PEARLS OF PHYSICS WORK AND ENERGY CHAPTER -4

Key Points
Work:- Work is the product of the magnitudes of the displacement and the component of the
force in the direction of displacement. W= F.d = Fdcosθ
• Work is the scalar quantity.
• If θ< 90° , work is +ve.
• If θ> 90° , work is –ve.
• Its unit is joule.

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Edited By: Zaheer Abbas Baloch Director The Scholars Academy, WahCantt.
PEARLS OF PHYSICS WORK AND ENERGY CHAPTER -4

Work done by variable force:-

For variable force, we divide the displacement into small patches then add work.
W= ∆𝑊1 + ∆𝑊2 + ∆𝑊3 + … … … … … ∆𝑊𝑁

WORK DONE BY GRAVITATIONAL FIELD:-

Work done by a gravitational field in closed path is zero also work is independent of path that’s
why gravitational fields is called conservative field.
POWER:- Power is the measure of the rate at which work is done.
∆𝑤
Power = = F.v Unit is watt and it is a scalar quantity
∆𝑡
Power = energy/time = P.E./time = k.E./ time = electrical energy/time
Energy = power × time
1 kwh = 1000 watt x 1 hr = 3.6x106J = 3.6MJ
Energy:-Ability to do work is known as energy.There are 2 types of energy.
1
Kinetic energy = mv2
2
𝑝2
➢ relation between momentum and kinetic energy: K.E.= 2𝑚
Potential energy: ability to do work is called Potential energy: P.E. = mgh
Work energy formula / theorem:-
W =∆𝐾. 𝐸 F.d = K.Ef – K.Ei
𝐺𝑀𝑚
Absolute Gravitational P.E. = U = −
𝑅
Escape velocity:-
Minimum velocity required to throw an object out of earth’s gravitational field is called escape
velocity. V = √2𝑔𝑅= 11.2 km/sec
Inter conversion of potential energy & kinetic energy:-
Loss in P.E = gain in K.E + work done against friction force
1
mgh = mv2 + fh where fh is work done against friction
2
2

1
work done against friction = mgh - mv2
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Edited By: Zaheer Abbas Baloch Director The Scholars Academy, WahCantt.
PEARLS OF PHYSICS WORK AND ENERGY CHAPTER -4

Non – conventional sources:-

Energy from tides:-Gravitational force of the moon give rise to tides in the sea of the water at the
high tidies trapped in a basin by constructing a dam, then we can use this as a source of energy.
Energy from waves:-The tidal movement and the winds blowing across the surface of ocean
produces strong waves. The energy of waves can be used to generate electricity.
Solar Energy:- The earth receives a huge amount of energy from sun directly each day its intensity is
1.4 kwh-2. This energy is reduced due to reflection, scattering and absorption by dust particles, water
vapors and other gasses. We can convert this energy to electricity by using semi conductor diodes.
Solar cells although are expensive but last for long time energy can be store in Ni-Cd Batteries by
connecting them to solar cells
Other source:-
Common source are:-
• Direct combustion.
• Fermentation.
• Energy from waste
production.
• Geothermal energy.
• Radioactive decay
• Residual heat of earth
• Compression of material

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Edited By: Zaheer Abbas Baloch Director The Scholars Academy, WahCantt.
PEARLS OF PHYSICS WORK AND ENERGY CHAPTER -4
work done to stretch by 5.0 cm from
the un-stretched position the work
Work & Energy
done to stretch it further by another
1. Person A does 5J in one second and B 5.0 cm is
does 10J in 2 second, then : a. 18.75 J b. 25.0 J
a. A and B has the same power c. 6.25 J d. 12.5 J
b. A is more powerful than B 7. In the tug of War team A is slowly
c. B is more powerful than A being defeated by team B. Net work is
d. None of the above done by
2. One ft-lb expressed in joule will be a. Team B b. Team A
a. 4.45 J b. 550 J c. Both d. None
c. 1.356 J d. 14.6 J 8. Block of mass m is taken to a height Re .
2
3. The mechanical gain in a machine to
The work done is
overcome a resistance W by an effort P
a. mgRe b. 2mgRe
will be 2 9

c. mgRe d. 3
a. W–P b. P x W MgRe
4 2
c. P/W d. W/P
9. Fig. shows the force distance curve of a
4. A force F acting on an object varies with
body moving along a straight line. The
distance x as sown in figure. The work work done by the force is
done by the force as the object moves
from x = 0m to x = 6m
5

4
Force (N)

0
0 1 2 3 4 5 6

displacement (m)

a. 20 J b. 15 J a. 10 J b. 20 J
c. 25 J d. 30 J c. 30 J d. 40 J
5. One Joule work is equivalent to 10. A loaded bus and an unloaded bus are
a. 0.738 ft. lb b. 0.378 ft. lb both moving with the same kinetic
c. 0.239 ft. lb d. None of these energy. The mass of the former is twice
6. A spring constant of a spring balance is that of the latter. Brakes are applied to
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5 x 103 Nm-1. It is initially stretched by

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both so as to exert equal retarding

Edited By: Zaheer Abbas Baloch Director The Scholars Academy, WahCantt.
PEARLS OF PHYSICS WORK AND ENERGY CHAPTER -4
forces. If S1 and S2 are the distance c. its momentum changes
covered by the two buses, respectively, d. it experiences an increase in energy
before coming to rest, then through a mechanical influence.
a. S1 = S2 b. 2S1 = S2 15. The work done is said to be negative
c. S1 = 2S2 d. S1 = 4S2 if:
11. The work done in holding a mass of a. θ=0 b. θ=∞
50 kg at a height of 2 m above the c. θ< 90o d. θ> 90o
ground is: 16. The force which can do no work on
a. 0 b. 25 J the body on which it acts is:
c. 100 J d. 980 J a. frictional force
12. A particle moves under the influence b. elastic force
of a force F = cx from x = 0 to c. gravitational force
x = x1, where c is a constant. The d. centripetal force

work in this process is 17. One erg is equal to :

1 a. 105 Joules b. 107 Joules

a. cx 2
1 b. cx12
2 c. 10-5 Joules d. 10-7 Joules
c. cx13 d. zero Conservative Force and Field
13. An object of mass 2kg, moving in a 18. Which of the following types of force
straight line,is accelerated from 2ms-1 can do no work on the particle on which
to 6ms-1 by a force of 5N acting along it operates?
the same direction. Then a. Centripetal force
a. the work done by the force is 20J b. Gravitational force
b. the distance traveled by the object c. Frictional force
is 6.4 m d. Shearing force
c. the time taken to change the 19. Which of the following is a property of a
velocity is 4s uniform gravitational field?
d. the increase in the kinetic energy a. It acts equally in all direction.
of the object is 32 J. b. Its field strength is the same at all
14. Work is always done on a body when point within it.
a. a force acts on it d. The gravitational potential has the
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b. it moves through a distance same value at all points within it.

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Edited By: Zaheer Abbas Baloch Director The Scholars Academy, WahCantt.
PEARLS OF PHYSICS WORK AND ENERGY CHAPTER -4
d. It produces zero force on a stationary 24. The engine of an inter-city train,
test mass placed in it. traveling at 50 m s-1 delivers a power of
20. The total work done in moving the body 2 MW. What is the tractive force
up and down in the gravitational- field exerted by the engine?
through the same height is a. 4x 104 N b. 1 x 105 N
a. Zero b. mgt c. 4 x 107 N d. 1 x 108 N
c. 2 mgt d. g t 25. A small electric motor is used to raise a
21. Which one of the following is not non weight of 2.0 N through a vertical height
conservative force. of 80 cm in 4.0 S. The efficiency of the
a. air resistance motor us 20%.What is the electrical
b. normal force power supplied to the motor?
c. electric force a. 0.080 W, b. 0.80 W
d. propulsion from rocket c. 2.0 W d. 200 W
22. A heavy weight is suspended from 26. Range of powers KW for electric heater,
the spring. A person raises, the pocket calculator and colour TV
weight till the spring becomes slack. respectively
The work done by him is W. The a. 120, 2000, 750
energy stored in the stretched spring b. 2, 7.5 x 10-7,1.2x10-1
was E. What will be the gain in c. 1.2 x 10-1, 7.5 x 10-4, 2 x 10-3
gravitational P.E. d. 2 x 103, 7.5 x 10-4, 120
a. W + E b. W – E 27. A force of 10 N displacement a body by
c. W d. E 6 m in 3 seconds. The power of the

Power agency applying the forces is

23. A car of mass m has an engine which a. 180W b. 5W

can be deliver power p. What is the c. 1.8 W d. none of above

minimum time in which the car can 28. For a constant force, the shape of The

be accelerated from rest to a speed graph between power and velocity is:

v? a. a circle b. a parabola

a. mv b. P c. a hyperbola d. a straight line

P mv

d. 2 P2
2
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c. mv
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2P mv

Edited By: Zaheer Abbas Baloch Director The Scholars Academy, WahCantt.
PEARLS OF PHYSICS WORK AND ENERGY CHAPTER -4
29. One horse power is equal to c. 225W d. 9000 H.P
a. 742 watt b. 646 watt 35. The time taken by an engine of power
c. 754 watt d. 746 watt 10 kW to lift a mass of 200 kg to a
30. A power station has an efficiency of 40% height of 40 m is (g=10 m/s2)
and generates 100 MW of electrical a. 2 s b. 4 s
power. What is input power and the c. 8 s d. 16 s
wasted power. 36. A 170 kg cart and rider start from rest
Input power Output power on a 20.0 m high incline.
A 1000 400
B 1000 600
C 1400 400
D 2500 1500
How much energy is transformed to heat
31. Approximate power of Jumbo Jet air
a) 4000J b) 7200 J
craft is
c) 8300 J d) 0 J
a. 1.3 x 1018 watt b. 2.9 x 106 watt 37. One mega watt-hour is equal to:
c. 130.0 MW d. 13000 KW a. 36 x 106 J b. 36 x 1012 J
32. A small electric motor is used to raise a c. 36 x 109 J d. 36 x 108 J
weight of 2.0 N through a vertical 38. A particle moves with a velocity
height of 80 cm in 4.0 sec. The ms-1 under the influence of a
6iˆ − 4 ˆj + 3kˆ
efficiency of the motor is 20% what is 
constant force F = 20iˆ + 15 ˆj − 5kˆN . The
the electrical power supplied to the
instantaneous power applied to the
motor?
particle is:
a. 0.080 W b. 0.80 W
a. 45 Js-1 b. 35 Js-1
c. 2.0 W d. 200 W
c. 25 Js-1 d. 195 Js-1
33. One watt-hour equals
39. The engine of a train traveling at
a. 3.6 x 103 J b. 3.6 x 103cal
50 ms-1, delivers a power of 2.0 MW
c. 3.6 x 106 J d. 3.6 x 106cal
a. 4 x 104N b. 4 x 107N
34. An electric motor creates a tension of 45
c. 1 x 105N d. 1 x 108N
N in a hoisting cable and reels it in at the
40. A constant force F is applied on a body.
rate of 2 m/s. the power of the motor is
The power (P) generated is related to
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a. 15kW b. 90W
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the time elapsed (t) as

Edited By: Zaheer Abbas Baloch Director The Scholars Academy, WahCantt.
PEARLS OF PHYSICS WORK AND ENERGY CHAPTER -4
a. P α t3/2 b. P α t 46. A child on a swing is 1m above the
c. P α t d. P α t2 ground at the lowest point and 6m
41. A body is moved along a straight line above the ground at the highest point.
by a machine delivering a constant The horizontal speed of the child at the
power. The distance moved by the lowest point of the swing is
body in time t is approximately
a. t1/2 b. t3/4 a. 8 m/s b. 10 m/s
c. t3/2 d. t2 x v2 c. 12 m/s d. 14 m/s

Energy and Conservation of Energy 47. A body of mass m=1 kg is dropped from

42. When the velocity of a body is doubled a height h= 40 cm on a horizontal

a. Its K.E. is doubled platform fixed to one end of an elastic

b. Its P.E. is doubled spring, the other being fixed to a base,

c. Its momentum is doubled as shown in figure. As a result the spring

d. Its acceleration is doubled is compressed by an amount x = 10 cm.

43. A moving body need not have What is the force constant of the spring.

a. kinetic energy b. momentum Take g = 10 ms-2.

c. potential energy d. velocity

44. Two spheres of the same size, one of
mass 5 kg and the other of mass 10 kg
are dropped simultaneously from a a. 600 Nm-1 b. 800 Nm-1

tower. When they are about to touch c. 1000 Nm-1 d. 1200 Nm-1

the ground, they have the same 48. A 1kg mass has a K.E of 1 joule when its

a. momentum b. kinetic energy speed is

c. potential energy d. acceleration a. 0.45 m/s b. 1 m/s

45. A car weighing 1 ton is moving twice as c. 1.4 m/s d. 4.4 m/s

fast as another car weighing 2 tons. The 49. A1 kg mass has a P.E of 1 joule relative

K.E. of the one ton car is to the ground when it is at a height of

a. less than that of the two-ton car a. 0.102m b. 1m

b. same as that of the two-ton car c. 9.8m d. 32m

c. more than that of the two-ton car

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d. its total momentum decreases

Edited By: Zaheer Abbas Baloch Director The Scholars Academy, WahCantt.
PEARLS OF PHYSICS WORK AND ENERGY CHAPTER -4
50. Two masses of 1g and 4g are moving 54. A 4.0kg body, moving with a speed of
with equal kinetic energies. The ratio of 2.0 m/s, collides with a spring bumper
the magnitudes of their linear of negligible mass and force constant
momenta is 100 N/m. the maximum compression

a. 4 : 1 b. 2 :1 of the spring is

c. 1 : 2 d. 2 : 1 a. 0.4 m b. 0.8m

51. A body of mass m is dropped from c. 1.6 m d. 2.0m

height h above the ground. The velocity 55. A particle at the origin is under the

v of the body when it has lost half its influence of a force F = kx, where k is a

initial potential energy is given by positive constant, if the potential

a. v = gh b. v = 2 gh energy U is zero at x = 0, the variation

of potential energy with the coordinate
gh
c. v = d. v = 2 gh x is represented by (see figure)
2
52. A particle is acted upon by a force of
constant magnitude which is always
perpendicular to the velocity of the
particle. The motion of the particle
take place in a plane. It follows that
a. the velocity of the particle is constant
b. the acceleration of the particle is
constant
56. The kinetic energy acquired by a body
c. the kinetic energy of the particle is
of mass m is traveling a certain
constant
distance starting from rest, under a
d. the particle moves in a circular path.
constant force is
53. Two particles of masses m1 and m2
a. directly proportional to m
have equal kinetic energies. The ratio
b. directly proportional to m
of there momenta is
c. inversely proportional to m
a. m1 : m2 b. m2 : m1
d. independent of m.
c. m1 : m2 d. m12 : m22
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PEARLS OF PHYSICS WORK AND ENERGY CHAPTER -4
57. The source of geothermal energy is: 61. Ratio of the escape velocity of earth to
a. The fission in atomic nuclei the moon. Will be approximately equal
b. The fusion in sun to (if Radius of moon is approximated to
c. The radioactive decay in the earth’s one forth of Radius of earth.)
interior. a. 4 b. 5
d. The rotation of earth around the sun. c. 6 d. ¼
e. The rotation of earth about its moon. 62. A ball of mass 1 kg is released from the
58. Suppose a 1 Kg block slides down a tower of Pisa. The kinetic energy
smooth inclined plane whose height is generated in it after 10 m will be
5m. What is the velocity of the block at a. 0.98 J b. 9.8 J
the bottom? c. 10 J d. 98 J
63. The linear momentum of a particle
a. 10 m sec-1 b. 9.8 m sec-1
increases by 50%. The increase in kinetic
c. 98 m sec-1 d. 7 2 m sec-1 energy should be
a. 225% b. 100%
59. A best moving at constant speed v
through still water experiences a total c. 50% d. 125%
friction drag F. What is the power
64. A body falls freely under gravity. Its
develop by the boat?
velocity is v when it lost potential
a. ½Fv b. Fv energy equal to PE. What is the mass of
c. ½ Fv2 d. Fv2 the body?
60. The earth may be considered to be a. 2PE/v2 b. PE/V2
uniform sphere of mass M and radius R. c. PE2/v2 d. 2PE2/v2
Which one of the following equation 65. The momentum of particle is
correctly relates the universal numerically equal to its kinetic energy.
gravitational constant G to the What is the velocity of the particle?
acceleration of free fall g at the surface a. 9 ms-1 b. 3 ms-1
of the Earth? c. 2 ms-1 d. 1 ms-1
a. G=
gM b. G=
R2
R2 gM
10

c. G=
gR 2 d. G=
M
M gR 2
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PEARLS OF PHYSICS WORK AND ENERGY CHAPTER -4
66. A gun of mass fires a bullet of mass m. a. maximum b. minimum
When will be the ratio of the recoil c. kx2 d. zero
energy of the gun to that of the bullet? 72. The gravitational potential energy of a 2
M kg body on earth’s surface will be
a. M b.
M +m m a. -1.25 x 108 J b. -1.25 J
m m c. 0.25 J d. 12.5 J
c. d.
M m+M 73. Which one is the biggest unit of energy?
67. Two electrons are brought closer a. Erg b. Joule
together. The potential energy of the
c. Kilowatt hour d. Foot – pound
system will be
74. If m is the mass of the body ad E is its
a. zero b. less
K.E. then linear momentum is
c. more d. infinity
a. m E b. 2 m E
68. Two masses of 1 gm and 4 gm are
c. mE d. 2mE
moving with the same kinetic energy.
75. An object of mass m passes a point x
The ratio of their liner momentum will
with a velocity v and slides up a
be
frictionless inclined to stop at point y
a. 1 : 16 b. 1 : 2
which is at a height h above x.
c. 2 : 1 d. 4 : 1

69. A spring of spring constant k is given a

sharp blow by a force F so that the
spring shows a compression x. Then
work done on the spring is
A second mass of mass ½ m passes x
a. 1 kx 2 b. Fx
2 with a velocity of ½ v to what height it
2
c. kx d. none of these will rise.
4
a. ½ h b. ¼ h
70. Watt-day is the unit of following
c. h d. h 2
physical quantity
76. What is the K.E of electron in electron
a. power b. momentum
volts having velocity 1.0 x 107 ms-1
c. energy d. force
a. 28.75 eV b. 287.5 eV
71. The potential energy of a system in the
11

c. 2.875eV d. 4.6 x 10eV

state of unstable equilibrium is
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Edited By: Zaheer Abbas Baloch Director The Scholars Academy, WahCantt.
PEARLS OF PHYSICS WORK AND ENERGY CHAPTER -4
77. The value of solar constant the maximum number of planks
a. 1.4 KWm2 b. 1.4KWm-2 through which it can pass.
c. 1.4 Wm-2 d. 140 MWm-2 a. 19 b. 20
78. Approximate energy values (in joule) c. 11 d. 10
for Fission of one atom of uranium and 83. The magnitude of momentum of a
K.E. of molecule of air body is increased by 100%. If the initial
a. 18 x 10-11 and 6 x 10-19 kinetic energy be K.E then what will be
b. 1.8 x 10-1 and 6 x 10-2 the kinetic energy now?
c. 1.8 x 10-21 and 6 x 10-11 a. 2KE b. 3 KE
d. 1.8 x 10-11 and 6 x 10-21 c. 4 KE d. 8 KE
79. A particle of mass m is moving in a 84. A vehicle is moving on a rough
horizontal circle of radius r, under a horizontal road with velocity “v”. The
centripetal force K where “K” is stopping distance will be directly
r2
proportional to.
constant. Find the total energy of the
a. v b. v2
particle.
−K K
c. v3 d. v
a. b.
r r 85. The K.E of a body varies directly as time
c. K d. −K
t elapsed. The force acting varies
2r 2r

80. Atomic power station has a generating directly as

capacity of 200 MW. The energy a. 1 b. t

t
generated in a day is c. 1/t d. t
a. 1.725 x 1010 J 86. When a body moves in an orbit its total
b. 17.28 x 109 J energy is
c. 1728 x 1010 J a. positive b. negative
d. None of these c. zero d. None
81. If the K.E of a particle increases by 44%. 87. Two bodies of mass and 4m are
Find the increase in momentum. moving with equal kinetic energies.
a. 44% b. 20% The ratio of their linear momenta is
c. 12% d. 32% a. 1 : 4 b. 4 : 1
12

82. A bullet loses 1/20th of its velocity

c.1 : 2 d. 1 : 2
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when it passes through a plank. Find

Edited By: Zaheer Abbas Baloch Director The Scholars Academy, WahCantt.
PEARLS OF PHYSICS WORK AND ENERGY CHAPTER -4
AGPE and Escape Velocity ratio radius of orbit of new satellite is
radius of orbit of old satellite
88. The ICBM are fired with :
a. 1 b. 1
a. Escape velocity 2 1

b. Greater than Escape velocity c. 2 d. 2

1 1
c. Less than Escape velocity 92. If ‘g’ is the acceleration due to gravity at the
d. Relativistic velocity surface of the earth, then the energy
89. Star X of mass 2M and star Y of mass M required to launch a satellite of mass m from
perform circular motion about their the surface of the earth into a circular orbit
common centre of mass their at an altitude of 3R, R being the radius of the

gravitaional attraction. earth, is:

a) mgR b) mgR
What is the rario force acting on X , ignoring
force acting on Y
6 3

c) 3mgR d) 5mgR
the effects of any other bodies. 4 6
a. 4 b. 2 93. A missile is released with a velocity less
c.1 d. ½ than escape velocity. The sum of its
90. A satellite of mass m is in a circular orbit potential and kinetic energies is
of radius r about the Earth, mass M, and a. mgh b. positive
remains at a vertical height h above the c. negative d. zero
Earth’s surface. Taking the zero of the 94. Expression for escape velocity from
gravitational potential to be at an earth surface if its radius becomes half
infinite distance from the Earth. What is and mass reduces to one third is
the gravitational potential energy of the
a. 2 GM b. 2
6 gr
R 3
satellite?
c. GM d. None of these
a.mgh b. –mgh
6R
c. − GMm d. − GMm
r 2r 95. Escape speed for Venus and Jupiter is
91. A communications satellite which takes (in Kms-1)
24 hours to orbit the Earth is replaced a. 4.3, 2.4 b. 5.0, 11.2
by a new satellite which has twice the c. 22.4, 37 d. 10.4, 61
mass of the first. If the new satellite also
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has an orbit time of 24 hours, then the

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PEARLS OF PHYSICS WORK AND ENERGY CHAPTER -4

ANSWER SHEET

Q Ans. Q Ans. Q Ans. Q Ans.

1 a 26 b 51 a 76 d
2 b 27 d 52 c 77 b
3 d 28 d 53 c 78 d
4 c 29 d 54 a 79 d
5 a 30 d 55 d 80 c
6 a 31 c 56 d 81 b
7 a 32 c 57 c 82 c
8 b 33 a 58 d 83 c
9 a 34 b 59 b 84 b
10 a 35 c 60 c 85 a
11 a 36 b 61 b 86 b
12 a 37 d 62 d 87 c
13 b,d 38 a 63 d 88 c
14 d 39 a 64 a 89 c
15 d 40 c 65 c 90 c
16 d 41 c 66 c 91 b
17 d 42 c 67 c 92 c
18 a 43 c 68 b 93 c
19 a 44 d 69 b 94 b
20 a 45 c 70 c 95 d
21 c 46 b 71 a 96
22 a 47 b 72 a 97
23 c 48 c 73 c 98
24 a 49 a 74 d 99
25 c 50 c 75 b 100
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Edited By: Zaheer Abbas Baloch Director The Scholars Academy, WahCantt.