BITSAT Past Year Paper- 2012 JEE Notes | EduRev

BITSAT Mock Tests Series & Past Year Papers

JEE : BITSAT Past Year Paper- 2012 JEE Notes | EduRev

 Page 1


PART - I : PHYSICS
1. What is the moment of inertia of a solid sphere of
density r and radius R about its diameter?
(a)
r
5
R
176
105
(b)
r
2
R
176
105
(c)
r
5
R
105
176
(d)
r
2
R
105
176
2. A body moves with uniform acceleration, then
which of the following graph is correct ?
(a)
a
t
(b)
a
t
(c)
a
t
(d)
a
t
3. A projectile can have the same range R for two
angles of projection. If t
1
 and t
2
 be the times of
flight in two cases, then what is the product of
two times of flight?
(a)t
1
t
2 
µ R (b) t
1
t
2 
µ R
2
(c)t
1
t
2 
µ1/R (d) t
1
t
2 
µ 1/R
2
4. A horizontal overhead powerline is at  height of
4m from the ground and carries a current of 100A
from east to west. The magnetic field directly
below it on the ground is (m
0
 = 4p × 10
–7
 Tm A
–1
)
(a) 2.5×10
–7
 T southward
(b) 5 × 10
–6
 T northward
(c) 5 × 10
–6
 T southward
(d) 2.5 × 10
–7
 T northward
5. A man of mass 100 kg. is standing on a platform
of mass 200 kg. which is kept on a smooth ice
surface. If the man starts moving on the platform
with a speed 30 m/sec relative to the platform then
calculate with what velocity relative to the ice the
platform will recoil?
(a) 5 m/sec (b) 10 m/sec
(c) 15 m/sec (d) 20 m/sec
6. If the unit of force and length be each increased
by four times, then the unit of energy is increased
by
(a) 16 times (b) 8 times
(c) 2 times (d) 4 times
7. Which of the following must be known in order
to determine the power output of an automobile?
(a) Final velocity and height
(b) Mass and amount of work performed
(c) Force exerted and distance of motion
(d) Work performed and elapsed time of work
8. If the force is given by F = at + bt
2
 with t as time.
The dimensions of a and b are
( a) [MLT
–4
] and [ML T
–2
]
(b) [ML T
–3
] and [ML T
–4
]
(c) [ML
2
T
–3
] and [ML
2
T
–2
]
(d) [ML
2
T
–3
] and [ML
3
T
–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 : 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. What is the moment of inertia of a solid sphere of
density r and radius R about its diameter?
(a)
r
5
R
176
105
(b)
r
2
R
176
105
(c)
r
5
R
105
176
(d)
r
2
R
105
176
2. A body moves with uniform acceleration, then
which of the following graph is correct ?
(a)
a
t
(b)
a
t
(c)
a
t
(d)
a
t
3. A projectile can have the same range R for two
angles of projection. If t
1
 and t
2
 be the times of
flight in two cases, then what is the product of
two times of flight?
(a)t
1
t
2 
µ R (b) t
1
t
2 
µ R
2
(c)t
1
t
2 
µ1/R (d) t
1
t
2 
µ 1/R
2
4. A horizontal overhead powerline is at  height of
4m from the ground and carries a current of 100A
from east to west. The magnetic field directly
below it on the ground is (m
0
 = 4p × 10
–7
 Tm A
–1
)
(a) 2.5×10
–7
 T southward
(b) 5 × 10
–6
 T northward
(c) 5 × 10
–6
 T southward
(d) 2.5 × 10
–7
 T northward
5. A man of mass 100 kg. is standing on a platform
of mass 200 kg. which is kept on a smooth ice
surface. If the man starts moving on the platform
with a speed 30 m/sec relative to the platform then
calculate with what velocity relative to the ice the
platform will recoil?
(a) 5 m/sec (b) 10 m/sec
(c) 15 m/sec (d) 20 m/sec
6. If the unit of force and length be each increased
by four times, then the unit of energy is increased
by
(a) 16 times (b) 8 times
(c) 2 times (d) 4 times
7. Which of the following must be known in order
to determine the power output of an automobile?
(a) Final velocity and height
(b) Mass and amount of work performed
(c) Force exerted and distance of motion
(d) Work performed and elapsed time of work
8. If the force is given by F = at + bt
2
 with t as time.
The dimensions of a and b are
( a) [MLT
–4
] and [ML T
–2
]
(b) [ML T
–3
] and [ML T
–4
]
(c) [ML
2
T
–3
] and [ML
2
T
–2
]
(d) [ML
2
T
–3
] and [ML
3
T
–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 : 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
9. A wheel of radius R rolls on the ground with a
uniform velocity v. The relative acceleration of
topmost point of the wheel with respect to the
bottom most point is
(a)
2
v
R
(b)
2
2v
R
A
B
v²
R
v²
R
(c)
2
v
2R
(d)
2
4v
R
10. If the radius of the earth were to shrink by one
per cent, its mass remaining the same, the value
of g on the earth’s surface would
(a) increase by 0.5% (b) increase by 2%
(c) decrease by 0.5% (d) decrease by 2%
11. The Young’s modulus of a perfectly rigid body
is
(a) unity (b) zero (c) infinity
(d) some finite non-zero constant
12. An ice block floats in a liquid whose density is
less than water. A part of block is outside the
liquid. When whole of ice has melted, the liquid
level will
(a) rise
(b) go down
(c) remain same
(d) first rise then go down
13. A large drop of oil (density 0.8 g/cm
3
 and
viscosity h
0
) floats up through a column of another
liquid (density 1.2 g/cm
3 
and viscosity h
L
).
Assuming that the two liquids do not mix, the
velocity with which the oil drop rises will depend
on :
(a) h
0
 only (b) h
L
only
(c) both on h
0
 and h
L
(d) neither h
0
 nor h
L
14. A solid body of constant heat capacity 1 J/°C is
being heated by keeping it in contact with
reservoirs in two ways :
(i) Sequentially keeping in contact with 2
reservoirs such that each reservoir supplies
same amount of heat.
(ii) Sequentially keeping in contact with 8
reservoirs such that each reservoir supplies
same amount of heat.
In both the cases body is brought from initial
temperature 100°C to final temperature 200°C.
Entropy change of the body in the two cases
respectively is :
(a) ln2, 2ln2 (b) 2ln2, 8ln2
(c) ln2, 4ln2 (d) ln2, ln2
15. Which of the following process is possible
according to the first law of thermodynamics?
(a) W > 0, Q < 0 and dU = 0
(b) W > 0, Q < 0 and dU > 0
(c) W > 0, Q < 0 and dU < 0
(d) W < 0, Q > 0 and dU < 0
16. For an isothermal expansion of a perfect gas, the
value of 
P
P
D
 is equal to
(a)
1/2
–
V
V
D
g
(b)
–
V
V
D
(c)
–
V
V
D
g
(d)
2
–
V
V
D
g
17. A sample of ideal monoatomic gas is taken round
the cycle ABCA as shown in the figure. The work
done during the cycle is
V
p
A (p, V) C (p, 3V)
B (4p, 3V)
(a) 3 pV (b) zero (c) 9 pV (d) 6 pV
18. The average translational kinetic energy of O
2
(molar mass 32) molecules at a particular
temperature is 0.048 eV . The translational kinetic
energy of N
2
 (molar mass 28) molecules in eV at
the same temperature is
(a) 0.0015 (b) 0.003 (c) 0.048 (d) 0.768
19. For a gas if ratio of specific heats at constant
pressure and volume is g then value of degrees
of freedom is
(a)
3 –1
2 –1
g
g
(b)
2
–1 g
(c)
9
( – 1)
2
g (d) 
25
( – 1)
2
g
20. One end of a long metallic wire of length L tied to
the ceiling. The other end is tied with a massless
spring of spring constant K. A mass hangs freely
from the free end of the spring. The area of cross
section and the young’s modulus of the wire are
A and Y respectively . If the mass slightly pulled
down and released, it will oscillate with a time
period T equal to :
(a) 2 (m / K) p
(b) 2 m(YA KL) / (YAK) p+
(c) 2 (m YA / KL) p
(d) 2 (mL / YA) p
Page 3


PART - I : PHYSICS
1. What is the moment of inertia of a solid sphere of
density r and radius R about its diameter?
(a)
r
5
R
176
105
(b)
r
2
R
176
105
(c)
r
5
R
105
176
(d)
r
2
R
105
176
2. A body moves with uniform acceleration, then
which of the following graph is correct ?
(a)
a
t
(b)
a
t
(c)
a
t
(d)
a
t
3. A projectile can have the same range R for two
angles of projection. If t
1
 and t
2
 be the times of
flight in two cases, then what is the product of
two times of flight?
(a)t
1
t
2 
µ R (b) t
1
t
2 
µ R
2
(c)t
1
t
2 
µ1/R (d) t
1
t
2 
µ 1/R
2
4. A horizontal overhead powerline is at  height of
4m from the ground and carries a current of 100A
from east to west. The magnetic field directly
below it on the ground is (m
0
 = 4p × 10
–7
 Tm A
–1
)
(a) 2.5×10
–7
 T southward
(b) 5 × 10
–6
 T northward
(c) 5 × 10
–6
 T southward
(d) 2.5 × 10
–7
 T northward
5. A man of mass 100 kg. is standing on a platform
of mass 200 kg. which is kept on a smooth ice
surface. If the man starts moving on the platform
with a speed 30 m/sec relative to the platform then
calculate with what velocity relative to the ice the
platform will recoil?
(a) 5 m/sec (b) 10 m/sec
(c) 15 m/sec (d) 20 m/sec
6. If the unit of force and length be each increased
by four times, then the unit of energy is increased
by
(a) 16 times (b) 8 times
(c) 2 times (d) 4 times
7. Which of the following must be known in order
to determine the power output of an automobile?
(a) Final velocity and height
(b) Mass and amount of work performed
(c) Force exerted and distance of motion
(d) Work performed and elapsed time of work
8. If the force is given by F = at + bt
2
 with t as time.
The dimensions of a and b are
( a) [MLT
–4
] and [ML T
–2
]
(b) [ML T
–3
] and [ML T
–4
]
(c) [ML
2
T
–3
] and [ML
2
T
–2
]
(d) [ML
2
T
–3
] and [ML
3
T
–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 : 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
9. A wheel of radius R rolls on the ground with a
uniform velocity v. The relative acceleration of
topmost point of the wheel with respect to the
bottom most point is
(a)
2
v
R
(b)
2
2v
R
A
B
v²
R
v²
R
(c)
2
v
2R
(d)
2
4v
R
10. If the radius of the earth were to shrink by one
per cent, its mass remaining the same, the value
of g on the earth’s surface would
(a) increase by 0.5% (b) increase by 2%
(c) decrease by 0.5% (d) decrease by 2%
11. The Young’s modulus of a perfectly rigid body
is
(a) unity (b) zero (c) infinity
(d) some finite non-zero constant
12. An ice block floats in a liquid whose density is
less than water. A part of block is outside the
liquid. When whole of ice has melted, the liquid
level will
(a) rise
(b) go down
(c) remain same
(d) first rise then go down
13. A large drop of oil (density 0.8 g/cm
3
 and
viscosity h
0
) floats up through a column of another
liquid (density 1.2 g/cm
3 
and viscosity h
L
).
Assuming that the two liquids do not mix, the
velocity with which the oil drop rises will depend
on :
(a) h
0
 only (b) h
L
only
(c) both on h
0
 and h
L
(d) neither h
0
 nor h
L
14. A solid body of constant heat capacity 1 J/°C is
being heated by keeping it in contact with
reservoirs in two ways :
(i) Sequentially keeping in contact with 2
reservoirs such that each reservoir supplies
same amount of heat.
(ii) Sequentially keeping in contact with 8
reservoirs such that each reservoir supplies
same amount of heat.
In both the cases body is brought from initial
temperature 100°C to final temperature 200°C.
Entropy change of the body in the two cases
respectively is :
(a) ln2, 2ln2 (b) 2ln2, 8ln2
(c) ln2, 4ln2 (d) ln2, ln2
15. Which of the following process is possible
according to the first law of thermodynamics?
(a) W > 0, Q < 0 and dU = 0
(b) W > 0, Q < 0 and dU > 0
(c) W > 0, Q < 0 and dU < 0
(d) W < 0, Q > 0 and dU < 0
16. For an isothermal expansion of a perfect gas, the
value of 
P
P
D
 is equal to
(a)
1/2
–
V
V
D
g
(b)
–
V
V
D
(c)
–
V
V
D
g
(d)
2
–
V
V
D
g
17. A sample of ideal monoatomic gas is taken round
the cycle ABCA as shown in the figure. The work
done during the cycle is
V
p
A (p, V) C (p, 3V)
B (4p, 3V)
(a) 3 pV (b) zero (c) 9 pV (d) 6 pV
18. The average translational kinetic energy of O
2
(molar mass 32) molecules at a particular
temperature is 0.048 eV . The translational kinetic
energy of N
2
 (molar mass 28) molecules in eV at
the same temperature is
(a) 0.0015 (b) 0.003 (c) 0.048 (d) 0.768
19. For a gas if ratio of specific heats at constant
pressure and volume is g then value of degrees
of freedom is
(a)
3 –1
2 –1
g
g
(b)
2
–1 g
(c)
9
( – 1)
2
g (d) 
25
( – 1)
2
g
20. One end of a long metallic wire of length L tied to
the ceiling. The other end is tied with a massless
spring of spring constant K. A mass hangs freely
from the free end of the spring. The area of cross
section and the young’s modulus of the wire are
A and Y respectively . If the mass slightly pulled
down and released, it will oscillate with a time
period T equal to :
(a) 2 (m / K) p
(b) 2 m(YA KL) / (YAK) p+
(c) 2 (m YA / KL) p
(d) 2 (mL / YA) p
21. The transverse displacement y(x, t) of a wave on
a string is given by 
–( 2)
22
( ,)
ax bt ab xt
yxte
++
=
This represents a
(a) wave moving in – x direction, speed 
b
a
(b) standing wave of frequency b
(c) standing wave of frequency 
1
b
(d) wave moving in + x direction, speed 
a
b
22. A sound souorce is moving towards stationary
listener with 
1
th
10
 of the speed of sound. The
ratio of apparent to read frequency is
(a)  
2
9
10
æö
ç÷
èø
(b)  
10
9
æö
ç÷
èø
(c)  
11
10
æö
ç÷
èø
(d)
2
11
10
æö
ç÷
èø
23. In a region of space having a uniform electric
field E, a hemispherical bowl of radius r is placed.
The electric flux f through the bowl is
(a)2p R E (b) 4p R
2
E (c)2pR
2
E (d) pR
2
E
24. The electric field intensity just sufficient to
balance the earth’s gravitational attraction on an
electron will be: (given mass and charge of an
electron respectively are 9.1 × 10
–31
 kg and 1.6 ×
10
–19
 C.)
(a) –5.6 × 10
–11
 N/C (b) –4.8 × 10
–15
 N / C
(c) –1.6 × 10
–19
 N/C (d) –3.2 × 10
–19
 N / C
25. Two capacitors C
1
 and C
2
 are charged to 120 V
and 200 V respectively. It is found that by
connecting them together the potential on each
one can be made zero. Then
(a)5C
1
 = 3C
2
(b) 3C
1
 = 5C
2
(c)3C
1
 + 5C
2
 = 0 (d) 9C
1
 = 4C
2
26. Three voltmeters A, B and C having resistances
R, 1.5 R and 3R, respectively, are connected as
shown. When some potential difference is
applied between X and Y , the voltmeter readings
are V
A
, V
B
 and V
C
 respectively . Then –
B
C
A X Y
(a)V
A
 ¹ V
B
 = V
C
(b) V
A
 = V
B
 ¹ V
C
(c)V
A
 ¹ V
B
 ¹ V
C
(d) V
A
 = V
B
 = V
C
27. The range of the particle when launched at an
angle of 15º with the horizontal is 1.5 km. What is
the range of the projectile when launched at an
angle of 45º to the horizontal.
(a) 1.5 km (b) 3.0 km (c) 6.0 km (d)   0.75 km
28. If m is magnetic moment and B is the magnetic
field, then the torque is given by
(a) . mB
r
r
(b)
||
||
m
B
r
r
(c) mB ´
r
r
(d) | |.|| mB
r
r
29. Magnetic moment of bar magnet is M. The work
done to turn the magnet by 90° of magnet in
direction of magnetic field B will be
(a) zero (b)
1
2
MB
(c) 2 MB (d) MB
30. The laws of electromagnetic induction have been
used in the construction of a
(a) galvanometer (b) voltmeter
(c) electric motor (d) generator
31. The impedance of a circuit consists of 3 W
resistance and 4 W reactance. The power factor of
the circuit is
(a) 0.4 (b) 0.6 (c) 0.8 (d) 1.0
32. The r.m.s. value of potential difference V shown
in the figure is
V
V
0
O
T/2 T
t
(a)V
0
(b)
0
V /2
(c)V
0
/2 (d)
0
V /3
33. A ray of light is incident at the glass-water
interface at an angle i, it emerges finally parallel to
the surface of water, then the value of m
g
 would
be
(a) (4/3)sini
Water
Air
Glass
r
r
i
(b) 1/sini
(c) 4/3
(d) 1
Page 4


PART - I : PHYSICS
1. What is the moment of inertia of a solid sphere of
density r and radius R about its diameter?
(a)
r
5
R
176
105
(b)
r
2
R
176
105
(c)
r
5
R
105
176
(d)
r
2
R
105
176
2. A body moves with uniform acceleration, then
which of the following graph is correct ?
(a)
a
t
(b)
a
t
(c)
a
t
(d)
a
t
3. A projectile can have the same range R for two
angles of projection. If t
1
 and t
2
 be the times of
flight in two cases, then what is the product of
two times of flight?
(a)t
1
t
2 
µ R (b) t
1
t
2 
µ R
2
(c)t
1
t
2 
µ1/R (d) t
1
t
2 
µ 1/R
2
4. A horizontal overhead powerline is at  height of
4m from the ground and carries a current of 100A
from east to west. The magnetic field directly
below it on the ground is (m
0
 = 4p × 10
–7
 Tm A
–1
)
(a) 2.5×10
–7
 T southward
(b) 5 × 10
–6
 T northward
(c) 5 × 10
–6
 T southward
(d) 2.5 × 10
–7
 T northward
5. A man of mass 100 kg. is standing on a platform
of mass 200 kg. which is kept on a smooth ice
surface. If the man starts moving on the platform
with a speed 30 m/sec relative to the platform then
calculate with what velocity relative to the ice the
platform will recoil?
(a) 5 m/sec (b) 10 m/sec
(c) 15 m/sec (d) 20 m/sec
6. If the unit of force and length be each increased
by four times, then the unit of energy is increased
by
(a) 16 times (b) 8 times
(c) 2 times (d) 4 times
7. Which of the following must be known in order
to determine the power output of an automobile?
(a) Final velocity and height
(b) Mass and amount of work performed
(c) Force exerted and distance of motion
(d) Work performed and elapsed time of work
8. If the force is given by F = at + bt
2
 with t as time.
The dimensions of a and b are
( a) [MLT
–4
] and [ML T
–2
]
(b) [ML T
–3
] and [ML T
–4
]
(c) [ML
2
T
–3
] and [ML
2
T
–2
]
(d) [ML
2
T
–3
] and [ML
3
T
–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 : 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
9. A wheel of radius R rolls on the ground with a
uniform velocity v. The relative acceleration of
topmost point of the wheel with respect to the
bottom most point is
(a)
2
v
R
(b)
2
2v
R
A
B
v²
R
v²
R
(c)
2
v
2R
(d)
2
4v
R
10. If the radius of the earth were to shrink by one
per cent, its mass remaining the same, the value
of g on the earth’s surface would
(a) increase by 0.5% (b) increase by 2%
(c) decrease by 0.5% (d) decrease by 2%
11. The Young’s modulus of a perfectly rigid body
is
(a) unity (b) zero (c) infinity
(d) some finite non-zero constant
12. An ice block floats in a liquid whose density is
less than water. A part of block is outside the
liquid. When whole of ice has melted, the liquid
level will
(a) rise
(b) go down
(c) remain same
(d) first rise then go down
13. A large drop of oil (density 0.8 g/cm
3
 and
viscosity h
0
) floats up through a column of another
liquid (density 1.2 g/cm
3 
and viscosity h
L
).
Assuming that the two liquids do not mix, the
velocity with which the oil drop rises will depend
on :
(a) h
0
 only (b) h
L
only
(c) both on h
0
 and h
L
(d) neither h
0
 nor h
L
14. A solid body of constant heat capacity 1 J/°C is
being heated by keeping it in contact with
reservoirs in two ways :
(i) Sequentially keeping in contact with 2
reservoirs such that each reservoir supplies
same amount of heat.
(ii) Sequentially keeping in contact with 8
reservoirs such that each reservoir supplies
same amount of heat.
In both the cases body is brought from initial
temperature 100°C to final temperature 200°C.
Entropy change of the body in the two cases
respectively is :
(a) ln2, 2ln2 (b) 2ln2, 8ln2
(c) ln2, 4ln2 (d) ln2, ln2
15. Which of the following process is possible
according to the first law of thermodynamics?
(a) W > 0, Q < 0 and dU = 0
(b) W > 0, Q < 0 and dU > 0
(c) W > 0, Q < 0 and dU < 0
(d) W < 0, Q > 0 and dU < 0
16. For an isothermal expansion of a perfect gas, the
value of 
P
P
D
 is equal to
(a)
1/2
–
V
V
D
g
(b)
–
V
V
D
(c)
–
V
V
D
g
(d)
2
–
V
V
D
g
17. A sample of ideal monoatomic gas is taken round
the cycle ABCA as shown in the figure. The work
done during the cycle is
V
p
A (p, V) C (p, 3V)
B (4p, 3V)
(a) 3 pV (b) zero (c) 9 pV (d) 6 pV
18. The average translational kinetic energy of O
2
(molar mass 32) molecules at a particular
temperature is 0.048 eV . The translational kinetic
energy of N
2
 (molar mass 28) molecules in eV at
the same temperature is
(a) 0.0015 (b) 0.003 (c) 0.048 (d) 0.768
19. For a gas if ratio of specific heats at constant
pressure and volume is g then value of degrees
of freedom is
(a)
3 –1
2 –1
g
g
(b)
2
–1 g
(c)
9
( – 1)
2
g (d) 
25
( – 1)
2
g
20. One end of a long metallic wire of length L tied to
the ceiling. The other end is tied with a massless
spring of spring constant K. A mass hangs freely
from the free end of the spring. The area of cross
section and the young’s modulus of the wire are
A and Y respectively . If the mass slightly pulled
down and released, it will oscillate with a time
period T equal to :
(a) 2 (m / K) p
(b) 2 m(YA KL) / (YAK) p+
(c) 2 (m YA / KL) p
(d) 2 (mL / YA) p
21. The transverse displacement y(x, t) of a wave on
a string is given by 
–( 2)
22
( ,)
ax bt ab xt
yxte
++
=
This represents a
(a) wave moving in – x direction, speed 
b
a
(b) standing wave of frequency b
(c) standing wave of frequency 
1
b
(d) wave moving in + x direction, speed 
a
b
22. A sound souorce is moving towards stationary
listener with 
1
th
10
 of the speed of sound. The
ratio of apparent to read frequency is
(a)  
2
9
10
æö
ç÷
èø
(b)  
10
9
æö
ç÷
èø
(c)  
11
10
æö
ç÷
èø
(d)
2
11
10
æö
ç÷
èø
23. In a region of space having a uniform electric
field E, a hemispherical bowl of radius r is placed.
The electric flux f through the bowl is
(a)2p R E (b) 4p R
2
E (c)2pR
2
E (d) pR
2
E
24. The electric field intensity just sufficient to
balance the earth’s gravitational attraction on an
electron will be: (given mass and charge of an
electron respectively are 9.1 × 10
–31
 kg and 1.6 ×
10
–19
 C.)
(a) –5.6 × 10
–11
 N/C (b) –4.8 × 10
–15
 N / C
(c) –1.6 × 10
–19
 N/C (d) –3.2 × 10
–19
 N / C
25. Two capacitors C
1
 and C
2
 are charged to 120 V
and 200 V respectively. It is found that by
connecting them together the potential on each
one can be made zero. Then
(a)5C
1
 = 3C
2
(b) 3C
1
 = 5C
2
(c)3C
1
 + 5C
2
 = 0 (d) 9C
1
 = 4C
2
26. Three voltmeters A, B and C having resistances
R, 1.5 R and 3R, respectively, are connected as
shown. When some potential difference is
applied between X and Y , the voltmeter readings
are V
A
, V
B
 and V
C
 respectively . Then –
B
C
A X Y
(a)V
A
 ¹ V
B
 = V
C
(b) V
A
 = V
B
 ¹ V
C
(c)V
A
 ¹ V
B
 ¹ V
C
(d) V
A
 = V
B
 = V
C
27. The range of the particle when launched at an
angle of 15º with the horizontal is 1.5 km. What is
the range of the projectile when launched at an
angle of 45º to the horizontal.
(a) 1.5 km (b) 3.0 km (c) 6.0 km (d)   0.75 km
28. If m is magnetic moment and B is the magnetic
field, then the torque is given by
(a) . mB
r
r
(b)
||
||
m
B
r
r
(c) mB ´
r
r
(d) | |.|| mB
r
r
29. Magnetic moment of bar magnet is M. The work
done to turn the magnet by 90° of magnet in
direction of magnetic field B will be
(a) zero (b)
1
2
MB
(c) 2 MB (d) MB
30. The laws of electromagnetic induction have been
used in the construction of a
(a) galvanometer (b) voltmeter
(c) electric motor (d) generator
31. The impedance of a circuit consists of 3 W
resistance and 4 W reactance. The power factor of
the circuit is
(a) 0.4 (b) 0.6 (c) 0.8 (d) 1.0
32. The r.m.s. value of potential difference V shown
in the figure is
V
V
0
O
T/2 T
t
(a)V
0
(b)
0
V /2
(c)V
0
/2 (d)
0
V /3
33. A ray of light is incident at the glass-water
interface at an angle i, it emerges finally parallel to
the surface of water, then the value of m
g
 would
be
(a) (4/3)sini
Water
Air
Glass
r
r
i
(b) 1/sini
(c) 4/3
(d) 1
34. A mica slit of thickness t and refractive index µ is
introduce d in the ra y from the firs t s ourc e S
1
. By
how much distance of fringes pattern will be
displaced ?
(a)
d
( 1)t
D
m- (b)
D
( 1)t
d
m-
(c)
d
( 1)D m-
(d)
D
( 1)
d
m-
35. In a Y oung’s double slit experiment the angular
width of a fringe formed on a distant screen is 1°.
The wavelength fo the light used is 6280 Å. What
is the distance between the two coherent sources?
(a) 0.036 mm (b) 0.12 mm
(c) 6 mm (d) 4 m m
36. A light having wavelength 300 nm fall on a metal
surface. The work function of metal is 2.54 eV ,
what is stopping potential ?
(a) 2 .3 V (b) 2.59 V (c) 1.59 V (d) 1.29 V
37. If the total binding energies of 
24
12
H, He,
56 235
26 92
Fe&U nuclei are 2.22, 28.3, 492 and 1786
MeV respectively, identify the most stable
nucleus of the following.
(a)
56
26
Fe (b)
2
1
H
(c)
235
92
U (d)
4
2
He
38. An oscillator is nothing but an amplifer with
(a) positive feedback
(b) negative feedback
(c) large gain
(d) no feedback
39. In an experiment on photoelectric effect photons
of wavelength 300 nm eject electrons from a metal
of work function 2.25eV. A photon of energy
equal to that of the most energetic electron
corresponds to the following transition in the
hydrogen atom:
(a) n = 2 to n = 1 state
(b) n = 3 to n = 1 state
(c) n = 3 to n = 2 state
(d) n = 4 to n = 3 state
40. A letter 'A' is constructed of a uniform wire with
resistance 1.0 W per cm, The sides of the letter
are 20 cm and the cross piece in the middle is 10
cm long. The apex angle is 60. The resistance
between the  ends of the legs is close to:
(a) 50.0 W (b) 10 W (c) 36.7 W (d) 26.7 W
PART - II : CHEMISTRY
41. Number of atoms of He in 100 amu of He (atomic
wt. of He is 4) are :
(a) 25 (b) 1 00
(c) 50 (d) 100 × 6 × 10
–23
42. If the radius of H is 0.53 Å, then what will be the
radius of 
3
Li
2+
 ?
(a) 0.17 Å (b) 0.36 Å
(c) 0.53 Å (d) 0.59 Å
43. Which of the following does not have valence
electron in 3d-subshell?
(a) Fe (III) (b) Mn (II)
(c) Cr (I) (d) P (0)
44. The vapour pressure of
 
2
NO
OH
 is higher than 
2
N O
OH
due to
(a) Dipole moment
(b) Dipole- dipole interaction
(c) H – bonding
(d) Lattice structure
45. An ideal gas can’t be liquefied because
(a) its critical temperature is always above 0°C
(b) its molecules are relatively smaller in size
(c) it solidifies before becoming a liquid
(d) forces operated between its molecules are
negligible
46. In which of the following reactions, standard
entropy change (DS°) is positive and standard
Gibb’s energy change (DG°) decreases sharply
with increasing temperature ?
(a) C (graphite) + 
1
2
O
2
(g) ® CO(g)
(b) CO(g) + 
1
2
O
2
(g) ® CO
2
(g)
(c) Mg(s) + 
1
2
O
2
(g) ® MgO(s)
(d)
1
2
C (graphite) +
1
2
O
2
(g) ® 
1
2
CO
2
(g)
47. Bond enthalpies of H
2
, X
2
 and HX are in the ratio
2 : 1 : 2. If enthalpy of formation of HX is –50 kJ
mol
–1
, the bond enthalpy of X
2
 is
(a) 100 kJ mol
–1
(b) 300 kJ mol
–1
(c) 200 kJ mol
–1
(d) 400 kJ mol
–1
Page 5


PART - I : PHYSICS
1. What is the moment of inertia of a solid sphere of
density r and radius R about its diameter?
(a)
r
5
R
176
105
(b)
r
2
R
176
105
(c)
r
5
R
105
176
(d)
r
2
R
105
176
2. A body moves with uniform acceleration, then
which of the following graph is correct ?
(a)
a
t
(b)
a
t
(c)
a
t
(d)
a
t
3. A projectile can have the same range R for two
angles of projection. If t
1
 and t
2
 be the times of
flight in two cases, then what is the product of
two times of flight?
(a)t
1
t
2 
µ R (b) t
1
t
2 
µ R
2
(c)t
1
t
2 
µ1/R (d) t
1
t
2 
µ 1/R
2
4. A horizontal overhead powerline is at  height of
4m from the ground and carries a current of 100A
from east to west. The magnetic field directly
below it on the ground is (m
0
 = 4p × 10
–7
 Tm A
–1
)
(a) 2.5×10
–7
 T southward
(b) 5 × 10
–6
 T northward
(c) 5 × 10
–6
 T southward
(d) 2.5 × 10
–7
 T northward
5. A man of mass 100 kg. is standing on a platform
of mass 200 kg. which is kept on a smooth ice
surface. If the man starts moving on the platform
with a speed 30 m/sec relative to the platform then
calculate with what velocity relative to the ice the
platform will recoil?
(a) 5 m/sec (b) 10 m/sec
(c) 15 m/sec (d) 20 m/sec
6. If the unit of force and length be each increased
by four times, then the unit of energy is increased
by
(a) 16 times (b) 8 times
(c) 2 times (d) 4 times
7. Which of the following must be known in order
to determine the power output of an automobile?
(a) Final velocity and height
(b) Mass and amount of work performed
(c) Force exerted and distance of motion
(d) Work performed and elapsed time of work
8. If the force is given by F = at + bt
2
 with t as time.
The dimensions of a and b are
( a) [MLT
–4
] and [ML T
–2
]
(b) [ML T
–3
] and [ML T
–4
]
(c) [ML
2
T
–3
] and [ML
2
T
–2
]
(d) [ML
2
T
–3
] and [ML
3
T
–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 : 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
9. A wheel of radius R rolls on the ground with a
uniform velocity v. The relative acceleration of
topmost point of the wheel with respect to the
bottom most point is
(a)
2
v
R
(b)
2
2v
R
A
B
v²
R
v²
R
(c)
2
v
2R
(d)
2
4v
R
10. If the radius of the earth were to shrink by one
per cent, its mass remaining the same, the value
of g on the earth’s surface would
(a) increase by 0.5% (b) increase by 2%
(c) decrease by 0.5% (d) decrease by 2%
11. The Young’s modulus of a perfectly rigid body
is
(a) unity (b) zero (c) infinity
(d) some finite non-zero constant
12. An ice block floats in a liquid whose density is
less than water. A part of block is outside the
liquid. When whole of ice has melted, the liquid
level will
(a) rise
(b) go down
(c) remain same
(d) first rise then go down
13. A large drop of oil (density 0.8 g/cm
3
 and
viscosity h
0
) floats up through a column of another
liquid (density 1.2 g/cm
3 
and viscosity h
L
).
Assuming that the two liquids do not mix, the
velocity with which the oil drop rises will depend
on :
(a) h
0
 only (b) h
L
only
(c) both on h
0
 and h
L
(d) neither h
0
 nor h
L
14. A solid body of constant heat capacity 1 J/°C is
being heated by keeping it in contact with
reservoirs in two ways :
(i) Sequentially keeping in contact with 2
reservoirs such that each reservoir supplies
same amount of heat.
(ii) Sequentially keeping in contact with 8
reservoirs such that each reservoir supplies
same amount of heat.
In both the cases body is brought from initial
temperature 100°C to final temperature 200°C.
Entropy change of the body in the two cases
respectively is :
(a) ln2, 2ln2 (b) 2ln2, 8ln2
(c) ln2, 4ln2 (d) ln2, ln2
15. Which of the following process is possible
according to the first law of thermodynamics?
(a) W > 0, Q < 0 and dU = 0
(b) W > 0, Q < 0 and dU > 0
(c) W > 0, Q < 0 and dU < 0
(d) W < 0, Q > 0 and dU < 0
16. For an isothermal expansion of a perfect gas, the
value of 
P
P
D
 is equal to
(a)
1/2
–
V
V
D
g
(b)
–
V
V
D
(c)
–
V
V
D
g
(d)
2
–
V
V
D
g
17. A sample of ideal monoatomic gas is taken round
the cycle ABCA as shown in the figure. The work
done during the cycle is
V
p
A (p, V) C (p, 3V)
B (4p, 3V)
(a) 3 pV (b) zero (c) 9 pV (d) 6 pV
18. The average translational kinetic energy of O
2
(molar mass 32) molecules at a particular
temperature is 0.048 eV . The translational kinetic
energy of N
2
 (molar mass 28) molecules in eV at
the same temperature is
(a) 0.0015 (b) 0.003 (c) 0.048 (d) 0.768
19. For a gas if ratio of specific heats at constant
pressure and volume is g then value of degrees
of freedom is
(a)
3 –1
2 –1
g
g
(b)
2
–1 g
(c)
9
( – 1)
2
g (d) 
25
( – 1)
2
g
20. One end of a long metallic wire of length L tied to
the ceiling. The other end is tied with a massless
spring of spring constant K. A mass hangs freely
from the free end of the spring. The area of cross
section and the young’s modulus of the wire are
A and Y respectively . If the mass slightly pulled
down and released, it will oscillate with a time
period T equal to :
(a) 2 (m / K) p
(b) 2 m(YA KL) / (YAK) p+
(c) 2 (m YA / KL) p
(d) 2 (mL / YA) p
21. The transverse displacement y(x, t) of a wave on
a string is given by 
–( 2)
22
( ,)
ax bt ab xt
yxte
++
=
This represents a
(a) wave moving in – x direction, speed 
b
a
(b) standing wave of frequency b
(c) standing wave of frequency 
1
b
(d) wave moving in + x direction, speed 
a
b
22. A sound souorce is moving towards stationary
listener with 
1
th
10
 of the speed of sound. The
ratio of apparent to read frequency is
(a)  
2
9
10
æö
ç÷
èø
(b)  
10
9
æö
ç÷
èø
(c)  
11
10
æö
ç÷
èø
(d)
2
11
10
æö
ç÷
èø
23. In a region of space having a uniform electric
field E, a hemispherical bowl of radius r is placed.
The electric flux f through the bowl is
(a)2p R E (b) 4p R
2
E (c)2pR
2
E (d) pR
2
E
24. The electric field intensity just sufficient to
balance the earth’s gravitational attraction on an
electron will be: (given mass and charge of an
electron respectively are 9.1 × 10
–31
 kg and 1.6 ×
10
–19
 C.)
(a) –5.6 × 10
–11
 N/C (b) –4.8 × 10
–15
 N / C
(c) –1.6 × 10
–19
 N/C (d) –3.2 × 10
–19
 N / C
25. Two capacitors C
1
 and C
2
 are charged to 120 V
and 200 V respectively. It is found that by
connecting them together the potential on each
one can be made zero. Then
(a)5C
1
 = 3C
2
(b) 3C
1
 = 5C
2
(c)3C
1
 + 5C
2
 = 0 (d) 9C
1
 = 4C
2
26. Three voltmeters A, B and C having resistances
R, 1.5 R and 3R, respectively, are connected as
shown. When some potential difference is
applied between X and Y , the voltmeter readings
are V
A
, V
B
 and V
C
 respectively . Then –
B
C
A X Y
(a)V
A
 ¹ V
B
 = V
C
(b) V
A
 = V
B
 ¹ V
C
(c)V
A
 ¹ V
B
 ¹ V
C
(d) V
A
 = V
B
 = V
C
27. The range of the particle when launched at an
angle of 15º with the horizontal is 1.5 km. What is
the range of the projectile when launched at an
angle of 45º to the horizontal.
(a) 1.5 km (b) 3.0 km (c) 6.0 km (d)   0.75 km
28. If m is magnetic moment and B is the magnetic
field, then the torque is given by
(a) . mB
r
r
(b)
||
||
m
B
r
r
(c) mB ´
r
r
(d) | |.|| mB
r
r
29. Magnetic moment of bar magnet is M. The work
done to turn the magnet by 90° of magnet in
direction of magnetic field B will be
(a) zero (b)
1
2
MB
(c) 2 MB (d) MB
30. The laws of electromagnetic induction have been
used in the construction of a
(a) galvanometer (b) voltmeter
(c) electric motor (d) generator
31. The impedance of a circuit consists of 3 W
resistance and 4 W reactance. The power factor of
the circuit is
(a) 0.4 (b) 0.6 (c) 0.8 (d) 1.0
32. The r.m.s. value of potential difference V shown
in the figure is
V
V
0
O
T/2 T
t
(a)V
0
(b)
0
V /2
(c)V
0
/2 (d)
0
V /3
33. A ray of light is incident at the glass-water
interface at an angle i, it emerges finally parallel to
the surface of water, then the value of m
g
 would
be
(a) (4/3)sini
Water
Air
Glass
r
r
i
(b) 1/sini
(c) 4/3
(d) 1
34. A mica slit of thickness t and refractive index µ is
introduce d in the ra y from the firs t s ourc e S
1
. By
how much distance of fringes pattern will be
displaced ?
(a)
d
( 1)t
D
m- (b)
D
( 1)t
d
m-
(c)
d
( 1)D m-
(d)
D
( 1)
d
m-
35. In a Y oung’s double slit experiment the angular
width of a fringe formed on a distant screen is 1°.
The wavelength fo the light used is 6280 Å. What
is the distance between the two coherent sources?
(a) 0.036 mm (b) 0.12 mm
(c) 6 mm (d) 4 m m
36. A light having wavelength 300 nm fall on a metal
surface. The work function of metal is 2.54 eV ,
what is stopping potential ?
(a) 2 .3 V (b) 2.59 V (c) 1.59 V (d) 1.29 V
37. If the total binding energies of 
24
12
H, He,
56 235
26 92
Fe&U nuclei are 2.22, 28.3, 492 and 1786
MeV respectively, identify the most stable
nucleus of the following.
(a)
56
26
Fe (b)
2
1
H
(c)
235
92
U (d)
4
2
He
38. An oscillator is nothing but an amplifer with
(a) positive feedback
(b) negative feedback
(c) large gain
(d) no feedback
39. In an experiment on photoelectric effect photons
of wavelength 300 nm eject electrons from a metal
of work function 2.25eV. A photon of energy
equal to that of the most energetic electron
corresponds to the following transition in the
hydrogen atom:
(a) n = 2 to n = 1 state
(b) n = 3 to n = 1 state
(c) n = 3 to n = 2 state
(d) n = 4 to n = 3 state
40. A letter 'A' is constructed of a uniform wire with
resistance 1.0 W per cm, The sides of the letter
are 20 cm and the cross piece in the middle is 10
cm long. The apex angle is 60. The resistance
between the  ends of the legs is close to:
(a) 50.0 W (b) 10 W (c) 36.7 W (d) 26.7 W
PART - II : CHEMISTRY
41. Number of atoms of He in 100 amu of He (atomic
wt. of He is 4) are :
(a) 25 (b) 1 00
(c) 50 (d) 100 × 6 × 10
–23
42. If the radius of H is 0.53 Å, then what will be the
radius of 
3
Li
2+
 ?
(a) 0.17 Å (b) 0.36 Å
(c) 0.53 Å (d) 0.59 Å
43. Which of the following does not have valence
electron in 3d-subshell?
(a) Fe (III) (b) Mn (II)
(c) Cr (I) (d) P (0)
44. The vapour pressure of
 
2
NO
OH
 is higher than 
2
N O
OH
due to
(a) Dipole moment
(b) Dipole- dipole interaction
(c) H – bonding
(d) Lattice structure
45. An ideal gas can’t be liquefied because
(a) its critical temperature is always above 0°C
(b) its molecules are relatively smaller in size
(c) it solidifies before becoming a liquid
(d) forces operated between its molecules are
negligible
46. In which of the following reactions, standard
entropy change (DS°) is positive and standard
Gibb’s energy change (DG°) decreases sharply
with increasing temperature ?
(a) C (graphite) + 
1
2
O
2
(g) ® CO(g)
(b) CO(g) + 
1
2
O
2
(g) ® CO
2
(g)
(c) Mg(s) + 
1
2
O
2
(g) ® MgO(s)
(d)
1
2
C (graphite) +
1
2
O
2
(g) ® 
1
2
CO
2
(g)
47. Bond enthalpies of H
2
, X
2
 and HX are in the ratio
2 : 1 : 2. If enthalpy of formation of HX is –50 kJ
mol
–1
, the bond enthalpy of X
2
 is
(a) 100 kJ mol
–1
(b) 300 kJ mol
–1
(c) 200 kJ mol
–1
(d) 400 kJ mol
–1
48. The pOH value of a solution whose hydroxide
ion concentration is 6.2 × 10
–9
 mol/litre is
(a) 8.21 (b) 6.21 (c) 7.75 (d) 7.21
49. Which of the following combinations would not
result in the formation of a buffer solution?
(a) NH
3
 + HCl (b) NH
4
Cl + NH
3
(c) CH
3
COOH + NaCl (d) NaOH + CH
3
COOH
50. The reaction, 
2 2 2 2
Cl SO Cl SO ¾® ¾ +
 is
exothermic and reversible. A mixture of SO
2
 (g),
Cl
2
 (g) and SO
2
Cl
2
 (l) is at equilibrium in a closed
container. Now a certain quantity of extra SO
2
 is
introduced into the container, the volume
remaining the same. Which of the following is/
are true?
(a) The pressure inside the container will not
change.
(b) The temperature will not change.
(c) The temperature will increase.
(d) The temperature will decrease.
51. In the reaction
- - -
+ + ® + +
3
–
3 2
2
3 2
HCO 6 BrO Br 5 O H 3 CO 6 Br 3
(a) Bromine is oxidised and carbonate is
reduced.
(b) Bromine is reduced and water is oxidised.
(c) Bromine is neither reduced nor oxidised.
(d) Bromine is both reduced and oxidised.
52. The boiling point of water is exceptionally high
because
(a) there is a covalent bond between H and O.
(b) water molecule is linear.
(c) water molecules associate due to hydrogen
bonding.
(d) water molecule is not linear.
53. Which of the following has correct increasing
basic strength?
(a) MgO < BeO < CaO < BaO
(b) BeO < MgO < CaO < BaO
(c) BaO < CaO < MgO < BeO
(d) CaO < BaO < BeO < MgO
54. The following two compounds are
CH
5 2
OH
OH H
H
CH
3
CH
5 2
OH
OH H
H
CH
3
 are
(a) enantiomers (b) diastereomers
(c) identical (d) epimers
55. In paper chromatography :
(a) Mobile phase is liquid and stationary phase
is solid.
(b) Mobile phase is solid and stationary phase
is liquid.
(c) Both phases are liquids.
(d) Both phases are solids.
56. In which case the NO
2
 will attack at the meta
position
3
CCl
(I)
     
NO
2
(II)
3
NH
+
(III)
O
–
(IV)
(a) I, II, III (b) II, IV
(c) II and III only (d) II only
57. Which alkene on ozonolysis gives CH
3
CH
2
CHO
and 
33
CH CCH
O
||
(a) CH CH CH = C
32
CH
3
CH
3
(b) CH
3
CH
2
CH = CHCH
2
CH
3
(c) CH
3
 CH
2
 CH = CH CH
3
(d)
3
3
|
3
CHCH
CH
C CH = -
58. Formation of ozone in the upper atmosphere from
oxygen takes place by the action of
(a) Nitrogen oxides (b) Ultraviolet rays
(c) Cosmic rays (d) Free radicals
59. CO
2
 goes to air, causes green house effect and
gets dissolved in water. What will be the effect
on soil fertility and pH of the water?
(a) Increases (b) Decreases
(c) Remain same (d) None of these
60. The van’t Hoff factor i for an electrolyte which
undergoes dissociation and association in
solvents are respectively
(a) greater than 1 and greater than 1
(b) less than 1 and greater than 1
(c) less than 1 and less than 1
(d) greater than 1 and less than 1
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