JEE Main 2021 Physics February 24 Shift 1 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


JEE (MAIN)-2021 : Phase-1(24-02-2021)-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. In a Young’s double slit experiment, the width
of the one of the slit is three times the other
slit. The amplitude of the light coming from a
slit is proportional to the slit-width. Find the
ratio of the maximum to the minimum intensity
in the interference pattern.
(1) 4 : 1 (2) 2 : 1
(3) 3 : 1 (4) 1 : 4
Answer (1)
Sol. I
1
 = I
0
I
2
 = 9I
0
as ?
2
IA
?
??
??
?
? ??
?? ?
??
? ??
?
2
2
21
max
2
min
21
II
I 31
4:1
I31
II
2. Each side of a box made of metal sheet in
cubic shape is ‘a’ at room temperature ‘T’, the
coefficient of linear expansion of the metal
sheet is ‘ ?’. The metal sheet is heated
uniformly, by a small temperature ?T, so that its
new temperature is T + ?T. Calculate the
increase in the volume of the metal box.
(1) 4 ?a
3
??T(2)3a
3
??T
(3)
???
3
4
aT
3
(4) 4a
3
??T
Answer (2)
Sol. V = a
3
, ? = 3 ?
? VV T ?? ??
?? ???
3
a (3 ) T
??
3
3a T ??
3. The focal length f is related to the radius of
curvature r of the spherical convex mirror by
(1) f = r (2)
?
1
f– r
2
(3) ??
1
fr
2
(4) f = –r
Answer (3)
Sol.
??
r
f
2
as f is positive for convex mirror.
4. Two equal capacitors are first connected in
series and then in parallel. The ratio of the
equivalent capacities in the two cases will be
(1) 1 : 2 (2) 2 : 1
(3) 1 : 4 (4) 4 : 1
Answer (3)
Sol. ?
1
C
C
2
for series
C
2
 = C + C = 2C for parallel
? ??
1
2
C
C 1
2
C2C 4
5. If Y, K and ? are the values of Young’s modulus,
bulk modulus and modulus of rigidity of any
material respectively. Choose the correct
relation for these parameters.
(1)
?
?
?
2
9K
YN/m
3K–
(2)
?
?
??
2
9K
YN/m
23K
(3)
2
Y
KN/m
9–3Y
?
?
?
(4)
??
?
2
3YK
N/m
9K Y
Answer (3)
Sol.
?
?
??
?
9K
  Y
3K
?
? ?
??
Y
  K
93Y
Page 2


JEE (MAIN)-2021 : Phase-1(24-02-2021)-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. In a Young’s double slit experiment, the width
of the one of the slit is three times the other
slit. The amplitude of the light coming from a
slit is proportional to the slit-width. Find the
ratio of the maximum to the minimum intensity
in the interference pattern.
(1) 4 : 1 (2) 2 : 1
(3) 3 : 1 (4) 1 : 4
Answer (1)
Sol. I
1
 = I
0
I
2
 = 9I
0
as ?
2
IA
?
??
??
?
? ??
?? ?
??
? ??
?
2
2
21
max
2
min
21
II
I 31
4:1
I31
II
2. Each side of a box made of metal sheet in
cubic shape is ‘a’ at room temperature ‘T’, the
coefficient of linear expansion of the metal
sheet is ‘ ?’. The metal sheet is heated
uniformly, by a small temperature ?T, so that its
new temperature is T + ?T. Calculate the
increase in the volume of the metal box.
(1) 4 ?a
3
??T(2)3a
3
??T
(3)
???
3
4
aT
3
(4) 4a
3
??T
Answer (2)
Sol. V = a
3
, ? = 3 ?
? VV T ?? ??
?? ???
3
a (3 ) T
??
3
3a T ??
3. The focal length f is related to the radius of
curvature r of the spherical convex mirror by
(1) f = r (2)
?
1
f– r
2
(3) ??
1
fr
2
(4) f = –r
Answer (3)
Sol.
??
r
f
2
as f is positive for convex mirror.
4. Two equal capacitors are first connected in
series and then in parallel. The ratio of the
equivalent capacities in the two cases will be
(1) 1 : 2 (2) 2 : 1
(3) 1 : 4 (4) 4 : 1
Answer (3)
Sol. ?
1
C
C
2
for series
C
2
 = C + C = 2C for parallel
? ??
1
2
C
C 1
2
C2C 4
5. If Y, K and ? are the values of Young’s modulus,
bulk modulus and modulus of rigidity of any
material respectively. Choose the correct
relation for these parameters.
(1)
?
?
?
2
9K
YN/m
3K–
(2)
?
?
??
2
9K
YN/m
23K
(3)
2
Y
KN/m
9–3Y
?
?
?
(4)
??
?
2
3YK
N/m
9K Y
Answer (3)
Sol.
?
?
??
?
9K
  Y
3K
?
? ?
??
Y
  K
93Y
JEE (MAIN)-2021 : Phase-1(24-02-2021)-M
6. A current through a wire depends on time as
?? ? ?
2
0
it t
where ?
0
 = 20 A/s and ? = 8 As
–2
. Find the
charge crossed through a section of the wire
in 15 s.
(1) 2100 C (2) 11250 C
(3) 2250 C (4) 260 C
Answer (2)
Sol. ?? ? ?
2
0
it t
??
??
??
15
2
0
dq 20t 8t dt
??
??
? ?? ?
??
??
22
33
15 –0 8
q 20 15 –0
23
= 11250 C
7. If an emitter current is changed by 4 mA, the
collector current changes by 3.5 mA. The
value of ? will be :
(1) 7 (2) 0.5
(3) 0.875 (4) 3.5
Answer (1)
Sol. ??
E
I4mA
??
C
I3.5mA
?? ? ??
B
I4–3.5mA
= 0.5 mA
?
??? ?
?
C
B
I 3.5
I0.5
 = 7
8. The work done by a gas molecule in an
isolated system is given by, ?
???
2
x
–
2
kT
We
,
where x is the displacement, k is the
Boltzmann constant and T is the temperature.
??and ??are constants. Then the dimensions of
??will be :
(1)
??
??
22
MLT (2)
??
??
2–2
MLT
(3)
??
??
–2
MLT (4)
??
??
00
MLT
Answer (3)
Sol. ?
???
2
x
–
2
kT
We
??
?
??
?
??
2
x
dimensionless
kT
?? ? ?? ?
2
–12
2–2
L
MT
MLT
and 
?? ?? ?
??
22–2
MLT
?? ?? ?
??
2–2
222–4
–1 2
MLT
MLT
MT
? ? ? ??
–2
MLT
9. n mole of a perfect gas undergoes a cyclic
process ABCA (see figure) consisting of the
following processes.
A ? B : Isothermal expansion at temperature T
so that the volume is doubled from V
1
to V
2
 = 2V
1
 and pressure changes from
P
1
 to P
2
.
B ? C : Isobaric compression at pressure P
2
to initial volume V
1
.
C ? A : Isochoric change leading to change of
pressure from P
2
 to P
1
.
Total workdone in the complete cycle ABCA is :
P
A
C
B
V V
1
V= 2V 
2 1
P
1
P
2
(1) 0 (2)
??
?
??
??
1
nRT In2
2
(3)
??
??
??
1
nRT In2–
2
(4) nRTIn 2
Answer (3)
Sol.
??
?
??
??
2
AB
1
V
WnRTln
V
= nRTln (2)
?? ??
BC C B
nRT
WnRT–T –
2
W
CA
 = 0
??
total
nRT
WnRTln2–
2
??
?
??
??
1
nRT ln2–
2
Page 3


JEE (MAIN)-2021 : Phase-1(24-02-2021)-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. In a Young’s double slit experiment, the width
of the one of the slit is three times the other
slit. The amplitude of the light coming from a
slit is proportional to the slit-width. Find the
ratio of the maximum to the minimum intensity
in the interference pattern.
(1) 4 : 1 (2) 2 : 1
(3) 3 : 1 (4) 1 : 4
Answer (1)
Sol. I
1
 = I
0
I
2
 = 9I
0
as ?
2
IA
?
??
??
?
? ??
?? ?
??
? ??
?
2
2
21
max
2
min
21
II
I 31
4:1
I31
II
2. Each side of a box made of metal sheet in
cubic shape is ‘a’ at room temperature ‘T’, the
coefficient of linear expansion of the metal
sheet is ‘ ?’. The metal sheet is heated
uniformly, by a small temperature ?T, so that its
new temperature is T + ?T. Calculate the
increase in the volume of the metal box.
(1) 4 ?a
3
??T(2)3a
3
??T
(3)
???
3
4
aT
3
(4) 4a
3
??T
Answer (2)
Sol. V = a
3
, ? = 3 ?
? VV T ?? ??
?? ???
3
a (3 ) T
??
3
3a T ??
3. The focal length f is related to the radius of
curvature r of the spherical convex mirror by
(1) f = r (2)
?
1
f– r
2
(3) ??
1
fr
2
(4) f = –r
Answer (3)
Sol.
??
r
f
2
as f is positive for convex mirror.
4. Two equal capacitors are first connected in
series and then in parallel. The ratio of the
equivalent capacities in the two cases will be
(1) 1 : 2 (2) 2 : 1
(3) 1 : 4 (4) 4 : 1
Answer (3)
Sol. ?
1
C
C
2
for series
C
2
 = C + C = 2C for parallel
? ??
1
2
C
C 1
2
C2C 4
5. If Y, K and ? are the values of Young’s modulus,
bulk modulus and modulus of rigidity of any
material respectively. Choose the correct
relation for these parameters.
(1)
?
?
?
2
9K
YN/m
3K–
(2)
?
?
??
2
9K
YN/m
23K
(3)
2
Y
KN/m
9–3Y
?
?
?
(4)
??
?
2
3YK
N/m
9K Y
Answer (3)
Sol.
?
?
??
?
9K
  Y
3K
?
? ?
??
Y
  K
93Y
JEE (MAIN)-2021 : Phase-1(24-02-2021)-M
6. A current through a wire depends on time as
?? ? ?
2
0
it t
where ?
0
 = 20 A/s and ? = 8 As
–2
. Find the
charge crossed through a section of the wire
in 15 s.
(1) 2100 C (2) 11250 C
(3) 2250 C (4) 260 C
Answer (2)
Sol. ?? ? ?
2
0
it t
??
??
??
15
2
0
dq 20t 8t dt
??
??
? ?? ?
??
??
22
33
15 –0 8
q 20 15 –0
23
= 11250 C
7. If an emitter current is changed by 4 mA, the
collector current changes by 3.5 mA. The
value of ? will be :
(1) 7 (2) 0.5
(3) 0.875 (4) 3.5
Answer (1)
Sol. ??
E
I4mA
??
C
I3.5mA
?? ? ??
B
I4–3.5mA
= 0.5 mA
?
??? ?
?
C
B
I 3.5
I0.5
 = 7
8. The work done by a gas molecule in an
isolated system is given by, ?
???
2
x
–
2
kT
We
,
where x is the displacement, k is the
Boltzmann constant and T is the temperature.
??and ??are constants. Then the dimensions of
??will be :
(1)
??
??
22
MLT (2)
??
??
2–2
MLT
(3)
??
??
–2
MLT (4)
??
??
00
MLT
Answer (3)
Sol. ?
???
2
x
–
2
kT
We
??
?
??
?
??
2
x
dimensionless
kT
?? ? ?? ?
2
–12
2–2
L
MT
MLT
and 
?? ?? ?
??
22–2
MLT
?? ?? ?
??
2–2
222–4
–1 2
MLT
MLT
MT
? ? ? ??
–2
MLT
9. n mole of a perfect gas undergoes a cyclic
process ABCA (see figure) consisting of the
following processes.
A ? B : Isothermal expansion at temperature T
so that the volume is doubled from V
1
to V
2
 = 2V
1
 and pressure changes from
P
1
 to P
2
.
B ? C : Isobaric compression at pressure P
2
to initial volume V
1
.
C ? A : Isochoric change leading to change of
pressure from P
2
 to P
1
.
Total workdone in the complete cycle ABCA is :
P
A
C
B
V V
1
V= 2V 
2 1
P
1
P
2
(1) 0 (2)
??
?
??
??
1
nRT In2
2
(3)
??
??
??
1
nRT In2–
2
(4) nRTIn 2
Answer (3)
Sol.
??
?
??
??
2
AB
1
V
WnRTln
V
= nRTln (2)
?? ??
BC C B
nRT
WnRT–T –
2
W
CA
 = 0
??
total
nRT
WnRTln2–
2
??
?
??
??
1
nRT ln2–
2
JEE (MAIN)-2021 : Phase-1(24-02-2021)-M
10. If the velocity-time graph has the shape AMB,
what would be the shape of the corresponding
acceleration-time graph?
V
AB
M
time (t)
(1)
t
a
(2)
t
a
(3)
t
a
(4)
a
t
Answer (4)
Sol. From A to M,
Acceleration is negative and constant
From M to B
Acceleration is positive and constant.
? 
a
t
11. In the given figure, the energy levels of
hydrogen atom have been shown along with
some transitions marked A, B, C, D and E.
The transitions A, B and C respectively
represent :
Continuum
n = 5
n = 4
n = 3
n = 2
B
C
D
A
n = 1
E
+ eV
0 eV
– 0.54 eV
– 0.85 eV
– 1.51eV
–3.4 eV
–13.6 eV
(1) The ionization potential of hydrogen,
second member of Balmer series and third
member of Paschen series.
(2) The series limit of Lyman series, third
member of Balmer series and second
member of Paschen series.
(3) The series limit of Lyman series, second
member of Balmer series and second
member of Paschen series
(4) The first member of the Lyman series, third
member of Balmer series and second
member of Paschen series.
Answer (2)
Sol. A corresponds to transition from ? to 1.
B corresponds to transition from n = 5 to n = 2.
C corresponds to transition from n = 5 to n = 3.
12. Consider two satellites S
1
 and S
2
 with periods
of revolution 1 hr. and 8 hr. respectively
revolving around a planet in circular orbits. The
ratio of angular velocity of satellite S
1
 to the
angular velocity of satellite S
2
 is :
(1) 1 : 4
(2) 1 : 8
(3) 2 : 1
(4) 8 : 1
Answer (4)
Sol.
1 22
21 1
TT 28
T2 T 1
? ? ?? ??
?? ? ?
??
??
?? ??
??
Page 4


JEE (MAIN)-2021 : Phase-1(24-02-2021)-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. In a Young’s double slit experiment, the width
of the one of the slit is three times the other
slit. The amplitude of the light coming from a
slit is proportional to the slit-width. Find the
ratio of the maximum to the minimum intensity
in the interference pattern.
(1) 4 : 1 (2) 2 : 1
(3) 3 : 1 (4) 1 : 4
Answer (1)
Sol. I
1
 = I
0
I
2
 = 9I
0
as ?
2
IA
?
??
??
?
? ??
?? ?
??
? ??
?
2
2
21
max
2
min
21
II
I 31
4:1
I31
II
2. Each side of a box made of metal sheet in
cubic shape is ‘a’ at room temperature ‘T’, the
coefficient of linear expansion of the metal
sheet is ‘ ?’. The metal sheet is heated
uniformly, by a small temperature ?T, so that its
new temperature is T + ?T. Calculate the
increase in the volume of the metal box.
(1) 4 ?a
3
??T(2)3a
3
??T
(3)
???
3
4
aT
3
(4) 4a
3
??T
Answer (2)
Sol. V = a
3
, ? = 3 ?
? VV T ?? ??
?? ???
3
a (3 ) T
??
3
3a T ??
3. The focal length f is related to the radius of
curvature r of the spherical convex mirror by
(1) f = r (2)
?
1
f– r
2
(3) ??
1
fr
2
(4) f = –r
Answer (3)
Sol.
??
r
f
2
as f is positive for convex mirror.
4. Two equal capacitors are first connected in
series and then in parallel. The ratio of the
equivalent capacities in the two cases will be
(1) 1 : 2 (2) 2 : 1
(3) 1 : 4 (4) 4 : 1
Answer (3)
Sol. ?
1
C
C
2
for series
C
2
 = C + C = 2C for parallel
? ??
1
2
C
C 1
2
C2C 4
5. If Y, K and ? are the values of Young’s modulus,
bulk modulus and modulus of rigidity of any
material respectively. Choose the correct
relation for these parameters.
(1)
?
?
?
2
9K
YN/m
3K–
(2)
?
?
??
2
9K
YN/m
23K
(3)
2
Y
KN/m
9–3Y
?
?
?
(4)
??
?
2
3YK
N/m
9K Y
Answer (3)
Sol.
?
?
??
?
9K
  Y
3K
?
? ?
??
Y
  K
93Y
JEE (MAIN)-2021 : Phase-1(24-02-2021)-M
6. A current through a wire depends on time as
?? ? ?
2
0
it t
where ?
0
 = 20 A/s and ? = 8 As
–2
. Find the
charge crossed through a section of the wire
in 15 s.
(1) 2100 C (2) 11250 C
(3) 2250 C (4) 260 C
Answer (2)
Sol. ?? ? ?
2
0
it t
??
??
??
15
2
0
dq 20t 8t dt
??
??
? ?? ?
??
??
22
33
15 –0 8
q 20 15 –0
23
= 11250 C
7. If an emitter current is changed by 4 mA, the
collector current changes by 3.5 mA. The
value of ? will be :
(1) 7 (2) 0.5
(3) 0.875 (4) 3.5
Answer (1)
Sol. ??
E
I4mA
??
C
I3.5mA
?? ? ??
B
I4–3.5mA
= 0.5 mA
?
??? ?
?
C
B
I 3.5
I0.5
 = 7
8. The work done by a gas molecule in an
isolated system is given by, ?
???
2
x
–
2
kT
We
,
where x is the displacement, k is the
Boltzmann constant and T is the temperature.
??and ??are constants. Then the dimensions of
??will be :
(1)
??
??
22
MLT (2)
??
??
2–2
MLT
(3)
??
??
–2
MLT (4)
??
??
00
MLT
Answer (3)
Sol. ?
???
2
x
–
2
kT
We
??
?
??
?
??
2
x
dimensionless
kT
?? ? ?? ?
2
–12
2–2
L
MT
MLT
and 
?? ?? ?
??
22–2
MLT
?? ?? ?
??
2–2
222–4
–1 2
MLT
MLT
MT
? ? ? ??
–2
MLT
9. n mole of a perfect gas undergoes a cyclic
process ABCA (see figure) consisting of the
following processes.
A ? B : Isothermal expansion at temperature T
so that the volume is doubled from V
1
to V
2
 = 2V
1
 and pressure changes from
P
1
 to P
2
.
B ? C : Isobaric compression at pressure P
2
to initial volume V
1
.
C ? A : Isochoric change leading to change of
pressure from P
2
 to P
1
.
Total workdone in the complete cycle ABCA is :
P
A
C
B
V V
1
V= 2V 
2 1
P
1
P
2
(1) 0 (2)
??
?
??
??
1
nRT In2
2
(3)
??
??
??
1
nRT In2–
2
(4) nRTIn 2
Answer (3)
Sol.
??
?
??
??
2
AB
1
V
WnRTln
V
= nRTln (2)
?? ??
BC C B
nRT
WnRT–T –
2
W
CA
 = 0
??
total
nRT
WnRTln2–
2
??
?
??
??
1
nRT ln2–
2
JEE (MAIN)-2021 : Phase-1(24-02-2021)-M
10. If the velocity-time graph has the shape AMB,
what would be the shape of the corresponding
acceleration-time graph?
V
AB
M
time (t)
(1)
t
a
(2)
t
a
(3)
t
a
(4)
a
t
Answer (4)
Sol. From A to M,
Acceleration is negative and constant
From M to B
Acceleration is positive and constant.
? 
a
t
11. In the given figure, the energy levels of
hydrogen atom have been shown along with
some transitions marked A, B, C, D and E.
The transitions A, B and C respectively
represent :
Continuum
n = 5
n = 4
n = 3
n = 2
B
C
D
A
n = 1
E
+ eV
0 eV
– 0.54 eV
– 0.85 eV
– 1.51eV
–3.4 eV
–13.6 eV
(1) The ionization potential of hydrogen,
second member of Balmer series and third
member of Paschen series.
(2) The series limit of Lyman series, third
member of Balmer series and second
member of Paschen series.
(3) The series limit of Lyman series, second
member of Balmer series and second
member of Paschen series
(4) The first member of the Lyman series, third
member of Balmer series and second
member of Paschen series.
Answer (2)
Sol. A corresponds to transition from ? to 1.
B corresponds to transition from n = 5 to n = 2.
C corresponds to transition from n = 5 to n = 3.
12. Consider two satellites S
1
 and S
2
 with periods
of revolution 1 hr. and 8 hr. respectively
revolving around a planet in circular orbits. The
ratio of angular velocity of satellite S
1
 to the
angular velocity of satellite S
2
 is :
(1) 1 : 4
(2) 1 : 8
(3) 2 : 1
(4) 8 : 1
Answer (4)
Sol.
1 22
21 1
TT 28
T2 T 1
? ? ?? ??
?? ? ?
??
??
?? ??
??
JEE (MAIN)-2021 : Phase-1(24-02-2021)-M
13. Moment of inertia (M. I.) of four bodies, having
same mass and radius, are reported as;
I
1
 = M.I. of thin circular ring about its diameter,
I
2
 = M.I. of circular disc about an axis
perpendicular to disc and going through the
centre,
I
3
 = M.I. of solid cylinder about its axis and
I
4
 = M.I. of solid sphere about its diameter.
Then :
(1) I
1
 + I
3
 < I
2
  + I
4
(2) I
1
 = I
2
 = I
3
 > I
4
(3) ?? ?
12 3 4
5
II I I
2
(4) I
1
 = I
2
 = I
3
 < I
4
Answer (2)
Sol. ?
2
1
MR
I
2
?
2
2
MR
I
2
?
2
3
MR
I
2
?
2
4
2
IMR
5
14. A cube of side ‘a’ has point charges +Q located
at each of its vertices except at the origin
where the charge is –Q. The electric field at the
centre of cube is :
x
+Q +Q
+Q
+Q
+Q
–Q
+Q
+Q
z
y
a
(1)
 
??
?
??
??
2
0
Q
xy z
33 a
(2)
 
?? ??
??
2
0
Q
xy z
33 a
(3)
 
?? ??
??
2
0
2Q
xy z
33 a
(4)
 
??
?
??
??
2
0
2Q
xy z
33 a
Answer (4)
Sol. Field due to all charges will cancel out except
two charges +Q and –Q placed along body
diagonal.
??
Q
2
0
ˆˆ ˆ xy z Q
E
3a 3
4
4
?
??
??
??

??
Q
2
0
ˆˆ ˆ Qx y z
E
3a 3
?
???
?
??

??
net
2
0
ˆˆ ˆ 2Q x y z
E
33 a
???
?
??

15. Four identical particles of equal masses 1 kg
made to move along the circumference of a
circle of radius 1 m under the action of their
own mutual gravitational attraction. The speed
of each particle will be :
(1)
??
? 122G
2
(2) ??
? G1 2 2
(3)
??
?
G
22 1
2
(4)
??
?
G
122
2
Answer (1)
Sol.Centripetal force is being provided by
gravitational force, F
g
r
??
??
22
g
22
2Gm Gm
F
4r
2r
??
22 2
2 2
mv Gm Gm
r
4r 2r
2
GG
v
4
2
??
??
122G
v
2
?
?
Page 5


JEE (MAIN)-2021 : Phase-1(24-02-2021)-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. In a Young’s double slit experiment, the width
of the one of the slit is three times the other
slit. The amplitude of the light coming from a
slit is proportional to the slit-width. Find the
ratio of the maximum to the minimum intensity
in the interference pattern.
(1) 4 : 1 (2) 2 : 1
(3) 3 : 1 (4) 1 : 4
Answer (1)
Sol. I
1
 = I
0
I
2
 = 9I
0
as ?
2
IA
?
??
??
?
? ??
?? ?
??
? ??
?
2
2
21
max
2
min
21
II
I 31
4:1
I31
II
2. Each side of a box made of metal sheet in
cubic shape is ‘a’ at room temperature ‘T’, the
coefficient of linear expansion of the metal
sheet is ‘ ?’. The metal sheet is heated
uniformly, by a small temperature ?T, so that its
new temperature is T + ?T. Calculate the
increase in the volume of the metal box.
(1) 4 ?a
3
??T(2)3a
3
??T
(3)
???
3
4
aT
3
(4) 4a
3
??T
Answer (2)
Sol. V = a
3
, ? = 3 ?
? VV T ?? ??
?? ???
3
a (3 ) T
??
3
3a T ??
3. The focal length f is related to the radius of
curvature r of the spherical convex mirror by
(1) f = r (2)
?
1
f– r
2
(3) ??
1
fr
2
(4) f = –r
Answer (3)
Sol.
??
r
f
2
as f is positive for convex mirror.
4. Two equal capacitors are first connected in
series and then in parallel. The ratio of the
equivalent capacities in the two cases will be
(1) 1 : 2 (2) 2 : 1
(3) 1 : 4 (4) 4 : 1
Answer (3)
Sol. ?
1
C
C
2
for series
C
2
 = C + C = 2C for parallel
? ??
1
2
C
C 1
2
C2C 4
5. If Y, K and ? are the values of Young’s modulus,
bulk modulus and modulus of rigidity of any
material respectively. Choose the correct
relation for these parameters.
(1)
?
?
?
2
9K
YN/m
3K–
(2)
?
?
??
2
9K
YN/m
23K
(3)
2
Y
KN/m
9–3Y
?
?
?
(4)
??
?
2
3YK
N/m
9K Y
Answer (3)
Sol.
?
?
??
?
9K
  Y
3K
?
? ?
??
Y
  K
93Y
JEE (MAIN)-2021 : Phase-1(24-02-2021)-M
6. A current through a wire depends on time as
?? ? ?
2
0
it t
where ?
0
 = 20 A/s and ? = 8 As
–2
. Find the
charge crossed through a section of the wire
in 15 s.
(1) 2100 C (2) 11250 C
(3) 2250 C (4) 260 C
Answer (2)
Sol. ?? ? ?
2
0
it t
??
??
??
15
2
0
dq 20t 8t dt
??
??
? ?? ?
??
??
22
33
15 –0 8
q 20 15 –0
23
= 11250 C
7. If an emitter current is changed by 4 mA, the
collector current changes by 3.5 mA. The
value of ? will be :
(1) 7 (2) 0.5
(3) 0.875 (4) 3.5
Answer (1)
Sol. ??
E
I4mA
??
C
I3.5mA
?? ? ??
B
I4–3.5mA
= 0.5 mA
?
??? ?
?
C
B
I 3.5
I0.5
 = 7
8. The work done by a gas molecule in an
isolated system is given by, ?
???
2
x
–
2
kT
We
,
where x is the displacement, k is the
Boltzmann constant and T is the temperature.
??and ??are constants. Then the dimensions of
??will be :
(1)
??
??
22
MLT (2)
??
??
2–2
MLT
(3)
??
??
–2
MLT (4)
??
??
00
MLT
Answer (3)
Sol. ?
???
2
x
–
2
kT
We
??
?
??
?
??
2
x
dimensionless
kT
?? ? ?? ?
2
–12
2–2
L
MT
MLT
and 
?? ?? ?
??
22–2
MLT
?? ?? ?
??
2–2
222–4
–1 2
MLT
MLT
MT
? ? ? ??
–2
MLT
9. n mole of a perfect gas undergoes a cyclic
process ABCA (see figure) consisting of the
following processes.
A ? B : Isothermal expansion at temperature T
so that the volume is doubled from V
1
to V
2
 = 2V
1
 and pressure changes from
P
1
 to P
2
.
B ? C : Isobaric compression at pressure P
2
to initial volume V
1
.
C ? A : Isochoric change leading to change of
pressure from P
2
 to P
1
.
Total workdone in the complete cycle ABCA is :
P
A
C
B
V V
1
V= 2V 
2 1
P
1
P
2
(1) 0 (2)
??
?
??
??
1
nRT In2
2
(3)
??
??
??
1
nRT In2–
2
(4) nRTIn 2
Answer (3)
Sol.
??
?
??
??
2
AB
1
V
WnRTln
V
= nRTln (2)
?? ??
BC C B
nRT
WnRT–T –
2
W
CA
 = 0
??
total
nRT
WnRTln2–
2
??
?
??
??
1
nRT ln2–
2
JEE (MAIN)-2021 : Phase-1(24-02-2021)-M
10. If the velocity-time graph has the shape AMB,
what would be the shape of the corresponding
acceleration-time graph?
V
AB
M
time (t)
(1)
t
a
(2)
t
a
(3)
t
a
(4)
a
t
Answer (4)
Sol. From A to M,
Acceleration is negative and constant
From M to B
Acceleration is positive and constant.
? 
a
t
11. In the given figure, the energy levels of
hydrogen atom have been shown along with
some transitions marked A, B, C, D and E.
The transitions A, B and C respectively
represent :
Continuum
n = 5
n = 4
n = 3
n = 2
B
C
D
A
n = 1
E
+ eV
0 eV
– 0.54 eV
– 0.85 eV
– 1.51eV
–3.4 eV
–13.6 eV
(1) The ionization potential of hydrogen,
second member of Balmer series and third
member of Paschen series.
(2) The series limit of Lyman series, third
member of Balmer series and second
member of Paschen series.
(3) The series limit of Lyman series, second
member of Balmer series and second
member of Paschen series
(4) The first member of the Lyman series, third
member of Balmer series and second
member of Paschen series.
Answer (2)
Sol. A corresponds to transition from ? to 1.
B corresponds to transition from n = 5 to n = 2.
C corresponds to transition from n = 5 to n = 3.
12. Consider two satellites S
1
 and S
2
 with periods
of revolution 1 hr. and 8 hr. respectively
revolving around a planet in circular orbits. The
ratio of angular velocity of satellite S
1
 to the
angular velocity of satellite S
2
 is :
(1) 1 : 4
(2) 1 : 8
(3) 2 : 1
(4) 8 : 1
Answer (4)
Sol.
1 22
21 1
TT 28
T2 T 1
? ? ?? ??
?? ? ?
??
??
?? ??
??
JEE (MAIN)-2021 : Phase-1(24-02-2021)-M
13. Moment of inertia (M. I.) of four bodies, having
same mass and radius, are reported as;
I
1
 = M.I. of thin circular ring about its diameter,
I
2
 = M.I. of circular disc about an axis
perpendicular to disc and going through the
centre,
I
3
 = M.I. of solid cylinder about its axis and
I
4
 = M.I. of solid sphere about its diameter.
Then :
(1) I
1
 + I
3
 < I
2
  + I
4
(2) I
1
 = I
2
 = I
3
 > I
4
(3) ?? ?
12 3 4
5
II I I
2
(4) I
1
 = I
2
 = I
3
 < I
4
Answer (2)
Sol. ?
2
1
MR
I
2
?
2
2
MR
I
2
?
2
3
MR
I
2
?
2
4
2
IMR
5
14. A cube of side ‘a’ has point charges +Q located
at each of its vertices except at the origin
where the charge is –Q. The electric field at the
centre of cube is :
x
+Q +Q
+Q
+Q
+Q
–Q
+Q
+Q
z
y
a
(1)
 
??
?
??
??
2
0
Q
xy z
33 a
(2)
 
?? ??
??
2
0
Q
xy z
33 a
(3)
 
?? ??
??
2
0
2Q
xy z
33 a
(4)
 
??
?
??
??
2
0
2Q
xy z
33 a
Answer (4)
Sol. Field due to all charges will cancel out except
two charges +Q and –Q placed along body
diagonal.
??
Q
2
0
ˆˆ ˆ xy z Q
E
3a 3
4
4
?
??
??
??

??
Q
2
0
ˆˆ ˆ Qx y z
E
3a 3
?
???
?
??

??
net
2
0
ˆˆ ˆ 2Q x y z
E
33 a
???
?
??

15. Four identical particles of equal masses 1 kg
made to move along the circumference of a
circle of radius 1 m under the action of their
own mutual gravitational attraction. The speed
of each particle will be :
(1)
??
? 122G
2
(2) ??
? G1 2 2
(3)
??
?
G
22 1
2
(4)
??
?
G
122
2
Answer (1)
Sol.Centripetal force is being provided by
gravitational force, F
g
r
??
??
22
g
22
2Gm Gm
F
4r
2r
??
22 2
2 2
mv Gm Gm
r
4r 2r
2
GG
v
4
2
??
??
122G
v
2
?
?
JEE (MAIN)-2021 : Phase-1(24-02-2021)-M
16. In the given figure, a mass M is attached to a
horizontal spring which is fixed on one side to
a rigid support. The spring constant of the
spring is k. The mass oscillates on a
frictionless surface with time period T and
amplitude A. When the mass is in equilibrium
position, as shown in the figure, another mass
m is gently fixed upon it. The new amplitude of
oscillation will be :
M
m
k
(1)
M–m
A
M
(2)
M
A
M–m
(3)
M
A
M+ m
(4)
M
A
M + m
Answer (3)
On putting m on M Let velocity becomes V
(m + M) V = MV
0
Now Kinetic Energy = ??
2
1
m + M V
2
??
??
22
0
2
MV 1
K' = m + M
2
m + M
??
22
0
MV 1
K' = 
2M + m
?
22
0
11
MV KA
22
??
2 1
K' = K A'
2
Hence, 
??
M
A' = A
M + m
17. A cell E
1
 of emf 6 V and internal resistance 2 ?
is connected with another cell E
2
 of emf 4 V
and internal resistance 8 ? (as shown in the
figure). The potential difference across points
X and Y is :
P
E
1
X
E
2
Y
6 V, 2 ? 4 V, 8 ?
(1) 3.6 V (2) 10.0 V
(3) 5.6 V (4) 2.0 V
Answer (3)
P X
Y
6 V, 2 ?
4 V, 8 ?
I
?
?
64
I = 0.2 A
10
V = 6 – 0.2 × 2
= 5.6 V
18. Given below are two statements:
Statement I : Two photons having equal linear
momenta have equal wavelengths
Statement II : If the wavelength of photon is
decreased, then the momentum
and energy of a photon will also
decrease
In the light of the above statements, choose
the correct answer from the options given
below
(1) Statement I is true but Statement II is false
(2) Both Statement I and Statement II are false
(3) Statement I is false but Statement II is true
(4) Both Statement I and Statement II are true
Answer (1)
??
hc h
E = ,p =
on decreasing wavelength photon and energy
will decrease
19. Two stars of masses m and 2m at a distance
d rotate about their common centre of mass in
free space. The period of revolution is :
(1)
?
3
d
2
3Gm
(2)
?
3
3Gm
2
d
(3)
?
3
13Gm
2
d
(4)
?
3
1d
2 3Gm
Answer (1)
2d
3
m 2m
??
??
??
??
2
2
2
2d 2Gm
m
3
d