KEAM 2026: KEAM Engineering entrance (Mathematics, Physics and Chemistry), session 3
Text of page 1
FINAL ANSWER KEY
Question Paper Code: 9/2026/OL
Exam:KEAM 2026 - 3
Date of Test: 19-04-2026
Let � = {�� , �� , �� , . . . , �� } be a set consisting of � elements. The relation �=
1. {(�� , �� ), (�� , �� ), (�� , �� ), . . . , (�� , �� )} on the set � is
A) reflexive, symmetric but not transitive
B) reflexive, transitive but not symmetric
C) transitive, symmetric but not reflexive
D) reflexive, symmetric and transitive
E) reflexive, not symmetric and not transitive
Correct Answer : Option D
Let � = {�, �, �, �, �, �} and � = {7, 8, 9, 10, 11} be two sets. Which one of the
2. following is true?
A) {(�, 8), (�, 7), (�, 9), (�, 10), (�, 11)} is an one-to-one function from � to �
B)
{(�, 7), (�, 11), (�, 8), (�, 10), (�, 9), (�, 11)}is an one-to-one function from � to �
C) {(�, 7), (�, 8), (�, 9), (�, 10), (�, 11)}is an one-to-one function from � to �
D) {(�, 11), (�, 10), (�, 9), (�, 8), (�, 7)(�, 9)} is an one-to-one function from � to �
E) one-to-one function cannot be defined from � to �
Correct Answer : Option E
�� � �
3. Let, �(�) =
���
, � ϵ ℝ, � ≠ 2 and ℎ(�) = �(�(�)) .Then ℎ(ℎ(10)) is equal to
A) 100
B) 20
C) 10
D) 1000
E) 1
Correct Answer : Option C
4. The inverse of the function �(�) = � � + 4� + 4, � ≤ − 2 is �
��
(�) =
A) −2 − √�, � ≥ 0
B) −2 − √� − 1, � ≥ 1
C) −2 − √�, � ≥ 2
D) −2 − √�, � ≥ 4
E) −2 − √�, � ≥ 5
Text of page 2
Correct Answer : Option A
�
5. Given that � = − 1 . Then � �� + � �� + � �� + . . . + � ���� is equal to
A) �−2
B) �+2
C) 2� + 1
D) �−1
E) −� + 1
Correct Answer : Option D
Let � and � be real numbers. If (3 + �)� + � + (1 − �)� + 3� − 4 = (2� + 1)� + (
6. � − � + 2)� , where � = √−1 , then the pair �, � is equal to
A) (1,2)
B) (0,2)
C) (0,-2)
D) (3,2)
E) (-1,-2)
Correct Answer : Option B
� � �� � � �� � � ���
Let �� = , �� = and �� = . Then �� �―� + �� �―� + �� �―� is equal
7. � � �� � � �� �� � �
to
A) 2
B) 1+2�
C) 1
D) 3
E) 1-2�
Correct Answer : Option D
(� � �) �
8. The value of , where � = √−1 and � is an integer,
(� � �) � � �
��
A)
�
B) 4� �
C) −4� �
D) -1
E) 1
Correct Answer : Option C
9. The number of terms in the sequence 2,6,18,...,1458 is
A) 14
Text of page 3
B) 12
C) 10
D) 8
E) 7
Correct Answer : Option E
10. Let �� , �� , �� , . . . , ��� � � , ��� � � , ��� be in G.P. with common ratio � . Then
A) �� , �� , �� , . . . , ��� � � , ��� � � , ��� � � are in G.P. with common ratio �
B) �� , �� , �� , . . . , ��� � � , ��� � � , ��� � � are in G.P. with common ratio � �
C) �� , �� , �� , . . . , ��� � � , ��� � � , ��� � � are in G.P. with common ratio � �
D) �� , �� , �� , . . . , ��� � � , ��� � � , ��� are in G.P. with common ratio � �
E) �� , �� , �� , . . . , ��� � � , ��� � � , ��� are in G.P. with common ratio � �
Correct Answer : Option C
� � � � � �� � � �
11. If
� � � �� �
is the Geometric Mean between 4 and 16, then the value of � is
�
A)
�
�
B)
�
C) 10
��
D)
�
E) 8
Correct Answer : Option D
The first and last term of a G.P. are 7 and 448 respectively. If the sum is 889, then the
12. common ratio is
A) 4
B) 2
�
C)
�
�
D)
�
E) 3
Correct Answer : Option B
There are two main entrances to a building with five floors. Each entrance leads to three
13. lifts and each lift can stop at all the five floors. A person enters the building and reaches a
floor. The number of possible ways that the person can reach the floor, is
A) 15
B) 25
Text of page 4
C) 10
D) 30
E) 50
Correct Answer : Option D
�
14. If 9�� = (504)( �� ) , then the value of � is equal to
A) 3
B) 2
C) 1
D) 4
E) 5
Correct Answer : Option B
15. The sum of all 3-digit numbers that can be formed using 1, 2, 3, 4 without repetitions is
A) 6668
B) 8886
C) 12486
D) 9876
E) 6660
Correct Answer : Option E
A box contains 24 identical balls of which one ball is black and the remaining balls are
16. green. Three balls are taken simultaneously and randomly. The number of ways of
getting only green balls, is
A) 1765
B) 1764
C) 1763
D) 1771
E) 1864
Correct Answer : Option D
� � �
17. The coefficient of
� � in the binomial expansion of �3� − � , is
��
�
A)
�
�
B)
�
�
C)
�
�
D)
�
��
E)
�
Text of page 5
Correct Answer : Option E
18.
A) -2
��
B)
�
C) -3
�
D)
�
��
E)
�
Correct Answer : Option D
19.
A) �
B) ��
C) � , the unit matrix of order 3
D) −� �
E) 2� �
Correct Answer : Option C
20.
A) 7100
B) 6800
C) 7300
D) 6900
E) 6700
Correct Answer : Option A
0 1⎤ � �
If � = ⎡ and (α � + β �) = � where � is 2 × 2 unit matrix,then α � − β
21. ⎣−1 0⎦
=
A) 2
B) -2
Text of page 6
C) -1
D) 1
E) 0
Correct Answer : Option E
22. Let � be a real number such that 5 < | � − 1 | < 15 . Then
A) −18 < � < − 3 � r 3 < � < 19
B) −14 < � < − 3 � r 6 < � < 17
C) −16 < � < − 2 � r 6 < � < 20
D) −14 < � < − 4 � r 6 < � < 16
E) −10 < � < − 1 � r 3 < � < 18
Correct Answer : Option D
���
23. Let � be a real number such that
���
≥ 1 . Then the solution set of the inequality is
A) ( − ∞, 3)
B) ( − ∞, 2)
C) [0, ∞)
D) ( − 9, ∞)
E) (0, 8)
Correct Answer : Option B
24. If ��� θ ��� θ > 0 , then θ lies
A) only in the first quadrant
B) only in the second quadrant
C) in the first quadrant or in the fourth quadrant
D) in the second quadrant or in the fourth quadrant
E)
in the first quadrant or in the third quadrant
Correct Answer : Option E
�
If 4��� �� − 2(1 + √3)���� + √3 = 0 and 15 < � < 150 � , then the values
25. of � are
A) 30o,45o,90o
B) 45o,100o,120o
C) 30o,60o,120o
D) 35o,45o,90o
E) 30o,45o,130o
Text of page 7
Correct Answer : Option C
� � �
26. If ��� α =
�
and ��� β =
��
, where 0 < α , β <
�
then α + β =
�
A)
�
�
B)
�
�
C)
�
�
D)
�
��
E)
�
Correct Answer : Option D
� � �
27. The value of ���6 ���36 ���66 + ���12 ����42 ����18 � is equal to
�
A) (���18 � + ���36 �)
��
�
B) (���18 � + ���36 �)
�
�
C) (���18 � + ���36 �)
��
�
D) (���18 � + ���36 �)
�
�
E) (���18 � + ���36 �)
�
Correct Answer : Option D
�
28. The domain of the function �(�) = 2��� ��(2� − 1) − is
�
A) [-1,1]
B) [0,1]
C) [0,2]
D) [2,5]
E) [-2,2]
Correct Answer : Option B
�� � � ��
29. The value of ��� ������ ��� + ��� ��� � is equal to
� � � �
��
A)
�
�
B)
�
�
C)
�
Text of page 8
�
D)
�
�
E)
�
Correct Answer : Option D
�
30. The value of ��� �2��� �� � is equal to
�
��
A)
��
��
B)
��
��
C)
��
��
D)
��
��
E)
��
Correct Answer : Option D
��
Let � = � (����� θ + ��� θ ), 8(����� θ − ��� θ )� , where θ is a variable
31. �
parameter. Then the locus of � is
�� ��
A) − =1
�� ��
�� ��
B) − =1
��� ���
�� ��
C) + =1
��� ���
�� ��
D) − =1
��� ���
�� ��
E) + =1
�� ��
Correct Answer : Option D
A straight linemakes � -intercept of 5. If the angle made by the line with �-axis is 60o and
32. the line intersects �-axis in the negative direction,then the equation of the line is
A) � + √3� + 5√3 = 0
B) � − √3� + 5√3 = 0
C) √3� − � + 5 = 0
D) √3� + � + 5 = 0
E) √3� − � + 5√3 = 0
Correct Answer : Option B
Text of page 9
The perpendicular drawn from the origin to the straight line √3� + � − 24 = 0 makes
33. an angle α with the positive direction of x-axis. Then α is equal to
A) 120o
B) 45o
C) 135o
D) 60o
E) 30o
Correct Answer : Option E
If the one end of a diameter of the circle � � + � � + 3� + � − 6 = 0 is at (-4,-2) , then
34.
the other end of the diameter is at
A) (4,-2)
B) (1,-1)
C) (1,1)
D) (-1,-1)
E) (1,-2)
Correct Answer : Option C
The vertex of a parabola is at (2,-5) and the focus is at (5,-5). The equation of the
35. parabola is
A) � � + 10� − 10� + 49 = 0
B) � � + 10� − 12� + 49 = 0
C) � � + 10� − 12� + 46 = 0
D) � � + 8� − 12� + 49 = 0
E) � � + 10� − 18� + 48 = 0
Correct Answer : Option B
(� � �) � (� � �) �
Let �( − 2, − 2) be a point and let + = 1 be an ellipse. If � and �
36. �� ��
are the foci of the ellipse, then �� + �� is equal to
A) 128
B) 61
C) 12
D) 10
E) 124
Correct Answer : Option D
37. The equation of the latus rectum of the parabola � � + 8� + 4� + 12 = 0 is
A) �+3=0
B) �+3=0
C) �+1=0
Text of page 10
D) �+2=0
E) �+2=0
Correct Answer : Option A
→ → → →
Let � be the origin. Let �� = � and �� = � be the position vectors of the points
38. � and � respectively. A point � divides the line segment �� internally in the ratio �: �
→
. Then �� is equal to
→ →
��(� � � )
A)
���
→ →
�(� � � )
B)
���
→ →
�(� � � )
C)
���
→ →
�(� � � )
D)
���
→ →
�(� � � )
E)
���
Correct Answer : Option D
^ ^ ^
^ − ^� + � = �(3�^ − 4�^ − 4�) + �(�^ − 3�^ − 5�) , where � and � are scalars,
If 2�
39.
then 3� + 5� is equal to
A) 2
B) -4
C) -2
D) 6
E) 14
Correct Answer : Option C
→ ^ ,→
2�^ − 2�^ + 4�
Let � = � = − 5�^ − ^� + 8� ^ and → � . If →
� = 3�^ + ^� − λ ^ �+
40. → → →
� + � and →
� − � +→ � are perpendicular, then the values of λ are
A) 4 and -12
B) -2 and 12
C) -6 and 14
D) -3 and 12
E) -4 and 12
Correct Answer : Option E
→ → → → ^ → →
41. ^ + ^� − 4� ,then � . � =
If |� | = √26, | � | = √3 and � × � = 5�
A) ±12
B) ±4
Text of page 11
C) ±10
D) ±8
E) ±6
Correct Answer : Option E
→
Consider the straight line � = (5�
^ ^
^ + 2�^ − 3�) + �(4�^ + 6�^ − 7�), t ϵ ℝ. Which
42.
one of the following points, is a point on the straight line?
A) (21,24,-31)
B) (17,20,-22)
C) (1,-4,5)
D) (25,32,-38)
E) (45,66,-36)
Correct Answer : Option D
�� � �
The equation of a line passing through (-1,2,-4) and parallel to the straight line =
�
43. �� � � �� � �
= , is
�� �
A) → ^) + �(4�^ + 6�^ − 7�
� = ( − ^� + 2�^ − 4� ^), � ϵ ℝ
B) → ^) + �(3�^ + 5�^ − 2�
� = ( − ^� + 2�^ − 4� ^), � ϵ ℝ
C) → ^) + �(8�^ + ^� + 6�
� = ( − ^� + 2�^ − 4� ^), � ϵ ℝ
D) → ^) + �(7�^ + 6�^ + 6�
� = ( − ^� + 2�^ − 4� ^), � ϵ ℝ
E) → ^) + �(8�^ + ^� + 6�
� = ( − ^� + 2�^ − 6� ^), � ϵ ℝ
Correct Answer : Option C
→
A straight line passes through the point whose position vector is � . The straight line
44. →
also passes through the point of intersection of the lines � = ^
→
� + λ ^� , λ ϵ ℝ and � = ^�
+ ��^, � ϵ ℝ . Then the equation of the straight line is
A) →
� =^
� + �(�^ + ^� − ^
�), � ϵ ℝ
B) →
� =^
� + �(�^ − ^� − ^
�), � ϵ ℝ
C) →
� =^
� + �(�^ − ^� + ^
�), � ϵ ℝ
D) →
� =^ ^), � ϵ ℝ
� + �( − ^� + ^� + 2�
E) →
� =^
� + �( − ^� + 2�^ − ^
�), � ϵ ℝ
Correct Answer : Option A
The shortest distance between the lines
→ ^, � ϵ ℝ and →
� = − ^� + �� � = − ^� + ��^, �
45.
ϵ ℝ , is
Text of page 12
A) 8
B) 5
C) 3
D) 4
E) 1
Correct Answer : Option E
46. The mean deviation about the mean for the data: 5, 6, 14, 15 is
A) 3.5
B) 4.5
C) 4.2
D) 3.8
E) 4.0
Correct Answer : Option B
47. The variance for the data : 65, 70, 75 is
��
A)
�
��
B)
�
��
C)
�
��
D)
�
E) 70
Correct Answer : Option A
48. A fair die is rolled once. Which one of the following is not true?
A) {1, 3} and{2, 4, 6} are mutually exclusive events
B) {1, 5},{2, 4} are {3, 6} mutually exclusive and exhaustive eve nts
C) {1, 2, 4, 3, 6, 5}is sure event
D) {1},{2} and {6} are elementary events
E) {1, 3, 2}and {2, 4, 6} are mutually exclusive events
Correct Answer : Option E
Let �, �, � be all the three possible mutually exclusive events of a random experiment.
49. Which one of the following is not permissible in terms of their probabilities?
� � �
A) �(�) = , �(�) = , �(�) =
�� �� ��
�� �� ��
B) �(�) = , �(�) = , �(�) =
�� �� ��
�� �� ��
C) �(�) = , �(�) = , �(�) =
��� ��� ���
Text of page 13
�� �� ��
D) �(�) = , �(�) = , �(�) =
�� �� ��
�� �� ��
E) �(�) = , �(�) = , �(�) =
��� ��� ���
Correct Answer : Option E
��� ��
50. The value of lim is equal to
� → � � � ����
A) 4
B) 2
�
C)
�
�
D)
�
E) 0
Correct Answer : Option B
���
51. The value of lim is equal to
� → � �√� � �
A) 3
�
B)
�
C) 2
�
D)
�
E) 0
Correct Answer : Option E
52.
A) 6
B) 8
C) -6
D) 7
E) -7
Correct Answer : Option D
�� � ���(� �)
53. The value of lim
� � ����
is equal to
�→�
�
A)
√�
B) √2
Text of page 14
�
C)
�√�
D) 2√2
E) 0
Correct Answer : Option B
���� (� � �)
54. The domain of the function �(�) =
� � � �� � �
, is
A) (1, ∞)
B) (10, ∞)
C) (5, ∞)
D) ℝ\{ − 4}
E) ℝ\{ − 4, 1}
Correct Answer : Option C
55. Which one of the following is not true?
A) �(�) = � | �| is differentiable in (-1,1)
B) �(�) = �|�| is differentiable in (4,5)
C) ℎ(�) = | � − 2 | + | � + 3| is differentiable in (3,2)
D) �(�) = | � + 1 | + | � − 6| is differentiable in (-1,6)
�(�) = � + [�], [�] is the greatest integer less than or equal to � , is differentiable at �
E)
=0
Correct Answer : Option E
�� � � �� � � � ��
56. Let � =
|�|
, � ≠ 0 . Then at � = − 2 is equal to
��
A) 14
B) -12
C) -14
D) 12
E) 10
Correct Answer : Option A
�
��
57. If (3 + 5�)� � = � , then is equal to
��
� �
A) log | | +
� � �� � � ��
� �� � �
B) log | | +
� � �� � � ��
� �� � �
C) log | | +
� � �� � � ��
�� ��� � �
D) log | | +
� � �� � � ��
Text of page 15
� � � ���
E) log | | +
� � �� � � ��
Correct Answer : Option A
�� � � �� ��
58. If � = � , then at
�� �
+ 2�
��
=
A) 2�
B) −2�
��
C)
�
D) −�
E) �
Correct Answer : Option B
�
Let �(�) and �(�) be two differentiable functions such that � (�) = �(�) and � �(�
59. ) = − �(�) .
�
Let ℎ(�) = (�(�)) + (�(�)) � and ℎ(3) = 100 .Then ℎ(100) is equal to
A) 100
B) 10
C) 50
D) 200
E) 300
Correct Answer : Option A
Let � and � be differentiable real valued functions on [0, ∞) . If � is increasing, � is
60. decreasing and ℎ(�) = �(�(�)) , then ℎ(2026) − ℎ(2025) is
A) greater than 1000 but less than 2000
B) greater than or equal to 0
C) less than or equal to 0
D) greater than 2025
E) greater than 2026
Correct Answer : Option C
�
Let �(�) = 10� � + ��, � ϵ ℝ be such that � � − 400 < 0. Let �(�) = �(�) + �
61.
(�) + �"(�) . Then �(�) is
A) greater than 100 but less than 200
B) greater than 10 but less than 100
C) less than 10
D) greater than 0
E) less than 1
Text of page 16
Correct Answer : Option D
� ��� � �
62. The minimum of �(�) =
� ��� � �
, � ϵ ℝ , is
A) -5
B) -1.5
C) -1
D) -2
E) -3
Correct Answer : Option C
63. Let �(�) = 1 + ����(� + √� � + 1) − √� � + 1, � ≥ 0 . Then
A) �(�) is increasing on (0, ∞)
B) �(�) is increasing only on (10, ∞)
C) �(�) is increasing only on (0, �)
D) �(�) is decreasing on (0, ∞)
E) �(�) is decreasing only on (100, ∞)
Correct Answer : Option A
���(��� ���)
64. ∫
� � ��
�� is equal to
��
A) −���(��� �) + �
B) ���(��� ���) + �
���(��� ���)
C) +�
� � ��
���(��� ���)
D) +�
�
����(��� ���)
E) +�
� � ��
Correct Answer : Option B
�
65. ∫ �1 + ���( � )�� =
� �
A) 16���( ) − 16���( ) + �
�� ��
� �
B) 16���( ) − 16���( ) + �
�� ��
� �
C) 16���( ) + 16���( ) + �
�� ��
� �
D) 16���( ) + 16���( ) + �
�� ��
� �
E) 8���( ) − 8���( ) + �
�� ��
Text of page 17
Correct Answer : Option B
� �
66. ∫ � (� � �) � − (� � �) � �� ��� is equal to
��
A) +�
(� � �) �
�
B) +�
(� � �) �
�
C) +�
(� � �) �
��� �
D) +�
(� � �) �
��
E) +�
(� � �) �
Correct Answer : Option E
�� � �
67. ∫ � � � �� is equal to
�� �� ��
A) + + +�+�
� � �
�� �� ��
B) + + + 2� + �
� � �
�� �� ��
C) − + −�+�
� � �
�� �� ��
D) − + − 2� + �
� � �
�� �� ��
E) − − − −�+�
� � �
Correct Answer : Option C
���� � ����
68. ∫ � �� � ������� ��� is equal to
� � � �(���� � ����)
A) ��� | | +�
�� � � �(���� � ����)
� � � �(���� � ����)
B) ��� | | +�
�� � � �(���� � ����)
� � � �(���� � ����)
C) ��� | | +�
�� � � �(���� � ����)
� � � �(���� � ����)
D) ��� | | +�
�� � � �(���� � ����)
� � � �(���� � ����)
E) ��� | | +�
�� � � �(���� � ����)
Correct Answer : Option A
Text of page 18
69.
A) 6
B) 12
C) 18
D) 4
E) 24
Correct Answer : Option B
70.
A)
B)
C)
D)
E)
Correct Answer : Option A
71.
�
A)
�
B) 2π
�
C)
�
D) 1
E) 4π
Correct Answer : Option C
72.
�
A)
��
�
B)
��
�
C)
��
Text of page 19
�
D)
��
�
E)
��
Correct Answer : Option C
Elimination of arbitrary constants � and � from � = �� � + �� ��� gives the
73.
differential equation
� �� ��
A)
� + − 2� = 0
�� ��
� �� ��
B)
� + + 2� = 0
�� ��
� �� ��
C)
� − − 2� = 0
�� ��
� �� ��
D)
� −2 +�=0
�� ��
� �� ��
E)
� +2 +�=0
�� ��
Correct Answer : Option A
74. The solution of the differential equation (� + 2�)�� + (2� − �)�� = 0 is
A) � � − � � + 6�� = �
B) � � − � � − 4�� = �
C) � � − � � + 4�� = �
D) � � − � � + 3�� = �
E) 2� � − � � + 4�� = �
Correct Answer : Option C
Consider the Linear Programming Problem (LPP): Maximize � = 30� + 60� subject to
75. the constraints � + 2� ≤ 12; 2� + � ≤ 12; 4� + 5� ≥ 20; � ≥ 0; � ≥ 0. . Then
the number of corner points of the feasible region is
A) 8
B) 6
C) 3
D) 4
E) 5
Correct Answer : Option E
76. The physical quantity that doesn’t have appropriate unit is
��
A) Compressibility -� ��
B) Latent heat - ��� ��
Text of page 20
C) Intensity - �� ��
D) Energy density - �� ��
E) Impulse - ��
Correct Answer : Option D
In the equation A = B/CD2 , if B, C and D have the dimensions of inductive reactance,
77. capacitive reactance and angular frequency respectively, then the dimensions of A are
A) M0LT2
B) ML0T2
C) M0L0T2
D) M-1L0T -2
E) M0L0T -2
Correct Answer : Option C
The position of a particle moving along � - axis is given as � = � � + 2� + 3 metre.
78.
The average acceleration of the particle between � = 3 s and � = 6 s (in ms-2) is
A) 2
B) 5
C) 4
D) 3
E) 6
Correct Answer : Option A
79. The ratio of distances traversed by a freely falling body in successive intervals of time is
A) 3:4:6:9
B) 1:3:6:9
C) 1:2:4:6
D) 2:5:7:9
E) 1:3:5:7
Correct Answer : Option E
^ ^
^ + 3�^ + 2� and 2�^ − 3�^ + 4� is 9, then the
If the scalar product of two vectors ��
80.
value of � is
A) 9
B) 5
C) 6
D) 1
E) 2
Correct Answer : Option B
Text of page 21
81. Among the following the INCORRECT statement is
A) Newton’s second law relates the net external force to its acceleration.
B) Impulse is equal to the change in momentum.
C) Newton’s second law is inconsistent with Newton’s first law.
Same force acting on different bodies for the same time brings the same change in
D)
momentum.
E) Action and reaction act on different bodies.
Correct Answer : Option C
A ball of 200 g mass moving with a speed of 5 ms-1collides with a wall and bounces back
82. with the same speed. If the force exerted on the wall is 1 N, then the ball is in contact with
the wall for
A) 2s
B) 1s
C) 0.5 s
D) 1.5 s
E) 0.75 s
Correct Answer : Option A
A block of 10 kg mass moving on a frictionless surface moving with 5 ms-1 compresses
83. the spring by 5 cm and comes to rest. The force constant of the spring
(in Nm-1) is
A) 2 × 10 �
B) 2.5 × 10 �
C) 3 × 10 �
D) 1.5 × 10 �
E) 1 × 10 �
Correct Answer : Option E
If a gun fires 25 bullets in one second, each of 10 g mass with a velocity of 20 ms-1, then
84. the recoil force on the gun in N is
A) 50
B) 5
C) 15
D) 10
E) 20
Correct Answer : Option B
The angular momentum of a uniform rod of mass m and length l, rotating in a horizontal
85. circle about one of its ends with an angular velocity ω is
A) �� � ω
Text of page 22
�
B) �� � ω
�
�
C) 2�� ω
�
D) �� � ω
�
�
E) �� � ω
�
Correct Answer : Option D
The moment of inertia of a solid sphere of radius 20 cm about its diameter is same as
86. that of a solid cylinder of same mass about its axis, then the radius of the cylinder in cm
is
A) 3 √5
B) 5√5
C) 2√5
D) 8√5
E) 7√5
Correct Answer : Option D
The maximum and minimum distances of a satellite revolving in an elliptical orbit are in
87. the ratio 3:1 . If the speed of the satellite at the nearest distance is � , then the speed at
the farthest distance is
�
A)
�
B) 3�
�
C)
�
D) 6�
E) 9�
Correct Answer : Option C
The ratio of the magnitudes of gravitational potential energy to that of kinetic energy of an
88. earth satellite of mass m revolving in any orbit is
A) 1:2
B) 2:1
C) 2:3
D) 1:3
E) 3:1
Correct Answer : Option B
89. Which one of the following materials has the highest modulus of elasticity?
A) steel
B) aluminium
Text of page 23
C) copper
D) glass
E) brass
Correct Answer : Option A
Two capillary tubes of radii in the ratio 1:2 are dipped in the same liquid. The ratio of
90. heights through which the liquid will rise in the tubes is
A) 1:1
B) 1:2
C) 1:4
D) 4:1
E) 2:1
Correct Answer : Option E
�
91. The relative viscosity of blood ( ) is constant between
� �����
A) 10 ⁰C and 47 ⁰C
B) 0 ⁰C and 47 ⁰C
C) 0 ⁰C and 37 ⁰C
D) 30 ⁰C and 40 ⁰C
E) 20 ⁰C and 47 ⁰C
Correct Answer : Option C
92. There is no change in internal energy of an ideal gas in an
A) isothermal process
B) adiabatic process
C) isobaric process
D) isochoric process
E) both in adiabatic process and isobaric process
Correct Answer : Option A
93. Which one is not an extensive variable?
A) total mass
B) internal energy
C) volume
D) density
E) workdone (PdV)
Correct Answer : Option D
Experimental P-V curves and theoretically predicted P-V curves are in good agreement
94. at
A) high temperature and high pressure
Text of page 24
B) high temperature and low pressure
C) low temperature and high pressure
D) low temperature and atmospheric pressure
E) low temperature and low pressure
Correct Answer : Option B
95. The mass of one molecule of water is approximately
A) 8 × 10 ��� kg
B) 6.5 × 10 ��� kg
C) 3.5 × 10 ��� kg
D) 2.5 × 10 ��� kg
E) 3 × 10 ���kg
Correct Answer : Option E
If the instantaneous displacement of a wave is � = 2(���2π � + √3���2π �)� m,
96.
then the amplitude of the wave in cm, is
A) 4
B) 3
C) 5
D) 2
E) 6
Correct Answer : Option A
The equation of a transverse wave in a string, � = 3���2π (25� + 0.4� )m . The
97.
wavelength of the wave is
A) 4.5 m
B) 3m
C) 2.5 m
D) 3.5 m
E) 6.5 m
Correct Answer : Option C
If a spherical conductor of 10 cm radius contains 5 x 106 electrons, then the electric field
98.
on its surface (in NC-1) is
A) 0.86
B) 0.36
C) 0.45
D) 1.44
E) 0.72
Text of page 25
Correct Answer : Option E
When a capacitor of 9 pF is connected to a battery, the electrostatic energy stored in the
99. capacitor is 18 x 10-8 J. The quantity of charge stored in the capacitor is
A) 1.2 nC
B) 1.8 nC
C) 2.7 nC
D) 3.6 nC
E) 2.4 nC
Correct Answer : Option B
If the electric potential is given by � = 3� � + 4� volt, then the magnitude of the electric
100. field at the point � = 1� is
A) 6�� ��
B) 4�� ��
C) 8�� ��
D) 10�� ��
E) 12�� ��
Correct Answer : Option D
101. Which one of the following statements is CORRECT?
A) The molecules of air are non-polar.
B) In a polar molecule, centres of positive and negative charges coincide.
C) A molecule of water is an example of a non-polar molecule.
D) Dielectrics are conducting substances.
E) In a non-polar molecule, centres of positive and negative charges coincide.
Correct Answer : Option E
If the drift velocity of electrons in a copper wire of cross-sectional area 2 mm2 carrying
102. current � is �� and that in another copper wire of cross-sectional area 1.5 mm2 carrying
current 2� is �� , then the ratio �� : �� is
A) 3:8
B) 2:4
C) 8:3
D) 4:2
E) 1:3
Correct Answer : Option A
A uniform metallic wire of radius r and length l is heated by passing a current through it.
103. The heat produced can be made 8 times if
Text of page 26
A) l is doubled
B) both l and r are halved
C) l is doubled and r is halved
D) r is doubled
E) both l and r are doubled
Correct Answer : Option C
Two cells each of 2 V and internal resistance 0.1 Ω are connected in parallel
104. combination. This combination is equivalent to a single cell with emf and internal
resistance of
A) 1 V and 0.05 Ω
B) 2 V and 0.05 Ω
C) 2 V and 0.1 Ω
D) 4 V and 0.05 Ω
E) 4 V and 0.1 Ω
Correct Answer : Option B
When a bar magnet placed parallel to the magnetic field is rotated by 45⁰, the amount of
105. work done is 2.07 J. The amount of work to be done to rotate the magnet further by 45⁰ is
A) 2.07 J
B) 3J
C) 4.41 J
D) 5J
E) 6.21 J
Correct Answer : Option D
Two charged particles 2q and q having equal momentum enter a uniform magnetic field
106. in a direction perpendicular to the magnetic field. Then their respective radii of circular
paths r1 and r2 are in the ratio
A) 2:1
B) 1:4
C) 1:2
D) 1:3
E) 4:1
Correct Answer : Option C
A wire of certain length carrying current I, when bent into a circular coil of single turn
107. produces a magnetic field B at its centre. If the same wire is bent into a circular coil of 3
turns and it carries the same current, then the magnetic field at the centre of the coil is
A) 12 B
B) 3B
C) 6B
D) 9B
E) 15 B
Text of page 27
Correct Answer : Option D
For an electron of mass �� and charge � revolving around the nucleus of an atom, the
108.
ratio of its angular momentum to magnetic moment is
�
A)
��
�
B)
���
��
C)
��
�
D)
���
E) ���
Correct Answer : Option B
If an air core solenoid with self-inductance of 0.5 mH is filled with soft iron of relative
109. permeability of 1500, its self-inductance becomes
A) 0.5 H
B) 1.5 H
C) 0.25 H
D) 1.25 H
E) 0.75 H
Correct Answer : Option E
110. The r.m.s current of an alternating current given by, � = 4 2��� ω � + 3 2��� ω �
√ √
is
A) 5�
B) 3�
C) 5√2�
D) 2.5�
E) 7√2�
Correct Answer : Option A
The law that is a symmetrical counterpart of Faraday’s law of electromagnetic induction
111. is
A) Ampere-Maxwell law
B) Gauss law
C) Lenz’s law
D) Ampere’s circuital law
E) Coulomb’s law
Correct Answer : Option A
Text of page 28
A real object is placed at distance of � in front of a convex mirror of focal length�. The
112. image will be formed at a distance
A) 2�
�
B)
�
C) �
�
D)
�
�
E)
�
Correct Answer : Option E
113. The magnifying power of a simple microscope can be increased by using
A) diverging lens of large radius of curvature
B) converging lens of small focal length
C) diverging lens of small focal length
D) converging lens of large focal length
E) diverging lens of large focal length
Correct Answer : Option B
The intensity of the transmitted light after passing through a first polaroid P1 is �� . If the
114. second polaroid P2 is rotated through an angle of 45⁰ with respect to P1, then the change
in the intensity of the transmitted light after passing through the second polaroid is
��
A)
�
��
B)
�
���
C)
�
��
D)
�
���
E)
�
Correct Answer : Option A
The order of the electric field required to pull out electrons from a metal by field emission
115. (in Vm-1) is
A) 102
B) 108
C) 105
D) 106
E) 104
Text of page 29
Correct Answer : Option B
If the threshold wavelengths of two metals are in the ratio 1:3 , then the work functions of
116. these metals are in the ratio
A) 1:3
B) 2:1
C) 3:1
D) 1:2
E) 3:2
Correct Answer : Option C
�
117. The radius of innermost orbit of an electron in the hydrogen atom is 0.53 �. Then, the
radius of the 3rd electron orbit is
�
A)
1.59 �
�
B)
2.38 �
�
C)
0.53 �
�
D)
4.77 �
�
E)
9.54 �
Correct Answer : Option D
235
118. The energy released by 2.35 g of U by fission in a nuclear reactor (in MeV) is
(Average energy released per fission is 200 MeV)
A) 1.2 × 10 ��
B) 0.4 × 10 ��
C) 0.6 × 10 ��
D) 0.8 × 10 ��
E) 2.4 × 10 ��
Correct Answer : Option A
119. In a silicon crystal containing N atoms, at absolute zero the 4 N energy states of
A) both the valence band and conduction band are completely occupied
B) the valence band is completely occupied and the conduction band is completely empty
C) both the valence band and conduction band are completely empty
D) the valence band is completely occupied and the conduction band is partially occupied
E) the valence band is completely empty and the conduction band is completely occupied
Correct Answer : Option B
Text of page 30
The rate of fall of the voltage across the capacitor in a filter used in a diode rectifier
120. depends
A) upon the difference of the capacitive reactance and load resistance
B) inversely only on the capacitance
C) directly on the product of the capacitance and load resistance
D) upon the sum of the capacitive reactance and load resistance
E)
on the inverse of the product of the capacitance and effective load resistance
Correct Answer : Option E
What is the volume of methanol needed for making 2 L of 0.4 M solution? (Density of
121. methanol = 0.64 kgL-1 and molar mass = 32 g mol-1)
A) 20 mL
B) 4 mL
C) 40 mL
D) 10 mL
E) 80 mL
Correct Answer : Option C
The minimum energy required to remove an electron from sodium atom is 3.313 × 10-19
122. J. What is the maximum wavelength of radiation that will eject photoelectron from sodium
metal? [h = 6.626 × 10-34 Js]
A) 400 nm
B) 500 nm
C) 700 nm
D) 200 nm
E) 600 nm
Correct Answer : Option E
Which of the following statements are correct about the postulates of quantum
mechanical model of an atom?
(i) The energy of electron in atom is quantized.
(ii) The existence of quantized electronic energy level is a result of the particle property of
electrons.
123. (iii) The path of the electron can be determined accurately.
(iv) In a multi electron atom, the electrons are filled in various orbitals in the order of
increasing energy.
(v) The probability of finding an electron at a point within an atom is proportional to the
square of the orbital wave function.
A) (i), (iv), (v)
B) (i), (ii), (iv)
C) (i), (iii), (v)
D) (ii), (iii), (v)
E) (i), (ii), (v)
Text of page 31
Correct Answer : Option A
Which of the following pair of elements have greater ability to form �� − �� multiple
124. bonds?
A) Carbon and Oxygen
B) Boron and Aluminium
C) Nitrogen and Phosphorus
D) Fluorine and Chlorine
E) Carbon and Silicon
Correct Answer : Option A
Which of the following statements are true about electronegativity?
(i) Electronegativity generally increases across a period and decreases down a group.
125. (ii) The electronegatitivity of a given element is constant.
(iii) The electronegativity values decreases with the increase in atomic radii.
(iv) Elecronegativity is directly related to the metallic property of the elements.
(v) Electronegativity is inversely related to the non-metallic property of the elements.
A) (i) and (iv)
B) (ii) and (iii)
C) (i) and (iii)
D) (iv) and (v)
E) (ii) and (v)
Correct Answer : Option C
Which of the following statements are correct about the PCl5 molecule?
(i) It has trigonal bipyramidal geometry.
(ii) It has three equatorial and two axial bonds.
126. (iii) The equatorial bond pairs suffer more repulsive interaction from the axial bond pair.
(iv) The equatorial bonds are slightly weaker than axial bonds.
(v) The hybridization involved in the molecule is sp3d.
A) (i), (ii), (iv)
B) (ii), (iii). (iv)
C) (i),(ii),(iii).
D) (ii), (iv),(v)
E) (i), (ii), (v)
Correct Answer : Option E
127. The geometry of a molecule of type AB3E2 with 3 bonding pairs and 2 lone pairs is
A) T-shape
B) trigonal pyramidal
C) trigonal bi-pyramidal
D) square pyramidal
E) see saw
Text of page 32
Correct Answer : Option A
The enthalpy of combustion of benzene, graphite and dihydrogen at 298 K are -3260 kJ
128. mol-1,-390 kJ mol-1and -290 kJ mol-1respectively. Enthalpy of formation of benzene is
A) ‒50 kJ mol-1
B) +50 kJ mol-1
C) +60 kJ mol-1
D) ‒60 kJ mol-1
E) +80 kJ mol-1
Correct Answer : Option B
Choose the correct pair
Bond Mean single bond enthalpy (kJ mol-1)
(a) C-H (i) 464
129. (b) O-H (ii) 569
(c) F-H (iii) 293
(d) Si-H (iv) 414
A) (a)-(iv), (b)-(i), (c)-(ii), (d)-(iii)
B) (a)-(ii), (b)-(iii), (c)-(i), (d)-(iv)
C) (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)
D) (a)-(iv), (b)-(i), (c)-(ii), (d)-(iii)
E) (a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)
Correct Answer:-Question Cancelled
For the equilibrium, X2(g) + O2(g)= 2XO(g), the equilibrium concentrations of X2(g) and
130. O2(g) are 4 x 10-3 M and 8 x 10-3 M respectively. What is the equilibrium concentration of
XO(g)? (Equilibrium constant Kc = 0.5)
A) 4 × 10-3 M
B) 6 × 10-3 M
C) 5 × 10-3 M
D) 2 × 10-3 M
E) 8 × 10-3 M
Correct Answer : Option A
-3 M. Its pH
131. The concentration of hydrogen ions in a hydrochloric acid solution is 3 x 10
value is about( log3 = 0.4771)
A) 2.32
B) 2.52
C) 2.47
D) 3.47
E) 5.52
Correct Answer : Option B
Text of page 33
What is the emf of the cell at 298 K in which the following reaction takes place?
132. Ni + 2+ ▫
(s) + 2Ag (0.002M) → Ni (0.04M) + 2Ag(s). (E cell at 298 K = 1.05V)
A) 1.16 V
B) 0.93 V
C) 0.73 V
D) 0.83 V
E) 1.32 V
Correct Answer : Option B
Which of the following metals are normally used in the preparation of dihydrogen in the
133. laboratory?
A) Na and Ca
B) Ca and Ba
C) Fe and Na
D) Zn and Mg
E) Na and Ba
Correct Answer : Option D
What is the mass of ethanoic acid required to prepare 0.5 m solution containing 100 g of
134. be water? (Molar mass of ethanoic acid = 60 g mol-1).
A) 3g
B) 6g
C) 0.3 g
D) 7.5 g
E) 2g
Correct Answer : Option A
In a first order reaction, N2O5(g) → 2NO2(g) + ½ O2(g), the initial concentration of N2O5
135. was 1.6 x 10-3mol lit-1 at 300 K. The concentration of N2O5 after 23 minutes was
0.8 x 10-3mol lit-1. The rate constant of the reaction at 300 K is (log2 = 0.3010).
A) 0.04 min-1
B) 0.06 min-1
C) 0.3 min-1
D) 0.6 min-1
E) 0.03 min-1
Correct Answer : Option E
Which of the following reactions are complex reactions?
(i) Oxidation of ethane
(ii) Thermal decomposition of HI on gold surface
136. (iii) Saponification of methyl acetate
(iv) Nitration of phenol
(v) Decomposition of NH3 on hot Pt surface.
Text of page 34
A) (i) and (iii)
B) (ii) and (iv)
C) (i) and (iv)
D) (ii) and (v)
E) (i) and (v)
Correct Answer : Option C
Which of the following transition metal has more than one metallic structure at
137. normal temperature?
A) Chromium
B) Nickel
C) Manganese
D) Vanadium
E) Copper
Correct Answer : Option C
138. In chemotherapy, the ligand used to remove the excess of copper is
A) ethylenediamine
B) D-penicillamine
C) cupron
D) ethylenediamine
E) α-nitroso-β-napthol
Correct Answer : Option B
Some transition metal ions given below contain spin only magnetic moment (BM). Which
139. of the following is not correctly matched?
A) Ni2+ (Z=28) 4.73
B) Ti2+ (Z=22) 2.84
C) Mn2+ (Z=25) 5.92
D) Fe2+ (Z=26) 4.90
E) Co2+ (Z=27) 3.87
Correct Answer : Option A
In Carious method, 0.40 g of an organic compound gave 0.188 g of AgBr. The
140. percentage of bromine in the compound is (Atomic mass of Ag = 108 g mol-1 and Br = 80
g mol-1).
A) 30 %
B) 25 %
C) 35 %
D) 24 %
E) 20 %
Text of page 35
Correct Answer : Option E
Which of the following are carcinogenic hydrocarbons?
141. 1,2-Benzathracene
(i) (ii) Pen-1-yne (iii) 1,2-Benzpyrene
(iv) Cyclohexane (v) 3-Methylcholanthrene
A) (i), (ii), (v)
B) (ii), (iii), (iv)
C) (i), (ii), (v)
D) (i), (iii), (v)
E) (ii), (iii), (iv)
Correct Answer : Option D
142. IUPAC name of (CH3)3C-CH2Br is
A) 1-Bromotrimethylpropane
B) neo-pentylbromide
C) 1-Bromo-2,2-dimethylpropane
D) 2,2-dimethylethylenediamine
E) 3-bromo-2,2-dimethylpropane
Correct Answer : Option C
143. In Swarts reaction, Freon-12 is manufactured from
A) dichloromethane
B) chloromethane
C) trichloromethane
D) methane
E) tetrachloromethane
Correct Answer : Option E
144. IUPAC name of CH3-CH(OH)-CH2-CH(OH)-CH(C2H5)-CH2CH3 is
A) 3-Ethylheptane-4, 6-diol
B) 3-Ethylheptane-4, 6-diol
C) 5, 5-Diethylpentane-2, 4-diol
D) 5-Ethylpentane-2, 4-diol
E) 2-Ethylheptane-4, 6-diol
Correct Answer:-Question Cancelled
145. Pyridiniumchlorochromate is a complex of
A) chromic aid with pyridine and Cl2
B) potassium chromate with pyridine and KCl
C) chromium trioxide with pyridine and HCl
D) potassium dichromate with pyridine and HCl
E) chromic trioxide with pyrrolidine and HCl
Text of page 36
Correct Answer : Option C
146. The reagent used for the conversion of decanol into decanoic acid is
A) Tollens’s reagent
B) Jones reagent
C) Grignard reagent
D) Fehling’s reagent
E) DIBAL-H
Correct Answer : Option B
An organic compound with molecular formula,C5H10O, does not reduce Tollen’s reagent
147. but forms an addition compound with sodium hydrogen sulphite and gives positive
iodoform test. On vigorous oxidation, it gives ethanoic and propanoic acids. The
compound is
A) pentan-3-one
B) pentanal
C) pentan-2-one
D) ethoxy ethane
E) pentanol
Correct Answer : Option C
148. The increasing order of boiling point of the following amines is
A) C2H5N(CH3)2<(C2H5)2NH<C4H9NH2
B) C4H9NH2<C2H5N(CH3)2< (C2H5)2NH
C) C2H5NH(CH3)2< C4H9NH2<(C2H5)2NH
D) (C2H5)2NH<C4H9NH2<C2H5N(CH3)2
E) (C2H5)2NH <C2H5N(CH3)2<C4H9NH2
Correct Answer : Option A
149. Which of the following amines does not form carbylamine?
A) Ethanamine
B) Benzenamine
C) Propan-2-amine
D) Propan-1-amine
E) N-Methylethanamine
Correct Answer : Option E
150. The vitamin present in vegetable oils and its deficiency causes muscular weakness is
A) vitamin-A
B) vitamin-E
C) vitamin-B6
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D) vitamin-B12
E) vitamin-D
Correct Answer : Option B
Official key not published for this paper.
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Source: Commissioner for Entrance Examinations. Question paper published by Commissioner for Entrance Examinations.