ] = 5 × 10 M and [H ] = 0.10 M
128.
Calculate the equilibrium constant for the reaction (in dm mol ) at 500 K.

N ( ) + 3H ( ) ⇋ 2NH ( )
A) 0.45
B) 4.5
C) 45.0
D) 4.5 × 10
E) 4.5 × 10

129. Which of the following is a Lewis acid?
A) HCl
B) HO
C) H O
D) Co
E) NH

Correct Answer : Option D

The EMF of the following cell at 298K is
130. Mg( ) │Mg (aq) (0.10M) ││ Ag (aq)(0.001M)│Ag( )
(Given: E =3.17V and 2.303RT/F = 0.06 V)
A) 3.32V
B) 2.96V
C) 3.02V
D) 3.17V
E) 3.47V

131. The electrolyte used in lead storage battery is
A) 10% H SO aqueous solution

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m
m .co

c. o B ) 60% H SO aqueous solution s e m
m a
se C) 38% H SO aqueous solution
ag l
D) 38% HCl aqueous solution
E) 60% HCl aqueous solution

132. The binary liquid mixture that has positive deviation from Raoult’s law is
A) Chloroform-Acetone
m
B)
m
Chloroethane-Bromoethane
.co
C) Phenol-Aniline
m .co s e m
D)
e
Benzene-Toluene
s l a
E)
la
Ethanol-Acetone
g ag
a

133. A first order reaction has a rate constant of 6.93 × 10 s at 300 K. What is the half
life period of the reaction in seconds at the same temperature?
A) 693
B) 6930
C) 10000
m
D) 1000
m .co
E) 500
s e
g la
Correct Answer : Option D
a
134. Which of the following is true in respect of a zero order reaction?
A) Plot of [Reactant] against time is a straight line with slope equal to k
B) Plot of [Reactant] against time is a straight line with slope equal to -k
C) Plot of [Reactant] against time is a straight line with slope equal to 2.303 k
D) Plot of [Reactant] against time is a straight line with slope equal to -2.303 k
E) Plot of [Reactant] against time is a straight line with slope equal to -k/2.303 m
m .co
m .coCorrect Answer : Option B
s e m
s e135. g l a stable state?
g la A ) Titanium
Which of the following 3d transition metal has +5 state as
a
the more
a
B) Vanadium
C) Manganese
D) Nickel
E) Silver

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 33 of 37

In acidic medium, dichromate behaves as an oxidizing agent which can be represented
as

136. Cr2O + xH + ye → 2Cr + zH O

The values of x, y and z are respectively
A) 6, 7 and 14
B) 7, 6 and 14
C) 14, 6 and 7
D) 14, 7 and 6
E) 6,12 and 7

137. Which of the following is not an interstitial compound?
A) Sc O
B) TiC
C) Mn N
D) TiH .
E) Fe H

Correct Answer : Option A

138. Which of the following transition metal has the highest magnetic moment?
A) Sc
B) Ti
C) Cr
D) Fe
E) Mn

139. Which of the following complex is optically active?
A) 𝑡𝑟𝑎𝑛𝑠 − [𝐶𝑟𝐶𝑙 (𝑜𝑥) ]
B) 𝑡𝑟𝑎𝑛𝑠 − [𝑃𝑡𝐶𝑙 (𝑒𝑛) ]
C) cis − [𝑃𝑡(𝑁𝐻 ) ]𝐶𝑙
D) 𝑡𝑟𝑎𝑛𝑠 − [𝑃𝑡(𝑁𝐻 ) ]𝐶𝑙
E) 𝑐𝑖𝑠 − [𝑃𝑡𝐶𝑙 (𝑒𝑛) ]

140. The number of bridging carbonyl groups in [Mn (CO) ] is

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m
m .co

c. o A ) 2 s e m
m a
se B)
C)
0
4 ag l
D) 3
E) 1

On complete combustion 0.12g of an organic compound gives 0.11g of CO . What is the
141. percentage of carbon in the organic compound?
m
m .co
.co
15%
A)
e m
B) 20%
em l as
C) 25%
l as ag
D)
E)
17.5%
21.5%ag

One mole of an alkene reacts with acidic KMnO to give two moles of ethanoic acid.
142. What is the alkene?
A) 2-Methylpropene
m
.co
B) 1-Butene
2-Pentene
C)
e m
D) 2-Butene
las
E) 2-Methyl-2-butene
ag
Correct Answer : Option D

143. Which of the following is a vicinal dihalide?
A) 1,1-Dibromopropane
B) 1,2-Dibromopropane
C) 1,3-Dibromopropane
m
.co
D) Benzal dibromide
m
.co m
E) 1,3-Dibromobutane
s e
s em Correct Answer : Option B g l a
g la a
a 144. S 1 reaction is most favoured by
A) Ethyl bromide
B) 2-methyl-2-bromopropane
C) 2-bromopropane
D) 1-bromopropane
E) 1-bromobutane

m .
.co m
s e
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 35 of 37

Phenol is treated with Con.𝐻 𝑆𝑂 to gives a product ‘X” which on treatment with Con.𝐻
145. 𝑁𝑂 gives compound ‘Y’. The compounds ‘X’ and ‘Y’ are respectively
A) Phenol-2- sulphonic acid and 2-nitrophenol
B) Phenol-2-sulphonic acid and 4-nitrophenol
C) Phenol-2-sulphonic acid, mixture of 2-nitrophenol and 4-nitrophenol
D) Phenol-2,4-disulphonic acid, mixture of 2-nitrophenol and 4-nitrophenol
E) Phenol-2,4-disulphonic acid and picric acid

146. Denatured alcohol with colour and foul smell is made now a days by mixing ethanol with
A) Methanol
B) ZnSO and thiophene
C) CuSO and pyridine
D) FeSO and furan
E) Fe (SO ) and hexane

147. Benzoyl chloride is converted to benzaldehyde by
A) Etard reaction
B) Stephen reaction
C) Gatterman reaction
D) Gatterman – Koch reaction
E) Rosenmund reaction

148. In which of the following liquid inter molecular hydrogen bonding does not exist?
A) 𝐶𝐻 𝐶𝑂𝑂𝐻
B) C H OH
C) Phenol
D) Diethylether
E) Ethylamine

Correct Answer : Option D

149. The IUPAC name of allylamine is
A) But-2-en-1-amine
B) But-1-en-2-amine
C) Prop-2-en-1-amine
D) Prop-1-en-2-amine
E) 2-Amino 1-propene

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C) cellulose
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E) glycogen
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