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 95
(B) Logical Reasoning Q. No. 96 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. An artificial satellite is moving in a circular orbit
around the earth with a speed equal to half the
magnitude of the escape velocity from the earth.
The height (h) of the satellite above the earth’s
surface is (Take radius of earth as R
e
)
(a)
2
e
hR = (b) h = R
e
(c) h = 2R
e
(d) h = 4R
e
2. In figure, two blocks are separated by a uniform
strut attached to each block with frictionless
pins. Block A weighs 400N, block B weighs 300N,
and the strut AB weigh 200N. If µ = 0.25 under
B, determine the minimum coefficient of friction
under A to prevent motion.
//////////////////////////////////
////////////////////////
A
B
30°
60°
(a) 0.4 (b) 0 .2 (c) 0 .8 (d) 0 .1
3. Two tuning forks with natural frequencies 340
Hz each move relative to a stationary observer.
One fork moves away from the observer, while
the other moves towards the observer at the
same speed. The observer hears beats of
frequency 3 Hz. Find the speed of the tuning
forks.
(a) 1.5 m/s (b) 2 m/s (c) 1 m/s (d) 2.5 m/s
4. The displacement of a particle is given at time t,
by:
2
sin( 2 ) sin xA tBt = w+w
Then,
(a) the motion of the particle is SHM with an
amplitude of
2
2
4
B
A +
(b) the motion of the particle is not SHM, but
oscillatory with a time period of T = p/w
(c) the motion of the particle is oscillatory with
a time period of T = p/2w
(d) the motion of the particle is a periodic.
5. A ray parallel to principal axis is incident at 30°
from normal on concave mirror having radius of
curvature R. The point on principal axis where
rays are focussed is Q such that PQ is
(a)
2
R
M
30°
C
Q
P
(b)
3
R
(c)
2
2
RR 
(d)
1
1
3
R
æö

ç÷
èø
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 95
(B) Logical Reasoning Q. No. 96 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. An artificial satellite is moving in a circular orbit
around the earth with a speed equal to half the
magnitude of the escape velocity from the earth.
The height (h) of the satellite above the earth’s
surface is (Take radius of earth as R
e
)
(a)
2
e
hR = (b) h = R
e
(c) h = 2R
e
(d) h = 4R
e
2. In figure, two blocks are separated by a uniform
strut attached to each block with frictionless
pins. Block A weighs 400N, block B weighs 300N,
and the strut AB weigh 200N. If µ = 0.25 under
B, determine the minimum coefficient of friction
under A to prevent motion.
//////////////////////////////////
////////////////////////
A
B
30°
60°
(a) 0.4 (b) 0 .2 (c) 0 .8 (d) 0 .1
3. Two tuning forks with natural frequencies 340
Hz each move relative to a stationary observer.
One fork moves away from the observer, while
the other moves towards the observer at the
same speed. The observer hears beats of
frequency 3 Hz. Find the speed of the tuning
forks.
(a) 1.5 m/s (b) 2 m/s (c) 1 m/s (d) 2.5 m/s
4. The displacement of a particle is given at time t,
by:
2
sin( 2 ) sin xA tBt = w+w
Then,
(a) the motion of the particle is SHM with an
amplitude of
2
2
4
B
A +
(b) the motion of the particle is not SHM, but
oscillatory with a time period of T = p/w
(c) the motion of the particle is oscillatory with
a time period of T = p/2w
(d) the motion of the particle is a periodic.
5. A ray parallel to principal axis is incident at 30°
from normal on concave mirror having radius of
curvature R. The point on principal axis where
rays are focussed is Q such that PQ is
(a)
2
R
M
30°
C
Q
P
(b)
3
R
(c)
2
2
RR 
(d)
1
1
3
R
æö

ç÷
èø
6. A solid sphere of radius R has a charge Q
distributed in its volume with a charge density r
= kr
a
, where k and a are constants and r is the
distance from its centre. If the electric field at r =
2
R
is
1
8
times that at r = R, the value of a is
(a)3 (b) 5 (c)2 (d) 7
7. A charged particle moving in a uniform magnetic
field and losses 4% of its kinetic energy. The
radius of curvature of its path changes by
(a) 2% (b) 4% (c) 10% (d) 12%
8. Calculate the wavelength of light used in an
interference experiment from the following data :
Fringe width = 0.03 cm. Distance between the
slits and eyepiece through which the
interference pattern is observed is 1m. Distance
between the images of the virtual source when a
convex lens of focal length 16 cm is used at a
distance of 80 cm from the eyepiece is 0.8 cm.
(a) 0.0006 Å (b) 0.0006 m
(c) 600 cm (d) 6000 Å
9. The masses of blocks A and B are m and M
respectively. Between A and B, there is a
constant frictional force F and B can slide on a
smooth horizontal surface. A is set in motion
with velocity while B is at rest. What is the
distance moved by A relative to B before they
move with the same velocity?
B M
A
m
v
0
(a)
( )
2
0
mMv
FmM 
(b)
( )
2
0
mMv
2FmM 
(c)
( )
2
0
mMv
FmM +
(d)
( )
2
0
mMv
2FMm +
10. An elastic string of unstretched length L and
force constant k is stretched by a small length x.
It is further stretched by another small length y .
The work done in the second stretching is
(a) 1/2 Ky
2
(b) 1/2 Ky(2x + y)
(c) 1/2 K(x
2
+ y
2
) (d) 1/2 k (x + y)
2
11. A body is thrown vertically upwards from A, the
top of the tower, reaches the ground in time t
1
. If
it is thrown vertically downwards from A with
the same speed, it reaches the ground in time t
2
.
If it is allowed to fall freely from A, then the time
it takes to reach the ground is given by
(a)
12
tt
t
2
+
= (b)
12
tt
t
2

=
(c)
12
t tt = (d)
1
2
t
t
t
=
12. 0.5 mole of an ideal gas at constant temperature
27°C kept inside a cylinder of length L and cross
section area A closed by a massless piston.
L
L
The cylinder is attached with a conducting rod
of length L
, crosssection area (1/9)
m
2
and
thermal conductivity k, whose other end is
maintained at 0°C. If piston is moved such that
rate of heat flow through the conducing rod is
constant then velocity of piston when it is at
height L/2 from the bottom of cylinder is :
[Neglect any kind of heat loss from system ]
(a)
k
m / sec
R
æö
ç÷
èø
(b)
k
m / sec
10R
æö
ç÷
èø
(c)
k
m / sec
100R
æö
ç÷
èø
(d)
k
m/sec
1000R
æö
ç÷
èø
13. A conducting square loop is placed in a magnetic
field B with its plane perpendicular to the field.
The sides of the loop start shrinking at a constant
rate a. The induced emf in the loop at an instant
when its side is ‘a’ is
(a)2aaB (b) a
2
aB(c)2a
2
aB (d) aaB
14. The beam of light has three wavelengths
4144Å,4972Å and 6216 Å with a total intensity
of 3.6 × 10
–3
Wm
2
equally distributed amongst
the three wavelengths. The beam falls normally
on the area 1 cm
2
of a clean metallic surface of
work function 2.3 eV. Assume that there is no
loss of light by reflection and that each
energetically capable photon ejects one electron.
Calculate the number of photoelectrons liberated
in 2s.
(a) 2 × 10
9
(b) 1.075 × 10
12
(c) 9 × 10
8
(d) 3.75 × 10
6
15. A square gate of size 1 m × 1m is hinged at its
midpoint. A fluid of density r fills the space to
the left of the gate. The force F required to hold
the gate stationary 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 95
(B) Logical Reasoning Q. No. 96 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. An artificial satellite is moving in a circular orbit
around the earth with a speed equal to half the
magnitude of the escape velocity from the earth.
The height (h) of the satellite above the earth’s
surface is (Take radius of earth as R
e
)
(a)
2
e
hR = (b) h = R
e
(c) h = 2R
e
(d) h = 4R
e
2. In figure, two blocks are separated by a uniform
strut attached to each block with frictionless
pins. Block A weighs 400N, block B weighs 300N,
and the strut AB weigh 200N. If µ = 0.25 under
B, determine the minimum coefficient of friction
under A to prevent motion.
//////////////////////////////////
////////////////////////
A
B
30°
60°
(a) 0.4 (b) 0 .2 (c) 0 .8 (d) 0 .1
3. Two tuning forks with natural frequencies 340
Hz each move relative to a stationary observer.
One fork moves away from the observer, while
the other moves towards the observer at the
same speed. The observer hears beats of
frequency 3 Hz. Find the speed of the tuning
forks.
(a) 1.5 m/s (b) 2 m/s (c) 1 m/s (d) 2.5 m/s
4. The displacement of a particle is given at time t,
by:
2
sin( 2 ) sin xA tBt = w+w
Then,
(a) the motion of the particle is SHM with an
amplitude of
2
2
4
B
A +
(b) the motion of the particle is not SHM, but
oscillatory with a time period of T = p/w
(c) the motion of the particle is oscillatory with
a time period of T = p/2w
(d) the motion of the particle is a periodic.
5. A ray parallel to principal axis is incident at 30°
from normal on concave mirror having radius of
curvature R. The point on principal axis where
rays are focussed is Q such that PQ is
(a)
2
R
M
30°
C
Q
P
(b)
3
R
(c)
2
2
RR 
(d)
1
1
3
R
æö

ç÷
èø
6. A solid sphere of radius R has a charge Q
distributed in its volume with a charge density r
= kr
a
, where k and a are constants and r is the
distance from its centre. If the electric field at r =
2
R
is
1
8
times that at r = R, the value of a is
(a)3 (b) 5 (c)2 (d) 7
7. A charged particle moving in a uniform magnetic
field and losses 4% of its kinetic energy. The
radius of curvature of its path changes by
(a) 2% (b) 4% (c) 10% (d) 12%
8. Calculate the wavelength of light used in an
interference experiment from the following data :
Fringe width = 0.03 cm. Distance between the
slits and eyepiece through which the
interference pattern is observed is 1m. Distance
between the images of the virtual source when a
convex lens of focal length 16 cm is used at a
distance of 80 cm from the eyepiece is 0.8 cm.
(a) 0.0006 Å (b) 0.0006 m
(c) 600 cm (d) 6000 Å
9. The masses of blocks A and B are m and M
respectively. Between A and B, there is a
constant frictional force F and B can slide on a
smooth horizontal surface. A is set in motion
with velocity while B is at rest. What is the
distance moved by A relative to B before they
move with the same velocity?
B M
A
m
v
0
(a)
( )
2
0
mMv
FmM 
(b)
( )
2
0
mMv
2FmM 
(c)
( )
2
0
mMv
FmM +
(d)
( )
2
0
mMv
2FMm +
10. An elastic string of unstretched length L and
force constant k is stretched by a small length x.
It is further stretched by another small length y .
The work done in the second stretching is
(a) 1/2 Ky
2
(b) 1/2 Ky(2x + y)
(c) 1/2 K(x
2
+ y
2
) (d) 1/2 k (x + y)
2
11. A body is thrown vertically upwards from A, the
top of the tower, reaches the ground in time t
1
. If
it is thrown vertically downwards from A with
the same speed, it reaches the ground in time t
2
.
If it is allowed to fall freely from A, then the time
it takes to reach the ground is given by
(a)
12
tt
t
2
+
= (b)
12
tt
t
2

=
(c)
12
t tt = (d)
1
2
t
t
t
=
12. 0.5 mole of an ideal gas at constant temperature
27°C kept inside a cylinder of length L and cross
section area A closed by a massless piston.
L
L
The cylinder is attached with a conducting rod
of length L
, crosssection area (1/9)
m
2
and
thermal conductivity k, whose other end is
maintained at 0°C. If piston is moved such that
rate of heat flow through the conducing rod is
constant then velocity of piston when it is at
height L/2 from the bottom of cylinder is :
[Neglect any kind of heat loss from system ]
(a)
k
m / sec
R
æö
ç÷
èø
(b)
k
m / sec
10R
æö
ç÷
èø
(c)
k
m / sec
100R
æö
ç÷
èø
(d)
k
m/sec
1000R
æö
ç÷
èø
13. A conducting square loop is placed in a magnetic
field B with its plane perpendicular to the field.
The sides of the loop start shrinking at a constant
rate a. The induced emf in the loop at an instant
when its side is ‘a’ is
(a)2aaB (b) a
2
aB(c)2a
2
aB (d) aaB
14. The beam of light has three wavelengths
4144Å,4972Å and 6216 Å with a total intensity
of 3.6 × 10
–3
Wm
2
equally distributed amongst
the three wavelengths. The beam falls normally
on the area 1 cm
2
of a clean metallic surface of
work function 2.3 eV. Assume that there is no
loss of light by reflection and that each
energetically capable photon ejects one electron.
Calculate the number of photoelectrons liberated
in 2s.
(a) 2 × 10
9
(b) 1.075 × 10
12
(c) 9 × 10
8
(d) 3.75 × 10
6
15. A square gate of size 1 m × 1m is hinged at its
midpoint. A fluid of density r fills the space to
the left of the gate. The force F required to hold
the gate stationary is
(a)
g
3
r
(b)
g
2
r
(c)
g
6
r
Hinge
F
(d)
g
8
r
16. When 0.50 Å Xrays strike a material, the
photoelectrons from the k shell are observed to
move in a circle of radius 23 mm in a magnetic
fie ld of 2 × 10
–2
tesla acting perpendicularly to
the direction of emission of photoelectrons.
What is the binding energy of kshell electrons?
(a) 3.5 keV (b) 6.2 keV
(c) 2.9 keV (d) 5.5 keV
17. In CE transistor amplifier, the audio signal voltage
across the collector resistance of 2 kW is 2 V. If
the base resistance is 1kW and the current
amplification of the transistor is 100, the input
signal voltage is
(a) 2 m V (b) 3 m V (c) 10 mV (d ) 0.1 mV
18. At the corners of an equilateral triangle of side a
(1 metre), three point charges are placed (each of
0.1 C). If this system is supplied energy at the
rate of 1 kw, then calculate the time required to
move one of the midpoint of the line joining the
other two.
A
B C
D
a
a
a
(a) 50 h (b) 60 h (c) 48 h (d) 54 h
19. A vessel of volume 20L contains a mixture of
hydrogen and helium at temperature of 27°C and
pressure 2 atm. The mass of mixture is 5g.
Assuming the gases to be ideal, the ratio of mass
of hydrogen to that of helium in the given mixture
will be
(a) 1 : 2 (b) 2 : 3 (c) 2 : 1 (d) 2 : 5
20. The resistance of a wire is R. It is bent at the
middle by 180° and both the ends are twisted
together to make a shorter wire. The resistance
of the new wire is
(a) 2 R (b) R/2 (c) R/4 (d) R/8
21. In a YDSE, the light of wavelength l = 5000 Å is
used, which emerges in phase from two slits a
distance d = 3 × 10
–7
m apart. A transparent sheet
of thickness t = 1.5 × 10
–7
m refractive index
m = 1.17 is placed over one of the slits. what is
the new angular position of the central maxima
of the interference pattern, from the centre of
the screen? Find the value of y.
(a)
( ) D 1t
4.9 and
2d
m
°
S
1
S
2
q
d sinq
d
p
y
q
(b)
( ) D 1t
4.9 and
d
m
°
(c)
( ) D 1t
3.9 and
d
m+
°
(d)
( ) 2D 1t
2.9 and
d
m+
°
22. The position of a projectile launched from the
origin at t = 0 is given by
( )
ˆˆ
40 50m r ij =+
r
at t =
2s. If the projectile was launched at an angle q
from the horizontal, then q is
(take g = 10 ms
–2
)
(a)
1
2
tan
3

(b)
1
3
tan
2

(c)
1
7
tan
4

(d)
1
4
tan
5

23. Water is flowing on a horizontal fixed surface,
such that its flow velocity varies with y (vertical
direction) as
23
23
2
æö
= ç÷
ç÷
èø
yy
vk
aa
. If coefficient of viscosity for
water is h, what will be shear stress between lay
ers of water at y =a.
(a)
k
a
h
(b)
ka
h
(c)
a
k
h
(d) None of these
24. A load of mass m falls from a height h on to the
scale pan hung from the spring as shown in the
figure. If the spring constant is k and mass of
the scale pan is zero and the mass m does not
bounce relative to the pan, then the amplitude
of vibration is
(a) mg/d
(b)
mg 1 2hk
k mg
+æö
ç÷
èø
m
h
K
(c)
mg mg 1 2hk
k k mg
+æö
+
ç÷
èø
(d)
mg 1 2hk mg
k mgk
+æö

ç÷
èø
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 95
(B) Logical Reasoning Q. No. 96 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. An artificial satellite is moving in a circular orbit
around the earth with a speed equal to half the
magnitude of the escape velocity from the earth.
The height (h) of the satellite above the earth’s
surface is (Take radius of earth as R
e
)
(a)
2
e
hR = (b) h = R
e
(c) h = 2R
e
(d) h = 4R
e
2. In figure, two blocks are separated by a uniform
strut attached to each block with frictionless
pins. Block A weighs 400N, block B weighs 300N,
and the strut AB weigh 200N. If µ = 0.25 under
B, determine the minimum coefficient of friction
under A to prevent motion.
//////////////////////////////////
////////////////////////
A
B
30°
60°
(a) 0.4 (b) 0 .2 (c) 0 .8 (d) 0 .1
3. Two tuning forks with natural frequencies 340
Hz each move relative to a stationary observer.
One fork moves away from the observer, while
the other moves towards the observer at the
same speed. The observer hears beats of
frequency 3 Hz. Find the speed of the tuning
forks.
(a) 1.5 m/s (b) 2 m/s (c) 1 m/s (d) 2.5 m/s
4. The displacement of a particle is given at time t,
by:
2
sin( 2 ) sin xA tBt = w+w
Then,
(a) the motion of the particle is SHM with an
amplitude of
2
2
4
B
A +
(b) the motion of the particle is not SHM, but
oscillatory with a time period of T = p/w
(c) the motion of the particle is oscillatory with
a time period of T = p/2w
(d) the motion of the particle is a periodic.
5. A ray parallel to principal axis is incident at 30°
from normal on concave mirror having radius of
curvature R. The point on principal axis where
rays are focussed is Q such that PQ is
(a)
2
R
M
30°
C
Q
P
(b)
3
R
(c)
2
2
RR 
(d)
1
1
3
R
æö

ç÷
èø
6. A solid sphere of radius R has a charge Q
distributed in its volume with a charge density r
= kr
a
, where k and a are constants and r is the
distance from its centre. If the electric field at r =
2
R
is
1
8
times that at r = R, the value of a is
(a)3 (b) 5 (c)2 (d) 7
7. A charged particle moving in a uniform magnetic
field and losses 4% of its kinetic energy. The
radius of curvature of its path changes by
(a) 2% (b) 4% (c) 10% (d) 12%
8. Calculate the wavelength of light used in an
interference experiment from the following data :
Fringe width = 0.03 cm. Distance between the
slits and eyepiece through which the
interference pattern is observed is 1m. Distance
between the images of the virtual source when a
convex lens of focal length 16 cm is used at a
distance of 80 cm from the eyepiece is 0.8 cm.
(a) 0.0006 Å (b) 0.0006 m
(c) 600 cm (d) 6000 Å
9. The masses of blocks A and B are m and M
respectively. Between A and B, there is a
constant frictional force F and B can slide on a
smooth horizontal surface. A is set in motion
with velocity while B is at rest. What is the
distance moved by A relative to B before they
move with the same velocity?
B M
A
m
v
0
(a)
( )
2
0
mMv
FmM 
(b)
( )
2
0
mMv
2FmM 
(c)
( )
2
0
mMv
FmM +
(d)
( )
2
0
mMv
2FMm +
10. An elastic string of unstretched length L and
force constant k is stretched by a small length x.
It is further stretched by another small length y .
The work done in the second stretching is
(a) 1/2 Ky
2
(b) 1/2 Ky(2x + y)
(c) 1/2 K(x
2
+ y
2
) (d) 1/2 k (x + y)
2
11. A body is thrown vertically upwards from A, the
top of the tower, reaches the ground in time t
1
. If
it is thrown vertically downwards from A with
the same speed, it reaches the ground in time t
2
.
If it is allowed to fall freely from A, then the time
it takes to reach the ground is given by
(a)
12
tt
t
2
+
= (b)
12
tt
t
2

=
(c)
12
t tt = (d)
1
2
t
t
t
=
12. 0.5 mole of an ideal gas at constant temperature
27°C kept inside a cylinder of length L and cross
section area A closed by a massless piston.
L
L
The cylinder is attached with a conducting rod
of length L
, crosssection area (1/9)
m
2
and
thermal conductivity k, whose other end is
maintained at 0°C. If piston is moved such that
rate of heat flow through the conducing rod is
constant then velocity of piston when it is at
height L/2 from the bottom of cylinder is :
[Neglect any kind of heat loss from system ]
(a)
k
m / sec
R
æö
ç÷
èø
(b)
k
m / sec
10R
æö
ç÷
èø
(c)
k
m / sec
100R
æö
ç÷
èø
(d)
k
m/sec
1000R
æö
ç÷
èø
13. A conducting square loop is placed in a magnetic
field B with its plane perpendicular to the field.
The sides of the loop start shrinking at a constant
rate a. The induced emf in the loop at an instant
when its side is ‘a’ is
(a)2aaB (b) a
2
aB(c)2a
2
aB (d) aaB
14. The beam of light has three wavelengths
4144Å,4972Å and 6216 Å with a total intensity
of 3.6 × 10
–3
Wm
2
equally distributed amongst
the three wavelengths. The beam falls normally
on the area 1 cm
2
of a clean metallic surface of
work function 2.3 eV. Assume that there is no
loss of light by reflection and that each
energetically capable photon ejects one electron.
Calculate the number of photoelectrons liberated
in 2s.
(a) 2 × 10
9
(b) 1.075 × 10
12
(c) 9 × 10
8
(d) 3.75 × 10
6
15. A square gate of size 1 m × 1m is hinged at its
midpoint. A fluid of density r fills the space to
the left of the gate. The force F required to hold
the gate stationary is
(a)
g
3
r
(b)
g
2
r
(c)
g
6
r
Hinge
F
(d)
g
8
r
16. When 0.50 Å Xrays strike a material, the
photoelectrons from the k shell are observed to
move in a circle of radius 23 mm in a magnetic
fie ld of 2 × 10
–2
tesla acting perpendicularly to
the direction of emission of photoelectrons.
What is the binding energy of kshell electrons?
(a) 3.5 keV (b) 6.2 keV
(c) 2.9 keV (d) 5.5 keV
17. In CE transistor amplifier, the audio signal voltage
across the collector resistance of 2 kW is 2 V. If
the base resistance is 1kW and the current
amplification of the transistor is 100, the input
signal voltage is
(a) 2 m V (b) 3 m V (c) 10 mV (d ) 0.1 mV
18. At the corners of an equilateral triangle of side a
(1 metre), three point charges are placed (each of
0.1 C). If this system is supplied energy at the
rate of 1 kw, then calculate the time required to
move one of the midpoint of the line joining the
other two.
A
B C
D
a
a
a
(a) 50 h (b) 60 h (c) 48 h (d) 54 h
19. A vessel of volume 20L contains a mixture of
hydrogen and helium at temperature of 27°C and
pressure 2 atm. The mass of mixture is 5g.
Assuming the gases to be ideal, the ratio of mass
of hydrogen to that of helium in the given mixture
will be
(a) 1 : 2 (b) 2 : 3 (c) 2 : 1 (d) 2 : 5
20. The resistance of a wire is R. It is bent at the
middle by 180° and both the ends are twisted
together to make a shorter wire. The resistance
of the new wire is
(a) 2 R (b) R/2 (c) R/4 (d) R/8
21. In a YDSE, the light of wavelength l = 5000 Å is
used, which emerges in phase from two slits a
distance d = 3 × 10
–7
m apart. A transparent sheet
of thickness t = 1.5 × 10
–7
m refractive index
m = 1.17 is placed over one of the slits. what is
the new angular position of the central maxima
of the interference pattern, from the centre of
the screen? Find the value of y.
(a)
( ) D 1t
4.9 and
2d
m
°
S
1
S
2
q
d sinq
d
p
y
q
(b)
( ) D 1t
4.9 and
d
m
°
(c)
( ) D 1t
3.9 and
d
m+
°
(d)
( ) 2D 1t
2.9 and
d
m+
°
22. The position of a projectile launched from the
origin at t = 0 is given by
( )
ˆˆ
40 50m r ij =+
r
at t =
2s. If the projectile was launched at an angle q
from the horizontal, then q is
(take g = 10 ms
–2
)
(a)
1
2
tan
3

(b)
1
3
tan
2

(c)
1
7
tan
4

(d)
1
4
tan
5

23. Water is flowing on a horizontal fixed surface,
such that its flow velocity varies with y (vertical
direction) as
23
23
2
æö
= ç÷
ç÷
èø
yy
vk
aa
. If coefficient of viscosity for
water is h, what will be shear stress between lay
ers of water at y =a.
(a)
k
a
h
(b)
ka
h
(c)
a
k
h
(d) None of these
24. A load of mass m falls from a height h on to the
scale pan hung from the spring as shown in the
figure. If the spring constant is k and mass of
the scale pan is zero and the mass m does not
bounce relative to the pan, then the amplitude
of vibration is
(a) mg/d
(b)
mg 1 2hk
k mg
+æö
ç÷
èø
m
h
K
(c)
mg mg 1 2hk
k k mg
+æö
+
ç÷
èø
(d)
mg 1 2hk mg
k mgk
+æö

ç÷
èø
25. In an ore containing uranium, the ratio of U
238
to
Pb
206
is 3. Calculate the age of the ore, assuming
that all the lead present in the ore is the final
stable product of U
238
. Take the halflife of U
238
to be 4.5 × 10
9
yr.
(a) 1.6 × 19
3
yr (b) 1.5 × 10
4
yr
(c) 1.867 × 10
9
yr (d) 2 × 10
5
yr
26. A direct current of 5A is superposed on an
alternating current I = 10 sin wt flowing through
the wire. The effective value of the resulting
current will be
(a) (15/2)A (b)
5 3A
(c)
5 5A
(d) 15 A
27. A planoconvex lens fits exactly into a
planoconcave lens. Their plane surface are parallel
to each other. If the lenses are made of different
materials of refractive indices µ
1
& µ
2
and R is
the radius of curvature of the curved surface of
the lenses, then focal length of combination is
(a)
12
–
R
µµ
(b)
12
2
–
R
µµ
(c)
( )
12
2–
R
µµ
(d)
( )
12
2–
R
µµ +
28. A thin rod of length 4l and mass 4m is bent at the
points as shown in figure. What is the moment
of inertia of the rod about the axis passes through
point O and perpendicular to the plane of paper?
(a)
2
M
3
l
(b)
2
10M
3
l
90°
O
l
90°
l
l
l
(c)
2
M
12
l
(d)
2
M
24
l
29. One of the lines in the emission spectrum of Li
2+
has the same wavelength as that of the 2
nd
line of
Balmer series in hydrogen spectrum. The
electronic transition corresponding to this line is
n = 12 ® n = x. Find the value of x.
(a)8 (b) 6 (c)7 (d) 5
30. Two particles X and Y having equal charges,
after being accelerated through the same
potential difference, enter a region of uniform
magnetic field and describe circular paths of radii
R
1
and R
2
, respectively . The ratio of masses of X
and Y is
(a) (R
1
/R
2
)
1/2
(b) (R
2
/R
1
)
(c) (R
1
/R
2
)
2
(d) (R
1
/R
2
)
31. A glass capillary tube of internal radius r = 0.25
mm is immersed in water. The top end of the tube
projected by 2 cm above the surface of the water.
At what angle does the liquid meet the tube?
Surface tension of water = 0.7 N/m.
(a) q = 90° (b) q = 70°
(c) q = 45° (d) q = 35°
32. A particle of mass 2 m is projected at an angle of
45° with the horizontal with a velocity of
202
m/s. After 1s, explosion takes place and
the particle is broken into two equal pieces. As a
result of explosion, one part comes to rest. The
maximum height from the ground attained by the
other part is
(a) 50 m (b) 25 m (c) 40 m (d) 3 5 m
33. A 2 m wide truck is moving with a uniform speed
v
0
= 8 m/s along a straight horizontal road. A
pedestrain starts to cross the road with a uniform
speed v when the truck is 4 m away from him. The
minimum value of v so that he can cross the road
safely is
v
v
0
4m
Man
Truck 2m
(a) 2.62 m/s (b) 4.6 m/s
(c) 3.57 m/s (d) 1.414 m/s
34. A neutron moving with speed v makes a head
on collision with a hydrogen atom in ground
state kept at rest. The minimum kinetic energy of
the neutron for which inelastic collision takes
place is
(a) 10.2 eV (b) 20.4 e V
(c) 12.1 e V (d) 16.8 e V
35. V ertical displacement of a Planck with a body of
mass m on it is varying according to law y = sin
wt + 3cost w . The minimum value of w for which
the mass just breaks off the Planck and the
moment it occurs first after t = 0, are given by
(a)
2
g / 2,
6 g
p
(b)
g2
, /g
3 2
p
(c)
g/2, 2/g
3
p
(d) 2g , 2 / 3g p
36. A parallel plate capacitor of capacitance C is
connected to a battery and is charged to a
potential difference V. Another capacitor of
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 95
(B) Logical Reasoning Q. No. 96 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. An artificial satellite is moving in a circular orbit
around the earth with a speed equal to half the
magnitude of the escape velocity from the earth.
The height (h) of the satellite above the earth’s
surface is (Take radius of earth as R
e
)
(a)
2
e
hR = (b) h = R
e
(c) h = 2R
e
(d) h = 4R
e
2. In figure, two blocks are separated by a uniform
strut attached to each block with frictionless
pins. Block A weighs 400N, block B weighs 300N,
and the strut AB weigh 200N. If µ = 0.25 under
B, determine the minimum coefficient of friction
under A to prevent motion.
//////////////////////////////////
////////////////////////
A
B
30°
60°
(a) 0.4 (b) 0 .2 (c) 0 .8 (d) 0 .1
3. Two tuning forks with natural frequencies 340
Hz each move relative to a stationary observer.
One fork moves away from the observer, while
the other moves towards the observer at the
same speed. The observer hears beats of
frequency 3 Hz. Find the speed of the tuning
forks.
(a) 1.5 m/s (b) 2 m/s (c) 1 m/s (d) 2.5 m/s
4. The displacement of a particle is given at time t,
by:
2
sin( 2 ) sin xA tBt = w+w
Then,
(a) the motion of the particle is SHM with an
amplitude of
2
2
4
B
A +
(b) the motion of the particle is not SHM, but
oscillatory with a time period of T = p/w
(c) the motion of the particle is oscillatory with
a time period of T = p/2w
(d) the motion of the particle is a periodic.
5. A ray parallel to principal axis is incident at 30°
from normal on concave mirror having radius of
curvature R. The point on principal axis where
rays are focussed is Q such that PQ is
(a)
2
R
M
30°
C
Q
P
(b)
3
R
(c)
2
2
RR 
(d)
1
1
3
R
æö

ç÷
èø
6. A solid sphere of radius R has a charge Q
distributed in its volume with a charge density r
= kr
a
, where k and a are constants and r is the
distance from its centre. If the electric field at r =
2
R
is
1
8
times that at r = R, the value of a is
(a)3 (b) 5 (c)2 (d) 7
7. A charged particle moving in a uniform magnetic
field and losses 4% of its kinetic energy. The
radius of curvature of its path changes by
(a) 2% (b) 4% (c) 10% (d) 12%
8. Calculate the wavelength of light used in an
interference experiment from the following data :
Fringe width = 0.03 cm. Distance between the
slits and eyepiece through which the
interference pattern is observed is 1m. Distance
between the images of the virtual source when a
convex lens of focal length 16 cm is used at a
distance of 80 cm from the eyepiece is 0.8 cm.
(a) 0.0006 Å (b) 0.0006 m
(c) 600 cm (d) 6000 Å
9. The masses of blocks A and B are m and M
respectively. Between A and B, there is a
constant frictional force F and B can slide on a
smooth horizontal surface. A is set in motion
with velocity while B is at rest. What is the
distance moved by A relative to B before they
move with the same velocity?
B M
A
m
v
0
(a)
( )
2
0
mMv
FmM 
(b)
( )
2
0
mMv
2FmM 
(c)
( )
2
0
mMv
FmM +
(d)
( )
2
0
mMv
2FMm +
10. An elastic string of unstretched length L and
force constant k is stretched by a small length x.
It is further stretched by another small length y .
The work done in the second stretching is
(a) 1/2 Ky
2
(b) 1/2 Ky(2x + y)
(c) 1/2 K(x
2
+ y
2
) (d) 1/2 k (x + y)
2
11. A body is thrown vertically upwards from A, the
top of the tower, reaches the ground in time t
1
. If
it is thrown vertically downwards from A with
the same speed, it reaches the ground in time t
2
.
If it is allowed to fall freely from A, then the time
it takes to reach the ground is given by
(a)
12
tt
t
2
+
= (b)
12
tt
t
2

=
(c)
12
t tt = (d)
1
2
t
t
t
=
12. 0.5 mole of an ideal gas at constant temperature
27°C kept inside a cylinder of length L and cross
section area A closed by a massless piston.
L
L
The cylinder is attached with a conducting rod
of length L
, crosssection area (1/9)
m
2
and
thermal conductivity k, whose other end is
maintained at 0°C. If piston is moved such that
rate of heat flow through the conducing rod is
constant then velocity of piston when it is at
height L/2 from the bottom of cylinder is :
[Neglect any kind of heat loss from system ]
(a)
k
m / sec
R
æö
ç÷
èø
(b)
k
m / sec
10R
æö
ç÷
èø
(c)
k
m / sec
100R
æö
ç÷
èø
(d)
k
m/sec
1000R
æö
ç÷
èø
13. A conducting square loop is placed in a magnetic
field B with its plane perpendicular to the field.
The sides of the loop start shrinking at a constant
rate a. The induced emf in the loop at an instant
when its side is ‘a’ is
(a)2aaB (b) a
2
aB(c)2a
2
aB (d) aaB
14. The beam of light has three wavelengths
4144Å,4972Å and 6216 Å with a total intensity
of 3.6 × 10
–3
Wm
2
equally distributed amongst
the three wavelengths. The beam falls normally
on the area 1 cm
2
of a clean metallic surface of
work function 2.3 eV. Assume that there is no
loss of light by reflection and that each
energetically capable photon ejects one electron.
Calculate the number of photoelectrons liberated
in 2s.
(a) 2 × 10
9
(b) 1.075 × 10
12
(c) 9 × 10
8
(d) 3.75 × 10
6
15. A square gate of size 1 m × 1m is hinged at its
midpoint. A fluid of density r fills the space to
the left of the gate. The force F required to hold
the gate stationary is
(a)
g
3
r
(b)
g
2
r
(c)
g
6
r
Hinge
F
(d)
g
8
r
16. When 0.50 Å Xrays strike a material, the
photoelectrons from the k shell are observed to
move in a circle of radius 23 mm in a magnetic
fie ld of 2 × 10
–2
tesla acting perpendicularly to
the direction of emission of photoelectrons.
What is the binding energy of kshell electrons?
(a) 3.5 keV (b) 6.2 keV
(c) 2.9 keV (d) 5.5 keV
17. In CE transistor amplifier, the audio signal voltage
across the collector resistance of 2 kW is 2 V. If
the base resistance is 1kW and the current
amplification of the transistor is 100, the input
signal voltage is
(a) 2 m V (b) 3 m V (c) 10 mV (d ) 0.1 mV
18. At the corners of an equilateral triangle of side a
(1 metre), three point charges are placed (each of
0.1 C). If this system is supplied energy at the
rate of 1 kw, then calculate the time required to
move one of the midpoint of the line joining the
other two.
A
B C
D
a
a
a
(a) 50 h (b) 60 h (c) 48 h (d) 54 h
19. A vessel of volume 20L contains a mixture of
hydrogen and helium at temperature of 27°C and
pressure 2 atm. The mass of mixture is 5g.
Assuming the gases to be ideal, the ratio of mass
of hydrogen to that of helium in the given mixture
will be
(a) 1 : 2 (b) 2 : 3 (c) 2 : 1 (d) 2 : 5
20. The resistance of a wire is R. It is bent at the
middle by 180° and both the ends are twisted
together to make a shorter wire. The resistance
of the new wire is
(a) 2 R (b) R/2 (c) R/4 (d) R/8
21. In a YDSE, the light of wavelength l = 5000 Å is
used, which emerges in phase from two slits a
distance d = 3 × 10
–7
m apart. A transparent sheet
of thickness t = 1.5 × 10
–7
m refractive index
m = 1.17 is placed over one of the slits. what is
the new angular position of the central maxima
of the interference pattern, from the centre of
the screen? Find the value of y.
(a)
( ) D 1t
4.9 and
2d
m
°
S
1
S
2
q
d sinq
d
p
y
q
(b)
( ) D 1t
4.9 and
d
m
°
(c)
( ) D 1t
3.9 and
d
m+
°
(d)
( ) 2D 1t
2.9 and
d
m+
°
22. The position of a projectile launched from the
origin at t = 0 is given by
( )
ˆˆ
40 50m r ij =+
r
at t =
2s. If the projectile was launched at an angle q
from the horizontal, then q is
(take g = 10 ms
–2
)
(a)
1
2
tan
3

(b)
1
3
tan
2

(c)
1
7
tan
4

(d)
1
4
tan
5

23. Water is flowing on a horizontal fixed surface,
such that its flow velocity varies with y (vertical
direction) as
23
23
2
æö
= ç÷
ç÷
èø
yy
vk
aa
. If coefficient of viscosity for
water is h, what will be shear stress between lay
ers of water at y =a.
(a)
k
a
h
(b)
ka
h
(c)
a
k
h
(d) None of these
24. A load of mass m falls from a height h on to the
scale pan hung from the spring as shown in the
figure. If the spring constant is k and mass of
the scale pan is zero and the mass m does not
bounce relative to the pan, then the amplitude
of vibration is
(a) mg/d
(b)
mg 1 2hk
k mg
+æö
ç÷
èø
m
h
K
(c)
mg mg 1 2hk
k k mg
+æö
+
ç÷
èø
(d)
mg 1 2hk mg
k mgk
+æö

ç÷
èø
25. In an ore containing uranium, the ratio of U
238
to
Pb
206
is 3. Calculate the age of the ore, assuming
that all the lead present in the ore is the final
stable product of U
238
. Take the halflife of U
238
to be 4.5 × 10
9
yr.
(a) 1.6 × 19
3
yr (b) 1.5 × 10
4
yr
(c) 1.867 × 10
9
yr (d) 2 × 10
5
yr
26. A direct current of 5A is superposed on an
alternating current I = 10 sin wt flowing through
the wire. The effective value of the resulting
current will be
(a) (15/2)A (b)
5 3A
(c)
5 5A
(d) 15 A
27. A planoconvex lens fits exactly into a
planoconcave lens. Their plane surface are parallel
to each other. If the lenses are made of different
materials of refractive indices µ
1
& µ
2
and R is
the radius of curvature of the curved surface of
the lenses, then focal length of combination is
(a)
12
–
R
µµ
(b)
12
2
–
R
µµ
(c)
( )
12
2–
R
µµ
(d)
( )
12
2–
R
µµ +
28. A thin rod of length 4l and mass 4m is bent at the
points as shown in figure. What is the moment
of inertia of the rod about the axis passes through
point O and perpendicular to the plane of paper?
(a)
2
M
3
l
(b)
2
10M
3
l
90°
O
l
90°
l
l
l
(c)
2
M
12
l
(d)
2
M
24
l
29. One of the lines in the emission spectrum of Li
2+
has the same wavelength as that of the 2
nd
line of
Balmer series in hydrogen spectrum. The
electronic transition corresponding to this line is
n = 12 ® n = x. Find the value of x.
(a)8 (b) 6 (c)7 (d) 5
30. Two particles X and Y having equal charges,
after being accelerated through the same
potential difference, enter a region of uniform
magnetic field and describe circular paths of radii
R
1
and R
2
, respectively . The ratio of masses of X
and Y is
(a) (R
1
/R
2
)
1/2
(b) (R
2
/R
1
)
(c) (R
1
/R
2
)
2
(d) (R
1
/R
2
)
31. A glass capillary tube of internal radius r = 0.25
mm is immersed in water. The top end of the tube
projected by 2 cm above the surface of the water.
At what angle does the liquid meet the tube?
Surface tension of water = 0.7 N/m.
(a) q = 90° (b) q = 70°
(c) q = 45° (d) q = 35°
32. A particle of mass 2 m is projected at an angle of
45° with the horizontal with a velocity of
202
m/s. After 1s, explosion takes place and
the particle is broken into two equal pieces. As a
result of explosion, one part comes to rest. The
maximum height from the ground attained by the
other part is
(a) 50 m (b) 25 m (c) 40 m (d) 3 5 m
33. A 2 m wide truck is moving with a uniform speed
v
0
= 8 m/s along a straight horizontal road. A
pedestrain starts to cross the road with a uniform
speed v when the truck is 4 m away from him. The
minimum value of v so that he can cross the road
safely is
v
v
0
4m
Man
Truck 2m
(a) 2.62 m/s (b) 4.6 m/s
(c) 3.57 m/s (d) 1.414 m/s
34. A neutron moving with speed v makes a head
on collision with a hydrogen atom in ground
state kept at rest. The minimum kinetic energy of
the neutron for which inelastic collision takes
place is
(a) 10.2 eV (b) 20.4 e V
(c) 12.1 e V (d) 16.8 e V
35. V ertical displacement of a Planck with a body of
mass m on it is varying according to law y = sin
wt + 3cost w . The minimum value of w for which
the mass just breaks off the Planck and the
moment it occurs first after t = 0, are given by
(a)
2
g / 2,
6 g
p
(b)
g2
, /g
3 2
p
(c)
g/2, 2/g
3
p
(d) 2g , 2 / 3g p
36. A parallel plate capacitor of capacitance C is
connected to a battery and is charged to a
potential difference V. Another capacitor of
capacitance 2C is similarly charge to a potential
difference 2V. The charging battery is now
disconnected and the capacitors are connected
in parallel to each other in such a way that the
positive terminal of one is connected to the
negative terminal of the other. The final energy
of the configuration is
(a) Zero (b)
2
3
CV
2
(c)
2
25
CV
6
(d)
2
9
CV
2
37. In the circuit shown below, the ac source has
voltage V = 20 cos(wt) volt with w = 2000 rad/s.
The amplitude of the current will be nearest to
(a) 2A
(b) 3.3A
(c) 2 / 5A
(d) 5A
38. A constant voltage is applied between the two
ends of a uniform metallic wire. Some heat is
developed in it. The heat developed is doubled if
(a) both the length and the radius of the wire
are halved.
(b) both the length and the radius of the wire
are doubled.
(c) the radius of the wire is doubled.
(d) the length of the wire is doubled.
39. The frequency of a sonometer wire is 100 Hz.
When the weights producing the tensions are
completely immersed in water, the frequency
becomes 80 Hz and on immersing the weights in
a certain liquid, the frequency becomes 60 Hz.
The specific gravity of the liquid is
(a) 1.42 (b) 1.77 (c) 1.82 (d) 1.21
40. A long straight wire along the Zaxis carries a
current I in the negative Zdirection. The
magnetic vector field
B
r
at a point having
coordinates (x, y) in the Z = 0 plane is
(a)
( )
( )
0
22
ˆˆ
2
I yi xj
xy
m
p+
(b)
( )
( )
0
22
ˆˆ
2
I xi yj
xy
m+
p+
(c)
( )
( )
0
22
ˆˆ
2
I xj yi
xy
m
p+
(d)
( )
( )
0
22
ˆˆ
2
I xi yj
xy
m
p+
PART  II: CHEMISTRY
41. Which of the following pollutants is main
product of automobiles exhaust?
(a) C O (b) CO
2
(c) NO (d) Hydrocarbons
42. The disease caused the high concentration of
hydrocarbon pollutants in atmosphere is/are
(a) silicosis (b) TB
(c) cancer (d) asthma
43. The element, with atomic number 118, will be
(a) alkali (b) noble gas
(c) lanthanide (d) transition element
44. Which law of the thermodynamics helps in
calculating the absolute entropies of various
substances at different temperatures?
(a) First law (b) Second law
(c) Third law (d) Zeroth law
45. The color of CoCl
3
.5NH
3
.H
2
O is
(a) red (b) orange
(c) orange  yellow (d) pink
46. The metal present in vitamin B
12
is
(a) magnesium (b) cobalt
(c) copper (d) zinc
47. Cobalt (60) isotope is used in the treatment of :
(a) Heart diseases (b) Skin diseases
(c) Diabetes (d) Cancer
48. Polymer used in bullet proof glass is
(a) Lexan (b) PMMA
(c) No mex (d) Kevlar
49. What is the correct increasing order of Bronsted
bases?
(a)
4 32
ClO ClO ClO ClO
 
<<<
(b)
4 32
ClO ClO ClO ClO
 
> >>
(c)
3 42
ClO ClO ClO ClO
 
<<<
(d)
3 24
ClO ClO ClO ClO
 
> ><
50. The boiling point of alkyl halide are higher than
those of corresponding alkanes because of
(a) dipoledipole interaction
(b) dipoleinduced dipole interaction
(c) Hbonding
(d) None of the above
51. Some salts containing two different metallic
elements give test for only one of them in
solution, such salts are
(a) double salts (b) normal salts
(c) complex salts (d) None of these
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