BITSAT Past Year Paper- 2014 JEE Notes | EduRev

BITSAT Mock Tests Series & Past Year Papers

JEE : BITSAT Past Year Paper- 2014 JEE Notes | EduRev

 Page 1


PART - I : PHYSICS
1. A rifle man, who together with his rifle has a mass
of 100 kg, stands on a smooth surface and fires 10
shots horizontally. Each bullet has a mass 10 g
and a muzzle velocity of  800 ms
–1
. The velocity
which the rifle man attains after  firing 10 shots is
(a) 8 ms
–1
(b) 0.8 ms
–1
(c) 0.08 ms
–1
(d) – 0.8 ms
–1
2. A train accelerating uniformly from rest attains a
maximum speed of 40 ms
–1
 in 20 s. It travels at
the speed for 20 s and is brought to rest with
uniform retardation in further 40 s. What is the
average velocity during the period ?
(a) 80 m/s (b) 25 m/s
(c) 40 m/s (d) 30 m/s
3. A projectile is fired with a velocity u making an
angle q with the horizontal. What is the magnitude
of change in velocity when it is at the highest
point –
(a) u cos q (b) u
(c) u sin q (d) u cos q – u
4. For the equation F = A
a
v
b
d
c
, where F is the force,
A is the area, v is the velocity and d is the density ,
the values of a, b and c are respectively
(a) 1, 2, 1 (b) 2, 1, 1 (c) 1, 1, 2 (d) 0, 1, 1
5. A person with his hand in his pocket is skating
on ice at the rate of 10m/s and describes a circle
of radius 50 m. What is his inclination to vertical:
(g = 10 m/sec
2
)
(a) tan
–1
(½) (b) tan
–1
 (1/5)
(c) tan
–1
 (3/5) (d) tan
–1
(1/10)
6. A small block of mass m is kept on a rough
inclined surface of inclination q fixed in a elevator.
The elevator goes up with a uniform velocity v
and the block does not slide on the wedge. The
work done by the force of friction on the block in
time t will be :
(a) zero (b) mgvt cos
2
q
(c) mgvt sin
2
q (d) mgvt sin 2q
7. An equilateral prism of
mass m rests on a rough
horizontal surface with
coefficient of friction µ.
F
a
a
a
A horizontal force F
is applied on the prism as shown in the figure.
If the coefficient of  friction is sufficiently high
so that the prism does not slide before toppling,
then the minimum force required to topple the
prism is –
(a)
mg
3
(b)
mg
4
(c)
mg
3
m
(d)
mg
4
m
8. A spherically symmetric gravitational system of
particles has a mass density 
0
forrR
0 forrR
r£ ì
r=
í
>
î
where r
0
 is a constant. A test mass can undergo
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 : Mathematics Q. No. 81 to 125
Part IV : (A) English Proficiency Q. No. 126 to 140
  (B) Logical Reasoning Q. No. 141 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
Page 2


PART - I : PHYSICS
1. A rifle man, who together with his rifle has a mass
of 100 kg, stands on a smooth surface and fires 10
shots horizontally. Each bullet has a mass 10 g
and a muzzle velocity of  800 ms
–1
. The velocity
which the rifle man attains after  firing 10 shots is
(a) 8 ms
–1
(b) 0.8 ms
–1
(c) 0.08 ms
–1
(d) – 0.8 ms
–1
2. A train accelerating uniformly from rest attains a
maximum speed of 40 ms
–1
 in 20 s. It travels at
the speed for 20 s and is brought to rest with
uniform retardation in further 40 s. What is the
average velocity during the period ?
(a) 80 m/s (b) 25 m/s
(c) 40 m/s (d) 30 m/s
3. A projectile is fired with a velocity u making an
angle q with the horizontal. What is the magnitude
of change in velocity when it is at the highest
point –
(a) u cos q (b) u
(c) u sin q (d) u cos q – u
4. For the equation F = A
a
v
b
d
c
, where F is the force,
A is the area, v is the velocity and d is the density ,
the values of a, b and c are respectively
(a) 1, 2, 1 (b) 2, 1, 1 (c) 1, 1, 2 (d) 0, 1, 1
5. A person with his hand in his pocket is skating
on ice at the rate of 10m/s and describes a circle
of radius 50 m. What is his inclination to vertical:
(g = 10 m/sec
2
)
(a) tan
–1
(½) (b) tan
–1
 (1/5)
(c) tan
–1
 (3/5) (d) tan
–1
(1/10)
6. A small block of mass m is kept on a rough
inclined surface of inclination q fixed in a elevator.
The elevator goes up with a uniform velocity v
and the block does not slide on the wedge. The
work done by the force of friction on the block in
time t will be :
(a) zero (b) mgvt cos
2
q
(c) mgvt sin
2
q (d) mgvt sin 2q
7. An equilateral prism of
mass m rests on a rough
horizontal surface with
coefficient of friction µ.
F
a
a
a
A horizontal force F
is applied on the prism as shown in the figure.
If the coefficient of  friction is sufficiently high
so that the prism does not slide before toppling,
then the minimum force required to topple the
prism is –
(a)
mg
3
(b)
mg
4
(c)
mg
3
m
(d)
mg
4
m
8. A spherically symmetric gravitational system of
particles has a mass density 
0
forrR
0 forrR
r£ ì
r=
í
>
î
where r
0
 is a constant. A test mass can undergo
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 : Mathematics Q. No. 81 to 125
Part IV : (A) English Proficiency Q. No. 126 to 140
  (B) Logical Reasoning Q. No. 141 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
circular motion under the influence of the
gravitational field of particles. Its speed V as a
function of distance r (0 < r < ¥) from the centre
of the system is represented by
(a)
V
R
r
(b)
V
R
r
(c)
V
R
r
(d)
V
R
r
9. The load versus elongation graph for four wires
is shown. The thinnest wire is
S
R
Q
P
Elongation
Load
(a) P (b) Q (c) R (d) S
10. The work done in blowing a soap bubble of
surface tension 0.06 × Nm
–1
 from 2 cm radius to
5 cm radius is
(a) 0.004168 J (b) 0.003168 J
(c) 0.003158 J (d) 0.004568 J
11. The wavelength of radiation emitted by a body
depends upon
(a) the nature of its surface
(b) the area of its surface
(c) the temperature of its surface
(d) All of the above
12. One mole of O
2
 gas having a volume equal to
22.4 Litres at 0°C and 1 atmospheric pressure in
compressed isothermally so that its volume
reduces to 11.2 litres. The work done in this
process is-
(a) 1672.5 J (b) 1728 J
(c) –1728 J (d) –1572.5 J
13. In a thermodynamic process, the pressure of a
fixed mass of a gas is changed in such a manner
that the gas releases 20 J of heat and 8 J of work
is done on the gas. If the initial internal energy of
the gas was 30 J, then the final internal energy
will be
(a) 2 J (b) 42 J
(c) 18 J (d) 58 J
14. In the kinetic theory of gases, which of these
statements is/are true ?
(i) The pressure of a gas is proportional to the
mean speed of the molecules.
(ii) The root mean square speed of the
molecules is proportional to the pressure.
(iii) The rate of diffusion is proportional to the
mean speed of the molecules.
(iv) The mean translational kinetic energy of a
gas is proportional to its kelvin temperature.
(a) (ii) and (iii) only (b) (i), (ii) and (iv) only
(c) (i) and (iii) only (d) (iii) and (iv) only
15. Two balloons are filled one with pure he gas and
other with air respectively. If the pressure and
temperature of these balloons are same, then the
number of molecules per unit volume is
(a) more in He gas filled balloon
(b) same in both balloons
(c) more in air filled balloon
(d) in the ratio 1 : 4
16. Two particles P and Q describe S.H.M. of same
amplitude a, same frequency f along the same
straight line. The maximum distance between the
two particles is a2 .
The initial phase difference between the particle
is –
(a) zero (b) p/2 (c) p/6 (d) p/3
17. A tunnel has been dug through the centre of the
earth and a ball is released in it. It executes S.H.M.
with time period
(a) 42 minutes (b) 1 day
(c) 1 hour (d) 84.6 minutes
18. A sound source, emitting sound of constant
frequency, moves with a constant speed and
crosses a stationary observer. The frequency (n)
of sound heard by the observer  is plotted against
time (t). Which of the following graphs represents
the correct variation ?
(a)
n
t
(b)
n
t
(c)
n
t
(d)
n
t
Page 3


PART - I : PHYSICS
1. A rifle man, who together with his rifle has a mass
of 100 kg, stands on a smooth surface and fires 10
shots horizontally. Each bullet has a mass 10 g
and a muzzle velocity of  800 ms
–1
. The velocity
which the rifle man attains after  firing 10 shots is
(a) 8 ms
–1
(b) 0.8 ms
–1
(c) 0.08 ms
–1
(d) – 0.8 ms
–1
2. A train accelerating uniformly from rest attains a
maximum speed of 40 ms
–1
 in 20 s. It travels at
the speed for 20 s and is brought to rest with
uniform retardation in further 40 s. What is the
average velocity during the period ?
(a) 80 m/s (b) 25 m/s
(c) 40 m/s (d) 30 m/s
3. A projectile is fired with a velocity u making an
angle q with the horizontal. What is the magnitude
of change in velocity when it is at the highest
point –
(a) u cos q (b) u
(c) u sin q (d) u cos q – u
4. For the equation F = A
a
v
b
d
c
, where F is the force,
A is the area, v is the velocity and d is the density ,
the values of a, b and c are respectively
(a) 1, 2, 1 (b) 2, 1, 1 (c) 1, 1, 2 (d) 0, 1, 1
5. A person with his hand in his pocket is skating
on ice at the rate of 10m/s and describes a circle
of radius 50 m. What is his inclination to vertical:
(g = 10 m/sec
2
)
(a) tan
–1
(½) (b) tan
–1
 (1/5)
(c) tan
–1
 (3/5) (d) tan
–1
(1/10)
6. A small block of mass m is kept on a rough
inclined surface of inclination q fixed in a elevator.
The elevator goes up with a uniform velocity v
and the block does not slide on the wedge. The
work done by the force of friction on the block in
time t will be :
(a) zero (b) mgvt cos
2
q
(c) mgvt sin
2
q (d) mgvt sin 2q
7. An equilateral prism of
mass m rests on a rough
horizontal surface with
coefficient of friction µ.
F
a
a
a
A horizontal force F
is applied on the prism as shown in the figure.
If the coefficient of  friction is sufficiently high
so that the prism does not slide before toppling,
then the minimum force required to topple the
prism is –
(a)
mg
3
(b)
mg
4
(c)
mg
3
m
(d)
mg
4
m
8. A spherically symmetric gravitational system of
particles has a mass density 
0
forrR
0 forrR
r£ ì
r=
í
>
î
where r
0
 is a constant. A test mass can undergo
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 : Mathematics Q. No. 81 to 125
Part IV : (A) English Proficiency Q. No. 126 to 140
  (B) Logical Reasoning Q. No. 141 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
circular motion under the influence of the
gravitational field of particles. Its speed V as a
function of distance r (0 < r < ¥) from the centre
of the system is represented by
(a)
V
R
r
(b)
V
R
r
(c)
V
R
r
(d)
V
R
r
9. The load versus elongation graph for four wires
is shown. The thinnest wire is
S
R
Q
P
Elongation
Load
(a) P (b) Q (c) R (d) S
10. The work done in blowing a soap bubble of
surface tension 0.06 × Nm
–1
 from 2 cm radius to
5 cm radius is
(a) 0.004168 J (b) 0.003168 J
(c) 0.003158 J (d) 0.004568 J
11. The wavelength of radiation emitted by a body
depends upon
(a) the nature of its surface
(b) the area of its surface
(c) the temperature of its surface
(d) All of the above
12. One mole of O
2
 gas having a volume equal to
22.4 Litres at 0°C and 1 atmospheric pressure in
compressed isothermally so that its volume
reduces to 11.2 litres. The work done in this
process is-
(a) 1672.5 J (b) 1728 J
(c) –1728 J (d) –1572.5 J
13. In a thermodynamic process, the pressure of a
fixed mass of a gas is changed in such a manner
that the gas releases 20 J of heat and 8 J of work
is done on the gas. If the initial internal energy of
the gas was 30 J, then the final internal energy
will be
(a) 2 J (b) 42 J
(c) 18 J (d) 58 J
14. In the kinetic theory of gases, which of these
statements is/are true ?
(i) The pressure of a gas is proportional to the
mean speed of the molecules.
(ii) The root mean square speed of the
molecules is proportional to the pressure.
(iii) The rate of diffusion is proportional to the
mean speed of the molecules.
(iv) The mean translational kinetic energy of a
gas is proportional to its kelvin temperature.
(a) (ii) and (iii) only (b) (i), (ii) and (iv) only
(c) (i) and (iii) only (d) (iii) and (iv) only
15. Two balloons are filled one with pure he gas and
other with air respectively. If the pressure and
temperature of these balloons are same, then the
number of molecules per unit volume is
(a) more in He gas filled balloon
(b) same in both balloons
(c) more in air filled balloon
(d) in the ratio 1 : 4
16. Two particles P and Q describe S.H.M. of same
amplitude a, same frequency f along the same
straight line. The maximum distance between the
two particles is a2 .
The initial phase difference between the particle
is –
(a) zero (b) p/2 (c) p/6 (d) p/3
17. A tunnel has been dug through the centre of the
earth and a ball is released in it. It executes S.H.M.
with time period
(a) 42 minutes (b) 1 day
(c) 1 hour (d) 84.6 minutes
18. A sound source, emitting sound of constant
frequency, moves with a constant speed and
crosses a stationary observer. The frequency (n)
of sound heard by the observer  is plotted against
time (t). Which of the following graphs represents
the correct variation ?
(a)
n
t
(b)
n
t
(c)
n
t
(d)
n
t
19. When a string is divided into three segments of
length l
1
, l
2
, and l
3
 the fundamental frequencies
of these three segments are v
1
, v
2
 and v
3
respectively . The original fundamental frequency
(v) of the string is
(a)
1 23
v v vv = ++
(b) v = v
1
 + v
2
 + v
3
(c)
1 23
1 1 11
v v vv
= ++
`
(d)
1 23
1 1 11
v v vv
= ++
20. Two point dipoles 
ˆ
pk and 
p
ˆ
k
2
 are located at
(0, 0, 0) and (1m, 0, 2m) respectively . The resultant
electric field due to the two dipoles at the point
(1m, 0, 0) is
(a)
0
9p
ˆ
k
32pÎ
(b)
0
7p
ˆ
k
32
-
pÎ
(c)
0
7p
ˆ
k
32pÎ
(d) None of these
21. Electric field in the region is given by 
3
M
ˆ
E i,
x
æö
=
ç÷
èø
then the correct expression for the potential in
the region is [assume potential at infinity is zero]
(a)
2
M
2x
(b) Mx
2
(c)
4
M
3x
(d)
2
M
x
22. Three capacitors C
1
 = 1 µF , C
2
 = 2 µF and C
3
 = 3
µF are connected as shown in figure, then the
equivalent capacitance between points A and B is
C
1
C
2
C
3
C
E D
B A
(a) 3 µF (b) 4 µF (c) 5 µF (d) 6 µF
23. Two long coaxial and conducting cylinders of
radius a and b are separated by a material of
conductivity s and a constant potential difference
V is maintained between them, by a battery . Then
the current, per unit length of the cylinder flowing
from one cylinder to the other is –
(a)
4
V
ln (b / a)
ps
(b)
4
V
(b a)
ps
+
(c)
2
V
ln (b / a)
ps
(d)
2
V
(b a)
ps
+
24. A wire X is half the diameter and half the length
of a wire Y of similar material. The ratio of
resistance of X to that of Y is
(a) 8 : 1 (b) 4 : 1 (c) 2 : 1 (d) 1 : 1
25. A narrow beam of protons and deuterons, each
having the same momentum, enters a region of
uniform magnetic field directed perpendicular to
their direction of momentum. The ratio of the radii
of the circular paths described by them is
(a) 1 : 2 (b) 1 : 1
(c) 2 : 1 (d) 1 : 3
26. For the circuit (figure), the current is to be
measured. The ammeter shown is a galvanometer
with a resistance R
G
 = 60.00W converted to an
ammeter by a shunt resistance r
s
 = 0.02W. The
value of the current is
A
3.00 V
3.00W
(a) 0.79 A (b) 0.29 A
(c) 0.99 A (d) 0.8 A
27. The susceptibility of a magnetism at 300 K is
1.2 × 10
–5
. The temperature at which the
susceptibility increases to 1.8 × 10
–5
 is
(a) 150 K (b) 200 K (c) 250 K (d) 20 K
28. A coil 10 turns and a resistance of 20W is connected
in series with B.G . of resistance 30W. The coil is
placed with its plane perpendicular to the direction
of a uniform magnetic field of induction 10
–2
 T . If it
is now turned through an angle of 60° about an axis
in its plane. Find the charge induced in the coil.
(Area of a coil = 10
–2
 m²)
(a) 2 × 10
–5
 C (b) 3.2 × 10
–5
 C
(c) 1 × 10
–5
 C (d) 5.5 × 10
–5
 C
29. V oltage V and current i in AC circuit are given by
V = 50 sin (50 t) volt, i = 50 sin 50t mA.
3
p æö
+
ç÷
èø
The power dissipated in the circuit is
(a) 5.0 W (b) 2.5 W
(c) 1.25 W (d) zero
30. Resolving power of the telescope will be more, if
the diameter of the objective is
(a) larger
(b) smaller
(c) it does not depends on diameter
(d) None of these
Page 4


PART - I : PHYSICS
1. A rifle man, who together with his rifle has a mass
of 100 kg, stands on a smooth surface and fires 10
shots horizontally. Each bullet has a mass 10 g
and a muzzle velocity of  800 ms
–1
. The velocity
which the rifle man attains after  firing 10 shots is
(a) 8 ms
–1
(b) 0.8 ms
–1
(c) 0.08 ms
–1
(d) – 0.8 ms
–1
2. A train accelerating uniformly from rest attains a
maximum speed of 40 ms
–1
 in 20 s. It travels at
the speed for 20 s and is brought to rest with
uniform retardation in further 40 s. What is the
average velocity during the period ?
(a) 80 m/s (b) 25 m/s
(c) 40 m/s (d) 30 m/s
3. A projectile is fired with a velocity u making an
angle q with the horizontal. What is the magnitude
of change in velocity when it is at the highest
point –
(a) u cos q (b) u
(c) u sin q (d) u cos q – u
4. For the equation F = A
a
v
b
d
c
, where F is the force,
A is the area, v is the velocity and d is the density ,
the values of a, b and c are respectively
(a) 1, 2, 1 (b) 2, 1, 1 (c) 1, 1, 2 (d) 0, 1, 1
5. A person with his hand in his pocket is skating
on ice at the rate of 10m/s and describes a circle
of radius 50 m. What is his inclination to vertical:
(g = 10 m/sec
2
)
(a) tan
–1
(½) (b) tan
–1
 (1/5)
(c) tan
–1
 (3/5) (d) tan
–1
(1/10)
6. A small block of mass m is kept on a rough
inclined surface of inclination q fixed in a elevator.
The elevator goes up with a uniform velocity v
and the block does not slide on the wedge. The
work done by the force of friction on the block in
time t will be :
(a) zero (b) mgvt cos
2
q
(c) mgvt sin
2
q (d) mgvt sin 2q
7. An equilateral prism of
mass m rests on a rough
horizontal surface with
coefficient of friction µ.
F
a
a
a
A horizontal force F
is applied on the prism as shown in the figure.
If the coefficient of  friction is sufficiently high
so that the prism does not slide before toppling,
then the minimum force required to topple the
prism is –
(a)
mg
3
(b)
mg
4
(c)
mg
3
m
(d)
mg
4
m
8. A spherically symmetric gravitational system of
particles has a mass density 
0
forrR
0 forrR
r£ ì
r=
í
>
î
where r
0
 is a constant. A test mass can undergo
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 : Mathematics Q. No. 81 to 125
Part IV : (A) English Proficiency Q. No. 126 to 140
  (B) Logical Reasoning Q. No. 141 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
circular motion under the influence of the
gravitational field of particles. Its speed V as a
function of distance r (0 < r < ¥) from the centre
of the system is represented by
(a)
V
R
r
(b)
V
R
r
(c)
V
R
r
(d)
V
R
r
9. The load versus elongation graph for four wires
is shown. The thinnest wire is
S
R
Q
P
Elongation
Load
(a) P (b) Q (c) R (d) S
10. The work done in blowing a soap bubble of
surface tension 0.06 × Nm
–1
 from 2 cm radius to
5 cm radius is
(a) 0.004168 J (b) 0.003168 J
(c) 0.003158 J (d) 0.004568 J
11. The wavelength of radiation emitted by a body
depends upon
(a) the nature of its surface
(b) the area of its surface
(c) the temperature of its surface
(d) All of the above
12. One mole of O
2
 gas having a volume equal to
22.4 Litres at 0°C and 1 atmospheric pressure in
compressed isothermally so that its volume
reduces to 11.2 litres. The work done in this
process is-
(a) 1672.5 J (b) 1728 J
(c) –1728 J (d) –1572.5 J
13. In a thermodynamic process, the pressure of a
fixed mass of a gas is changed in such a manner
that the gas releases 20 J of heat and 8 J of work
is done on the gas. If the initial internal energy of
the gas was 30 J, then the final internal energy
will be
(a) 2 J (b) 42 J
(c) 18 J (d) 58 J
14. In the kinetic theory of gases, which of these
statements is/are true ?
(i) The pressure of a gas is proportional to the
mean speed of the molecules.
(ii) The root mean square speed of the
molecules is proportional to the pressure.
(iii) The rate of diffusion is proportional to the
mean speed of the molecules.
(iv) The mean translational kinetic energy of a
gas is proportional to its kelvin temperature.
(a) (ii) and (iii) only (b) (i), (ii) and (iv) only
(c) (i) and (iii) only (d) (iii) and (iv) only
15. Two balloons are filled one with pure he gas and
other with air respectively. If the pressure and
temperature of these balloons are same, then the
number of molecules per unit volume is
(a) more in He gas filled balloon
(b) same in both balloons
(c) more in air filled balloon
(d) in the ratio 1 : 4
16. Two particles P and Q describe S.H.M. of same
amplitude a, same frequency f along the same
straight line. The maximum distance between the
two particles is a2 .
The initial phase difference between the particle
is –
(a) zero (b) p/2 (c) p/6 (d) p/3
17. A tunnel has been dug through the centre of the
earth and a ball is released in it. It executes S.H.M.
with time period
(a) 42 minutes (b) 1 day
(c) 1 hour (d) 84.6 minutes
18. A sound source, emitting sound of constant
frequency, moves with a constant speed and
crosses a stationary observer. The frequency (n)
of sound heard by the observer  is plotted against
time (t). Which of the following graphs represents
the correct variation ?
(a)
n
t
(b)
n
t
(c)
n
t
(d)
n
t
19. When a string is divided into three segments of
length l
1
, l
2
, and l
3
 the fundamental frequencies
of these three segments are v
1
, v
2
 and v
3
respectively . The original fundamental frequency
(v) of the string is
(a)
1 23
v v vv = ++
(b) v = v
1
 + v
2
 + v
3
(c)
1 23
1 1 11
v v vv
= ++
`
(d)
1 23
1 1 11
v v vv
= ++
20. Two point dipoles 
ˆ
pk and 
p
ˆ
k
2
 are located at
(0, 0, 0) and (1m, 0, 2m) respectively . The resultant
electric field due to the two dipoles at the point
(1m, 0, 0) is
(a)
0
9p
ˆ
k
32pÎ
(b)
0
7p
ˆ
k
32
-
pÎ
(c)
0
7p
ˆ
k
32pÎ
(d) None of these
21. Electric field in the region is given by 
3
M
ˆ
E i,
x
æö
=
ç÷
èø
then the correct expression for the potential in
the region is [assume potential at infinity is zero]
(a)
2
M
2x
(b) Mx
2
(c)
4
M
3x
(d)
2
M
x
22. Three capacitors C
1
 = 1 µF , C
2
 = 2 µF and C
3
 = 3
µF are connected as shown in figure, then the
equivalent capacitance between points A and B is
C
1
C
2
C
3
C
E D
B A
(a) 3 µF (b) 4 µF (c) 5 µF (d) 6 µF
23. Two long coaxial and conducting cylinders of
radius a and b are separated by a material of
conductivity s and a constant potential difference
V is maintained between them, by a battery . Then
the current, per unit length of the cylinder flowing
from one cylinder to the other is –
(a)
4
V
ln (b / a)
ps
(b)
4
V
(b a)
ps
+
(c)
2
V
ln (b / a)
ps
(d)
2
V
(b a)
ps
+
24. A wire X is half the diameter and half the length
of a wire Y of similar material. The ratio of
resistance of X to that of Y is
(a) 8 : 1 (b) 4 : 1 (c) 2 : 1 (d) 1 : 1
25. A narrow beam of protons and deuterons, each
having the same momentum, enters a region of
uniform magnetic field directed perpendicular to
their direction of momentum. The ratio of the radii
of the circular paths described by them is
(a) 1 : 2 (b) 1 : 1
(c) 2 : 1 (d) 1 : 3
26. For the circuit (figure), the current is to be
measured. The ammeter shown is a galvanometer
with a resistance R
G
 = 60.00W converted to an
ammeter by a shunt resistance r
s
 = 0.02W. The
value of the current is
A
3.00 V
3.00W
(a) 0.79 A (b) 0.29 A
(c) 0.99 A (d) 0.8 A
27. The susceptibility of a magnetism at 300 K is
1.2 × 10
–5
. The temperature at which the
susceptibility increases to 1.8 × 10
–5
 is
(a) 150 K (b) 200 K (c) 250 K (d) 20 K
28. A coil 10 turns and a resistance of 20W is connected
in series with B.G . of resistance 30W. The coil is
placed with its plane perpendicular to the direction
of a uniform magnetic field of induction 10
–2
 T . If it
is now turned through an angle of 60° about an axis
in its plane. Find the charge induced in the coil.
(Area of a coil = 10
–2
 m²)
(a) 2 × 10
–5
 C (b) 3.2 × 10
–5
 C
(c) 1 × 10
–5
 C (d) 5.5 × 10
–5
 C
29. V oltage V and current i in AC circuit are given by
V = 50 sin (50 t) volt, i = 50 sin 50t mA.
3
p æö
+
ç÷
èø
The power dissipated in the circuit is
(a) 5.0 W (b) 2.5 W
(c) 1.25 W (d) zero
30. Resolving power of the telescope will be more, if
the diameter of the objective is
(a) larger
(b) smaller
(c) it does not depends on diameter
(d) None of these
31. The magnifying power of a telescope is 9. When
it is adjusted for parallel rays, the distance
between the objective and the eye piece is found
to be 20 cm. The focal length of lenses are
(a) 18 cm, 2 cm (b) 11 cm, 9 cm
(c) 10 cm, 10 cm (d) 15 cm, 5 cm
32. The angular size of the central maxima due to a
single slit diffraction is (a ® slit width)
(a)
a
l
(b)
2
a
l
(c)
3
2a
l
(d)
2a
l
33. Find the final intensity of light (I"), if the angle
between the axes of two polaroids is 60°.
I'
Unpolaised
Light
I
0
I"
(a)
0
3I
2
(b)
0
I
2
(c)
0
I
4
(d)
0
I
8
34. The threshold wavelength of the tungsten is 2300
Å. If ultraviolet light of wavelength 1800 Å is
incident on it, then the maximum kinetic energy
of photoelectrons would be about –
(a) 1.49 eV (b) 2.2 e V (c) 3.0 eV  (d) 5.0 eV
35. Graph betwen stopping potential for most
energetic emitted photoelectrons (V
s
) with
frequency (u) of incident radiation on metal is
given below . V alue of AB/BC, in graph is
[where h = plank’s constant, e = electronic
charge]
C
A
B
(V)
S
u
(a)h (b) e (c) h/e (d) e/h
36. If hydrogen atom, an electron jumps from bigger
orbit to smaller orbit so that radius of smaller
orbit is one-fourth of radius of bigger orbit. If
speed of electron in bigger orbit was v , then speed
in smaller orbit is
(a)
v
4
(b)
v
2
(c)v (d) 2v
37. A nucleus of uranium decays at rest into nuclei
of thorium and helium. Then :
(a) the helium nucleus has less momentum than
the thorium nucleus
(b) the helium nucleus has more momentum
than the thorium nucleus
(c) the helium nucleus has less kinetic energy
than the thorium nucleus
(d) the helium nucleus has more kinetic energy
than the thorium nucleus
38. Let binding energy per nucleon of nucleus is
denoted by E
bn
 and radius of nucleus is denoted
as r. If mass number of nuclei A, B and 64 and 125
respectively then
(a)r
A
 < r
B
, E
bnA
 < E
bnB
(b) r
A
 > r
B
, E
bnA
 > E
bnB
(c)
A B bnA bnB
4
r r,EE
5
=<
(d) r
A
 < r
B
, E
bnA
 > E
bnB
39. For a CE transistor amplifier, the audio signal
voltage across the collector resistance of 2.0 kW
is 2.0 V . Suppose the current amplification factor
of the transistor is 100, What should be the value
of R
B
 in series with V
BB
 supply of 2.0V if the dc
base current has to be 10 times the signal current?
(a) 14 kW(b) 18 kW (c) 10 kW(d) 5 kW
40. The combination of gates shown below yields
A
B
X
(a) OR gate (b) NOT gate
(c) XOR gate (d) NAND gate
PART - II : CHEMISTRY
41. The formation of CO and CO
2
 illustrates the law
of
(a) reciprocal proportion
(b) conservation of mass
(c) multiple proportion
(d) constant composition
42. The wave number of the limiting line in Lyman
series of hydrogen is 109678 cm
–1
. The wave
number of the limiting line in Balmer series of He
+
would be :
(a) 54839 cm
–1
(b) 109678 cm
–1
(c) 219356 cm
–1
(d) 438712 cm
–1
Page 5


PART - I : PHYSICS
1. A rifle man, who together with his rifle has a mass
of 100 kg, stands on a smooth surface and fires 10
shots horizontally. Each bullet has a mass 10 g
and a muzzle velocity of  800 ms
–1
. The velocity
which the rifle man attains after  firing 10 shots is
(a) 8 ms
–1
(b) 0.8 ms
–1
(c) 0.08 ms
–1
(d) – 0.8 ms
–1
2. A train accelerating uniformly from rest attains a
maximum speed of 40 ms
–1
 in 20 s. It travels at
the speed for 20 s and is brought to rest with
uniform retardation in further 40 s. What is the
average velocity during the period ?
(a) 80 m/s (b) 25 m/s
(c) 40 m/s (d) 30 m/s
3. A projectile is fired with a velocity u making an
angle q with the horizontal. What is the magnitude
of change in velocity when it is at the highest
point –
(a) u cos q (b) u
(c) u sin q (d) u cos q – u
4. For the equation F = A
a
v
b
d
c
, where F is the force,
A is the area, v is the velocity and d is the density ,
the values of a, b and c are respectively
(a) 1, 2, 1 (b) 2, 1, 1 (c) 1, 1, 2 (d) 0, 1, 1
5. A person with his hand in his pocket is skating
on ice at the rate of 10m/s and describes a circle
of radius 50 m. What is his inclination to vertical:
(g = 10 m/sec
2
)
(a) tan
–1
(½) (b) tan
–1
 (1/5)
(c) tan
–1
 (3/5) (d) tan
–1
(1/10)
6. A small block of mass m is kept on a rough
inclined surface of inclination q fixed in a elevator.
The elevator goes up with a uniform velocity v
and the block does not slide on the wedge. The
work done by the force of friction on the block in
time t will be :
(a) zero (b) mgvt cos
2
q
(c) mgvt sin
2
q (d) mgvt sin 2q
7. An equilateral prism of
mass m rests on a rough
horizontal surface with
coefficient of friction µ.
F
a
a
a
A horizontal force F
is applied on the prism as shown in the figure.
If the coefficient of  friction is sufficiently high
so that the prism does not slide before toppling,
then the minimum force required to topple the
prism is –
(a)
mg
3
(b)
mg
4
(c)
mg
3
m
(d)
mg
4
m
8. A spherically symmetric gravitational system of
particles has a mass density 
0
forrR
0 forrR
r£ ì
r=
í
>
î
where r
0
 is a constant. A test mass can undergo
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 : Mathematics Q. No. 81 to 125
Part IV : (A) English Proficiency Q. No. 126 to 140
  (B) Logical Reasoning Q. No. 141 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
circular motion under the influence of the
gravitational field of particles. Its speed V as a
function of distance r (0 < r < ¥) from the centre
of the system is represented by
(a)
V
R
r
(b)
V
R
r
(c)
V
R
r
(d)
V
R
r
9. The load versus elongation graph for four wires
is shown. The thinnest wire is
S
R
Q
P
Elongation
Load
(a) P (b) Q (c) R (d) S
10. The work done in blowing a soap bubble of
surface tension 0.06 × Nm
–1
 from 2 cm radius to
5 cm radius is
(a) 0.004168 J (b) 0.003168 J
(c) 0.003158 J (d) 0.004568 J
11. The wavelength of radiation emitted by a body
depends upon
(a) the nature of its surface
(b) the area of its surface
(c) the temperature of its surface
(d) All of the above
12. One mole of O
2
 gas having a volume equal to
22.4 Litres at 0°C and 1 atmospheric pressure in
compressed isothermally so that its volume
reduces to 11.2 litres. The work done in this
process is-
(a) 1672.5 J (b) 1728 J
(c) –1728 J (d) –1572.5 J
13. In a thermodynamic process, the pressure of a
fixed mass of a gas is changed in such a manner
that the gas releases 20 J of heat and 8 J of work
is done on the gas. If the initial internal energy of
the gas was 30 J, then the final internal energy
will be
(a) 2 J (b) 42 J
(c) 18 J (d) 58 J
14. In the kinetic theory of gases, which of these
statements is/are true ?
(i) The pressure of a gas is proportional to the
mean speed of the molecules.
(ii) The root mean square speed of the
molecules is proportional to the pressure.
(iii) The rate of diffusion is proportional to the
mean speed of the molecules.
(iv) The mean translational kinetic energy of a
gas is proportional to its kelvin temperature.
(a) (ii) and (iii) only (b) (i), (ii) and (iv) only
(c) (i) and (iii) only (d) (iii) and (iv) only
15. Two balloons are filled one with pure he gas and
other with air respectively. If the pressure and
temperature of these balloons are same, then the
number of molecules per unit volume is
(a) more in He gas filled balloon
(b) same in both balloons
(c) more in air filled balloon
(d) in the ratio 1 : 4
16. Two particles P and Q describe S.H.M. of same
amplitude a, same frequency f along the same
straight line. The maximum distance between the
two particles is a2 .
The initial phase difference between the particle
is –
(a) zero (b) p/2 (c) p/6 (d) p/3
17. A tunnel has been dug through the centre of the
earth and a ball is released in it. It executes S.H.M.
with time period
(a) 42 minutes (b) 1 day
(c) 1 hour (d) 84.6 minutes
18. A sound source, emitting sound of constant
frequency, moves with a constant speed and
crosses a stationary observer. The frequency (n)
of sound heard by the observer  is plotted against
time (t). Which of the following graphs represents
the correct variation ?
(a)
n
t
(b)
n
t
(c)
n
t
(d)
n
t
19. When a string is divided into three segments of
length l
1
, l
2
, and l
3
 the fundamental frequencies
of these three segments are v
1
, v
2
 and v
3
respectively . The original fundamental frequency
(v) of the string is
(a)
1 23
v v vv = ++
(b) v = v
1
 + v
2
 + v
3
(c)
1 23
1 1 11
v v vv
= ++
`
(d)
1 23
1 1 11
v v vv
= ++
20. Two point dipoles 
ˆ
pk and 
p
ˆ
k
2
 are located at
(0, 0, 0) and (1m, 0, 2m) respectively . The resultant
electric field due to the two dipoles at the point
(1m, 0, 0) is
(a)
0
9p
ˆ
k
32pÎ
(b)
0
7p
ˆ
k
32
-
pÎ
(c)
0
7p
ˆ
k
32pÎ
(d) None of these
21. Electric field in the region is given by 
3
M
ˆ
E i,
x
æö
=
ç÷
èø
then the correct expression for the potential in
the region is [assume potential at infinity is zero]
(a)
2
M
2x
(b) Mx
2
(c)
4
M
3x
(d)
2
M
x
22. Three capacitors C
1
 = 1 µF , C
2
 = 2 µF and C
3
 = 3
µF are connected as shown in figure, then the
equivalent capacitance between points A and B is
C
1
C
2
C
3
C
E D
B A
(a) 3 µF (b) 4 µF (c) 5 µF (d) 6 µF
23. Two long coaxial and conducting cylinders of
radius a and b are separated by a material of
conductivity s and a constant potential difference
V is maintained between them, by a battery . Then
the current, per unit length of the cylinder flowing
from one cylinder to the other is –
(a)
4
V
ln (b / a)
ps
(b)
4
V
(b a)
ps
+
(c)
2
V
ln (b / a)
ps
(d)
2
V
(b a)
ps
+
24. A wire X is half the diameter and half the length
of a wire Y of similar material. The ratio of
resistance of X to that of Y is
(a) 8 : 1 (b) 4 : 1 (c) 2 : 1 (d) 1 : 1
25. A narrow beam of protons and deuterons, each
having the same momentum, enters a region of
uniform magnetic field directed perpendicular to
their direction of momentum. The ratio of the radii
of the circular paths described by them is
(a) 1 : 2 (b) 1 : 1
(c) 2 : 1 (d) 1 : 3
26. For the circuit (figure), the current is to be
measured. The ammeter shown is a galvanometer
with a resistance R
G
 = 60.00W converted to an
ammeter by a shunt resistance r
s
 = 0.02W. The
value of the current is
A
3.00 V
3.00W
(a) 0.79 A (b) 0.29 A
(c) 0.99 A (d) 0.8 A
27. The susceptibility of a magnetism at 300 K is
1.2 × 10
–5
. The temperature at which the
susceptibility increases to 1.8 × 10
–5
 is
(a) 150 K (b) 200 K (c) 250 K (d) 20 K
28. A coil 10 turns and a resistance of 20W is connected
in series with B.G . of resistance 30W. The coil is
placed with its plane perpendicular to the direction
of a uniform magnetic field of induction 10
–2
 T . If it
is now turned through an angle of 60° about an axis
in its plane. Find the charge induced in the coil.
(Area of a coil = 10
–2
 m²)
(a) 2 × 10
–5
 C (b) 3.2 × 10
–5
 C
(c) 1 × 10
–5
 C (d) 5.5 × 10
–5
 C
29. V oltage V and current i in AC circuit are given by
V = 50 sin (50 t) volt, i = 50 sin 50t mA.
3
p æö
+
ç÷
èø
The power dissipated in the circuit is
(a) 5.0 W (b) 2.5 W
(c) 1.25 W (d) zero
30. Resolving power of the telescope will be more, if
the diameter of the objective is
(a) larger
(b) smaller
(c) it does not depends on diameter
(d) None of these
31. The magnifying power of a telescope is 9. When
it is adjusted for parallel rays, the distance
between the objective and the eye piece is found
to be 20 cm. The focal length of lenses are
(a) 18 cm, 2 cm (b) 11 cm, 9 cm
(c) 10 cm, 10 cm (d) 15 cm, 5 cm
32. The angular size of the central maxima due to a
single slit diffraction is (a ® slit width)
(a)
a
l
(b)
2
a
l
(c)
3
2a
l
(d)
2a
l
33. Find the final intensity of light (I"), if the angle
between the axes of two polaroids is 60°.
I'
Unpolaised
Light
I
0
I"
(a)
0
3I
2
(b)
0
I
2
(c)
0
I
4
(d)
0
I
8
34. The threshold wavelength of the tungsten is 2300
Å. If ultraviolet light of wavelength 1800 Å is
incident on it, then the maximum kinetic energy
of photoelectrons would be about –
(a) 1.49 eV (b) 2.2 e V (c) 3.0 eV  (d) 5.0 eV
35. Graph betwen stopping potential for most
energetic emitted photoelectrons (V
s
) with
frequency (u) of incident radiation on metal is
given below . V alue of AB/BC, in graph is
[where h = plank’s constant, e = electronic
charge]
C
A
B
(V)
S
u
(a)h (b) e (c) h/e (d) e/h
36. If hydrogen atom, an electron jumps from bigger
orbit to smaller orbit so that radius of smaller
orbit is one-fourth of radius of bigger orbit. If
speed of electron in bigger orbit was v , then speed
in smaller orbit is
(a)
v
4
(b)
v
2
(c)v (d) 2v
37. A nucleus of uranium decays at rest into nuclei
of thorium and helium. Then :
(a) the helium nucleus has less momentum than
the thorium nucleus
(b) the helium nucleus has more momentum
than the thorium nucleus
(c) the helium nucleus has less kinetic energy
than the thorium nucleus
(d) the helium nucleus has more kinetic energy
than the thorium nucleus
38. Let binding energy per nucleon of nucleus is
denoted by E
bn
 and radius of nucleus is denoted
as r. If mass number of nuclei A, B and 64 and 125
respectively then
(a)r
A
 < r
B
, E
bnA
 < E
bnB
(b) r
A
 > r
B
, E
bnA
 > E
bnB
(c)
A B bnA bnB
4
r r,EE
5
=<
(d) r
A
 < r
B
, E
bnA
 > E
bnB
39. For a CE transistor amplifier, the audio signal
voltage across the collector resistance of 2.0 kW
is 2.0 V . Suppose the current amplification factor
of the transistor is 100, What should be the value
of R
B
 in series with V
BB
 supply of 2.0V if the dc
base current has to be 10 times the signal current?
(a) 14 kW(b) 18 kW (c) 10 kW(d) 5 kW
40. The combination of gates shown below yields
A
B
X
(a) OR gate (b) NOT gate
(c) XOR gate (d) NAND gate
PART - II : CHEMISTRY
41. The formation of CO and CO
2
 illustrates the law
of
(a) reciprocal proportion
(b) conservation of mass
(c) multiple proportion
(d) constant composition
42. The wave number of the limiting line in Lyman
series of hydrogen is 109678 cm
–1
. The wave
number of the limiting line in Balmer series of He
+
would be :
(a) 54839 cm
–1
(b) 109678 cm
–1
(c) 219356 cm
–1
(d) 438712 cm
–1
43. The valency shell of element A contains 3
electrons while the valency shell of element B
contains 6 electrons. If A combines with B, the
probable formula of the compound formed will be
(a) AB
2
(b) A
2
B
(c)A
2
B
3
(d)   A
3
B
2
44. The enthalpy of sublimation of aluminium is 330
kJ/mol. Its I
st
, II
nd
 and III
rd
 ionization enthalpies
are 580, 1820 and 2740 kJ respectively . How much
heat has too be supplied (in kJ) to convert 13.5 g
of aluminium into Al
3+
 ions and electrons at 298 k
(a) 5470 (b) 2735
(c) 4105 (d) 3765
45. Which one of the following pairs is isostructural
(i.e., having the same shape and hybridization)?
(a)
33
BCl and BrCl
-
éù
ëû
(b)
33
NH and NO
-
éù
ëû
(c) [ ]
33
NF and BF
(d)
44
BF and NH
-+
éù
ëû
46. N
2
 and O
2
 are converted into mono anions, N
2
–
and O
2
–
 respectively. Which of the following
statements is wrong ?
(a) In N
2
, the N—N bond weakens
(b) In O
2
, the O—O bond order increases
(c) In O
2
, bond length decreases
(d) N
2
–
 becomes diamagnetic
47. If the enthalpy of vaporization of water is 186.5
kJmol
–1
, the entropy if its vaporization will be :
(a) 0.5 k JK
–1
mol
–1
(b) 1.0 k JK
–1
mol
–1
(c) 1.5 k JK
–1
mol
–1
(d) 2.0 k JK
–1
mol
–1
48. The heats of neutralisation of CH
3
COOH,
HCOOH, HCN and H
2
S are – 13.2, – 13.4, – 2.9
and – 3.8 kCal per equivalent respectively.
Arrange the acids in increasing order of acidic
strength.
(a) HCOOH > COOH CH
3
 > S H
2
 > HCN
(b) COOH CH
3
 > HCOOH > S H
2
 > HCN
(c) S H
2
 > HCOOH > COOH CH
3
 > HCN
(d) HCOOH > S H
2
 > COOH CH
3
 > HCN
49. K
c
 for the the reaction, [Ag(CN)
2
]
–
 ?Ag
+
 + 2CN
–
,
the equillibrium constant at 25°C is 4.0 × 10
–19
,
then the silver ion concentration in a solution
which was originally 0.1 molar in KCN and 0.03
molar in AgNO
3
 is :
(a) 7.5 × 10
18
(b) 7.5 × 10
–19
(c) 7.5 × 10
19
(d) 7.5 × 10
–18
50. The ratio of oxidation states of Cl in potassium
chloride to that in potassium chlorate is
(a)
1
5
+
(b)
1
5
-
(c)
2
5
-
(d)
3
5
+
51. Which of the following among alkali metal is most
reactive ?
(a) Na (b) K
(c) Rb (d) Cs
52. Which of the following compounds has wrong
IUP AC name?
(a) CH
3 
– CH
2 
– CH
2
 – COO – CH
2
CH
3
® Ethyl butanoate
(b) CH – CH – CH – CHO
32
CH
3
|
® 3-Methyl-butanal
(c) CH CH CH CH
3 3
||
OH CH
3
- --
® 2-Methyl-3-butanol
(d)
O
||
CH CH C CH CH
3 23
|
CH
3
- ---
® 2-Methyl-3-pentanone
53. The compound which gives the most stable
carbonium ion on dehydration is
(a) CH
3
CH(CH
3
)CH
2
OH
(b) (CH
3
)
3
COH
(c) CH
2
 = CHCH
2
CH
2
OH
(d) CH
3
CHOHCH
2
CH
3
54. The correct order of increasing C - O bond length
CO, 
2
3
CO
-
, CO
2
 is:
(a) CO < CO
2
 < 
2
3
CO
-
(b) CO
2
 < 
2
3
CO
-
 < CO
(c) CO <  
2
3
CO
-
< CO
2
(d)
2
3
CO
-
< CO
3
 < CO
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