KEAM 2025: KEAM Engineering entrance (Mathematics, Physics and Chemistry), session 4
Text of page 1
FINAL ANSWER KEY
Question Paper Code: 13/2025/OL
Exam:KEAM 2025 ENGG-4
Date of Test: 27-04-2025
The relation
R = {(4, 4)(4, 5), (5, 7), (4, 8), (5, 5), (7, 8), (7, 7), (7, 5), (8, 8), (8, 7), (8, 5), (9, 9)}on the set
1. A={4, 5, 7, 8, 9 } is
A) transitive
B) symmetric
C) reflexive
D) equivalence relation
E) a function
Correct Answer : Option C
Let A ={ 1, 2, 3, 4} and B ={ 7, 8, 3, 4} Then the number of elements common to
2. both A × B and
B × A is
A) 8
B) 6
C) 12
D) 4
E) 2
Correct Answer : Option D
3. The range of the function f(x) = log 4x − 4x + 1 , where x ≠ is
A) ( − ∞, 0)
B) [0, ∞)
C) (0, ∞)
D) ( − ∞, 0)
E) ( − ∞, ∞)
Correct Answer : Option E
4. The domain of the function f(x) = √x + 2x − 15 is
A) ( − ∞, − 5) ∪ (3, ∞)
B) ( − ∞, − 5) ∪ [3, ∞)
C) ( − ∞, − 5] ∪ (3, ∞)
D) ( − ∞, − 5] ∪ [3, ∞)
E) [ − 5, 3]
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Correct Answer : Option D
5. All the points in A = ; λ ϵ ℝ lie on
A) a circle with radius √2
B) a circle with radius 2
C) a circle with radius
D) a circle with radius 1
E) a straight line with slope 1
Correct Answer : Option D
6. ,is equal to
=
A) i+1
B) i−1
C) −i − 1
D) −i + 1
E) −i
Correct Answer : Option B
7. If x, y ϵ ℝ and x + iy = − (6 + i) , i = − 1, then x − y is equal to
A) 93
B) -93
C) 91
D) -91
E) -107
Correct Answer : Option D
8. Let z = x + iy, where x, y ϵ ℝ and i = − 1. If|z − i | = | z − 1|, then y =
A) −x
B) x+1
C) −x − 1
D) x+2
E) x
Correct Answer : Option E
9. If a, b, c are real numbers such that (a − 2) + (b − 2) + (c − 2) = 0
A) a, b, c are in G.P. and a + b + c = 6
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B) a, b, c are in G.P. and a + b + c = 4
C) a, b, c are not in G.P.
D) a, b, c are in G.P. and a + b + c = 8
E) a, b, c are not in G.P. and a + b + c = 16
Correct Answer : Option A
Let a, , ar , ar , . . . be in G.P. where r > 0 If the product of first four terms of the
10.
G.P. is then a is equal to
A)
B)
C)
D)
E) 1
Correct Answer : Option D
Let a , a , . . . . , a be positive non-zero real numbers. If a , a , . . . . , a = k then
11. the minimum value of a + a + . . . . + a is
A) n(k) /
B) n(k) /
C) (k) /
D) (k) /
E) 2n(k) /
Correct Answer:-Question Cancelled
Let λ be the A.M. between and and also G.M. between and . Then α +
12.
β =
A) 3α β
B) αβ
C) αβ
D) 4α β
E) 2α β
Correct Answer : Option E
13. The number of integers greater than 7000 using 2,4,6,7,8 without repetition, is
A) 168
B) 336
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C) 196
D) 256
E) 512
Correct Answer : Option A
14.
A) − C (4) (3)
B) C (4) (3)
C) C (4) (3)
D) C (4) (3)
E) 0
Correct Answer : Option E
Five digit number is formed using the digits 0,1,2,3,4 and 5 without repetitions. Number of
15. five digit numbers which are divisible by 10 is
A) 360
B) 240
C) 120
D) 480
E) 520
Correct Answer : Option C
16.
A) -160
B) 160
C) -180
D) 180
E) 0
Correct Answer : Option A
17.
A) 18
B) 16
C) 17
D) 21
E) 19
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Correct Answer : Option A
Let A = a ,B = b and C = c .Which one of the following
18. × × ×
products, is not defined ?
A) C AB
B) A AB
C) (AB) C
D) (AB)C
E) B C
Correct Answer : Option D
19. Let A be a square matrix of order 3 and |A | = 9 Then |adj(adjA) | =
A) 6561
B) 6564
C) 6569
D) 8187
E) 8164
Correct Answer : Option A
20.
A) 2,3
B) -2,3
C) -2,-3
D) 1,2,3
E) -1,2,-3
Correct Answer : Option C
21.
A) 14
B) -14
C) 12
D) -12
E) 15
Correct Answer : Option B
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22. The solution set for −12x > 38, where x is a natural number, is
A) {1,2,3}
B) {1,2}
C) {1}
D) empty set
E) {-1,-2,-3}
Correct Answer : Option D
23. Let x be a real number such that x + + < 13 .Then the solution set is
A)
B)
C)
D)
E)
Correct Answer : Option A
24. cos75 ∘cos45 ∘cos15 ∘=
A)
√
B)
√
C)
√
D)
√
E)
√
Correct Answer : Option C
25. If α + β + ν = 2π , then tan + tan + tan =
A)
B) -tan tan tan
C) 2 tan tan tan
D) 3 tan tan tan
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E) 4 tan tan tan
Correct Answer : Option A
26. ∘ ∘
tan (315 ) cot (-405 ) =
A) -1
B) 1
C)
√
√
D)
E)
Correct Answer : Option B
27. =
A) cot
B) cos
C) 1 + sin
D) 1 + cos
E) tan
Correct Answer : Option E
28.
A)
B)
C)
D)
E)
Correct Answer : Option B
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29.
A) -2
B) -4
C) 2
D) 4
E) -1
Correct Answer:-Question Cancelled
30.
A)
B) π
C) 1
D)
E)
Correct Answer : Option E
Let a ≠ 1 be non-zero real number. If the lines 2x + ay = 1 and x + 2y = 1 are
31. perpendicular, then the value of a is equal to
A) 1
B) -2
C) 2
D) -1
E) −
Correct Answer : Option D
Let P(1, 2), Q(a, b), R(5, 7)and S(2, 3
32. ) be the vertices of a parallelogram PQRS . Then
A) a = 4, b = 2
B) a = 6, b = 2
C) a = 6, b = 4
D) a = 3, b = 2
E) a = 4, b = 6
Correct Answer : Option E
Which one of the following lines, passes through the point of intersection of
33. x + y = 5 and 2x + y = 7 ?
A) 4x + 3y = − 1
B) 3x + 2y = 7
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C) 4x − 3y = − 1
D) 4x + 3y − 2 = 0
E) 4x + 3y + 3 = 0
Correct Answer : Option C
The axis of a parabola is x = 0 . If the vertex is at a distance 3 from the origin above the
34. x -axis. The vertex of the parabola is at
A) (3,0)
B) (-3,0)
C) (3,-3)
D) (3,3)
E) (0,3)
Correct Answer : Option E
35. Length of the Latus rectum of the ellipse + = 1 is
A)
B) 8
C)
D) 2
E)
Correct Answer : Option C
36. The centre of the ellipse 4x + 24x + 9y − 18y + 9 = 0 is
A) (1, 3)
B) (1, − 3)
C) (3, − 1)
D) ( − 3, 1)
E) (3, − 3)
Correct Answer : Option D
37. The line x − y + 4 = 0 touches the ellipse x + 3y = 12 at
A) (1,3)
B) (3,1)
C) (0,2)
D) (0,-2)
E) (-3,1)
Correct Answer : Option E
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→ ^ → ^ → ^
^ + 3ȷ^ − 5k, OB = 3ı^ + ^ȷ − 2k; OC = 6ı^ − 5ȷ^ + 7k be the
38. Let OA = 2ı
position vectors of the points ,A B and C. Then
A)
→ →
AC = 3AB
B)
→ →
AB = 3BC
C)
→ →
AC = 2AB
D)
→ →
AB = 3BC
E)
→ →
AC = 4AB
Correct Answer : Option E
→ →
^ and AC ^ .If θ is the angle between
39. Let AB = 2ı^ + 10ȷ^ + 11k = − ^ı + 2ȷ^ + 2k
→ →
AB and AC then sinθ=
√
A)
√
B)
√
C)
√
D)
E)
Correct Answer : Option D
Let → ^ ×→
^ = 2ı^ + 3ȷ^ + 4k
a × 2ı^ + 3ȷ^ + 4k →+→
b . If |a b | = √29 ,then →
→
a+b
40.
=
A) ^
2ı^ + 3ȷ^ − 4k
B) − 2ı^ + 3ȷ^ − 4k^
C) ^
± 2ı^ + 3ȷ^ + 4k
D) ^
± 2ı^ − 3ȷ^ + 4k
E) ^
±√29 2ı^ + 3ȷ^ + 4k
Correct Answer : Option C
41. Let →
a = ^ı + 2ȷ^ + 4k
→
^ ,b ^ and →
= 2ı^ + 4ȷ^ + 8k ^ .Then
c = 2ı^ + 4ȷ^ + 3k
→
.c =
A) 4
B) 6
C) 8
D) 2
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E) 0
Correct Answer : Option E
42. The point of intersection of the lines = = and = = is
A)
B)
C)
D)
E)
Correct Answer:-Question Cancelled
43. The equation of the line passing through (0, 0, 1) and (1,1,0) is
→
r =^ k + λ ^ı + ^ȷ − ^
A) k ,λ ϵℝ
→
r = ^ȷ + λ ^ı − ^ȷ + ^
B) k ,λ ϵ ℝ
→
r = ^ı + λ ^ı + ^ȷ + ^
C) k ,λ ϵℝ
→
r = ^ı + ^ȷ + λ ^ı − ^ȷ − ^
D) k ,λ ϵ ℝ
→
r = ^ı + ^ȷ + ^
k + λ ^ı + ^ȷ − ^
E) k ,λ ϵ ℝ
Correct Answer : Option A
Which one of the following is a vector parallel to the straight line
44. → ^ + λ 3ı^ − 5ȷ^ + 2k
r = ^ı − 11ȷ^ + 101k ^ ,λ ϵℝ
A) −3ı^ + 5ȷ^ − 2k^
B) ^
3ı^ + 5ȷ^ + 2k
C) ^ı − 11ȷ^ + 101k^
D) −ı^ + 11ȷ^ + 101k^
E) −4ı^ − 16ȷ^ + 103k^
Correct Answer : Option A
A straight line through the point (1,-1,0) meets the line = = at right angle
45.
. It's equation is
Text of page 12
A) = =
B) = =
C) = =
D) = =
E) = =
Correct Answer : Option A
The mean deviation about the mean for the following data
46.
A) 2
B) 2.5
C) 4
D) 6
E) 5
Correct Answer : Option B
47. If P(A) = 0.7, P(B) = 0.5 and P(A ∪ B) = 0.9 . Then P(A / B ) is
A) 0.3
B) 0.4
C) 0.5
D) 0.6
E) 0.7
Correct Answer : Option D
48. The variance of 240, 260, 270, 280 is
A)
B)
C)
D)
E)
Correct Answer : Option E
Text of page 13
Four unbiased coins are tossed simultaneously. Probability of getting atmost two heads,
49. is
A)
B)
C)
D)
E)
Correct Answer : Option C
( )
50. lim =
→
A)
B) π
C) 2π
D) π
E)
Correct Answer : Option B
[ ]
51. If [x] is the greatest integer less than or equal to x, then lim is equal to
→ [ ]
A) 1
B) sin 1
C) -1
D) 0
E) -sin 1
Correct Answer : Option B
( ) ( )
52. lim is equal to
→
A) 4
B) 8
C) 12
D) -8
E) -12
Correct Answer : Option C
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53. lim is equal to
→
A) 4
B) 2
C) -2
D) 0
E) 1
Correct Answer : Option E
54.
A) 2
B) 1
C) 3
D) 0
E) 4
Correct Answer : Option C
55. If f(x) = sin( | x | ) − | x | , x ϵ ℝ, then f is
A) not differentiable at x =
B) not differentiable at x =
C) not differentiable at x =
D) not differentiable at x = π
E) not differentiable at x = 0
Correct Answer:-Question Cancelled
56. The function f(x) = | x − 3x + 2| ,xϵ ℝ is not differentiable at
A) x = 1 and x = 3
B) x = 1 and x = 2
C) x = 2 and x = 4
D) x = 4 and x = 5
E) x = − 1 and x = − 2
Correct Answer : Option B
57. If e + x y + xy = e , then at (0,1) is equal to
A)
B) e
C) −e
D)
Text of page 15
E)
Correct Answer : Option E
58. If f(x) = x | x|, then f ( − 10)=
A) -20
B) -10
C) -40
D) 20
E) 40
Correct Answer : Option D
59. If y = (tan x) , then =
A) log(tan x) + 2x cosec(2x)
B) log(tanx) +x cosec(2x)
C) x log(tan x) + 2xcosec(2x)
D) xlog(tan x) + x cosec(2x)
E) log(tanx) + cosec(2x)
Correct Answer : Option A
60. The minimum of f(x) = | x + 2 | , x ϵ ℝ occurs at
A) x=0
B) x=2
C) x=1
D) x= −2
E) x= −1
Correct Answer : Option D
61. If g(x) = x − x, x ϵ ℝ, then g(x) is increasing in
A) ( − ∞, ∞)
B) ( − ∞, 0)
C) (0, − ∞)
D) (-5,5)
E)
Correct Answer : Option E
Text of page 16
The distance travelled by a moving particle is given by s = t − 6t + 10 , where is
62.
the time in seconds. The particle is at rest when =
A) 1
B) 4
C) 6
D) 3
E) 8
Correct Answer : Option D
63. The maximum value of the function f(x) = x√4x − x is
A) √3
B) 4√3
C) 5√3
D) 3√3
E) 6√3
Correct Answer : Option D
64. ∫ dx =
A) sinx + C
B) 2cosx + C
C) −cosx + C
D) −sinx + C
E) 2sinx + C
Correct Answer : Option E
( )
65. ∫ ( )
dx =
A) log(1 + x) + C
B) [log(1 + x)] + C
C) [log(1 + x)] + C
D) log(1 + x) + C
E) x log(1 + x) + C
Correct Answer : Option B
66. ∫ dθ =
A)
Text of page 17
B)
C)
D)
E)
Correct Answer : Option E
67. ∫ sin √x + cos √x dx =
A) +C
B) +C
C) +C
D) +C
E) +C
Correct Answer : Option D
68. ∫ e −
( )
dx =
A) +C
B) +C
C) e (1 + x) + C
D) +C
( )
E) +C
Correct Answer : Option A
69.
A)
B) log(5)
C) log(2)
Text of page 18
D)
E)
Correct Answer : Option A
70.
A) -3
B) -6
C) -4
D) -2
E) 0
Correct Answer : Option A
71.
A)
B) π
C)
D)
E) 0
Correct Answer : Option E
72.
A) 3
B) 6
C) 4
D) 8
E) 0
Correct Answer : Option C
73. The integrating factor of the differential equation − 2y = 2x − 3 is
A) e
B) e
Text of page 19
C) e
D) e
E) e
Correct Answer : Option E
The elimination of arbitrary constants c , c , c , c from y = (c + c )sin(2x + c )
74.
+c e gives a differential equation of order
A) 2
B) 4
C) 3
D) 1
E) 5
Correct Answer : Option C
Consider the linear programming problem.
Minimize z=x+y
75. Subject to the constraint
2x + 3y ≥ 6, x ≥ 0, y ≥ 0
Then the solution of L.P.P. is
A) 0
B) 2
C) 3
D) 5
E) 6
Correct Answer : Option B
The dimensions of where m is the magnetic moment, B, the magnetic flux density, k,
76.
Boltzmann constant and T, the absolute temperature are:
A) ML T
B) ML T
C) MLT
D) ML T
E) M L T
Correct Answer : Option E
77. The SI unit of surface tension is
A) Nm
B) Nm
Text of page 20
C) Nm
D) Nm
E) N
Correct Answer : Option A
A car starting from rest moves such that its acceleration varies with time as a = 6t (ms )
78.
. Its velocity (in ms and displacement (in m) after 4 seconds, respectively, are
A) 48, 64
B) 16, 24
C) 16, 38
D) 24, 32
E) 32, 24
Correct Answer : Option A
For the graph shown below between time t and velocity v of the motion of a body, the
correct statement is:
79.
A) The body comes to rest at infinite time
B) At t = 0, acceleration is positive
C) At t = 0, acceleration is negative
D) At t = 0, the body has maximum velocity
E) The displacement of the particle is zero.
Correct Answer : Option D
80. The coefficient of friction is defined as the ratio of
A) frictional force to applied force
B) frictional force to normal force
C) normal force to frictional force
D) weight of the object to frictional force
E) applied force to frictional force
Correct Answer : Option B
A tennis ball of mass 150 g is moving at 20 ms . A racket strikes it, reversing its
81. direction with a final speed of 30 ms . If the contact time is 0.02 s, then the magnitude
of the force (in N) exerted by the racket is
Text of page 21
A) 1.5 N
B) 3.75 N
C) 15 N
D) 150 N
E) 375 N
Correct Answer : Option E
A traffic light of mass 10 √3 kg is suspended by two cables making 30° with the vertical.
82.
The tension in each cable is:
A) 10 N
B) 9.8 N
C) 98 N
D) 19.6 N
E) 20 N
Correct Answer : Option C
A car moves at a speed of 20 ms under a force of 500 N. The power output of the car
83.
is
A) 9.8 kW
B) 980 kW
C) 98 kW
D) 10 kW
E) 100 kW
Correct Answer : Option D
A spring is stretched twice its initial extension. Compared to its initial value, the potential
84. energy
A) becomes four times
B) is doubled
C) is halved
D) remains the same
E) becomes zero
Correct Answer : Option A
85. If a spinning object contracts, its angular velocity
A) remains the same
B) becomes zero
C) becomes negative
D) increases
E) decreases
Correct Answer : Option D
Text of page 22
A boy whirls a ball on a string along a horizontal circle of radius 98 cm. The angular
86. velocity (in rad s ) with which the ball has to be whirled so that its acceleration towards
the centre of the circle has the same magnitude as acceleration due to gravity is
A) √10
B)
√
C) 10
D) 0.1
E) 100
Correct Answer : Option A
87. The centre of mass of a thin uniform rod of length L lies at a distance (from one end)
A)
B)
C)
D)
E)
Correct Answer : Option C
88. The ratio of the escape velocity to the orbital velocity of the earth is
A) 2
B) √2
C)
√
D)
E) √3
Correct Answer : Option B
The gravitational potential energy of a body of mass m on the surface of earth of mass M
89. and radius R is (G - Gravitational constant)
A)
B)
C) mgR
D) -mgR
E) Zero
Correct Answer:-Question Cancelled
90. In a liquid medium, if the depth increases, the pressure at that place
Text of page 23
A) decreases
B) increases
C) remains constant
D) depends on the shape of the container
E) is zero
Correct Answer : Option B
91. The angle of contact is the angle between
A) the normals to the liquid surface and the container wall
B) the liquid surface and the container wall
C) the tangent to the liquid surface and solid surface within the liquid at the point of contact
D) the liquid surface and solid surface outside the liquid
E) the line joining the centres of curvature of the liquid meniscus
Correct Answer : Option C
Water flows at 3 ms in a horizontal pipe under a pressure of 2 × 10 Nm The pipe
92. narrows to half its original diameter at one end. The speed of water (in ms ) in this
narrow section is
A) 3
B) 4
C) 6
D) 12
E) 24
Correct Answer : Option D
A Carnot engine is working between 127 °C and 27 °C. Keeping the sink temperature
93. unaltered, the temperature at which the source has to be kept so as to double its
efficiency is
A) 400°C
B) 273 °C
C) 327°C
D) 525 °C
E) 600°C
Correct Answer : Option C
The ratio of specific heat capacities of a diatomic gas at constant pressure and constant
94. volume is
A) 1.4
B) 1.6
C) 1.7
D) 1.8
E) 1.5
Text of page 24
Correct Answer : Option A
The translational kinetic energy of an ideal gas containing N molecules at temperature T
95. is (k - Boltzmann constant)
A) NkT
B) NkT
C) NkT
D) NkT
E) NkT
Correct Answer : Option C
For an ideal gas of molar mass M, the slope of the plot between the rms velocity (v
96.
along the y-axis) and the square root of absolute temperature ( √T along the x-axis) is
A)
B)
C)
D)
E)
Correct Answer : Option B
97. In a simple harmonic motion,
A) the velocity is constant
B) the motion is periodic
C) the acceleration is directly proportional to velocity
D) the acceleration is along the direction of displacement
E) the motion must be along a straight line
Correct Answer : Option B
98. The principle of superposition in wave motion states that
A) the net displacement is the vector sum of individual displacements
B) waves interfere with each other and lose energy
C) waves cannot occupy the same space at the same time
D) it is applicable to sound waves only
Text of page 25
E) it is applicable to standing waves only
Correct Answer : Option A
99. The number of nodes and antinodes in a guitar string vibrating in the third harmonic is:
A) 5 nodes, 4 antinodes
B) 4 nodes, 3 antinodes
C) 3 nodes, 2 antinodes
D) 2 nodes, 3 antinodes
E) 1 node, 2 antinodes
Correct Answer : Option B
100. The electric field inside a uniformly charged spherical shell of radius R is:
A) directly proportional to the charge within the shell
B) inversely proportional to R
C) same as that outside the shell
D) zero
E) maximum at the centre
Correct Answer : Option D
The torque on an electric dipole consisting of charges q and -q of dipole moment P in a
101. uniform electric field E is
A) qE
B) -qE
C) Zero
D) P.E
E) P×E
Correct Answer : Option E
102. The direction of the electric field due to a positive charge is:
A) circular around the charge
B) radially inwards towards the charge
C) radially outwards away from the charge
D) along a fixed straight line away from the charge
E) along a fixed straight line towards the charge
Correct Answer : Option C
103. A Wheatstone bridge is used to measure
A) unknown resistances
B) direct current
C) alternating current
D) electric power
Text of page 26
E) voltage
Correct Answer : Option A
The current carrying rail of a subway track is made of steel and has a cross-sectional
104. area of about 20 cm . The resistance of 2 km of the track is (in ohm) as a multiple of the
specific resistance of steel, ρ is:
A) 10 ρ
B) 10 ρ
C) 10 ρ
D) 10 ρ
E) 10 ρ
Correct Answer : Option E
If n identical cells each of emf E and internal resistance r are connected in parallel, the
105. total EMF and total internal resistance of the combination, respectively, are
A) nE, nr
B) E, nr
C) E,
D) nE, 2nr
E) nE,
Correct Answer : Option C
106. The line integral of the magnetic field around a closed loop is directly proportional to the:
A) current enclosed
B) charge enclosed
C) voltage across the loop
D) length of the loop
E) electric field around the loop
Correct Answer : Option A
The magnetic dipole moment of a current loop carrying current I and of area A with n
107. turns is
A)
B)
C)
D) nIA
E) IA
Text of page 27
Correct Answer : Option D
108. A galvanometer is converted into a voltmeter by connecting
A) a high resistance in series
B) a low resistance in series
C) a high resistance in parallel
D) a low resistance in parallel
E) an inductance in series
Correct Answer : Option A
109. The resistance of a semiconductor
A) increases with increase in temperature
B) decreases with increase in temperature
C) is independent of temperature
D) becomes infinite at high temperature
E) becomes zero at high temperature
Correct Answer : Option B
A metal rod of length 0.5 m moves with its length perpendicular to a uniform magnetic
110. field of 0.2 T with a velocity of 3 ms . The induced emf in the rod is
A) 0.1 V
B) 0.2 V
C) 0.3 V
D) 0.4 V
E) 0.6 V
Correct Answer : Option C
111. The speed of electromagnetic waves in a medium depends on the
A) intensity of the wave
B) initial phase of the wave
C) permittivity and permeability of the medium
D) energy it carries
E) reflectivity of the medium
Correct Answer : Option C
112. When a beam of white light enters into an optical prism, the most deviated colour is
A) green
B) violet
C) yellow
D) red
E) blue
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Correct Answer : Option B
113. The phenomenon of diffraction is most significant when the slit width is
A) much larger than the wavelength
B) much smaller than the wavelength
C) comparable to the wavelength
D) equal to the screen distance
E) independent of the wavelength
Correct Answer : Option C
114. In Huygens construction, the secondary wavelets move
A) in all directions
B) only radially outward
C) only radially inward
D) only in the backward direction of the incident light
E) in a direction perpendicular to the direction of the incident light
Correct Answer : Option A
The plot of maximum kinetic energy of photo-electrons to the energy of the incident
115. photon above its threshold frequency on a photo-sensitive material of work function φ is
A) an oblique straight line with a positive slope.
B) an oblique straight line with a negative slope.
C) an oblique straight line passing through the origin.
D) an exponential curve.
E) a polynomial curve of order 2.
Correct Answer : Option A
The ratio of the respective de Broglie wavelengths of two particles with kinetic energy of
116. 0.02 eV and 2 eV, respectively, is
A) 1:1
B) 10 : 1
C) 1 : 10
D) 1 : √10
E) √10 : 1
Correct Answer : Option B
In the following nuclear reaction, Z is a/an
117.
X→ Y+Z+v
A) α particle
B) β particle
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C) β particle
D) proton
E) neutron
Correct Answer : Option B
If a radioactive element disintegrates for a period of time equal to its mean life, then the
118. fraction of the original amount remaining undisintegrated is
A) e-
B) 1-e
C) 1-
D)
E) 2e
Correct Answer : Option D
In a Germanium crystal containing N atoms, the total number of outer electrons in the
119. crystal is
A) N
B) 2N
C) 3N
D) 6N
E) 4N
Correct Answer : Option E
120. The donor level in an n-type semiconductor lies
A) just below the conduction band
B) exactly at the middle of the band gap
C) just below the valence band
D) just above the conduction band
E) on the valence band
Correct Answer : Option A
Ten grams of calcium carbonate which is only 90% pure is treated with excess
121. hydrochloric acid. What is the mass of CO gas liberated? (Atomic mass: Ca=40, C=12
& O=16)
A) 4.4g
B) 3.96g
C) 2.2g
D) 0.44g
E) 0.22g
Text of page 30
Correct Answer : Option B
For any sub-shell defined by ‘l value how many values of magnetic quantum number (m
122. ) are possible?
A) (2l)
B) (2l -1)
C) (2l +1)
D) (l +1)
E) (l-1)
Correct Answer : Option C
123. What is the total number of orbitals associated with the principal quantum number n=3?
A) 3
B) 6
C) 9
D) 10
E) 14
Correct Answer : Option C
124. The alkali metal with the highest first enthalpy of ionization is
A) Cs
B) Rb
C) K
D) Na
E) Li
Correct Answer : Option E
125. Which one of the following molecules contains two 'sigma' bonds and two 'pi' bonds?
A) O
B) N
C) C H
D) CO
E) CO
Correct Answer : Option D
12g of pure graphite is burnt completely in a bomb calorimeter in excess of oxygen at 298
K at 1 atm. pressure. During combustion, the temperature rises from 298 K to 308 K. The
126. heat capacity of the bomb calorimeter is 20.7 kJ K . What is the enthalpy change for
combustion of 1 mole of graphite
(in kJ mol ) at 298 K and 1 atm. pressure? (R=8.3 JK mol )
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A) -2070
B) -207
C) +2070
D) +207
E) +2.07
Correct Answer : Option B
If water vapour is assumed to be a perfect gas, molar enthalpy change for vapourisation
of 1 mol of water at 1bar and 100°C is 41kJ mol . Calculate the internal energy change
127.
(in kJ mol ) when 1 mole of water is vaporized at 100°C at 1 bar assuming water
vapour as an ideal gas. (R=8.3 JK mol )
A) 43.1
B) 37.9
C) -43.1
D) -37.9
E) 41.0
Correct Answer : Option B
If “S” is the solubility of X Y in pure water, assuming that neither kind of ion reacts with
128. water, then, the solubility product, K is
A) 27 S
B) 108 S
C) 108 S
D) 27 S
E) 27 S
Correct Answer : Option B
129. In which of the following equilibrium K =K ?
A) CaCO ( ) ⇋ CaO( ) + CO ( )
B) 2SO ( ) + O ( ) ⇋ 2SO ( )
C) PCl ( ) ⇋ PCl ( ) + Cl ( )
D) H ( ) + I ( ) ⇋ 2HI( )
E) N2O ( ) ⇋ 2NO ( )
Correct Answer : Option D
In the following cell reaction,
Zn + Cu (0.1 M) ⇋ Zn (0.001 M) + Cu , at 298 K,
130.
Calculate the E at 298 K if E at this temperature is 1.1V. (2.303 RT/F = 0.059 V
at 298 K)
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A) 1.218 V
B) 1.118 V
C) 1.159 V
D) 1.041 V
E) 0.982 V
Correct Answer : Option C
For which of the following electrode reactions the standard electrode potential is the
131. highest at 298 K? The ions are present in aqueous solution.
A) Co + e → Co
B) Cl ( ) + 2e → 2Cl
C) MnO ( ) + 4H + 2e → Mn + 2H O
D) F ( ) + 2e → 2F
AgCl( ) + e → Ag( ) + Cl
E)
Correct Answer : Option D
The vapour pressure of pure benzene (molar mass=78 g mol ) at a certain
temperature is 0.85 bar. When 0.5 g of a non-volatile, non-electrolyte is added to 39 g of
132.
benzene, the vapour pressure was found to be 0.845 bar at the same temperature. What
is the molar mass of the substance?
A) 85 g mol
B) 127.5 g mol
C) 170 g mol
D) 210 g mol
E) 145 g mol
Correct Answer : Option C
A first order reaction is 75% completed in 6000 s at 300 K. What is its half life period at
133. the same temperature? (log 2 = 0.3010)
A) 15 min
B) 25 min
C) 75 min
D) 50 min
E) 60 min
Correct Answer : Option D
134. Ammonium ion (NH ) reacts with nitrite ion (NO ) according to the following equation:
NH + NO N ( ) + 2H O(l)
The following initial rates of reaction have been measured for the given reactant
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concentrations.
Which of the following is the rate law (rate equation) for this reaction?
A) Rate = k[NH ] / [NO ]
B) Rate = k[NH ] [NO ]
C) Rate = k[NH ] [NO ]
D) Rate = k[NH ] [NO ] /
E) Rate = k[NH ] [NO ]
Correct Answer : Option E
135. Acidified potassium dichromate cannot oxidize
A) Iodides to iodine
B) Iron (II) salt to iron (III) salt
C) Tin (II) salt to tin (IV) salt
D) H S to sulphur
E) Fluoride to fluorine
Correct Answer : Option E
136. Which of the following is a basic oxide?
A) CrO
B) CrO
C) Mn O
D) Cr O
E) V O
Correct Answer : Option A
137. The transistion metal ion with the highest magnetic moment is
A) Fe
B) Mn
C) Ni
D) Co
E) Cr
Correct Answer : Option B
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138. The transition metal with the highest melting point is
A) Mo
B) Mn
C) W
D) Cr
E) Au
Correct Answer : Option C
139. Which of the following complex has the least conductivity?
A) [Co(NH ) Cl]Cl
B) Cis-[Co(NH ) Cl ]Cl
C) [Co(NH ) ]Cl
D) [Co(NH ) Cl ]
E) trans-[Co(NH ) Cl ]Cl
Correct Answer : Option D
140. Which one of the following is an ambidentate ligand?
A) Oxalate
B) Carbon monoxide
C) Ethylene diamine
D) Ammonia
E) Nitrite
Correct Answer : Option E
The empirical formula of an organic compound is CH . The molar mass of the
141.
compound is 56g mol . The organic compound is
A) n-Butane
B) Propene
C) Propane
D) 2-Methylpropane
E) Cyclobutane
Correct Answer : Option E
Which of the following finely divided metals can be used as catalyst in the hydrogenation
142. of alkenes and alkynes?
(i) Pt (ii) Fe (iii) Ni (iv) Pd
A) (i), (ii) & (iii)
B) (ii), (iii) & (iv)
C) (i), (iii) & (iv)
D) (ii) & (iii)
E) (i), (ii), (iii) & (iv)
Text of page 35
Correct Answer : Option C
143. The solvent used in Wurtz reaction is
A) Water
B) Methanol
C) Ethanol
D) Dry ether
E) Aqueous ethanol
Correct Answer : Option D
When chlorobenzene is treated with Cl in the presence of anhydrous FeCl catalyst
144. gives a mixture of 1,2-dichlorobenzene and 1,4-dichlorobenzene. This reaction is an
example of
A) Nucleophilic substitution reaction
B) Electrophilic substitution reaction
C) Free radical substitution reaction
D) Nucleophilic addition reaction
E) Electrophilic addition reaction
Correct Answer : Option B
Which of the following compound contains two primary alcoholic and one secondary
145. alcoholic groups?
A) Ethylene glycol
B) Isopropyl alcohol
C) 3° Butyl alcohol
D) Glycerol
E) 2° Butyl alcohol
Correct Answer : Option D
146. Propene on hydroboration-oxidation gives
A) 1-propanol
B) 2-propanol
C) propanal
D) propanone
E) etanoic acid
Correct Answer : Option A
When propanone is treated with Zn/Hg and Con.HCl propane is formed. This reaction is
147. known as
A) Wolf-Kishner reaction
B) Clemmensen reaction
C) Hoffman reaction
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D) Kolbe’s reaction
E) Cannizzaro reaction
Correct Answer : Option B
148. Benzoyl chloride can be converted to benzaldehyde by
A) Rosenmund reduction
B) Etard reaction
C) Stephen reaction
D) Gatterman reaction
E) Gatterman-Koch reaction
Correct Answer : Option A
149. The amine with the highest pK value is
A) Methanamine
B) N-methylmethanamine
C) Benzeneamine
D) N-Methylaniline
E) Ethanamine
Correct Answer : Option C
150. The base that is not present in DNA is
A) uracil
B) adenine
C) guanine
D) thymine
E) cytosine
Correct Answer : Option A
Official key not published for this paper.
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Source: Commissioner for Entrance Examinations. Question paper published by Commissioner for Entrance Examinations.