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. What should be the velocity of rotation of earth
due to rotation about its own axis so that the
weight of a person becomes
5
3
of the present
weight at the equator. Equatorial radius of the
earth is 6400 km.
(a) 8.7 × 10
–7
rad/s (b) 7.8 × 10
–4
rad/s
(c) 6.7 × 10
–4
rad/s (d) 7.4 × 10
–3
rad/s
2. Block A of mass m and block B of mass 2m are
placed on a fixed triangular wedge by means of a
massless, inextensible string and a frictionless
pulley as shown in figure.
45° 45°
m 2m
A B
The wedge is inclined at 45° to the horizontal on
both the sides. If the coefficient of friction
between the block A and the wedge is 2/3 and
that between the block B and the wedge is 1/3
and both the blocks A and B are released from
rest, the acceleration of A will be
(a) –1 ms
–2
(b) 1.2 ms
–2
(c) 0.2 ms
–2
(d) zero
3. The surface charge density of a thin charged disc
of radius R is s. The value of the electric field at
the centre of the disc is
0
2
s
Î
. With respect to
the field at the centre, the electric field along the
axis at a distance R from the centre of the disc
(a) reduces by 70.7% (b) reduces by 29.3%
(c) reduces by 9.7% (d) reduces by 14.6%
4. The molecules of a given mass of a gas have
r.m.s. velocity of 200 ms
–1
at 27°C and 1.0 × 10
5
Nm
–2
pressure. When the temperature and
pressure of the gas are respectively, 127°C and
0.05 × 10
5
Nm
–2
, the r.m.s. velocity of its molecules
in ms
–1
is :
(a) 100 2 (b)
400
3
(c)
100 2
3
(d)
100
3
5. An inductor of inductance L = 400 mH and
resistors of resistance R
1
= 2W and R
2
= 2W are
connected to a battery of emf 12 V as shown in
the figure. The internal resistance of the battery
is negligible. The switch S is closed at t = 0. The
potential drop across L as a function of time is
(a)
3
12
V
t
e
t

(b)
( )
/ 0.2
61V
t
e


E
S
L
R
2
R
1
(c) 12e
–5t
V
(d) 6e
–5t
V
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. What should be the velocity of rotation of earth
due to rotation about its own axis so that the
weight of a person becomes
5
3
of the present
weight at the equator. Equatorial radius of the
earth is 6400 km.
(a) 8.7 × 10
–7
rad/s (b) 7.8 × 10
–4
rad/s
(c) 6.7 × 10
–4
rad/s (d) 7.4 × 10
–3
rad/s
2. Block A of mass m and block B of mass 2m are
placed on a fixed triangular wedge by means of a
massless, inextensible string and a frictionless
pulley as shown in figure.
45° 45°
m 2m
A B
The wedge is inclined at 45° to the horizontal on
both the sides. If the coefficient of friction
between the block A and the wedge is 2/3 and
that between the block B and the wedge is 1/3
and both the blocks A and B are released from
rest, the acceleration of A will be
(a) –1 ms
–2
(b) 1.2 ms
–2
(c) 0.2 ms
–2
(d) zero
3. The surface charge density of a thin charged disc
of radius R is s. The value of the electric field at
the centre of the disc is
0
2
s
Î
. With respect to
the field at the centre, the electric field along the
axis at a distance R from the centre of the disc
(a) reduces by 70.7% (b) reduces by 29.3%
(c) reduces by 9.7% (d) reduces by 14.6%
4. The molecules of a given mass of a gas have
r.m.s. velocity of 200 ms
–1
at 27°C and 1.0 × 10
5
Nm
–2
pressure. When the temperature and
pressure of the gas are respectively, 127°C and
0.05 × 10
5
Nm
–2
, the r.m.s. velocity of its molecules
in ms
–1
is :
(a) 100 2 (b)
400
3
(c)
100 2
3
(d)
100
3
5. An inductor of inductance L = 400 mH and
resistors of resistance R
1
= 2W and R
2
= 2W are
connected to a battery of emf 12 V as shown in
the figure. The internal resistance of the battery
is negligible. The switch S is closed at t = 0. The
potential drop across L as a function of time is
(a)
3
12
V
t
e
t

(b)
( )
/ 0.2
61V
t
e


E
S
L
R
2
R
1
(c) 12e
–5t
V
(d) 6e
–5t
V
6. Two wires are made of the same material and have
the same volume. However wire 1 has cross
sectional area A and wire 2 has crosssectional
area 3A. If the length of wire 1 increases by Dx on
applying force F, how much force is needed to
stretch wire 2 by the same amount?
(a) 4 F (b) 6 F (c) 9 F (d) F
7. Two spheres of different materials one with double
the radius and onefourth wall thickness of the
other are filled with ice. If the time taken for
complete melting of ice in the larger sphere is 25
minute and for smaller one is 16 minute, the ratio
of thermal conductivities of the materials of larger
spheres to that of smaller sphere is
(a) 4 : 5 (b) 5 : 4 (c) 25 : 8 (d) 8 : 25
8. A biconvex lens has a radius of curvature of
magnitude 20 cm. Which one of the following
options best describe the image formed of an
object of height 2 cm placed 30 cm from the lens?
(a) V irtual, upright, height = 1 cm
(b) V irtual, upright, height = 0.5 cm
(c) Real, inverted, height = 4 cm
(d) Real, inverted, height = 1cm
9. In the figure below , what is the potential difference
between the point A and B and between B and C
respectively in steady state
(a) 100
AB BC
V VV ==
(b) 75 , 25
AB BC
V VVV ==
(c) 25 , 75
AB BC
VVVV ==
(d) 50
AB BC
V VV ==
10. A radioactive element X converts into another
stable element Y . Half life of X is 2 hrs. Initially
only X is present. After time t, the ratio of atoms
of X and Y is found to be 1 : 4, then t in hours is
(a)2 (b) 4
(c) between 4 and 6 (d) 6
11. The approximate depth of an ocean is 2700 m. The
compressibility of water is 45.4 × 10
–11
Pa
–1
and
density of water is 10
3
kg/m
3
.What fractional
compression of water will be obtained at the
bottom of the ocean ?
(a) 1.0 × 10
–2
(b) 1.2 × 10
–2
(c) 1.4 × 10
–2
(d) 0.8 × 10
–2
12. A frictionless wire AB is fixed on a sphere of
radius R. A very small spherical ball slips on this
wire. The time taken by this ball to slip from A to
B is
(a)
2
cos q
gR
g
(b)
cos
2. gR
g
q
(c) 2
R
g
q
O
R
C
B
A
(d)
cos
gR
g q
13. A string of length l is fixed at both ends. It is
vibrating in its 3
rd
overtone with maximum
amplitude 'a'. The amplitude at a distance l/3 from
one end is
(a)a (b) 0 (c)
3a
2
(d)
a
2
14. A deuteron of kinetic energy 50 keV is describing
a circular orbit of radius 0.5 metre in a plane
perpendicular to the magnetic field B. The kinetic
energy of the proton that describes a circular orbit
of radius 0.5 metre in the same plane with the
same B is
(a) 25 keV (b) 50 keV
(c) 200 keV (d) 100 keV
15. In the circuit shown in the figure, find the current
in 45 W.
180V
90W
90W
45W
100W
100W
100W
50W 50W
50W
(a) 4 A (b) 2.5A
(c) 2 A (d) None of these
16. Kepler's third law states that square of period of
revolution (T) of a planet around the sun, is
proportional to third power of average distance r
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. What should be the velocity of rotation of earth
due to rotation about its own axis so that the
weight of a person becomes
5
3
of the present
weight at the equator. Equatorial radius of the
earth is 6400 km.
(a) 8.7 × 10
–7
rad/s (b) 7.8 × 10
–4
rad/s
(c) 6.7 × 10
–4
rad/s (d) 7.4 × 10
–3
rad/s
2. Block A of mass m and block B of mass 2m are
placed on a fixed triangular wedge by means of a
massless, inextensible string and a frictionless
pulley as shown in figure.
45° 45°
m 2m
A B
The wedge is inclined at 45° to the horizontal on
both the sides. If the coefficient of friction
between the block A and the wedge is 2/3 and
that between the block B and the wedge is 1/3
and both the blocks A and B are released from
rest, the acceleration of A will be
(a) –1 ms
–2
(b) 1.2 ms
–2
(c) 0.2 ms
–2
(d) zero
3. The surface charge density of a thin charged disc
of radius R is s. The value of the electric field at
the centre of the disc is
0
2
s
Î
. With respect to
the field at the centre, the electric field along the
axis at a distance R from the centre of the disc
(a) reduces by 70.7% (b) reduces by 29.3%
(c) reduces by 9.7% (d) reduces by 14.6%
4. The molecules of a given mass of a gas have
r.m.s. velocity of 200 ms
–1
at 27°C and 1.0 × 10
5
Nm
–2
pressure. When the temperature and
pressure of the gas are respectively, 127°C and
0.05 × 10
5
Nm
–2
, the r.m.s. velocity of its molecules
in ms
–1
is :
(a) 100 2 (b)
400
3
(c)
100 2
3
(d)
100
3
5. An inductor of inductance L = 400 mH and
resistors of resistance R
1
= 2W and R
2
= 2W are
connected to a battery of emf 12 V as shown in
the figure. The internal resistance of the battery
is negligible. The switch S is closed at t = 0. The
potential drop across L as a function of time is
(a)
3
12
V
t
e
t

(b)
( )
/ 0.2
61V
t
e


E
S
L
R
2
R
1
(c) 12e
–5t
V
(d) 6e
–5t
V
6. Two wires are made of the same material and have
the same volume. However wire 1 has cross
sectional area A and wire 2 has crosssectional
area 3A. If the length of wire 1 increases by Dx on
applying force F, how much force is needed to
stretch wire 2 by the same amount?
(a) 4 F (b) 6 F (c) 9 F (d) F
7. Two spheres of different materials one with double
the radius and onefourth wall thickness of the
other are filled with ice. If the time taken for
complete melting of ice in the larger sphere is 25
minute and for smaller one is 16 minute, the ratio
of thermal conductivities of the materials of larger
spheres to that of smaller sphere is
(a) 4 : 5 (b) 5 : 4 (c) 25 : 8 (d) 8 : 25
8. A biconvex lens has a radius of curvature of
magnitude 20 cm. Which one of the following
options best describe the image formed of an
object of height 2 cm placed 30 cm from the lens?
(a) V irtual, upright, height = 1 cm
(b) V irtual, upright, height = 0.5 cm
(c) Real, inverted, height = 4 cm
(d) Real, inverted, height = 1cm
9. In the figure below , what is the potential difference
between the point A and B and between B and C
respectively in steady state
(a) 100
AB BC
V VV ==
(b) 75 , 25
AB BC
V VVV ==
(c) 25 , 75
AB BC
VVVV ==
(d) 50
AB BC
V VV ==
10. A radioactive element X converts into another
stable element Y . Half life of X is 2 hrs. Initially
only X is present. After time t, the ratio of atoms
of X and Y is found to be 1 : 4, then t in hours is
(a)2 (b) 4
(c) between 4 and 6 (d) 6
11. The approximate depth of an ocean is 2700 m. The
compressibility of water is 45.4 × 10
–11
Pa
–1
and
density of water is 10
3
kg/m
3
.What fractional
compression of water will be obtained at the
bottom of the ocean ?
(a) 1.0 × 10
–2
(b) 1.2 × 10
–2
(c) 1.4 × 10
–2
(d) 0.8 × 10
–2
12. A frictionless wire AB is fixed on a sphere of
radius R. A very small spherical ball slips on this
wire. The time taken by this ball to slip from A to
B is
(a)
2
cos q
gR
g
(b)
cos
2. gR
g
q
(c) 2
R
g
q
O
R
C
B
A
(d)
cos
gR
g q
13. A string of length l is fixed at both ends. It is
vibrating in its 3
rd
overtone with maximum
amplitude 'a'. The amplitude at a distance l/3 from
one end is
(a)a (b) 0 (c)
3a
2
(d)
a
2
14. A deuteron of kinetic energy 50 keV is describing
a circular orbit of radius 0.5 metre in a plane
perpendicular to the magnetic field B. The kinetic
energy of the proton that describes a circular orbit
of radius 0.5 metre in the same plane with the
same B is
(a) 25 keV (b) 50 keV
(c) 200 keV (d) 100 keV
15. In the circuit shown in the figure, find the current
in 45 W.
180V
90W
90W
45W
100W
100W
100W
50W 50W
50W
(a) 4 A (b) 2.5A
(c) 2 A (d) None of these
16. Kepler's third law states that square of period of
revolution (T) of a planet around the sun, is
proportional to third power of average distance r
between sun and planet i.e. T
2
= Kr
3
here K is
constant. If the masses of sun and planet are M
and m respectively then as per Newton's law of
gravitation force of attraction between them is
F =
2
GMm
,
r
here G is gravitational constant. The
relation between G and K is described as
(a) GMK = 4p
2
(b) K = G
(c) K =
1
G
(d) GK = 4p
2
17. Find the number of photon emitted per second
by a 25 watt source of monochromatic light of
wavelength 6600 Å. What is the photoelectric
current assuming 3% efficiency for photoelectric
effect ?
(a)
19
25
10 J,0.4amp
3
´
(b)
19
25
10 J,6.2amp
4
´
(c)
19
25
10 J,0.8amp
2
´
(d) None of these
18. A ray of light of intensity I is incident on a parallel
glass slab at point A as shown in diagram. It
undergoes partial reflection and refraction. At each
reflection, 25% of incident energy is reflected. The
rays AB and A'B' undergo interference. The ratio
of I
max
and I
min
is :
A
B
C
A'
B'
C'
(a) 49 : 1 (b) 7 : 1 (c) 4 : 1 (d) 8 : 1
19. A capillary tube of radius r is immersed vertically
in a liquid such that liquid rises in it to height h
(less than the length of the tube). Mass of liquid
in the capillary tube is m. If radius of the capillary
tube is increased by 50%, then mass of liquid that
will rise in the tube, is
(a)
2
m
3
(b) m (c)
3
m
2
(d)
9
m
4
20. The drift velocity of electrons in silver wire with
crosssectional area 3.14 × 10
–6
m
2
carrying a
current of 20 A is. Given atomic weight of Ag =
108, density of silver
= 10.5 × 10
3
kg/m
3
.
(a) 2.798 × 10
–4
m/sec.
(b) 67.98 × 10
–4
m/sec.
(c) 0.67 × 10
–4
m/sec.
(d) 6.798 × 10
–4
m/sec.
21. A parallel plate capacitor of area ‘A’ plate
separation ‘d’ is filled with two dielectrics as
shown. What is the capacitance of the
arrangement ?
K d
K
d
2
A/2 A/2
(a)
0
3
4
KA
d
e
(b)
0
4
3
KA
d
e
(c)
( )
0
1
2
KA
d
+e
(d)
( )
( )
0
3
21
KKA
Kd
+e
+
22. In the Young’s doubleslit experiment, the
intensity of light at a point on the screen where
the path difference is l is K, (l being the wave
length of light used). The intensity at a point
where the path difference is l/4, will be :
(a)K (b) K/4 (c) K/2 (d) Zero
23. The mass of
7
N
15
is 15.00011 amu, mass of
8
O
16
is 15.99492 amu and m
P
= 1.00783 amu. Determine
binding energy of last proton of
8
O
16
.
(a) 2.13 MeV (b) 0.13 MeV
(c) 10 MeV (d) 12.13 Me V
24. A wire carrying current I has the shape as shown
in adjoining figure. Linear parts of the wire are
very long and parallel to Xaxis while semicircular
portion of radius R is lying in Y Z plane. Magnetic
field at point O is :
I
I
X
R
Z
Y
O
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. What should be the velocity of rotation of earth
due to rotation about its own axis so that the
weight of a person becomes
5
3
of the present
weight at the equator. Equatorial radius of the
earth is 6400 km.
(a) 8.7 × 10
–7
rad/s (b) 7.8 × 10
–4
rad/s
(c) 6.7 × 10
–4
rad/s (d) 7.4 × 10
–3
rad/s
2. Block A of mass m and block B of mass 2m are
placed on a fixed triangular wedge by means of a
massless, inextensible string and a frictionless
pulley as shown in figure.
45° 45°
m 2m
A B
The wedge is inclined at 45° to the horizontal on
both the sides. If the coefficient of friction
between the block A and the wedge is 2/3 and
that between the block B and the wedge is 1/3
and both the blocks A and B are released from
rest, the acceleration of A will be
(a) –1 ms
–2
(b) 1.2 ms
–2
(c) 0.2 ms
–2
(d) zero
3. The surface charge density of a thin charged disc
of radius R is s. The value of the electric field at
the centre of the disc is
0
2
s
Î
. With respect to
the field at the centre, the electric field along the
axis at a distance R from the centre of the disc
(a) reduces by 70.7% (b) reduces by 29.3%
(c) reduces by 9.7% (d) reduces by 14.6%
4. The molecules of a given mass of a gas have
r.m.s. velocity of 200 ms
–1
at 27°C and 1.0 × 10
5
Nm
–2
pressure. When the temperature and
pressure of the gas are respectively, 127°C and
0.05 × 10
5
Nm
–2
, the r.m.s. velocity of its molecules
in ms
–1
is :
(a) 100 2 (b)
400
3
(c)
100 2
3
(d)
100
3
5. An inductor of inductance L = 400 mH and
resistors of resistance R
1
= 2W and R
2
= 2W are
connected to a battery of emf 12 V as shown in
the figure. The internal resistance of the battery
is negligible. The switch S is closed at t = 0. The
potential drop across L as a function of time is
(a)
3
12
V
t
e
t

(b)
( )
/ 0.2
61V
t
e


E
S
L
R
2
R
1
(c) 12e
–5t
V
(d) 6e
–5t
V
6. Two wires are made of the same material and have
the same volume. However wire 1 has cross
sectional area A and wire 2 has crosssectional
area 3A. If the length of wire 1 increases by Dx on
applying force F, how much force is needed to
stretch wire 2 by the same amount?
(a) 4 F (b) 6 F (c) 9 F (d) F
7. Two spheres of different materials one with double
the radius and onefourth wall thickness of the
other are filled with ice. If the time taken for
complete melting of ice in the larger sphere is 25
minute and for smaller one is 16 minute, the ratio
of thermal conductivities of the materials of larger
spheres to that of smaller sphere is
(a) 4 : 5 (b) 5 : 4 (c) 25 : 8 (d) 8 : 25
8. A biconvex lens has a radius of curvature of
magnitude 20 cm. Which one of the following
options best describe the image formed of an
object of height 2 cm placed 30 cm from the lens?
(a) V irtual, upright, height = 1 cm
(b) V irtual, upright, height = 0.5 cm
(c) Real, inverted, height = 4 cm
(d) Real, inverted, height = 1cm
9. In the figure below , what is the potential difference
between the point A and B and between B and C
respectively in steady state
(a) 100
AB BC
V VV ==
(b) 75 , 25
AB BC
V VVV ==
(c) 25 , 75
AB BC
VVVV ==
(d) 50
AB BC
V VV ==
10. A radioactive element X converts into another
stable element Y . Half life of X is 2 hrs. Initially
only X is present. After time t, the ratio of atoms
of X and Y is found to be 1 : 4, then t in hours is
(a)2 (b) 4
(c) between 4 and 6 (d) 6
11. The approximate depth of an ocean is 2700 m. The
compressibility of water is 45.4 × 10
–11
Pa
–1
and
density of water is 10
3
kg/m
3
.What fractional
compression of water will be obtained at the
bottom of the ocean ?
(a) 1.0 × 10
–2
(b) 1.2 × 10
–2
(c) 1.4 × 10
–2
(d) 0.8 × 10
–2
12. A frictionless wire AB is fixed on a sphere of
radius R. A very small spherical ball slips on this
wire. The time taken by this ball to slip from A to
B is
(a)
2
cos q
gR
g
(b)
cos
2. gR
g
q
(c) 2
R
g
q
O
R
C
B
A
(d)
cos
gR
g q
13. A string of length l is fixed at both ends. It is
vibrating in its 3
rd
overtone with maximum
amplitude 'a'. The amplitude at a distance l/3 from
one end is
(a)a (b) 0 (c)
3a
2
(d)
a
2
14. A deuteron of kinetic energy 50 keV is describing
a circular orbit of radius 0.5 metre in a plane
perpendicular to the magnetic field B. The kinetic
energy of the proton that describes a circular orbit
of radius 0.5 metre in the same plane with the
same B is
(a) 25 keV (b) 50 keV
(c) 200 keV (d) 100 keV
15. In the circuit shown in the figure, find the current
in 45 W.
180V
90W
90W
45W
100W
100W
100W
50W 50W
50W
(a) 4 A (b) 2.5A
(c) 2 A (d) None of these
16. Kepler's third law states that square of period of
revolution (T) of a planet around the sun, is
proportional to third power of average distance r
between sun and planet i.e. T
2
= Kr
3
here K is
constant. If the masses of sun and planet are M
and m respectively then as per Newton's law of
gravitation force of attraction between them is
F =
2
GMm
,
r
here G is gravitational constant. The
relation between G and K is described as
(a) GMK = 4p
2
(b) K = G
(c) K =
1
G
(d) GK = 4p
2
17. Find the number of photon emitted per second
by a 25 watt source of monochromatic light of
wavelength 6600 Å. What is the photoelectric
current assuming 3% efficiency for photoelectric
effect ?
(a)
19
25
10 J,0.4amp
3
´
(b)
19
25
10 J,6.2amp
4
´
(c)
19
25
10 J,0.8amp
2
´
(d) None of these
18. A ray of light of intensity I is incident on a parallel
glass slab at point A as shown in diagram. It
undergoes partial reflection and refraction. At each
reflection, 25% of incident energy is reflected. The
rays AB and A'B' undergo interference. The ratio
of I
max
and I
min
is :
A
B
C
A'
B'
C'
(a) 49 : 1 (b) 7 : 1 (c) 4 : 1 (d) 8 : 1
19. A capillary tube of radius r is immersed vertically
in a liquid such that liquid rises in it to height h
(less than the length of the tube). Mass of liquid
in the capillary tube is m. If radius of the capillary
tube is increased by 50%, then mass of liquid that
will rise in the tube, is
(a)
2
m
3
(b) m (c)
3
m
2
(d)
9
m
4
20. The drift velocity of electrons in silver wire with
crosssectional area 3.14 × 10
–6
m
2
carrying a
current of 20 A is. Given atomic weight of Ag =
108, density of silver
= 10.5 × 10
3
kg/m
3
.
(a) 2.798 × 10
–4
m/sec.
(b) 67.98 × 10
–4
m/sec.
(c) 0.67 × 10
–4
m/sec.
(d) 6.798 × 10
–4
m/sec.
21. A parallel plate capacitor of area ‘A’ plate
separation ‘d’ is filled with two dielectrics as
shown. What is the capacitance of the
arrangement ?
K d
K
d
2
A/2 A/2
(a)
0
3
4
KA
d
e
(b)
0
4
3
KA
d
e
(c)
( )
0
1
2
KA
d
+e
(d)
( )
( )
0
3
21
KKA
Kd
+e
+
22. In the Young’s doubleslit experiment, the
intensity of light at a point on the screen where
the path difference is l is K, (l being the wave
length of light used). The intensity at a point
where the path difference is l/4, will be :
(a)K (b) K/4 (c) K/2 (d) Zero
23. The mass of
7
N
15
is 15.00011 amu, mass of
8
O
16
is 15.99492 amu and m
P
= 1.00783 amu. Determine
binding energy of last proton of
8
O
16
.
(a) 2.13 MeV (b) 0.13 MeV
(c) 10 MeV (d) 12.13 Me V
24. A wire carrying current I has the shape as shown
in adjoining figure. Linear parts of the wire are
very long and parallel to Xaxis while semicircular
portion of radius R is lying in Y Z plane. Magnetic
field at point O is :
I
I
X
R
Z
Y
O
(a)
$
( )
0
I
B – i 2k
4R
m
= m´
p
ur
$
(b)
$
( )
0
I
B – i 2k
4R
m
= p+
p
ur
$
(c)
$
( )
0
I
B i – 2k
4R
m
=p
p
ur
$
(d)
$
( )
0
I
B i 2k
4R
m
= p+
p
ur
$
25. A stone projected with a velocity u at an angle q
with the horizontal reaches maximum height H
1
.
When it is projected with velocity u at an angle
2
pæö
q
ç÷
èø
with the horizontal, it reaches maximum
height H
2
. The relation between the horizontal
range R of the projectile, heights H
1
and H
2
is
(a)
12
R 4 HH = (b) R = 4(H
1
– H
2
)
(c) R = 4 (H
1
+ H
2
) (d)
2
1
2
2
H
R
H
=
26. If the series limit wavelength of Lyman series for
the hydrogen atom is 912 Å, then the series limit
wavelength for Balmer series of hydrogen atoms
is
(a) 912 Å (b) 912 × 2 Å
(c) 912 × 4 Å (d)
912
Å
2
27. In the shown arrangement of the experiment of
the meter bridge if AC corresponding to null
deflection of galvanometer is x, what would be
its value if the radius of the wire AB is doubled?
G
C A
R
1
R
2
B
x
(a) x (b) x /4 (c) 4 x (d) 2 x
28. A 1 kg mass is attached to a spring of force
constant 600 N/m and rests on a smooth
horizontal surface with other end of the spring
tied to wall as shown in figure. A second mass of
0.5 kg slides along the surface towards the first at
3m/s. If the masses make a perfectly inelastic
collision, then find amplitude and time period of
oscillation of combined mass.
////////////////////////////////////////////////////
///////////////
0.5kg
1 kg
3m/s
(a) 5cm, s
10
p
(b) 5cm, s
5
p
(c) 4cm,
2
s
5
p
(d) 4cm, s
3
p
29. The frequency of vibration of string is given by
½
m
F
2
p
v
ú
û
ù
ê
ë
é
=
l
Here p is number of segments in the string and l
is the length. The dimensional formula for m will
be
(a) [M
0
LT
–1
] (b) [ML
0
T
–1
]
(c) [ML
–1
T
0
] (d) [M
0
L
0
T
0
]
30. For the angle of minimum deviation of a prism to
be equal to its refracting angle, the prism must be
made of a material whose refractive index :
(a) lies between
2
and 1
(b) lies between 2 and 2
(c) is less than 1
(d) is greater than 2
31. Consider elastic collision of a particle of mass m
moving with a velocity u with another particle of
the same mass at rest. After the collision the
projectile and the struck particle move in directions
making angles q
1
and q
2
respectively with the
initial direction of motion. The sum of the angles
q
1
+ q
2
, is :
(a) 45° (b) 90° (c) 135° (d) 180°
32. A conducting circular loop is placed in a uniform
magnetic field of 0.04 T with its plane
perpendicular to the magnetic field. The radius
of the loop starts shrinking at 2 mm/s. The
induced emf in the loop when the radius is 2 cm
is
(a) 4.8 p m V (b) 0.8 p m V
(c) 1.6 p m V (d) 3.2 p m V
33. Figure below shows two paths that may be taken
by a gas to go from a state A to a state (c)
2 × 10 m 4 × 10 m
–
3 3 –33
2×10 Pa
4
6×10 Pa
4
P
B C
A
V
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. What should be the velocity of rotation of earth
due to rotation about its own axis so that the
weight of a person becomes
5
3
of the present
weight at the equator. Equatorial radius of the
earth is 6400 km.
(a) 8.7 × 10
–7
rad/s (b) 7.8 × 10
–4
rad/s
(c) 6.7 × 10
–4
rad/s (d) 7.4 × 10
–3
rad/s
2. Block A of mass m and block B of mass 2m are
placed on a fixed triangular wedge by means of a
massless, inextensible string and a frictionless
pulley as shown in figure.
45° 45°
m 2m
A B
The wedge is inclined at 45° to the horizontal on
both the sides. If the coefficient of friction
between the block A and the wedge is 2/3 and
that between the block B and the wedge is 1/3
and both the blocks A and B are released from
rest, the acceleration of A will be
(a) –1 ms
–2
(b) 1.2 ms
–2
(c) 0.2 ms
–2
(d) zero
3. The surface charge density of a thin charged disc
of radius R is s. The value of the electric field at
the centre of the disc is
0
2
s
Î
. With respect to
the field at the centre, the electric field along the
axis at a distance R from the centre of the disc
(a) reduces by 70.7% (b) reduces by 29.3%
(c) reduces by 9.7% (d) reduces by 14.6%
4. The molecules of a given mass of a gas have
r.m.s. velocity of 200 ms
–1
at 27°C and 1.0 × 10
5
Nm
–2
pressure. When the temperature and
pressure of the gas are respectively, 127°C and
0.05 × 10
5
Nm
–2
, the r.m.s. velocity of its molecules
in ms
–1
is :
(a) 100 2 (b)
400
3
(c)
100 2
3
(d)
100
3
5. An inductor of inductance L = 400 mH and
resistors of resistance R
1
= 2W and R
2
= 2W are
connected to a battery of emf 12 V as shown in
the figure. The internal resistance of the battery
is negligible. The switch S is closed at t = 0. The
potential drop across L as a function of time is
(a)
3
12
V
t
e
t

(b)
( )
/ 0.2
61V
t
e


E
S
L
R
2
R
1
(c) 12e
–5t
V
(d) 6e
–5t
V
6. Two wires are made of the same material and have
the same volume. However wire 1 has cross
sectional area A and wire 2 has crosssectional
area 3A. If the length of wire 1 increases by Dx on
applying force F, how much force is needed to
stretch wire 2 by the same amount?
(a) 4 F (b) 6 F (c) 9 F (d) F
7. Two spheres of different materials one with double
the radius and onefourth wall thickness of the
other are filled with ice. If the time taken for
complete melting of ice in the larger sphere is 25
minute and for smaller one is 16 minute, the ratio
of thermal conductivities of the materials of larger
spheres to that of smaller sphere is
(a) 4 : 5 (b) 5 : 4 (c) 25 : 8 (d) 8 : 25
8. A biconvex lens has a radius of curvature of
magnitude 20 cm. Which one of the following
options best describe the image formed of an
object of height 2 cm placed 30 cm from the lens?
(a) V irtual, upright, height = 1 cm
(b) V irtual, upright, height = 0.5 cm
(c) Real, inverted, height = 4 cm
(d) Real, inverted, height = 1cm
9. In the figure below , what is the potential difference
between the point A and B and between B and C
respectively in steady state
(a) 100
AB BC
V VV ==
(b) 75 , 25
AB BC
V VVV ==
(c) 25 , 75
AB BC
VVVV ==
(d) 50
AB BC
V VV ==
10. A radioactive element X converts into another
stable element Y . Half life of X is 2 hrs. Initially
only X is present. After time t, the ratio of atoms
of X and Y is found to be 1 : 4, then t in hours is
(a)2 (b) 4
(c) between 4 and 6 (d) 6
11. The approximate depth of an ocean is 2700 m. The
compressibility of water is 45.4 × 10
–11
Pa
–1
and
density of water is 10
3
kg/m
3
.What fractional
compression of water will be obtained at the
bottom of the ocean ?
(a) 1.0 × 10
–2
(b) 1.2 × 10
–2
(c) 1.4 × 10
–2
(d) 0.8 × 10
–2
12. A frictionless wire AB is fixed on a sphere of
radius R. A very small spherical ball slips on this
wire. The time taken by this ball to slip from A to
B is
(a)
2
cos q
gR
g
(b)
cos
2. gR
g
q
(c) 2
R
g
q
O
R
C
B
A
(d)
cos
gR
g q
13. A string of length l is fixed at both ends. It is
vibrating in its 3
rd
overtone with maximum
amplitude 'a'. The amplitude at a distance l/3 from
one end is
(a)a (b) 0 (c)
3a
2
(d)
a
2
14. A deuteron of kinetic energy 50 keV is describing
a circular orbit of radius 0.5 metre in a plane
perpendicular to the magnetic field B. The kinetic
energy of the proton that describes a circular orbit
of radius 0.5 metre in the same plane with the
same B is
(a) 25 keV (b) 50 keV
(c) 200 keV (d) 100 keV
15. In the circuit shown in the figure, find the current
in 45 W.
180V
90W
90W
45W
100W
100W
100W
50W 50W
50W
(a) 4 A (b) 2.5A
(c) 2 A (d) None of these
16. Kepler's third law states that square of period of
revolution (T) of a planet around the sun, is
proportional to third power of average distance r
between sun and planet i.e. T
2
= Kr
3
here K is
constant. If the masses of sun and planet are M
and m respectively then as per Newton's law of
gravitation force of attraction between them is
F =
2
GMm
,
r
here G is gravitational constant. The
relation between G and K is described as
(a) GMK = 4p
2
(b) K = G
(c) K =
1
G
(d) GK = 4p
2
17. Find the number of photon emitted per second
by a 25 watt source of monochromatic light of
wavelength 6600 Å. What is the photoelectric
current assuming 3% efficiency for photoelectric
effect ?
(a)
19
25
10 J,0.4amp
3
´
(b)
19
25
10 J,6.2amp
4
´
(c)
19
25
10 J,0.8amp
2
´
(d) None of these
18. A ray of light of intensity I is incident on a parallel
glass slab at point A as shown in diagram. It
undergoes partial reflection and refraction. At each
reflection, 25% of incident energy is reflected. The
rays AB and A'B' undergo interference. The ratio
of I
max
and I
min
is :
A
B
C
A'
B'
C'
(a) 49 : 1 (b) 7 : 1 (c) 4 : 1 (d) 8 : 1
19. A capillary tube of radius r is immersed vertically
in a liquid such that liquid rises in it to height h
(less than the length of the tube). Mass of liquid
in the capillary tube is m. If radius of the capillary
tube is increased by 50%, then mass of liquid that
will rise in the tube, is
(a)
2
m
3
(b) m (c)
3
m
2
(d)
9
m
4
20. The drift velocity of electrons in silver wire with
crosssectional area 3.14 × 10
–6
m
2
carrying a
current of 20 A is. Given atomic weight of Ag =
108, density of silver
= 10.5 × 10
3
kg/m
3
.
(a) 2.798 × 10
–4
m/sec.
(b) 67.98 × 10
–4
m/sec.
(c) 0.67 × 10
–4
m/sec.
(d) 6.798 × 10
–4
m/sec.
21. A parallel plate capacitor of area ‘A’ plate
separation ‘d’ is filled with two dielectrics as
shown. What is the capacitance of the
arrangement ?
K d
K
d
2
A/2 A/2
(a)
0
3
4
KA
d
e
(b)
0
4
3
KA
d
e
(c)
( )
0
1
2
KA
d
+e
(d)
( )
( )
0
3
21
KKA
Kd
+e
+
22. In the Young’s doubleslit experiment, the
intensity of light at a point on the screen where
the path difference is l is K, (l being the wave
length of light used). The intensity at a point
where the path difference is l/4, will be :
(a)K (b) K/4 (c) K/2 (d) Zero
23. The mass of
7
N
15
is 15.00011 amu, mass of
8
O
16
is 15.99492 amu and m
P
= 1.00783 amu. Determine
binding energy of last proton of
8
O
16
.
(a) 2.13 MeV (b) 0.13 MeV
(c) 10 MeV (d) 12.13 Me V
24. A wire carrying current I has the shape as shown
in adjoining figure. Linear parts of the wire are
very long and parallel to Xaxis while semicircular
portion of radius R is lying in Y Z plane. Magnetic
field at point O is :
I
I
X
R
Z
Y
O
(a)
$
( )
0
I
B – i 2k
4R
m
= m´
p
ur
$
(b)
$
( )
0
I
B – i 2k
4R
m
= p+
p
ur
$
(c)
$
( )
0
I
B i – 2k
4R
m
=p
p
ur
$
(d)
$
( )
0
I
B i 2k
4R
m
= p+
p
ur
$
25. A stone projected with a velocity u at an angle q
with the horizontal reaches maximum height H
1
.
When it is projected with velocity u at an angle
2
pæö
q
ç÷
èø
with the horizontal, it reaches maximum
height H
2
. The relation between the horizontal
range R of the projectile, heights H
1
and H
2
is
(a)
12
R 4 HH = (b) R = 4(H
1
– H
2
)
(c) R = 4 (H
1
+ H
2
) (d)
2
1
2
2
H
R
H
=
26. If the series limit wavelength of Lyman series for
the hydrogen atom is 912 Å, then the series limit
wavelength for Balmer series of hydrogen atoms
is
(a) 912 Å (b) 912 × 2 Å
(c) 912 × 4 Å (d)
912
Å
2
27. In the shown arrangement of the experiment of
the meter bridge if AC corresponding to null
deflection of galvanometer is x, what would be
its value if the radius of the wire AB is doubled?
G
C A
R
1
R
2
B
x
(a) x (b) x /4 (c) 4 x (d) 2 x
28. A 1 kg mass is attached to a spring of force
constant 600 N/m and rests on a smooth
horizontal surface with other end of the spring
tied to wall as shown in figure. A second mass of
0.5 kg slides along the surface towards the first at
3m/s. If the masses make a perfectly inelastic
collision, then find amplitude and time period of
oscillation of combined mass.
////////////////////////////////////////////////////
///////////////
0.5kg
1 kg
3m/s
(a) 5cm, s
10
p
(b) 5cm, s
5
p
(c) 4cm,
2
s
5
p
(d) 4cm, s
3
p
29. The frequency of vibration of string is given by
½
m
F
2
p
v
ú
û
ù
ê
ë
é
=
l
Here p is number of segments in the string and l
is the length. The dimensional formula for m will
be
(a) [M
0
LT
–1
] (b) [ML
0
T
–1
]
(c) [ML
–1
T
0
] (d) [M
0
L
0
T
0
]
30. For the angle of minimum deviation of a prism to
be equal to its refracting angle, the prism must be
made of a material whose refractive index :
(a) lies between
2
and 1
(b) lies between 2 and 2
(c) is less than 1
(d) is greater than 2
31. Consider elastic collision of a particle of mass m
moving with a velocity u with another particle of
the same mass at rest. After the collision the
projectile and the struck particle move in directions
making angles q
1
and q
2
respectively with the
initial direction of motion. The sum of the angles
q
1
+ q
2
, is :
(a) 45° (b) 90° (c) 135° (d) 180°
32. A conducting circular loop is placed in a uniform
magnetic field of 0.04 T with its plane
perpendicular to the magnetic field. The radius
of the loop starts shrinking at 2 mm/s. The
induced emf in the loop when the radius is 2 cm
is
(a) 4.8 p m V (b) 0.8 p m V
(c) 1.6 p m V (d) 3.2 p m V
33. Figure below shows two paths that may be taken
by a gas to go from a state A to a state (c)
2 × 10 m 4 × 10 m
–
3 3 –33
2×10 Pa
4
6×10 Pa
4
P
B C
A
V
In process AB, 400 J of heat is added to the system
and in process BC, 100 J of heat is added to the
system. The heat absorbed by the system in the
process AC will be
(a) 500 J (b) 460 J (c) 300 J (d) 380 J
34. Two resistances at 0° C with temperature
coefficient of resistance a
1
and a
2
joined in series
act as a single resistance in a circuit. The
temperature coefficient of their single resistance
will be
(a)
12
a +a (b)
12
12
aa
a +a
(c)
12
2
a a
(d)
12
2
a +a
35. Two identical charged spheres suspended from a
common point by two massless strings of lengths
l, are initially at a distance d (d << l ) apart because
of their mutual repulsion. The charges begin to
leak from both the spheres at a constant rate. As
a result, the spheres approach each other with a
velocity v. Then v varies as a function of the
distance x between the spheres, as :
(a)
1
2
vx µ
(b) vx µ
(c)
1
2
vx

µ (d)
1
vx

µ
36. A point particle of mass 0.1 kg is executing S.H.M.
of amplitude of 0.1 m. When the particle passes
through the mean position, its kinetic energy is 8
× 10
–3
Joule. Obtain the equation of motion of
this particle if this initial phase of oscillation is
45º.
(a)
y 0.1sin 4t
4
p æö
= ±+
ç÷
èø
(b)
y 0.2sin 4t
4
p æö
= ±+
ç÷
èø
(c)
y 0.1sin 2t
4
p æö
= ±+
ç÷
èø
(d)
y 0.2sin 2t
4
p æö
= ±+
ç÷
èø
37. A source of sound S emitting waves of frequency
100 Hz and an observor O are located at some
distance from each other. The source is moving
with a speed of 19.4 ms
–1
at an angle of 60° with
the source observer line as shown in the figure.
The observor is at rest. The apparent frequency
observed by the observer is (velocity of sound in
air 330 ms
–1
)
60°
S
O
(a) 103 Hz (b) 106 Hz
(c) 97 Hz (d) 100 Hz
38. A resistor of resistance R, capacitor of capacitance
C and inductor of inductance L are connected in
parallel to AC power source of voltage e
0
sin wt.
The maximum current through the resistance is
half of the maximum current through the power
source. Then value of R is
(a)
3
1
– C
L
w
w
(b)
1
3–L
C
w
w
(c)
1
5–L
C
w
w
(d) None of these
39. A lens having focal length f and aperture of
diameter d forms an image of intensity I. Aperture
of diameter
2
d
in central region of lens is covered
by a black paper. Focal length of lens and intensity
of image now will be respectively:
(a) f and
4
I
(b)
3
4
f
and
2
I
(c) f and
3
4
I
(d)
2
f
and
2
I
40. A circular disc of radius R and thickness
6
R
has
moment inertia I about an axis passing through
its centre perpendicular to its plane. It is melted
and recasted into a solid sphere. The moment of
inertia of the sphere about its diameter is
(a) I (b)
2
8
I
(c)
5
I
(d)
10
I
PART  II: CHEMISTRY
41. In
– 3
4
PO , the formal charge on each oxygen atom
and the P  O bond order respectively are
(a) –0.75, 0.6 (b) –0.75, 1.0
(c) –0.75, 1.25 (d) –3, 1.25
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