KEAM 2026: KEAM Engineering entrance (Mathematics, Physics and Chemistry), session 6
Text of page 1
FINAL ANSWER KEY
Question Paper Code: 13/2026/OL
Exam:KEAM 2026 - 6
Date of Test: 22-04-2026
Let � = {1, 2, 3}, � = {1, 2, 3, 4} and let �: � → � be a relation. If � = {(1, 2),
1. (2, 3), (3, 4)} , then � ∘ � is
A) {(1, 2), (2, 3), (3, 4)}
B) {(1, 2), (2, 1), (3, 4)}
C) {(1, 3), (2, 1), (3, 2)}
D) {(1, 1), (2, 3), (3, 2)}
E) {(1, 2), (2, 1), (3, 3)}
Correct Answer:-Question Cancelled
2. The inverse function of �(�) = λ � + 1, � ϵ ℝ is itself. Then the value of λ is
A) 1
B) -1
�
C)
�
�
D) -
�
E) 2
Correct Answer : Option B
3. If �(�) = � + 1 , and �(�) = � � ,then �
��
(�(�)) is equal to
A) �−1
B) �� + 2
C) �+1
D) �� + �
E) �� − 1
Correct Answer : Option E
The range of �(�) = [����] , where [�] is the greatest integer less than or equal to �
4. , is
A) (-1,1)
B) {-1,0}
C) {1,0}
D) {-1,0,1}
E) [-1,1]
Correct Answer : Option D
Text of page 2
5. The equation Im(1 − �)� = 1 represents the line
A) �=�+1
B) �=1−�
C) �=�−1
D) �=�+2
E) �= −�−1
Correct Answer : Option A
6. The domain of the function �(�) = ��� ��(√2 − �) is
A) [0,1]
B) [-1,1]
C) [1,2]
D) [-1,0]
E) [0,2]
Correct Answer:-Question Cancelled
����� � � ������ �
7. The imaginary part of
����� � � ������ �
is equal to
A) ���10 �
B) ���80 �
C) ���50 �
D) ���40 �
E) ���40 �
Correct Answer:-Question Cancelled
√� � � √� � �
8. The value of �
�
+ � +�
� �
− � is equal to
�
A) 3√3
B) 2√3
C) 2
D) 0
E) -1
Correct Answer : Option D
9. The 3rd and 6th terms of a G.P. are, respectively 108 and -32 . Then the first term is
A) -81
B) -243
C) 243
D) 81
E) 27
Correct Answer : Option C
Text of page 3
10. The three geometric means between 4 and 324 are
A) 12,46,108
B) 12,36,128
C) 14,36,108
D) 12,36,98
E) 12,36,108
Correct Answer : Option E
If the 3rd, 7th, 11th terms of a geometric progression are a, b, c respectively, then (��
11.
)� =
A) ��
B) ��
C) ��
D) ��
E) � ��
Correct Answer : Option A
�
12. If �, �, �, � are in G.P. , then (� + �) =
A) (� + �)(� + �)
B) (� + �)(� + �)
C) (� + 2�)(� + �)
D) (� + �)(� + 2�)
E) (� + 2�)(� + 2�)
Correct Answer : Option A
The number of 3-digit even numbers that can be formed with the digits
13. 0, 1, 2, 3, 4, 5, 6 are
A) 30
B) 75
C) 105
D) 140
E) 150
Correct Answer : Option C
A cricket team of 11 players from 16 players is to be selected. If three particular players
14. are always included in the team, then the number of ways of selecting the team is
A) 1287
B) 1187
C) 1117
D) 1298
Text of page 4
E) 1349
Correct Answer : Option A
If six persons are to be selected to form a committee from a group of seven women and
15. four men so that at least three women are there on the committee, then the number of
ways it can be done, is
A) 641
B) 545
C) 591
D) 441
E) 139
Correct Answer : Option D
� �
If the coefficient of � � in the binomial expansion of �2α − � is -7 , then the value
16. �
of α is equal to
�
A)
�
B) 2
C) 3
D) 6
E) 8
Correct Answer : Option A
�
Let (1 + ��)(1 − 2�) = ∑�� = � �� � � , where � is a constant. If �� = 0 , then the
17.
value of � is
A) 1
B) 9
C) 3
D) 5
E) 2
Correct Answer : Option E
18.
A) -2
B) -1
C) 0
D) 1
E) 2
Text of page 5
Correct Answer : Option C
�
If � is a non-singular matrix of order � satisfying the matrix equation � + � + � +
� ��
19. � + . . . + � = � , where � and � are, respectively, unit and null matrices of
��
order � , then � =
A) � ��
B) �
C) �
D) �+�
E) �
Correct Answer : Option A
��
If � is a square matrix of order � such that |���(����) | = | �| , then � is
20.
equal to
A) 6
B) 4
C) 5
D) 3
E) 7
Correct Answer:-Question Cancelled
��� � � ���
21. If
�
− 9 ≤ 0 and
�
+ 1 ≥ 0, � ϵ ℝ , then � lies in the interval
A) [-2,1]
B) [-2,2]
C) [-1,2]
D) [2,4]
E) [-2,4]
Correct Answer : Option B
22. If |2� − 3 | < 5,� ϵ ℝ , then � lies in the interval
A) [-1,1]
B) [-1,4]
C) (-1,4)
D) (-2,4)
E) [-2,4]
Correct Answer : Option C
√�(����� � � ����� �)
23. The value of
����� � � ����� �
is
A) 1
B) √3
Text of page 6
C) √2
�
D)
�
E) 0
Correct Answer : Option A
�
24. If ��� � θ + ��� � θ = 7, 0 < θ < , then ���2θ is equal to
�
A) 1
B) √3
C) √2
D) -√3
E) 0
Correct Answer : Option D
����� � � ����� �
25. The value of
����� � � ����� �
is equal to
�
A)
√�
B) √3
C) 1
D) -√3
�
E)
√�
Correct Answer : Option E
� �
26. The value of 4���36 ���72 is equal to
A) 1
B) 2
C) √2
D) 2
E) 0
Correct Answer : Option A
�
27. Let �(�) = (8���� + 15���� + 3) − 15, � ϵ ℝ. Then the maximum value of � is
A) 325
B) 365
C) 385
D) 430
E) 455
Text of page 7
Correct Answer : Option C
�� ��
28. The value of ��� ������ � + ��� ������ � is equal to
� �
�
A) -
�
��
B) -
�
�
C)
�
�
D)
�
E) π
Correct Answer : Option E
29. The value of ��� �(��� ��(3)) is
A) 8
B) 4
C) 6
D) 1
E) 10
Correct Answer : Option A
���� � √����� �
30. The value of ��� ��� � , where 0 < � < is
√����� � ���� �
�
A) −�
�
�
B) −�
�
�
C) −�
�
�
D) −�
�
E) π −�
Correct Answer : Option A
The �-intercept and �-intercept of a line are three times and four times of the � -
31. intercept and �-intercept of the line 3� + 2� = 6 , respectively. Then the equation of
the line is
A) 2� − � = 12
B) 2� + � = 12
C) 2� − � = − 12
D) � + 2� = 12
E) 2� + 2� = 12
Text of page 8
Correct Answer : Option B
If the foot of the perpendicular drawn from the origin to the line � = �� + � is (1,1)
32. then the value of � and � are, respectively,
A) 1 and 2
B) 1 and -2
C) -1 and 2
D) 2 and 2
E) -1 and -2
Correct Answer : Option C
The perpendicular distance between the lines 3� + 4� − 6 = 0 and 6� + 8� + 18
33. = 0 is
A) 15
B) 12
C) 9
D) 3
E) 0
Correct Answer : Option D
If the circle � � + � � − 6� − 12� − 55 = 0 intercepts the �-axis at two points �
34. and � , then |��| is equal to
A) 6
B) 8
C) 10
D) 12
E) 16
Correct Answer : Option E
If the focus and vertex of a parabola are at a distance of 3 units and 6 units,
35. respectively, from the origin on the positive � -axis, then the equation of the parabola is
A) � � = − 12(� − 6)
B) � � = − 9(� − 6)
C) � � = − 16(� − 6)
D) � = 16(� − 6) �
E) � � = 14(� − 6)
Correct Answer : Option A
If the foci and vertices of an ellipse are respectively ( ± 2, 0) and ( ± 3, 0) then its
36. eccentricity is
Text of page 9
�
A)
�
√�
B)
�
√�
C)
�
�
D)
�
�
E)
√�
Correct Answer : Option A
The equation of a hyperbola is 9� � − 16� � = 144 . If � and � are, respectively,
37. the focus and the vertex of one section of the hyperbola, then the length of �� is
�
A)
�
�
B)
�
�
C)
�
D) 2
E) 1
Correct Answer : Option E
→ ^ → ^
^ + 3�^ + � and � = ��^ − ��^ + 2� is acute,
38. If the angle between the vectors � = ��
then � lies is
A) ( − ∞, − 1) ∪ (1, ∞)
B) ( − ∞, − 1) ∪ (2, ∞)
C) ( − ∞, 1) ∪ (2, ∞)
D) ( − ∞, 0) ∪ (1, ∞)
E) ( − ∞, 0) ∪ (2, ∞)
Correct Answer : Option C
→ →
^ and �� →
^ . If the point � lies on ��
�� = 2�^ − 2�^ − 2�
Let = 2�^ + ^� + 2�
39. → →
and �� bisects the angle < ��� , then 2 �� is
A) 4�^ − ^� + ^
�
B) 4�^ − ^� − ^
�
C) 4�^ + ^� + ^
�
D) 4�^ + ^� − ^
�
E) −4�^ + ^� + ^
�
Text of page 10
Correct Answer : Option A
→ → →+→
� × (�^ − ^� + ^
If �) = (�^ − ^� + ^
�) × � and |� � | = 3√3 , then the
40. → →
possible values of (� + � ) . (3�^ + 2�^ + ^
�) are
A) ±1
B) ±2
C) ±4
D) ±6
E) ±8
Correct Answer : Option D
→→ →� be pairwise non-collinear vectors. If →
Let the three vectors � , � , and
→
� + 2� is
41. → → → → → → →
collinear with � and if � + 2 � is collinear with � , then � + 2� + 5 � is equal to
A)
→
0
B)
→�
C)
→
�
D)
→�
E)
→
2�
Correct Answer : Option D
→
The angle between the lines� = (3 + α )�^ + 2(1 + α )�^ + 2( − 2 + α )�^ and →
�
42. ^
= (5 + 3β )�^ + 2(1 + β )�^ + 6β � , where α and β are parameters, is
��
A) ��� ��� �
��
��
B) ��� ��� �
��
�
C) ��� ��� �
��
��
D) 2��� ��� �
��
��
E) ��� ��� �
��
Correct Answer : Option E
��� ��� ���
The equation of line which is parallel to = = and passing through the
43. �� � �
point (1,1,1) , is
��� ��� ���
A) = =
� � �
Text of page 11
��� ��� ���
B) = =
� � �
��� ��� ���
C) = =
� �� �
��� ��� ���
D) = =
�� � �
��� ��� ���
E) = =
� � ��
Correct Answer : Option B
→ ^ + λ (2�^ + 2�
� = ^� + ^� + 3�
The shortest distance between the lines
^ +^� ) and →
�
44. ^ , where λ and μ are parameters, is
= (2μ + 1)�^ + (2μ − 1)�^ + (μ + 1)�
A) 1
B) 6
C) 3
D) 4
E) 2
Correct Answer : Option E
��� ��� ���
45. The vector form of the straight line
�
=
��
=
��
is
A) → ^
� = (2 + μ )�^ + (1 − μ )�^ + (1 + 2μ )�
B) → ^
� = (2 + μ )�^ + (1 + μ )�^ + (1 − 2μ )�
C) →
� = (2 + μ )�^ + (1 − 2μ )�^ + (1 − 2μ )�^
D) →
� = (2 + 3μ )�^ + (1 − μ )�^ + (1 − 2μ )�^
E) → ^
� = (2 + μ )�^ + (1 − μ )�^ + (1 − 2μ )�
Correct Answer : Option E
The combined mean age of a group of boys and girls in a school is 12. If the mean of the
46. boys in that group is 14 and the mean of the girls is 9, then the percentage of boys in that
group is
A) 24%
B) 36%
C) 40%
D) 60%
E) 85%
Correct Answer : Option D
If the mean and standard deviation of 10 observations are 24 and 4 respectively, then the
47. sum of the squares of all observations is
A) 5920
Text of page 12
B) 5820
C) 5720
D) 5640
E) 5660
Correct Answer : Option A
� � �
48. If �(� / �) =
�
, �(� / �) = and �(� ∩ �) = then �(� ∪ �) is
� �
�
A)
�
�
B)
�
�
C)
�
�
D)
�
�
E)
�
Correct Answer : Option E
A box contains 5 white balls, one red ball and 4 black balls. If three balls are drawn at
49. random, then the probability of getting no red ball is
�
A)
��
�
B)
��
�
C)
��
�
D)
��
�
E)
�
Correct Answer : Option C
���
50. The domain of the function �(�) = � is
���
A) [1,2)
B) [-1,2]
C) [-1,2)
D) [-1,3)
E) (-1,3)
Correct Answer : Option C
[�] � �
51. The value of lim � is
�→� ���
Text of page 13
A) -2
B) 4
C) 2
D) 1
E) 0
Correct Answer : Option E
52.
A) -1,-4
B) 1,-4
C) 4,-4
D) 4,-1
E) 1,4
Correct Answer : Option B
√� � �� � √� � ��
53. The value of lim
�→� �
is
A) 0
B) 1
�
C)
�
�
D)
�
E) 3
Correct Answer : Option E
� � � ����
54. The range of the function �(�) = ( )
�
is
� �
A) �− , �
� ��
� �
B) �− , �
� �
� �
C) � , �
� �
� �
D) � , �
�� �
� �
E) � , �
�� �
Correct Answer : Option D
�
55. If �(�) =
�� � �
, then the point(s) of discontinuity of �(�(�)) is/are
Text of page 14
�
A) 2,
�
B) 3,4
C) 1,3
D) 4
E) 3
Correct Answer : Option A
� � �(� � ���) � �(�)
56. If � (5) =
�
, then the value of lim
�
is equal to
�→�
A) 1
B) 2
C) 3
D) 5
E) 6
Correct Answer : Option E
|�| �
57. If �(�) =
� � , then � (2) is equal to
�
A)
�
�
B)
�
�
C) -
�
�
D) -
�
�
E) -
�
Correct Answer : Option D
����� � �����
58. If �(�) = ��� ��� � , then the value � �(1) is
����� � �����
A) 1
�
B)
�
�
C)
�
D) -1
�
E) -
�
Correct Answer : Option D
59. " �
If �(�) = (2� + 3)� �� , then � (1) − 10� (1) is equal to
Text of page 15
A) 250� �
B) 125� �
C) 25� �
D) -25� �
E) −125� �
Correct Answer : Option E
60. The function �(�) = 2� � − 15� � + 36� − 24 is strictly decreasing in the interval is
A) (2,3)
B) (1,3)
C) (2,4)
D) (1,4)
E) (2,5)
Correct Answer : Option A
The distance � in meters travelled by a particle in � seconds is given by � = � �(4���3�
61. + 5���3�) . Then the velocity of the particle at time � is given by
A) � �(19���3� − 7���3�)
B) � �(12���3� − 7���3�)
C) � �(16���3� + 9���3�)
D) � �(14���3� − 9���3�)
E) � �(19���3� + 7���3�)
Correct Answer : Option A
If �(�) = 2� � − 3� � − λ � + 1, ��[0, 3] attains a local minimum at � = 2 , then
62. the value λ is equal to
A) -12
B) -36
C) 12
D) 36
E) -6
Correct Answer : Option C
�
63. Let �(�) = � � − 10� + 16, � ϵ ℝ. If � (�) is equal to slope of the straight line
joining the points (2,0) and (8,0), then the value of � is
A) 1
B) 2
C) 4
D) 5
E) 6
Text of page 16
Correct Answer : Option D
���� � ����
64. ∫ � � ��� �� �� is equal to
A) ��� | ���� | + �
B) 2��� | ���� | + �
C) ��� | ���� | + �
D) ��� | ���� | + �
E) 2��� | ���� | + �
Correct Answer : Option A
65. ∫ � ��(1 + (1 − �)����)�� is equal to
A) (�����)� � + �
B) (� �����)� �� + �
C) (� �����)� ��� + �
D) (�����)� �� + �
E) (�����)� ��� + �
Correct Answer : Option D
� � ��
66. ∫ �√� � � � x equal to
A) 2�√1 + � + �
B) �√1 − � + �
C) � �√1 + � + �
D) (� − 1)√1 + � + �
E) �√1 + � + �
Correct Answer:-Question Cancelled
����� � ����
67. ∫
��
�� is equal to
����
A) +�
�
�����
B) +�
�
����
C) +�
��
����
D) +�
�
�����
E) +�
�
Correct Answer : Option D
Text of page 17
68. ∫ �(1 + 2����)� x is equal to
A) ����� + �
B) � ����� + �
C) � ����� + �
D) 2����� + �
E) 3����� + �
Correct Answer : Option B
69.
A) -1
B) -2
C) 1
D) 2
E) 3
Correct Answer : Option A
70.
A) π +2
B) 2π -2
C) 2π -1
D) π -2
E) π +1
Correct Answer : Option D
71.
A) 18
B) 15
C) 12
D) 10
E) 8
Correct Answer : Option B
72.
A) π
��
B)
�
�
C)
�
Text of page 18
�
D)
�
E) 2π
Correct Answer : Option D
�� �� ��
The order and the degree of the differential equation 2 − 3� = �2� − � �
73. �� ��
respectively, are
A) 1 and 1
B) 1 and 3
C) 1 and 4
D) 2 and 3
E) 2 and 4
Correct Answer : Option C
The solution of the differential equation (� + � �)�� = ���, � > 0 is a curve which
74.
passes through the point (1,0). The equation of the curve is
A) � = �(� + 1)
B) � = �(� − 1)
C) � = � �(� − 1)
D) � = � �(� + 1)
E) � = �(� � − 1)
Correct Answer : Option B
Consider the Linear Programming Problem:
75. Maximize � = � + 2�
Subject to 2� + 3� ≤ 12, � ≥ 0, � ≥ 0 . The optimal value is
A) 3
B) 7
C) 8
D) 10
E) 12
Correct Answer : Option C
Of the given numbers,
(1) 25300
76. (2) 5.600
(3) 0.07200
the number of significant figures for
A) (1) is five
B) (2) is two
C) (3) is three
D) (1) and (2) are four
Text of page 19
E) (2) and (3) are four
Correct Answer : Option E
The mismatch between the physical quantity and the dimensional formula in the following
77. is
A) Force : M LT-2
B) Torque : M L2 T-1
C) Pressure : M L-1 T-2
D) Heat energy : M L2 T-2
E) Thermal conductivity : M L T-3 K-1
Correct Answer : Option B
If a ball is thrown horizontally with a velocity of 10 ms-1 from the tower of height 45 m,
78.
then it strikes the ground at a distance of (g = 10 ms-2)
A) 25 m
B) 40 m
C) 20 m
D) 30 m
E) 45 m
Correct Answer : Option D
→ ^→ ^ →
If the vectors � = ��^
� + �� ^� + �� �, � = ��^� + �� ^� + �� � and � = ��^� + �� ^�
79. + �� ^ → → → →
� are defining the vector � = � − � + � , then the � - component of the
vector �� is
A) �� − �� + ��
B) �� − �� + ��
C) �� − �� + ��
D) �� − �� + ��
E) �� − �� + ��
Correct Answer : Option B
A particle moves along a semi circular path of radius � in time � with constant speed,
80. then its
��
A) average speed is
��
�
B) average velocity is
�
C) displacement is 2π �
D) distance travelled is 2�
�� �
E) average acceleration is
��
Text of page 20
Correct Answer : Option E
A hanging rope can withstand a tension of 750 N. The minimum acceleration for a man of
81. 50 kg to climb up without breaking the rope is (g = 10 ms-2)
A) 6 ms-2
B) 4 ms-2
C) 5 ms-2
D) 7 ms-2
E) 2 ms-2
Correct Answer:-Question Cancelled
If the area under the graph between the force on an object and time is 20 units, then the
82. object experiences
A) an impulse of 10 units
B) a change of momentum of 10 units
C) an impulse of 20 units
D) a change of force by 20 units
E) a change of acceleration of 20 units
Correct Answer : Option C
A bob of mass m tied to one end of a light string of length 50 cm whirled in a vertical
83. circle. The minimum velocity with which it has to move so that the string remains taut,
when it reaches the top most point of the circle is (g = 10 ms-2)
A) 10 ms-1
B) 8 ms-1
C) 15 ms-1
D) 5 ms-1
E) 12 ms-1
Correct Answer : Option D
The power generated by a turbine operated by the fall of water from a height of 100 m at
84. the rate of 24 kg s-1 is 21 kW. The percentage loss in power is
A) 10 %
B) 12.5 %
C) 15 %
D) v
E) 5%
Correct Answer : Option B
A solid cylinder of mass 6 kg of length ℓ is inserted tightly into a hollow cylinder of outer
85. radius 0.6 m and length ℓ without any air gap between them. If the moment of inertia of
this setup about its own axis is 1.44 kgm2, then the mass of the hollow cylinder is
A) 1 kg
Text of page 21
B) 3 kg
C) 4 kg
D) 2 kg
E) 5 kg
Correct Answer : Option D
The objects and the corresponding positions of centre of mass are given below. The
86. FALSE one is
A) Uniform rod : middle point of the rod
B) Circular ring : centre of the ring
C) Triangular lamina : point of intersection of altitudes
D) Cylinder : middle point on it axis
E) Cubical box : intersection of diagonals
Correct Answer : Option C
The height at which the weight of a body becomes one third of its weight on the surface
87. of earth is (R is the radius of earth)
�
A)
�
B) 0.732 �
C) 0.414 �
�
D)
�
�
E)
��
Correct Answer : Option B
If the ratio of the distances of a planet from the sun at perihelion and aphelion is 2 : 3,
88. then the ratio of their respective velocities at the perihelion and aphelion is
A) 2:3
B) 2:5
C) 3:5
D) 3:2
E) 1:1
Correct Answer : Option D
The flow of oil of density 800 kgm-3 through a horizontal pipe is streamlined. If the
89. pressure between two points separated by 1m in the tube falls by 1.6 Nm-2, then the
change in kinetic energy per kg of the liquid between these points is
A) 16 x 10-4 J kg-1
B) 2 x 10-3 J kg-1
C) 4 x 10-3 J kg-1
D) 8 x 10-4 J kg-1
Text of page 22
E) 32 x 10-2 J kg-1
Correct Answer : Option B
If the work done in increasing the area of a thin soap film from � to 3 � is � , then the
90. surface tension of the soap solution is
�
A)
�
�
B)
��
C) ��
D) 2��
�
E)
��
Correct Answer : Option B
91. The MISMATCH among the following phase transition processes is
A) Solid to liquid : melting
B) Liquid to solid : freezing
C) Liquid to vapour : vaporisation
D) Solid to vapour : sublimation
E) Vapour to solid : regelation
Correct Answer : Option E
If 300 J of heat energy is used to raise the temperature of one mole of an ideal gas by 10
92. K at constant pressure, then heat energy required to raise its temperature by 10 K at
constant volume is (� = 8.3 J mol-1K-1)
A) 117 J
B) 150 J
C) 183 J
D) 217 J
E) 300 J
Correct Answer : Option D
To increase the efficiency of a Carnot engine working between a source at 500 K and a
93. sink at 300 K by 10 % , with the same sink temperature the source temperature should
be increased to
A) 550 K
B) 600 K
C) 700 K
D) 750 K
E) 800 K
Correct Answer : Option B
Text of page 23
If � represents the intermolecular force between molecules and �, is the volume
occupied by the gas molecules, then at high pressure and at low temperatures, the gas
94. shows large deviation from the ideal behaviour because the fact that
A) � is negligible
B) both � and � are negligible
C) � is negligible
D) � is appreciable and � is negligible
E) � is appreciable and � is not negligible
Correct Answer : Option E
A cylinder contains 18 moles of oxygen at pressure of 15 atmosphere at temperature 300
95. K. If the pressure reduces to 9 atmospheres by the withdrawal of 6 moles of oxygen, then
the temperature of the cylinder will be reduced to
A) 200 K
B) 230 K
C) 270 K
D) 220 K
E) 250 K
Correct Answer : Option C
The graph drawn between the velocity of sound in a gas and pressure of the gas at a
96. given temperature is
A) a straight line with negative slope
B) a straight line with positive slope
C) a straight line parallel to pressure axis
D) a parabola
E) an exponential curve
Correct Answer : Option C
97. Which one of the following motions is not simple harmonic motion?
A) Rotation of earth about its axis
B) Small oscillations of a mass attached to a spring
C) Oscillation of mercury column in a U tube
D) Oscillation of a second’s pendulum
E) The projection of uniform circular motion on the diameter of the circle
Correct Answer : Option A
In a uniform electric field E, the work done in rotating the electric dipole of dipole moment
98. P from -45o to 45o with respect to the field direction is
A) 0.5 PE
B) 0.414 PE
C) 0.866 PE
Text of page 24
D) PE
E) zero
Correct Answer : Option E
A uniformly charged cube of side one cm having surface charge density of 8.85 µC
99. cm-2is placed inside a hollow metal sphere. The total flux emerging out of the sphere in
Nm2C-1 is (ɛ0 = 8.85 x 10-12 C2N-1m-2)
A) 8.85 × 106
B) 12 × 106
C) 19.7 × 106
D) 3 × 106
E)
6 × 106
Correct Answer : Option E
The INCORRECT formula representing the energy stored in a parallel plate capacitor in
100. usual notation is
�
A) �� �
�
�
B) ��
�
�
C) ��
��
� �
D) � �
�
�
E) ϵ � ���
� �
Correct Answer : Option D
The distance between the centres of two identical solid spheres each of radius 5 cm kept
101. in free space is 40 cm. If each one is holding a charge of 2 µC, then the work done in
bringing their centres to a separation of 30 cm is
A) 36 x 10-2 J
B) 12 x 10-2 J
C) 6 x 10-2 J
D) 18 x 10-2 J
E) 3 x 10-2 J
Correct Answer : Option E
If the resistance of a uniform wire of length 1m of cross-sectional area 0.1 m2 is 12 Ω,
102. then the resistance of wire of length 2 m of the same material with area of cross section
0.2 m2 is
A) 24 Ω
Text of page 25
B) 6Ω
C) 12Ω
D) 40Ω
E) 4Ω
Correct Answer : Option C
103. With increase in temperature, the resistivity of
A) both Cu and Ge increases
B) both nichrome and Ge decreases
C) nichrome decreases and that of Ge increases
D) both Cu and nichrome increases
E) Cu, nichrome and Ge increases
Correct Answer : Option D
If three cells each of emf 2 V and internal resistance 1Ω are connected to a resistor of 4
.5 Ω as shown, then the current through the resistor is
104.
A) 1A
B) 0.67 A
C) 0.33 A
D) 2A
E) 0.5 A
Correct Answer : Option B
105. Regarding the magnetic property, the TRUE statement is
A) Ag and Al have permanent dipole moment
B) Magnetic susceptibility of Ag and Pb is small and negative
C) Magnetic susceptibility of Al and Pb is small and negative
D) Al and Pb have the tendency to move from weak to strong field
E) Relative permeability of Ag and Al is greater than one
Correct Answer : Option B
106. When a bar magnet of dipole moment m is suspended in a uniform magnetic field B, then
A) the force on it is m x B
B) its potential energy is -m.B
C) the torque on it is zero
D) both torque and force on it are zero
E) it moves away from the field B
Text of page 26
Correct Answer : Option B
Two long straight conductors carrying equal current � kept parallel at a separation of �
metre experience a force � per unit length. If the distance of separation is made 2� , then
107. to maintain the same force � per unit length on each conductor, the current in each
conductor should be increased to
A) 2�
B) √2�
C) √3�
D) 1.5 �
E) 3�
Correct Answer : Option B
The shunt resistance to be connected across a galvanometer of resistance 50 Ω to send
108. �
th of the main circuit current through the galvanometer is nearly
����
A) 0.01Ω
B) 0.2Ω
C) 0.05Ω
D) 0.02Ω
E) 0.5Ω
Correct Answer : Option C
If the current in a coil of inductance 10 mH is increased from 1 A to 5 A in0.2 s, then the
109. emf produced in it is
A) 0.1 �
B) 0.3 �
C) 0.5 �
D) 0.4 �
E) 0.2 �
Correct Answer : Option E
For a given ac supply voltage 60 sin ωt, the reactances offered by L and C, are found to
be 20 Ω each. If the resistance of the resistor is also 20 Ω , then the current in the circuit
is
110.
A) 1A
B) 3A
Text of page 27
C) 2.12 A
D) 1.73 A
E) zero
Correct Answer:-Question Cancelled
In a plane electromagnetic wave if the amplitude of oscillating electric field is 45
111. Vm-1 then the amplitude of the oscillating magnetic field is
A) 2.5 x 10-8 T
B) 1.5 x 10-7 T
C) 3 x 10-8 T
D) 1.5 x 10-8 T
E) 2.5 x 10-7 T
Correct Answer : Option B
If a coin at the bottom of a lake appears to be at a depth of 6 m, then the gauge pressure
112. on the coin in pascal is (µ of water is 4/3)
A) 8.2 x 103
B) 78.4 x 103
C) 38.2 x 103
D) 4.5 x 104
E) 29.4 x 103
Correct Answer : Option B
If an object is placed at a distance of 12 cm from a thin lens of power 5D, then the
113. distance of the image from the lens with proper sign convention is
A) -30 cm
B) 20 cm
C) 15 cm
D) 24 cm
E) -12 cm
Correct Answer : Option A
If two waves of same wavelength with their intensities in the ratio 25 : 9 produce
114. interference, then the ratio of the maximum to minimum intensity is
A) 9:2
B) 9:1
C) 5:3
D) 16 : 3
E) 16 : 1
Correct Answer : Option E
Text of page 28
If the energy of the incident radiation on a metal is increased by 10 %, the kinetic energy
115. of the emitted photoelectrons increases from 0.5eV to 0.75 eV, then the work function of
the metal is
A) 2 eV
B) 1.5 eV
C) 1 eV
D) 2.5 eV
E) 1.8 eV
Correct Answer : Option A
If the de Broglie wavelengths of deuteron, positron and electron are in the ratio 1 : 2 : 3,
116. then the ratio of their respective momenta is
A) 1:2:3
B) √3: √2: 1
C) 6:3: 2
D) 3:2:1
E)
1:4:9
Correct Answer : Option C
If r and � represent, respectively, the orbital radius and orbital velocity of the electron in
117. the Bohr’s theory of hydrogen atom, then they are proportional to the orbit number � as
A) � ∝ � and � ∝ �
B) � ∝ � and � ∝ � �
�
C) � ∝ � � and � ∝ �
�
D) �∝ and � ∝ �
�
�
E) � ∝ � and � ∝ �
Correct Answer : Option C
If a radioactive substance is reduced to 6.25 % of its initial amount in 256 days then its
118. half-life period is
A) 126 days
B) 64 days
C) 50 days
D) 25 days
E) 12.5 days
Correct Answer : Option B
In a diode rectifier, the capacitors with large values of C are used in filter circuits in order
119. to
A) increase the ac ripple
Text of page 29
B) to reduce the peak voltage at the output
C) increase the time constant to high value
D) discharge quickly the voltage across it
E) to double the input ac peak value
Correct Answer : Option C
If 5 mA current is drawn from the voltage source in the circuit connected with two
resistors each of 2.4 kΩ and four ideal diodes, then the source voltage is
120.
A) 12 V
B) 6V
C) 24 V
D) 10 V
E) 8V
Correct Answer : Option A
3.0 g of a salt of molecular weight 30 is dissolved in 250 mL of water. The molarity of the
121. solution is
A) 0.1 M
B) 0.2 M
C) 0.3 M
D) 0.4 M
E) 0.5 M
Correct Answer : Option D
The quantum number symbols are given in List-I and the informations about them are
given in List-II. The correct match is
List-I
List-II
122. I) ml a) Shape of orbital
II) ms b) Size of orbital
III) l c) Orientation of orbital
d) Orientation of electron
IV) n
spin
A) I-d, II-a, III-c, IV-b
B) I-c, II-d, III-a, IV-b
C) I-b, II-c, III-d, IV-a
Text of page 30
D) I-c, II-a, III-d, IV-b
E)
I-b, II-d, III-a, IV-c
Correct Answer : Option B
The transition energy of the electron from higher to lower level is 3.0 × 10-19 J. The
123. wavelength of the emitted light is about
(h = 6.625 × 10-34 J s, c = 3 × 108 m s-1)
A) 330 nm
B) 660 nm
C) 990 nm
D) 310 nm
E)
230 nm
Correct Answer : Option B
Which of the following represents the correct increasing order of first ionization enthalpy
124. for Ca, Ba, S, Se and Ar?
A) Ca < S < Ba < Se < Ar
B) Ar < S < Ba < Se < Ca
C) Ba < Ca < Se < S <Ar
D) Ba < Ca < S < Se <Ar
E) Ca < S < Ar < Se < Ba
Correct Answer : Option C
125. Which of the following statement is incorrect about the periodic trend?
Atomic radii decrease while going from left to right in a period and increase with atomic
A)
number in a group.
B) Ionisation enthalpies generally decrease across a period and increase down a group.
C) Electronegativity generally increases across a period and decreases down a group.
Electron gain enthalpies in general, become more negative across a period and less
D)
negative down a group.
Among representative elements, the valence is equal to the number of electrons in the
E)
outermost orbital.
Correct Answer : Option B
126. The correct increasing order of average bond length for C=C, N=O, C-C, N-O is
A) C=C < N=O < C-C < N-O
B) N-O < N=O < C-C < C=C
C) C=C < C-C < N=O < N-O
D) C-C < N=O < C=C < N-O
E) N=O < C= C < N-O < C-C
Text of page 31
Correct Answer : Option E
127. Which of the following set of molecules are having zero dipole moment?
A) HI, CO2 and CCl4
B) H2, CO2 and BF3
C) NH3, CO2 and CCl4
D) HI, CH4 and CCl4
E) HI, HCl and CCl4
Correct Answer : Option B
5 moles of an ideal gas at 100 K are allowed to undergo reversible adiabatic compression
128. till its temperature becomes 200 K. If Cv = 30 JK-1 mol-1, calculate ΔU and Δ(pV) for this
process. (R = 8.0 JK-1 mol-1)
A) ΔU = 10 kJ; Δ(pV) = 2 kJ
B) ΔU = 12 kJ; Δ(pV) = 4 kJ
C) ΔU = 14 kJ; Δ(pV) = 4 kJ
D) ΔU = 15 kJ; Δ(pV) = 4 kJ
E) ΔU = 3.0 kJ; Δ(pV) = 2 kJ
Correct Answer : Option D
129. Which of the following reaction has the positive value of standard enthalpy of reaction?
A) C2H5OH(l) + 3O2(g) → 2CO2(g) + 3H2O(l)
B) 2SO2(g) + O2(g) → 2SO3(g)
C) 2NH3(g)→N2(g) + 3H2(g)
D) C(s) + O2(g)→CO2(g)
E) CO(g) + ½ O2(g) → CO2(g)
Correct Answer : Option C
The reaction between N2 and O2 is carried out in a sealed vessel at 300 K. At
130. equilibrium, [N2] = 2×10-3 M, [O2] = 4×10-3 M and [NO] =2× 10-3 M. What is the value of
Kp for the reaction N2(g) + O2(g)⇋2 NO(g) at 300 K? (R = 0.08 bar lit mol-1 K)
A) 0.5
B) 12
C) 120
D) 5
E) 50
Correct Answer : Option A
131. The acid which has the highest ionization constant (Ka) at 298 K is
A) HNO2
Text of page 32
B) C6H5OH
C) HClO
D) C5H4NCOOH
E) HF
Correct Answer : Option E
132. Which of the following statement is incorrect about the standard electrode potential?
A negative E˚ value means the redox couple is a stronger reducing agent than the H+/H2
A)
couple.
A positive E˚ value of potential means the redox couple is a weaker reducing agent than
B)
the H+/H2 couple.
C) The standard electrode potential value of hydrogen electrode is 0.0
The trend in E˚ value from top to bottom shows the increasing strength of reducing
D)
agent.
The trend in E˚ value from top to bottom shows the increasing strength of oxidising
E)
agent.
Correct Answer : Option D
133. Chlorine has oxidation number +7 in
A) NaCl
B) SiCl4
C) HCl
D) HClO4
E) KCl
Correct Answer : Option D
134. The compound which has the highest freezing point (in K) is
A) CS2
B) CHCl3
C) (C2H5)2O
D) H2O
E) C2H5OH
Correct Answer : Option D
135. Which of the following statement is incorrect?
A) All natural radioactive processes follow first order kinetics.
B) Thermal decomposition of HI on gold surface is a zero-order reaction.
C) Decomposition of hydrogen peroxide catalysed by iodide in an alkaline medium is a first
order reaction.
D) The unit of second order rate constant is mol-1L s-1.
Text of page 33
E) The experimental rate expression of the reaction, CHCl3 + Cl2→CCl4 + HCl is, Rate = k
[CHCl3] [Cl2].
Correct Answer : Option E
The rate constants of a reaction at 300 K and 400 K are 1.5 s-1 and 3 s-1 respectively.
136.
The Ea value is [log 2 = 0.3010, 2.303 R = 19 JK-1 mol-1]
A) 7.86 kJ
B) 68.6 kJ
C) 78.6 kJ
D) 6.86 kJ
E) 5.86 kJ
Correct Answer : Option D
137. The highest possible oxidation states of uranium and plutonium, respectively, are
A) 7 and 6
B) 6 and 4
C) 6 and 7
D) 7 and 5
E) 4 and 6
Correct Answer : Option C
The type of isomerism exhibited by the complexes [Co(NH3)(SO4)]Br
138. and [Co(NH ) Br]SO is
3 5 4
A) Ionisation isomerism
B) Linkage isomerism
C) Coordinate isomerism
D) Geometrical isomerism
E) Optical isomerism
Correct Answer : Option A
139. The ligand which is used in the treatment of lead poisoning is
A) D-penicillamine
B) EDTA
C) desferrioxime B
D) cis-platin
E) CO
Correct Answer : Option B
140. The compound which gives the most stable carbocation in elimination reaction is
A) (CH3)3COH
Text of page 34
B) CH3CH2CH2CH2OH
C) CH3CH(CH3)CH2OH
D) CH3CH(OH)CH2CH3
E) CH3CH2OH
Correct Answer : Option A
141. Which of the following compound is aromatic?
A)
B)
C)
D)
E)
Correct Answer : Option A
142. Which of the following statement is incorrect with Williamson synthesis?
A) It is used to prepare symmetrical and unsymmetrical ethers.
B) It involves reaction between alkyl halide and sodium alkoxide.
C) This reaction involves SN2 attack.
D) Secondary or tertiary alkyl halides gives better results of ether formation.
E) Alkoxides are not only nucleophiles but also strong bases.
Correct Answer : Option D
143. Which of the following is used in the production of freon refrigerant R-22?
A) CHCl3
B) CH3Cl
C) (C2H5)2O
D) CCl4
E) CH2Cl2
Correct Answer : Option A
Text of page 35
An organic liquid ‘A’ containing C, H and O with pKa value 15.9, used in polishing woods,
on heating with concentrated sulphuric acid gives a gaseous product ‘B’ with the
144. empirical formula, CH2. ‘B’ decolourises bromine water as well as dilute permanganate
solution. The compound A and B are respectively
A) methanol and methane
B) ethanol and ethane
C) Phenol and ethanol
D) ethanol and ethene
E) ethanol and methane
Correct Answer : Option D
145. When phenol is treated with excess of bromine water, it gives
A) o-bromophenol
B) o- and p-bromophenol
C) 1,3,5-tribromophenol
D) 2,4-dibromophenol
E) 2,4,6-tribromophenol
Correct Answer : Option E
Which is the reagent used for the following conversion?
146.
A) NaCN/HCl
B) NaBH4
C) SOCl2
D) O3/Zn-H2O
E) [Ag(NH3)2]+
Correct Answer : Option E
An organic compound ‘A’ with the molecular formula C6H4NO2Br is treated with
magnesium in dry ether gives an organometallic compound which on treated with CO2
147.
(dry ice) and gives compound ‘B’. ‘B’ on hydrolysis gives ‘C’. The name of the products A
and C are
A) 2-bromoaniline and terephthalic acid
B) 2-nitrobromobenzene and terephthalic acid
C) 3-nitrobromobenzene and 3-nitrobenzoic acid
D) 3-nitrobromobenzene and 3-bromobenzoic acid
E) 3-nitrobromobenzene and 2-nitrobenzoic acid
Correct Answer : Option C
148. Match the following:
Text of page 36
A) (i)-(b), (ii)-(c), (iii)-(e), (iv)-(d), (v)-(a)
B) (i)-(b), (ii)-(c), (iii)-(d), (iv)-(e), (v)-(a)
C) (i)-(e), (ii)-(c), (iii)-(b), (iv)-(d), (v)-(a)
D) (i)-(c), (ii)-(b), (iii)-(e), (iv)-(d), (v)-(a)
E) (i)-(b), (ii)-(c), (iii)-(a), (iv)-(d), (v)-(e)
Correct Answer : Option B
149. The decreasing order of acid strength of the following is
A) FCH2COOH > NCCH2COOH > NO2CH2COOH > ClCH2COOH
B) CNCH2COOH > O2NCH2COOH > FCH2COOH > ClCH2COOH
C) NO2CH2COOH > NCCH2COOH > FCH2COOH > ClCH2COOH
D) NO2CH2COOH > FCH2COOH >NCCH2COOH > ClCH2COOH
E) ClCH2COOH > FCH2COOH >NCCH2COOH > NO2CH2COOH
Correct Answer : Option C
150. Two forms of D-glucopyranose, are called
A) enantiomers
B) anomers
C) epimers
D) diastereomers
E) tautomers
Correct Answer : Option B
Official key not published for this paper.
Page 1 of 36
Source: Commissioner for Entrance Examinations. Question paper published by Commissioner for Entrance Examinations.