WBJEE Previous Year Question Paper - 2014 | WBJEE Sample Papers, Section Wise & Full Mock Tests 2026 PDF Download

 Page 1


Physics
Category I
Directions (Q. Nos. 1-45) Carry one mark each, for which only one option is correct. Any wrong answer will
lead to deduction of 1/3 mark.
1. Consider three vectors A i j k = + -
$ $ $
, 2
B i j k = - +
$ $ $
andC i j k = - + 2 3 4
$ $ $
. A vectorX of
the form a b A B + (a and b are numbers) is
perpendicular toC. The ratio ofa andb is
(a) 1 : 1 (b) 2 : 1
(c)-1 1 : (d) 3 : 1
2. Three capacitors 3 6 m m F F , and 6mF are
connected in series to a source of 120 V. The
potential difference, in volt, across the 3mF
capacitor will be
(a) 24 (b) 30 (c) 40 (d) 60
3. A galvanometer having internal resistance
10W requires 0.01 A for a full scale deflection.
To convert this galvanometer to a voltmeter of
full-scale deflection at 120 V, we need to
connect a resistance of
(a) 11990 W in series
(b) 11990 W in parallel
(c) 12010 W in series
(d) 12010 W in parallel
4. A whistle whose air column is open at both
ends has a fundamental frequency of 5100 Hz.
If the speed of sound in air is 340
1
ms
-
, the
length of the whistle, in cm, is
(a) 5/3 (b) 10/3
(c) 5 (d) 20/3
5. The output Y of the logic circuit given below is
(a) A B + (b) A
(c)( ) A B A + × (d)( ) A B A + ×
6. One mole of an ideal monoatomic gas is heated
at a constant pressure from 0°C to 100°C. Then
the change in the internal energy of the gas is
(Given, R=
- -
8.32 J mol K
1 1
)
(a) 0.83 J ´ 10
3
(b) 4.6 J ´ 10
3
(c)2.08 J ´ 10
3
(d)1.25 J ´ 10
3
7. The ionization energy of hydrogen is 13.6 eV.
The energy of the photon released when an
electron jumps from the first excited state
( ) n = 2 to the ground state of a hydrogen atom is
(a) 3.4 eV (b) 4.53 eV
(c) 10.2 eV (d) 13.6 eV
8. A parallel plate capacitor is charged and then
disconnected from the charging battery. If the
plates are now moved farther apart by pulling
at them by means of insulating handles, then
(a) the energy stored in the capacitor decreases
(b) the capacitance of the capacitor increases
(c) the charge on the capacitor decreases
(d) the voltage across the capacitor increases
A
B
Y
WB JEE
Engineering Entrance Exam
Solved Paper 2014
Page 1 of 56
Page 2


Physics
Category I
Directions (Q. Nos. 1-45) Carry one mark each, for which only one option is correct. Any wrong answer will
lead to deduction of 1/3 mark.
1. Consider three vectors A i j k = + -
$ $ $
, 2
B i j k = - +
$ $ $
andC i j k = - + 2 3 4
$ $ $
. A vectorX of
the form a b A B + (a and b are numbers) is
perpendicular toC. The ratio ofa andb is
(a) 1 : 1 (b) 2 : 1
(c)-1 1 : (d) 3 : 1
2. Three capacitors 3 6 m m F F , and 6mF are
connected in series to a source of 120 V. The
potential difference, in volt, across the 3mF
capacitor will be
(a) 24 (b) 30 (c) 40 (d) 60
3. A galvanometer having internal resistance
10W requires 0.01 A for a full scale deflection.
To convert this galvanometer to a voltmeter of
full-scale deflection at 120 V, we need to
connect a resistance of
(a) 11990 W in series
(b) 11990 W in parallel
(c) 12010 W in series
(d) 12010 W in parallel
4. A whistle whose air column is open at both
ends has a fundamental frequency of 5100 Hz.
If the speed of sound in air is 340
1
ms
-
, the
length of the whistle, in cm, is
(a) 5/3 (b) 10/3
(c) 5 (d) 20/3
5. The output Y of the logic circuit given below is
(a) A B + (b) A
(c)( ) A B A + × (d)( ) A B A + ×
6. One mole of an ideal monoatomic gas is heated
at a constant pressure from 0°C to 100°C. Then
the change in the internal energy of the gas is
(Given, R=
- -
8.32 J mol K
1 1
)
(a) 0.83 J ´ 10
3
(b) 4.6 J ´ 10
3
(c)2.08 J ´ 10
3
(d)1.25 J ´ 10
3
7. The ionization energy of hydrogen is 13.6 eV.
The energy of the photon released when an
electron jumps from the first excited state
( ) n = 2 to the ground state of a hydrogen atom is
(a) 3.4 eV (b) 4.53 eV
(c) 10.2 eV (d) 13.6 eV
8. A parallel plate capacitor is charged and then
disconnected from the charging battery. If the
plates are now moved farther apart by pulling
at them by means of insulating handles, then
(a) the energy stored in the capacitor decreases
(b) the capacitance of the capacitor increases
(c) the charge on the capacitor decreases
(d) the voltage across the capacitor increases
A
B
Y
WB JEE
Engineering Entrance Exam
Solved Paper 2014
Page 1 of 56
9. When a particle executing SHM oscillates with
a frequency n, then the kinetic energy of the
particle
(a) changes periodically with a frequency ofn
(b) changes periodically with a frequency of2n
(c) changes periodically with a frequency ofn/2
(d) remains constant
10. In which of the following pairs, the two
physical quantities have different dimensions?
(a) Planck’s constant and angular momentum
(b) Impulse and linear momentum
(c) Moment of inertia and moment of a force
(d) Energy and torque
11. A cricket ball thrown across a field is at heights
h
1
and h
2
from the point of projection at times t
1
and t
2
respectively after the throw. The ball is
caught by a fielder at the same height as that of
projection. The time of flight of the ball in this
journey is
(a)
h t h t
h t h t
1 2
2
2 1
2
1 2 2 1
-
-
(b)
h t h t
h t h t
1 1
2
2 2
2
2 1 1 2
+
+
(c)
h t h t
h t h t
1 2
2
2 1
2
1 2 2 1
+
+
(d)
ht h t
ht h t
1 1
2
2 2
2
1 1 2 2
-
-
12. A small metal sphere of radius a is falling with
a velocity v through a vertical column of a
viscous liquid. If the coefficient of viscosity of
the liquid ish, then the sphere encounters an
opposing force of
(a)6
2
pha v (b)
6h
p
v
a
(c)6phav (d)
phv
a 6
3
13. A scientist proposes a new temperature scale
in which the ice point is 25 X (X is the new unit
of temperature) and the steam point is 305 X.
The specific heat capacity of water in this new
scale is (in J kg X
- - 1 1
)
(a) 4.2 ´ 10
3
(b) 3.0 ´ 10
3
(c)1.2 ´ 10
3
(d)1.5 ´ 10
3
14. One mole of a van der Waals’ gas obeying the
equation
p
a
V
V b RT +
æ
è
ç
ö
ø
÷ - =
2
( )
undergoes the quasi-static cyclic process which
is shown in the p-V diagram. The net heat
absorbed by the gas in this process is
(a)
1
2
1 2 1 2
( )( ) p p V V - -
(b)
1
2
1 2 1 2
( )( ) p p V V + -
(c)
1
2
1
1
2
2
2
2
1 2
p
a
V
p
a
V
V V + - -
æ
è
ç
ç
ö
ø
÷
÷
- ( )
(d)
1
2
1
1
2
2
2
2
1 2
p
a
V
p
a
V
V V + + +
æ
è
ç
ç
ö
ø
÷
÷
- ( )
15. A wooden block is floating on water kept in a
beaker. 40% of the block is above the water
surface. Now the beaker is kept inside a lift
that starts going upward with acceleration
equal to g/ 2. The block will then
(a) sink
(b) float with 10% above the water surface
(c) float with 40% above the water surface
(d) float with 70% above the water surface
16. A smooth massless string passes over a smooth
fixed pulley. Two masses m
1
and m
2
, ( ) m m
1 2
>
are tied at the two ends of the string. The
masses are allowed to move under gravity
starting from rest. The total external force
acting on the two masses is
(a)( ) m m g
1 2
+ (b)
( ) m m
m m
g
1 2
2
1 2
-
+
(c)( ) m m g
1 2
- (d)
( ) m m
m m
g
1 2
2
1 2
+
-
17. To determine the coefficient of friction between
a rough surface and a block, the surface is kept
inclined at 45° and the block is released from
rest. The block takes a time t in moving a
distance d. The rough surface is then replaced
by a smooth surface and the same experiment
is repeated. The block now takes a time t/ 2 in
moving down the same distance d. The
coefficient of friction is
(a) 3/4 (b) 5/4 (c) 1/2 (d)1 2 /
p
p
1
p
2
V
2
V
1
V
Page 2 of 56
Page 3


Physics
Category I
Directions (Q. Nos. 1-45) Carry one mark each, for which only one option is correct. Any wrong answer will
lead to deduction of 1/3 mark.
1. Consider three vectors A i j k = + -
$ $ $
, 2
B i j k = - +
$ $ $
andC i j k = - + 2 3 4
$ $ $
. A vectorX of
the form a b A B + (a and b are numbers) is
perpendicular toC. The ratio ofa andb is
(a) 1 : 1 (b) 2 : 1
(c)-1 1 : (d) 3 : 1
2. Three capacitors 3 6 m m F F , and 6mF are
connected in series to a source of 120 V. The
potential difference, in volt, across the 3mF
capacitor will be
(a) 24 (b) 30 (c) 40 (d) 60
3. A galvanometer having internal resistance
10W requires 0.01 A for a full scale deflection.
To convert this galvanometer to a voltmeter of
full-scale deflection at 120 V, we need to
connect a resistance of
(a) 11990 W in series
(b) 11990 W in parallel
(c) 12010 W in series
(d) 12010 W in parallel
4. A whistle whose air column is open at both
ends has a fundamental frequency of 5100 Hz.
If the speed of sound in air is 340
1
ms
-
, the
length of the whistle, in cm, is
(a) 5/3 (b) 10/3
(c) 5 (d) 20/3
5. The output Y of the logic circuit given below is
(a) A B + (b) A
(c)( ) A B A + × (d)( ) A B A + ×
6. One mole of an ideal monoatomic gas is heated
at a constant pressure from 0°C to 100°C. Then
the change in the internal energy of the gas is
(Given, R=
- -
8.32 J mol K
1 1
)
(a) 0.83 J ´ 10
3
(b) 4.6 J ´ 10
3
(c)2.08 J ´ 10
3
(d)1.25 J ´ 10
3
7. The ionization energy of hydrogen is 13.6 eV.
The energy of the photon released when an
electron jumps from the first excited state
( ) n = 2 to the ground state of a hydrogen atom is
(a) 3.4 eV (b) 4.53 eV
(c) 10.2 eV (d) 13.6 eV
8. A parallel plate capacitor is charged and then
disconnected from the charging battery. If the
plates are now moved farther apart by pulling
at them by means of insulating handles, then
(a) the energy stored in the capacitor decreases
(b) the capacitance of the capacitor increases
(c) the charge on the capacitor decreases
(d) the voltage across the capacitor increases
A
B
Y
WB JEE
Engineering Entrance Exam
Solved Paper 2014
Page 1 of 56
9. When a particle executing SHM oscillates with
a frequency n, then the kinetic energy of the
particle
(a) changes periodically with a frequency ofn
(b) changes periodically with a frequency of2n
(c) changes periodically with a frequency ofn/2
(d) remains constant
10. In which of the following pairs, the two
physical quantities have different dimensions?
(a) Planck’s constant and angular momentum
(b) Impulse and linear momentum
(c) Moment of inertia and moment of a force
(d) Energy and torque
11. A cricket ball thrown across a field is at heights
h
1
and h
2
from the point of projection at times t
1
and t
2
respectively after the throw. The ball is
caught by a fielder at the same height as that of
projection. The time of flight of the ball in this
journey is
(a)
h t h t
h t h t
1 2
2
2 1
2
1 2 2 1
-
-
(b)
h t h t
h t h t
1 1
2
2 2
2
2 1 1 2
+
+
(c)
h t h t
h t h t
1 2
2
2 1
2
1 2 2 1
+
+
(d)
ht h t
ht h t
1 1
2
2 2
2
1 1 2 2
-
-
12. A small metal sphere of radius a is falling with
a velocity v through a vertical column of a
viscous liquid. If the coefficient of viscosity of
the liquid ish, then the sphere encounters an
opposing force of
(a)6
2
pha v (b)
6h
p
v
a
(c)6phav (d)
phv
a 6
3
13. A scientist proposes a new temperature scale
in which the ice point is 25 X (X is the new unit
of temperature) and the steam point is 305 X.
The specific heat capacity of water in this new
scale is (in J kg X
- - 1 1
)
(a) 4.2 ´ 10
3
(b) 3.0 ´ 10
3
(c)1.2 ´ 10
3
(d)1.5 ´ 10
3
14. One mole of a van der Waals’ gas obeying the
equation
p
a
V
V b RT +
æ
è
ç
ö
ø
÷ - =
2
( )
undergoes the quasi-static cyclic process which
is shown in the p-V diagram. The net heat
absorbed by the gas in this process is
(a)
1
2
1 2 1 2
( )( ) p p V V - -
(b)
1
2
1 2 1 2
( )( ) p p V V + -
(c)
1
2
1
1
2
2
2
2
1 2
p
a
V
p
a
V
V V + - -
æ
è
ç
ç
ö
ø
÷
÷
- ( )
(d)
1
2
1
1
2
2
2
2
1 2
p
a
V
p
a
V
V V + + +
æ
è
ç
ç
ö
ø
÷
÷
- ( )
15. A wooden block is floating on water kept in a
beaker. 40% of the block is above the water
surface. Now the beaker is kept inside a lift
that starts going upward with acceleration
equal to g/ 2. The block will then
(a) sink
(b) float with 10% above the water surface
(c) float with 40% above the water surface
(d) float with 70% above the water surface
16. A smooth massless string passes over a smooth
fixed pulley. Two masses m
1
and m
2
, ( ) m m
1 2
>
are tied at the two ends of the string. The
masses are allowed to move under gravity
starting from rest. The total external force
acting on the two masses is
(a)( ) m m g
1 2
+ (b)
( ) m m
m m
g
1 2
2
1 2
-
+
(c)( ) m m g
1 2
- (d)
( ) m m
m m
g
1 2
2
1 2
+
-
17. To determine the coefficient of friction between
a rough surface and a block, the surface is kept
inclined at 45° and the block is released from
rest. The block takes a time t in moving a
distance d. The rough surface is then replaced
by a smooth surface and the same experiment
is repeated. The block now takes a time t/ 2 in
moving down the same distance d. The
coefficient of friction is
(a) 3/4 (b) 5/4 (c) 1/2 (d)1 2 /
p
p
1
p
2
V
2
V
1
V
Page 2 of 56
18. A metal rod is fixed rigidly at two ends so as to
prevent its thermal expansion. If L,a and Y
respectively denote the length of the rod,
coefficient of linear thermal expansion and
Young’s modulus of its material, then for an
increase in temperature of the rod by DT, the
longitudinal stress developed in the rod is
(a) inversely proportional toa
(b) inversely proportional to Y
(c) directly proportional toDT Y /
(d) independent of L
19. A particle is moving uniformly in a circular
path of radius r. When it moves through an
angular displacementq, then the magnitude of
the corresponding linear displacement will be
(a)2
2
r cos
q æ
è
ç
ö
ø
÷
(b)2
2
r cot
q æ
è
ç
ö
ø
÷
(c)2
2
r tan
q æ
è
ç
ö
ø
÷
(d)2
2
r sin
q æ
è
ç
ö
ø
÷
20. A uniform rod is suspended horizontally from
its mid-point. A piece of metal whose weight is
w is suspended at a distance l from the
mid-point. Another weight W
1
is suspended on
the other side at a distance l
1
from the
mid-point to bring the rod to a horizontal
position. When w is completely immersed in
water, w
1
needs to be kept at a distance l
2
from
the mid-point to get the rod back into
horizontal position. The specific gravity of the
metal piece is
(a)
w
w
1
(b)
w
w w
l
l l
1
1 2
-
(c)
l
l l
1
1 2
-
(d)
l
l
1
2
21. A drop of some liquid of volume 0.04 cm
3
is
placed on the surface of a glass slide. Then
another glass slide is placed on it in such a way
that the liquid forms a thin layer of area 20
2
cm
between the surfaces of the two slides. To
separate the slides a force of 16 10
5
´ dyne has
to be applied normal to the surfaces. The
surface tension of the liquid is (in dyne-cm
-1
)
(a) 60 (b) 70 (c) 80 (d) 90
22. An electron in a circular orbit of radius 0.05 nm
performs 10
16
revolutions per second. The
magnetic moment due to this rotation of
electron is (in Am
2
)
(a)2.16 ´
-
10
23
(b) 3.21´
-
10
22
(c) 3.21´
-
10
24
(d)1.26 ´
-
10
23
23. A very small circular loop of radius a is initially
(at t = 0) coplanar and concentric with a much
larger fixed circular loop of radius b. A
constant current I flows in the larger loop. The
smaller loop is rotated with a constant angular
speed w about the common diameter. The emf
induced in the smaller loop as a function of
time t is
(a)
p m
w w
a I
b
t
2
0
2
cos ( ) (b)
p m
w w
a I
b
t
2
0 2 2
2
sin( )
(c)
p m
w w
a I
b
t
2
0
2
sin( ) (d)
p m
w w
a I
b
t
2
0 2
2
sin ( )
24. A luminous object is separated from a screen
by distance d. A convex lens is placed between
the object and the screen such that it forms a
distinct image on the screen. The maximum
possible focal length of this convex lens is
(a) 4d (b)2d
(c)
d
2
(d)
d
4
25. An infinite sheet carrying a uniform surface
charge densitys lies on the xy-plane. The work
done to carry a charge q from the point
A i j k = + + a(
$ $ $
) 2 3 to the point B i j k = - + a(
$ $ $
) 2 6
(where a is a constant with the dimension of
length and e
0
is the permittivity of free space)
is
(a)
3
2
0
s
e
aq
(b)
2
0
s
e
aq
(c)
5
2
0
s
e
aq
(d)
3
0
s
e
aq
26. The intensity of magnetization of a bar magnet
is 5.0 Am ´
-
10
4 1
. The magnetic length and the
area of cross-section of the magnet are 12 cm
and 1
2
cm respectively. The magnitude of
magnetic moment of this bar magnet is
(in SI unit)
(a) 0.6 (b) 1.3 (c) 1.24 (d) 2.4
27. A particle moves with constant acceleration
along a straight line starting from rest. The
percentage increase in its displacement during
the 4th second compared to that in the
3rd second is
(a) 33% (b) 40% (c) 66% (d) 77%
Page 3 of 56
Page 4


Physics
Category I
Directions (Q. Nos. 1-45) Carry one mark each, for which only one option is correct. Any wrong answer will
lead to deduction of 1/3 mark.
1. Consider three vectors A i j k = + -
$ $ $
, 2
B i j k = - +
$ $ $
andC i j k = - + 2 3 4
$ $ $
. A vectorX of
the form a b A B + (a and b are numbers) is
perpendicular toC. The ratio ofa andb is
(a) 1 : 1 (b) 2 : 1
(c)-1 1 : (d) 3 : 1
2. Three capacitors 3 6 m m F F , and 6mF are
connected in series to a source of 120 V. The
potential difference, in volt, across the 3mF
capacitor will be
(a) 24 (b) 30 (c) 40 (d) 60
3. A galvanometer having internal resistance
10W requires 0.01 A for a full scale deflection.
To convert this galvanometer to a voltmeter of
full-scale deflection at 120 V, we need to
connect a resistance of
(a) 11990 W in series
(b) 11990 W in parallel
(c) 12010 W in series
(d) 12010 W in parallel
4. A whistle whose air column is open at both
ends has a fundamental frequency of 5100 Hz.
If the speed of sound in air is 340
1
ms
-
, the
length of the whistle, in cm, is
(a) 5/3 (b) 10/3
(c) 5 (d) 20/3
5. The output Y of the logic circuit given below is
(a) A B + (b) A
(c)( ) A B A + × (d)( ) A B A + ×
6. One mole of an ideal monoatomic gas is heated
at a constant pressure from 0°C to 100°C. Then
the change in the internal energy of the gas is
(Given, R=
- -
8.32 J mol K
1 1
)
(a) 0.83 J ´ 10
3
(b) 4.6 J ´ 10
3
(c)2.08 J ´ 10
3
(d)1.25 J ´ 10
3
7. The ionization energy of hydrogen is 13.6 eV.
The energy of the photon released when an
electron jumps from the first excited state
( ) n = 2 to the ground state of a hydrogen atom is
(a) 3.4 eV (b) 4.53 eV
(c) 10.2 eV (d) 13.6 eV
8. A parallel plate capacitor is charged and then
disconnected from the charging battery. If the
plates are now moved farther apart by pulling
at them by means of insulating handles, then
(a) the energy stored in the capacitor decreases
(b) the capacitance of the capacitor increases
(c) the charge on the capacitor decreases
(d) the voltage across the capacitor increases
A
B
Y
WB JEE
Engineering Entrance Exam
Solved Paper 2014
Page 1 of 56
9. When a particle executing SHM oscillates with
a frequency n, then the kinetic energy of the
particle
(a) changes periodically with a frequency ofn
(b) changes periodically with a frequency of2n
(c) changes periodically with a frequency ofn/2
(d) remains constant
10. In which of the following pairs, the two
physical quantities have different dimensions?
(a) Planck’s constant and angular momentum
(b) Impulse and linear momentum
(c) Moment of inertia and moment of a force
(d) Energy and torque
11. A cricket ball thrown across a field is at heights
h
1
and h
2
from the point of projection at times t
1
and t
2
respectively after the throw. The ball is
caught by a fielder at the same height as that of
projection. The time of flight of the ball in this
journey is
(a)
h t h t
h t h t
1 2
2
2 1
2
1 2 2 1
-
-
(b)
h t h t
h t h t
1 1
2
2 2
2
2 1 1 2
+
+
(c)
h t h t
h t h t
1 2
2
2 1
2
1 2 2 1
+
+
(d)
ht h t
ht h t
1 1
2
2 2
2
1 1 2 2
-
-
12. A small metal sphere of radius a is falling with
a velocity v through a vertical column of a
viscous liquid. If the coefficient of viscosity of
the liquid ish, then the sphere encounters an
opposing force of
(a)6
2
pha v (b)
6h
p
v
a
(c)6phav (d)
phv
a 6
3
13. A scientist proposes a new temperature scale
in which the ice point is 25 X (X is the new unit
of temperature) and the steam point is 305 X.
The specific heat capacity of water in this new
scale is (in J kg X
- - 1 1
)
(a) 4.2 ´ 10
3
(b) 3.0 ´ 10
3
(c)1.2 ´ 10
3
(d)1.5 ´ 10
3
14. One mole of a van der Waals’ gas obeying the
equation
p
a
V
V b RT +
æ
è
ç
ö
ø
÷ - =
2
( )
undergoes the quasi-static cyclic process which
is shown in the p-V diagram. The net heat
absorbed by the gas in this process is
(a)
1
2
1 2 1 2
( )( ) p p V V - -
(b)
1
2
1 2 1 2
( )( ) p p V V + -
(c)
1
2
1
1
2
2
2
2
1 2
p
a
V
p
a
V
V V + - -
æ
è
ç
ç
ö
ø
÷
÷
- ( )
(d)
1
2
1
1
2
2
2
2
1 2
p
a
V
p
a
V
V V + + +
æ
è
ç
ç
ö
ø
÷
÷
- ( )
15. A wooden block is floating on water kept in a
beaker. 40% of the block is above the water
surface. Now the beaker is kept inside a lift
that starts going upward with acceleration
equal to g/ 2. The block will then
(a) sink
(b) float with 10% above the water surface
(c) float with 40% above the water surface
(d) float with 70% above the water surface
16. A smooth massless string passes over a smooth
fixed pulley. Two masses m
1
and m
2
, ( ) m m
1 2
>
are tied at the two ends of the string. The
masses are allowed to move under gravity
starting from rest. The total external force
acting on the two masses is
(a)( ) m m g
1 2
+ (b)
( ) m m
m m
g
1 2
2
1 2
-
+
(c)( ) m m g
1 2
- (d)
( ) m m
m m
g
1 2
2
1 2
+
-
17. To determine the coefficient of friction between
a rough surface and a block, the surface is kept
inclined at 45° and the block is released from
rest. The block takes a time t in moving a
distance d. The rough surface is then replaced
by a smooth surface and the same experiment
is repeated. The block now takes a time t/ 2 in
moving down the same distance d. The
coefficient of friction is
(a) 3/4 (b) 5/4 (c) 1/2 (d)1 2 /
p
p
1
p
2
V
2
V
1
V
Page 2 of 56
18. A metal rod is fixed rigidly at two ends so as to
prevent its thermal expansion. If L,a and Y
respectively denote the length of the rod,
coefficient of linear thermal expansion and
Young’s modulus of its material, then for an
increase in temperature of the rod by DT, the
longitudinal stress developed in the rod is
(a) inversely proportional toa
(b) inversely proportional to Y
(c) directly proportional toDT Y /
(d) independent of L
19. A particle is moving uniformly in a circular
path of radius r. When it moves through an
angular displacementq, then the magnitude of
the corresponding linear displacement will be
(a)2
2
r cos
q æ
è
ç
ö
ø
÷
(b)2
2
r cot
q æ
è
ç
ö
ø
÷
(c)2
2
r tan
q æ
è
ç
ö
ø
÷
(d)2
2
r sin
q æ
è
ç
ö
ø
÷
20. A uniform rod is suspended horizontally from
its mid-point. A piece of metal whose weight is
w is suspended at a distance l from the
mid-point. Another weight W
1
is suspended on
the other side at a distance l
1
from the
mid-point to bring the rod to a horizontal
position. When w is completely immersed in
water, w
1
needs to be kept at a distance l
2
from
the mid-point to get the rod back into
horizontal position. The specific gravity of the
metal piece is
(a)
w
w
1
(b)
w
w w
l
l l
1
1 2
-
(c)
l
l l
1
1 2
-
(d)
l
l
1
2
21. A drop of some liquid of volume 0.04 cm
3
is
placed on the surface of a glass slide. Then
another glass slide is placed on it in such a way
that the liquid forms a thin layer of area 20
2
cm
between the surfaces of the two slides. To
separate the slides a force of 16 10
5
´ dyne has
to be applied normal to the surfaces. The
surface tension of the liquid is (in dyne-cm
-1
)
(a) 60 (b) 70 (c) 80 (d) 90
22. An electron in a circular orbit of radius 0.05 nm
performs 10
16
revolutions per second. The
magnetic moment due to this rotation of
electron is (in Am
2
)
(a)2.16 ´
-
10
23
(b) 3.21´
-
10
22
(c) 3.21´
-
10
24
(d)1.26 ´
-
10
23
23. A very small circular loop of radius a is initially
(at t = 0) coplanar and concentric with a much
larger fixed circular loop of radius b. A
constant current I flows in the larger loop. The
smaller loop is rotated with a constant angular
speed w about the common diameter. The emf
induced in the smaller loop as a function of
time t is
(a)
p m
w w
a I
b
t
2
0
2
cos ( ) (b)
p m
w w
a I
b
t
2
0 2 2
2
sin( )
(c)
p m
w w
a I
b
t
2
0
2
sin( ) (d)
p m
w w
a I
b
t
2
0 2
2
sin ( )
24. A luminous object is separated from a screen
by distance d. A convex lens is placed between
the object and the screen such that it forms a
distinct image on the screen. The maximum
possible focal length of this convex lens is
(a) 4d (b)2d
(c)
d
2
(d)
d
4
25. An infinite sheet carrying a uniform surface
charge densitys lies on the xy-plane. The work
done to carry a charge q from the point
A i j k = + + a(
$ $ $
) 2 3 to the point B i j k = - + a(
$ $ $
) 2 6
(where a is a constant with the dimension of
length and e
0
is the permittivity of free space)
is
(a)
3
2
0
s
e
aq
(b)
2
0
s
e
aq
(c)
5
2
0
s
e
aq
(d)
3
0
s
e
aq
26. The intensity of magnetization of a bar magnet
is 5.0 Am ´
-
10
4 1
. The magnetic length and the
area of cross-section of the magnet are 12 cm
and 1
2
cm respectively. The magnitude of
magnetic moment of this bar magnet is
(in SI unit)
(a) 0.6 (b) 1.3 (c) 1.24 (d) 2.4
27. A particle moves with constant acceleration
along a straight line starting from rest. The
percentage increase in its displacement during
the 4th second compared to that in the
3rd second is
(a) 33% (b) 40% (c) 66% (d) 77%
Page 3 of 56
28. A proton of mass m and charge q is moving in a
plane with kinetic energy E. If there exists a
uniform magnetic field B, perpendicular to the
plane of the motion, the proton will move in a
circular path of radius
(a)
2Em
qB
(b)
2Em
qB
(c)
Em
qB 2
(d)
2Eq
mB
29. An artificial satellite moves in a circular orbit
around the earth. Total energy of the satellite
is given by E. The potential energy of the
satellite is
(a)-2E (b)2E (c)
2
3
E
(d) -
2
3
E
30. In which of the following phenomena, the heat
waves travel along straight lines with the
speed of light?
(a) Thermal conduction (b) Forced convection
(c) Natural convection (d) Thermal radiation
31. In the bandgap between valence band and
conduction band in a material is 5.0 eV, then
the material is
(a) semiconductor (b) good conductor
(c) superconductor (d) insulator
32. A uniform solid spherical ball is rolling down a
smooth inclined plane from a height h. The
velocity attained by the ball when it reaches
the bottom of the inclined plane is v. If the ball
is now thrown vertically upwards with the
same velocity v, the maximum height to which
the ball will rise is
(a)
5
8
h
(b)
3
5
h
(c)
5
7
h
(d)
7
9
h
33. Two coherent monochromatic beams of
intensities I and 4I respectively are
superposed. The maximum and minimum
intensities in the resulting pattern are
(a) 5 3 I I and (b) 9 3 I I and
(c) 4I I and (d) 9I I and
34. In the circuit shown assume the diode to be
ideal. When V
i
increases from 2V to 6 V, the
change in the current is (in mA)
(a) zero (b) 20
(c) 80/3 (d) 40
35. If n denotes a positive integer, h the Planck’s
constant, q the charge and B the magnetic
field, then the quantity
nh
qB 2p
é
ë
ê
ù
û
ú
has the
dimension of
(a) area (b) length
(c) speed (d) acceleration
36. In a transistor output characteristics
commonly used in common emitter
configuration, the base current I
B
,the collector
current I
C
and the collector-emitter voltage
V
CE
have values of the following orders of
magnitude in the active region
(a) I I
B C
and both are inmA andV
CE
in volt
(b) I
B
is inmA and I
C
is in mA andV
CE
in volt
(c) I
B
is in mA and I
C
is inmA andV
CE
in mV
(d) I
B
is in mA and I
C
is in mA andV
CE
in mV
37. The displacement of a particle in a periodic
motion is given by y
t
t =
æ
è
ç
ö
ø
÷ 4
2
1000
2
cos sin ( ).
This displacement may be considered as the
result of superposition of n independent
harmonic oscillations. Here n is
(a) 1 (b) 2 (c) 3 (d) 4
38. Consider a black body radiation in a cubical
box at absolute temperature T. If the length of
each side of the box is doubled and the
temperature of the walls of the box and that of
the radiation is halved, then the total energy
(a) halves (b) doubles
(c) quadruples (d) remains the same
39. Consider two concentric spherical metal shells
of radii r
1
and r
2
( ) r r
2 1
> . If the outer shell has a
charge q and the inner one is grounded, the
charge on the inner shell is
(a)
-r
r
q
2
1
(b) zero
(c)
-r
r
q
1
2
(d) -q
40. Four cells, each of emf E and internal
resistance r, are connected in series across an
external resistance R. By mistake one of the
cells is connected in reverse. Then the current
in the external circuit is
(a)
2
4
E
r R +
(b)
3
4
E
r R +
(c)
3
3
E
r R +
(d)
2
3
E
r R +
V
i 150 W +3V
Page 4 of 56
Page 5


Physics
Category I
Directions (Q. Nos. 1-45) Carry one mark each, for which only one option is correct. Any wrong answer will
lead to deduction of 1/3 mark.
1. Consider three vectors A i j k = + -
$ $ $
, 2
B i j k = - +
$ $ $
andC i j k = - + 2 3 4
$ $ $
. A vectorX of
the form a b A B + (a and b are numbers) is
perpendicular toC. The ratio ofa andb is
(a) 1 : 1 (b) 2 : 1
(c)-1 1 : (d) 3 : 1
2. Three capacitors 3 6 m m F F , and 6mF are
connected in series to a source of 120 V. The
potential difference, in volt, across the 3mF
capacitor will be
(a) 24 (b) 30 (c) 40 (d) 60
3. A galvanometer having internal resistance
10W requires 0.01 A for a full scale deflection.
To convert this galvanometer to a voltmeter of
full-scale deflection at 120 V, we need to
connect a resistance of
(a) 11990 W in series
(b) 11990 W in parallel
(c) 12010 W in series
(d) 12010 W in parallel
4. A whistle whose air column is open at both
ends has a fundamental frequency of 5100 Hz.
If the speed of sound in air is 340
1
ms
-
, the
length of the whistle, in cm, is
(a) 5/3 (b) 10/3
(c) 5 (d) 20/3
5. The output Y of the logic circuit given below is
(a) A B + (b) A
(c)( ) A B A + × (d)( ) A B A + ×
6. One mole of an ideal monoatomic gas is heated
at a constant pressure from 0°C to 100°C. Then
the change in the internal energy of the gas is
(Given, R=
- -
8.32 J mol K
1 1
)
(a) 0.83 J ´ 10
3
(b) 4.6 J ´ 10
3
(c)2.08 J ´ 10
3
(d)1.25 J ´ 10
3
7. The ionization energy of hydrogen is 13.6 eV.
The energy of the photon released when an
electron jumps from the first excited state
( ) n = 2 to the ground state of a hydrogen atom is
(a) 3.4 eV (b) 4.53 eV
(c) 10.2 eV (d) 13.6 eV
8. A parallel plate capacitor is charged and then
disconnected from the charging battery. If the
plates are now moved farther apart by pulling
at them by means of insulating handles, then
(a) the energy stored in the capacitor decreases
(b) the capacitance of the capacitor increases
(c) the charge on the capacitor decreases
(d) the voltage across the capacitor increases
A
B
Y
WB JEE
Engineering Entrance Exam
Solved Paper 2014
Page 1 of 56
9. When a particle executing SHM oscillates with
a frequency n, then the kinetic energy of the
particle
(a) changes periodically with a frequency ofn
(b) changes periodically with a frequency of2n
(c) changes periodically with a frequency ofn/2
(d) remains constant
10. In which of the following pairs, the two
physical quantities have different dimensions?
(a) Planck’s constant and angular momentum
(b) Impulse and linear momentum
(c) Moment of inertia and moment of a force
(d) Energy and torque
11. A cricket ball thrown across a field is at heights
h
1
and h
2
from the point of projection at times t
1
and t
2
respectively after the throw. The ball is
caught by a fielder at the same height as that of
projection. The time of flight of the ball in this
journey is
(a)
h t h t
h t h t
1 2
2
2 1
2
1 2 2 1
-
-
(b)
h t h t
h t h t
1 1
2
2 2
2
2 1 1 2
+
+
(c)
h t h t
h t h t
1 2
2
2 1
2
1 2 2 1
+
+
(d)
ht h t
ht h t
1 1
2
2 2
2
1 1 2 2
-
-
12. A small metal sphere of radius a is falling with
a velocity v through a vertical column of a
viscous liquid. If the coefficient of viscosity of
the liquid ish, then the sphere encounters an
opposing force of
(a)6
2
pha v (b)
6h
p
v
a
(c)6phav (d)
phv
a 6
3
13. A scientist proposes a new temperature scale
in which the ice point is 25 X (X is the new unit
of temperature) and the steam point is 305 X.
The specific heat capacity of water in this new
scale is (in J kg X
- - 1 1
)
(a) 4.2 ´ 10
3
(b) 3.0 ´ 10
3
(c)1.2 ´ 10
3
(d)1.5 ´ 10
3
14. One mole of a van der Waals’ gas obeying the
equation
p
a
V
V b RT +
æ
è
ç
ö
ø
÷ - =
2
( )
undergoes the quasi-static cyclic process which
is shown in the p-V diagram. The net heat
absorbed by the gas in this process is
(a)
1
2
1 2 1 2
( )( ) p p V V - -
(b)
1
2
1 2 1 2
( )( ) p p V V + -
(c)
1
2
1
1
2
2
2
2
1 2
p
a
V
p
a
V
V V + - -
æ
è
ç
ç
ö
ø
÷
÷
- ( )
(d)
1
2
1
1
2
2
2
2
1 2
p
a
V
p
a
V
V V + + +
æ
è
ç
ç
ö
ø
÷
÷
- ( )
15. A wooden block is floating on water kept in a
beaker. 40% of the block is above the water
surface. Now the beaker is kept inside a lift
that starts going upward with acceleration
equal to g/ 2. The block will then
(a) sink
(b) float with 10% above the water surface
(c) float with 40% above the water surface
(d) float with 70% above the water surface
16. A smooth massless string passes over a smooth
fixed pulley. Two masses m
1
and m
2
, ( ) m m
1 2
>
are tied at the two ends of the string. The
masses are allowed to move under gravity
starting from rest. The total external force
acting on the two masses is
(a)( ) m m g
1 2
+ (b)
( ) m m
m m
g
1 2
2
1 2
-
+
(c)( ) m m g
1 2
- (d)
( ) m m
m m
g
1 2
2
1 2
+
-
17. To determine the coefficient of friction between
a rough surface and a block, the surface is kept
inclined at 45° and the block is released from
rest. The block takes a time t in moving a
distance d. The rough surface is then replaced
by a smooth surface and the same experiment
is repeated. The block now takes a time t/ 2 in
moving down the same distance d. The
coefficient of friction is
(a) 3/4 (b) 5/4 (c) 1/2 (d)1 2 /
p
p
1
p
2
V
2
V
1
V
Page 2 of 56
18. A metal rod is fixed rigidly at two ends so as to
prevent its thermal expansion. If L,a and Y
respectively denote the length of the rod,
coefficient of linear thermal expansion and
Young’s modulus of its material, then for an
increase in temperature of the rod by DT, the
longitudinal stress developed in the rod is
(a) inversely proportional toa
(b) inversely proportional to Y
(c) directly proportional toDT Y /
(d) independent of L
19. A particle is moving uniformly in a circular
path of radius r. When it moves through an
angular displacementq, then the magnitude of
the corresponding linear displacement will be
(a)2
2
r cos
q æ
è
ç
ö
ø
÷
(b)2
2
r cot
q æ
è
ç
ö
ø
÷
(c)2
2
r tan
q æ
è
ç
ö
ø
÷
(d)2
2
r sin
q æ
è
ç
ö
ø
÷
20. A uniform rod is suspended horizontally from
its mid-point. A piece of metal whose weight is
w is suspended at a distance l from the
mid-point. Another weight W
1
is suspended on
the other side at a distance l
1
from the
mid-point to bring the rod to a horizontal
position. When w is completely immersed in
water, w
1
needs to be kept at a distance l
2
from
the mid-point to get the rod back into
horizontal position. The specific gravity of the
metal piece is
(a)
w
w
1
(b)
w
w w
l
l l
1
1 2
-
(c)
l
l l
1
1 2
-
(d)
l
l
1
2
21. A drop of some liquid of volume 0.04 cm
3
is
placed on the surface of a glass slide. Then
another glass slide is placed on it in such a way
that the liquid forms a thin layer of area 20
2
cm
between the surfaces of the two slides. To
separate the slides a force of 16 10
5
´ dyne has
to be applied normal to the surfaces. The
surface tension of the liquid is (in dyne-cm
-1
)
(a) 60 (b) 70 (c) 80 (d) 90
22. An electron in a circular orbit of radius 0.05 nm
performs 10
16
revolutions per second. The
magnetic moment due to this rotation of
electron is (in Am
2
)
(a)2.16 ´
-
10
23
(b) 3.21´
-
10
22
(c) 3.21´
-
10
24
(d)1.26 ´
-
10
23
23. A very small circular loop of radius a is initially
(at t = 0) coplanar and concentric with a much
larger fixed circular loop of radius b. A
constant current I flows in the larger loop. The
smaller loop is rotated with a constant angular
speed w about the common diameter. The emf
induced in the smaller loop as a function of
time t is
(a)
p m
w w
a I
b
t
2
0
2
cos ( ) (b)
p m
w w
a I
b
t
2
0 2 2
2
sin( )
(c)
p m
w w
a I
b
t
2
0
2
sin( ) (d)
p m
w w
a I
b
t
2
0 2
2
sin ( )
24. A luminous object is separated from a screen
by distance d. A convex lens is placed between
the object and the screen such that it forms a
distinct image on the screen. The maximum
possible focal length of this convex lens is
(a) 4d (b)2d
(c)
d
2
(d)
d
4
25. An infinite sheet carrying a uniform surface
charge densitys lies on the xy-plane. The work
done to carry a charge q from the point
A i j k = + + a(
$ $ $
) 2 3 to the point B i j k = - + a(
$ $ $
) 2 6
(where a is a constant with the dimension of
length and e
0
is the permittivity of free space)
is
(a)
3
2
0
s
e
aq
(b)
2
0
s
e
aq
(c)
5
2
0
s
e
aq
(d)
3
0
s
e
aq
26. The intensity of magnetization of a bar magnet
is 5.0 Am ´
-
10
4 1
. The magnetic length and the
area of cross-section of the magnet are 12 cm
and 1
2
cm respectively. The magnitude of
magnetic moment of this bar magnet is
(in SI unit)
(a) 0.6 (b) 1.3 (c) 1.24 (d) 2.4
27. A particle moves with constant acceleration
along a straight line starting from rest. The
percentage increase in its displacement during
the 4th second compared to that in the
3rd second is
(a) 33% (b) 40% (c) 66% (d) 77%
Page 3 of 56
28. A proton of mass m and charge q is moving in a
plane with kinetic energy E. If there exists a
uniform magnetic field B, perpendicular to the
plane of the motion, the proton will move in a
circular path of radius
(a)
2Em
qB
(b)
2Em
qB
(c)
Em
qB 2
(d)
2Eq
mB
29. An artificial satellite moves in a circular orbit
around the earth. Total energy of the satellite
is given by E. The potential energy of the
satellite is
(a)-2E (b)2E (c)
2
3
E
(d) -
2
3
E
30. In which of the following phenomena, the heat
waves travel along straight lines with the
speed of light?
(a) Thermal conduction (b) Forced convection
(c) Natural convection (d) Thermal radiation
31. In the bandgap between valence band and
conduction band in a material is 5.0 eV, then
the material is
(a) semiconductor (b) good conductor
(c) superconductor (d) insulator
32. A uniform solid spherical ball is rolling down a
smooth inclined plane from a height h. The
velocity attained by the ball when it reaches
the bottom of the inclined plane is v. If the ball
is now thrown vertically upwards with the
same velocity v, the maximum height to which
the ball will rise is
(a)
5
8
h
(b)
3
5
h
(c)
5
7
h
(d)
7
9
h
33. Two coherent monochromatic beams of
intensities I and 4I respectively are
superposed. The maximum and minimum
intensities in the resulting pattern are
(a) 5 3 I I and (b) 9 3 I I and
(c) 4I I and (d) 9I I and
34. In the circuit shown assume the diode to be
ideal. When V
i
increases from 2V to 6 V, the
change in the current is (in mA)
(a) zero (b) 20
(c) 80/3 (d) 40
35. If n denotes a positive integer, h the Planck’s
constant, q the charge and B the magnetic
field, then the quantity
nh
qB 2p
é
ë
ê
ù
û
ú
has the
dimension of
(a) area (b) length
(c) speed (d) acceleration
36. In a transistor output characteristics
commonly used in common emitter
configuration, the base current I
B
,the collector
current I
C
and the collector-emitter voltage
V
CE
have values of the following orders of
magnitude in the active region
(a) I I
B C
and both are inmA andV
CE
in volt
(b) I
B
is inmA and I
C
is in mA andV
CE
in volt
(c) I
B
is in mA and I
C
is inmA andV
CE
in mV
(d) I
B
is in mA and I
C
is in mA andV
CE
in mV
37. The displacement of a particle in a periodic
motion is given by y
t
t =
æ
è
ç
ö
ø
÷ 4
2
1000
2
cos sin ( ).
This displacement may be considered as the
result of superposition of n independent
harmonic oscillations. Here n is
(a) 1 (b) 2 (c) 3 (d) 4
38. Consider a black body radiation in a cubical
box at absolute temperature T. If the length of
each side of the box is doubled and the
temperature of the walls of the box and that of
the radiation is halved, then the total energy
(a) halves (b) doubles
(c) quadruples (d) remains the same
39. Consider two concentric spherical metal shells
of radii r
1
and r
2
( ) r r
2 1
> . If the outer shell has a
charge q and the inner one is grounded, the
charge on the inner shell is
(a)
-r
r
q
2
1
(b) zero
(c)
-r
r
q
1
2
(d) -q
40. Four cells, each of emf E and internal
resistance r, are connected in series across an
external resistance R. By mistake one of the
cells is connected in reverse. Then the current
in the external circuit is
(a)
2
4
E
r R +
(b)
3
4
E
r R +
(c)
3
3
E
r R +
(d)
2
3
E
r R +
V
i 150 W +3V
Page 4 of 56
41. Same quantity of ice is filled in each of the two
metal containers P and Q having the same
size, shape and wall thickness but made of
different materials. The containers are kept in
identical surroundings. The ice in P melts
completely in time t
1
whereas in Q takes a time
t
2
. The ratio of thermal conductivities of the
materials of P and Q is
(a)t t
2 1
:
(b)t t
1 2
:
(c)t t
1
2
2
2
:
(d)t t
2
2
1
2
:
42. For the radioactive nuclei that undergo eithera or
b decay, which one of the following cannot occur?
(a) Isobar of original nucleus is produced
(b) Isotope of the original nucleus is produced
(c) Nuclei with higher atomic number than that of the
original nucleus is produced
(d) Nuclei with lower atomic number than that of the
original nucleus is produced
43. A car is moving with a speed of 72 km-h
-1
towards a roadside source that emits sound at
a frequency of 850 Hz. The car driver listens to
the sound while approaching the source and
again while moving away from the source after
crossing it. If the velocity of sound is 340
1
ms
-
,
the difference of the two frequencies, the driver
hears is
(a) 50 Hz (b) 85 Hz (c) 100 Hz (d) 150 Hz
44. The energy of gamma ( ) g ray photon is E
g
and
that of an X-ray photon is E
X
. If the visible
light photon has an energy of E
v
, then we can
say that
(a) E E E
X v
> >
g
(b) E E E
v x g
> >
(c) E E E
X v g
> > (d) E E E
X v
> >
g
45. The intermediate image formed by the
objective of a compound microscope is
(a) real, inverted and magnified
(b) real, erect and magnified
(c) virtual, erect and magnified
(d) virtual, inverted and magnified
Category II
Directions(Q. Nos.46-55) Carry two marks each, for which only one option is correct. Any wrong answer will
lead to deduction of 2/3 mark.
46. A solid uniform sphere resting on a rough
horizontal plane is given a horizontal impulse
directed through its centre so that it starts
sliding with an initial velocity v
0
. When it
finally starts rolling without slipping the speed
of its centre is
(a)
2
7
0
v (b)
3
7
0
v (c)
5
7
0
v (d)
6
7
0
v
47. The de-Broglie wavelength of an electron is the
same as that of a 50 keV X-ray photon. The
ratio of the energy of the photon to the kinetic
energy of the electron is (the energy equivalent
of electron mass is 0.5 MeV)
(a) 1 : 50 (b) 1 : 20
(c) 20 : 1 (d) 50 : 1
48. A glass slab consists of thin uniform layers of
progressively decreasing refractive indices RI
(see figure) such that the RI of any layer is
m m - m D . Here,m and Dm denote the RI of 0th
layer and the difference in RI between any two
consecutive layers, respectively. The integer
m = 0 1 2 3 , , , ,K denotes the numbers of the
successive layers.
A ray of light from the 0th layer enters the 1st
layer at an angle of incidence of 30°. After
undergoing the mth refraction, the ray
emerges parallel to the interface. Ifm = 1.5 and
Dm = 0.015, the value of m is
(a) 20 (b) 30 (c) 40 (d) 50
m D m –m
m D m –2
m D m –
30°
m
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