WBJEE Previous Year Question Paper - 2019 | WBJEE Sample Papers, Section Wise & Full Mock Tests 2026 PDF Download

 Page 1


Category I (Q. Nos. 1 to 30)
Carry 1 marks each and only one option is
correct. In case of incorrect answer or any
combination of more than one answer, 1/4 mark
will be deducted.
1. A ray of light is reflected by a plane mirror.
$
e
0
,
$
e and
$
n be the unit vectors along the
incident ray, reflected ray and the normal to
the reflecting surface respectively.
Which of the following gives an expression
for
$
e?
(a)
$
(
$ $
)
$
e e nn
0 0
2 + · (b)
$
(
$ $
)
$
e e nn
0 0
2 - ·
(c)
$
(
$ $
)
$
e e nn
0 0
- · (d)
$
(
$ $
)
$
e e nn
0 0
+ ·
2. A parent nucleus X undergoes a-decay with a
half-life of 75000 yrs. The daughter nucleus
Y undergoes ß-decay with a half-life of 9
months. In a particular sample, it is found
that the rate of emission of ß-particles is
nearly constant (over several months) at
10
7
/h. What will be the number of a-particles
emitted in an hour?
(a)10
2
(b)10
7
(c)10
12
(d)10
14
3. A proton and an electron initially at rest are
accelerated by the same potential difference.
Assuming that a proton is 2000 times heavier
than an electron, what will be the relation
between the de Broglie wavelength of the
proton( ) ?
p
and that of electron( ) ?
e
?
(a) ? ?
p e
=2000 (b) ?
?
p
e
=
2000
(c) ? ?
p e
=20 5 (d) ?
?
p
e
=
20 5
4. To which of the following the angular
velocity of the electron in the n-th Bohr orbit
is proportional?
(a) n
2
(b)
1
2
n
(c)
1
3 2
n
/
(d)
1
3
n
5. In the circuit shown, what will be the current
through the 6V zener?
(a) 6 mA, from A toB (b) 2 mA, from A toB
(c) 2 mA, from B to A (d) Zero
6. Each of the two inputs A and B can assume
values either 0 or 1. Then which of the
following will be equal to A B · ?
(a) A B + (b) A B +
(c) A B · (d) A B +
7. The correct dimensional formula for impulse
is given by
Physics
e
0
n
e
? ?
?
1 kO
1 kO 6 V 10 V
A
B
WB JEE
Engineering Entrance Exam
Solved Paper 2019
Page 1 of 46
Page 2


Category I (Q. Nos. 1 to 30)
Carry 1 marks each and only one option is
correct. In case of incorrect answer or any
combination of more than one answer, 1/4 mark
will be deducted.
1. A ray of light is reflected by a plane mirror.
$
e
0
,
$
e and
$
n be the unit vectors along the
incident ray, reflected ray and the normal to
the reflecting surface respectively.
Which of the following gives an expression
for
$
e?
(a)
$
(
$ $
)
$
e e nn
0 0
2 + · (b)
$
(
$ $
)
$
e e nn
0 0
2 - ·
(c)
$
(
$ $
)
$
e e nn
0 0
- · (d)
$
(
$ $
)
$
e e nn
0 0
+ ·
2. A parent nucleus X undergoes a-decay with a
half-life of 75000 yrs. The daughter nucleus
Y undergoes ß-decay with a half-life of 9
months. In a particular sample, it is found
that the rate of emission of ß-particles is
nearly constant (over several months) at
10
7
/h. What will be the number of a-particles
emitted in an hour?
(a)10
2
(b)10
7
(c)10
12
(d)10
14
3. A proton and an electron initially at rest are
accelerated by the same potential difference.
Assuming that a proton is 2000 times heavier
than an electron, what will be the relation
between the de Broglie wavelength of the
proton( ) ?
p
and that of electron( ) ?
e
?
(a) ? ?
p e
=2000 (b) ?
?
p
e
=
2000
(c) ? ?
p e
=20 5 (d) ?
?
p
e
=
20 5
4. To which of the following the angular
velocity of the electron in the n-th Bohr orbit
is proportional?
(a) n
2
(b)
1
2
n
(c)
1
3 2
n
/
(d)
1
3
n
5. In the circuit shown, what will be the current
through the 6V zener?
(a) 6 mA, from A toB (b) 2 mA, from A toB
(c) 2 mA, from B to A (d) Zero
6. Each of the two inputs A and B can assume
values either 0 or 1. Then which of the
following will be equal to A B · ?
(a) A B + (b) A B +
(c) A B · (d) A B +
7. The correct dimensional formula for impulse
is given by
Physics
e
0
n
e
? ?
?
1 kO
1 kO 6 V 10 V
A
B
WB JEE
Engineering Entrance Exam
Solved Paper 2019
Page 1 of 46
(a)ML T
2 2 -
(b)MLT
1 -
(c)ML T
2 1 -
(d)MLT
2 -
8. The density of the material of a cube can be
estimated by measuring its mass and the
length of one of its sides. If the maximum
error in the measurement of mass and length
are 0.3% and 0.2% respectively, the
maximum error in the estimation of the
density of the cube is approximately.
(a) 1.1% (b) 0.5% (c) 0.9% (d) 0.7%
9. Two weights of the mass m
1
and m m
2 1
( ) > are
joined by an inextensible string of negligible
mass passing over a fixed frictionless pulley.
The magnitude of the acceleration of the
loads is
(a) g (b)
m m
m
g
2 1
2
-
(c)
m
m m
g
1
2 1
+
(d)
m m
m m
g
2 1
2 1
-
+
10. A body starts from rest, under the action of
an engine working at a constant power and
moves along a straight line. The displacement
s is given as a function of time() t as
(a) s at bt = +
2
, a and b are constants
(b) s bt =
2
, b is a constant
(c) s at =
3 2 /
, a is a constant
(d) s at = , a is a constant
11. Two particles are simultaneously projected in
the horizontal direction from a point P at a
certain height. The initial velocities of the
particles are oppositely directed to each other
and have magnitude v each. The separation
between the particles at a time when their
position vectors (drawn from the point P) are
mutually perpendicular, is
(a)
v
g
2
2
(b)
v
g
2
(c)
4
2
v
g
(d)
2
2
v
g
12. Assume that the earth moves around the sun
in a circular orbit of radius R and there exists
a planet which also move around the sun in a
circular orbit with an angular speed twice as
large as that of the earth. The radius of the
orbit of the planet is
(a)2
2 3 - /
R (b)2
2 3 /
R (c)2
1 3 - /
R (d)
R
2
13. A compressive force is applied to a uniform
rod of rectangular cross-section so that its
length decreases by 1%. If the Poisson’s ratio
for the material of the rod be 0.2, which of
the following statements is correct?
“The volume approximately ...........”
(a) decreases by 1% (b) decreases by 0.8%
(c) decreases by 0.6% (d) increases by 0.2%
14. A small spherical body of radius r and density
? moves with the terminal velocity v in a fluid
of coefficient of viscosity ? and density s.
What will be the net force on the body?
(a)
4
3
3
p
? s r g ( ) - (b) 6p?rv
(c) Zero (d) Infinity
15. Two black bodies A and B have equal surface
areas and are maintained at temperatures
27ºC and 177ºC respectively. What will be the
ratio of the thermal energy radiated per
second by A to that by B?
(a) 4 : 9 (b) 2 : 3 (c) 16 : 81 (d) 27 : 177
16. What will be the molar specific heat at
constant volume of an ideal gas consisting of
rigid diatomic molecules?
(a)
3
2
R (b)
5
2
R
(c) R (d) 3R
17. Consider the given diagram. An ideal gas is
contained in a chamber (left) of volume V
and is at an absolute temperatureT. It is
allowed to rush freely into the right chamber
of volume V which is initially vacuum. The
whole system is thermally isolated. What will
be the final temperature of the equilibrium
has been attained?
(a)T (b)
T
2
(c)2T (d)
T
4
V
Ideal gas
V
Vacuum
Page 2 of 46
Page 3


Category I (Q. Nos. 1 to 30)
Carry 1 marks each and only one option is
correct. In case of incorrect answer or any
combination of more than one answer, 1/4 mark
will be deducted.
1. A ray of light is reflected by a plane mirror.
$
e
0
,
$
e and
$
n be the unit vectors along the
incident ray, reflected ray and the normal to
the reflecting surface respectively.
Which of the following gives an expression
for
$
e?
(a)
$
(
$ $
)
$
e e nn
0 0
2 + · (b)
$
(
$ $
)
$
e e nn
0 0
2 - ·
(c)
$
(
$ $
)
$
e e nn
0 0
- · (d)
$
(
$ $
)
$
e e nn
0 0
+ ·
2. A parent nucleus X undergoes a-decay with a
half-life of 75000 yrs. The daughter nucleus
Y undergoes ß-decay with a half-life of 9
months. In a particular sample, it is found
that the rate of emission of ß-particles is
nearly constant (over several months) at
10
7
/h. What will be the number of a-particles
emitted in an hour?
(a)10
2
(b)10
7
(c)10
12
(d)10
14
3. A proton and an electron initially at rest are
accelerated by the same potential difference.
Assuming that a proton is 2000 times heavier
than an electron, what will be the relation
between the de Broglie wavelength of the
proton( ) ?
p
and that of electron( ) ?
e
?
(a) ? ?
p e
=2000 (b) ?
?
p
e
=
2000
(c) ? ?
p e
=20 5 (d) ?
?
p
e
=
20 5
4. To which of the following the angular
velocity of the electron in the n-th Bohr orbit
is proportional?
(a) n
2
(b)
1
2
n
(c)
1
3 2
n
/
(d)
1
3
n
5. In the circuit shown, what will be the current
through the 6V zener?
(a) 6 mA, from A toB (b) 2 mA, from A toB
(c) 2 mA, from B to A (d) Zero
6. Each of the two inputs A and B can assume
values either 0 or 1. Then which of the
following will be equal to A B · ?
(a) A B + (b) A B +
(c) A B · (d) A B +
7. The correct dimensional formula for impulse
is given by
Physics
e
0
n
e
? ?
?
1 kO
1 kO 6 V 10 V
A
B
WB JEE
Engineering Entrance Exam
Solved Paper 2019
Page 1 of 46
(a)ML T
2 2 -
(b)MLT
1 -
(c)ML T
2 1 -
(d)MLT
2 -
8. The density of the material of a cube can be
estimated by measuring its mass and the
length of one of its sides. If the maximum
error in the measurement of mass and length
are 0.3% and 0.2% respectively, the
maximum error in the estimation of the
density of the cube is approximately.
(a) 1.1% (b) 0.5% (c) 0.9% (d) 0.7%
9. Two weights of the mass m
1
and m m
2 1
( ) > are
joined by an inextensible string of negligible
mass passing over a fixed frictionless pulley.
The magnitude of the acceleration of the
loads is
(a) g (b)
m m
m
g
2 1
2
-
(c)
m
m m
g
1
2 1
+
(d)
m m
m m
g
2 1
2 1
-
+
10. A body starts from rest, under the action of
an engine working at a constant power and
moves along a straight line. The displacement
s is given as a function of time() t as
(a) s at bt = +
2
, a and b are constants
(b) s bt =
2
, b is a constant
(c) s at =
3 2 /
, a is a constant
(d) s at = , a is a constant
11. Two particles are simultaneously projected in
the horizontal direction from a point P at a
certain height. The initial velocities of the
particles are oppositely directed to each other
and have magnitude v each. The separation
between the particles at a time when their
position vectors (drawn from the point P) are
mutually perpendicular, is
(a)
v
g
2
2
(b)
v
g
2
(c)
4
2
v
g
(d)
2
2
v
g
12. Assume that the earth moves around the sun
in a circular orbit of radius R and there exists
a planet which also move around the sun in a
circular orbit with an angular speed twice as
large as that of the earth. The radius of the
orbit of the planet is
(a)2
2 3 - /
R (b)2
2 3 /
R (c)2
1 3 - /
R (d)
R
2
13. A compressive force is applied to a uniform
rod of rectangular cross-section so that its
length decreases by 1%. If the Poisson’s ratio
for the material of the rod be 0.2, which of
the following statements is correct?
“The volume approximately ...........”
(a) decreases by 1% (b) decreases by 0.8%
(c) decreases by 0.6% (d) increases by 0.2%
14. A small spherical body of radius r and density
? moves with the terminal velocity v in a fluid
of coefficient of viscosity ? and density s.
What will be the net force on the body?
(a)
4
3
3
p
? s r g ( ) - (b) 6p?rv
(c) Zero (d) Infinity
15. Two black bodies A and B have equal surface
areas and are maintained at temperatures
27ºC and 177ºC respectively. What will be the
ratio of the thermal energy radiated per
second by A to that by B?
(a) 4 : 9 (b) 2 : 3 (c) 16 : 81 (d) 27 : 177
16. What will be the molar specific heat at
constant volume of an ideal gas consisting of
rigid diatomic molecules?
(a)
3
2
R (b)
5
2
R
(c) R (d) 3R
17. Consider the given diagram. An ideal gas is
contained in a chamber (left) of volume V
and is at an absolute temperatureT. It is
allowed to rush freely into the right chamber
of volume V which is initially vacuum. The
whole system is thermally isolated. What will
be the final temperature of the equilibrium
has been attained?
(a)T (b)
T
2
(c)2T (d)
T
4
V
Ideal gas
V
Vacuum
Page 2 of 46
18. Five identical capacitors, of capacitance20µF
each, are connected to a battery of 150 V, in a
combination as shown in the diagram. What
is the total amount of charge stored?
(a)15 10
3
×
-
C
(b)12 10
3
×
-
C
(c)10 10
3
×
-
C
(d) 3 10
3
×
-
C
19. Eleven equal point charges, all of them
having a charge + Q, are placed at all the
hour positions of a circular clock of radius r,
except at the 10 h position. What is the
electric field strength at the centre of the
clock?
(a)
Q
r 4
0
2
pe
from the centre towards the mark 10
(b)
Q
r 4
0
2
pe
from the mark 10 towards the centre
(c)
Q
r 4
0
2
pe
from the centre towards the mark 6
(d) Zero.
20. A negative charge is placed at the midpoint
between two fixed equal positive charges,
separated by a distance2d. If the negative
charge is given a small displacement x x d ( ) < <
perpendicular to the line joining the positive
charges, how the force( ) F developed on it will
approximately depend on x?
(a) F x ? (b) F
x
?
1
(c) F x ?
2
(d) F
x
?
1
2
21. To which of the following quantities, the
radius of the circular path of a charged
particle moving at right angles to a uniform
magnetic field is directly proportional?
(a) energy of the particle
(b) magnetic field
(c) charge of the particle
(d) momentum of the particle
22. An electric current ‘I’ enters and leaves a
uniform circular wire of radius r through
diametrically opposite points. A particle
carrying a charge q moves along the axis of
the circular wire with speed v. What is the
magnetic force experienced by the particle
when it passes through the centre of the circle?
(a)qv
i
a
µ
0
(b)qv
i
a
µ
0
2
(c)qv
i
a
µ
p
0
2
(d) Zero
23. A current ‘I’ is flowing along an infinite,
straight wire, in the positive Z-direction and
the same current is flowing along a similar
parallel wire 5 m apart, in the negative
Z-direction. A point P is at a perpendicular
distance 3m from the first wire and 4m from
the second. What will be magnitude of the
magnetic fieldB of P?
(a)
5
12
0
( ) µ I (b)
7
24
0
( ) µ I
(c)
5
24
0
( ) µ I (d)
25
288
0
( ) µ I
24. A square conducting loop is
placed near an infinitely long
current carrying wire with one
edge parallel to the wire as shown
in the figure. If the current in the
straight wire is suddenly halved,
which of the following statements
will be true?
“The loop will .............”.
(a) stay stationary
(b) move towards the wire
(c) move away from the wire
(d) move parallel to the wire
25. What is the current I shown in the given
circuit?
(a)
V
R 2
(b)
V
R
(c)
V
R 16
(d)
V
R 8
2R V 2R 2R 2R 2R
R R R
I
I
Page 3 of 46
Page 4


Category I (Q. Nos. 1 to 30)
Carry 1 marks each and only one option is
correct. In case of incorrect answer or any
combination of more than one answer, 1/4 mark
will be deducted.
1. A ray of light is reflected by a plane mirror.
$
e
0
,
$
e and
$
n be the unit vectors along the
incident ray, reflected ray and the normal to
the reflecting surface respectively.
Which of the following gives an expression
for
$
e?
(a)
$
(
$ $
)
$
e e nn
0 0
2 + · (b)
$
(
$ $
)
$
e e nn
0 0
2 - ·
(c)
$
(
$ $
)
$
e e nn
0 0
- · (d)
$
(
$ $
)
$
e e nn
0 0
+ ·
2. A parent nucleus X undergoes a-decay with a
half-life of 75000 yrs. The daughter nucleus
Y undergoes ß-decay with a half-life of 9
months. In a particular sample, it is found
that the rate of emission of ß-particles is
nearly constant (over several months) at
10
7
/h. What will be the number of a-particles
emitted in an hour?
(a)10
2
(b)10
7
(c)10
12
(d)10
14
3. A proton and an electron initially at rest are
accelerated by the same potential difference.
Assuming that a proton is 2000 times heavier
than an electron, what will be the relation
between the de Broglie wavelength of the
proton( ) ?
p
and that of electron( ) ?
e
?
(a) ? ?
p e
=2000 (b) ?
?
p
e
=
2000
(c) ? ?
p e
=20 5 (d) ?
?
p
e
=
20 5
4. To which of the following the angular
velocity of the electron in the n-th Bohr orbit
is proportional?
(a) n
2
(b)
1
2
n
(c)
1
3 2
n
/
(d)
1
3
n
5. In the circuit shown, what will be the current
through the 6V zener?
(a) 6 mA, from A toB (b) 2 mA, from A toB
(c) 2 mA, from B to A (d) Zero
6. Each of the two inputs A and B can assume
values either 0 or 1. Then which of the
following will be equal to A B · ?
(a) A B + (b) A B +
(c) A B · (d) A B +
7. The correct dimensional formula for impulse
is given by
Physics
e
0
n
e
? ?
?
1 kO
1 kO 6 V 10 V
A
B
WB JEE
Engineering Entrance Exam
Solved Paper 2019
Page 1 of 46
(a)ML T
2 2 -
(b)MLT
1 -
(c)ML T
2 1 -
(d)MLT
2 -
8. The density of the material of a cube can be
estimated by measuring its mass and the
length of one of its sides. If the maximum
error in the measurement of mass and length
are 0.3% and 0.2% respectively, the
maximum error in the estimation of the
density of the cube is approximately.
(a) 1.1% (b) 0.5% (c) 0.9% (d) 0.7%
9. Two weights of the mass m
1
and m m
2 1
( ) > are
joined by an inextensible string of negligible
mass passing over a fixed frictionless pulley.
The magnitude of the acceleration of the
loads is
(a) g (b)
m m
m
g
2 1
2
-
(c)
m
m m
g
1
2 1
+
(d)
m m
m m
g
2 1
2 1
-
+
10. A body starts from rest, under the action of
an engine working at a constant power and
moves along a straight line. The displacement
s is given as a function of time() t as
(a) s at bt = +
2
, a and b are constants
(b) s bt =
2
, b is a constant
(c) s at =
3 2 /
, a is a constant
(d) s at = , a is a constant
11. Two particles are simultaneously projected in
the horizontal direction from a point P at a
certain height. The initial velocities of the
particles are oppositely directed to each other
and have magnitude v each. The separation
between the particles at a time when their
position vectors (drawn from the point P) are
mutually perpendicular, is
(a)
v
g
2
2
(b)
v
g
2
(c)
4
2
v
g
(d)
2
2
v
g
12. Assume that the earth moves around the sun
in a circular orbit of radius R and there exists
a planet which also move around the sun in a
circular orbit with an angular speed twice as
large as that of the earth. The radius of the
orbit of the planet is
(a)2
2 3 - /
R (b)2
2 3 /
R (c)2
1 3 - /
R (d)
R
2
13. A compressive force is applied to a uniform
rod of rectangular cross-section so that its
length decreases by 1%. If the Poisson’s ratio
for the material of the rod be 0.2, which of
the following statements is correct?
“The volume approximately ...........”
(a) decreases by 1% (b) decreases by 0.8%
(c) decreases by 0.6% (d) increases by 0.2%
14. A small spherical body of radius r and density
? moves with the terminal velocity v in a fluid
of coefficient of viscosity ? and density s.
What will be the net force on the body?
(a)
4
3
3
p
? s r g ( ) - (b) 6p?rv
(c) Zero (d) Infinity
15. Two black bodies A and B have equal surface
areas and are maintained at temperatures
27ºC and 177ºC respectively. What will be the
ratio of the thermal energy radiated per
second by A to that by B?
(a) 4 : 9 (b) 2 : 3 (c) 16 : 81 (d) 27 : 177
16. What will be the molar specific heat at
constant volume of an ideal gas consisting of
rigid diatomic molecules?
(a)
3
2
R (b)
5
2
R
(c) R (d) 3R
17. Consider the given diagram. An ideal gas is
contained in a chamber (left) of volume V
and is at an absolute temperatureT. It is
allowed to rush freely into the right chamber
of volume V which is initially vacuum. The
whole system is thermally isolated. What will
be the final temperature of the equilibrium
has been attained?
(a)T (b)
T
2
(c)2T (d)
T
4
V
Ideal gas
V
Vacuum
Page 2 of 46
18. Five identical capacitors, of capacitance20µF
each, are connected to a battery of 150 V, in a
combination as shown in the diagram. What
is the total amount of charge stored?
(a)15 10
3
×
-
C
(b)12 10
3
×
-
C
(c)10 10
3
×
-
C
(d) 3 10
3
×
-
C
19. Eleven equal point charges, all of them
having a charge + Q, are placed at all the
hour positions of a circular clock of radius r,
except at the 10 h position. What is the
electric field strength at the centre of the
clock?
(a)
Q
r 4
0
2
pe
from the centre towards the mark 10
(b)
Q
r 4
0
2
pe
from the mark 10 towards the centre
(c)
Q
r 4
0
2
pe
from the centre towards the mark 6
(d) Zero.
20. A negative charge is placed at the midpoint
between two fixed equal positive charges,
separated by a distance2d. If the negative
charge is given a small displacement x x d ( ) < <
perpendicular to the line joining the positive
charges, how the force( ) F developed on it will
approximately depend on x?
(a) F x ? (b) F
x
?
1
(c) F x ?
2
(d) F
x
?
1
2
21. To which of the following quantities, the
radius of the circular path of a charged
particle moving at right angles to a uniform
magnetic field is directly proportional?
(a) energy of the particle
(b) magnetic field
(c) charge of the particle
(d) momentum of the particle
22. An electric current ‘I’ enters and leaves a
uniform circular wire of radius r through
diametrically opposite points. A particle
carrying a charge q moves along the axis of
the circular wire with speed v. What is the
magnetic force experienced by the particle
when it passes through the centre of the circle?
(a)qv
i
a
µ
0
(b)qv
i
a
µ
0
2
(c)qv
i
a
µ
p
0
2
(d) Zero
23. A current ‘I’ is flowing along an infinite,
straight wire, in the positive Z-direction and
the same current is flowing along a similar
parallel wire 5 m apart, in the negative
Z-direction. A point P is at a perpendicular
distance 3m from the first wire and 4m from
the second. What will be magnitude of the
magnetic fieldB of P?
(a)
5
12
0
( ) µ I (b)
7
24
0
( ) µ I
(c)
5
24
0
( ) µ I (d)
25
288
0
( ) µ I
24. A square conducting loop is
placed near an infinitely long
current carrying wire with one
edge parallel to the wire as shown
in the figure. If the current in the
straight wire is suddenly halved,
which of the following statements
will be true?
“The loop will .............”.
(a) stay stationary
(b) move towards the wire
(c) move away from the wire
(d) move parallel to the wire
25. What is the current I shown in the given
circuit?
(a)
V
R 2
(b)
V
R
(c)
V
R 16
(d)
V
R 8
2R V 2R 2R 2R 2R
R R R
I
I
Page 3 of 46
26. When the value of R in the balanced
Wheatstone bridge, shown in the figure, is
increased from5O to7O, the value of S has to
be increased by3O in order to maintain the
balance. What is the initial values of S?
(a)25 . O (b) 3 O
(c) 5 O (d)75 . O
27. When a 60 mH inductor and a resistor are
connected in series with an AC voltage source,
the voltage leads the current by 60º. If the
inductor is replaced by a05 . µF capacitor, the
voltage lags behind the current by 30º.What is
the frequency of the AC supply?
(a)
1
2
10
4
p
× Hz (b)
1
10
4
p
× Hz
(c)
3
2
10
4
p
× Hz (d)
1
2
10
8
p
× Hz
28. A point object is placed on the axis of a thin
convex lens of focal length 0.05 m at a distance
of 0.2 m from the lens and its image is formed
on the axis. If the object is now made to
oscillate along the axis with a small amplitude
of A cm, then what is the amplitude of
oscillation of the image?
you may assume, where
1
1
1 1
+
˜ - < <
?
?
?
?
?
?
x
x x ,
(a)
4
9
10
2
A
×
-
m (b)
5
9
10
2
A
×
-
m
(c)
A
3
10
2
×
-
m (d)
A
9
10
2
×
-
m
29. In Young’s experiment for the interference of
light, the separation between the slits is d and
the distance of the screen from the slits is D. If
D is increased by 0.5% and d is decreased by
0.3% then for the light of a given wavelength,
which one of the following is true?
“The fringe width .............
(a) increases by 0.8% (b) decreases by 0.8%
(c) increases by 0.2% (d) decreases by 0.2%
30. When the frequency of the light used is
changed from 4 10
14 1
×
-
s to5 10
14 1
×
-
s , the
angular width of the principal (central)
maximum in a single slit Fraunhoffer
diffraction pattern changes by 0.6 radian.
What is the width of the slit (assume that
the experiment is performed in vacuum)?
(a)15 10
7
. ×
-
m (b) 3 10
7
×
-
m
(c) 5 10
7
×
-
m (d) 6 10
7
×
-
m
Category II (Q. Nos. 31 to 35)
Carry 2 marks each and only one option is
correct. In case of incorrect answer or any
combination of more than one answer, 1/2 mark
will be deducted.
31. A capacitor of capacitanceC is connected in
series with a resistance R andDC source of
emf E through a key. The capacitor starts
charging when the key is closed. By the
time the capacitor has been fully charged,
what amount of energy is dissipated in the
resistance R?
(a)
1
2
2
CE (b) 0 (c)CE
2
(d)
E
R
2
32. A horizontal fire hose with a nozzle of
cross-sectional area
5
21
10
3
×
-
m
2
delivers
a cubic metre of water in 10s. What will be
the maximum possible increase in the
temperature of water while it hits a rigid
wall (neglecting the effect of gravity)?
(a) 1ºC (b) 0.1ºC (c) 10ºC (d) 0.01ºC
33. Two identical blocks of ice move in opposite
directions with equal speed and collide with
each other. What will be the minimum
speed required to make both the blocks
melt completely, if the initial temperatures
of the blocks were -8ºC each?
(Specific heat of ice is 2100 Jkg K
1 1 - -
and
latent heat of fusion of ice is3.36 10 Jkg
5 1
×
-
)
(a) 840
1
ms
-
(b) 420
1
ms
-
(c) 84
1
. ms
-
(d) 84
1
ms
-
G
P Q
R S
C
E
R
Page 4 of 46
Page 5


Category I (Q. Nos. 1 to 30)
Carry 1 marks each and only one option is
correct. In case of incorrect answer or any
combination of more than one answer, 1/4 mark
will be deducted.
1. A ray of light is reflected by a plane mirror.
$
e
0
,
$
e and
$
n be the unit vectors along the
incident ray, reflected ray and the normal to
the reflecting surface respectively.
Which of the following gives an expression
for
$
e?
(a)
$
(
$ $
)
$
e e nn
0 0
2 + · (b)
$
(
$ $
)
$
e e nn
0 0
2 - ·
(c)
$
(
$ $
)
$
e e nn
0 0
- · (d)
$
(
$ $
)
$
e e nn
0 0
+ ·
2. A parent nucleus X undergoes a-decay with a
half-life of 75000 yrs. The daughter nucleus
Y undergoes ß-decay with a half-life of 9
months. In a particular sample, it is found
that the rate of emission of ß-particles is
nearly constant (over several months) at
10
7
/h. What will be the number of a-particles
emitted in an hour?
(a)10
2
(b)10
7
(c)10
12
(d)10
14
3. A proton and an electron initially at rest are
accelerated by the same potential difference.
Assuming that a proton is 2000 times heavier
than an electron, what will be the relation
between the de Broglie wavelength of the
proton( ) ?
p
and that of electron( ) ?
e
?
(a) ? ?
p e
=2000 (b) ?
?
p
e
=
2000
(c) ? ?
p e
=20 5 (d) ?
?
p
e
=
20 5
4. To which of the following the angular
velocity of the electron in the n-th Bohr orbit
is proportional?
(a) n
2
(b)
1
2
n
(c)
1
3 2
n
/
(d)
1
3
n
5. In the circuit shown, what will be the current
through the 6V zener?
(a) 6 mA, from A toB (b) 2 mA, from A toB
(c) 2 mA, from B to A (d) Zero
6. Each of the two inputs A and B can assume
values either 0 or 1. Then which of the
following will be equal to A B · ?
(a) A B + (b) A B +
(c) A B · (d) A B +
7. The correct dimensional formula for impulse
is given by
Physics
e
0
n
e
? ?
?
1 kO
1 kO 6 V 10 V
A
B
WB JEE
Engineering Entrance Exam
Solved Paper 2019
Page 1 of 46
(a)ML T
2 2 -
(b)MLT
1 -
(c)ML T
2 1 -
(d)MLT
2 -
8. The density of the material of a cube can be
estimated by measuring its mass and the
length of one of its sides. If the maximum
error in the measurement of mass and length
are 0.3% and 0.2% respectively, the
maximum error in the estimation of the
density of the cube is approximately.
(a) 1.1% (b) 0.5% (c) 0.9% (d) 0.7%
9. Two weights of the mass m
1
and m m
2 1
( ) > are
joined by an inextensible string of negligible
mass passing over a fixed frictionless pulley.
The magnitude of the acceleration of the
loads is
(a) g (b)
m m
m
g
2 1
2
-
(c)
m
m m
g
1
2 1
+
(d)
m m
m m
g
2 1
2 1
-
+
10. A body starts from rest, under the action of
an engine working at a constant power and
moves along a straight line. The displacement
s is given as a function of time() t as
(a) s at bt = +
2
, a and b are constants
(b) s bt =
2
, b is a constant
(c) s at =
3 2 /
, a is a constant
(d) s at = , a is a constant
11. Two particles are simultaneously projected in
the horizontal direction from a point P at a
certain height. The initial velocities of the
particles are oppositely directed to each other
and have magnitude v each. The separation
between the particles at a time when their
position vectors (drawn from the point P) are
mutually perpendicular, is
(a)
v
g
2
2
(b)
v
g
2
(c)
4
2
v
g
(d)
2
2
v
g
12. Assume that the earth moves around the sun
in a circular orbit of radius R and there exists
a planet which also move around the sun in a
circular orbit with an angular speed twice as
large as that of the earth. The radius of the
orbit of the planet is
(a)2
2 3 - /
R (b)2
2 3 /
R (c)2
1 3 - /
R (d)
R
2
13. A compressive force is applied to a uniform
rod of rectangular cross-section so that its
length decreases by 1%. If the Poisson’s ratio
for the material of the rod be 0.2, which of
the following statements is correct?
“The volume approximately ...........”
(a) decreases by 1% (b) decreases by 0.8%
(c) decreases by 0.6% (d) increases by 0.2%
14. A small spherical body of radius r and density
? moves with the terminal velocity v in a fluid
of coefficient of viscosity ? and density s.
What will be the net force on the body?
(a)
4
3
3
p
? s r g ( ) - (b) 6p?rv
(c) Zero (d) Infinity
15. Two black bodies A and B have equal surface
areas and are maintained at temperatures
27ºC and 177ºC respectively. What will be the
ratio of the thermal energy radiated per
second by A to that by B?
(a) 4 : 9 (b) 2 : 3 (c) 16 : 81 (d) 27 : 177
16. What will be the molar specific heat at
constant volume of an ideal gas consisting of
rigid diatomic molecules?
(a)
3
2
R (b)
5
2
R
(c) R (d) 3R
17. Consider the given diagram. An ideal gas is
contained in a chamber (left) of volume V
and is at an absolute temperatureT. It is
allowed to rush freely into the right chamber
of volume V which is initially vacuum. The
whole system is thermally isolated. What will
be the final temperature of the equilibrium
has been attained?
(a)T (b)
T
2
(c)2T (d)
T
4
V
Ideal gas
V
Vacuum
Page 2 of 46
18. Five identical capacitors, of capacitance20µF
each, are connected to a battery of 150 V, in a
combination as shown in the diagram. What
is the total amount of charge stored?
(a)15 10
3
×
-
C
(b)12 10
3
×
-
C
(c)10 10
3
×
-
C
(d) 3 10
3
×
-
C
19. Eleven equal point charges, all of them
having a charge + Q, are placed at all the
hour positions of a circular clock of radius r,
except at the 10 h position. What is the
electric field strength at the centre of the
clock?
(a)
Q
r 4
0
2
pe
from the centre towards the mark 10
(b)
Q
r 4
0
2
pe
from the mark 10 towards the centre
(c)
Q
r 4
0
2
pe
from the centre towards the mark 6
(d) Zero.
20. A negative charge is placed at the midpoint
between two fixed equal positive charges,
separated by a distance2d. If the negative
charge is given a small displacement x x d ( ) < <
perpendicular to the line joining the positive
charges, how the force( ) F developed on it will
approximately depend on x?
(a) F x ? (b) F
x
?
1
(c) F x ?
2
(d) F
x
?
1
2
21. To which of the following quantities, the
radius of the circular path of a charged
particle moving at right angles to a uniform
magnetic field is directly proportional?
(a) energy of the particle
(b) magnetic field
(c) charge of the particle
(d) momentum of the particle
22. An electric current ‘I’ enters and leaves a
uniform circular wire of radius r through
diametrically opposite points. A particle
carrying a charge q moves along the axis of
the circular wire with speed v. What is the
magnetic force experienced by the particle
when it passes through the centre of the circle?
(a)qv
i
a
µ
0
(b)qv
i
a
µ
0
2
(c)qv
i
a
µ
p
0
2
(d) Zero
23. A current ‘I’ is flowing along an infinite,
straight wire, in the positive Z-direction and
the same current is flowing along a similar
parallel wire 5 m apart, in the negative
Z-direction. A point P is at a perpendicular
distance 3m from the first wire and 4m from
the second. What will be magnitude of the
magnetic fieldB of P?
(a)
5
12
0
( ) µ I (b)
7
24
0
( ) µ I
(c)
5
24
0
( ) µ I (d)
25
288
0
( ) µ I
24. A square conducting loop is
placed near an infinitely long
current carrying wire with one
edge parallel to the wire as shown
in the figure. If the current in the
straight wire is suddenly halved,
which of the following statements
will be true?
“The loop will .............”.
(a) stay stationary
(b) move towards the wire
(c) move away from the wire
(d) move parallel to the wire
25. What is the current I shown in the given
circuit?
(a)
V
R 2
(b)
V
R
(c)
V
R 16
(d)
V
R 8
2R V 2R 2R 2R 2R
R R R
I
I
Page 3 of 46
26. When the value of R in the balanced
Wheatstone bridge, shown in the figure, is
increased from5O to7O, the value of S has to
be increased by3O in order to maintain the
balance. What is the initial values of S?
(a)25 . O (b) 3 O
(c) 5 O (d)75 . O
27. When a 60 mH inductor and a resistor are
connected in series with an AC voltage source,
the voltage leads the current by 60º. If the
inductor is replaced by a05 . µF capacitor, the
voltage lags behind the current by 30º.What is
the frequency of the AC supply?
(a)
1
2
10
4
p
× Hz (b)
1
10
4
p
× Hz
(c)
3
2
10
4
p
× Hz (d)
1
2
10
8
p
× Hz
28. A point object is placed on the axis of a thin
convex lens of focal length 0.05 m at a distance
of 0.2 m from the lens and its image is formed
on the axis. If the object is now made to
oscillate along the axis with a small amplitude
of A cm, then what is the amplitude of
oscillation of the image?
you may assume, where
1
1
1 1
+
˜ - < <
?
?
?
?
?
?
x
x x ,
(a)
4
9
10
2
A
×
-
m (b)
5
9
10
2
A
×
-
m
(c)
A
3
10
2
×
-
m (d)
A
9
10
2
×
-
m
29. In Young’s experiment for the interference of
light, the separation between the slits is d and
the distance of the screen from the slits is D. If
D is increased by 0.5% and d is decreased by
0.3% then for the light of a given wavelength,
which one of the following is true?
“The fringe width .............
(a) increases by 0.8% (b) decreases by 0.8%
(c) increases by 0.2% (d) decreases by 0.2%
30. When the frequency of the light used is
changed from 4 10
14 1
×
-
s to5 10
14 1
×
-
s , the
angular width of the principal (central)
maximum in a single slit Fraunhoffer
diffraction pattern changes by 0.6 radian.
What is the width of the slit (assume that
the experiment is performed in vacuum)?
(a)15 10
7
. ×
-
m (b) 3 10
7
×
-
m
(c) 5 10
7
×
-
m (d) 6 10
7
×
-
m
Category II (Q. Nos. 31 to 35)
Carry 2 marks each and only one option is
correct. In case of incorrect answer or any
combination of more than one answer, 1/2 mark
will be deducted.
31. A capacitor of capacitanceC is connected in
series with a resistance R andDC source of
emf E through a key. The capacitor starts
charging when the key is closed. By the
time the capacitor has been fully charged,
what amount of energy is dissipated in the
resistance R?
(a)
1
2
2
CE (b) 0 (c)CE
2
(d)
E
R
2
32. A horizontal fire hose with a nozzle of
cross-sectional area
5
21
10
3
×
-
m
2
delivers
a cubic metre of water in 10s. What will be
the maximum possible increase in the
temperature of water while it hits a rigid
wall (neglecting the effect of gravity)?
(a) 1ºC (b) 0.1ºC (c) 10ºC (d) 0.01ºC
33. Two identical blocks of ice move in opposite
directions with equal speed and collide with
each other. What will be the minimum
speed required to make both the blocks
melt completely, if the initial temperatures
of the blocks were -8ºC each?
(Specific heat of ice is 2100 Jkg K
1 1 - -
and
latent heat of fusion of ice is3.36 10 Jkg
5 1
×
-
)
(a) 840
1
ms
-
(b) 420
1
ms
-
(c) 84
1
. ms
-
(d) 84
1
ms
-
G
P Q
R S
C
E
R
Page 4 of 46
34. A particle with charge q moves with a velocity
v in a direction perpendicular to the
directions of uniform electric and magnetic
fields, E and B respectively, which are
mutually perpendicular to each other. Which
one of the following gives the condition for
which the particle moves undeflected in its
original trajectory?
(a) v
E
B
= (b) v
B
E
= (c) v
E
B
= (d) v q
B
E
=
35. A parallel plate capacitor in series with a
resistance of100 O, an inductor of20 mH
and an AC voltage source of variable
frequency shows resonance at a frequency of
1250
p
Hz.
If this capacitor is charged by aDC voltage
source to a voltage 25 V, what amount of
charge will be stored in each plate of the
capacitor?
(a) 0 2 . µC (b)2 mC (c) 0 2 . mC (d) 0 2 . C
Category III (Q. Nos. 36 to 40)
Carry 2 marks each and one or more option(s)
is/are correct. 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. If any wrong option is
marked or if any combination including a wrong
option is marked, the answer will be considered
wrong, but there is no negative marking for the
same and zero marks will be awarded.
36. Electrons are emitted with kinetic energyT
from a metal plate by an irradiation of light
of intensity J and frequency ?. Then, which
of the following will be true?
(a)T J ?
(b)T linearly increasing with ?
(c)T ? time of irradiation
(d) Number of electrons emitted ?J
37. The initial pressure and volume of a given
mass of an ideal gas with
C
C
p
V
=
?
?
?
?
?
?
? , taken in
a cylinder fitted with a piston, are p
0
and V
0
respectively. At this stage the gas has the
same temperature as that of the surrounding
medium which isT
0
. It is adiabatically
compressed to a volume equal to
V
0
2
.
Subsequently the gas is allowed to come to
thermal equilibrium with the surroundings.
What is the heat released to the
surrounding?
(a) 0 (b)( ) 2 1
1
1
0 0
?
?
-
-
-
p V
(c) ?p V
0 0
2 ln (d)
p V
0 0
1 2(? - )
38. A projectile thrown with an initial velocity of
10
1
ms
-
at an angle a with the horizontal,
has a range of 5 m. Taking g =
-
10
2
ms and
neglecting air resistance, what will be the
estimated value of a?
(a) 15º (b) 30º (c) 45º (d) 75º
39. In the circuit shown in the figure all the
resistance are identical and each has the
value r O. The equivalent resistance of the
combination between the points A and B will
remain unchanged even when the following
pairs of points marked in the figure are
connected through a resistance R.
(a) 2 and 6 (b) 3 and 6
(c) 4 and 7 (d) 4 and 6
40. A metallic loop is placed in a uniform
magnetic fieldB with the plane of the loop
perpendicular toB. Under which condition(s)
given an emf will be induced in the loop?
“If the loop is ............”
(a) moved along the direction ofB
(b) squeezed to a smaller area
(c) rotated about its axis
(d) rotated about one of its diameters
r
1
r
2
r
3
r
4
r
5
r
r
6
r
7
r
A B
y
E
B
v
z
x
Page 5 of 46