KEAM 2026: KEAM Engineering entrance (Mathematics, Physics and Chemistry), session 1
Text of page 1
FINAL ANSWER KEY
Question Paper Code: 5/2026/OL
Exam:KEAM 2026 - 1
Date of Test: 17-04-2026
Let � and � be two subsets of a universal set �. If �(�) = 116 ,�(� ∪ �) = 99 , �(
1.
�) = 61 and �(� ∩ �) = 28 , then �(� �) is equal to
A) 47
B) 45
C) 53
D) 48
E) 50
Correct Answer : Option E
Let �(�) = ��� ��� and �(�) = � − 2 . To define the composite function � ∘ � , the
2. largest domain of �(�) has to be
A) [2, 5]
B) [1, 3]
C) [0, 2]
D) [ − 1, 3]
E) [ − 3, 3]
Correct Answer : Option B
��
3. Let �(�) =
� � ����� � �����
,� ϵ ℝ . Then the range of the function � is
�
A) [ , 5]
�
� ��
B) [ , ]
� �
�
C) [ , 5]
�
�
D) [ , 5]
�
� ��
E) [ , ]
� �
Correct Answer : Option C
Let �(�) = � � − 10� and �(�) = � � + 5 for � ϵ ℝ . Then, for all �,�(2�) − (�
4. ∘ �)(�) =
A) 30
B) 20
C) -30
Text of page 2
D) -20
E) 15
Correct Answer : Option A
―= � � ��
If the complex number � = � + �� satisfies the equation 5� − 2� , then the
5. ���
value of � + � is equal to
A) 7
B) -3
C) 3
D) -1
E) -7
Correct Answer : Option D
―
���
6. Let � = 1 + � , where � = √−1 . If � −
��
= λ � , then the value of λ is equal to
A) 12
B) 13
C) 18
D) 23
E) 24
Correct Answer : Option B
��(�) ��(�) �
7. The complex number � satisfying the equation
���
+
� � ��
=
� � ��
, is
A) 6-5i
B) -4+5i
C) 5-4i
D) 3-5i
E) 4-5i
Correct Answer : Option E
� � ��
If α is a real number satisfying α � − = 2 , then the value of �α + � is equal
8. �� �
to
A) 2048
B) 4096
C) 2024
D) 4048
E) 5096
Correct Answer : Option B
Text of page 3
The sum of the first two terms of a geometric series is 12 and the third term is 16. Then
9. the common ratio r > 0 of the geometric progression is
�
A)
�
�
B)
�
C) 2
D) 3
�
E)
�
Correct Answer : Option C
The sum of four consecutive terms in a geometric progression is 960. If the fourth term is
10. 8 times as large as the first term, then the smallest number in the geometric progression
is
A) 40
B) 64
C) 128
D) 160
E) 240
Correct Answer : Option B
�
If ��� θ ,√2��� θ and √3��� θ , where 0 < � < , are the second, third and
�
11. fourth terms of a geometric series, respectively, then the first term of the geometric series
is
�
A)
�√�
�
B)
�√�
�
C)
√�
�
D)
√�
�
E)
√�
Correct Answer : Option A
The A.M. and G.M. of two positive real numbers � and � (� > � )are � and �
12. respectively. If �: � = 5: 3 ,
�
then � � + � : �� =
A) 83:9
B) 82:9
C) 83:6
D) 82:7
E) 9:1
Text of page 4
Correct Answer : Option B
Let S be the set of all 3-digit numbers containing the digits 3, 5 and 7 without repetition.
13. The sum of all numbers in S is
A) 3330
B) 2220
C) 4590
D) 1110
E) 4440
Correct Answer : Option A
There are 3 boys and 4 girls in a group. The number of ways they can sit in a row so that
14. between any two boys there is a girl and between any two girls there is a boy, is
A) 88
B) 96
C) 124
D) 144
E) 288
Correct Answer : Option D
�
= �� + �� � + �� � � + . . . . . + �� � � . Then the value of �� + ��
Let (2 − �)
15.
+ �� + . . . . . + �� is equal to
A) -511
B) 510
C) -512
D) 512
E) -510
Correct Answer : Option E
The number of arrangements of the letters of the word BANANA so that the arrangement
16. starts and ends with the same letter, is
A) 12
B) 16
C) 18
D) 20
E) 24
Correct Answer : Option B
�
If the coefficient of � � in the binomial expansion of (2 + �) is 160, then the coefficient
17. � �
of � � in the binomial expansion of (2 − � ) is
A) 160
Text of page 5
B) 320
C) -160
D) -320
E) -960
Correct Answer : Option C
A system of equations is given in the matrix form as
18.
where α is an integer. If the system of equations does not have a unique solution, then
the value of α is equal to
A) 1
B) 2
C) 3
D) 4
E) 5
Correct Answer : Option A
2 �⎤ 3 2⎤ 3� + 2 10⎤ � �
Let � = ⎡ ,� = ⎡ and � = ⎡ .If � � = � ,then the value
19. ⎣3 1⎦ ⎣1 4⎦ ⎣14 − � 10⎦
of � is equal to
A) 1
B) 2
C) 3
D) 4
E) 5
Correct Answer : Option B
20.
A) 3,-3
B) 0,5
C) 6,-6
D) 5,-5
E) 0,-5
Correct Answer : Option A
�
Let � be a non-singular square matrix of order 3. If � − � = 20 � , where � is the
21. -�
unit matrix of order 3, then � =
A) 20 �
Text of page 6
�
B) (� − �)
��
C) 20(� − �)
�
D) �
��
�
E) ��
��
Correct Answer : Option B
22. The solution set of the inequality 6(2� + 3) + � > 53 − 2� is
A)
B)
C)
D)
E)
Correct Answer : Option A
� �
In a right-angled trapezium ���� ,∠ � = 90 ,∠ � = 90 , �� = 7� + 1 , �� =
23. 3� + 1 and �� = 3a . If the perimeter of the trapezium is greater than 56 but less than
92, then the range of possible values of � , is
��
A) 4<�<
�
�
B) <�<5
�
�
C) 3<�<
�
D) 3<�<7
E) 3<�<5
Correct Answer : Option E
� � � � � � �
The value of the product cot 10 cot 20 cot 30 cot 45 cot 60 cot 70 cot 80 is
24.
equal to
A) √3
√�
B)
�
C) 3
D) 3√3
E) 1
Text of page 7
Correct Answer : Option E
�
25. If tan α = , then the value of ��� �(2α )��� �(2α ) is equal to
�
���
A)
�
���
B)
�
���
C)
��
���
D)
��
���
E)
��
Correct Answer : Option D
�
26. If (3���� − 2����) = 9��� �� + 4��� �� + � , where � is a constant, then the
value of � is equal to
A) 12
B) -12
C) -4
D) 8
E) -8
Correct Answer : Option E
�
If α and β are real constants such that α − β = , then the value of (��� α + ���
27. �
β ) � + (��� α + ��� β ) � is equal to
A) 2
B) √2
C) 2√2
D) 2+√2
E) 2-√2
Correct Answer : Option D
28. If ��� ��(� − 2) = ��� ��(� + 1) then the variables � and � satisfy the equation
A) � � + � � − 4� + 2� + 4 = 0
B) � � + � � − 4� + 2� + 5 = 0
C) � � + � � − 4� + 2� + 6 = 0
D) � � + � � − 2� + � + 4 = 0
E) � � + � � + 4� + 2� + 4 = 0
Text of page 8
Correct Answer : Option A
� �
29. If 2��� ��� � = ��� ��� � , then the value of � is equal to
� �
�
A)
��
�
B)
��
�
C)
�
�
D)
�
�
E)
�
Correct Answer : Option D
�
The point �� , α �, where α is a constant, lies on the curve with equation
�
30. ��� ��(3�) + 2��� ��(�) = � , | � | ≤ � , | � | ≤ 1, then the value of α is
� �
equal to
�
A)
�
B) 2
�
C)
�
D) 4
E) 0
Correct Answer : Option A
Let O be the origin and P be a point on a line such that OP is perpendicular to that line. If
�
31. OP makes an obtuse angle α with the x-axis, OP = 5 and ��� α =
�
, then the
equation of the line is
A) 3� − 4� − 25 = 0
B) 4� + 3� + 25 = 0
C) 3� − 4� + 25 = 0
D) 4� − 3� − 25 = 0
E) 4� − 3� + 25 = 0
Correct Answer : Option E
If the equation of the straight line passing through the points (3,-4) and (4,a) is x-y =7 ,
32. then the value of a is equal to
A) 3
B) 2
Text of page 9
C) -3
D) -2
E) 0
Correct Answer : Option C
The straight line passing through the points (1,5) and (3,-5) meets the coordinate axes at
33. the points A and B. Then the area of the triangle Δ OAB, where O is the origin, is
A) 2
B) 4
C) 5
D) 8
E) 10
Correct Answer : Option E
The area of the circle � � + � � + 8� − 6� + � = 0 is 75π . Then the value of � is
34.
equal to
A) -50
B) 50
C) 25
D) -25
E) -40
Correct Answer : Option A
�� �� �� ��
If the foci of the hyperbola − = 1 coincide with the foci of the ellipse + =
35. �� �� �� ��
�
1, then the value of � � + � is equal to
A) 25
B) 36
C) 85
D) 169
E) 13
Correct Answer : Option E
36. The vertex of the parabola 2� = − 3� � + 48� − 200, is
A) (8,-8)
B) (8,-6)
C) (-4,8)
D) (8,-4)
E) (-4,-8)
Correct Answer : Option D
Text of page 10
�
If the distance between the foci of an ellipse is 4 and its eccentricity is , then the length
37. �
of its latus rectum is
A) 4
B) 8
C) 6
D) 12
E) 10
Correct Answer : Option C
→ ^
^ − λ ^� + 5� and � = μ ^� +7�^→
The position vectors of the points A and B are � = 2�
38. + 3� ^ respectively. If the position vector of the mid-point of the line segment AB is→
� =
^ , then the value of λ + μ is equal to
3�^ + 2�^ + 4�
A) 6
B) 7
C) 8
D) 9
E) 10
Correct Answer : Option B
^
^ and � . If |�
Let θ be the angle between the unit vectors � ^−�| = ^ √�
, then the
39. �
value of ��� θ is
�
A)
�
�
B)
�
�
C)
�
�
D)
�
�
E)
�
Correct Answer : Option C
→ ^ → ^
^ + λ ^� − 6� and � = − 6�^ + 12�^ + 9� are collinear, then the value of
40. If � = 4�
λ is equal to
A) -4
B) 4
C) -6
D) -8
E) 8
Text of page 11
Correct Answer : Option D
→ ^,
41. Let �(2, 1, − 3) be a given point. If the point � is such that �� = 3�^ − ^� + 5�
then the distance of � from the origin � is
A) √29
B) √33
C) √59
D) √69
E) √79
Correct Answer : Option A
If the straight line passing through the points (1,-1,2) and (3,2,8) makes angle β with
42. the y-axis, then the value of ��� β is equal to
�
A)
�
�
B)
�
�
C)
�
�
D)
�
�
E)
�
Correct Answer : Option B
A unit vector parallel to the straight line
→
� = − (5 + 4�)�^ + (7 − 2�)�^ + (3 + 4�)
43. ^
� , where � is the parameter of the line, is
���^ � ^ ^
� � ��
A)
�
��� � ^
^ ^
� � ��
B)
�
���^ � ^ ^
� � ��
C)
�
��� � ^
^ ^
� � ��
D)
�
��� � ^
^ ^
� � ��
E)
�
Correct Answer : Option A
44. The shortest distance from the point (-10,10,-10) to the z-axis, is
A) 2√10
Text of page 12
B) 10√3
C) 10
D) 3√10
E) 10√2
Correct Answer : Option E
The straight line passing through the points (3,2,3) and (5,-1,-2) is perpendicular to the
45. straight line passing through the points(1,3,1) and (α , α , α ) . Then the value of α is
equal to
A) 1
B) 2
C) 3
D) 4
E) 5
Correct Answer : Option B
There are 20 boys and 5 girls in a class. Three students are selected at random. If E is
46. an event of selecting one boy and two girls, then P(E) is equal to
�
A)
��
�
B)
��
�
C)
��
�
D)
��
�
E)
��
Correct Answer : Option E
A die is rolled twice. Let A be an event of getting 1 in the first roll and let B be an event of
47. getting 4 in the second roll. Then P(A|B) is equal to
�
A)
�
�
B)
�
�
C)
�
�
D)
��
�
E)
��
Correct Answer : Option A
Text of page 13
48. Given the data: 5, 7, 9, 11, 13. The variance of the data, is
A) 11
B) 10
C) 9
D) 8
E) 7
Correct Answer : Option D
49. The mean of the data : 4, 7, x, 13, 16 is 10. Then the mean deviation of the data is
A) 3
B) 3.3
C) 3.6
D) 3.8
E) 4
Correct Answer : Option C
� � ���(��)
50. The value of lim is equal to
� → � ���(��)
�
A) −
�
�
B)
�
C) -2
D) 1
E) -1
Correct Answer : Option E
51.
A) -3
B) 3
C) 1
D) -1
E) 9
Correct Answer : Option B
� �
52. Let �(�) = , 0 < � < . Then � ��(�) =
� � ���� �
� � ����
A)
����
�
B) ��� ��� �
���
Text of page 14
���
C) ��� ��� �
�
�
D) ��� ��� �
���
����
E)
� � ����
Correct Answer : Option C
(√� � �)(√� � �)
53. Let �(�) =
���
for � ≠ 1 . Then lim �(�) is equal to
�→�
A) 2
B) 4
C) √2
D) 1
E) 0
Correct Answer : Option D
Let �(�) = ���� (9�) for � > 0 and ℎ(�) = �(�) + �(� �) + �(� �) . Then the
54. � �
value of ℎ� � � � is equal to
�
A) 1
B) 2
C) 3
D) 4
E) 5
Correct Answer : Option B
The point �(�, �) , where � = 4���� (2) , lies on the curve with equation � = ���� (
55. ��
� � + 24) . Then the value of at the point P is
��
��
A)
�
�
B)
�
��
C)
�
�
D)
�
�
E)
�
Correct Answer : Option D
56. ��
A cubic curve � = �(�) passes through the points (1,-7) and (2,11) . If = 6� � + �
��
Text of page 15
� − 5 , where � is a constant, then �(�) =
A) 2� � + 6� � − 5� − 7
B) 2� � + 3� � − 5� − 7
C) 2� � + 3� � − 5� − 4
D) 2� � + 3� � − 5� − 5
E) 2� � + 6� � − 5� − 5
Correct Answer : Option B
� ��
Let � = 4� �� − 2� ��� − � ���, � ϵ ℝ. If = � � �(4� �� − 8� � − 9) for all x,
57. �� �
then the value of the constant α is
A)
-3
B) -2
C) 3
D) 2
E) -1
Correct Answer : Option A
� ��
58. If � = 4√� , then
�� �
=
� ��
A)
� � ��
�� ��
B)
� � ��
�� ��
C)
� � ��
�� ��
D)
� � ��
� ��
E)
� � ��
Correct Answer : Option C
� � ��� �� � � �
59. Let �(�) = �
� � ��� �
for 0 < � <
�
.Then the value of � (
�
) is equal to
�
A)
√�
B) √2
C) 2√2
D) 1
E) 0
Correct Answer : Option C
Text of page 16
If the maximum value of the function �(�) = α − 4� − � � is 1, then the value of α
60.
is equal to
A) -3
B) 3
C) -5
D) 5
E) 0
Correct Answer : Option A
The surface area of a cube is increasing at the constant rate of 0.5 cm2 /s . Then the rate
61. at which the volume of the cube is increasing (in cm3/s ), when its surface area has
reached 12 cm2, is
�
A)
√�
�
B)
�√�
�
C)
�√�
�
D)
�√�
�
E)
�√�
Correct Answer : Option D
� �
62. Let �(�) = ( − 3), � > 0 . Then �(�) is decreasing in
� � �
√
A) (1,4)
B) (0,3)
C) (1,3)
D) (2,5)
E) (0,2)
Correct Answer : Option E
�
63. Let �(�) = ��������� +
�
� � ϵ ℝ . Then the minimum value of � is equal to
�
A)
�
��
B)
�
�
C)
�
��
D)
�
�
E)
�
Text of page 17
Correct Answer : Option B
������
64. ∫ ���� � ���� �� =
A) �(���� − ����) + ���� + ���� + �
B) �(���� − ���� + �
C) �(���� + ����) + ���� − ���� + �
D) �(���� + ����) − �������� + �
E) ��������� + �
Correct Answer : Option A
65. ∫ (���2� + �����2�)�� =
A) 2���� | ���� | + �
�
B) ���� | ���� | + �
�
C) ���� | ���� | + �
D) 2���� | ���� | + �
E) ���� | ���� | + �
Correct Answer : Option E
�√�(�� � � �)
If ∫ �� = 8�� � + �√� + � , where � is a constant and � is the
66. �
constant of integration, then the value of � is
A) 20
B) -20
C) -10
D) 10
E) -8
Correct Answer : Option C
� � � �� � �
67. ∫ (� � �) �
�� =
�
A) �− +�
���
��
B) �− +�
���
�
C) �+ +�
���
��
D) �+ +�
���
�
E) �+ +�
���
Text of page 18
Correct Answer : Option C
�√� � �
68. ∫ √�
�� =
�
�
A) �√� + 1� � + �
�
�
�
B) �√� + 1� � + �
�
�
�
C) �√� + 1� � + �
�
�
�
D) �√� + 1� � + �
�
�
�
E) �√� + 1� � + �
�
Correct Answer : Option A
� ���� �� � | � | �
69. The value of ∫��
� � | �|
�� is equal to
�
A) (���� 2) �
�
B) 2(���� 2) �
C) (���� 2) �
D) ���� 2
E) 0
Correct Answer : Option C
� � �
Let �(�) = (� − 5) � ,� ϵ ℝ. If ∫�� �(�)�� = ∫� �(�)�� , where � > 5 is a
70. ��
real constant, then the value of � is equal to
A) 10
B) 12
C) 15
D) 18
E) 20
Correct Answer : Option C
A curve with equation � = � � − 8� � + 16� meets the �-axis at the origin O and at a
71. point A. Then the area of the region, bounded by the curve and the straight-line segment
OA, is
��
A)
�
Text of page 19
��
B)
�
��
C)
�
��
D)
�
��
E)
�
Correct Answer : Option C
�/�
72. The value of the integral ∫� √�������2x �� is equal to
√�
A)
�
�√�
B)
�
�
C)
�
�
D)
�√�
�√�
E)
�
Correct Answer : Option B
��
73. The general solution of the differential equation � � + 3� �� = ���� is
��
����
A) �= +�
��
����
B) � = � + ��
�
����
C) �= � +�
�
���� � �
D) �=
��
���� � �
E) �=
��
Correct Answer : Option E
The integrating factor of the differential equation 2�� = (� + ����)�� is
74.
A) � ���
B) � �� / �
C) � ��
D) �� / �
E) −� � / �
Text of page 20
Correct Answer : Option B
The minimum of the following linear programming problem occurs at:
75. Minimize � = 7� + 10�
subject to � + � ≥ 3, � + 2� ≥ 4, �, � ≥ 0
A) (3,0)
B) (4,0)
C) (0,2)
D) (2,1)
E) (0,3)
Correct Answer : Option D
76. The dimensions of Planck’s constant are the same as those of
A) energy
B) power
C) angular frequency
D) angular momentum
E) linear momentum
Correct Answer : Option D
77. The number of significant figures in 50000.040 ×10-3 is
A) 8
B) 3
C) 5
D) 6
E) 7
Correct Answer : Option A
A car travels half the distance with a velocity of 20 kmh-1 and another half distance with a
78.
velocity of 30 kmh-1 along a straight road. The average velocity of the car in km h-1 is
A) 35
B) 25
C) 48
D) 50
E) 24
Correct Answer : Option E
→ ^ →
^ − 4� . The vector parallel to � and magnitude the
A vector is given as � = 3�
79. same as that of the vector ^
� − 2�^ is
Text of page 21
A)
� ^ ^)
(3� − 4�
�
B) √5(3�^ − 2�
^)
� ^
C) (3� − 2�^)
�
D)
� ^)
(3�^ − 4�
√�
E) √5(3� ^)
^ − 4�
Correct Answer : Option D
A body is projected up with a velocity of 30 ms-1 at an angle of 30o. The ratio of
80.
maximum height reached to the height reached in the first second is (� = 10�� ��)
A) 10 : 9
B) 10 : 8
C) 9:8
D) 9:5
E) 5:4
Correct Answer : Option C
The linear momentum of a particle as a function of time is given as � = (3� � + 2� + 1)
81.
���� �� . Then, the force acting on the particle at � = 3� will be
A) 20 N
B) 10 N
C) 15 N
D) 2N
E) 8N
Correct Answer : Option A
What will be the maximum speed of a car on a circular road of radius 12 m if the
82. coefficient of friction between the tyres and the road is 0.3? � = 10�� ��
A) 3.6 ms-1
B) 36 ms-1
C) 60 ms-1
D) 10 ms-1
E) 6 ms-1
Correct Answer : Option E
83. The kinetic energy of a body of mass 5 kg having a linear momentum 4 kg ms-1 is
A) 2.6 J
B) 1.6 J
C) 1.5 J
Text of page 22
D) 2.5 J
E) 3.6 J
Correct Answer : Option B
84. In an elastic collision,
A) both momentum and kinetic energy are conserved
B) only momentum is conserved
C) only kinetic energy is conserved
D) neither kinetic energy nor momentum is conserved
E) forces involved are non-conservative forces
Correct Answer : Option A
If the moment of inertia, rotational kinetic energy and angular momentum of a body are �
85. , � and � respectively, then,
�
A) �=
�
B) � = ��
C) � = 2��
D) � = √2��
�
E) 2� =
�
Correct Answer : Option D
The torque transmitted by an engine to a rotor in 100 Nm. If the power of the engine is
86. 15 kW, the angular speed of the engine is
A) 100 rad s-1
B) 200 rad s-1
C) 125 rad s-1
D) 150 rad s-1
E) 15 rad s- 1
Correct Answer : Option D
The height above the surface of the earth at which the acceleration due to gravity
�
becomes in terms of radius of earth � is ( � is acceleration due to gravity at the
87. �
surface of the earth)
�
A)
�
�
B)
�
�
C)
�
Text of page 23
D) 2R
E) 3R
Correct Answer : Option D
The escape velocities of two planets A and B are in the ratio 2 : 3. If the ratio of their radii
88. is 3 : 4 , then the ratio of acceleration due to gravity at the surface of the planet A to that
at the surface of the planet B is
A) 4:9
B) 4:3
C) 16 : 27
D) 4 : 27
E) 16 : 9
Correct Answer : Option C
Two copper wires have the lengths in the ratio 1 : 2 and their radii are in the ratio 3 : 1. If
89. they are stretched by the same force, the ratio of the respective longitudinal strains in the
two wires is
A) 1:9
B) 9:1
C) 1 : 27
D) 27 : 1
E) 1:3
Correct Answer : Option A
90. Bernoulli’s equation holds good for
A) non-viscous and incompressible fluids in turbulent flow
B) highly viscous and compressible fluids in streamline flow
C) non-viscous and compressible fluids in turbulent flow
D) highly viscous and incompressible fluids in streamline flow
E) non-viscous and incompressible fluids in streamline flow
Correct Answer : Option E
γ � is the ratio of the specific heat capacities of the rigid diatomic gas at constant
pressure to that at constant volume and γ � is the corresponding value for a non-rigid
91.
diatomic gas molecule with an additional vibrational mode, then the ratio of γ � to γ � is
A) 49 : 45
B) 7:5
C) 9:7
D) 7:9
E) 49 : 30
Text of page 24
Correct Answer : Option A
A carnot engine works between the temperatures 327oC and 227oC. If the work output
92. of the engine is 1 kJ, then the amount of heat absorbed by the engine is
A) 2 kJ
B) 6 kJ
C) 30 kJ
D) 3 kJ
E) 40 kJ
Correct Answer : Option B
�
When a monoatomic gas at a pressure P is suddenly compressed to ( ) of its original
93. �
volume, the pressure of the gas becomes
A) 8P
B) 5P
C) 3P
D) 32P
E) 16P
Correct Answer : Option D
The root mean square velocity of a gas molecule is 100 ms-1. The mass of the molecule
94. is increased four times keeping the temperature constant. Then, the root mean square
velocity is
A) 25 ms-1
B) 50 ms-1
C) 75 ms-1
D) 2500 ms-1
E) 125 ms-1
Correct Answer : Option B
�
The mean free path of moving gas molecules is expressed as α ∝ � �� where � is
95. the number of molecules per unit volume and � is the size of the molecules. Then the
values of � and � respectively , are
A) 2,-2
B) -1,-2
C) 1,2
D) 1,-2
E) -2,-2
Correct Answer : Option B
Text of page 25
When an open pipe is suddenly closed at one end, the frequency of the third harmonic of
96. the closed pipe is found to be 50 Hz more than the fundamental frequency of the open
pipe. The fundamental frequency of the open pipe is
A) 100 Hz
B) 50 Hz
C) 200 Hz
D) 300 Hz
E) 350 Hz
Correct Answer : Option A
��
In the given wave equation y=0.05 ��� (x-200t) m, the velocity of the wave (in
�
97. ms-1) is
A) 2√200
B) 400
C) 200√2
D) 2√300
E) 200
Correct Answer : Option E
Two metallic spheres of radii in the ratio 1 : 2 are charged and joined by a connecting
98. wire. The ratio of electric field intensities at the surfaces of the spheres is
A) 2:1
B) 1:2
C) 1:3
D) 3:1
E) 2:3
Correct Answer : Option A
A proton travels through a distance of 5 m in the direction of uniform electric field of
99. intensity 4 NC-1. The work done on the proton by the electric field is
A) 10 eV
B) 30 eV
C) 20 eV
D) 16 eV
E) 32 eV
Correct Answer : Option C
An electric dipole is placed at an angle of 30o with an electric field intensity
5 -1
100. 3×10 NC experiences a torque 3 Nm. If the length of dipole is 2 cm, the charge on the
dipole is
(in milli coloumb)
Text of page 26
A) 2
B) 3
C) 1.5
D) 1
E) 4
Correct Answer : Option D
Two air core capacitors of equal capacitance C are connected in series. If one of them is
101. filled with a dielectric substance of dielectric constant k, the effective capacitance
becomes
A) (� + 1)�
��
B)
���
���
C)
���
(� � �)�
D)
�
�
E)
(� � �)�
Correct Answer : Option B
��
A uniform wire of area of cross section 1 × 10 � � carries a current of 1.6 A. If the
102. number density of electrons is 5 × 10 ��� �� , the drift velocity of electrons (in mm s-1)
is
A) 1
B) 3
C) 2
D) 4
E) 1.5
Correct Answer : Option C
A battery supplies 0.6 A current when a 3 Ω resistor is connected with it. When the
103. resistor 3Ω is replaced by 6 Ω , the current is reduced to 0.4 A. Then, the internal
resistance of the battery is
A) 3Ω
B) 9Ω
C) 6Ω
D) 12Ω
E) 2Ω
Correct Answer : Option A
104. Kirchhoff’s first and second laws are respectively based on the conservation of
A) energy and momentum
Text of page 27
B) charge and energy
C) charge and momentum
D) energy and charge
E) momentum and energy
Correct Answer : Option B
A particle of charge 10 times that of an electron is revolving in a circular path of radius
105. 0.5 m. If the frequency of rotation is 10 rotations per second, the magnetic field at the
centre of the circular path is approximately (µo = 4π×10-7 Hm-1)
A) 4 × 10 ����
B) 2 × 10 ����
C) 2 × 10 ����
D) 8 × 10 ����
E) 2 × 10 ����
Correct Answer : Option E
A wire of length 6 m is bent to form a circular loop of single turn. If the current through the
106. loop is 2 A, the magnetic moment of the circular loop (in Am2 ) is
A) 18π
��
B)
�
��
C)
�
D) 36π
�
E)
�
Correct Answer : Option B
The current through a galvanometer of resistance 50 Ω is only 4% of the main current
107. when a shunt resistance is connected. The value of the shunt resistance is
approximately
A) 3Ω
B) 4Ω
C) 5Ω
D) 1Ω
E) 2Ω
Correct Answer : Option E
108. The INCORRECT statement is
A) Nickel is ferromagnetic and Aluminium is paramagnetic
B) Cobalt is ferromagnetic and calcium is paramagnetic
Text of page 28
C) Nickel is ferromagnetic and cobalt is paramagnetic
D) Both iron and cobalt are ferromagnetic
E) Both copper and lead are diamagnetic
Correct Answer : Option C
A current of 2 A produces a magnetic flux of 10 -3 weber per turn in a coil of 1000 turns.
109. Then, the self-inductance of the coil is
A) 0.10 H
B) 0.25 H
C) 0.20 H
D) 0.30 H
E) 0.50 H
Correct Answer : Option E
110. The transformer core is laminated in order to
A) minimize eddy current loss
B) reduce copper loss
C) reduce cost
D) reduce hysteresis loss
E) reduce flux leakage
Correct Answer : Option A
111. The CORRECT statement among the following regarding electromagnetic waves is
A) They can travel through vacuum
B) They consist of only electric field
C) They consist of only magnetic field
D) They require a medium to propagate
E) They move with a velocity of 3×108 cms-1
Correct Answer : Option A
A biconvex lens with equal radii of curvature � has a focal length �. If the refractive
112. index of the lens is � , the focal length of the lens is
�
A) R
�
B)
�
C) 2R
�
D) R
�
E) 3R
Correct Answer : Option A
Text of page 29
The width of a fringe is 0.5 mm in Young’s double slit experiment for a light of wavelength
113. 500nm. If the wave length of light alone is changed to 600 nm, the width of the fringe
becomes
A) 0.4 mm
B) 0.3 mm
C) 0.2 mm
D) 0.6 mm
E) 0.55 mm
Correct Answer : Option D
114. The primary purpose of using polaroids in sunglasses is to
A) make the sunglasses look fashionable
B) change the colour of the objects
C) control the intensity of light from the objects
D) magnify the object
E) make the sunglasses cheaper
Correct Answer : Option C
An electron and a proton possess same kinetic energy. If the de Broglie wavelengths of
115. the electron and the proton are λe and λp respectively, identity the CORRECT relation.
A) λe > λp
B) λe = λ p
C) λp=√1836 λe
D) λp=1836 λe
E) λp=183 λe
Correct Answer : Option A
The work function of a material is 6.6 eV. Then, the threshold wavelength of the metal is
116. approximately (Take h = 6.6 ×10-34J.s)
A) 108 nm
B) 188 nm
C) 208 nm
D) 228 nm
E) 250 nm
Correct Answer : Option B
The ratio of the longest wavelength of the Lyman series to that of Ballmer series of the
117. hydrogen spectrum is
A) 3:29
B) 7:27
C) 5:27
D) 4:29
Text of page 30
E) 5:29
Correct Answer : Option C
The mass of a proton is 1.0073u and that of a neutron is 1.0087u. The binding energy of
118. �
� �� is approximately (Given: helium nucleus mass = 4.0015u)
A) 24.8 MeV
B) 24.4 MeV
C) 2.48 MeV
D) 2.84 MeV
E) 28.4 MeV
Correct Answer : Option E
Which of the following can be used in the output circuit of a diode rectifier to filter ac
119. ripples?
A) A capacitor in series with the load
B) An inductor in parallel with the load
C) A capacitor in parallel with the load
D) Both capacitor and inductor in parallel with the load
E) Both capacitor and inductor in series with the load
Correct Answer : Option C
120. When a PN junction diode is forward biased, the CORRECT statement is
A) the majority carrier current is zero
B) the junction resistance is large
C) the width of depletion layer is reduced
D) the width of depletion layer is increased
E) the minority carrier current is large
Correct Answer : Option C
An organic compound contains 40% C and 6.7% H2. What is the empirical formula of the
121. compound?
A) CH4
B) CH2O
C) CH3
D) CH4O
E) CH3O2
Correct Answer : Option B
The kinetic energy of a fast-moving particle of mass 1 x 10-31kg is associated with a de
122.
Broglie wavelength 63nm is (h = 6.3 x 10-34 Js)
Text of page 31
A) 5 x 10-21J
B) 1 x 10-22J
C) 5 x 10-22J
D) 1 x 10-21J
E) 2 x 10-21J
Correct Answer : Option C
Consider the following metals: Li, Na, K, Cu, Mg and Ag. The metals with the lowest and
123. highest work function are respectively
A) Na and Cu
B) K and Cu
C) Li and Ag
D) Mg and Cu
E) K and Ag
Correct Answer : Option B
The IUPAC nomenclature of the element with atomic number 105 is unnilpentium. What
124. is its official IUPAC name?
A) Lawrencium
B) Nobelium
C) Seaborgium
D) Meitnerium
E) Dubnium
Correct Answer : Option E
125. The correct increasing order of metallic character of the elements Si, Be, Mg, Na and P is
A) P < Si < Be < Mg < Na
B) Si < P < Be < Mg < Na
C) Be < P < Si < Na < Mg
D)
Na < Mg < Be < Si < P
E) Mg < Si < Na < P < Be
Correct Answer : Option A
126. Which of the following statement is correct?
A) CO2 molecule contains one C-O and one C=O bonds and one lone pair on each oxygen
atom.
B) CO2 molecule contains two C-O bonds and one lone pair on each oxygen atom
C) CO2 molecule contains one C-O bond and one C=O bond with two lone pairs on each
oxygen atom.
Text of page 32
D) CO2 molecule contains one C-O bond and one C≡O and one lone pair on each oxygen
atom.
E)
CO2 molecule contains two C=O bonds and two lone pairs on each oxygen atom.
Correct Answer : Option E
127. The molecule with square planar structure containing two lone pairs at the central atom is
A) Platinum(IV) fluoride
B) Carbon(IV) fluoride
C) Silicon(IV) fluoride
D) Xenon (IV) fluoride
E) Nickel (IV) fluoride
Correct Answer : Option D
The enthalpy of vapourisation of diethyl ether is 26.0 kJ mol-1 and its normal boiling point
128. is 350C. What is the value of ΔS0 for the conversion of liquid diethyl ether to vapour at
350C?
A) -84.4 JK-1mol-1
B) +742.9JK-1mol-1
C) -8.44 JK-1mol-1
D) +84.4 JK-1mol-1
E) -742.9JK-1mol-1
Correct Answer : Option D
The standard enthalpies of formation of C6H6(l), CO2(g) and H2O(l) are respectively
129. +49kJ mol-1, -394kJ mol-1 and -286kJ mol-1 respectively. What is the value of standard
enthalpy of combustion of C6H6(l)?
A) -3222 kJ mol-1
B) -3173 kJ mol-1
C) -3271 kJ mol-1
D) +3173 kJ mol-1
E) -3122 kJ mol-1
Correct Answer : Option C
The equilibrium constant KP of a homogenous equilibrium reaction is 1 x 10-6 at 227˚ C.
130. What is the value of ΔG0 of the reaction at the same temperature?
(R = 8.3JK-1mol-1)
A) 26.3 kJ mol-1
B) +57.3 kJ mol-1
C) -57.3 kJ mol-1
Text of page 33
D) -26.3 kJ mol-1
E) -573 kJ mol-1
Correct Answer : Option B
For the gas phase homogenous equilibrium N2(g) + O2(g)⇋ 2NO(g), KC= 0.1 at 1500K.If
131. the initial concentrations of N2(g) and O2(g) are each 0.04 mol L-1what is the equilibrium
concentration of NO(g)?
A) 0.100 mol L-1
B) 0.0100mol L-1
C) 0.022 mol L-1
D) 0.02 mol L-1
E) 0.011 mol L-1
Correct Answer : Option E
132. In which one of the following reactions, +2 state in a reactant is reduced to +1 state?
A) Mg + S → MgS
B) 2HgCl2+ SnCl2 → Hg2Cl2 + SnCl4
C) CH4+2O2 → CO2 +2H2O
D) 2K4[Fe(CN)6]+H2O2→ 2K3[Fe(CN)6] + 2KOH
E) 2H2S + O2→ S + 2H2O
Correct Answer : Option B
In the following redox reaction P4(s) + 3OH-(aq)+3H2O(l)→PH3(g) + 3H2PO2-(aq), the
133.
oxidation state of phosphorus changes from
A) 0 to -3 and 0 to -1
B) 0 to +1 and 0 to +3
C) 0 to -1 and 0 to +5
D) 0 to -3 and 0 to +1
E) -3 to 0 and +1 to +3
Correct Answer : Option D
If ‘c’ is the molarity of a solution, ‘m’ the molality, M2 the molecular weight of the solute in
134. a binary solution and ‘ρ’, is the density of the solution in g/cm3, then the relationship
between molality ‘m’ and molarity ‘c’ is given by
A) m = c/[ρ-cM2/1000] mol kg-1
B) m = 1000c/[ρ-cM2] mol kg-1
C) m = cρ/[1+cM2/100] mol kg-1
D) m = 1000c/ρmol kg-1
E) m = 1000c/[1000ρ+cM2]
Text of page 34
Correct Answer : Option A
In a first order reaction at a given temperature the time required to complete 99% of the
135. reaction (T1) is related to time required for 90% completion(T2) as
A) T1 = T2
B) T1 =4T2
C) T1 = 3T2
D) T1 = 2T2
E) T1 =5T2
Correct Answer : Option D
The overall order of the following reaction is
136. KClO3 + 6FeSO4 + 3H2SO4→ KCl + 3Fe2 (SO4)3 + 3H2O
A) ten
B) six
C) two
D) three
E) one
Correct Answer : Option C
Which of the following element of first transition series has the lowest atomization
137. enthalpy?
A) Ti
B) V
C) Cr
D) Mn
E) Fe
Correct Answer : Option D
138. Which of the following complex has the lowest molar conductivity?
A) Dichlorotetrammineplatinum(IV) chloride
B) Dichlorotetramminecobalt(III) chloride
C) Potassium hexacyanidoferrate(II)
D) Hexaaquochromium(III) chloride
E) Pentacarbonyliron(0)
Correct Answer : Option E
139. The complexes [Co(NH3)6] [Cr(CN)6] and [Cr(NH3)6 ][Co(CN)6] are examples of
A) linkage isomerism
B) ionisation isomerism
C) solvate isomerism
Text of page 35
D) coordination isomerism
E) geometrical isomerism
Correct Answer : Option D
140. The number of C-C, C-H and C=C bonds in but-2-en-1-yne are, respectively
A) 3, 8, 2
B) 4, 6, 3
C) 3, 6, 2
D) 2, 6, 3
E) 3, 5, 2
Correct Answer:-Question Cancelled
141. The alkane that cannot be prepared in pure state by Kolbe’s electrolysis is
A) ethane
B) 2,3-dimethyl butane
C) propane
D) n-butane
E) n-hexane
Correct Answer : Option C
142. 1-Chlorocyclohexene is an example of
A) alkyl halide
B) aryl halide
C) benzylic halide
D) vinylic halide
E) allylic halide
Correct Answer : Option D
143. Which of the following is an ambident nucleophile?
A) OH-
B) NH2-
C) I-
D) CH3O-
E) CN-
Correct Answer : Option E
144. Identify the allylic alcohol in the following.
A) C6H5CH2OH
B) C6H5-CH=CH-C(CH3)2-OH
C) CH2=CH-OH
D) C6H5-CH2-CH2-OH
Text of page 36
E) CH2=CH-CH2-CH2-OH
Correct Answer : Option B
145. p-Bromophenol is the major product formed when phenol is treated with
A) Bromine water
B) Br2 in acetic acid at 300K
C) Br2 in CCl4 at 300K
D) Br2 in CS2 at 273K
E) Br2 in acetone at 273K
Correct Answer : Option D
146. The IUPAC name of mesityl oxide is
A) 2-Methylpent-2-en-3-one
B) 3-Methylpent-2-en-4-one
C) 4-Methylpent-2-en-3-one
D) 4-Methylpent-3-en-2-one
E) 2-Methylpent-3-en-4-one
Correct Answer : Option D
147. Which of the following carboxylic acid has the highest pKa value?
A) O2N-CH2-COOH
B) F-CH2-COOH
C) HCOOH
D) CN-CH2COOH
E) Cl-CH2COOH
Correct Answer : Option C
148. Choose the correct decreasing order of basic strength of amines in aqueous solution:
A) NH3 > CH3NH2 > (CH3)2NH > (CH3)3N
B) (CH3)2NH > (CH3)3N > NH3 > CH3NH2
C) (CH3)3N > NH3 > CH3NH2 > (CH3)2NH
D) (CH3)2NH > CH3NH2 > (CH3)3N > NH3
E) CH3NH2 > (CH3)2NH > (CH3)3N > NH3
Correct Answer : Option D
149. Hinsberg’s reagent is
A) HCl/ZnCl2
B) Sn/HCl
C) ammoniacal AgNO3
Text of page 37
D) FeBr3
E) benzenesulphonyl chloride
Correct Answer : Option E
150. Lactose, the milk sugar is composed of
A) two β-D-glucose units
B) one β-D-glucose and one α-D-glucose units
C) two α-D-glucose units
D) one α-D-galactose and one β-D-glucose units
E) one β-D-galactose and one β-D-glucose units
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.