JEE Main 2022 Question Paper 25 June Shift 2 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
(Held On Saturday 25
th
June, 2022)    TIME : 3:00 PM  to  6:00 PM
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. Given below are two statements. One is labelled as
Assertion A and the other is labelled as Reason R.
Assertion A :Two identical balls A and B thrown
with same velocity ‘u’ at two different angles with
horizontal attained the same range R. If A and B
reached the maximum height h
1
 and h
2 
respectively, then 
12
R 4 h h ?
Reason R: Product of said heights. 
2 2 2 2
12
u sin u cos
h h .
2g 2g
? ? ? ?
??
? ? ? ? ?
? ? ? ?
? ? ? ?
Choose the CORRECT answer : 
(A) Both A and R are true and R is the correct
explanation of A. 
(B) Both A and R are true but R is NOT the correct
explanation of A. 
(C) A is true but R is false
(D) A is false but R is true
Official Ans. by NTA (A) 
 
Sol. For same range 
0
12
90 ? ? ? ?
?
?
?
?
u
u
R
22
1
1
u sin
h
2g
?
?
22
2
2
u sin
h
2g
?
?
2 2 2 2
12
12
u sin u sin
hh
2g 2g
??
??
21
90 ? ? ? ?
2 2 2 2
11
12
u sin u cos
h h .
2g 2g
??
?
= 
2
2
11
u sin cos
2g
?? ??
??
??
2
22
11
u sin cos R
2g 2 16
?? ? ? ?
? ? ?
??
??
12
R 4 h h ?
So R is correct explanation of A 
2. Two buses P and Q start from a point at the same
time and move in a straight line and their positions
are represented by ? ?
2
P
X t t t ? ? ? ? and
? ?
2
Q
X t ft t ?? . At what time, both the buses have
same velocity ?
(A) 
f
1
??
??
(B) 
? ?
f
21
??
??
(C)  
? ?
f
21
??
??
(D) 
? ?
f
21
??
??
Official Ans. by NTA (D) 
 
Sol. ? ?
2
P
X t t t ? ? ? ?
2
Q
X ft t ??
? ?
P
V t 2 t ? ? ? ?
Q
V f 2t ??
PQ
VV ?
2 t f 2t ? ? ? ? ?
f
t
22
??
?
??
Page 2


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
(Held On Saturday 25
th
June, 2022)    TIME : 3:00 PM  to  6:00 PM
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. Given below are two statements. One is labelled as
Assertion A and the other is labelled as Reason R.
Assertion A :Two identical balls A and B thrown
with same velocity ‘u’ at two different angles with
horizontal attained the same range R. If A and B
reached the maximum height h
1
 and h
2 
respectively, then 
12
R 4 h h ?
Reason R: Product of said heights. 
2 2 2 2
12
u sin u cos
h h .
2g 2g
? ? ? ?
??
? ? ? ? ?
? ? ? ?
? ? ? ?
Choose the CORRECT answer : 
(A) Both A and R are true and R is the correct
explanation of A. 
(B) Both A and R are true but R is NOT the correct
explanation of A. 
(C) A is true but R is false
(D) A is false but R is true
Official Ans. by NTA (A) 
 
Sol. For same range 
0
12
90 ? ? ? ?
?
?
?
?
u
u
R
22
1
1
u sin
h
2g
?
?
22
2
2
u sin
h
2g
?
?
2 2 2 2
12
12
u sin u sin
hh
2g 2g
??
??
21
90 ? ? ? ?
2 2 2 2
11
12
u sin u cos
h h .
2g 2g
??
?
= 
2
2
11
u sin cos
2g
?? ??
??
??
2
22
11
u sin cos R
2g 2 16
?? ? ? ?
? ? ?
??
??
12
R 4 h h ?
So R is correct explanation of A 
2. Two buses P and Q start from a point at the same
time and move in a straight line and their positions
are represented by ? ?
2
P
X t t t ? ? ? ? and
? ?
2
Q
X t ft t ?? . At what time, both the buses have
same velocity ?
(A) 
f
1
??
??
(B) 
? ?
f
21
??
??
(C)  
? ?
f
21
??
??
(D) 
? ?
f
21
??
??
Official Ans. by NTA (D) 
 
Sol. ? ?
2
P
X t t t ? ? ? ?
2
Q
X ft t ??
? ?
P
V t 2 t ? ? ? ?
Q
V f 2t ??
PQ
VV ?
2 t f 2t ? ? ? ? ?
f
t
22
??
?
??
 
2 
 
 
3. A disc with a flat small bottom beaker placed on it 
at a distance R from its center is revolving about an 
axis passing through the center and perpendicular 
to its plane with an angular velocity ?. The 
coefficient of static friction between the bottom of 
the beaker and the surface of the disc is ?. The 
beaker will revolve with the disc if : 
 (A) 
2
g
R
2
?
?
?
 (B) 
2
g
R
?
?
?
  
 (C) 
2
g
R
2
?
?
?
 (D) 
2
g
R
?
?
?
 
 Official Ans. by NTA (B) 
  
Sol. For beaker to move with disc 
 
R
?
fs
 
 
2
s
f m R ?? 
 We know that
S s max
ff ? 
 
2
m R mg ? ? ? 
 
2
g
R
?
?
?
 
4. A solid metallic cube having total surface area 24 
m
2
 is uniformly heated. If its temperature is 
increased by 10°C, calculate the increase in 
volume of the cube 
? ?
41
Given : 5.0 10 C
??
? ? ? ? 
 (A) 
63
2.4 10 cm ? 
 (B) 
53
1.2 10 cm ? 
 (C) 
43
6.0 10 cm ? 
 (D) 
53
4.8 10 cm ? 
 Official Ans. by NTA (B) 
  
 
Sol. Increase in volume
0
V V T ? ? ? ? 
 3 ? ? ? 
 So ? ?
0
V 3 V T ? ? ? ? 
 Total surface area = 
2
6a ,  where a is side length 
 
2
24 6a ?    a= 2m  
 Volume 
? ?
3
3
0
V 2 8m ?? 
 
? ? ? ?
4
V 3 5 10 8 10
?
? ? ? ? ? 
 
53
1.2 10 cm ?? 
5. A copper block of mass 5.0 kg is heated to a 
temperature of 500°C and is placed on a large ice 
block. What is the maximum amount of ice that 
can melt? [Specific heat of copper: 
11
0.39J g C
??
? 
and latent heat of fusion of water : 335 J g
–1
] 
 (A) 1.5 kg   (B) 5.8 kg 
 (C) 2.9 kg  (D) 3.8 kg 
 Official Ans. by NTA (C) 
  
Sol. Heat given by block to get 0ºC temperature  
 
? ? ? ?
3
1
Q 5 0.39 10 500 0 ? ? ? ? ? ? 
 = 
3
975 10 J ? 
 Heat absorbed by ice to melt m mass  
 
? ?
3
2
Q m 335 10 J ? ? ? ? 
 
12
QQ ? ? ? 
 
? ?
33
m 335 10 975 10 ? ? ? ? 
 
975
m 2.910
335
?? kg 
6. The ratio of specific heats 
P
V
C
C
??
??
??
 in terms of 
degree of freedom (f) is given by: 
 (A) 
f
1
3
??
?
??
??
  (B)
2
1
f
??
?
??
??
 
 
 (C) 
f
1
2
??
?
??
??
  (D) 
1
1
f
??
?
??
??
 
 Official Ans. by NTA (B) 
  
Page 3


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
(Held On Saturday 25
th
June, 2022)    TIME : 3:00 PM  to  6:00 PM
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. Given below are two statements. One is labelled as
Assertion A and the other is labelled as Reason R.
Assertion A :Two identical balls A and B thrown
with same velocity ‘u’ at two different angles with
horizontal attained the same range R. If A and B
reached the maximum height h
1
 and h
2 
respectively, then 
12
R 4 h h ?
Reason R: Product of said heights. 
2 2 2 2
12
u sin u cos
h h .
2g 2g
? ? ? ?
??
? ? ? ? ?
? ? ? ?
? ? ? ?
Choose the CORRECT answer : 
(A) Both A and R are true and R is the correct
explanation of A. 
(B) Both A and R are true but R is NOT the correct
explanation of A. 
(C) A is true but R is false
(D) A is false but R is true
Official Ans. by NTA (A) 
 
Sol. For same range 
0
12
90 ? ? ? ?
?
?
?
?
u
u
R
22
1
1
u sin
h
2g
?
?
22
2
2
u sin
h
2g
?
?
2 2 2 2
12
12
u sin u sin
hh
2g 2g
??
??
21
90 ? ? ? ?
2 2 2 2
11
12
u sin u cos
h h .
2g 2g
??
?
= 
2
2
11
u sin cos
2g
?? ??
??
??
2
22
11
u sin cos R
2g 2 16
?? ? ? ?
? ? ?
??
??
12
R 4 h h ?
So R is correct explanation of A 
2. Two buses P and Q start from a point at the same
time and move in a straight line and their positions
are represented by ? ?
2
P
X t t t ? ? ? ? and
? ?
2
Q
X t ft t ?? . At what time, both the buses have
same velocity ?
(A) 
f
1
??
??
(B) 
? ?
f
21
??
??
(C)  
? ?
f
21
??
??
(D) 
? ?
f
21
??
??
Official Ans. by NTA (D) 
 
Sol. ? ?
2
P
X t t t ? ? ? ?
2
Q
X ft t ??
? ?
P
V t 2 t ? ? ? ?
Q
V f 2t ??
PQ
VV ?
2 t f 2t ? ? ? ? ?
f
t
22
??
?
??
 
2 
 
 
3. A disc with a flat small bottom beaker placed on it 
at a distance R from its center is revolving about an 
axis passing through the center and perpendicular 
to its plane with an angular velocity ?. The 
coefficient of static friction between the bottom of 
the beaker and the surface of the disc is ?. The 
beaker will revolve with the disc if : 
 (A) 
2
g
R
2
?
?
?
 (B) 
2
g
R
?
?
?
  
 (C) 
2
g
R
2
?
?
?
 (D) 
2
g
R
?
?
?
 
 Official Ans. by NTA (B) 
  
Sol. For beaker to move with disc 
 
R
?
fs
 
 
2
s
f m R ?? 
 We know that
S s max
ff ? 
 
2
m R mg ? ? ? 
 
2
g
R
?
?
?
 
4. A solid metallic cube having total surface area 24 
m
2
 is uniformly heated. If its temperature is 
increased by 10°C, calculate the increase in 
volume of the cube 
? ?
41
Given : 5.0 10 C
??
? ? ? ? 
 (A) 
63
2.4 10 cm ? 
 (B) 
53
1.2 10 cm ? 
 (C) 
43
6.0 10 cm ? 
 (D) 
53
4.8 10 cm ? 
 Official Ans. by NTA (B) 
  
 
Sol. Increase in volume
0
V V T ? ? ? ? 
 3 ? ? ? 
 So ? ?
0
V 3 V T ? ? ? ? 
 Total surface area = 
2
6a ,  where a is side length 
 
2
24 6a ?    a= 2m  
 Volume 
? ?
3
3
0
V 2 8m ?? 
 
? ? ? ?
4
V 3 5 10 8 10
?
? ? ? ? ? 
 
53
1.2 10 cm ?? 
5. A copper block of mass 5.0 kg is heated to a 
temperature of 500°C and is placed on a large ice 
block. What is the maximum amount of ice that 
can melt? [Specific heat of copper: 
11
0.39J g C
??
? 
and latent heat of fusion of water : 335 J g
–1
] 
 (A) 1.5 kg   (B) 5.8 kg 
 (C) 2.9 kg  (D) 3.8 kg 
 Official Ans. by NTA (C) 
  
Sol. Heat given by block to get 0ºC temperature  
 
? ? ? ?
3
1
Q 5 0.39 10 500 0 ? ? ? ? ? ? 
 = 
3
975 10 J ? 
 Heat absorbed by ice to melt m mass  
 
? ?
3
2
Q m 335 10 J ? ? ? ? 
 
12
QQ ? ? ? 
 
? ?
33
m 335 10 975 10 ? ? ? ? 
 
975
m 2.910
335
?? kg 
6. The ratio of specific heats 
P
V
C
C
??
??
??
 in terms of 
degree of freedom (f) is given by: 
 (A) 
f
1
3
??
?
??
??
  (B)
2
1
f
??
?
??
??
 
 
 (C) 
f
1
2
??
?
??
??
  (D) 
1
1
f
??
?
??
??
 
 Official Ans. by NTA (B) 
  
 
 
3 
 
 
Sol. Molar heat capacity at constant volume 
V
fR
C
2
? 
where f is degree of freedom. 
 Molar heat capacity at constant pressure can be 
written as 
PV
fR f
C R C R 1 R
22
??
? ? ? ? ? ?
??
??
 
 So 
P
v
C 2
1
Cf
?? 
7. For a particle in uniform circular motion, the 
acceleration a at any point P(R, ?) on the circular 
path of radius R is (when ? is measured from the 
positive x –axis and v is uniform speed) : 
 (A) 
22
vv
ˆˆ
sin i cos j
RR
? ? ? ? 
 (B) 
22
vv
ˆˆ
cos i sin j
RR
? ? ? ? 
 (C) 
22
vv
ˆˆ
cos i sin j
RR
? ? ? ?   
 (D) 
22
vv
ˆˆ
ij
RR
?? 
 Official Ans. by NTA (C) 
  
Sol. 
2
V
a | a |
R
?? 
 
?
a
 
 
ˆˆ
a a cos i a sin j ? ? ? ? ? 
 
22
VV
ˆˆ
cos i sin j
RR
? ? ? ? ? 
8. Two metallic plates form a parallel plate capacitor. 
The distance between the plates is ‘d’. A metal 
sheet of thickness 
d
2
 and of area equal to area of 
each plate is introduced between the plates. What 
will be the ratio  of the new capacitance to the 
original capacitance of the capacitor ? 
 (A) 2:1  (B) 1:2  
 (C) 1:4  (D) 4:1 
 Official Ans. by NTA (A) 
  
Sol. 
0
1
A
C
d
?
? 
 
00
2
A 2 A
C
d d / 2
d
2
??
??
?
?
 
 
2
1
C2
C1
? 
9. Two cells of same emf but different internal 
resistances r
1
 and r
2
 are connected in series with a 
resistance R. The value of resistance R, for which 
the potential difference across second cell is zero, 
is 
 (A) 
21
rr ?  (B)
12
rr ?  
 (C) r
1
 (D) r
2 
 Official Ans. by NTA (A) 
  
Sol. 
12
2E
I
R r r
?
??
…..( i ) 
 
E
r
1 r
2
B
R
I
A
E
 
 But 
A B 2
V V E Ir 0 ? ? ? ? 
 
2
E
I
r
?? ….(ii) 
 Comparing values of I from (i) and (ii) 
 
2 1 2
E 2E
r R r r
?
??
 
 
21
R r r ? ? ?
 
 
Page 4


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
(Held On Saturday 25
th
June, 2022)    TIME : 3:00 PM  to  6:00 PM
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. Given below are two statements. One is labelled as
Assertion A and the other is labelled as Reason R.
Assertion A :Two identical balls A and B thrown
with same velocity ‘u’ at two different angles with
horizontal attained the same range R. If A and B
reached the maximum height h
1
 and h
2 
respectively, then 
12
R 4 h h ?
Reason R: Product of said heights. 
2 2 2 2
12
u sin u cos
h h .
2g 2g
? ? ? ?
??
? ? ? ? ?
? ? ? ?
? ? ? ?
Choose the CORRECT answer : 
(A) Both A and R are true and R is the correct
explanation of A. 
(B) Both A and R are true but R is NOT the correct
explanation of A. 
(C) A is true but R is false
(D) A is false but R is true
Official Ans. by NTA (A) 
 
Sol. For same range 
0
12
90 ? ? ? ?
?
?
?
?
u
u
R
22
1
1
u sin
h
2g
?
?
22
2
2
u sin
h
2g
?
?
2 2 2 2
12
12
u sin u sin
hh
2g 2g
??
??
21
90 ? ? ? ?
2 2 2 2
11
12
u sin u cos
h h .
2g 2g
??
?
= 
2
2
11
u sin cos
2g
?? ??
??
??
2
22
11
u sin cos R
2g 2 16
?? ? ? ?
? ? ?
??
??
12
R 4 h h ?
So R is correct explanation of A 
2. Two buses P and Q start from a point at the same
time and move in a straight line and their positions
are represented by ? ?
2
P
X t t t ? ? ? ? and
? ?
2
Q
X t ft t ?? . At what time, both the buses have
same velocity ?
(A) 
f
1
??
??
(B) 
? ?
f
21
??
??
(C)  
? ?
f
21
??
??
(D) 
? ?
f
21
??
??
Official Ans. by NTA (D) 
 
Sol. ? ?
2
P
X t t t ? ? ? ?
2
Q
X ft t ??
? ?
P
V t 2 t ? ? ? ?
Q
V f 2t ??
PQ
VV ?
2 t f 2t ? ? ? ? ?
f
t
22
??
?
??
 
2 
 
 
3. A disc with a flat small bottom beaker placed on it 
at a distance R from its center is revolving about an 
axis passing through the center and perpendicular 
to its plane with an angular velocity ?. The 
coefficient of static friction between the bottom of 
the beaker and the surface of the disc is ?. The 
beaker will revolve with the disc if : 
 (A) 
2
g
R
2
?
?
?
 (B) 
2
g
R
?
?
?
  
 (C) 
2
g
R
2
?
?
?
 (D) 
2
g
R
?
?
?
 
 Official Ans. by NTA (B) 
  
Sol. For beaker to move with disc 
 
R
?
fs
 
 
2
s
f m R ?? 
 We know that
S s max
ff ? 
 
2
m R mg ? ? ? 
 
2
g
R
?
?
?
 
4. A solid metallic cube having total surface area 24 
m
2
 is uniformly heated. If its temperature is 
increased by 10°C, calculate the increase in 
volume of the cube 
? ?
41
Given : 5.0 10 C
??
? ? ? ? 
 (A) 
63
2.4 10 cm ? 
 (B) 
53
1.2 10 cm ? 
 (C) 
43
6.0 10 cm ? 
 (D) 
53
4.8 10 cm ? 
 Official Ans. by NTA (B) 
  
 
Sol. Increase in volume
0
V V T ? ? ? ? 
 3 ? ? ? 
 So ? ?
0
V 3 V T ? ? ? ? 
 Total surface area = 
2
6a ,  where a is side length 
 
2
24 6a ?    a= 2m  
 Volume 
? ?
3
3
0
V 2 8m ?? 
 
? ? ? ?
4
V 3 5 10 8 10
?
? ? ? ? ? 
 
53
1.2 10 cm ?? 
5. A copper block of mass 5.0 kg is heated to a 
temperature of 500°C and is placed on a large ice 
block. What is the maximum amount of ice that 
can melt? [Specific heat of copper: 
11
0.39J g C
??
? 
and latent heat of fusion of water : 335 J g
–1
] 
 (A) 1.5 kg   (B) 5.8 kg 
 (C) 2.9 kg  (D) 3.8 kg 
 Official Ans. by NTA (C) 
  
Sol. Heat given by block to get 0ºC temperature  
 
? ? ? ?
3
1
Q 5 0.39 10 500 0 ? ? ? ? ? ? 
 = 
3
975 10 J ? 
 Heat absorbed by ice to melt m mass  
 
? ?
3
2
Q m 335 10 J ? ? ? ? 
 
12
QQ ? ? ? 
 
? ?
33
m 335 10 975 10 ? ? ? ? 
 
975
m 2.910
335
?? kg 
6. The ratio of specific heats 
P
V
C
C
??
??
??
 in terms of 
degree of freedom (f) is given by: 
 (A) 
f
1
3
??
?
??
??
  (B)
2
1
f
??
?
??
??
 
 
 (C) 
f
1
2
??
?
??
??
  (D) 
1
1
f
??
?
??
??
 
 Official Ans. by NTA (B) 
  
 
 
3 
 
 
Sol. Molar heat capacity at constant volume 
V
fR
C
2
? 
where f is degree of freedom. 
 Molar heat capacity at constant pressure can be 
written as 
PV
fR f
C R C R 1 R
22
??
? ? ? ? ? ?
??
??
 
 So 
P
v
C 2
1
Cf
?? 
7. For a particle in uniform circular motion, the 
acceleration a at any point P(R, ?) on the circular 
path of radius R is (when ? is measured from the 
positive x –axis and v is uniform speed) : 
 (A) 
22
vv
ˆˆ
sin i cos j
RR
? ? ? ? 
 (B) 
22
vv
ˆˆ
cos i sin j
RR
? ? ? ? 
 (C) 
22
vv
ˆˆ
cos i sin j
RR
? ? ? ?   
 (D) 
22
vv
ˆˆ
ij
RR
?? 
 Official Ans. by NTA (C) 
  
Sol. 
2
V
a | a |
R
?? 
 
?
a
 
 
ˆˆ
a a cos i a sin j ? ? ? ? ? 
 
22
VV
ˆˆ
cos i sin j
RR
? ? ? ? ? 
8. Two metallic plates form a parallel plate capacitor. 
The distance between the plates is ‘d’. A metal 
sheet of thickness 
d
2
 and of area equal to area of 
each plate is introduced between the plates. What 
will be the ratio  of the new capacitance to the 
original capacitance of the capacitor ? 
 (A) 2:1  (B) 1:2  
 (C) 1:4  (D) 4:1 
 Official Ans. by NTA (A) 
  
Sol. 
0
1
A
C
d
?
? 
 
00
2
A 2 A
C
d d / 2
d
2
??
??
?
?
 
 
2
1
C2
C1
? 
9. Two cells of same emf but different internal 
resistances r
1
 and r
2
 are connected in series with a 
resistance R. The value of resistance R, for which 
the potential difference across second cell is zero, 
is 
 (A) 
21
rr ?  (B)
12
rr ?  
 (C) r
1
 (D) r
2 
 Official Ans. by NTA (A) 
  
Sol. 
12
2E
I
R r r
?
??
…..( i ) 
 
E
r
1 r
2
B
R
I
A
E
 
 But 
A B 2
V V E Ir 0 ? ? ? ? 
 
2
E
I
r
?? ….(ii) 
 Comparing values of I from (i) and (ii) 
 
2 1 2
E 2E
r R r r
?
??
 
 
21
R r r ? ? ?
 
 
 
4 
 
 
10. Given below are two statements:  
 Statement – I : Susceptibilities of paramagnetic 
and ferromagnetic substances increase with 
decrease in temperature.  
 Statement – II: Diamagnetism is a result of orbital 
motions of electrons developing magnetic 
moments opposite to the applied magnetic field.  
 Choose the CORRECT answer from the options 
given below : - 
 (A) Both statement – I and statement -II are true. 
 (B) Both statement – I and Statement – II are false. 
 (C) Statement – I is true but statement – II is false. 
 (D) Statement-I is false but Statement-II is true.  
 Official Ans. by NTA (A) 
  
Sol. According to curie's law, magnetic susceptibility is 
inversely proportional to temperature for a fixed 
value of external magnetic field i.e. ??
C
T
. 
 The same is applicable for ferromagnet & the 
relation is given as ??
?
C
C
TT
 (T
C
 is curie 
temperature) 
 Diamagnetism is due to non-cooperative behaviour 
of orbiting electrons when exposed to external 
magnetic field. 
 Hence option (A).   
11. A long solenoid carrying a current produces a 
magnetic field B along its axis. If the current is 
doubled and the number of turns per cm is halved, 
the new value of magnetic field will be equal to  
 (A) B (B) 2 B 
 (C) 4 B  (D) 
B
2
 
 Official Ans. by NTA (A) 
  
Sol. 
10
B nI ?? 
 ? ?
20
n
B 2I
2
??
??
??
??
 
 ?B
1
 = B
2 
12. A sinusoidal voltage V(t) = 210 sin 3000t volt is 
applied to a series LCR circuit in which L = 10 
mH, C = 25 ?F and R = 100 ?. The phase 
difference ( ?) between the applied voltage and 
resultant current will be : 
 (A) tan
–1
 (0.17) (B) tan
–1
 (9.46)  
 (C) tan
–1
 (0.30) (D) tan
–1
 (13.33) 
 Official Ans. by NTA (A) 
  
Sol. 
2
L
X 10 3000 30
?
? ? ? ? 
 
C
6
1 40
X
3
3000 25 10
?
? ? ?
??
 
 X = X
L
 –X
C 
 
40 50
30
33
? ? ? 
 
X 50 1
tan
R 3 100 6
? ? ? ?
?
 
 ? ?
11
1
tan tan 0.17
6
??
??
? ? ?
??
??
 
13. The electromagnetic waves travel in a medium at a 
speed of 2.0 × 10
8
 m/s.The relative permeability of 
the medium is 1.0. The relative permittivity of the 
medium will be: 
 (A) 2.25  (B) 4.25  
 (C) 6.25  (D) 8.25 
 Official Ans. by NTA (A) 
  
Sol. 
8
V 2 10 m / s ?? 
 
8
C 3 10 m / s ?? 
 
rr
C
V
? ? ? 
 
r
9
1
4
? ? ? 
 
r
9
2.25
4
? ? ? 
Page 5


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
(Held On Saturday 25
th
June, 2022)    TIME : 3:00 PM  to  6:00 PM
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. Given below are two statements. One is labelled as
Assertion A and the other is labelled as Reason R.
Assertion A :Two identical balls A and B thrown
with same velocity ‘u’ at two different angles with
horizontal attained the same range R. If A and B
reached the maximum height h
1
 and h
2 
respectively, then 
12
R 4 h h ?
Reason R: Product of said heights. 
2 2 2 2
12
u sin u cos
h h .
2g 2g
? ? ? ?
??
? ? ? ? ?
? ? ? ?
? ? ? ?
Choose the CORRECT answer : 
(A) Both A and R are true and R is the correct
explanation of A. 
(B) Both A and R are true but R is NOT the correct
explanation of A. 
(C) A is true but R is false
(D) A is false but R is true
Official Ans. by NTA (A) 
 
Sol. For same range 
0
12
90 ? ? ? ?
?
?
?
?
u
u
R
22
1
1
u sin
h
2g
?
?
22
2
2
u sin
h
2g
?
?
2 2 2 2
12
12
u sin u sin
hh
2g 2g
??
??
21
90 ? ? ? ?
2 2 2 2
11
12
u sin u cos
h h .
2g 2g
??
?
= 
2
2
11
u sin cos
2g
?? ??
??
??
2
22
11
u sin cos R
2g 2 16
?? ? ? ?
? ? ?
??
??
12
R 4 h h ?
So R is correct explanation of A 
2. Two buses P and Q start from a point at the same
time and move in a straight line and their positions
are represented by ? ?
2
P
X t t t ? ? ? ? and
? ?
2
Q
X t ft t ?? . At what time, both the buses have
same velocity ?
(A) 
f
1
??
??
(B) 
? ?
f
21
??
??
(C)  
? ?
f
21
??
??
(D) 
? ?
f
21
??
??
Official Ans. by NTA (D) 
 
Sol. ? ?
2
P
X t t t ? ? ? ?
2
Q
X ft t ??
? ?
P
V t 2 t ? ? ? ?
Q
V f 2t ??
PQ
VV ?
2 t f 2t ? ? ? ? ?
f
t
22
??
?
??
 
2 
 
 
3. A disc with a flat small bottom beaker placed on it 
at a distance R from its center is revolving about an 
axis passing through the center and perpendicular 
to its plane with an angular velocity ?. The 
coefficient of static friction between the bottom of 
the beaker and the surface of the disc is ?. The 
beaker will revolve with the disc if : 
 (A) 
2
g
R
2
?
?
?
 (B) 
2
g
R
?
?
?
  
 (C) 
2
g
R
2
?
?
?
 (D) 
2
g
R
?
?
?
 
 Official Ans. by NTA (B) 
  
Sol. For beaker to move with disc 
 
R
?
fs
 
 
2
s
f m R ?? 
 We know that
S s max
ff ? 
 
2
m R mg ? ? ? 
 
2
g
R
?
?
?
 
4. A solid metallic cube having total surface area 24 
m
2
 is uniformly heated. If its temperature is 
increased by 10°C, calculate the increase in 
volume of the cube 
? ?
41
Given : 5.0 10 C
??
? ? ? ? 
 (A) 
63
2.4 10 cm ? 
 (B) 
53
1.2 10 cm ? 
 (C) 
43
6.0 10 cm ? 
 (D) 
53
4.8 10 cm ? 
 Official Ans. by NTA (B) 
  
 
Sol. Increase in volume
0
V V T ? ? ? ? 
 3 ? ? ? 
 So ? ?
0
V 3 V T ? ? ? ? 
 Total surface area = 
2
6a ,  where a is side length 
 
2
24 6a ?    a= 2m  
 Volume 
? ?
3
3
0
V 2 8m ?? 
 
? ? ? ?
4
V 3 5 10 8 10
?
? ? ? ? ? 
 
53
1.2 10 cm ?? 
5. A copper block of mass 5.0 kg is heated to a 
temperature of 500°C and is placed on a large ice 
block. What is the maximum amount of ice that 
can melt? [Specific heat of copper: 
11
0.39J g C
??
? 
and latent heat of fusion of water : 335 J g
–1
] 
 (A) 1.5 kg   (B) 5.8 kg 
 (C) 2.9 kg  (D) 3.8 kg 
 Official Ans. by NTA (C) 
  
Sol. Heat given by block to get 0ºC temperature  
 
? ? ? ?
3
1
Q 5 0.39 10 500 0 ? ? ? ? ? ? 
 = 
3
975 10 J ? 
 Heat absorbed by ice to melt m mass  
 
? ?
3
2
Q m 335 10 J ? ? ? ? 
 
12
QQ ? ? ? 
 
? ?
33
m 335 10 975 10 ? ? ? ? 
 
975
m 2.910
335
?? kg 
6. The ratio of specific heats 
P
V
C
C
??
??
??
 in terms of 
degree of freedom (f) is given by: 
 (A) 
f
1
3
??
?
??
??
  (B)
2
1
f
??
?
??
??
 
 
 (C) 
f
1
2
??
?
??
??
  (D) 
1
1
f
??
?
??
??
 
 Official Ans. by NTA (B) 
  
 
 
3 
 
 
Sol. Molar heat capacity at constant volume 
V
fR
C
2
? 
where f is degree of freedom. 
 Molar heat capacity at constant pressure can be 
written as 
PV
fR f
C R C R 1 R
22
??
? ? ? ? ? ?
??
??
 
 So 
P
v
C 2
1
Cf
?? 
7. For a particle in uniform circular motion, the 
acceleration a at any point P(R, ?) on the circular 
path of radius R is (when ? is measured from the 
positive x –axis and v is uniform speed) : 
 (A) 
22
vv
ˆˆ
sin i cos j
RR
? ? ? ? 
 (B) 
22
vv
ˆˆ
cos i sin j
RR
? ? ? ? 
 (C) 
22
vv
ˆˆ
cos i sin j
RR
? ? ? ?   
 (D) 
22
vv
ˆˆ
ij
RR
?? 
 Official Ans. by NTA (C) 
  
Sol. 
2
V
a | a |
R
?? 
 
?
a
 
 
ˆˆ
a a cos i a sin j ? ? ? ? ? 
 
22
VV
ˆˆ
cos i sin j
RR
? ? ? ? ? 
8. Two metallic plates form a parallel plate capacitor. 
The distance between the plates is ‘d’. A metal 
sheet of thickness 
d
2
 and of area equal to area of 
each plate is introduced between the plates. What 
will be the ratio  of the new capacitance to the 
original capacitance of the capacitor ? 
 (A) 2:1  (B) 1:2  
 (C) 1:4  (D) 4:1 
 Official Ans. by NTA (A) 
  
Sol. 
0
1
A
C
d
?
? 
 
00
2
A 2 A
C
d d / 2
d
2
??
??
?
?
 
 
2
1
C2
C1
? 
9. Two cells of same emf but different internal 
resistances r
1
 and r
2
 are connected in series with a 
resistance R. The value of resistance R, for which 
the potential difference across second cell is zero, 
is 
 (A) 
21
rr ?  (B)
12
rr ?  
 (C) r
1
 (D) r
2 
 Official Ans. by NTA (A) 
  
Sol. 
12
2E
I
R r r
?
??
…..( i ) 
 
E
r
1 r
2
B
R
I
A
E
 
 But 
A B 2
V V E Ir 0 ? ? ? ? 
 
2
E
I
r
?? ….(ii) 
 Comparing values of I from (i) and (ii) 
 
2 1 2
E 2E
r R r r
?
??
 
 
21
R r r ? ? ?
 
 
 
4 
 
 
10. Given below are two statements:  
 Statement – I : Susceptibilities of paramagnetic 
and ferromagnetic substances increase with 
decrease in temperature.  
 Statement – II: Diamagnetism is a result of orbital 
motions of electrons developing magnetic 
moments opposite to the applied magnetic field.  
 Choose the CORRECT answer from the options 
given below : - 
 (A) Both statement – I and statement -II are true. 
 (B) Both statement – I and Statement – II are false. 
 (C) Statement – I is true but statement – II is false. 
 (D) Statement-I is false but Statement-II is true.  
 Official Ans. by NTA (A) 
  
Sol. According to curie's law, magnetic susceptibility is 
inversely proportional to temperature for a fixed 
value of external magnetic field i.e. ??
C
T
. 
 The same is applicable for ferromagnet & the 
relation is given as ??
?
C
C
TT
 (T
C
 is curie 
temperature) 
 Diamagnetism is due to non-cooperative behaviour 
of orbiting electrons when exposed to external 
magnetic field. 
 Hence option (A).   
11. A long solenoid carrying a current produces a 
magnetic field B along its axis. If the current is 
doubled and the number of turns per cm is halved, 
the new value of magnetic field will be equal to  
 (A) B (B) 2 B 
 (C) 4 B  (D) 
B
2
 
 Official Ans. by NTA (A) 
  
Sol. 
10
B nI ?? 
 ? ?
20
n
B 2I
2
??
??
??
??
 
 ?B
1
 = B
2 
12. A sinusoidal voltage V(t) = 210 sin 3000t volt is 
applied to a series LCR circuit in which L = 10 
mH, C = 25 ?F and R = 100 ?. The phase 
difference ( ?) between the applied voltage and 
resultant current will be : 
 (A) tan
–1
 (0.17) (B) tan
–1
 (9.46)  
 (C) tan
–1
 (0.30) (D) tan
–1
 (13.33) 
 Official Ans. by NTA (A) 
  
Sol. 
2
L
X 10 3000 30
?
? ? ? ? 
 
C
6
1 40
X
3
3000 25 10
?
? ? ?
??
 
 X = X
L
 –X
C 
 
40 50
30
33
? ? ? 
 
X 50 1
tan
R 3 100 6
? ? ? ?
?
 
 ? ?
11
1
tan tan 0.17
6
??
??
? ? ?
??
??
 
13. The electromagnetic waves travel in a medium at a 
speed of 2.0 × 10
8
 m/s.The relative permeability of 
the medium is 1.0. The relative permittivity of the 
medium will be: 
 (A) 2.25  (B) 4.25  
 (C) 6.25  (D) 8.25 
 Official Ans. by NTA (A) 
  
Sol. 
8
V 2 10 m / s ?? 
 
8
C 3 10 m / s ?? 
 
rr
C
V
? ? ? 
 
r
9
1
4
? ? ? 
 
r
9
2.25
4
? ? ? 
 
 
5 
 
 
14. The interference pattern is obtained with two 
coherent light sources of intensity ratio 4 :1. And 
the ratio 
max min
max min
II 5
is
I I x
?
?
. Then, the value of x 
will be equal to : 
 (A) 3  (B) 4  
 (C) 2  (D) 1 
 Official Ans. by NTA (B) 
  
Sol. 
1
2
I
4
I
? 
 
2
12 max
min 12
II I
I II
??
?
???
?
??
??
 
 
2
22 max
min 22
2 I I I
I 2 I I
??
?
???
?
??
??
 
 
max
min
I
9
I
? 
 
max min
max min
II 10
I I 8
?
?
?
 
 
5 10
x8
? 
 x = 4 
15. A light whose electric field vectors are completely 
removed by using a good Polaroid, allowed to 
incident on the surface of the prism at Brewster’s 
angle. Choose the most suitable option for the 
phenomenon related to the prism. 
 (A) Reflected and refracted rays will be    
perpendicular to each other 
 (B) Wave will propagate along the surface of prism 
 (C) No refraction, and there will be total reflection 
of light.  
 (D) No reflection and there will be total 
transmission of light. 
 Official Ans. by NTA (D ) 
  
Sol. 
 
90° 
Refracted, partially 
polarized light 
Incident, 
ordinary 
light 
Reflected 
polarised 
light 
Brewster's law 
 
 But as the incident light electric field vectors are 
completely removed so there will be no reflection 
and there will be total transmission of light, 
explained by an experiment in NCERT. 
 [Reference NCERT Part-2 Pg-380, (A special case 
of total transmission)] 
 Note : Since direction of polarization is not 
mentioned hence most suitable option (D) 
corresponding to case in which electric field is 
absent perpendicular to plane consisting incident 
and normal.  
16. A proton, a neutron, an electron and an ?-particle 
have same energy. If 
p n e
,, ? ? ? and 
?
? are the de 
Broglie’s wavelengths of proton, neutron, electron 
and ? particle respectively, then choose the correct 
relation from the following : 
 (A) 
p n e ?
? ? ? ? ? ? ? 
 (B) 
n p e ?
? ? ? ? ? ? ? 
 (C)
e p n ?
? ? ? ? ? ? ?
 (D) 
e p n ?
? ? ? ? ? ? ? 
 Official Ans. by NTA (B) 
  
Sol. 
h
2Em
?? 
 
1
m
?? 
? 
e p n ?
? ? ? ? ? ? ?