JEE Main 2021 Physics February 24 Shift 2 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


JEE (MAIN)-2021 Phase-1 (24-02-2021)-E
PART–A : PHYSICS
SECTION - I
Multiple Choice Questions: This section contains
20 multiple choice questions. Each question has
4 choices (1), (2), (3) and (4), out of which ONL Y ONE
is correct.
Choose the correct answer :
1. Zener breakdown occurs in a p-n junction
having p and n both
(1) Lightly doped and have narrow depletion
layer
(2) Heavily doped and have narrow depletion
layer
(3) Heavily doped and have wide depletion
layer
(4) Lightly doped and have wide depletion layer
Answer (2)
Sol. Zener diode has both p and n side highly doped
and depletion layer is very thin.
2. If the source of light used in a Young’s double
slit experiment is changed from red to violet
(1) The fringes will become brighter
(2) The central bright fringe will become a dark
fringe
(3) Consecutive fringe lines will come closer
(4) The intensity of minima will increase
Answer (3)
Sol. ?
D
d
?
??
and ?
v
 < ?
red
? Fringe width will decrease.
? Fringe lines will come closer.
3. C
A
B
The logic circuit shown above is equivalent to
(1) C
A
B
(2) C
A
B
(3) C
A
B
(4) C
A
B
Answer (1)
Sol. From gates diagram,
(AB) AB AB ?? ? ? ?
? C
A
B
4. Which of the following equations represents a
travelling wave?
(1) y = Asin(15x – 2t)
(2) y = Ae
x
cos( ?t – ?)
(3) y = Asinx cos ?t
(4)
?
???
2
x
yAe (vt )
Answer (1)
Sol. Travelling wave equation,
y = f(± kx ± ?t)
? y = A sin(15x – 2t) is a travelling wave.
5. Figure shows a circuit that contains four
identical resistors with resistance R = 2.0 ?,
two identical inductors with inductance
L = 2.0 mH and an ideal battery with emf
E = 9 V. The current ‘i’ just after the switch ‘S’
is closed will be
A 
S
R
R
R
L
R
L
i E = 9 V
(1) 3.37 A
(2) 3.0 A
(3) 2.25 A
(4) 9 A
Answer (3)
Page 2


JEE (MAIN)-2021 Phase-1 (24-02-2021)-E
PART–A : PHYSICS
SECTION - I
Multiple Choice Questions: This section contains
20 multiple choice questions. Each question has
4 choices (1), (2), (3) and (4), out of which ONL Y ONE
is correct.
Choose the correct answer :
1. Zener breakdown occurs in a p-n junction
having p and n both
(1) Lightly doped and have narrow depletion
layer
(2) Heavily doped and have narrow depletion
layer
(3) Heavily doped and have wide depletion
layer
(4) Lightly doped and have wide depletion layer
Answer (2)
Sol. Zener diode has both p and n side highly doped
and depletion layer is very thin.
2. If the source of light used in a Young’s double
slit experiment is changed from red to violet
(1) The fringes will become brighter
(2) The central bright fringe will become a dark
fringe
(3) Consecutive fringe lines will come closer
(4) The intensity of minima will increase
Answer (3)
Sol. ?
D
d
?
??
and ?
v
 < ?
red
? Fringe width will decrease.
? Fringe lines will come closer.
3. C
A
B
The logic circuit shown above is equivalent to
(1) C
A
B
(2) C
A
B
(3) C
A
B
(4) C
A
B
Answer (1)
Sol. From gates diagram,
(AB) AB AB ?? ? ? ?
? C
A
B
4. Which of the following equations represents a
travelling wave?
(1) y = Asin(15x – 2t)
(2) y = Ae
x
cos( ?t – ?)
(3) y = Asinx cos ?t
(4)
?
???
2
x
yAe (vt )
Answer (1)
Sol. Travelling wave equation,
y = f(± kx ± ?t)
? y = A sin(15x – 2t) is a travelling wave.
5. Figure shows a circuit that contains four
identical resistors with resistance R = 2.0 ?,
two identical inductors with inductance
L = 2.0 mH and an ideal battery with emf
E = 9 V. The current ‘i’ just after the switch ‘S’
is closed will be
A 
S
R
R
R
L
R
L
i E = 9 V
(1) 3.37 A
(2) 3.0 A
(3) 2.25 A
(4) 9 A
Answer (3)
JEE (MAIN)-2021 Phase-1 (24-02-2021)-E
Sol. At t = 0, inductor behaves as an open switch.
?
2 ?
9 V
2 ?
?
9
i2.25A
4
??
6. An X-ray tube is operated at 1.24 million volt.
The shortest wavelength of the produced
photon will be
(1) 10
–3
 nm (2) 10
–2
 nm
(3) 10
–4
 nm (4) 10
–1
 nm
Answer (1)
Sol.
min
hc
eV
??
= 
34 8
19 6
6.63 10 3 10
1.6 10 1.24 10
?
?
???
?? ?
= 1.0 × 10
–12
 m
= 10
–3
 nm
7. The de Broglie wavelength of a proton and
?-particle are equal. The ratio of their velocities
is
(1) 1 : 4 (2) 4 : 3
(3) 4 : 1 (4) 4 : 2
Answer (3)
Sol.
p
pp
h
mv
??
?
h
mv
?
??
??
?
? ?
p
 = ?
?
? m
p
v
p
 = m
?
v
?
?
p
p
v
m 4
vm 1
?
?
??
8. Given below are two statements :
Statement I : PN junction diodes can be used to
function as transistor, simply by connecting two
diodes, back to back, which acts as the base
terminal.
Statement II : In the study of transistor, the
amplification factor ? indicates ratio of the
collector current to the base current.
In the light of the above statements, choose the
correct answer from the options given below.
(1) Both Statement I and Statement II are false
(2) Statement I is true but Statement II is false
(3) Statement I is false but Statement II is true
(4) Both statement I and Statement II are true
Answer (3)
Sol. Transistor is formed by formation of two
p-n junctions by sandwiching a thin base layer.
So, statement I is false.
?
C
B
I
I
?
??
?
 and for DC, 
C
B
I
I
??
So, statement II is true.
9. A circular hole of radius 
??
??
??
a
2
 is cut out of a
circular disc of radius ‘a’ as shown in figure.
The centroid of the remaining circular portion
with respect to point ‘O’ will be
a/2
a
X-axis
Y-axis
O
(1)
1
a
6
(2)
2
a
3
(3)
10
a
11
(4)
5
a
6
Answer (4)
Sol. Let mass of hole be (–m), then mass of
complete disc will be 4m.
a/2
a
O
C
? Centre of mass w.r.t. point O is
CM
3
4m a ( m) a
5 2
Xa
(4m m) 6
??
?? ? ?
??
??
??
?
Page 3


JEE (MAIN)-2021 Phase-1 (24-02-2021)-E
PART–A : PHYSICS
SECTION - I
Multiple Choice Questions: This section contains
20 multiple choice questions. Each question has
4 choices (1), (2), (3) and (4), out of which ONL Y ONE
is correct.
Choose the correct answer :
1. Zener breakdown occurs in a p-n junction
having p and n both
(1) Lightly doped and have narrow depletion
layer
(2) Heavily doped and have narrow depletion
layer
(3) Heavily doped and have wide depletion
layer
(4) Lightly doped and have wide depletion layer
Answer (2)
Sol. Zener diode has both p and n side highly doped
and depletion layer is very thin.
2. If the source of light used in a Young’s double
slit experiment is changed from red to violet
(1) The fringes will become brighter
(2) The central bright fringe will become a dark
fringe
(3) Consecutive fringe lines will come closer
(4) The intensity of minima will increase
Answer (3)
Sol. ?
D
d
?
??
and ?
v
 < ?
red
? Fringe width will decrease.
? Fringe lines will come closer.
3. C
A
B
The logic circuit shown above is equivalent to
(1) C
A
B
(2) C
A
B
(3) C
A
B
(4) C
A
B
Answer (1)
Sol. From gates diagram,
(AB) AB AB ?? ? ? ?
? C
A
B
4. Which of the following equations represents a
travelling wave?
(1) y = Asin(15x – 2t)
(2) y = Ae
x
cos( ?t – ?)
(3) y = Asinx cos ?t
(4)
?
???
2
x
yAe (vt )
Answer (1)
Sol. Travelling wave equation,
y = f(± kx ± ?t)
? y = A sin(15x – 2t) is a travelling wave.
5. Figure shows a circuit that contains four
identical resistors with resistance R = 2.0 ?,
two identical inductors with inductance
L = 2.0 mH and an ideal battery with emf
E = 9 V. The current ‘i’ just after the switch ‘S’
is closed will be
A 
S
R
R
R
L
R
L
i E = 9 V
(1) 3.37 A
(2) 3.0 A
(3) 2.25 A
(4) 9 A
Answer (3)
JEE (MAIN)-2021 Phase-1 (24-02-2021)-E
Sol. At t = 0, inductor behaves as an open switch.
?
2 ?
9 V
2 ?
?
9
i2.25A
4
??
6. An X-ray tube is operated at 1.24 million volt.
The shortest wavelength of the produced
photon will be
(1) 10
–3
 nm (2) 10
–2
 nm
(3) 10
–4
 nm (4) 10
–1
 nm
Answer (1)
Sol.
min
hc
eV
??
= 
34 8
19 6
6.63 10 3 10
1.6 10 1.24 10
?
?
???
?? ?
= 1.0 × 10
–12
 m
= 10
–3
 nm
7. The de Broglie wavelength of a proton and
?-particle are equal. The ratio of their velocities
is
(1) 1 : 4 (2) 4 : 3
(3) 4 : 1 (4) 4 : 2
Answer (3)
Sol.
p
pp
h
mv
??
?
h
mv
?
??
??
?
? ?
p
 = ?
?
? m
p
v
p
 = m
?
v
?
?
p
p
v
m 4
vm 1
?
?
??
8. Given below are two statements :
Statement I : PN junction diodes can be used to
function as transistor, simply by connecting two
diodes, back to back, which acts as the base
terminal.
Statement II : In the study of transistor, the
amplification factor ? indicates ratio of the
collector current to the base current.
In the light of the above statements, choose the
correct answer from the options given below.
(1) Both Statement I and Statement II are false
(2) Statement I is true but Statement II is false
(3) Statement I is false but Statement II is true
(4) Both statement I and Statement II are true
Answer (3)
Sol. Transistor is formed by formation of two
p-n junctions by sandwiching a thin base layer.
So, statement I is false.
?
C
B
I
I
?
??
?
 and for DC, 
C
B
I
I
??
So, statement II is true.
9. A circular hole of radius 
??
??
??
a
2
 is cut out of a
circular disc of radius ‘a’ as shown in figure.
The centroid of the remaining circular portion
with respect to point ‘O’ will be
a/2
a
X-axis
Y-axis
O
(1)
1
a
6
(2)
2
a
3
(3)
10
a
11
(4)
5
a
6
Answer (4)
Sol. Let mass of hole be (–m), then mass of
complete disc will be 4m.
a/2
a
O
C
? Centre of mass w.r.t. point O is
CM
3
4m a ( m) a
5 2
Xa
(4m m) 6
??
?? ? ?
??
??
??
?
JEE (MAIN)-2021 Phase-1 (24-02-2021)-E
10. A particle is projected with velocity v
0
 along
x-axis. A damping force is acting on the particle
which is proportional to the square of the
distance from the origin i.e. ma = – ?x
2
. The
distance at which the particle stops
(1)
??
??
??
?
??
1
2
3
0
3v
2
(2)
??
??
??
?
??
1
2
2
0
3v
2
(3)
??
??
??
?
??
1
2
2
0
2v
3
(4)
??
??
?
??
1
3
0
2v
3
Answer (1)
Sol. Loss in KE = work against damping
?
x
22
0
x0
1
mv x dx
2
?
??
?
?
3
2
0
1x
mv
23
?
?
?
1
2
3
0
3mv
x
2
??
???
??
?
??
11. When a particle executes SHM, the nature of
graphical representation of velocity as a
function of displacement is :
(1) parabolic (2) straight line
(3) circular (4) elliptical
Answer (4)
Sol. ?? ?
22
vA x
??
?
2
22
2
v
xA
12. The period of oscillation of a simple pendulum
is ??
L
T2 .
g
 Measured value of ‘L’ is 1.0 m
from meter scale having a minimum division  of
1 mm and time of one complete oscillation is
1.95 s measured from stopwatch of 0.01 s
resolution. The percentage error in the
determination of ‘g’ will be :
(1) 1.30%
(2) 1.33%
(3) 1.13%
(4) 1.03%
Answer (3)
Sol. ??

2
2
g4
T
??


dg d 2dT
gT
dg 1 2 0.01 1.13
g 1000 1.95 100
?
?? ?
13. In the given figure, a body of mass M is held
between two massless spring, on a smooth
inclined plane. The free ends of the springs are
attached to firm supports. If each spring has
spring constant k, the frequency of oscillation
of given body is :
M
k
k
?
(1)
?
12k
2M
(2)
?
1k
22M
(3)
??
12k
2Mgsin
(4)
??
1k
2Mgsin
Answer (1)
Sol. ??
eq
M
T2
k
?
?
eq
k
1
f
2M
?
eq
k2k
14. Match List-I with List-II.
List-I List-II
(a) Source of (i) Radioactive decay
microwave of nucleus
frequency
(b) Source of (ii) Magnetron
infrared
frequency
(c) Source of (iii) Inner shell electrons
Gamma Rays
(d) Source of X-rays (iv) Vibration of atoms
and molecules
(v) LASER
(vi) RC circuit
Choose the correct answer from the options
given below :
Page 4


JEE (MAIN)-2021 Phase-1 (24-02-2021)-E
PART–A : PHYSICS
SECTION - I
Multiple Choice Questions: This section contains
20 multiple choice questions. Each question has
4 choices (1), (2), (3) and (4), out of which ONL Y ONE
is correct.
Choose the correct answer :
1. Zener breakdown occurs in a p-n junction
having p and n both
(1) Lightly doped and have narrow depletion
layer
(2) Heavily doped and have narrow depletion
layer
(3) Heavily doped and have wide depletion
layer
(4) Lightly doped and have wide depletion layer
Answer (2)
Sol. Zener diode has both p and n side highly doped
and depletion layer is very thin.
2. If the source of light used in a Young’s double
slit experiment is changed from red to violet
(1) The fringes will become brighter
(2) The central bright fringe will become a dark
fringe
(3) Consecutive fringe lines will come closer
(4) The intensity of minima will increase
Answer (3)
Sol. ?
D
d
?
??
and ?
v
 < ?
red
? Fringe width will decrease.
? Fringe lines will come closer.
3. C
A
B
The logic circuit shown above is equivalent to
(1) C
A
B
(2) C
A
B
(3) C
A
B
(4) C
A
B
Answer (1)
Sol. From gates diagram,
(AB) AB AB ?? ? ? ?
? C
A
B
4. Which of the following equations represents a
travelling wave?
(1) y = Asin(15x – 2t)
(2) y = Ae
x
cos( ?t – ?)
(3) y = Asinx cos ?t
(4)
?
???
2
x
yAe (vt )
Answer (1)
Sol. Travelling wave equation,
y = f(± kx ± ?t)
? y = A sin(15x – 2t) is a travelling wave.
5. Figure shows a circuit that contains four
identical resistors with resistance R = 2.0 ?,
two identical inductors with inductance
L = 2.0 mH and an ideal battery with emf
E = 9 V. The current ‘i’ just after the switch ‘S’
is closed will be
A 
S
R
R
R
L
R
L
i E = 9 V
(1) 3.37 A
(2) 3.0 A
(3) 2.25 A
(4) 9 A
Answer (3)
JEE (MAIN)-2021 Phase-1 (24-02-2021)-E
Sol. At t = 0, inductor behaves as an open switch.
?
2 ?
9 V
2 ?
?
9
i2.25A
4
??
6. An X-ray tube is operated at 1.24 million volt.
The shortest wavelength of the produced
photon will be
(1) 10
–3
 nm (2) 10
–2
 nm
(3) 10
–4
 nm (4) 10
–1
 nm
Answer (1)
Sol.
min
hc
eV
??
= 
34 8
19 6
6.63 10 3 10
1.6 10 1.24 10
?
?
???
?? ?
= 1.0 × 10
–12
 m
= 10
–3
 nm
7. The de Broglie wavelength of a proton and
?-particle are equal. The ratio of their velocities
is
(1) 1 : 4 (2) 4 : 3
(3) 4 : 1 (4) 4 : 2
Answer (3)
Sol.
p
pp
h
mv
??
?
h
mv
?
??
??
?
? ?
p
 = ?
?
? m
p
v
p
 = m
?
v
?
?
p
p
v
m 4
vm 1
?
?
??
8. Given below are two statements :
Statement I : PN junction diodes can be used to
function as transistor, simply by connecting two
diodes, back to back, which acts as the base
terminal.
Statement II : In the study of transistor, the
amplification factor ? indicates ratio of the
collector current to the base current.
In the light of the above statements, choose the
correct answer from the options given below.
(1) Both Statement I and Statement II are false
(2) Statement I is true but Statement II is false
(3) Statement I is false but Statement II is true
(4) Both statement I and Statement II are true
Answer (3)
Sol. Transistor is formed by formation of two
p-n junctions by sandwiching a thin base layer.
So, statement I is false.
?
C
B
I
I
?
??
?
 and for DC, 
C
B
I
I
??
So, statement II is true.
9. A circular hole of radius 
??
??
??
a
2
 is cut out of a
circular disc of radius ‘a’ as shown in figure.
The centroid of the remaining circular portion
with respect to point ‘O’ will be
a/2
a
X-axis
Y-axis
O
(1)
1
a
6
(2)
2
a
3
(3)
10
a
11
(4)
5
a
6
Answer (4)
Sol. Let mass of hole be (–m), then mass of
complete disc will be 4m.
a/2
a
O
C
? Centre of mass w.r.t. point O is
CM
3
4m a ( m) a
5 2
Xa
(4m m) 6
??
?? ? ?
??
??
??
?
JEE (MAIN)-2021 Phase-1 (24-02-2021)-E
10. A particle is projected with velocity v
0
 along
x-axis. A damping force is acting on the particle
which is proportional to the square of the
distance from the origin i.e. ma = – ?x
2
. The
distance at which the particle stops
(1)
??
??
??
?
??
1
2
3
0
3v
2
(2)
??
??
??
?
??
1
2
2
0
3v
2
(3)
??
??
??
?
??
1
2
2
0
2v
3
(4)
??
??
?
??
1
3
0
2v
3
Answer (1)
Sol. Loss in KE = work against damping
?
x
22
0
x0
1
mv x dx
2
?
??
?
?
3
2
0
1x
mv
23
?
?
?
1
2
3
0
3mv
x
2
??
???
??
?
??
11. When a particle executes SHM, the nature of
graphical representation of velocity as a
function of displacement is :
(1) parabolic (2) straight line
(3) circular (4) elliptical
Answer (4)
Sol. ?? ?
22
vA x
??
?
2
22
2
v
xA
12. The period of oscillation of a simple pendulum
is ??
L
T2 .
g
 Measured value of ‘L’ is 1.0 m
from meter scale having a minimum division  of
1 mm and time of one complete oscillation is
1.95 s measured from stopwatch of 0.01 s
resolution. The percentage error in the
determination of ‘g’ will be :
(1) 1.30%
(2) 1.33%
(3) 1.13%
(4) 1.03%
Answer (3)
Sol. ??

2
2
g4
T
??


dg d 2dT
gT
dg 1 2 0.01 1.13
g 1000 1.95 100
?
?? ?
13. In the given figure, a body of mass M is held
between two massless spring, on a smooth
inclined plane. The free ends of the springs are
attached to firm supports. If each spring has
spring constant k, the frequency of oscillation
of given body is :
M
k
k
?
(1)
?
12k
2M
(2)
?
1k
22M
(3)
??
12k
2Mgsin
(4)
??
1k
2Mgsin
Answer (1)
Sol. ??
eq
M
T2
k
?
?
eq
k
1
f
2M
?
eq
k2k
14. Match List-I with List-II.
List-I List-II
(a) Source of (i) Radioactive decay
microwave of nucleus
frequency
(b) Source of (ii) Magnetron
infrared
frequency
(c) Source of (iii) Inner shell electrons
Gamma Rays
(d) Source of X-rays (iv) Vibration of atoms
and molecules
(v) LASER
(vi) RC circuit
Choose the correct answer from the options
given below :
JEE (MAIN)-2021 Phase-1 (24-02-2021)-E
(1) (a)-(ii), (b)-(iv), (c)-(vi), (d)-(iii)
(2) (a)-(vi), (b)-(v), (c)-(i), (d)-(iv)
(3) (a)-(vi), (b)-(iv), (c)-(i), (d)-(v)
(4) (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)
Answer (4)
Sol. Source of Gamma Rays is radioactive decay
source X-Ray is transition of inner shell
electron and that of microwave is magnetron.
15. If one mole of an ideal gas at (P
1
, V
1
) is allowed
to expand reversibly and isothermally (A to B)
its pressure is reduced to one-half of the
original pressure (see figure). This is followed
by a constant volume cooling till its pressure is
reduced to one-fourth of the initial value
(B ? C). Then it is restored to its initial state by
a reversible adiabatic compression (C to A).
The net work done by the gas is equal to :
P
P
1
P
1
2
P
1
4
A
B
C
V
2V
1
V
1
(1)
??
?
? ?
RT
21
(2)
??
?
??
??
??
1
RT ln2
2( 1)
(3) 0 (4) RTln2
Answer (2)
Sol.
?
?
AB 1 1
WPVln(2)
?
?
BC
W0
?
?
?
? ?
11
CA
PV
W
2( 1)
16. A soft ferromagnetic material is placed in an
external magnetic field. The magnetic domains:
(1) decrease in size and changes orientation.
(2) may increase or decrease in size and
change its orientation.
(3) increase in size but no change in
orientation.
(4) have no relation with external magnetic
field
Answer (2)
Sol. Domains aligned in the direction of field
increases in size and those aligned in the
direction opposite to the field reduces in size.
17. A body weighs 49 N on a spring balance at the
north pole. What will be its weight recorded on
the same weighing machine, if it is shifted to
the equator?
[ ?
2
GM
Useg
R
 = 9.8 ms
–2
 and radius of earth,
R = 6400 km.]
(1) 49.83 N (2) 49 N
(3) 48.83 N (4) 49.17 N
Answer (3)
Sol. g ? = g –??
2
R
Weight at equator will decrease.
18. According to Bohr atom model, in which of the
following transitions will the frequency be
maximum?
(1) n = 3 to n = 2 (2) n = 5 to n = 4
(3) n = 4 to n = 3 (4) n = 2 to n = 1
Answer (4)
Sol. Energy in transition is maximum for n = 2 to
n = 1, hence the frequency.
19. On the basis of kinetic theory of gases, the gas
exerts pressure because its molecules :
(1) suffer change in momentum when impinge
on the walls of container.
(2) continuously stick to the walls of container.
(3) continuously lose their energy till it reaches
wall.
(4) are attracted by the walls of container.
Answer (1)
Sol. Pressure is due to force exerted by molecules
on wall
20. Two electrons each are fixed at a distance ‘2d’.
A third charge proton placed at the midpoint is
displaced slightly by a distance x(x << d)
perpendicular to the line joining the two fixed
charges. Proton will execute simple harmonic
motion having angular frequency: (m = mass of
charged particle)
(1)
??
??
??
??
??
1
2
2
3
0
q
2md
(2)
??
??
??
??
??
1
3
2
0
2
2md
q
(3)
??
??
??
??
??
1
2
2
3
0
2q
md
(4)
??
??
??
??
??
1
3
2
0
2
md
2q
Answer (1)
Page 5


JEE (MAIN)-2021 Phase-1 (24-02-2021)-E
PART–A : PHYSICS
SECTION - I
Multiple Choice Questions: This section contains
20 multiple choice questions. Each question has
4 choices (1), (2), (3) and (4), out of which ONL Y ONE
is correct.
Choose the correct answer :
1. Zener breakdown occurs in a p-n junction
having p and n both
(1) Lightly doped and have narrow depletion
layer
(2) Heavily doped and have narrow depletion
layer
(3) Heavily doped and have wide depletion
layer
(4) Lightly doped and have wide depletion layer
Answer (2)
Sol. Zener diode has both p and n side highly doped
and depletion layer is very thin.
2. If the source of light used in a Young’s double
slit experiment is changed from red to violet
(1) The fringes will become brighter
(2) The central bright fringe will become a dark
fringe
(3) Consecutive fringe lines will come closer
(4) The intensity of minima will increase
Answer (3)
Sol. ?
D
d
?
??
and ?
v
 < ?
red
? Fringe width will decrease.
? Fringe lines will come closer.
3. C
A
B
The logic circuit shown above is equivalent to
(1) C
A
B
(2) C
A
B
(3) C
A
B
(4) C
A
B
Answer (1)
Sol. From gates diagram,
(AB) AB AB ?? ? ? ?
? C
A
B
4. Which of the following equations represents a
travelling wave?
(1) y = Asin(15x – 2t)
(2) y = Ae
x
cos( ?t – ?)
(3) y = Asinx cos ?t
(4)
?
???
2
x
yAe (vt )
Answer (1)
Sol. Travelling wave equation,
y = f(± kx ± ?t)
? y = A sin(15x – 2t) is a travelling wave.
5. Figure shows a circuit that contains four
identical resistors with resistance R = 2.0 ?,
two identical inductors with inductance
L = 2.0 mH and an ideal battery with emf
E = 9 V. The current ‘i’ just after the switch ‘S’
is closed will be
A 
S
R
R
R
L
R
L
i E = 9 V
(1) 3.37 A
(2) 3.0 A
(3) 2.25 A
(4) 9 A
Answer (3)
JEE (MAIN)-2021 Phase-1 (24-02-2021)-E
Sol. At t = 0, inductor behaves as an open switch.
?
2 ?
9 V
2 ?
?
9
i2.25A
4
??
6. An X-ray tube is operated at 1.24 million volt.
The shortest wavelength of the produced
photon will be
(1) 10
–3
 nm (2) 10
–2
 nm
(3) 10
–4
 nm (4) 10
–1
 nm
Answer (1)
Sol.
min
hc
eV
??
= 
34 8
19 6
6.63 10 3 10
1.6 10 1.24 10
?
?
???
?? ?
= 1.0 × 10
–12
 m
= 10
–3
 nm
7. The de Broglie wavelength of a proton and
?-particle are equal. The ratio of their velocities
is
(1) 1 : 4 (2) 4 : 3
(3) 4 : 1 (4) 4 : 2
Answer (3)
Sol.
p
pp
h
mv
??
?
h
mv
?
??
??
?
? ?
p
 = ?
?
? m
p
v
p
 = m
?
v
?
?
p
p
v
m 4
vm 1
?
?
??
8. Given below are two statements :
Statement I : PN junction diodes can be used to
function as transistor, simply by connecting two
diodes, back to back, which acts as the base
terminal.
Statement II : In the study of transistor, the
amplification factor ? indicates ratio of the
collector current to the base current.
In the light of the above statements, choose the
correct answer from the options given below.
(1) Both Statement I and Statement II are false
(2) Statement I is true but Statement II is false
(3) Statement I is false but Statement II is true
(4) Both statement I and Statement II are true
Answer (3)
Sol. Transistor is formed by formation of two
p-n junctions by sandwiching a thin base layer.
So, statement I is false.
?
C
B
I
I
?
??
?
 and for DC, 
C
B
I
I
??
So, statement II is true.
9. A circular hole of radius 
??
??
??
a
2
 is cut out of a
circular disc of radius ‘a’ as shown in figure.
The centroid of the remaining circular portion
with respect to point ‘O’ will be
a/2
a
X-axis
Y-axis
O
(1)
1
a
6
(2)
2
a
3
(3)
10
a
11
(4)
5
a
6
Answer (4)
Sol. Let mass of hole be (–m), then mass of
complete disc will be 4m.
a/2
a
O
C
? Centre of mass w.r.t. point O is
CM
3
4m a ( m) a
5 2
Xa
(4m m) 6
??
?? ? ?
??
??
??
?
JEE (MAIN)-2021 Phase-1 (24-02-2021)-E
10. A particle is projected with velocity v
0
 along
x-axis. A damping force is acting on the particle
which is proportional to the square of the
distance from the origin i.e. ma = – ?x
2
. The
distance at which the particle stops
(1)
??
??
??
?
??
1
2
3
0
3v
2
(2)
??
??
??
?
??
1
2
2
0
3v
2
(3)
??
??
??
?
??
1
2
2
0
2v
3
(4)
??
??
?
??
1
3
0
2v
3
Answer (1)
Sol. Loss in KE = work against damping
?
x
22
0
x0
1
mv x dx
2
?
??
?
?
3
2
0
1x
mv
23
?
?
?
1
2
3
0
3mv
x
2
??
???
??
?
??
11. When a particle executes SHM, the nature of
graphical representation of velocity as a
function of displacement is :
(1) parabolic (2) straight line
(3) circular (4) elliptical
Answer (4)
Sol. ?? ?
22
vA x
??
?
2
22
2
v
xA
12. The period of oscillation of a simple pendulum
is ??
L
T2 .
g
 Measured value of ‘L’ is 1.0 m
from meter scale having a minimum division  of
1 mm and time of one complete oscillation is
1.95 s measured from stopwatch of 0.01 s
resolution. The percentage error in the
determination of ‘g’ will be :
(1) 1.30%
(2) 1.33%
(3) 1.13%
(4) 1.03%
Answer (3)
Sol. ??

2
2
g4
T
??


dg d 2dT
gT
dg 1 2 0.01 1.13
g 1000 1.95 100
?
?? ?
13. In the given figure, a body of mass M is held
between two massless spring, on a smooth
inclined plane. The free ends of the springs are
attached to firm supports. If each spring has
spring constant k, the frequency of oscillation
of given body is :
M
k
k
?
(1)
?
12k
2M
(2)
?
1k
22M
(3)
??
12k
2Mgsin
(4)
??
1k
2Mgsin
Answer (1)
Sol. ??
eq
M
T2
k
?
?
eq
k
1
f
2M
?
eq
k2k
14. Match List-I with List-II.
List-I List-II
(a) Source of (i) Radioactive decay
microwave of nucleus
frequency
(b) Source of (ii) Magnetron
infrared
frequency
(c) Source of (iii) Inner shell electrons
Gamma Rays
(d) Source of X-rays (iv) Vibration of atoms
and molecules
(v) LASER
(vi) RC circuit
Choose the correct answer from the options
given below :
JEE (MAIN)-2021 Phase-1 (24-02-2021)-E
(1) (a)-(ii), (b)-(iv), (c)-(vi), (d)-(iii)
(2) (a)-(vi), (b)-(v), (c)-(i), (d)-(iv)
(3) (a)-(vi), (b)-(iv), (c)-(i), (d)-(v)
(4) (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)
Answer (4)
Sol. Source of Gamma Rays is radioactive decay
source X-Ray is transition of inner shell
electron and that of microwave is magnetron.
15. If one mole of an ideal gas at (P
1
, V
1
) is allowed
to expand reversibly and isothermally (A to B)
its pressure is reduced to one-half of the
original pressure (see figure). This is followed
by a constant volume cooling till its pressure is
reduced to one-fourth of the initial value
(B ? C). Then it is restored to its initial state by
a reversible adiabatic compression (C to A).
The net work done by the gas is equal to :
P
P
1
P
1
2
P
1
4
A
B
C
V
2V
1
V
1
(1)
??
?
? ?
RT
21
(2)
??
?
??
??
??
1
RT ln2
2( 1)
(3) 0 (4) RTln2
Answer (2)
Sol.
?
?
AB 1 1
WPVln(2)
?
?
BC
W0
?
?
?
? ?
11
CA
PV
W
2( 1)
16. A soft ferromagnetic material is placed in an
external magnetic field. The magnetic domains:
(1) decrease in size and changes orientation.
(2) may increase or decrease in size and
change its orientation.
(3) increase in size but no change in
orientation.
(4) have no relation with external magnetic
field
Answer (2)
Sol. Domains aligned in the direction of field
increases in size and those aligned in the
direction opposite to the field reduces in size.
17. A body weighs 49 N on a spring balance at the
north pole. What will be its weight recorded on
the same weighing machine, if it is shifted to
the equator?
[ ?
2
GM
Useg
R
 = 9.8 ms
–2
 and radius of earth,
R = 6400 km.]
(1) 49.83 N (2) 49 N
(3) 48.83 N (4) 49.17 N
Answer (3)
Sol. g ? = g –??
2
R
Weight at equator will decrease.
18. According to Bohr atom model, in which of the
following transitions will the frequency be
maximum?
(1) n = 3 to n = 2 (2) n = 5 to n = 4
(3) n = 4 to n = 3 (4) n = 2 to n = 1
Answer (4)
Sol. Energy in transition is maximum for n = 2 to
n = 1, hence the frequency.
19. On the basis of kinetic theory of gases, the gas
exerts pressure because its molecules :
(1) suffer change in momentum when impinge
on the walls of container.
(2) continuously stick to the walls of container.
(3) continuously lose their energy till it reaches
wall.
(4) are attracted by the walls of container.
Answer (1)
Sol. Pressure is due to force exerted by molecules
on wall
20. Two electrons each are fixed at a distance ‘2d’.
A third charge proton placed at the midpoint is
displaced slightly by a distance x(x << d)
perpendicular to the line joining the two fixed
charges. Proton will execute simple harmonic
motion having angular frequency: (m = mass of
charged particle)
(1)
??
??
??
??
??
1
2
2
3
0
q
2md
(2)
??
??
??
??
??
1
3
2
0
2
2md
q
(3)
??
??
??
??
??
1
2
2
3
0
2q
md
(4)
??
??
??
??
??
1
3
2
0
2
md
2q
Answer (1)
JEE (MAIN)-2021 Phase-1 (24-02-2021)-E
Sol. F
net
 = 2F cos ?
?
F
d
+q
F
x
d
+q
?
?? ?
2
22
0
q
F
4(x d)
?
?? ?
2
net
223/2
0
2q x
F
4(x d)
??
??
2
2
3
0
qx
–mx
2d
??
??
2
2
3
0
q
2md
SECTION - II
Numerical Value Type Questions: This section
contains 10 questions. In Section II, attempt any five
questions out of 10. The answer to each question is a
NUMERICAL VALUE. For each question, enter the
correct numerical value (in decimal notation,
truncated/rounded-off to the second decimal place;
e.g. 06.25, 07.00, –00.33, –00.30, 30.27, –27.30) using
the mouse and the on-screen virtual numeric keypad
in the place designated to enter the answer.
1. The root mean square speed of molecules of a
given mass of a gas at 27°C and 1 atmosphere
pressure is 200 ms
–1
. The root mean square
speed of molecules of the gas at 127°C and
2 atmosphere pressure is 
–1
x
ms
3
. The value
of x will be_______.
Answer (400)
Sol. u
rms
 = 
3RT
M
2
1
u
u
 = 
2
1
T
T
u
2
= 
?
?
1
273 127
.u
273 27
= 
2
.200
3
= 
400
m/s
3
2. An electromagnetic wave of frequency 3 GHz
enters a dielectric medium of relative electric
permittivity 2.25 from vacuum. The wavelength
of this wave in that medium will be
______× 10
–2
 cm.
Answer (667)
Sol. Assuming relative permeability of the medium
to be 1.
n =  ??
rr
 = 1.5
u = ??
8
C
210m/s
n
? = 
8
9
u210
m
f
310
?
?
?
= 666.67 × 10
–2
 cm
3. A point charge of + 12 ?C is at a distance 6 cm
vertically above the centre of a square of side
12 cm as shown in figure. The magnitude of
the electric flux through the square will be
______ × 10
3
 Nm
2
/C.
6 cm
12 cm
12 cm
+q
Answer (226)
Sol.
r r
a/2
a
Q
? = 
?
0
Q
6
= 
?
??? ?
–6
9
12 10
4910
6
= 226.28 × 10
3
 
2
N-m
C
4. Two solids A and B of mass 1 kg and 2 kg
respectively are moving with equal linear
momentum. The ratio of their kinetic energies
(K.E)
A
 : (K.E.)
B
 will be 
A
1
, so the value of A will
be________.
Answer (2)