KEAM 2026: KEAM Engineering entrance (Mathematics, Physics and Chemistry), session 5
Text of page 1
FINAL ANSWER KEY
Question Paper Code: 12/2026/OL
Exam:KEAM 2026 - 5
Date of Test: 21-04-2026
Let R be a relation in ℕ defined by {(�: �): � + 3� = 10, �, � ϵ ℕ}Then the range of
1. R is
A) {1, 2, 3, 4}
B) {2, 3, 4}
C) \(\{1,3,4\}\)
D) {1, 2, 3, }
E) {1, 3, }
Correct Answer : Option D
�� � �
2. The domain of �(�) =
�� � � � �
is
A) ℝ
B) ℝ − {2}
C) ℝ − {1}
D) ℝ − {0}
E) ℝ − {1, − 1}
Correct Answer : Option A
Let A and B be two sets of having 3 and 2 elements respectively. Then the number of
3. subsets of � × � having at least three elements is
A) 24
B) 52
C) 42
D) 64
E) 60
Correct Answer : Option C
The number of elements in the set {(�, �): 2� � + 3� � = 35, �, �� ℤ} , where ℤ is
4.
the set of all integers, is
A) 4
B) 6
C) 16
D) 12
E) 8
Correct Answer : Option E
Text of page 2
5. If |� + 4 | = 2 | � + 1 |, where � is a complex number, then |�| is equal to
A) 0
B) 2
C) 4
D) 8
E) 16
Correct Answer : Option B
6. If �(3 − �) = 2 + � , then � � =
�
A)
�
��
B)
�
�
C)
�
��
D)
�
���
E)
�
Correct Answer : Option A
� � �√�
7. The imaginary part of
� � �√�
is
��
A)
�
�
B)
�
√�
C)
�
�√�
D)
�
√�
E)
�
Correct Answer : Option D
8. The sum of � � + � � + . . . upto 25 terms is equal to
A) 0
B) �
C) -�
D) 1
E) -1
Correct Answer : Option E
Text of page 3
In a geometric progression of positive terms, if any term is equal to the sum of the next
9. two terms, then the common ratio of the geometric progression is equal to
√� � �
A)
�
√� � �
B)
�
√� � �
C)
�
√� � �
D)
�
√�
E)
�
Correct Answer : Option B
A geometric progression has an even number of terms. If the sum of all terms is five
10. times the sum of all odd terms, then the common ratio is equal to
A) 4
�
B)
�
C) 2
�
D)
�
�
E)
�
Correct Answer : Option A
If �, �, � are three unequal numbers such that �, �, � are in arithmetic progression and
11. � − �, � − �, � are in geometric progression, then �: �: � is
A) 3:4:5
B) 1:2:3
C) 1:3:2
D) 2:1:3
E) 1:4:3
Correct Answer : Option B
12. If three geometric means are inserted between 2 and 32, then the three numbers are
A) 4,6,8
B) 6,8,10
C) 4,8,32
D) 4,6,12
E) 4,8,16
Correct Answer : Option E
Text of page 4
�� �� ��
��� � ���
13. If
�
=
�
=
�
, then
A) � � = �(� + �)
B) � � = �(� + �)
C) � � = �(� + �)
D) � � = �(� + �)
E) � � = �(� + �)
Correct Answer : Option C
The number of ways in which we can choose a committee from 3 men and 6 women so
14. that the committee includes at least two men and exactly twice as many women as men
is
A) 35
B) 42
C) 46
D) 52
E) 55
Correct Answer : Option C
� � �
15. If
�!
+ =
�! ��!
, then the value of � is equal to
A) 100
B) 80
C) 90
D) 72
E) 120
Correct Answer:-Question Cancelled
There are two women participants in a badminton tournament. The number of games the
men played between themselves exceeds by 12 the number of games they played with
16. women. If each player played one game with each other, then the number of men in the
tournament was
A) 4
B) 6
C) 7
D) 8
E) 10
Correct Answer : Option D
��
If the 17th and 18th term in the expansion of (2 + �) are equal, then the value of �
17.
is equal to
A) 1
B) 2
C) 4
Text of page 5
D) 6
E) 8
Correct Answer : Option A
� 1
Let �(�) = � � . If f(x) is an odd function, �( − �) = �(�) and
�
18. ���2π x 2�
λ �(1)�(1) = 4 Then the value of λ is equal to
A) 1
B) -4
C) 0
D) 4
E) -1
Correct Answer : Option E
−4 − 5⎤
19. The value of the determinant of the inverse of the matrix ⎡ is
⎣ 2 2 ⎦
�
A)
�
�
B)
�
��
C)
�
D) 1
E) 2
Correct Answer : Option B
3 �−3 3 2⎤ 7 1 ⎤
20. If � = � � �=⎡ and �� = ⎡ , then λ is equal to
−1 1 ⎣⎢ 2 1⎦⎥ ⎣⎢−1 -1⎦⎥
A) 2
B) 4
C) 6
D) 7
E) 8
Correct Answer:-Question Cancelled
1 1⎤ � �⎤
If � = ⎡ and � = ⎡
��
21. then � + � is equal to
⎣⎢ 0 � ⎦⎥ ⎣⎢ � � ⎥⎦
A) 0
B) �
C) -�
D) 1
E) -1
Text of page 6
Correct Answer : Option A
22. If (� − 1)(� � − 5� + 7) < (� − 1) ,then � belongs to
A) ( − ∞, − 1) ∪ (2, 3)
B) ( − ∞, − 1] ∪ [2, 3]
C) ( − ∞, 1) ∪ (2, 3)
D) ( − ∞, 1) ∪ [2, 3)
E) ( − ∞, 1) ∪ (2, 3]
Correct Answer : Option C
�
23. The solution set of |� +
�
| >2 is
A) ℝ
B) ℝ − {0}
C) ℝ − {1, − 1}
D) ℝ − { − 1}
E) ℝ − { − 1, 0, 1}
Correct Answer : Option E
Let L be an arc of a circle which subtends 45o at the centre. If the radius of circle is 4
24. cm, then the length of the L in centimeter is
�
A)
�
B) π
�
C)
�
�
D)
�
�
E)
�
Correct Answer : Option B
25.
A) 2
B) 0
C) 1
D) -1
E) 4
Correct Answer : Option A
Text of page 7
� �
26. If ����
�
+ θ � = then the value of ���2θ is
�
��
A)
�
�
B)
�
��
C)
�
�
D)
�
E) 1
Correct Answer : Option C
� �
27. If 1 + ���� = α , 0 ≤ � ≤
�
, then ���
�
is equal to
���
A) � �
���
B) � �
�
C) �2 − �
���
D) � �
���
E) � �
Correct Answer : Option B
�√� �
28. The value of ��� -� � � + ��� ��� � is equal to
� �
�
A)
�
�
B)
�
�
C)
�
�
D)
�
E) π
Correct Answer : Option E
� �
29. The value of 2��� ��� � + ��� ��� � =
� �
�
A)
�
Text of page 8
��
B)
�
�
C)
�
�
D)
�
�
E)
�
Correct Answer : Option E
��
If α and β are respectively the minimum and maximum values of + 2���� ��� −
�
30. � � �
� , then =
� �
A) 10
B) 4
C) 6
D) 2
E) 12
Correct Answer : Option A
31. If the points (3,-2),(� ,2),(8,8) are collinear, then the value of � is
A) 0
B) 2
C) 4
D) 5
E) 6
Correct Answer : Option D
��
If the slope of the line joining the points (3,4) and (-2,� ) is equal to , then the value
32. �
of � is equal to
A) 0
B) 2
C) 3
D) 4
E) 6
Correct Answer : Option E
33. The distance of the point �(1, − 3) from the line 2� − 3� = 4 is
A) √13 units
B) 13 units
C) 7 units
Text of page 9
D) √7units
E) 2√13 units
Correct Answer : Option A
The line � − 1 = 0 is the directrix of the parabola, � � − �� + 8 = 0 . Then, the
34. values of � are
A) 8,4
B) 8,-4
C) -8,-4
D) 8
E) -8,4
Correct Answer : Option E
35. The length of the latus rectum of � � = − 9� is equal to
A) 9 units
�
B) units
�
C) 4 units
D) 3 units
�
E) units
�
Correct Answer : Option A
36. The centre and radius of the circle � � + � � − 2� + 4� = 8 respectively are
A) (1,2),√13
B) (-1,2),√13
C) (-1,-1),√13
D) (1,-2),√13
E) (2,1),√13
Correct Answer : Option D
If the length of the major axis of an ellipse is thrice the length of the minor axis, then its
37. eccentricity is equal to
�√�
A)
�
√�
B)
√�
�
C)
�
�
D)
√�
Text of page 10
�
E)
�√�
Correct Answer : Option A
→→→ → →
� + � +→
Let � , � , � be such that If
→ →
→ | = 3 ,|�
� = 0 .If |� | = 4 ,|→
� | =5
38. → → → → → →
then |� . � + � . � + � . � | =
A) 20
B) 24
C) 25
D) 30
E) 35
Correct Answer : Option C
→ → → →
If θ is the angle between two vectors � and � such that |� | = 7,|� | = 1 and |
39. → → � →.→
� × � | = � � − (� � ) � then the value(s) of k is/are
A) 5
B) -5
C) 3
D) -3
E) ±7
Correct Answer : Option E
→
40. If � is the origin and � is the midpoint of �( − 2, 1) and �(4, − 3) , then �� is
A) ^� + ^�
B) −�^ + − ^�
�^ �
C) � + ^�
� �
D) ^� − ^�
E) −�^ + ^�
Correct Answer : Option D
→ ^ → ^ → →
41. If � = ^
� + ^� + � and � = ^� − ^� + � , then the projection of � on � is
A) √3
�
B)
√�
��
C)
√�
D) -√3
�
E)
�
Text of page 11
Correct Answer : Option B
�� � � ��� ��� ��� ��� ���
If the lines = = and = = are perpendicular to
42. � � � � � �
each other, then the value of � is equal to
�
A)
�
�
B)
�
�
C)
�
D) 2
E) 1
Correct Answer : Option E
43. The equation of straight line passing through (�, �, �)and parallel to �-axis is
��� ��� ���
A) = =
� � �
��� ��� ���
B) = =
� � �
��� ��� ���
C) = =
� � �
��� ��� ���
D) = =
� � �
��� ��� ���
E) = =
� � �
Correct Answer : Option A
The equation of a line passing through the point (1,-2,3) and equally inclined to the axes
44. are
A) �+1=�−2=�+3
B) �+1=�−2=�−3
C) �−1=�−2=�+3
D) �−1=�+2=�+3
E) �−1=�+2=�−3
Correct Answer : Option E
��� ��� ���
45. The vector equation of the straight line
�
=
�
=
�
is
A) ^) + �(3�^ − 2�^ − 2�
(2�^ − ^� − 3� ^)
B) ^) + μ (3�^ + 2�^ + 2�
(2�^ − ^� + 3� ^) , where µ is a scalar.
C) (3�^ − 2�^ − 2�^) + μ (2�^ − ^� − 3�
^) , where µ is a scalar.
D) ^) + μ (2�^ − ^� + 3�
(3�^ + 2�^ + 2� ^) , where µ is a scalar.
Text of page 12
E) ^) + μ (2�^ + ^� + 3�
(3�^ + 2�^ + 2� ^) , where µ is a scalar.
Correct Answer : Option B
A dice is thrown three times. If the first thrown is five, the probability of getting 14 as the
46. sum is
�
A)
�
�
B)
�
�
C)
�
�
D)
�
�
E)
�
Correct Answer : Option A
47. If the variance of 1, 2, 3, . . . , � is 10, then the value of � is
A) 5
B) 9
C) 11
D) 13
E) 15
Correct Answer : Option C
� � � � � � �
If �(�) = , �(�) = and �(� ∩ �) = , then �(� / � ) = ( � and �
48. � � �
denote the complements of A and B respectively)
��
A)
��
��
B)
��
��
C)
��
��
D)
��
��
E)
��
Correct Answer : Option A
We have two data sets each of size 5. The variances are 4 and 5 and the corresponding
49. means are 2 and 4 respectively. Then the variance of the combined data set is
�
A)
�
Text of page 13
�
B)
�
C) 6
��
D)
�
��
E)
�
Correct Answer : Option D
�� � � �
50. The value of lim �
� � �� � � �
� is
�→�
A) 32
B) 16
C) 8
D) 4
E) 0
Correct Answer : Option C
√� � �����
51. The value of lim
�→� |�|
is equal to
A) -2
B) -√2
C) √2
D) 1
E) 2
Correct Answer : Option C
�� � ��
52. The positive integer n, such that lim = 108
�→� ���
A) 3
B) 12
C) 6
D) 9
E) 4
Correct Answer : Option E
�(�)
Let lim �(�)�(�) = 16 and lim = 4 If both lim �(�) and lim �(�)
�→� � → � �(�) �→� �→�
53.
exists, then lim �[(�) + �(�)] =
�→�
A) ±10
B) -16
C) ±2
Text of page 14
D) 16
E) ±4
Correct Answer : Option A
� ��(�) � �(�)
54. If �(1) = 2; � (1) = 1 , then lim �
���
�=
�→�
A) 0
B) -2
C) -1
D) 2
E) 1
Correct Answer : Option E
"
Let �(�) and �(�) be twice differentiable functions defined on [0,2] such that � (�)
55. − � "(�) = 0, � �(1) = 4, � �(1) = 2, �(2) = 9, �(2) = 3.
At � = 3/2, �(�) − �(�) =
A) 2
B) 3
C) 5
D) 8
E) 10
Correct Answer : Option C
��� ��
56. If � = ����� � then =
��� ��
�
A)
�(� � �)(� � �)
�
B)
�(� � �)(� � �)
�
C)
(� � �)(� � �)
�
D)
(� � �)(� � �)
�
E)
�(� � �)(� � �)
Correct Answer : Option B
� ��
57. If � = 3 + � � + � � + � � , then at � = 3 is equal to
��
A) � � + 27���� 3 + 54
B) � � + 27���� 3 + 27
Text of page 15
C) � � + 54���� 3 + 27
D) � � + 54���� 3 + 54
E) � � + 54���� 3 + 54
Correct Answer:-Question Cancelled
� � ��
58. If � = ���� + � , then
�� �
is equal to
� � � ����
A)
(���� � � �) �
� � � ����
B)
(���� � � �) �
� � � ����
C)
(���� � � �) �
���� � � �
D)
(���� � � �) �
���� � � �
E)
(���� � � �) �
Correct Answer : Option E
��
59. If � = ����� � + ���� � , then
��
is equal to
� � ����� �
A)
�
� � ���� ��
B)
�
C) � + ����� �
D) � + ���� 10
� �
E) [ + 1]
� ���� ��
Correct Answer : Option E
60. The function �(�) = � � − 2� � is strictly increasing on
A) (-2,0) and [1,∞ )
B) [-1,0] and [2,∞ )
C) [-1,0] and [1,∞ )
D) (-2,0] and [0,∞ )
E) [-2,0] and (1,∞ )
Correct Answer : Option C
If the rate of increase of the radius of circle 5 cm/sec, then the rate of increase of its area
61. when the radius is 20 cms, will be
A) 10π �� � / ���
Text of page 16
B) 20π �� � / ���
C) 100π �� � / ���
D) 200π �� � / ���
E) 400π �� � / ���
Correct Answer : Option D
If the function �(�) = � � + �� + 1 is increasing on [1,2] , then � is greater than or
62.
equal to
A) -2
B) -5
C) -4
D) -7
E) -3
Correct Answer : Option A
63. The absolute maximum value of the function �(�) = � � − 3� + 2 in [0,2] is
A) 0
B) 1
C) 2
D) 3
E) 4
Correct Answer : Option E
� � �
64. If ∫ �3� ����( ) − ����( ��� = �(�)���( ) + � then �(2) is equal to
� � �
A) -2
B) 2
C) 4
D) 8
E) 16
Correct Answer : Option D
�� / �
65. If ∫ � �� = �2 � / � + � then � is equal to
�
�
A)
����
B) ���4
�
C)
����
��
D)
����
Text of page 17
��
E)
����
Correct Answer : Option E
� � ����
66. ∫ � �� � � ���� ��� =
A) � ����� + �
B) −� ����� + �
�
C) � ���� + �
�
�
D) −� ���� + �
�
�
E) 2� ���� + �
�
Correct Answer : Option D
67. If � = ∫ � � ������,� = ∫ � �������, then � + � =
A) −� � + �
B) �� + �
C) −� � + �
D) �� + �
E) 2� � + �
Correct Answer : Option D
68. ∫ ��� ��� ��������� =
��� ��
A) +�
�
���� ��
B) +�
�
���� ��
C) +�
�
��� ��
D) +�
�
���� ��
E) +�
�
Correct Answer : Option D
69.
A) 1 and 1
B) 0 and 1
C) 1 and -1
Text of page 18
D) -1 and 0
E) -1 and 1
Correct Answer : Option E
70.
�
A)
�
�
B)
�
�
C)
�
�
D)
��
�
E)
�
Correct Answer : Option D
The area of the region bounded by the lines, � = � + 2, � = 0, � = 1 and � = 0 is
71.
A) 2 sq.units
�
B) sq.units
�
�
C) sq.units
�
D) 9 sq.units
E) 12 sq.units
Correct Answer : Option B
72.
A) 1
B) √2+1
C) √2-1
D) 1-√2
E) -√2
Correct Answer : Option A
73. The solution of (� � + 1)������ + � ������� = 0 is
A) (� � + 1)���� = �
B) (� � + 1) = �����
C) � � = �����
Text of page 19
D) (� � − 1)���� = �
E) (� � + 1)���� = �
Correct Answer : Option A
74. The function � = �� � + �� �� , � and � are constants, is a solution of
A) �" + � = 0
B) �" − � = 0
C) �" + � = 0
D) � " − 2� = 0
E) � " + �� = 0
Correct Answer : Option B
Which one of the following point is not in a feasible region bounded by the inequalities �
75. ≤ 4, � ≤ 6, � + � ≤ 6, � ≥ 0, � ≥ 0
A) (0,0)
B) (4,0)
C) (4,2)
D) (0,6)
E) (6,0)
Correct Answer : Option E
76. A physical quantity that has the same dimensions as those of Boltzmann constant is
A) energy
B) bulk modulus
C) power
D) gas constant R
E) thermal conductivity
Correct Answer:-Question Cancelled
Taking into consideration of significant figures, in the conversion relation
77. 2.0 ms-2 = X km h-2, the value of X is
A) 2.6 x 104
B) 2.592 x 104
C) 2 x 104
D) 2.592 x 105
E) 2.60 x 105
Correct Answer : Option A
A body starts moving from the origin along a straight line at a speed of 20 kmh-1 for 1
78. hour. Then it turns perpendicular to its path and moves with the same velocity for 30
minutes. Then the magnitude of its displacement is
Text of page 20
A) 10 km
B) 20 km
C) 10√5km
D) 10√2km
E) 20√5km
Correct Answer : Option C
If the angular speed of a particle moving in a circular path of radius 1.2 m is increased
79. from 2 rads-1 to 4 rads-1 keeping its radius constant, then its linear speed is increased by
A) 1.6 ms-1
B) 2.4 ms-1
C) 3.6 ms-1
D) 4.8 ms-1
E) 6 ms-1
Correct Answer : Option B
→ ^ →
^ + √3� �^� + 5� with � in m and t in s,
If the position vector of a particle is � = 2��
80.
then at t=1s the angle made by the velocity vector with x-axis is
A) 30o
B) 45o
C) 60o
D) 120o
E) 90o
Correct Answer : Option C
If the maximum acceleration of a moving platform to keep a box of mass 5 kg on it
81. without sliding is 3�� �� , then the static friction between the box and floor of the
platform is (� = 10�� ��)
A) 0.15
B) 0.25
C) 0.30
D) 0.35
E) 0.4
Correct Answer : Option C
If 10 identical silver coins each of mass m are placed one over the other, then force on
82. the 6th coin from the bottom is
A) 10 mg
B) 8 mg
C) 6 mg
Text of page 21
D) 4 mg
E) zero
Correct Answer:-Question Cancelled
A body initially at rest breaks up into two pieces of masses M and 3M and move with a
83. total kinetic energy of � , then the kinetic energy of the piece of mass M is
��
A)
�
�
B)
�
��
C)
�
�
D)
�
�
E)
�
Correct Answer : Option A
If a proton, a deuteron and an α -particle have the same speed, then the kinetic energy
84. is
A) same for all particles
B) the lowest for proton
C) the highest for deuteron
D) same for proton and deuteron
E) the lowest for α-particle
Correct Answer : Option B
The moment of inertia of a system of two masses 2 kg and 4 kg lying in the x-y plane at
85. distances, 2 m and 4 m, respectively from the origin about the z-axis is (in kgm2)
A) 36
B) 48
C) 64
D) 72
E) 80
Correct Answer : Option D
86. A swimmer jumps from a height is able to increase the number of loops made in air by
A) stretching his legs outwards
B) decreasing angular velocity
C) by stretching his arms
D) by pulling his legs and arms inward
E) by pulling his legs inward and stretching his arms outward
Correct Answer : Option D
Text of page 22
The ratio of the weights of an object of mass m at a height R and 2R from the surface of
87. earth is (R is the radius of earth)
A) 4 : 9
B) 1 : 1
C) 9 : 4
D) 1 : 2
E) 4 : 1
Correct Answer : Option C
If the magnitude of gravitational potential energy of an object of mass 200 kg at a height
� �
88. of 3.6 × 10 � from the earth surface is 6 × 10 � then its value at a height of 5.6 ×
10 �� is (Radius of earth is 6.4 × 10 ��)
A) 5 × 10 � �
B) 4 × 10 � �
C) 3 × 10 � �
D) 2 × 10 � �
E) 10 � �
Correct Answer : Option A
The force required to increase the length of a thin copper wire of cross-sectional area 0.1
89. ��
cm2 by 0.1 % is (Young’s modulus of copper is 11 × 10 �� ��)
A) 550 �
B) 11 × 10 ��
C) 10.5 × 10 ��
D) 1100 �
E) 5.5 × 10 ��
Correct Answer : Option D
If a huge tank has a small side hole at a depth of 2 m from the surface of water, then the
90. velocity of water flowing through the hole is (� = 10�� �� )
A) 2 √5�� ��
B) 2√10�� ��
C) √10�� ��
D) 4√10�� ��
E) 4√5�� ��
Correct Answer : Option B
91. Lakes and ponds freeze at the top surface with water below. This phenomenon is due to
A) high pressure at their bottom
Text of page 23
B) low pressure at their bottom
C) the maximum density of water at 4o C
D) the maximum density of water at 0o C
E) elevation of freezing point of water
Correct Answer : Option C
If the temperature of 2 moles of krypton gas is increased from -11oC to 89oC at
92. constant volume, then (specific heat at constant volume of krypton is CV)
A) work done on the gas is not zero
B) internal energy is not changed
C) work is done by the gas
D) amount of heat added is 200 CV
E) internal energy is increased by 100 CV
Correct Answer : Option D
If an ideal heat engine with an efficiency of 40 % rejects heat at 27oC , then it should
93. have absorbed heat at
A) 377oC
B) 500oC
C) 227oC
D) 427oC
E) 460oC
Correct Answer : Option C
Two perfect monoatomic gases at temperatures 300 K and 410 K are mixed without any
94. loss of heat. If 1024 and 1023 are the number of molecules in the respective gases, then
the temperature of the mixture is
A) 340 K
B) 310 K
C) 360 K
D) 350 K
E) 370 K
Correct Answer : Option B
If the temperature T of oxygen molecule is raised to 9T, then its root mean square speed
95. � is increased to
A) 3�
B) 2�
C) √2�
D) √3�
Text of page 24
�
E) ���
Correct Answer : Option A
For a particle executing simple harmonic motion with amplitude A and time period T
96. along x-axis, the time taken by the particle to move from x = 0 to
x = A is
�
A)
�
�
B)
�
�
C)
�
�
D)
�
�
E)
�
Correct Answer : Option C
With Laplace correction in Newton’s formula for the velocity of sound in gases, the
97. velocity of sound in monoatomic gas at STP is
��
A) � ��
��
B) � ��
��
C) � ��
��
D) � ��
�
E) ��
Correct Answer : Option B
A, B and C are three points in space forming an equilateral triangle of side 10 cm. If a
98. point charge 8 µC is placed at A , then the work done in moving a unit charge from B to
C is
A) zero
B) 720 J
C) 7200 J
D) 360 J
E) 3600 J
Correct Answer : Option A
Text of page 25
Three capacitors A,B,C with respective capacitance of 1µF, 2µF and 3 µF are connected
99. as shown. For a given voltage source V connected across them, the combination that can
store the maximum energy is
A)
B)
C)
D)
E)
Correct Answer : Option E
The equipotential surface of a system of two point charge 5 µC and -5µC at points A and
100. B separated by 80 cm is a plane perpendicular to the line connecting A and B at
A) 0.4 m from A
B) 0.6 m from A
C) 0.5 m from A
D) 0.6 m from B
E)
0.5 m from B
Correct Answer : Option A
If an infinitely long uniformly charged wire produces an electric field of intensity E at a
101. distance of d from it, then the linear charge density λ of the wire is
A) π ϵ � ��
�
B) ϵ ��
� �
�
C) ϵ ��
� �
D) 2π ϵ � ��
E) ϵ � ��
Correct Answer : Option D
Text of page 26
The ratio of the rate of flow of electrons through three resistors connected in parallel to a
102. voltage source V is 3 : 2 : 1, then the ratio of their respective resistance values is
A) 1:1:1
B) 6 :3 :2
C) 2 :3:6
D) 9 :4 : 1
E) √6:√4:√2
Correct Answer : Option C
The ratio of the heat produced in a 2Ω and a 4 Ω resistor connected in series with a
103. voltage source of 12 V is
A) 2:1
B) 1 :4
C) 4:1
D) 1:2
E) 1: 8
Correct Answer : Option D
Three cells of 3 V, 4 V and 4 V with respective internal resistances 0.5Ω, 0.75 Ω and
0.75 Ω are connected is series to a resistor of 4 Ω. Then the current in the circuit is
104.
A) 1A
B) 0.5 A
C) 0.25 A
D) 0.75 A
E) 0.67 A
Correct Answer : Option B
105. If a current carrying circular loop is suspended in a uniform magnetic field B , then
A) a couple will act on the loop
B) the loop will start to rotate
C) areal vector of the loop will be set in the direction of B
D) areal vector of the loop will be perpendicular to the direction of B
E) loop will be deflected away from the field B
Correct Answer : Option C
In a uniform magnetic field B, a bar magnet of magnetic moment � is kept suspended
106. at an angle of 600 with respect to B. The work done to turn it from 60o to 90o with
respect to the field is
Text of page 27
A) ��
B) √2��
C) 0
D) 2��
��
E)
�
Correct Answer : Option E
The flow of current of 2A through a straight solenoid of length 2 m produces a magnetic
107. field of 2π x 10-4T at its centre. Then the number of turns in the solenoid is
A) 600
B) 500
C) 3500
D) 5000
E) 700
Correct Answer : Option B
A wire of length 4 m carrying a current of 1 A is bent to form a circular loop. The magnetic
108. moment of the loop (in Am2) is
�
A)
��
�
B)
��
�
C)
�
�
D)
�
E) 4π
Correct Answer : Option D
The plane of a circular loop of area 150 cm2 is perpendicular to a uniform magnetic field
109. of 0.5 T. If the loop is turned such that its plane is in the direction of the field in 0.5 s, then
the induced emf produced is
A) 25 mV
B) 10 mV
C) 2.5 mV
D) 15 mV
E) 7.5 mV
Correct Answer : Option D
��
Two identical transformers A and B each with = 2 are connected such that the
��
110. secondary output obtained from A is given as the primary input voltage for B. If the
primary ac voltage of A is 200 V, then the secondary voltage from B is
Text of page 28
A) 100 V
B) 200 V
C) 50 V
D) 400 V
E) 500 V
Correct Answer : Option C
111. Microwaves are
A) used in radio and television communications
B) having frequency range from 54 MHz to 890 MHz
C) short wavelength radio waves
D) produced by hot bodies and molecules
E) absorbed by ordinary glass
Correct Answer : Option C
An object placed at 10 cm in front of a concave mirror of focal length of 8 cm gives
112. image of magnification of
A) 4
B) 6
C) 8
D) 2
E) 10
Correct Answer : Option A
The magnifying power of a telescope of length 76 cm in the normal adjustment is 75.
113. Then the focal lengths of the objective and eyepiece lenses are, respectively,
A) 50 cm, 25 cm
B) 70 cm, 5 cm
C) 75 cm, 1 cm
D) 73 cm, 2 cm
E) 60 cm, 15 cm
Correct Answer : Option C
The fringe width obtained in a given Young’s double slit experimental set up for red light,
114. blue light and green light are, respectively, βR ,βB and βG .Then
A) βB > βR
B) βR > β G
C) βG > βR
D) βB > β R
E) βR = β B = β G
Text of page 29
Correct Answer : Option B
If the de Broglie wavelength associated with an electron is 0.1227 nm, then its
115. accelerating potential is
A) 64 V
B) 200 V
C) 100 V
D) 160 V
E) 36 V
Correct Answer : Option C
If a radiation of energy 5.2 eV falls on the photosensitive surfaces of Mo and Ni, they emit
116. photoelectrons with maximum kinetic energy of 0.5eV and 1 eV, respectively. Then the
work function of
A) Mo is 2.6 eV
B) Ni is 6.2 eV
C) Mo is 6.2 eV
D) Ni is 4.2 eV
E) Mo is 4.2 eV
Correct Answer : Option D
���
If a radioactive parent nucleus �� � emits two alpha particles and two β particles
117.
successively to reach the daughter nucleus �� � , then the values of � and � are
A) 224 and 90
B) 220 and 94
C) 228 and 92
D) 230 and 92
E) 226 and 92
Correct Answer : Option C
The difference in magnitudes of angular momentum of the electrons revolving in 5th
118.
Bohr’s orbit and 3rd Bohr’s orbit of hydrogen atom is
��
A)
�
�
B)
�
�
C)
��
��
D)
��
��
E)
��
Text of page 30
Correct Answer : Option B
119. Intrinsic semiconductors Ge or Si doped with
A) indium becomes an n-type semiconductor
B) antimony becomes a p-type semiconductor
C) phosphorus becomes a n-type semiconductor
D) boron becomes a n-type semiconductor
E) arsenic becomes a p-type semiconductor
Correct Answer : Option C
Four ideal diodes are connected as shown then the current drawn from the battery is
120.
A) zero
B) 10 mA
C) 100 mA
D) 50 mA
E) 20 mA
Correct Answer : Option B
The empirical formula of a metal oxide which has 54 % metal (M) and 46 % oxygen (O) is
121. (Atomic mass of M = 27 amu and O= 16 amu)
A) M 3O 2
B) MO2
C) M 2O 3
D) M 2O 5
E) M 2O
Correct Answer : Option C
The threshold wavelength of a metal is 6000 A▫. The work function of the metal is ( h =
122.
6.62 × 10-34 J s )
A) 3.31 ×1019 J
B) 3.31 ×10-19 J
C) 13.2 ×10-19 J
D) 13.2 ×1019 J
E) 1.5 ×10-19 J
Text of page 31
Correct Answer : Option B
123. The radius of the first orbit He+ is
A) 52.9 pm
B) 13.24 pm
C) 211.6 pm
D) 105.8 pm
E)
26.45 pm
Correct Answer : Option E
124. In Mosley experiment, the X-ray spectrum is obtained by plotting
A) square root of frequency vs atomic mass
B) square root of frequency vs atomic number
C) square of frequency vs atomic mass
D) square root of wavelength vs atomic number
E) square root of wavelength vs atomic mass
Correct Answer : Option B
Which of the following elements have the highest and the lowest first ionization enthalpy?
125. (i) Be (ii) B (iii) C (iv) N (v) O
A) (ii) and (iv)
B) (i) and (v)
C) (i) and (iii)
D) (ii) and (iii)
E) (i) and (ii)
Correct Answer:-Question Cancelled
126. The correct increasing order of dipole moment of the following molecules is
A) NF3 < CHCl3 < NH3 < H2O
B) NF3 < CHCl3 < H2O < NH3
C) H2O < NF3 < CHCl3 < NH3
D) CHCl3 < NF3 < H2O < NH3
E)
NH3 < NF3 < CHCl3 < H2O
Correct Answer : Option A
The number of bonding pairs and lone pairs of electrons in BrF5 molecule are
127. respectively
A) 4 and 2
B) 3 and 2
C) 4 and 1
D) 5 and 1
Text of page 32
E) 3 and 1
Correct Answer : Option D
128. Which of the following bond has highest mean bond enthalpy?
A) N=N
B) O=O
C) N≡N
D) C≡C
E) C≡O
Correct Answer : Option E
The correct increasing order of enthalpy of fusion of ΔfusH˚ (in kJ mol-1) of the following
129.
compounds is
A) CH3COCH3 < CCl4 < C6H6
B) CH3COCH3 < C6H6 < CCl4
C) CCl4 < C6H6 < CH3COCH3
D) CCl4 < CH3COCH3 < C6H6
E) C6H6 < CH3COCH3 < CCl4
Correct Answer : Option D
The solubility product, Ksp of a sparingly soluble salt, AX2, is
130.
3.2 × 10-14 mol3lit-3. Its solubility is
A) 4 × 10-3mol lit-1
B) 2 × 10-2mol lit-1
C) 2 × 10-5mol lit-1
D) 8 × 10-4mol lit-1
E) 2 × 10-3mol lit-1
Correct Answer : Option C
Match the correct pH value with the following substances:
(a) Milk of magnesia (i) pH = 6.8
131. (b) Black coffee (ii) pH = 7.8
( c) Egg white (iii) pH = 5
(d) Milk (iv) pH = 10
A) (a)-(iv), (b)-(ii), (c)–(i). (d)-(ii)
B) (a)-(iv), (b)-(ii),(c)–(iii), (d)-(i)
C) (a)-(i), (b)-(iv), (c)–(iii). (d)-(ii)
D) (a)-(i), (b)-(iii), (c)–(ii), (d)-(iv)
E) (a)-(iv), (b)-(iii), (c)–(ii). (d)-(i)
Correct Answer : Option E
Text of page 33
The ΔrG▫ of the galvanic cell in which the following cell reaction takes place,
132. 2Cr(s) + 3Cd2+(aq) → 2Cr3+(aq) + 3Cd(s), is
(E▫Cr3+/Cr = -0.74 V and E▫Cd2+/Cd = -0.40 V )
A) -196.86 kJ mol-1
B) +196.86 kJ mol-1
C) -96.50 kJ mol-1
D) + 96.50 kJ mol-1
E) +98.12 kJ mol-1
Correct Answer : Option A
The molar conductivity of a weak mono basic acid, HA at 298 K is 70 Scm2mol-1. What
133. is the percentage ionisation of HA at 298 K?
[At infinite dilution λH+ = 340 Scm2mol-1 and λA- = 80 Scm2mol-1]
A) 8.35 %
B) 16.7 %
C) 20 %
D) 32.5 %
E) 15.3 %
Correct Answer : Option B
134. The percentage of helium present in air used by scuba divers is
A) 56.2 %
B) 11.7 %
C) 32.1%
D) 19.7%
E) 21.5%
Correct Answer : Option B
A first order reaction follows the equation k = (4 x 1010 s-1) e-2000/T . The value of Ea for
135.
the reaction is about (R = 8.314 J K-1 mol-1)
A) 17.4kJ mol-1
B) 18.5kJ mol-1
C) 17.5kJ mol-1
D) 16.6kJ mol-1
E) 17.8kJ mol-1
Correct Answer : Option D
136. In a pseudo first order reaction, the following results were obtained.
Text of page 34
Average rate of the reaction between 20 and 40 seconds is
A) 0.01 mol lit-1 s-1
B) 0.02 mol lit-1 s-1
C) 0.001 mol lit-1 s-1
D) 0.1 mol lit-1 s-1
E) 0.04 mol lit-1 s-1
Correct Answer : Option A
137. Which of the following compound of manganese is a mixed oxide?
A) MnO
B) Mn3O4
C) Mn2O3
D) MnO2
E) Mn2O7
Correct Answer : Option B
138. The formula of Pentaamminecarbonatocobalt(III)chloride is
A) [Co(NH3)5(CO)]Cl2
B) [Co(NH3)5(CO3)]Cl
C) [Co(NH3)5(CO)3]Cl2
D) [Co(NH3)5(CO3)]Cl2
E) [Co(NH3)5(CO3)]Cl3
Correct Answer : Option B
The correct increasing order of wavelength of absorption of the following complexes is
139. (i) [CoCl(NH3)5]2+ (ii) [Co(NH3)5(H2O)]3+ (iii) [Co(NH3)6]3+ (iv) [Co(CN)6]3-
A) (i) < (ii) < (iii) < (iv)
B) (i) < (ii) < (iv) < (iii)
C) (ii) < (i) < (iv) < (iii)
D) (iv) < (iii) < (ii) < (i)
E) (iv) < (i) < (ii) < (iii)
Correct Answer : Option D
Text of page 35
When sodium fusion extract is treated with sodium nitropruside, the appearance of violet
140. colour is due to the formation of
A) [Fe(CN)5NO]2-
B) [Fe(CN)5NO]2+
C) [Fe(CN)5NOS]4-
D) [Fe(CN)5NOS]2-
E) [Fe(CN)5NOS]2+
Correct Answer : Option C
Which of the following gives 2-methylbutane on hydrogenation?
(i) 2-methylbut-1-ene (ii) 3-mehtylbut-1-yne (iii)2-methylbut-2-ene
141.
(iv)3-methylbut-1-ene (v) pent-2-ene
A) (i) and (iii)
B) (ii), (iii), (iv)
C) (ii), (iii), (v)
D) (i), (ii), (v)
E) (i), (iii), (iv)
Correct Answer:-Question Cancelled
An alkene, C3H6 (X), on treatment with HBr in presence of peroxide gives(Y). The
142. compound(Y) on treatment with AgNO2 in ethanol gives (Z). The compounds (X), (Y) and
(Z) are respectively
A) propene, 1-bromopropane, 1-nitropropane
B) propene, 2-bromopropane, 2-nitropropane
C) propene, 2-bromopropane, 1-nitropropane
D) propyne, 1-bromopropane, 1-nitropropane
E) propene, 1,2-dibromopropane, 1,2-dinitropropane
Correct Answer : Option A
143. The reaction CH3Br + AgF → CH3F + AgBr is termed as
A) Stephen reaction
B) Swarts reaction
C) Sandmayer reaction
D) Kolbe’s reaction
E) Riemer-Tiemann reaction
Correct Answer : Option B
When 2-methylbutan-2-ol is treated with Lucas reagent con.HCl and ZnCl2 at room
144. temperature, the product obtained is
A) 2-chlorobutane
B) 2-chloro-2-methylbutane
C) 1-chlorobutane
Text of page 36
D) 1-chloropentane
E) 2-chloro-2-methylbutene
Correct Answer : Option B
The relative ease of dehydration of the following alcohols is
145.
(i) Propan-2-ol (ii) Propan-1-ol (iii) 2-Methylpropan-2-ol
A) (iii) > (ii) > (i)
B) (ii) > (i) > (iii)
C) (ii) > (iii) > (i)
D) (i) > (ii) > (iii)
E) (iii) > (i) > (ii)
Correct Answer : Option E
146. Which of the following is a commercial method of manufacture of benzaldehyde?
A) Hydrogenation of benzoylchloride with Pd/BaSO4 as catalyst.
B) Oxidation of toluene with chromyl chloride followed by hydrolysis
C) Toluene is treated with Cr2O3 in acetic anhydride followed by hydrolysis
D) Side chain chlorination of toluene followed by hydrolysis.
E) Benzene is treated with CO and HClin the presence of anhydrous AlCl3.
Correct Answer : Option D
Vigorous oxidation of n-propylbenzene with alkaline potassium permanganate (KMnO4-
147. KOH/∆) followed by hydrolysis gives
A) phenol
B) phenyl acetic acid
C) phenyl propionic acid
D) benzaldehyde
E) benzoid acid
Correct Answer:-Question Cancelled
The descending order of basic strength of the following amines is
148. (i) N-Methylbenzenamine (ii) N.N’-Dimethylbenzenamine (iii) Benzenamine (iv)
Phenylmethanamine
A) (i) > (ii) > (iv) > (iii)
B) (iv) > (i) > (ii) > (iii)
C) (iv) > (ii) > (i) > (iii)
D) (iv) > (iii) > (ii) > (i)
E) (i) > (iv) > (ii) > (iii)
Correct Answer : Option C
Benzene diazoniumchloride on treatment with HCl in the presence of copper powder
149. gives chlorobenzene. This reaction is termed as
Text of page 37
A) Sandmeyer reaction
B) Gatterman reaction
C) Stephen reaction
D) Gatterman Koch reaction
E) Etard reaction
Correct Answer : Option B
Which of the following statements are true about sucrose?
(i) It is a dissacharide
(ii) It is a reducing sugar
150. (iii) It is laevorotatory
(iv) Sucrose on hydrolysis gives equimolar mixture of D(+) glucose and D-(-)fructose.
(v) In sucrose, two monosacharides are held together by a glycosidic linkage
A) (i), (ii), (iii)
B) (i), (ii), (v)
C) (ii), (iii), (v)
D) (i), (iii), (v)
E) (i), (iv), (v)
Correct Answer : Option E
Official key not published for this paper.
Page 1 of 37
Source: Commissioner for Entrance Examinations. Question paper published by Commissioner for Entrance Examinations.