WBJEE Previous Year Question Paper - 2018 | WBJEE Sample Papers, Section Wise & Full Mock Tests 2026 PDF Download

 Page 1


Category-I (Q. Nos. 1 to 30)
Only one answer is correct. Correct answer will
fetch full marks 1. Incorrect answer or any
combination of more than one answer will fetch
-
1
4
marks. No answer will fetch 0 marks.
1. Four resistors,100 O,200 300 O, O and 400 O
are connected to form four sides of a square.
The resistors can be connected in any order.
What is the maximum possible equivalent
resistance across the diagonal of the square?
(a)210O (b)240O
(c) 300O (d)250O
2. What will be current through the200 O
resistor in the given circuit, a long time after
the switch K is made on?
(a) Zero (b) 100 mA
(c) 10 mA (d) 1 mA
3. A point source is placed at coordinates (0, 1)
in xy-plane. A ray of light from the source is
reflected on a plane mirror placed along the
X-axis and perpendicular to the xy-plane.
The reflected ray passes through the point
(3, 3). What is the path length of the ray
from (0, 1) to (3, 3)?
(a) 5 (b) 13
(c)2 3 (d) 1 2 3 +
4. Two identical
equiconvex lenses,
each of focal length f
are placed side by side
in contact with each
other with a layer of
water in between
them as shown in the figure. If refractive
index of the material of the lenses is greater
than that of water, how the combined focal
length F is related to f?
(a) F f > (b)
f
F f
2
< <
(c) F
f
<
2
(d) F f =
5. There is a small air bubble at the centre of a
solid glass sphere of radius r and refractive
index µ. What will be the apparent distance
of the bubble from the centre of the sphere,
when viewed from outside?
(a) r (b)
r
µ
(c) r 1
1
-
?
?
?
?
?
?
µ
(d) Zero
Physics
100O 400O
200O 300O
2 F µ
1 F µ
K
6V
WB JEE
Engineering Entrance Exam
Solved Paper 2018
Page 1 of 44
Page 2


Category-I (Q. Nos. 1 to 30)
Only one answer is correct. Correct answer will
fetch full marks 1. Incorrect answer or any
combination of more than one answer will fetch
-
1
4
marks. No answer will fetch 0 marks.
1. Four resistors,100 O,200 300 O, O and 400 O
are connected to form four sides of a square.
The resistors can be connected in any order.
What is the maximum possible equivalent
resistance across the diagonal of the square?
(a)210O (b)240O
(c) 300O (d)250O
2. What will be current through the200 O
resistor in the given circuit, a long time after
the switch K is made on?
(a) Zero (b) 100 mA
(c) 10 mA (d) 1 mA
3. A point source is placed at coordinates (0, 1)
in xy-plane. A ray of light from the source is
reflected on a plane mirror placed along the
X-axis and perpendicular to the xy-plane.
The reflected ray passes through the point
(3, 3). What is the path length of the ray
from (0, 1) to (3, 3)?
(a) 5 (b) 13
(c)2 3 (d) 1 2 3 +
4. Two identical
equiconvex lenses,
each of focal length f
are placed side by side
in contact with each
other with a layer of
water in between
them as shown in the figure. If refractive
index of the material of the lenses is greater
than that of water, how the combined focal
length F is related to f?
(a) F f > (b)
f
F f
2
< <
(c) F
f
<
2
(d) F f =
5. There is a small air bubble at the centre of a
solid glass sphere of radius r and refractive
index µ. What will be the apparent distance
of the bubble from the centre of the sphere,
when viewed from outside?
(a) r (b)
r
µ
(c) r 1
1
-
?
?
?
?
?
?
µ
(d) Zero
Physics
100O 400O
200O 300O
2 F µ
1 F µ
K
6V
WB JEE
Engineering Entrance Exam
Solved Paper 2018
Page 1 of 44
6. If Young’s double slit experiment is done
with white light, which of the following
statements will be true?
(a) All the bright fringes will be coloured.
(b) All the bright fringes will be white.
(c) The central fringe will be white.
(d) No stable interference pattern will be visible.
7. How the linear velocity v of an electron in the
Bohr orbit is related to its quantum numbern?
(a) v
n
?
1
(b) v
n
?
1
2
(c) v
n
?
1
(d) v n ?
8. If the half-life of a radioactive nucleus is
3 days, nearly what fraction of the initial
number of nuclei will decay on the third day?
(Given, 0.25
3
063 ˜ . )
(a) 0.63 (b) 0.5 (c) 0.37 (d) 0.13
9. An electron accelerated through a potential
of 10000 V from rest has a de-Broglie wave
length ?. What should be the accelerating
potential, so that the wavelength is doubled?
(a) 20000 V (b) 40000 V (c) 5000 V (d) 2500 V
10. In the circuit shown, inputs A and B are in
states 1 and 0 respectively. What is the only
possible stable state of the outputs X and Y?
(a) X = 1, Y = 1 (b) X = 1, Y = 0
(c) X = 0, Y = 1 (d) X = 0, Y = 0
11. What will be the current flowing through the
6kO resistor in the circuit shown, where the
breakdown voltage of the Zener is 6 V?
(a)
2
3
mA (b)1mA (c) 10 mA (d)
3
2
mA
12. In case of a simple harmonic motion, if the
velocity is plotted along the X-axis and the
displacement (from the equilibrium position)
is plotted along the Y-axis, the resultant
curve happens to be an ellipse with the ratio:
majoraxis(along )
minoraxis(along )
X
Y
=20p
What is the frequency of the simple harmonic
motion?
(a) 100 Hz (b) 20 Hz (c) 10 Hz (d)
1
10
Hz
13. A block of mass m
2
is placed on a horizontal
table and another block of mass m
1
is placed
on top of it. An increasing horizontal force
F t = a is exerted on the upper block but the
lower block never moves as a result. If the
coefficient of friction between the blocks is µ
1
and that between the lower block and the
table is µ
2
, then what is the maximum
possible value of µ µ
1 2
/ ?
(a)
m
m
2
1
(b)1
2
1
+
m
m
(c)
m
m
1
2
(d)1
1
2
+
m
m
14. In a triangle ABC, the sides AB and AC are
represented by the vectors3
$ $ $
i j k + + and
$ $ $
i j k + + 2 , respectively. Calculate the angle
?ABC.
(a)cos
-1
5
11
(b)cos
-1
6
11
(c) 90
5
11
1
° -
?
?
?
?
?
?
-
cos (d) 180
5
11
1
° -
?
?
?
?
?
?
-
cos
15. The velocity() v of a particle (under a force F)
depends on its distance( ) x from the origin
(with x >0) v
x
?
1
. Find how the magnitude
of the force (F) on the particle depends on x?
(a) F
x
?
1
3 2 /
(b) F
x
?
1
(c) F
x
?
1
2
(d) F x ?
16. The ratio of accelerations due to gravity g g
1 2
:
on the surfaces of two planets is 5 : 2 and the
ratio of their respective average densities
? ?
1 2
: is 2 : 1. What is the ratio of respective
escape velocities v v
1 2
: from the surface of the
planets?
(a) 5 2 : (b) 5 2 : (c) 5 2 2 : (d)25 4 :
(1)
(0)
A
B
X
Y
6 kO
10V
4 kO
Page 2 of 44
Page 3


Category-I (Q. Nos. 1 to 30)
Only one answer is correct. Correct answer will
fetch full marks 1. Incorrect answer or any
combination of more than one answer will fetch
-
1
4
marks. No answer will fetch 0 marks.
1. Four resistors,100 O,200 300 O, O and 400 O
are connected to form four sides of a square.
The resistors can be connected in any order.
What is the maximum possible equivalent
resistance across the diagonal of the square?
(a)210O (b)240O
(c) 300O (d)250O
2. What will be current through the200 O
resistor in the given circuit, a long time after
the switch K is made on?
(a) Zero (b) 100 mA
(c) 10 mA (d) 1 mA
3. A point source is placed at coordinates (0, 1)
in xy-plane. A ray of light from the source is
reflected on a plane mirror placed along the
X-axis and perpendicular to the xy-plane.
The reflected ray passes through the point
(3, 3). What is the path length of the ray
from (0, 1) to (3, 3)?
(a) 5 (b) 13
(c)2 3 (d) 1 2 3 +
4. Two identical
equiconvex lenses,
each of focal length f
are placed side by side
in contact with each
other with a layer of
water in between
them as shown in the figure. If refractive
index of the material of the lenses is greater
than that of water, how the combined focal
length F is related to f?
(a) F f > (b)
f
F f
2
< <
(c) F
f
<
2
(d) F f =
5. There is a small air bubble at the centre of a
solid glass sphere of radius r and refractive
index µ. What will be the apparent distance
of the bubble from the centre of the sphere,
when viewed from outside?
(a) r (b)
r
µ
(c) r 1
1
-
?
?
?
?
?
?
µ
(d) Zero
Physics
100O 400O
200O 300O
2 F µ
1 F µ
K
6V
WB JEE
Engineering Entrance Exam
Solved Paper 2018
Page 1 of 44
6. If Young’s double slit experiment is done
with white light, which of the following
statements will be true?
(a) All the bright fringes will be coloured.
(b) All the bright fringes will be white.
(c) The central fringe will be white.
(d) No stable interference pattern will be visible.
7. How the linear velocity v of an electron in the
Bohr orbit is related to its quantum numbern?
(a) v
n
?
1
(b) v
n
?
1
2
(c) v
n
?
1
(d) v n ?
8. If the half-life of a radioactive nucleus is
3 days, nearly what fraction of the initial
number of nuclei will decay on the third day?
(Given, 0.25
3
063 ˜ . )
(a) 0.63 (b) 0.5 (c) 0.37 (d) 0.13
9. An electron accelerated through a potential
of 10000 V from rest has a de-Broglie wave
length ?. What should be the accelerating
potential, so that the wavelength is doubled?
(a) 20000 V (b) 40000 V (c) 5000 V (d) 2500 V
10. In the circuit shown, inputs A and B are in
states 1 and 0 respectively. What is the only
possible stable state of the outputs X and Y?
(a) X = 1, Y = 1 (b) X = 1, Y = 0
(c) X = 0, Y = 1 (d) X = 0, Y = 0
11. What will be the current flowing through the
6kO resistor in the circuit shown, where the
breakdown voltage of the Zener is 6 V?
(a)
2
3
mA (b)1mA (c) 10 mA (d)
3
2
mA
12. In case of a simple harmonic motion, if the
velocity is plotted along the X-axis and the
displacement (from the equilibrium position)
is plotted along the Y-axis, the resultant
curve happens to be an ellipse with the ratio:
majoraxis(along )
minoraxis(along )
X
Y
=20p
What is the frequency of the simple harmonic
motion?
(a) 100 Hz (b) 20 Hz (c) 10 Hz (d)
1
10
Hz
13. A block of mass m
2
is placed on a horizontal
table and another block of mass m
1
is placed
on top of it. An increasing horizontal force
F t = a is exerted on the upper block but the
lower block never moves as a result. If the
coefficient of friction between the blocks is µ
1
and that between the lower block and the
table is µ
2
, then what is the maximum
possible value of µ µ
1 2
/ ?
(a)
m
m
2
1
(b)1
2
1
+
m
m
(c)
m
m
1
2
(d)1
1
2
+
m
m
14. In a triangle ABC, the sides AB and AC are
represented by the vectors3
$ $ $
i j k + + and
$ $ $
i j k + + 2 , respectively. Calculate the angle
?ABC.
(a)cos
-1
5
11
(b)cos
-1
6
11
(c) 90
5
11
1
° -
?
?
?
?
?
?
-
cos (d) 180
5
11
1
° -
?
?
?
?
?
?
-
cos
15. The velocity() v of a particle (under a force F)
depends on its distance( ) x from the origin
(with x >0) v
x
?
1
. Find how the magnitude
of the force (F) on the particle depends on x?
(a) F
x
?
1
3 2 /
(b) F
x
?
1
(c) F
x
?
1
2
(d) F x ?
16. The ratio of accelerations due to gravity g g
1 2
:
on the surfaces of two planets is 5 : 2 and the
ratio of their respective average densities
? ?
1 2
: is 2 : 1. What is the ratio of respective
escape velocities v v
1 2
: from the surface of the
planets?
(a) 5 2 : (b) 5 2 : (c) 5 2 2 : (d)25 4 :
(1)
(0)
A
B
X
Y
6 kO
10V
4 kO
Page 2 of 44
17. A spherical liquid drop is placed on a
horizontal plane. A small disturbance causes
the volume of the drop to oscillate. The time
period of oscillation (T) of the liquid drop
depends on radius() r of the drop, density( ?)
and surface tension() S of the liquid. Which
among the following will be a possible
expression forT (where, k is a dimensionless
constant)?
(a) k
r
S
?
(b) k
r
S
?
2
(c) k
r
S
?
3
(d) k
r
S
?
3
2
18. The stress along the length of a rod (with
rectangular cross-section) is 1% of the
Young’s modulus of its material. What is the
approximate percentage of change of its
volume? (Poisson’s ratio of the material of
the rod is 0.3.)
(a) 3% (b) 1% (c) 0.7% (d) 0.4%
19. What will be the approximate terminal velocity
of a rain drop of diameter1.8 ×
-
10
3
m, when
density of rain water ˜10
3
kgm
3 -
and the
coefficient of viscosity of air ˜ ×
-
1.8 10
5
N-sm
-2
? (Neglect buoyancy of air)
(a) 49ms
1 -
(b) 98ms
1 -
(c) 392ms
1 -
(d) 980ms
1 -
20. The water equivalent of a calorimeter is 10 g
and it contains 50 g of water at 15°C. Some
amount of ice, initially at - ° 10 C is dropped
in it and half of the ice melts till equilibrium
is reached. What was the initial amount of
ice that was dropped (when specific heat of
ice =05 . calgm
1 -
°
-
C
1
, specific heat of water
=10 . calgm
1 -
°
-
C
1
and latent heat of melting
of ice =80 calgm
1 -
)?
(a) 10 g (b) 18 g (c) 20 g (d) 30 g
21. One mole of a monoatomic ideal gas
undergoes a quasistatic process, which is
depicted by a straight line joining points
( , ) V T
0 0
and( , ) 2 3
0 0
V T in a V-T diagram. What
is the value of the heat capacity of the gas at
the point( , ) V T
0 0
?
(a) R (b)
3
2
R
(c)2R (d) 0
22. For an ideal gas with initial pressure and
volume p
i
and V
i
respectively, a reversible
isothermal expansion happens, when its
volume becomes V
0
. Then, it is compressed to
its original volume V
i
by a reversible
adiabatic process. If the final pressure is p
f
,
then which of the following statement(s)
is/are true?
(a) p p
f i
= (b) p p
f i
>
(c) p p
f i
< (d)
p
V
p
V
f i
i 0
=
23. A point charge - q is carried from a point A to
another point B on the axis of a charged ring
of radius r carrying a charge + q. If the point
A is at a distance
4
3
r from the centre of the
ring and the point B is
3
4
r from the centre but
on the opposite side, what is the net work
that need to be done for this?
(a) - ·
7
5 4
2
0
q
r pe
(b) - ·
1
5 4
2
0
q
r pe
(c)
7
5 4
2
0
·
q
r pe
(d)
1
5 4
2
0
·
q
r pe
24. Consider a region in free space bounded by
the surfaces of an imaginary cube having
sides of length a as shown in the figure. A
charge + Q is placed at the centre O of the
cube. P is such a point outside the cube that
the line OP perpendicularly intersects the
surface ABCD at R and also OR RP a = = /2.
A charge + Q is placed at point P also. What is
the total electric flux through the five faces
of the cube other than ABCD?
(a)
Q
e
0
(b)
5
6
0
Q
e
(c)
10
6
0
Q
e
(d) zero
a
A
B
O
a/2
+Q
a
a C
D
a/2
R
P
+Q
Page 3 of 44
Page 4


Category-I (Q. Nos. 1 to 30)
Only one answer is correct. Correct answer will
fetch full marks 1. Incorrect answer or any
combination of more than one answer will fetch
-
1
4
marks. No answer will fetch 0 marks.
1. Four resistors,100 O,200 300 O, O and 400 O
are connected to form four sides of a square.
The resistors can be connected in any order.
What is the maximum possible equivalent
resistance across the diagonal of the square?
(a)210O (b)240O
(c) 300O (d)250O
2. What will be current through the200 O
resistor in the given circuit, a long time after
the switch K is made on?
(a) Zero (b) 100 mA
(c) 10 mA (d) 1 mA
3. A point source is placed at coordinates (0, 1)
in xy-plane. A ray of light from the source is
reflected on a plane mirror placed along the
X-axis and perpendicular to the xy-plane.
The reflected ray passes through the point
(3, 3). What is the path length of the ray
from (0, 1) to (3, 3)?
(a) 5 (b) 13
(c)2 3 (d) 1 2 3 +
4. Two identical
equiconvex lenses,
each of focal length f
are placed side by side
in contact with each
other with a layer of
water in between
them as shown in the figure. If refractive
index of the material of the lenses is greater
than that of water, how the combined focal
length F is related to f?
(a) F f > (b)
f
F f
2
< <
(c) F
f
<
2
(d) F f =
5. There is a small air bubble at the centre of a
solid glass sphere of radius r and refractive
index µ. What will be the apparent distance
of the bubble from the centre of the sphere,
when viewed from outside?
(a) r (b)
r
µ
(c) r 1
1
-
?
?
?
?
?
?
µ
(d) Zero
Physics
100O 400O
200O 300O
2 F µ
1 F µ
K
6V
WB JEE
Engineering Entrance Exam
Solved Paper 2018
Page 1 of 44
6. If Young’s double slit experiment is done
with white light, which of the following
statements will be true?
(a) All the bright fringes will be coloured.
(b) All the bright fringes will be white.
(c) The central fringe will be white.
(d) No stable interference pattern will be visible.
7. How the linear velocity v of an electron in the
Bohr orbit is related to its quantum numbern?
(a) v
n
?
1
(b) v
n
?
1
2
(c) v
n
?
1
(d) v n ?
8. If the half-life of a radioactive nucleus is
3 days, nearly what fraction of the initial
number of nuclei will decay on the third day?
(Given, 0.25
3
063 ˜ . )
(a) 0.63 (b) 0.5 (c) 0.37 (d) 0.13
9. An electron accelerated through a potential
of 10000 V from rest has a de-Broglie wave
length ?. What should be the accelerating
potential, so that the wavelength is doubled?
(a) 20000 V (b) 40000 V (c) 5000 V (d) 2500 V
10. In the circuit shown, inputs A and B are in
states 1 and 0 respectively. What is the only
possible stable state of the outputs X and Y?
(a) X = 1, Y = 1 (b) X = 1, Y = 0
(c) X = 0, Y = 1 (d) X = 0, Y = 0
11. What will be the current flowing through the
6kO resistor in the circuit shown, where the
breakdown voltage of the Zener is 6 V?
(a)
2
3
mA (b)1mA (c) 10 mA (d)
3
2
mA
12. In case of a simple harmonic motion, if the
velocity is plotted along the X-axis and the
displacement (from the equilibrium position)
is plotted along the Y-axis, the resultant
curve happens to be an ellipse with the ratio:
majoraxis(along )
minoraxis(along )
X
Y
=20p
What is the frequency of the simple harmonic
motion?
(a) 100 Hz (b) 20 Hz (c) 10 Hz (d)
1
10
Hz
13. A block of mass m
2
is placed on a horizontal
table and another block of mass m
1
is placed
on top of it. An increasing horizontal force
F t = a is exerted on the upper block but the
lower block never moves as a result. If the
coefficient of friction between the blocks is µ
1
and that between the lower block and the
table is µ
2
, then what is the maximum
possible value of µ µ
1 2
/ ?
(a)
m
m
2
1
(b)1
2
1
+
m
m
(c)
m
m
1
2
(d)1
1
2
+
m
m
14. In a triangle ABC, the sides AB and AC are
represented by the vectors3
$ $ $
i j k + + and
$ $ $
i j k + + 2 , respectively. Calculate the angle
?ABC.
(a)cos
-1
5
11
(b)cos
-1
6
11
(c) 90
5
11
1
° -
?
?
?
?
?
?
-
cos (d) 180
5
11
1
° -
?
?
?
?
?
?
-
cos
15. The velocity() v of a particle (under a force F)
depends on its distance( ) x from the origin
(with x >0) v
x
?
1
. Find how the magnitude
of the force (F) on the particle depends on x?
(a) F
x
?
1
3 2 /
(b) F
x
?
1
(c) F
x
?
1
2
(d) F x ?
16. The ratio of accelerations due to gravity g g
1 2
:
on the surfaces of two planets is 5 : 2 and the
ratio of their respective average densities
? ?
1 2
: is 2 : 1. What is the ratio of respective
escape velocities v v
1 2
: from the surface of the
planets?
(a) 5 2 : (b) 5 2 : (c) 5 2 2 : (d)25 4 :
(1)
(0)
A
B
X
Y
6 kO
10V
4 kO
Page 2 of 44
17. A spherical liquid drop is placed on a
horizontal plane. A small disturbance causes
the volume of the drop to oscillate. The time
period of oscillation (T) of the liquid drop
depends on radius() r of the drop, density( ?)
and surface tension() S of the liquid. Which
among the following will be a possible
expression forT (where, k is a dimensionless
constant)?
(a) k
r
S
?
(b) k
r
S
?
2
(c) k
r
S
?
3
(d) k
r
S
?
3
2
18. The stress along the length of a rod (with
rectangular cross-section) is 1% of the
Young’s modulus of its material. What is the
approximate percentage of change of its
volume? (Poisson’s ratio of the material of
the rod is 0.3.)
(a) 3% (b) 1% (c) 0.7% (d) 0.4%
19. What will be the approximate terminal velocity
of a rain drop of diameter1.8 ×
-
10
3
m, when
density of rain water ˜10
3
kgm
3 -
and the
coefficient of viscosity of air ˜ ×
-
1.8 10
5
N-sm
-2
? (Neglect buoyancy of air)
(a) 49ms
1 -
(b) 98ms
1 -
(c) 392ms
1 -
(d) 980ms
1 -
20. The water equivalent of a calorimeter is 10 g
and it contains 50 g of water at 15°C. Some
amount of ice, initially at - ° 10 C is dropped
in it and half of the ice melts till equilibrium
is reached. What was the initial amount of
ice that was dropped (when specific heat of
ice =05 . calgm
1 -
°
-
C
1
, specific heat of water
=10 . calgm
1 -
°
-
C
1
and latent heat of melting
of ice =80 calgm
1 -
)?
(a) 10 g (b) 18 g (c) 20 g (d) 30 g
21. One mole of a monoatomic ideal gas
undergoes a quasistatic process, which is
depicted by a straight line joining points
( , ) V T
0 0
and( , ) 2 3
0 0
V T in a V-T diagram. What
is the value of the heat capacity of the gas at
the point( , ) V T
0 0
?
(a) R (b)
3
2
R
(c)2R (d) 0
22. For an ideal gas with initial pressure and
volume p
i
and V
i
respectively, a reversible
isothermal expansion happens, when its
volume becomes V
0
. Then, it is compressed to
its original volume V
i
by a reversible
adiabatic process. If the final pressure is p
f
,
then which of the following statement(s)
is/are true?
(a) p p
f i
= (b) p p
f i
>
(c) p p
f i
< (d)
p
V
p
V
f i
i 0
=
23. A point charge - q is carried from a point A to
another point B on the axis of a charged ring
of radius r carrying a charge + q. If the point
A is at a distance
4
3
r from the centre of the
ring and the point B is
3
4
r from the centre but
on the opposite side, what is the net work
that need to be done for this?
(a) - ·
7
5 4
2
0
q
r pe
(b) - ·
1
5 4
2
0
q
r pe
(c)
7
5 4
2
0
·
q
r pe
(d)
1
5 4
2
0
·
q
r pe
24. Consider a region in free space bounded by
the surfaces of an imaginary cube having
sides of length a as shown in the figure. A
charge + Q is placed at the centre O of the
cube. P is such a point outside the cube that
the line OP perpendicularly intersects the
surface ABCD at R and also OR RP a = = /2.
A charge + Q is placed at point P also. What is
the total electric flux through the five faces
of the cube other than ABCD?
(a)
Q
e
0
(b)
5
6
0
Q
e
(c)
10
6
0
Q
e
(d) zero
a
A
B
O
a/2
+Q
a
a C
D
a/2
R
P
+Q
Page 3 of 44
25. Four equal charges of value + Q are placed at
any four vertices of a regular hexagon of side
‘a’. By suitably choosing the vertices, what
can be the maximum possible magnitude of
electric field at the centre of the hexagon?
(a)
Q
a 4
0
2
pe
(b)
2
4
0
2
Q
a pe
(c)
3
4
0
2
Q
a pe
(d)
2
4
0
2
Q
a pe
26. A proton of mass m moving with a speed v
(<< c, velocity of light in vacuum) completes
a circular orbit in timeT in a uniform
magnetic field. If the speed of the proton is
increased to 2 v, what will be time needed to
complete the circular orbit?
(a) 2T (b)T
(c)
T
2
(d)
T
2
27. A uniform current is flowing along the length
of an infinite, straight, thin, hollow cylinder
of radius R. The magnetic field B produced at
a perpendicular distance d from the axis of
the cylinder is plotted in a graph. Which of
the following figures looks like the plot?
28. A circular loop of radius r of conducting wire
connected with a voltage source of zero
internal resistance produces a magnetic field
B at its centre. If instead, a circular loop of
radius2r, made of same material, having the
same cross-section is connected to the same
voltage source, what will be the magnetic
field at its centre?
(a)
B
2
(b)
B
4
(c)2B (d) B
29. An alternating current is flowing through a
series L-C-R circuit. It is found that the
current reaches a value of 1 mA at both
200 Hz and 800 Hz frequency. What is the
resonance frequency of the circuit?
(a) 600 Hz (b) 300 Hz
(c) 500 Hz (d) 400 Hz
30. An electric bulb, a capacitor, a battery and a
switch are all in series in a circuit. How does
the intensity of light vary when the switch is
turn on?
(a) Continues to increase gradually
(b) Gradually increases for sometime and then
becomes steady
(c) Sharply rises initially and then gradually
decreases
(d) Gradually increases for sometime and then
gradually decreases
Category-II (Q. Nos. 31 to 35)
Only one answer is correct. Correct answer will
fetch full marks 2. Incorrect answer or any
combination of more than one answer will fetch
-
1
2
marks. No answer will fetch 0 marks.
31. A light charged particle is revolving in a
circle of radius r in electrostatic attraction of
a static heavy particle with opposite charge.
How does the magnetic field B at the centre
of the circle due to the moving charge
depend on r ?
(a) B
r
?
1
(b) B
r
?
1
2
(c) B
r
?
1
3 2 /
(d) B
r
?
1
5 2 /
32. As shown in the figure, a rectangular loop of
a conducting wire is moving away with a
constant velocity v in a perpendicular
direction from a very long straight conductor
carrying a steady current I. When the
B
(a)
(b)
R
d
B
R
d
(c)
B
R
d
(d)
B
R
d
Page 4 of 44
Page 5


Category-I (Q. Nos. 1 to 30)
Only one answer is correct. Correct answer will
fetch full marks 1. Incorrect answer or any
combination of more than one answer will fetch
-
1
4
marks. No answer will fetch 0 marks.
1. Four resistors,100 O,200 300 O, O and 400 O
are connected to form four sides of a square.
The resistors can be connected in any order.
What is the maximum possible equivalent
resistance across the diagonal of the square?
(a)210O (b)240O
(c) 300O (d)250O
2. What will be current through the200 O
resistor in the given circuit, a long time after
the switch K is made on?
(a) Zero (b) 100 mA
(c) 10 mA (d) 1 mA
3. A point source is placed at coordinates (0, 1)
in xy-plane. A ray of light from the source is
reflected on a plane mirror placed along the
X-axis and perpendicular to the xy-plane.
The reflected ray passes through the point
(3, 3). What is the path length of the ray
from (0, 1) to (3, 3)?
(a) 5 (b) 13
(c)2 3 (d) 1 2 3 +
4. Two identical
equiconvex lenses,
each of focal length f
are placed side by side
in contact with each
other with a layer of
water in between
them as shown in the figure. If refractive
index of the material of the lenses is greater
than that of water, how the combined focal
length F is related to f?
(a) F f > (b)
f
F f
2
< <
(c) F
f
<
2
(d) F f =
5. There is a small air bubble at the centre of a
solid glass sphere of radius r and refractive
index µ. What will be the apparent distance
of the bubble from the centre of the sphere,
when viewed from outside?
(a) r (b)
r
µ
(c) r 1
1
-
?
?
?
?
?
?
µ
(d) Zero
Physics
100O 400O
200O 300O
2 F µ
1 F µ
K
6V
WB JEE
Engineering Entrance Exam
Solved Paper 2018
Page 1 of 44
6. If Young’s double slit experiment is done
with white light, which of the following
statements will be true?
(a) All the bright fringes will be coloured.
(b) All the bright fringes will be white.
(c) The central fringe will be white.
(d) No stable interference pattern will be visible.
7. How the linear velocity v of an electron in the
Bohr orbit is related to its quantum numbern?
(a) v
n
?
1
(b) v
n
?
1
2
(c) v
n
?
1
(d) v n ?
8. If the half-life of a radioactive nucleus is
3 days, nearly what fraction of the initial
number of nuclei will decay on the third day?
(Given, 0.25
3
063 ˜ . )
(a) 0.63 (b) 0.5 (c) 0.37 (d) 0.13
9. An electron accelerated through a potential
of 10000 V from rest has a de-Broglie wave
length ?. What should be the accelerating
potential, so that the wavelength is doubled?
(a) 20000 V (b) 40000 V (c) 5000 V (d) 2500 V
10. In the circuit shown, inputs A and B are in
states 1 and 0 respectively. What is the only
possible stable state of the outputs X and Y?
(a) X = 1, Y = 1 (b) X = 1, Y = 0
(c) X = 0, Y = 1 (d) X = 0, Y = 0
11. What will be the current flowing through the
6kO resistor in the circuit shown, where the
breakdown voltage of the Zener is 6 V?
(a)
2
3
mA (b)1mA (c) 10 mA (d)
3
2
mA
12. In case of a simple harmonic motion, if the
velocity is plotted along the X-axis and the
displacement (from the equilibrium position)
is plotted along the Y-axis, the resultant
curve happens to be an ellipse with the ratio:
majoraxis(along )
minoraxis(along )
X
Y
=20p
What is the frequency of the simple harmonic
motion?
(a) 100 Hz (b) 20 Hz (c) 10 Hz (d)
1
10
Hz
13. A block of mass m
2
is placed on a horizontal
table and another block of mass m
1
is placed
on top of it. An increasing horizontal force
F t = a is exerted on the upper block but the
lower block never moves as a result. If the
coefficient of friction between the blocks is µ
1
and that between the lower block and the
table is µ
2
, then what is the maximum
possible value of µ µ
1 2
/ ?
(a)
m
m
2
1
(b)1
2
1
+
m
m
(c)
m
m
1
2
(d)1
1
2
+
m
m
14. In a triangle ABC, the sides AB and AC are
represented by the vectors3
$ $ $
i j k + + and
$ $ $
i j k + + 2 , respectively. Calculate the angle
?ABC.
(a)cos
-1
5
11
(b)cos
-1
6
11
(c) 90
5
11
1
° -
?
?
?
?
?
?
-
cos (d) 180
5
11
1
° -
?
?
?
?
?
?
-
cos
15. The velocity() v of a particle (under a force F)
depends on its distance( ) x from the origin
(with x >0) v
x
?
1
. Find how the magnitude
of the force (F) on the particle depends on x?
(a) F
x
?
1
3 2 /
(b) F
x
?
1
(c) F
x
?
1
2
(d) F x ?
16. The ratio of accelerations due to gravity g g
1 2
:
on the surfaces of two planets is 5 : 2 and the
ratio of their respective average densities
? ?
1 2
: is 2 : 1. What is the ratio of respective
escape velocities v v
1 2
: from the surface of the
planets?
(a) 5 2 : (b) 5 2 : (c) 5 2 2 : (d)25 4 :
(1)
(0)
A
B
X
Y
6 kO
10V
4 kO
Page 2 of 44
17. A spherical liquid drop is placed on a
horizontal plane. A small disturbance causes
the volume of the drop to oscillate. The time
period of oscillation (T) of the liquid drop
depends on radius() r of the drop, density( ?)
and surface tension() S of the liquid. Which
among the following will be a possible
expression forT (where, k is a dimensionless
constant)?
(a) k
r
S
?
(b) k
r
S
?
2
(c) k
r
S
?
3
(d) k
r
S
?
3
2
18. The stress along the length of a rod (with
rectangular cross-section) is 1% of the
Young’s modulus of its material. What is the
approximate percentage of change of its
volume? (Poisson’s ratio of the material of
the rod is 0.3.)
(a) 3% (b) 1% (c) 0.7% (d) 0.4%
19. What will be the approximate terminal velocity
of a rain drop of diameter1.8 ×
-
10
3
m, when
density of rain water ˜10
3
kgm
3 -
and the
coefficient of viscosity of air ˜ ×
-
1.8 10
5
N-sm
-2
? (Neglect buoyancy of air)
(a) 49ms
1 -
(b) 98ms
1 -
(c) 392ms
1 -
(d) 980ms
1 -
20. The water equivalent of a calorimeter is 10 g
and it contains 50 g of water at 15°C. Some
amount of ice, initially at - ° 10 C is dropped
in it and half of the ice melts till equilibrium
is reached. What was the initial amount of
ice that was dropped (when specific heat of
ice =05 . calgm
1 -
°
-
C
1
, specific heat of water
=10 . calgm
1 -
°
-
C
1
and latent heat of melting
of ice =80 calgm
1 -
)?
(a) 10 g (b) 18 g (c) 20 g (d) 30 g
21. One mole of a monoatomic ideal gas
undergoes a quasistatic process, which is
depicted by a straight line joining points
( , ) V T
0 0
and( , ) 2 3
0 0
V T in a V-T diagram. What
is the value of the heat capacity of the gas at
the point( , ) V T
0 0
?
(a) R (b)
3
2
R
(c)2R (d) 0
22. For an ideal gas with initial pressure and
volume p
i
and V
i
respectively, a reversible
isothermal expansion happens, when its
volume becomes V
0
. Then, it is compressed to
its original volume V
i
by a reversible
adiabatic process. If the final pressure is p
f
,
then which of the following statement(s)
is/are true?
(a) p p
f i
= (b) p p
f i
>
(c) p p
f i
< (d)
p
V
p
V
f i
i 0
=
23. A point charge - q is carried from a point A to
another point B on the axis of a charged ring
of radius r carrying a charge + q. If the point
A is at a distance
4
3
r from the centre of the
ring and the point B is
3
4
r from the centre but
on the opposite side, what is the net work
that need to be done for this?
(a) - ·
7
5 4
2
0
q
r pe
(b) - ·
1
5 4
2
0
q
r pe
(c)
7
5 4
2
0
·
q
r pe
(d)
1
5 4
2
0
·
q
r pe
24. Consider a region in free space bounded by
the surfaces of an imaginary cube having
sides of length a as shown in the figure. A
charge + Q is placed at the centre O of the
cube. P is such a point outside the cube that
the line OP perpendicularly intersects the
surface ABCD at R and also OR RP a = = /2.
A charge + Q is placed at point P also. What is
the total electric flux through the five faces
of the cube other than ABCD?
(a)
Q
e
0
(b)
5
6
0
Q
e
(c)
10
6
0
Q
e
(d) zero
a
A
B
O
a/2
+Q
a
a C
D
a/2
R
P
+Q
Page 3 of 44
25. Four equal charges of value + Q are placed at
any four vertices of a regular hexagon of side
‘a’. By suitably choosing the vertices, what
can be the maximum possible magnitude of
electric field at the centre of the hexagon?
(a)
Q
a 4
0
2
pe
(b)
2
4
0
2
Q
a pe
(c)
3
4
0
2
Q
a pe
(d)
2
4
0
2
Q
a pe
26. A proton of mass m moving with a speed v
(<< c, velocity of light in vacuum) completes
a circular orbit in timeT in a uniform
magnetic field. If the speed of the proton is
increased to 2 v, what will be time needed to
complete the circular orbit?
(a) 2T (b)T
(c)
T
2
(d)
T
2
27. A uniform current is flowing along the length
of an infinite, straight, thin, hollow cylinder
of radius R. The magnetic field B produced at
a perpendicular distance d from the axis of
the cylinder is plotted in a graph. Which of
the following figures looks like the plot?
28. A circular loop of radius r of conducting wire
connected with a voltage source of zero
internal resistance produces a magnetic field
B at its centre. If instead, a circular loop of
radius2r, made of same material, having the
same cross-section is connected to the same
voltage source, what will be the magnetic
field at its centre?
(a)
B
2
(b)
B
4
(c)2B (d) B
29. An alternating current is flowing through a
series L-C-R circuit. It is found that the
current reaches a value of 1 mA at both
200 Hz and 800 Hz frequency. What is the
resonance frequency of the circuit?
(a) 600 Hz (b) 300 Hz
(c) 500 Hz (d) 400 Hz
30. An electric bulb, a capacitor, a battery and a
switch are all in series in a circuit. How does
the intensity of light vary when the switch is
turn on?
(a) Continues to increase gradually
(b) Gradually increases for sometime and then
becomes steady
(c) Sharply rises initially and then gradually
decreases
(d) Gradually increases for sometime and then
gradually decreases
Category-II (Q. Nos. 31 to 35)
Only one answer is correct. Correct answer will
fetch full marks 2. Incorrect answer or any
combination of more than one answer will fetch
-
1
2
marks. No answer will fetch 0 marks.
31. A light charged particle is revolving in a
circle of radius r in electrostatic attraction of
a static heavy particle with opposite charge.
How does the magnetic field B at the centre
of the circle due to the moving charge
depend on r ?
(a) B
r
?
1
(b) B
r
?
1
2
(c) B
r
?
1
3 2 /
(d) B
r
?
1
5 2 /
32. As shown in the figure, a rectangular loop of
a conducting wire is moving away with a
constant velocity v in a perpendicular
direction from a very long straight conductor
carrying a steady current I. When the
B
(a)
(b)
R
d
B
R
d
(c)
B
R
d
(d)
B
R
d
Page 4 of 44
breadth of the rectangular loop is very small
compared to its distance from the straight
conductor, how does the emf. E induced in
the loop vary with time t ?
(a) E
t
?
1
2
(b) E
t
?
1
(c) E t ?-ln( ) (d) E
t
?
1
3
33. A solid spherical ball and a hollow spherical
ball of two different materials of densities ?
1
and ?
2
respectively have same outer radii and
same mass. What will be the ratio, the
moment of inertia (about an axis passing
through the centre) of the hollow sphere to
that of the solid sphere?
(a)
?
?
?
?
2
1
2
1
5
3
1 -
?
?
?
?
?
? (b)
?
?
?
?
2
1
2
1
5
3
1 1 - -
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
(c)
?
?
?
?
2
1
1
2
5
3
1 -
?
?
?
?
?
? (d)
?
?
?
?
2
1
1
2
5
3
1 1 - -
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
34. The insulated plates of a charged parallel
plate capacitor (with small separation
between the plates) are approaching each
other due to electrostatic attraction.
Assuming no other force to be operative and
no radiation taking place, which of the
following graphs approximately shows the
variation with time() t of the potential
difference( ) V between the plates?
35. The bob of a pendulum of mass m,
suspended by an inextensible string of length
L as shown in the figure carries a small
charge q. An infinite horizontal plane
conductor with uniform surface charge
density s is placed below it. What will be the
time period of the pendulum for small
amplitude oscillations?
(a)2
0
p
e s
L
g
mq
-
?
?
?
?
?
?
(b)
L
g
mq
-
?
?
?
?
?
?
s
e
0
(c)
1
2
0
p s
e
L
g
q
m
-
?
?
?
?
?
?
(d)2
0
p
s
e
L
g
q
m
-
?
?
?
?
?
?
Category-III (Q. Nos. 36 to 40)
One or more answer(s) is (are) correct. Correct
answer(s) will fetch full marks 2. Any combination
containing one or more incorrect answer will fetch
0 marks. Also, no answer will fetch 0 marks. If all
correct answers are not marked and also no
incorrect answer is marked then score
= × 2 number of correct answers marked ÷ actual
number of correct answers.
36. A non-zero current passes through the
galvanometerG shown in the circuit when
the key K is closed and its value does not
change when the key is opened. Then, which
of the following statement(s) is/are true?
(a) The galvanometer resistance is infinite.
(b) The current through the galvanometer is 40 mA.
(c) After the key is closed, the current through the
200 O resistor is same as the current through
the 300 O resistor.
(d) The galvanometer resistance is 150 O.
v
I
m
L
s
V
t
O
O
O
O
(a)
(c)
(b)
(d)
V
t
V
t
V
t
200 O
300 O
100 O
G
K
10 V
Page 5 of 44