Page 1
INSTRUCTIONS
· This question paper contains total 150 questions divided into four parts:
Part I : Physics Q. No. 1 to 40
Part II : Chemistry Q. No. 41 to 80
Part III : (A) English Proficiency Q. No. 81 to 90
(B) Logical Reasoning Q. No. 91 to 105
Part IV : Mathematics Q. No. 106 to 150
· All questions are multiple choice questions with four options, only one of them is correct.
· Each correct answer awarded 3 marks and –1 for each incorrect answer.
· Duration of paper-3 Hours
PART - I : PHYSICS
1. What is the minimum energy required to launch a
satellite of mass m from the surface of a planet of
mass M and radius R in a circular orbit at an altitude
of 2R?
(a)
5GmM
6R
(b)
2GmM
3R
(c)
GmM
2R
(d)
GmM
2R
2. A mercury drop of radius 1 cm is sprayed into 10
6
drops of equal size. The energy expressed in joule
is (surface tension of Mercury is 460 × 10
–3
N/m)
(a) 0.057 (b) 5.7
(c) 5.7 × 10
–4
(d) 5.7 × 10
–6
3. Two plano-concave lenses (1 and
2) of glass of refractive index 1.5
have radii of curvature 25 cm and
20 cm. They are placed in contact
1 2
with their curved surface towards each other and
the space between them is filled with liquid of
refractive index 4/3. Then the combination is
(a) convex lens of focal length 70 cm
(b) concave lens of focal length 70 cm
(c) concave lens of focal length 66.6 cm
(d) convex lens of focal length 66.6 cm
4. A charged particle moves through a magnetic
field perpendicular to its direction. Then
(a) kinetic energy changes but the momentum
is constant
(b) the momentum changes but the kinetic
energy is constant
(c) both momentum and kinetic energy of the
particle are not constant
(d) both momentum and kinetic energy of the
particle are constant
5. After two hours, one-sixteenth of the starting
amount of a certain radioactive isotope remained
undecayed. The half life of the isotope is
(a) 15 minutes (b) 30 minutes
(c) 45 minutes (d) 4 hour
6. A coil of inductance 300 mH and resistance 2W is
connected to a source of voltage 2 V . The current
reaches half of its steady state value in
(a) 0.1 s (b) 0.05 s (c) 0.3 s (d) 0.15 s
7. Two concentric conducting thin spherical shells
A, and B having radii r
A
and r
B
((r
B
> r
A
) are
charged to Q
A
and –Q
B
(|Q
B
| > |Q
A
|). The electric
field along a line passing through the centre is
(a) (b)
(c) (d)
Page 2
INSTRUCTIONS
· This question paper contains total 150 questions divided into four parts:
Part I : Physics Q. No. 1 to 40
Part II : Chemistry Q. No. 41 to 80
Part III : (A) English Proficiency Q. No. 81 to 90
(B) Logical Reasoning Q. No. 91 to 105
Part IV : Mathematics Q. No. 106 to 150
· All questions are multiple choice questions with four options, only one of them is correct.
· Each correct answer awarded 3 marks and –1 for each incorrect answer.
· Duration of paper-3 Hours
PART - I : PHYSICS
1. What is the minimum energy required to launch a
satellite of mass m from the surface of a planet of
mass M and radius R in a circular orbit at an altitude
of 2R?
(a)
5GmM
6R
(b)
2GmM
3R
(c)
GmM
2R
(d)
GmM
2R
2. A mercury drop of radius 1 cm is sprayed into 10
6
drops of equal size. The energy expressed in joule
is (surface tension of Mercury is 460 × 10
–3
N/m)
(a) 0.057 (b) 5.7
(c) 5.7 × 10
–4
(d) 5.7 × 10
–6
3. Two plano-concave lenses (1 and
2) of glass of refractive index 1.5
have radii of curvature 25 cm and
20 cm. They are placed in contact
1 2
with their curved surface towards each other and
the space between them is filled with liquid of
refractive index 4/3. Then the combination is
(a) convex lens of focal length 70 cm
(b) concave lens of focal length 70 cm
(c) concave lens of focal length 66.6 cm
(d) convex lens of focal length 66.6 cm
4. A charged particle moves through a magnetic
field perpendicular to its direction. Then
(a) kinetic energy changes but the momentum
is constant
(b) the momentum changes but the kinetic
energy is constant
(c) both momentum and kinetic energy of the
particle are not constant
(d) both momentum and kinetic energy of the
particle are constant
5. After two hours, one-sixteenth of the starting
amount of a certain radioactive isotope remained
undecayed. The half life of the isotope is
(a) 15 minutes (b) 30 minutes
(c) 45 minutes (d) 4 hour
6. A coil of inductance 300 mH and resistance 2W is
connected to a source of voltage 2 V . The current
reaches half of its steady state value in
(a) 0.1 s (b) 0.05 s (c) 0.3 s (d) 0.15 s
7. Two concentric conducting thin spherical shells
A, and B having radii r
A
and r
B
((r
B
> r
A
) are
charged to Q
A
and –Q
B
(|Q
B
| > |Q
A
|). The electric
field along a line passing through the centre is
(a) (b)
(c) (d)
8. A capillary tube of radius R is immersed in water
and water rises in it to a height H. Mass of water
in the capillary tube is M. If the radius of the tube
is doubled, mass of water that will rise in the
capillary tube will now be :
(a) M (b) 2 M (c) M/2 (d) 4 M
9. A sonometer wire resonates with a given tuning
fork forming standing waves with five antinodes
between the two bridges when a mass of 9 kg is
suspended from the wire. When this mass is
replaced by a mass M, the wire resonates with
the same tuning fork forming three antinodes for
the same positions of the bridges. The value of M
is
(a) 25 kg (b) 5 kg
(c) 12.5 kg (d) 1/25 kg
10. When a metal surface is illuminated by light of
wavelengths 400 nm and 250 nm, the maximum
velocities of the photoelectrons ejected are v and
2v respectively . The work function of the metal is
(h - Planck's constant, c = velocity of light in air)
(a) 2 hc ×10
6
J (b) 1.5 hc × 10
6
J
(c) hc × 10
6
J (d) 0.5 hc × 10
6
J
11. Two conducting shells of radius a and b are
connected by conducting wire as shown in figure.
The capacity of system is :
a b
(a) 4 pe
0
ab
ba -
(b) 4 pe
0
(a + b)
(c) zero (d) infinite
12. When
92
U
235
undergoes fission, 0.1% of its
original mass is changed into energy . How much
energy is released if 1 kg of
92
U
235
undergoes
fission
(a) 9 × 10
10
J (b) 9 × 10
11
J
(c) 9 × 10
12
J (d) 9 × 10
13
J
13. One mole of an ideal gas is taken from state A to
state B by three different processes,
P
V
B
E
C
A
D
(i) ACB (ii) ADB (iii) AEB as shown in the P-V
diagram. The heat absorbed by the gas is
(a) greater in process (ii) than in (i)
(b) the least in process (ii)
(c) the same in (i) and (iii)
(d) less in (iii) than in (ii)
14. In the formula X = 3 YZ
2
, X and Z have dimen-
sions of capacitance and magnetic induction re-
spectively. The dimensions of Y in MKSA sys-
tem are :
(a) [M
–3
L
–2
T
–2
A
–4
] (b) [ML
–2
]
(c) [M
–3
L
–2
A
4
T
8
] (d) [M
–3
L
2
A
4
T
4
]
15. Two very long, straight, parallel wires carry steady
currents I and -I respectively. The distance
between the wires is d. At a certain instant of
time, a point charge q is at a point equidistant
from the two wires, in the plane of the wires. Its
instantaneous velocity v is perpendicular to this
plane. The magnitude of the force due to the
magnetic field acting on the charge at this instant
is
(a)
0
2
qv
d
mI
p
(b)
0
qv
d
mI
p
(c)
0
2 qv
d
mI
p
(d) 0
16. Two projectiles A and B thrown with speeds in
the ratio 1 : 2 acquired the same heights. If A is
thrown at an angle of 45° with the horizontal, the
angle of projection of B will be
(a) 0° (b) 60° (c) 30° (d) 45°
17. A meter bridge is set up as shown, to determine
an unknown resistance ‘X’ using a standard 10
ohm resistor. The galvanometer shows null point
when tapping-key is at 52 cm mark. The end-
corrections are 1 cm and 2 cm respectively for the
ends A and B. The determined value of ‘X’ is
(a) 10.2 ohm (b) 10.6 o hm
(c) 10.8 ohm (d) 11.1 o hm
18. A disk of radius a / 4 having a uniformly
distributed charge 6 C is placed in the x - y plane
with its centre at (–a / 2, 0, 0). A rod of length a
carrying a uniformly distributed charge 8 C is
placed on the x-axis from x = a /4 to x = 5a / 4.
Two point charges – 7 C and 3 C are placed at (a
/ 4, – a /4, 0) and (– 3a /4, 3a / 4, 0), respectively .
Consider a cubical surface formed by six surfaces
x = ± a / 2, y = ± a / 2, z = ± a / 2. The electric flux
through this cubical surface is
Page 3
INSTRUCTIONS
· This question paper contains total 150 questions divided into four parts:
Part I : Physics Q. No. 1 to 40
Part II : Chemistry Q. No. 41 to 80
Part III : (A) English Proficiency Q. No. 81 to 90
(B) Logical Reasoning Q. No. 91 to 105
Part IV : Mathematics Q. No. 106 to 150
· All questions are multiple choice questions with four options, only one of them is correct.
· Each correct answer awarded 3 marks and –1 for each incorrect answer.
· Duration of paper-3 Hours
PART - I : PHYSICS
1. What is the minimum energy required to launch a
satellite of mass m from the surface of a planet of
mass M and radius R in a circular orbit at an altitude
of 2R?
(a)
5GmM
6R
(b)
2GmM
3R
(c)
GmM
2R
(d)
GmM
2R
2. A mercury drop of radius 1 cm is sprayed into 10
6
drops of equal size. The energy expressed in joule
is (surface tension of Mercury is 460 × 10
–3
N/m)
(a) 0.057 (b) 5.7
(c) 5.7 × 10
–4
(d) 5.7 × 10
–6
3. Two plano-concave lenses (1 and
2) of glass of refractive index 1.5
have radii of curvature 25 cm and
20 cm. They are placed in contact
1 2
with their curved surface towards each other and
the space between them is filled with liquid of
refractive index 4/3. Then the combination is
(a) convex lens of focal length 70 cm
(b) concave lens of focal length 70 cm
(c) concave lens of focal length 66.6 cm
(d) convex lens of focal length 66.6 cm
4. A charged particle moves through a magnetic
field perpendicular to its direction. Then
(a) kinetic energy changes but the momentum
is constant
(b) the momentum changes but the kinetic
energy is constant
(c) both momentum and kinetic energy of the
particle are not constant
(d) both momentum and kinetic energy of the
particle are constant
5. After two hours, one-sixteenth of the starting
amount of a certain radioactive isotope remained
undecayed. The half life of the isotope is
(a) 15 minutes (b) 30 minutes
(c) 45 minutes (d) 4 hour
6. A coil of inductance 300 mH and resistance 2W is
connected to a source of voltage 2 V . The current
reaches half of its steady state value in
(a) 0.1 s (b) 0.05 s (c) 0.3 s (d) 0.15 s
7. Two concentric conducting thin spherical shells
A, and B having radii r
A
and r
B
((r
B
> r
A
) are
charged to Q
A
and –Q
B
(|Q
B
| > |Q
A
|). The electric
field along a line passing through the centre is
(a) (b)
(c) (d)
8. A capillary tube of radius R is immersed in water
and water rises in it to a height H. Mass of water
in the capillary tube is M. If the radius of the tube
is doubled, mass of water that will rise in the
capillary tube will now be :
(a) M (b) 2 M (c) M/2 (d) 4 M
9. A sonometer wire resonates with a given tuning
fork forming standing waves with five antinodes
between the two bridges when a mass of 9 kg is
suspended from the wire. When this mass is
replaced by a mass M, the wire resonates with
the same tuning fork forming three antinodes for
the same positions of the bridges. The value of M
is
(a) 25 kg (b) 5 kg
(c) 12.5 kg (d) 1/25 kg
10. When a metal surface is illuminated by light of
wavelengths 400 nm and 250 nm, the maximum
velocities of the photoelectrons ejected are v and
2v respectively . The work function of the metal is
(h - Planck's constant, c = velocity of light in air)
(a) 2 hc ×10
6
J (b) 1.5 hc × 10
6
J
(c) hc × 10
6
J (d) 0.5 hc × 10
6
J
11. Two conducting shells of radius a and b are
connected by conducting wire as shown in figure.
The capacity of system is :
a b
(a) 4 pe
0
ab
ba -
(b) 4 pe
0
(a + b)
(c) zero (d) infinite
12. When
92
U
235
undergoes fission, 0.1% of its
original mass is changed into energy . How much
energy is released if 1 kg of
92
U
235
undergoes
fission
(a) 9 × 10
10
J (b) 9 × 10
11
J
(c) 9 × 10
12
J (d) 9 × 10
13
J
13. One mole of an ideal gas is taken from state A to
state B by three different processes,
P
V
B
E
C
A
D
(i) ACB (ii) ADB (iii) AEB as shown in the P-V
diagram. The heat absorbed by the gas is
(a) greater in process (ii) than in (i)
(b) the least in process (ii)
(c) the same in (i) and (iii)
(d) less in (iii) than in (ii)
14. In the formula X = 3 YZ
2
, X and Z have dimen-
sions of capacitance and magnetic induction re-
spectively. The dimensions of Y in MKSA sys-
tem are :
(a) [M
–3
L
–2
T
–2
A
–4
] (b) [ML
–2
]
(c) [M
–3
L
–2
A
4
T
8
] (d) [M
–3
L
2
A
4
T
4
]
15. Two very long, straight, parallel wires carry steady
currents I and -I respectively. The distance
between the wires is d. At a certain instant of
time, a point charge q is at a point equidistant
from the two wires, in the plane of the wires. Its
instantaneous velocity v is perpendicular to this
plane. The magnitude of the force due to the
magnetic field acting on the charge at this instant
is
(a)
0
2
qv
d
mI
p
(b)
0
qv
d
mI
p
(c)
0
2 qv
d
mI
p
(d) 0
16. Two projectiles A and B thrown with speeds in
the ratio 1 : 2 acquired the same heights. If A is
thrown at an angle of 45° with the horizontal, the
angle of projection of B will be
(a) 0° (b) 60° (c) 30° (d) 45°
17. A meter bridge is set up as shown, to determine
an unknown resistance ‘X’ using a standard 10
ohm resistor. The galvanometer shows null point
when tapping-key is at 52 cm mark. The end-
corrections are 1 cm and 2 cm respectively for the
ends A and B. The determined value of ‘X’ is
(a) 10.2 ohm (b) 10.6 o hm
(c) 10.8 ohm (d) 11.1 o hm
18. A disk of radius a / 4 having a uniformly
distributed charge 6 C is placed in the x - y plane
with its centre at (–a / 2, 0, 0). A rod of length a
carrying a uniformly distributed charge 8 C is
placed on the x-axis from x = a /4 to x = 5a / 4.
Two point charges – 7 C and 3 C are placed at (a
/ 4, – a /4, 0) and (– 3a /4, 3a / 4, 0), respectively .
Consider a cubical surface formed by six surfaces
x = ± a / 2, y = ± a / 2, z = ± a / 2. The electric flux
through this cubical surface is
x
y
(a)
0
–2C
e
(b)
0
2C
e
(c)
0
10C
e
(d)
0
12C
e
19. A particle of mass m moving in the x direction
with speed 2v is hit by another particle of mass
2m moving in the y direction with speed v. If the
collision is perfectly inelastic, the percentage loss
in the energy during the collision is close to
(a) 56% (b) 62% (c) 44% (d) 50%
20. A coil is suspended in a uniform magnetic field,
with the plane of the coil parallel to the magnetic
lines of force. When a current is passed through
the coil it starts oscillating; It is very difficult to
stop. But if an aluminium plate is placed near to
the coil, it stops. This is due to :
(a) developement of air current when the plate
is placed
(b) induction of electrical charge on the plate
(c) shielding of magnetic lines of force as
aluminium is a paramagnetic material.
(d) electromagnetic induction in the aluminium
plate giving rise to electromagnetic
damping.
21. A steel wire of length ‘L’ at 40°C is suspended
from the ceiling and then a mass ‘m’ is hung from
its free end. The wire is cooled down from 40°C to
30°C to regain its original length ‘L’. The
coefficient of linear thermal expansion of the steel
is 10–5 /° C, Young’s modulus of steel is 10
11
N/
m
2
and radius of the wire is 1 mm. Assume that L
>>diameter of the wire. Then the value of ‘m’ in
kg is nearly
(a)1 (b) 2 (c)3 (d) 5
22. On a hypotenuse of a right prism (30° – 60° – 90°)
of refractive index 1.50, a drop of liquid is placed
as shown in figure. Light is allowed to fall normally
on the short face of the prism. In order that the
ray of light may get totally reflected, the maximum
value of refractive index is :
(a) 1.30 (b) 1.47 (c) 1.20 (d) 1.25
23. A tuning fork of frequency 392 Hz, resonates with
50 cm length of a string under tension (T). If length
of the string is decreased by 2%, keeping the
tension constant, the number of beats heard when
the string and the tuning fork made to vibrate
simultaneously is :
(a)4 (b) 6 (c)8 (d) 1 2
24. Hydrogen (H), deuterium (D), singly ionized
helium (He
+
) and doubly ionized lithium (Li
++
) all
have one electron around the nucleus. Consider
n = 2 to n = 1 transition. The wavelengths of
emitted radiations are l
1
, l
2
, l
3
and l
4
respectively .
Then approximately :
(a) l
1
= l
2
= 4 l
3
= 9 l
4
(b) 4 l
1
= 2 l
2
= 2 l
3
= l
4
(c) l
1
= 2 l
2
= 2Ö 2 l
3
= 3Ö 2 l
4
(d) l
1
= l
2
= 2 l
3
= 3Ö 2 l
4
25. The following figure depict a circular motion. The
radius of the circle, the period of revolution, the
initial position and the sense of revolution are
indicated on the figure.
a
45°
T = 4s
y
Pt ( = 0)
x
The simple harmonic motion of the x-projection
of the radius vector of the rotating particle P can
be shown as :
(a)
2
( ) cos
44
t
xta
pp æö
=+
ç÷
èø
(b)
( ) cos
44
t
xta
pp æö
=+
ç÷
èø
(c)
2
( ) sin
44
t
xta
pp æö
=+
ç÷
èø
(d) ( ) cos
32
t
xta
pp æö
=+
ç÷
èø
26. There are two sources kept at distances 2 l. A
large screen is perpendicular to line joining the
sources. Number of maximas on the screen in
this case is (l = wavelength of light)
S
1
S
2
2l
¥
¥
(a)1 (b) 3 (c)5 (d) 7
Page 4
INSTRUCTIONS
· This question paper contains total 150 questions divided into four parts:
Part I : Physics Q. No. 1 to 40
Part II : Chemistry Q. No. 41 to 80
Part III : (A) English Proficiency Q. No. 81 to 90
(B) Logical Reasoning Q. No. 91 to 105
Part IV : Mathematics Q. No. 106 to 150
· All questions are multiple choice questions with four options, only one of them is correct.
· Each correct answer awarded 3 marks and –1 for each incorrect answer.
· Duration of paper-3 Hours
PART - I : PHYSICS
1. What is the minimum energy required to launch a
satellite of mass m from the surface of a planet of
mass M and radius R in a circular orbit at an altitude
of 2R?
(a)
5GmM
6R
(b)
2GmM
3R
(c)
GmM
2R
(d)
GmM
2R
2. A mercury drop of radius 1 cm is sprayed into 10
6
drops of equal size. The energy expressed in joule
is (surface tension of Mercury is 460 × 10
–3
N/m)
(a) 0.057 (b) 5.7
(c) 5.7 × 10
–4
(d) 5.7 × 10
–6
3. Two plano-concave lenses (1 and
2) of glass of refractive index 1.5
have radii of curvature 25 cm and
20 cm. They are placed in contact
1 2
with their curved surface towards each other and
the space between them is filled with liquid of
refractive index 4/3. Then the combination is
(a) convex lens of focal length 70 cm
(b) concave lens of focal length 70 cm
(c) concave lens of focal length 66.6 cm
(d) convex lens of focal length 66.6 cm
4. A charged particle moves through a magnetic
field perpendicular to its direction. Then
(a) kinetic energy changes but the momentum
is constant
(b) the momentum changes but the kinetic
energy is constant
(c) both momentum and kinetic energy of the
particle are not constant
(d) both momentum and kinetic energy of the
particle are constant
5. After two hours, one-sixteenth of the starting
amount of a certain radioactive isotope remained
undecayed. The half life of the isotope is
(a) 15 minutes (b) 30 minutes
(c) 45 minutes (d) 4 hour
6. A coil of inductance 300 mH and resistance 2W is
connected to a source of voltage 2 V . The current
reaches half of its steady state value in
(a) 0.1 s (b) 0.05 s (c) 0.3 s (d) 0.15 s
7. Two concentric conducting thin spherical shells
A, and B having radii r
A
and r
B
((r
B
> r
A
) are
charged to Q
A
and –Q
B
(|Q
B
| > |Q
A
|). The electric
field along a line passing through the centre is
(a) (b)
(c) (d)
8. A capillary tube of radius R is immersed in water
and water rises in it to a height H. Mass of water
in the capillary tube is M. If the radius of the tube
is doubled, mass of water that will rise in the
capillary tube will now be :
(a) M (b) 2 M (c) M/2 (d) 4 M
9. A sonometer wire resonates with a given tuning
fork forming standing waves with five antinodes
between the two bridges when a mass of 9 kg is
suspended from the wire. When this mass is
replaced by a mass M, the wire resonates with
the same tuning fork forming three antinodes for
the same positions of the bridges. The value of M
is
(a) 25 kg (b) 5 kg
(c) 12.5 kg (d) 1/25 kg
10. When a metal surface is illuminated by light of
wavelengths 400 nm and 250 nm, the maximum
velocities of the photoelectrons ejected are v and
2v respectively . The work function of the metal is
(h - Planck's constant, c = velocity of light in air)
(a) 2 hc ×10
6
J (b) 1.5 hc × 10
6
J
(c) hc × 10
6
J (d) 0.5 hc × 10
6
J
11. Two conducting shells of radius a and b are
connected by conducting wire as shown in figure.
The capacity of system is :
a b
(a) 4 pe
0
ab
ba -
(b) 4 pe
0
(a + b)
(c) zero (d) infinite
12. When
92
U
235
undergoes fission, 0.1% of its
original mass is changed into energy . How much
energy is released if 1 kg of
92
U
235
undergoes
fission
(a) 9 × 10
10
J (b) 9 × 10
11
J
(c) 9 × 10
12
J (d) 9 × 10
13
J
13. One mole of an ideal gas is taken from state A to
state B by three different processes,
P
V
B
E
C
A
D
(i) ACB (ii) ADB (iii) AEB as shown in the P-V
diagram. The heat absorbed by the gas is
(a) greater in process (ii) than in (i)
(b) the least in process (ii)
(c) the same in (i) and (iii)
(d) less in (iii) than in (ii)
14. In the formula X = 3 YZ
2
, X and Z have dimen-
sions of capacitance and magnetic induction re-
spectively. The dimensions of Y in MKSA sys-
tem are :
(a) [M
–3
L
–2
T
–2
A
–4
] (b) [ML
–2
]
(c) [M
–3
L
–2
A
4
T
8
] (d) [M
–3
L
2
A
4
T
4
]
15. Two very long, straight, parallel wires carry steady
currents I and -I respectively. The distance
between the wires is d. At a certain instant of
time, a point charge q is at a point equidistant
from the two wires, in the plane of the wires. Its
instantaneous velocity v is perpendicular to this
plane. The magnitude of the force due to the
magnetic field acting on the charge at this instant
is
(a)
0
2
qv
d
mI
p
(b)
0
qv
d
mI
p
(c)
0
2 qv
d
mI
p
(d) 0
16. Two projectiles A and B thrown with speeds in
the ratio 1 : 2 acquired the same heights. If A is
thrown at an angle of 45° with the horizontal, the
angle of projection of B will be
(a) 0° (b) 60° (c) 30° (d) 45°
17. A meter bridge is set up as shown, to determine
an unknown resistance ‘X’ using a standard 10
ohm resistor. The galvanometer shows null point
when tapping-key is at 52 cm mark. The end-
corrections are 1 cm and 2 cm respectively for the
ends A and B. The determined value of ‘X’ is
(a) 10.2 ohm (b) 10.6 o hm
(c) 10.8 ohm (d) 11.1 o hm
18. A disk of radius a / 4 having a uniformly
distributed charge 6 C is placed in the x - y plane
with its centre at (–a / 2, 0, 0). A rod of length a
carrying a uniformly distributed charge 8 C is
placed on the x-axis from x = a /4 to x = 5a / 4.
Two point charges – 7 C and 3 C are placed at (a
/ 4, – a /4, 0) and (– 3a /4, 3a / 4, 0), respectively .
Consider a cubical surface formed by six surfaces
x = ± a / 2, y = ± a / 2, z = ± a / 2. The electric flux
through this cubical surface is
x
y
(a)
0
–2C
e
(b)
0
2C
e
(c)
0
10C
e
(d)
0
12C
e
19. A particle of mass m moving in the x direction
with speed 2v is hit by another particle of mass
2m moving in the y direction with speed v. If the
collision is perfectly inelastic, the percentage loss
in the energy during the collision is close to
(a) 56% (b) 62% (c) 44% (d) 50%
20. A coil is suspended in a uniform magnetic field,
with the plane of the coil parallel to the magnetic
lines of force. When a current is passed through
the coil it starts oscillating; It is very difficult to
stop. But if an aluminium plate is placed near to
the coil, it stops. This is due to :
(a) developement of air current when the plate
is placed
(b) induction of electrical charge on the plate
(c) shielding of magnetic lines of force as
aluminium is a paramagnetic material.
(d) electromagnetic induction in the aluminium
plate giving rise to electromagnetic
damping.
21. A steel wire of length ‘L’ at 40°C is suspended
from the ceiling and then a mass ‘m’ is hung from
its free end. The wire is cooled down from 40°C to
30°C to regain its original length ‘L’. The
coefficient of linear thermal expansion of the steel
is 10–5 /° C, Young’s modulus of steel is 10
11
N/
m
2
and radius of the wire is 1 mm. Assume that L
>>diameter of the wire. Then the value of ‘m’ in
kg is nearly
(a)1 (b) 2 (c)3 (d) 5
22. On a hypotenuse of a right prism (30° – 60° – 90°)
of refractive index 1.50, a drop of liquid is placed
as shown in figure. Light is allowed to fall normally
on the short face of the prism. In order that the
ray of light may get totally reflected, the maximum
value of refractive index is :
(a) 1.30 (b) 1.47 (c) 1.20 (d) 1.25
23. A tuning fork of frequency 392 Hz, resonates with
50 cm length of a string under tension (T). If length
of the string is decreased by 2%, keeping the
tension constant, the number of beats heard when
the string and the tuning fork made to vibrate
simultaneously is :
(a)4 (b) 6 (c)8 (d) 1 2
24. Hydrogen (H), deuterium (D), singly ionized
helium (He
+
) and doubly ionized lithium (Li
++
) all
have one electron around the nucleus. Consider
n = 2 to n = 1 transition. The wavelengths of
emitted radiations are l
1
, l
2
, l
3
and l
4
respectively .
Then approximately :
(a) l
1
= l
2
= 4 l
3
= 9 l
4
(b) 4 l
1
= 2 l
2
= 2 l
3
= l
4
(c) l
1
= 2 l
2
= 2Ö 2 l
3
= 3Ö 2 l
4
(d) l
1
= l
2
= 2 l
3
= 3Ö 2 l
4
25. The following figure depict a circular motion. The
radius of the circle, the period of revolution, the
initial position and the sense of revolution are
indicated on the figure.
a
45°
T = 4s
y
Pt ( = 0)
x
The simple harmonic motion of the x-projection
of the radius vector of the rotating particle P can
be shown as :
(a)
2
( ) cos
44
t
xta
pp æö
=+
ç÷
èø
(b)
( ) cos
44
t
xta
pp æö
=+
ç÷
èø
(c)
2
( ) sin
44
t
xta
pp æö
=+
ç÷
èø
(d) ( ) cos
32
t
xta
pp æö
=+
ç÷
èø
26. There are two sources kept at distances 2 l. A
large screen is perpendicular to line joining the
sources. Number of maximas on the screen in
this case is (l = wavelength of light)
S
1
S
2
2l
¥
¥
(a)1 (b) 3 (c)5 (d) 7
27. In the circuit shown in figure th`e current through
3W
2W
2W
2W
8W 9V
2W
2W
8W 4W
(a) the 3 W resistor is 0.50 A.
(b) the 3 W resistor is 0.25 A.
(c) the 4 W resistor is 0.50 A
(d) the 4 W resistor is 0.25 A.
28. A telescope has an objective lens of 10 cm
diameter and is situated at a distance of one
kilometer from two objects. The minimum
distance between these two objects, which can
be resolved by the telescope, when the mean
wavelength of light is 5000 Å, is of the order of
(a) 5 cm (b) 0.5 m (c) 5 m (d) 5 m m
29. During vapourisation
I. change of state from liquid to vapour state
occurs.
II. temperature remains constant.
III. both liquid and vapour states coexist in
equilibrium.
IV . specific heat of substance increases.
Correct statements are
(a) I, II and IV (b) II, III and IV
(c) I, III and IV (d) I , II and III
30. A wire is connected to a battery between the
point M and N as shown in the figure (1). The
same wire is bent in the form of a square and then
connected to the battery between the points M
and N as shown in the figure (2). Which of the
following quantities increases ?
( )
M N
( )
M N
(1) (2)
(a) Heat produced in the wire and resistance
offered by the wire.
(b) Resistance offered by the wire and current
through the wire.
(c) Heat produced in the wire, resistance offered
by the wire and current through the wire.
(d) Heat produced in the wire and current
through the wire.
31. A body moves in a circular orbit of radius R under
the action of a central force. Potential due to the
central force is given by V(r) = kr (k is a positive
constant). Period of revolution of the body is pro-
portional to :
(a) R
1/2
(b) R
–1/2
(c) R
–3/2
(d) R
–5/2
32. Two equal heavy spheres, each of radius r, are in
equilibrium within a smooth cup of radius 3r. The
ratio of reaction between the cup and one sphere
and that between the two sphere is
(a)1 (b) 2 (c)3 (d) 4
33. A long, hollow conducting cylinder is kept
coaxially inside another long, hollow conducting
cylinder of larger radius. Both the cylinders are
initially electrically neutral
(a) A potential difference appears between the
two cylinders when a charge density is
given to the inner cylinder.
(b) A potential difference appears between two
cylinders when a charge density is given to
the outer cylinder.
(c) No potential difference appears between the
two cylinders when a uniform line charge is
kept along the axis of the cylinders.
(d) No potential difference appears between the
two cylinders when same charge density is
given to both the cylinders.
34. A thin but rigid semicircular wire frame of radius
r is hinged at O and can rotate in its own vertical
plane. A smooth peg P starts from O and moves
horizontally with constant speed v
0
, lifting the
frame upward as shown in figure.
Find the angular velocity w of the frame when its
diameter makes an angle of 60° with the vertical :
(a) v
0
/ r (b) v
0
/ 2 r (c) 2 v
0
/ r (d) v
0
r
Page 5
INSTRUCTIONS
· This question paper contains total 150 questions divided into four parts:
Part I : Physics Q. No. 1 to 40
Part II : Chemistry Q. No. 41 to 80
Part III : (A) English Proficiency Q. No. 81 to 90
(B) Logical Reasoning Q. No. 91 to 105
Part IV : Mathematics Q. No. 106 to 150
· All questions are multiple choice questions with four options, only one of them is correct.
· Each correct answer awarded 3 marks and –1 for each incorrect answer.
· Duration of paper-3 Hours
PART - I : PHYSICS
1. What is the minimum energy required to launch a
satellite of mass m from the surface of a planet of
mass M and radius R in a circular orbit at an altitude
of 2R?
(a)
5GmM
6R
(b)
2GmM
3R
(c)
GmM
2R
(d)
GmM
2R
2. A mercury drop of radius 1 cm is sprayed into 10
6
drops of equal size. The energy expressed in joule
is (surface tension of Mercury is 460 × 10
–3
N/m)
(a) 0.057 (b) 5.7
(c) 5.7 × 10
–4
(d) 5.7 × 10
–6
3. Two plano-concave lenses (1 and
2) of glass of refractive index 1.5
have radii of curvature 25 cm and
20 cm. They are placed in contact
1 2
with their curved surface towards each other and
the space between them is filled with liquid of
refractive index 4/3. Then the combination is
(a) convex lens of focal length 70 cm
(b) concave lens of focal length 70 cm
(c) concave lens of focal length 66.6 cm
(d) convex lens of focal length 66.6 cm
4. A charged particle moves through a magnetic
field perpendicular to its direction. Then
(a) kinetic energy changes but the momentum
is constant
(b) the momentum changes but the kinetic
energy is constant
(c) both momentum and kinetic energy of the
particle are not constant
(d) both momentum and kinetic energy of the
particle are constant
5. After two hours, one-sixteenth of the starting
amount of a certain radioactive isotope remained
undecayed. The half life of the isotope is
(a) 15 minutes (b) 30 minutes
(c) 45 minutes (d) 4 hour
6. A coil of inductance 300 mH and resistance 2W is
connected to a source of voltage 2 V . The current
reaches half of its steady state value in
(a) 0.1 s (b) 0.05 s (c) 0.3 s (d) 0.15 s
7. Two concentric conducting thin spherical shells
A, and B having radii r
A
and r
B
((r
B
> r
A
) are
charged to Q
A
and –Q
B
(|Q
B
| > |Q
A
|). The electric
field along a line passing through the centre is
(a) (b)
(c) (d)
8. A capillary tube of radius R is immersed in water
and water rises in it to a height H. Mass of water
in the capillary tube is M. If the radius of the tube
is doubled, mass of water that will rise in the
capillary tube will now be :
(a) M (b) 2 M (c) M/2 (d) 4 M
9. A sonometer wire resonates with a given tuning
fork forming standing waves with five antinodes
between the two bridges when a mass of 9 kg is
suspended from the wire. When this mass is
replaced by a mass M, the wire resonates with
the same tuning fork forming three antinodes for
the same positions of the bridges. The value of M
is
(a) 25 kg (b) 5 kg
(c) 12.5 kg (d) 1/25 kg
10. When a metal surface is illuminated by light of
wavelengths 400 nm and 250 nm, the maximum
velocities of the photoelectrons ejected are v and
2v respectively . The work function of the metal is
(h - Planck's constant, c = velocity of light in air)
(a) 2 hc ×10
6
J (b) 1.5 hc × 10
6
J
(c) hc × 10
6
J (d) 0.5 hc × 10
6
J
11. Two conducting shells of radius a and b are
connected by conducting wire as shown in figure.
The capacity of system is :
a b
(a) 4 pe
0
ab
ba -
(b) 4 pe
0
(a + b)
(c) zero (d) infinite
12. When
92
U
235
undergoes fission, 0.1% of its
original mass is changed into energy . How much
energy is released if 1 kg of
92
U
235
undergoes
fission
(a) 9 × 10
10
J (b) 9 × 10
11
J
(c) 9 × 10
12
J (d) 9 × 10
13
J
13. One mole of an ideal gas is taken from state A to
state B by three different processes,
P
V
B
E
C
A
D
(i) ACB (ii) ADB (iii) AEB as shown in the P-V
diagram. The heat absorbed by the gas is
(a) greater in process (ii) than in (i)
(b) the least in process (ii)
(c) the same in (i) and (iii)
(d) less in (iii) than in (ii)
14. In the formula X = 3 YZ
2
, X and Z have dimen-
sions of capacitance and magnetic induction re-
spectively. The dimensions of Y in MKSA sys-
tem are :
(a) [M
–3
L
–2
T
–2
A
–4
] (b) [ML
–2
]
(c) [M
–3
L
–2
A
4
T
8
] (d) [M
–3
L
2
A
4
T
4
]
15. Two very long, straight, parallel wires carry steady
currents I and -I respectively. The distance
between the wires is d. At a certain instant of
time, a point charge q is at a point equidistant
from the two wires, in the plane of the wires. Its
instantaneous velocity v is perpendicular to this
plane. The magnitude of the force due to the
magnetic field acting on the charge at this instant
is
(a)
0
2
qv
d
mI
p
(b)
0
qv
d
mI
p
(c)
0
2 qv
d
mI
p
(d) 0
16. Two projectiles A and B thrown with speeds in
the ratio 1 : 2 acquired the same heights. If A is
thrown at an angle of 45° with the horizontal, the
angle of projection of B will be
(a) 0° (b) 60° (c) 30° (d) 45°
17. A meter bridge is set up as shown, to determine
an unknown resistance ‘X’ using a standard 10
ohm resistor. The galvanometer shows null point
when tapping-key is at 52 cm mark. The end-
corrections are 1 cm and 2 cm respectively for the
ends A and B. The determined value of ‘X’ is
(a) 10.2 ohm (b) 10.6 o hm
(c) 10.8 ohm (d) 11.1 o hm
18. A disk of radius a / 4 having a uniformly
distributed charge 6 C is placed in the x - y plane
with its centre at (–a / 2, 0, 0). A rod of length a
carrying a uniformly distributed charge 8 C is
placed on the x-axis from x = a /4 to x = 5a / 4.
Two point charges – 7 C and 3 C are placed at (a
/ 4, – a /4, 0) and (– 3a /4, 3a / 4, 0), respectively .
Consider a cubical surface formed by six surfaces
x = ± a / 2, y = ± a / 2, z = ± a / 2. The electric flux
through this cubical surface is
x
y
(a)
0
–2C
e
(b)
0
2C
e
(c)
0
10C
e
(d)
0
12C
e
19. A particle of mass m moving in the x direction
with speed 2v is hit by another particle of mass
2m moving in the y direction with speed v. If the
collision is perfectly inelastic, the percentage loss
in the energy during the collision is close to
(a) 56% (b) 62% (c) 44% (d) 50%
20. A coil is suspended in a uniform magnetic field,
with the plane of the coil parallel to the magnetic
lines of force. When a current is passed through
the coil it starts oscillating; It is very difficult to
stop. But if an aluminium plate is placed near to
the coil, it stops. This is due to :
(a) developement of air current when the plate
is placed
(b) induction of electrical charge on the plate
(c) shielding of magnetic lines of force as
aluminium is a paramagnetic material.
(d) electromagnetic induction in the aluminium
plate giving rise to electromagnetic
damping.
21. A steel wire of length ‘L’ at 40°C is suspended
from the ceiling and then a mass ‘m’ is hung from
its free end. The wire is cooled down from 40°C to
30°C to regain its original length ‘L’. The
coefficient of linear thermal expansion of the steel
is 10–5 /° C, Young’s modulus of steel is 10
11
N/
m
2
and radius of the wire is 1 mm. Assume that L
>>diameter of the wire. Then the value of ‘m’ in
kg is nearly
(a)1 (b) 2 (c)3 (d) 5
22. On a hypotenuse of a right prism (30° – 60° – 90°)
of refractive index 1.50, a drop of liquid is placed
as shown in figure. Light is allowed to fall normally
on the short face of the prism. In order that the
ray of light may get totally reflected, the maximum
value of refractive index is :
(a) 1.30 (b) 1.47 (c) 1.20 (d) 1.25
23. A tuning fork of frequency 392 Hz, resonates with
50 cm length of a string under tension (T). If length
of the string is decreased by 2%, keeping the
tension constant, the number of beats heard when
the string and the tuning fork made to vibrate
simultaneously is :
(a)4 (b) 6 (c)8 (d) 1 2
24. Hydrogen (H), deuterium (D), singly ionized
helium (He
+
) and doubly ionized lithium (Li
++
) all
have one electron around the nucleus. Consider
n = 2 to n = 1 transition. The wavelengths of
emitted radiations are l
1
, l
2
, l
3
and l
4
respectively .
Then approximately :
(a) l
1
= l
2
= 4 l
3
= 9 l
4
(b) 4 l
1
= 2 l
2
= 2 l
3
= l
4
(c) l
1
= 2 l
2
= 2Ö 2 l
3
= 3Ö 2 l
4
(d) l
1
= l
2
= 2 l
3
= 3Ö 2 l
4
25. The following figure depict a circular motion. The
radius of the circle, the period of revolution, the
initial position and the sense of revolution are
indicated on the figure.
a
45°
T = 4s
y
Pt ( = 0)
x
The simple harmonic motion of the x-projection
of the radius vector of the rotating particle P can
be shown as :
(a)
2
( ) cos
44
t
xta
pp æö
=+
ç÷
èø
(b)
( ) cos
44
t
xta
pp æö
=+
ç÷
èø
(c)
2
( ) sin
44
t
xta
pp æö
=+
ç÷
èø
(d) ( ) cos
32
t
xta
pp æö
=+
ç÷
èø
26. There are two sources kept at distances 2 l. A
large screen is perpendicular to line joining the
sources. Number of maximas on the screen in
this case is (l = wavelength of light)
S
1
S
2
2l
¥
¥
(a)1 (b) 3 (c)5 (d) 7
27. In the circuit shown in figure th`e current through
3W
2W
2W
2W
8W 9V
2W
2W
8W 4W
(a) the 3 W resistor is 0.50 A.
(b) the 3 W resistor is 0.25 A.
(c) the 4 W resistor is 0.50 A
(d) the 4 W resistor is 0.25 A.
28. A telescope has an objective lens of 10 cm
diameter and is situated at a distance of one
kilometer from two objects. The minimum
distance between these two objects, which can
be resolved by the telescope, when the mean
wavelength of light is 5000 Å, is of the order of
(a) 5 cm (b) 0.5 m (c) 5 m (d) 5 m m
29. During vapourisation
I. change of state from liquid to vapour state
occurs.
II. temperature remains constant.
III. both liquid and vapour states coexist in
equilibrium.
IV . specific heat of substance increases.
Correct statements are
(a) I, II and IV (b) II, III and IV
(c) I, III and IV (d) I , II and III
30. A wire is connected to a battery between the
point M and N as shown in the figure (1). The
same wire is bent in the form of a square and then
connected to the battery between the points M
and N as shown in the figure (2). Which of the
following quantities increases ?
( )
M N
( )
M N
(1) (2)
(a) Heat produced in the wire and resistance
offered by the wire.
(b) Resistance offered by the wire and current
through the wire.
(c) Heat produced in the wire, resistance offered
by the wire and current through the wire.
(d) Heat produced in the wire and current
through the wire.
31. A body moves in a circular orbit of radius R under
the action of a central force. Potential due to the
central force is given by V(r) = kr (k is a positive
constant). Period of revolution of the body is pro-
portional to :
(a) R
1/2
(b) R
–1/2
(c) R
–3/2
(d) R
–5/2
32. Two equal heavy spheres, each of radius r, are in
equilibrium within a smooth cup of radius 3r. The
ratio of reaction between the cup and one sphere
and that between the two sphere is
(a)1 (b) 2 (c)3 (d) 4
33. A long, hollow conducting cylinder is kept
coaxially inside another long, hollow conducting
cylinder of larger radius. Both the cylinders are
initially electrically neutral
(a) A potential difference appears between the
two cylinders when a charge density is
given to the inner cylinder.
(b) A potential difference appears between two
cylinders when a charge density is given to
the outer cylinder.
(c) No potential difference appears between the
two cylinders when a uniform line charge is
kept along the axis of the cylinders.
(d) No potential difference appears between the
two cylinders when same charge density is
given to both the cylinders.
34. A thin but rigid semicircular wire frame of radius
r is hinged at O and can rotate in its own vertical
plane. A smooth peg P starts from O and moves
horizontally with constant speed v
0
, lifting the
frame upward as shown in figure.
Find the angular velocity w of the frame when its
diameter makes an angle of 60° with the vertical :
(a) v
0
/ r (b) v
0
/ 2 r (c) 2 v
0
/ r (d) v
0
r
35. Given that A + B = R and A = B = R. What should
be the angle between A and B ?
(a)0 (b) p/3 (c)2p/3 (d) p
36. The basic magnetization curve for a
ferromagnetic material is shown in figure. Then,
the value of relative permeability is highest for
the point
P
Q
R
S
B(Tesla)
H (× 10 A/m)
3
1 2 3 4 5 67
0
0.5
1.0
1.5
O
(a)P (b) Q (c)R (d) S
37. Five gas molecules chosen at random are found
to have speeds of 500, 600, 700, 800 and 900 m/s:
(a) The root mean square speed and the
average speed are the same.
(b) The root mean square speed is 14 m/s
higher than the average speed.
(c) The root mean square speed is 14 m/s lower
than the average speed.
(d) The root mean square speed is Ö14 m/s
higher than the average speed.
38. What is equivalent capacitance of circuit between
points A and B?
A
3 F m 9 F m 27 F m
27 F m 9 F m 3 F m
Infinite section
B
(a)
2
3
F m
(b)
4
3
F m
(c) Infinite (d) ( )
13 F +m
39. A cyclic process ABCD is shown in the figure P-
V diagram. Which of the following curves
represent the same process
P B
C
A
V
D
(a)
P
B
C
A
T
D
(b)
P
B
C
A
T
D
(c)
P
B
C
A
T
D
(d)
P
B
C
A
T
D
40. In the circuit given below, V(t) is the sinusoidal
voltage source, voltage drop V
AB
(t) across the
resistance R is
(a) is half wave rectified
(b) is full wave rectified
(c) has the same peak value in the positive and
negative half cycles
(d) has different peak values during positive
and negative half cycle
PART - II : CHEMISTRY
41. Which of the following can be repeatedly soften
on heating?
(i) Polystyrene (ii) Melamine
(iii) Polyesters (iv) Polyethylene
(v) Neoprene
(a) (i) and (iii) (b) (i) and (iv)
(c) (iii), (iv) and (v) (d) (ii) and (iv)
42. Which one of the following complexes is an outer
orbital complex ?
(a) [Co(NH
3
)
6
]
3+
(b) [Mn(CN)
6
]
4–
(c) [Fe(CN)
6
]
4–
(d) [Ni(NH
3
)
6
]
2+
43. For the reaction H
2
(g) + Br
2
(g) ® 2HBr (g), the
experimental data suggest, rate = k[H
2
][Br
2
]
1/2
.
The molecularity and order of the reaction are
respectively
(a)
3
2,
2
(b)
33
,
22
(c) 1, 1 (d)
1
1,
2
44. Dead burn plaster is
(a) CaSO
4
.2H
2
O (b) MgSO
4
. 7H
2
O
(c) CaSO
4
.½ H
2
O (d) CaSO
4
45. Stronger is oxidising agent, more is
(a) standard reduction potential of that species
(b) the tendency to get it self oxidised
(c) the tendency to lose electrons by that
species
(d) standard oxidation potential of that species
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