JEE Main 2021 Physics February 25 Shift 1 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


JEE (MAIN)-2021 : Phase-1(25-02-2021)-M
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 ONLY ONE
is correct.
Choose the correct answer :
1. Two satellites A and B of masses 200 kg and
400 kg are revolving round the earth at height
of 600 km and 1600 km respectively.
If T
A
 and T
B
 are the time periods of A and B
respectively then the value of T
B
 – T
A
 :
B
A
E
[Given : radius of earth = 6400 km,  mass of
earth = 6 × 10
24
 kg]
(1) 4.24 × 10
2
 s (2) 1.33 × 10
3
 s
(3) 4.24 × 10
3
 s (4) 3.33 × 10
2
 s
Answer (2)
Sol.
3
r
T2
GM
??
?
?? ? ?
3/2 3/2
66
BA
2
TT 810 710
GM
?
??
?? ? ? ? ??
??
93/2 3/2
11 24
2
10 8 7
6.67 10 6 10
?
?
???
???
1300 s ?
2. A student is performing the experiment of
resonance column. The diameter of the column
tube is 6 cm. The frequency of the tuning fork
is 504 Hz. Speed of the sound at the given
temperature is 336 m/s. The zero of the metre
scale coincides with the top end of the
resonance column tube. The reading of the
water level in the column when the first
resonance occurs is :
(1) 13 cm (2) 16.6 cm
(3) 14.8 cm (4) 18.4 cm
Answer (3)
Sol.
v 336 2
 mm
504 3
?? ? ?
?
?
le
4
?
??
?
2
100
3
l0.6 3
4
?
?? ?
? l = 14.8 cm
3. The coherent light sources having intensity in
the ratio 2x produce an interference pattern.
The ratio 
?
?
max min
max min
II
II
 will be
(1)
?
2x
2x 1
(2)
?
2x
x1
(3)
?
22x
x1
(4)
?
22x
2x 1
Answer (4)
Sol.
2
1
I
2X
I
?
?
22
22
11
max min
22
max min
22
11
II
11
II
II
II
II
11
II
??? ?
?? ? ??? ?
??? ?
?
??? ?
?
?
??? ?
?? ? ??? ?
??? ?
??? ?
= 
????
????
22
22
2x 1 2x 1
2x 1 2x 1
?? ?
?? ?
= 
42x
4x 2 ?
 = 
22x
2x 1 ?
4. A solid sphere of radius R gravitationally
attracts a particle placed at 3R from its centre
with a force F
1
. Now a spherical cavity of
radius 
??
??
??
R
2
 is made in the sphere (as shown in
figure) and the force becomes F
2
. The value of
F
1
 : F
2
 is :
A B
m
2R
O
M
(1) 36 : 25 (2) 50 : 41
(3) 41 : 50 (4) 25 : 36
Page 2


JEE (MAIN)-2021 : Phase-1(25-02-2021)-M
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 ONLY ONE
is correct.
Choose the correct answer :
1. Two satellites A and B of masses 200 kg and
400 kg are revolving round the earth at height
of 600 km and 1600 km respectively.
If T
A
 and T
B
 are the time periods of A and B
respectively then the value of T
B
 – T
A
 :
B
A
E
[Given : radius of earth = 6400 km,  mass of
earth = 6 × 10
24
 kg]
(1) 4.24 × 10
2
 s (2) 1.33 × 10
3
 s
(3) 4.24 × 10
3
 s (4) 3.33 × 10
2
 s
Answer (2)
Sol.
3
r
T2
GM
??
?
?? ? ?
3/2 3/2
66
BA
2
TT 810 710
GM
?
??
?? ? ? ? ??
??
93/2 3/2
11 24
2
10 8 7
6.67 10 6 10
?
?
???
???
1300 s ?
2. A student is performing the experiment of
resonance column. The diameter of the column
tube is 6 cm. The frequency of the tuning fork
is 504 Hz. Speed of the sound at the given
temperature is 336 m/s. The zero of the metre
scale coincides with the top end of the
resonance column tube. The reading of the
water level in the column when the first
resonance occurs is :
(1) 13 cm (2) 16.6 cm
(3) 14.8 cm (4) 18.4 cm
Answer (3)
Sol.
v 336 2
 mm
504 3
?? ? ?
?
?
le
4
?
??
?
2
100
3
l0.6 3
4
?
?? ?
? l = 14.8 cm
3. The coherent light sources having intensity in
the ratio 2x produce an interference pattern.
The ratio 
?
?
max min
max min
II
II
 will be
(1)
?
2x
2x 1
(2)
?
2x
x1
(3)
?
22x
x1
(4)
?
22x
2x 1
Answer (4)
Sol.
2
1
I
2X
I
?
?
22
22
11
max min
22
max min
22
11
II
11
II
II
II
II
11
II
??? ?
?? ? ??? ?
??? ?
?
??? ?
?
?
??? ?
?? ? ??? ?
??? ?
??? ?
= 
????
????
22
22
2x 1 2x 1
2x 1 2x 1
?? ?
?? ?
= 
42x
4x 2 ?
 = 
22x
2x 1 ?
4. A solid sphere of radius R gravitationally
attracts a particle placed at 3R from its centre
with a force F
1
. Now a spherical cavity of
radius 
??
??
??
R
2
 is made in the sphere (as shown in
figure) and the force becomes F
2
. The value of
F
1
 : F
2
 is :
A B
m
2R
O
M
(1) 36 : 25 (2) 50 : 41
(3) 41 : 50 (4) 25 : 36
JEE (MAIN)-2021 : Phase-1(25-02-2021)-M
Answer (2)
Sol. 
1
22
GMm GMm
F
(3R) 9R
??
2
22 2
M
Gm
GMm 41 GMm
8
F
450
(3R) R
5R
2
??
??
??
?? ?
??
??
??
?
1
2
F 1 450 50
F 9 41 41
?
??
?
5. A 5 V battery is connected across the points
X and Y. Assume D
1
 and D
2
 to be normal silicon
diodes. Find the current supplied by the battery
if the +ve terminal of the battery is connected
to point X.
D
1
D
2
10 ?
5 ?
XY
(1)
~ 1.5 A
(2)
~ 0.5 A
(3)
~ 0.43 A
(4)
~ 0.86 A
Answer (3)
Sol.
D
1 10 ?
5 ?
i
5 V
(5 0.7)
i
10
?
~
?
i0.43 A ~
6. Match List-I with List-II :
List-I List-II
(a) h (Planck’s constant) (i) [MLT
–1
]
(b) E (kinetic energy) (ii) [ML
2
T
–1
]
(c) V (electric potential) (iii) [ML
2
T
–2
]
(d) P (linear momentum) (iv) [ML
2
I
–1
T
–3
]
Choose the correct answer from the options
given below :
(1) (a) ? (i), (b) ? (ii), (c) ? (iv), (d) ? (iii)
(2) (a) ? (ii), (b) ? (iii), (c) ? (iv), (d) ? (i)
(3) (a) ? (iii), (b) ? (ii), (c) ? (iv), (d) ? (i)
(4) (a) ? (iii), (b) ? (iv), (c) ? (ii), (d) ? (i)
Answer (2)
Sol. ? ? ?? ?
2–2
hET MLT T
= ML
2
T
–1
[E] = ML
2
T
–2
??
??
?? ?
??
??
2–2
2–3–1
UMLT
VMLTI
qAI
? ??? ?
–1–1
PMLT MLT
? a ? (ii), b ? (iii), c ? (iv), d ? (i)
7. Given below are two statements : one is
labelled as Assertion A and the other is
labelled as Reason R.
Assertion A: When a rod lying freely is heated,
no thermal stress is developed in it.
Reason R: On heating, the length of the rod
increases.
In the light of the above statements, choose
the correct answer from the options given
below:
(1) A is true but R is false
(2) A is false but R is true
(3) Both A and R are true but R is NOT the
correct explanation of A
(4) Both A and R are true and R is the correct
explanation of A
Answer (3)
Sol. In free expansion, thermal stress = 0
So, statement A is true.
Statement R is also true but it is not correct
reason for A.
8. A diatomic gas, having ?
P
7
CR
2
 and ?
V
5
CR,
2
is heated at constant pressure. The ratio
dU : dQ : dW :
(1) 5 : 7 : 2 (2) 3 : 5 : 2
(3) 3 : 7 : 2 (4) 5 : 7 : 3
Answer (1)
Sol. At constant pressure,
??
?? ?
??
??
7R
dQ n · T
2
Page 3


JEE (MAIN)-2021 : Phase-1(25-02-2021)-M
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 ONLY ONE
is correct.
Choose the correct answer :
1. Two satellites A and B of masses 200 kg and
400 kg are revolving round the earth at height
of 600 km and 1600 km respectively.
If T
A
 and T
B
 are the time periods of A and B
respectively then the value of T
B
 – T
A
 :
B
A
E
[Given : radius of earth = 6400 km,  mass of
earth = 6 × 10
24
 kg]
(1) 4.24 × 10
2
 s (2) 1.33 × 10
3
 s
(3) 4.24 × 10
3
 s (4) 3.33 × 10
2
 s
Answer (2)
Sol.
3
r
T2
GM
??
?
?? ? ?
3/2 3/2
66
BA
2
TT 810 710
GM
?
??
?? ? ? ? ??
??
93/2 3/2
11 24
2
10 8 7
6.67 10 6 10
?
?
???
???
1300 s ?
2. A student is performing the experiment of
resonance column. The diameter of the column
tube is 6 cm. The frequency of the tuning fork
is 504 Hz. Speed of the sound at the given
temperature is 336 m/s. The zero of the metre
scale coincides with the top end of the
resonance column tube. The reading of the
water level in the column when the first
resonance occurs is :
(1) 13 cm (2) 16.6 cm
(3) 14.8 cm (4) 18.4 cm
Answer (3)
Sol.
v 336 2
 mm
504 3
?? ? ?
?
?
le
4
?
??
?
2
100
3
l0.6 3
4
?
?? ?
? l = 14.8 cm
3. The coherent light sources having intensity in
the ratio 2x produce an interference pattern.
The ratio 
?
?
max min
max min
II
II
 will be
(1)
?
2x
2x 1
(2)
?
2x
x1
(3)
?
22x
x1
(4)
?
22x
2x 1
Answer (4)
Sol.
2
1
I
2X
I
?
?
22
22
11
max min
22
max min
22
11
II
11
II
II
II
II
11
II
??? ?
?? ? ??? ?
??? ?
?
??? ?
?
?
??? ?
?? ? ??? ?
??? ?
??? ?
= 
????
????
22
22
2x 1 2x 1
2x 1 2x 1
?? ?
?? ?
= 
42x
4x 2 ?
 = 
22x
2x 1 ?
4. A solid sphere of radius R gravitationally
attracts a particle placed at 3R from its centre
with a force F
1
. Now a spherical cavity of
radius 
??
??
??
R
2
 is made in the sphere (as shown in
figure) and the force becomes F
2
. The value of
F
1
 : F
2
 is :
A B
m
2R
O
M
(1) 36 : 25 (2) 50 : 41
(3) 41 : 50 (4) 25 : 36
JEE (MAIN)-2021 : Phase-1(25-02-2021)-M
Answer (2)
Sol. 
1
22
GMm GMm
F
(3R) 9R
??
2
22 2
M
Gm
GMm 41 GMm
8
F
450
(3R) R
5R
2
??
??
??
?? ?
??
??
??
?
1
2
F 1 450 50
F 9 41 41
?
??
?
5. A 5 V battery is connected across the points
X and Y. Assume D
1
 and D
2
 to be normal silicon
diodes. Find the current supplied by the battery
if the +ve terminal of the battery is connected
to point X.
D
1
D
2
10 ?
5 ?
XY
(1)
~ 1.5 A
(2)
~ 0.5 A
(3)
~ 0.43 A
(4)
~ 0.86 A
Answer (3)
Sol.
D
1 10 ?
5 ?
i
5 V
(5 0.7)
i
10
?
~
?
i0.43 A ~
6. Match List-I with List-II :
List-I List-II
(a) h (Planck’s constant) (i) [MLT
–1
]
(b) E (kinetic energy) (ii) [ML
2
T
–1
]
(c) V (electric potential) (iii) [ML
2
T
–2
]
(d) P (linear momentum) (iv) [ML
2
I
–1
T
–3
]
Choose the correct answer from the options
given below :
(1) (a) ? (i), (b) ? (ii), (c) ? (iv), (d) ? (iii)
(2) (a) ? (ii), (b) ? (iii), (c) ? (iv), (d) ? (i)
(3) (a) ? (iii), (b) ? (ii), (c) ? (iv), (d) ? (i)
(4) (a) ? (iii), (b) ? (iv), (c) ? (ii), (d) ? (i)
Answer (2)
Sol. ? ? ?? ?
2–2
hET MLT T
= ML
2
T
–1
[E] = ML
2
T
–2
??
??
?? ?
??
??
2–2
2–3–1
UMLT
VMLTI
qAI
? ??? ?
–1–1
PMLT MLT
? a ? (ii), b ? (iii), c ? (iv), d ? (i)
7. Given below are two statements : one is
labelled as Assertion A and the other is
labelled as Reason R.
Assertion A: When a rod lying freely is heated,
no thermal stress is developed in it.
Reason R: On heating, the length of the rod
increases.
In the light of the above statements, choose
the correct answer from the options given
below:
(1) A is true but R is false
(2) A is false but R is true
(3) Both A and R are true but R is NOT the
correct explanation of A
(4) Both A and R are true and R is the correct
explanation of A
Answer (3)
Sol. In free expansion, thermal stress = 0
So, statement A is true.
Statement R is also true but it is not correct
reason for A.
8. A diatomic gas, having ?
P
7
CR
2
 and ?
V
5
CR,
2
is heated at constant pressure. The ratio
dU : dQ : dW :
(1) 5 : 7 : 2 (2) 3 : 5 : 2
(3) 3 : 7 : 2 (4) 5 : 7 : 3
Answer (1)
Sol. At constant pressure,
??
?? ?
??
??
7R
dQ n · T
2
JEE (MAIN)-2021 : Phase-1(25-02-2021)-M
??
?? ?
??
??
5R
dU n · T
2
dW = n × R × ?T
?
?
57
dU:dQ:dW : :1
22
= 5 : 7 : 2
9. An ? particle and a proton are accelerated
from rest by a potential difference of 200 V.
After this, de Broglie wavelengths are 
?
? and
?
P
 respectively. The ratio 
?
?
?
P
 is :
(1) 8 (2) 2.8
(3) 3.8 (4) 7.8
Answer (2)
Sol.
??
??
??
P
p
h
2m e V
??
?
?
??
??
h
2m 2e V
?
?
?
?
??? ?
?
P
P
m
242
m
?22 = 2.8
10. Two radioactive substance X and Y originally
have N
1
 and N
2
 nuclei respectively. Half life of
X is half of the half life of Y. After three half
lives of Y, number of nuclei of both are equal.
The ratio 
1
2
N
N
 will be equal to :
(1)
1
3
(2)
8
1
(3)
1
8
(4)
3
1
Answer (2)
Sol. ??
x y
1
TT
2
? ?
y x
3T 6T
?
?
1
x 6
N
N
2
and, ?
2
y 3
N
N
2
?
? ? ?
1 2
xy
N N
NN
64 8
? ?
1
2
N 8
N1
11. Given below are two statements : one is
labelled as Assertion A and the other is labelled
as Reason R.
Assertion A : The escape velocities of planet A
and B are same. But A and B are of unequal
mass.
Reason R : The product of their mass and
radius must be same. M
1
R
1
 = M
2
R
2
In the light of the above statements, choose the
most appropriate answer from the options
given below :
(1) A is not correct but R is correct
(2) Both A and R are correct but R is NOT the
correct explanation of A
(3) A is correct but R is not correct
(4) Both A and R are correct and R is the
correct explanation of A
Answer (3)
Sol.
?
es
GM
V
R
12. If the time period of a two meter long simple
pendulum is 2 s, the acceleration due to gravity
at the place where pendulum is executing
S.H.M. is :
(1) 9.8 ms
–2
(2) ?
2
ms
–2
(3) 16 m/s
2
(4) 2 ?
2
ms
–2
Answer (4)
Sol.
??

T2
g
??
2
22
g
g = 2 ?
2
 m/s
2
Page 4


JEE (MAIN)-2021 : Phase-1(25-02-2021)-M
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 ONLY ONE
is correct.
Choose the correct answer :
1. Two satellites A and B of masses 200 kg and
400 kg are revolving round the earth at height
of 600 km and 1600 km respectively.
If T
A
 and T
B
 are the time periods of A and B
respectively then the value of T
B
 – T
A
 :
B
A
E
[Given : radius of earth = 6400 km,  mass of
earth = 6 × 10
24
 kg]
(1) 4.24 × 10
2
 s (2) 1.33 × 10
3
 s
(3) 4.24 × 10
3
 s (4) 3.33 × 10
2
 s
Answer (2)
Sol.
3
r
T2
GM
??
?
?? ? ?
3/2 3/2
66
BA
2
TT 810 710
GM
?
??
?? ? ? ? ??
??
93/2 3/2
11 24
2
10 8 7
6.67 10 6 10
?
?
???
???
1300 s ?
2. A student is performing the experiment of
resonance column. The diameter of the column
tube is 6 cm. The frequency of the tuning fork
is 504 Hz. Speed of the sound at the given
temperature is 336 m/s. The zero of the metre
scale coincides with the top end of the
resonance column tube. The reading of the
water level in the column when the first
resonance occurs is :
(1) 13 cm (2) 16.6 cm
(3) 14.8 cm (4) 18.4 cm
Answer (3)
Sol.
v 336 2
 mm
504 3
?? ? ?
?
?
le
4
?
??
?
2
100
3
l0.6 3
4
?
?? ?
? l = 14.8 cm
3. The coherent light sources having intensity in
the ratio 2x produce an interference pattern.
The ratio 
?
?
max min
max min
II
II
 will be
(1)
?
2x
2x 1
(2)
?
2x
x1
(3)
?
22x
x1
(4)
?
22x
2x 1
Answer (4)
Sol.
2
1
I
2X
I
?
?
22
22
11
max min
22
max min
22
11
II
11
II
II
II
II
11
II
??? ?
?? ? ??? ?
??? ?
?
??? ?
?
?
??? ?
?? ? ??? ?
??? ?
??? ?
= 
????
????
22
22
2x 1 2x 1
2x 1 2x 1
?? ?
?? ?
= 
42x
4x 2 ?
 = 
22x
2x 1 ?
4. A solid sphere of radius R gravitationally
attracts a particle placed at 3R from its centre
with a force F
1
. Now a spherical cavity of
radius 
??
??
??
R
2
 is made in the sphere (as shown in
figure) and the force becomes F
2
. The value of
F
1
 : F
2
 is :
A B
m
2R
O
M
(1) 36 : 25 (2) 50 : 41
(3) 41 : 50 (4) 25 : 36
JEE (MAIN)-2021 : Phase-1(25-02-2021)-M
Answer (2)
Sol. 
1
22
GMm GMm
F
(3R) 9R
??
2
22 2
M
Gm
GMm 41 GMm
8
F
450
(3R) R
5R
2
??
??
??
?? ?
??
??
??
?
1
2
F 1 450 50
F 9 41 41
?
??
?
5. A 5 V battery is connected across the points
X and Y. Assume D
1
 and D
2
 to be normal silicon
diodes. Find the current supplied by the battery
if the +ve terminal of the battery is connected
to point X.
D
1
D
2
10 ?
5 ?
XY
(1)
~ 1.5 A
(2)
~ 0.5 A
(3)
~ 0.43 A
(4)
~ 0.86 A
Answer (3)
Sol.
D
1 10 ?
5 ?
i
5 V
(5 0.7)
i
10
?
~
?
i0.43 A ~
6. Match List-I with List-II :
List-I List-II
(a) h (Planck’s constant) (i) [MLT
–1
]
(b) E (kinetic energy) (ii) [ML
2
T
–1
]
(c) V (electric potential) (iii) [ML
2
T
–2
]
(d) P (linear momentum) (iv) [ML
2
I
–1
T
–3
]
Choose the correct answer from the options
given below :
(1) (a) ? (i), (b) ? (ii), (c) ? (iv), (d) ? (iii)
(2) (a) ? (ii), (b) ? (iii), (c) ? (iv), (d) ? (i)
(3) (a) ? (iii), (b) ? (ii), (c) ? (iv), (d) ? (i)
(4) (a) ? (iii), (b) ? (iv), (c) ? (ii), (d) ? (i)
Answer (2)
Sol. ? ? ?? ?
2–2
hET MLT T
= ML
2
T
–1
[E] = ML
2
T
–2
??
??
?? ?
??
??
2–2
2–3–1
UMLT
VMLTI
qAI
? ??? ?
–1–1
PMLT MLT
? a ? (ii), b ? (iii), c ? (iv), d ? (i)
7. Given below are two statements : one is
labelled as Assertion A and the other is
labelled as Reason R.
Assertion A: When a rod lying freely is heated,
no thermal stress is developed in it.
Reason R: On heating, the length of the rod
increases.
In the light of the above statements, choose
the correct answer from the options given
below:
(1) A is true but R is false
(2) A is false but R is true
(3) Both A and R are true but R is NOT the
correct explanation of A
(4) Both A and R are true and R is the correct
explanation of A
Answer (3)
Sol. In free expansion, thermal stress = 0
So, statement A is true.
Statement R is also true but it is not correct
reason for A.
8. A diatomic gas, having ?
P
7
CR
2
 and ?
V
5
CR,
2
is heated at constant pressure. The ratio
dU : dQ : dW :
(1) 5 : 7 : 2 (2) 3 : 5 : 2
(3) 3 : 7 : 2 (4) 5 : 7 : 3
Answer (1)
Sol. At constant pressure,
??
?? ?
??
??
7R
dQ n · T
2
JEE (MAIN)-2021 : Phase-1(25-02-2021)-M
??
?? ?
??
??
5R
dU n · T
2
dW = n × R × ?T
?
?
57
dU:dQ:dW : :1
22
= 5 : 7 : 2
9. An ? particle and a proton are accelerated
from rest by a potential difference of 200 V.
After this, de Broglie wavelengths are 
?
? and
?
P
 respectively. The ratio 
?
?
?
P
 is :
(1) 8 (2) 2.8
(3) 3.8 (4) 7.8
Answer (2)
Sol.
??
??
??
P
p
h
2m e V
??
?
?
??
??
h
2m 2e V
?
?
?
?
??? ?
?
P
P
m
242
m
?22 = 2.8
10. Two radioactive substance X and Y originally
have N
1
 and N
2
 nuclei respectively. Half life of
X is half of the half life of Y. After three half
lives of Y, number of nuclei of both are equal.
The ratio 
1
2
N
N
 will be equal to :
(1)
1
3
(2)
8
1
(3)
1
8
(4)
3
1
Answer (2)
Sol. ??
x y
1
TT
2
? ?
y x
3T 6T
?
?
1
x 6
N
N
2
and, ?
2
y 3
N
N
2
?
? ? ?
1 2
xy
N N
NN
64 8
? ?
1
2
N 8
N1
11. Given below are two statements : one is
labelled as Assertion A and the other is labelled
as Reason R.
Assertion A : The escape velocities of planet A
and B are same. But A and B are of unequal
mass.
Reason R : The product of their mass and
radius must be same. M
1
R
1
 = M
2
R
2
In the light of the above statements, choose the
most appropriate answer from the options
given below :
(1) A is not correct but R is correct
(2) Both A and R are correct but R is NOT the
correct explanation of A
(3) A is correct but R is not correct
(4) Both A and R are correct and R is the
correct explanation of A
Answer (3)
Sol.
?
es
GM
V
R
12. If the time period of a two meter long simple
pendulum is 2 s, the acceleration due to gravity
at the place where pendulum is executing
S.H.M. is :
(1) 9.8 ms
–2
(2) ?
2
ms
–2
(3) 16 m/s
2
(4) 2 ?
2
ms
–2
Answer (4)
Sol.
??

T2
g
??
2
22
g
g = 2 ?
2
 m/s
2
JEE (MAIN)-2021 : Phase-1(25-02-2021)-M
13. The current (i) at time t = 0 and t = ?
respectively for the given circuit is :
5 ? 5 ?
1 ? 4 ?
E
i
L
(1)
5E 10E
,
18 33
(2)
18E 5E
,
55 18
(3)
5E 18E
,
18 55
(4)
10E 5E
,
33 18
Answer (1)
Sol.
?? ? ?
EE 5E
i(at t 0)
69 18
?? ? ? ?
EE 10E
i(at t )
54
33
25
14. Magnetic fields at two points on the axis of a
circular coil at a distance of 0.05 m and 0.2 m
from the centre are in the ratio 8 : 1. The radius
of coil is ___
(1) 0.15 m
(2) 0.1 m
(3) 0.2 m
(4) 1.0 m
Answer (2)
Sol. 
??
?
?
3/2
22
1
B
Rx
??
?
??
??
??
?
??
3/2
22
1
3/2
22
2
BR(0.2) 8
B1
R (0.05)
?
?
?
2
2
R0.04 4
1
R0.0025
R
2
 + 0.04 = 4R
2
 + 0.01
R = 0.1 m
15. The angular frequency of alternating current in
a L-C-R circuit is 100 rad/s. The components
connected are shown in the figure. Find the
value of inductance of the coil and capacity of
condenser.
R = 60 ?
15 V
R = 40 ??
10 V
L 20 V C
(1) 1.33 H and 250 ?F (2) 0.8 H and 150 ?F
(3) 0.8 H and 250 ?F (4) 1.33 H and 150 ?F
Answer (3)
Sol.
?
L
X 4
R3
X
L
 = 80 ?
100 × L = 80 ?
L = 0.8 H
12
60
C3
??
?
?
?
1
C
100 40
C = 250 ?F
16. A proton, a deuteron and an ? particle are
moving with same momentum in a uniform
magnetic field. The ratio of magnetic forces
acting on them is ____ and their speed is ____ in
the ratio
(1) 1 : 2 : 4 and 1 : 1 : 2
(2) 1 : 2 : 4 and 2 : 1 : 1
(3) 4 : 2 : 1 and 2 : 1 : 1
(4) 2 : 1 : 1 and 4 : 2 : 1
Answer (4)
Sol.
?
p
V
m
?
?
pd
V:V:V 4:2:1
???
?
pd pp dd
f :f :f q V :q V :q V
= 4 : 2 : 2
= 2 : 1 : 1
Page 5


JEE (MAIN)-2021 : Phase-1(25-02-2021)-M
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 ONLY ONE
is correct.
Choose the correct answer :
1. Two satellites A and B of masses 200 kg and
400 kg are revolving round the earth at height
of 600 km and 1600 km respectively.
If T
A
 and T
B
 are the time periods of A and B
respectively then the value of T
B
 – T
A
 :
B
A
E
[Given : radius of earth = 6400 km,  mass of
earth = 6 × 10
24
 kg]
(1) 4.24 × 10
2
 s (2) 1.33 × 10
3
 s
(3) 4.24 × 10
3
 s (4) 3.33 × 10
2
 s
Answer (2)
Sol.
3
r
T2
GM
??
?
?? ? ?
3/2 3/2
66
BA
2
TT 810 710
GM
?
??
?? ? ? ? ??
??
93/2 3/2
11 24
2
10 8 7
6.67 10 6 10
?
?
???
???
1300 s ?
2. A student is performing the experiment of
resonance column. The diameter of the column
tube is 6 cm. The frequency of the tuning fork
is 504 Hz. Speed of the sound at the given
temperature is 336 m/s. The zero of the metre
scale coincides with the top end of the
resonance column tube. The reading of the
water level in the column when the first
resonance occurs is :
(1) 13 cm (2) 16.6 cm
(3) 14.8 cm (4) 18.4 cm
Answer (3)
Sol.
v 336 2
 mm
504 3
?? ? ?
?
?
le
4
?
??
?
2
100
3
l0.6 3
4
?
?? ?
? l = 14.8 cm
3. The coherent light sources having intensity in
the ratio 2x produce an interference pattern.
The ratio 
?
?
max min
max min
II
II
 will be
(1)
?
2x
2x 1
(2)
?
2x
x1
(3)
?
22x
x1
(4)
?
22x
2x 1
Answer (4)
Sol.
2
1
I
2X
I
?
?
22
22
11
max min
22
max min
22
11
II
11
II
II
II
II
11
II
??? ?
?? ? ??? ?
??? ?
?
??? ?
?
?
??? ?
?? ? ??? ?
??? ?
??? ?
= 
????
????
22
22
2x 1 2x 1
2x 1 2x 1
?? ?
?? ?
= 
42x
4x 2 ?
 = 
22x
2x 1 ?
4. A solid sphere of radius R gravitationally
attracts a particle placed at 3R from its centre
with a force F
1
. Now a spherical cavity of
radius 
??
??
??
R
2
 is made in the sphere (as shown in
figure) and the force becomes F
2
. The value of
F
1
 : F
2
 is :
A B
m
2R
O
M
(1) 36 : 25 (2) 50 : 41
(3) 41 : 50 (4) 25 : 36
JEE (MAIN)-2021 : Phase-1(25-02-2021)-M
Answer (2)
Sol. 
1
22
GMm GMm
F
(3R) 9R
??
2
22 2
M
Gm
GMm 41 GMm
8
F
450
(3R) R
5R
2
??
??
??
?? ?
??
??
??
?
1
2
F 1 450 50
F 9 41 41
?
??
?
5. A 5 V battery is connected across the points
X and Y. Assume D
1
 and D
2
 to be normal silicon
diodes. Find the current supplied by the battery
if the +ve terminal of the battery is connected
to point X.
D
1
D
2
10 ?
5 ?
XY
(1)
~ 1.5 A
(2)
~ 0.5 A
(3)
~ 0.43 A
(4)
~ 0.86 A
Answer (3)
Sol.
D
1 10 ?
5 ?
i
5 V
(5 0.7)
i
10
?
~
?
i0.43 A ~
6. Match List-I with List-II :
List-I List-II
(a) h (Planck’s constant) (i) [MLT
–1
]
(b) E (kinetic energy) (ii) [ML
2
T
–1
]
(c) V (electric potential) (iii) [ML
2
T
–2
]
(d) P (linear momentum) (iv) [ML
2
I
–1
T
–3
]
Choose the correct answer from the options
given below :
(1) (a) ? (i), (b) ? (ii), (c) ? (iv), (d) ? (iii)
(2) (a) ? (ii), (b) ? (iii), (c) ? (iv), (d) ? (i)
(3) (a) ? (iii), (b) ? (ii), (c) ? (iv), (d) ? (i)
(4) (a) ? (iii), (b) ? (iv), (c) ? (ii), (d) ? (i)
Answer (2)
Sol. ? ? ?? ?
2–2
hET MLT T
= ML
2
T
–1
[E] = ML
2
T
–2
??
??
?? ?
??
??
2–2
2–3–1
UMLT
VMLTI
qAI
? ??? ?
–1–1
PMLT MLT
? a ? (ii), b ? (iii), c ? (iv), d ? (i)
7. Given below are two statements : one is
labelled as Assertion A and the other is
labelled as Reason R.
Assertion A: When a rod lying freely is heated,
no thermal stress is developed in it.
Reason R: On heating, the length of the rod
increases.
In the light of the above statements, choose
the correct answer from the options given
below:
(1) A is true but R is false
(2) A is false but R is true
(3) Both A and R are true but R is NOT the
correct explanation of A
(4) Both A and R are true and R is the correct
explanation of A
Answer (3)
Sol. In free expansion, thermal stress = 0
So, statement A is true.
Statement R is also true but it is not correct
reason for A.
8. A diatomic gas, having ?
P
7
CR
2
 and ?
V
5
CR,
2
is heated at constant pressure. The ratio
dU : dQ : dW :
(1) 5 : 7 : 2 (2) 3 : 5 : 2
(3) 3 : 7 : 2 (4) 5 : 7 : 3
Answer (1)
Sol. At constant pressure,
??
?? ?
??
??
7R
dQ n · T
2
JEE (MAIN)-2021 : Phase-1(25-02-2021)-M
??
?? ?
??
??
5R
dU n · T
2
dW = n × R × ?T
?
?
57
dU:dQ:dW : :1
22
= 5 : 7 : 2
9. An ? particle and a proton are accelerated
from rest by a potential difference of 200 V.
After this, de Broglie wavelengths are 
?
? and
?
P
 respectively. The ratio 
?
?
?
P
 is :
(1) 8 (2) 2.8
(3) 3.8 (4) 7.8
Answer (2)
Sol.
??
??
??
P
p
h
2m e V
??
?
?
??
??
h
2m 2e V
?
?
?
?
??? ?
?
P
P
m
242
m
?22 = 2.8
10. Two radioactive substance X and Y originally
have N
1
 and N
2
 nuclei respectively. Half life of
X is half of the half life of Y. After three half
lives of Y, number of nuclei of both are equal.
The ratio 
1
2
N
N
 will be equal to :
(1)
1
3
(2)
8
1
(3)
1
8
(4)
3
1
Answer (2)
Sol. ??
x y
1
TT
2
? ?
y x
3T 6T
?
?
1
x 6
N
N
2
and, ?
2
y 3
N
N
2
?
? ? ?
1 2
xy
N N
NN
64 8
? ?
1
2
N 8
N1
11. Given below are two statements : one is
labelled as Assertion A and the other is labelled
as Reason R.
Assertion A : The escape velocities of planet A
and B are same. But A and B are of unequal
mass.
Reason R : The product of their mass and
radius must be same. M
1
R
1
 = M
2
R
2
In the light of the above statements, choose the
most appropriate answer from the options
given below :
(1) A is not correct but R is correct
(2) Both A and R are correct but R is NOT the
correct explanation of A
(3) A is correct but R is not correct
(4) Both A and R are correct and R is the
correct explanation of A
Answer (3)
Sol.
?
es
GM
V
R
12. If the time period of a two meter long simple
pendulum is 2 s, the acceleration due to gravity
at the place where pendulum is executing
S.H.M. is :
(1) 9.8 ms
–2
(2) ?
2
ms
–2
(3) 16 m/s
2
(4) 2 ?
2
ms
–2
Answer (4)
Sol.
??

T2
g
??
2
22
g
g = 2 ?
2
 m/s
2
JEE (MAIN)-2021 : Phase-1(25-02-2021)-M
13. The current (i) at time t = 0 and t = ?
respectively for the given circuit is :
5 ? 5 ?
1 ? 4 ?
E
i
L
(1)
5E 10E
,
18 33
(2)
18E 5E
,
55 18
(3)
5E 18E
,
18 55
(4)
10E 5E
,
33 18
Answer (1)
Sol.
?? ? ?
EE 5E
i(at t 0)
69 18
?? ? ? ?
EE 10E
i(at t )
54
33
25
14. Magnetic fields at two points on the axis of a
circular coil at a distance of 0.05 m and 0.2 m
from the centre are in the ratio 8 : 1. The radius
of coil is ___
(1) 0.15 m
(2) 0.1 m
(3) 0.2 m
(4) 1.0 m
Answer (2)
Sol. 
??
?
?
3/2
22
1
B
Rx
??
?
??
??
??
?
??
3/2
22
1
3/2
22
2
BR(0.2) 8
B1
R (0.05)
?
?
?
2
2
R0.04 4
1
R0.0025
R
2
 + 0.04 = 4R
2
 + 0.01
R = 0.1 m
15. The angular frequency of alternating current in
a L-C-R circuit is 100 rad/s. The components
connected are shown in the figure. Find the
value of inductance of the coil and capacity of
condenser.
R = 60 ?
15 V
R = 40 ??
10 V
L 20 V C
(1) 1.33 H and 250 ?F (2) 0.8 H and 150 ?F
(3) 0.8 H and 250 ?F (4) 1.33 H and 150 ?F
Answer (3)
Sol.
?
L
X 4
R3
X
L
 = 80 ?
100 × L = 80 ?
L = 0.8 H
12
60
C3
??
?
?
?
1
C
100 40
C = 250 ?F
16. A proton, a deuteron and an ? particle are
moving with same momentum in a uniform
magnetic field. The ratio of magnetic forces
acting on them is ____ and their speed is ____ in
the ratio
(1) 1 : 2 : 4 and 1 : 1 : 2
(2) 1 : 2 : 4 and 2 : 1 : 1
(3) 4 : 2 : 1 and 2 : 1 : 1
(4) 2 : 1 : 1 and 4 : 2 : 1
Answer (4)
Sol.
?
p
V
m
?
?
pd
V:V:V 4:2:1
???
?
pd pp dd
f :f :f q V :q V :q V
= 4 : 2 : 2
= 2 : 1 : 1
JEE (MAIN)-2021 : Phase-1(25-02-2021)-M
17. An engine of a train, moving with uniform
acceleration, passes the signal-post with
velocity u and the last compartment with
velocity v. The velocity with which middle point
of the train passes the signal post is :
(1)
?
22
vu
2
(2)
? vu
2
(3)
?
22
vu
2
(4)
? uv
2
Answer (3)
Sol.
v
2
 – u
2
 = 2 ax
Let velocity of middle point be v
1
??
22
1
vu 9x
?
?
22
1
uv
v
2
18. In an octagon ABCDEFGH of equal side, what
is the sum of
?? ? ? ? ?
        
AB AC AD AE AF AG AH,
if ?? ?

ˆ ˆˆ
AO 2i 3j 4k
A B
C
D
E
F
G
H
O
(1)?? ?
ˆ ˆˆ
16i 24j 32k (2) ??
ˆ ˆˆ
16i 24j 32k
(3) ??
ˆ ˆˆ
16i 24j 32k (4) ??
ˆ ˆˆ
16i 24j 32k
Answer (3)
Sol.
?? ? ? ? ?
     
AB AC AD AE AF AG AH
?

8AO
19. Given below are two statements :
Statement I : A speech signal of 2 kHz is used
to modulate a carrier signal of 1 MHz. The band
width requirement for the signal is 4 kHz.
Statement II : The side band frequencies are
1002 kHz and 998 kHz.
In the light of the above statements, choose the
correct answer from the options given below :
(1) Both Statement I and Statement II are true
(2) Statement I is false but Statement II is true
(3) Statement I is true but Statement II  is false
(4) Both Statement I and Statement II are false
Answer (1)
Sol. Side band frequency are = (1000 ± 2) kHz
Bandwidth = 4 kHz
20. The pitch of the screw gauge is 1 mm and there
are 100 divisions on the circular scale. When
nothing is put in between the jaws, the zero of
the circular scale lies 8 divisions below the
reference line. When a wire is placed between
the jaws, the first linear scale division is clearly
visible while 72
nd
 division on circular scale
coincides with the reference line. The radius of
the wire is :
(1) 0.82 mm (2) 1.64 mm
(3) 1.80 mm (4) 0.90 mm
Answer (1)
Sol. LC = 0.01 mm
Zero Error = 0.08 mm
Diameter = 1.72 – 0.08 = 1.64 mm
? Radius = 
1.64
 mm
2
 = 0.82 mm
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. A coil of inductance 2 H having negligible
resistance is connected to a source of supply
whose voltage is given by V = 3t volt. (where t
is in second). If the voltage is applied when
t = 0, then the energy stored in the coil after
4 s is _________ J.
Answer (144)
Sol.
??
di
VL 0
dt
?
??
it
00
V
di dt
L
?
2
3
it
4
= 12 A at t = 4 second
?
2
1
ULi
2
= 144 J