JEE Main 2022 Question Paper 24 June Shift 1 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
(Held On Friday 24
th
 June, 2022)  TIME : 9 : 00 AM  to  12 : 00 PM 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. The bulk modulus of a liquid is 3 × 10
10
 Nm
-2
. The
pressure required to reduce the volume of liquid by
2% is :
(A) 3 × 10
8
 Nm
-2
(B) 9 × 10
8
 Nm
-2
(C) 6 × 10
8
 Nm
-2
(D) 12 × 10
8
 Nm
-2
Official Ans. by NTA (C) 
 
Sol. B = 3 × 10
10
 
V
0.02
V
?
??
?? ??
? ? ? ? ?
??
?
??
?
PV
B P B
V
V
v
10
(3 10 )(0.02) ??
82
6 10 N / m ??
2. Given below are two statements : One is labelled
as Assertion (A) and the other is labelled as
Reason (R).
Assertion (A) : In an uniform magnetic field,
speed and energy remains the same for a moving
charged particle.
Reason (R) : Moving charged particle experiences
magnetic force perpendicular to its direction of
motion.
(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. F q(v B) ?? 
Fv ?
Work done ?? FS 
Work done = 0 
3. Two identical cells each of emf 1.5 V are
connected in parallel across a parallel combination 
of two resistors each of resistance 20?. A 
voltmeter connected in the circuit measures 1.2 V. 
The internal resistance of each cell is 
(A) 2.5 ? (B) 4 ?
(C) 5? (D) 10 ?
Official Ans. by NTA (C) 
 
Sol. 
1.5V
1.5V
r/2
1.5V
r
10 ?
20 ?
20 ?
r
V = E – ir/2 
1.2 = 1.5 – i 
r
2
??
??
??
r
i 0.3
2
?
1.5 ir
i 10i 1.5
r
2
10
2
? ? ? ?
?
10i = 1.5 – 0.3 
i = 0.12 A 
0.6
r5
0.12
? ? ? ?
Page 2


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
(Held On Friday 24
th
 June, 2022)  TIME : 9 : 00 AM  to  12 : 00 PM 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. The bulk modulus of a liquid is 3 × 10
10
 Nm
-2
. The
pressure required to reduce the volume of liquid by
2% is :
(A) 3 × 10
8
 Nm
-2
(B) 9 × 10
8
 Nm
-2
(C) 6 × 10
8
 Nm
-2
(D) 12 × 10
8
 Nm
-2
Official Ans. by NTA (C) 
 
Sol. B = 3 × 10
10
 
V
0.02
V
?
??
?? ??
? ? ? ? ?
??
?
??
?
PV
B P B
V
V
v
10
(3 10 )(0.02) ??
82
6 10 N / m ??
2. Given below are two statements : One is labelled
as Assertion (A) and the other is labelled as
Reason (R).
Assertion (A) : In an uniform magnetic field,
speed and energy remains the same for a moving
charged particle.
Reason (R) : Moving charged particle experiences
magnetic force perpendicular to its direction of
motion.
(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. F q(v B) ?? 
Fv ?
Work done ?? FS 
Work done = 0 
3. Two identical cells each of emf 1.5 V are
connected in parallel across a parallel combination 
of two resistors each of resistance 20?. A 
voltmeter connected in the circuit measures 1.2 V. 
The internal resistance of each cell is 
(A) 2.5 ? (B) 4 ?
(C) 5? (D) 10 ?
Official Ans. by NTA (C) 
 
Sol. 
1.5V
1.5V
r/2
1.5V
r
10 ?
20 ?
20 ?
r
V = E – ir/2 
1.2 = 1.5 – i 
r
2
??
??
??
r
i 0.3
2
?
1.5 ir
i 10i 1.5
r
2
10
2
? ? ? ?
?
10i = 1.5 – 0.3 
i = 0.12 A 
0.6
r5
0.12
? ? ? ?
 
2 
 
4. Identify the pair of physical quantities which have 
different dimensions :  
 (A) Wave number and Rydberg’s constant   
 (B) Stress and Coefficient of elasticity 
 (C) Coercivity and Magnetisation   
 (D) Specific heat capacity and Latent heat  
 Official Ans. by NTA (D) 
  
Sol. ??
??
QJ
S
m T Kg C
 
 
QJ
L
m Kg
??  
5. A projectile is projected with velocity of 25 m/s at 
an angle ? ?with the horizontal. After t seconds its 
inclination with horizontal becomes zero. If R 
represents horizontal range of the projectile, the 
value of ? will be : [use g = 10 m/s
2
] 
 (A) 
2
1
1 5t
sin
2 4R
?
??
??
??
 (B) 
?
??
??
??
1
2
1 4R
sin
2 5t
  
 (C) 
2
1
4t
tan
5R
?
??
??
??
 (D) 
1
2
R
cot
20t
?
??
??
??
 
 Official Ans. by NTA (D) 
  
Sol. 
2
V (2sin cos )
R
g
??
? 
 
?
? ? ?
?
Vsin gt
tV
g sin
 
 
22
2
g t 2sin cos
R.
g sin
??
??
?
 
 
2
2gt
tan
R
?? 
2
20t
R
? 
 
2
R
cot
20t
?? 
6. A block of mass 10 kg starts sliding on a surface 
with an initial velocity of 9.8 ms
-1
. The coefficient 
of friction between the surface and bock is 0.5. The 
distance covered by the block before coming to 
rest is : [use g = 9.8 ms
-2
]  
 (A) 4.9 m  (B) 9.8 m
 
 
 (C) 12.5 m  (D) 19.6 m  
 Official Ans. by NTA (B) 
  
Sol. 
2
a g 0.5 9.8 4.9m / s ? ? ? ? ? ? ? ? 
 
2
v 9.8 9.8
d
2a 2(4.9)
?
?? 
 = 9.8 m 
7. A boy ties a stone of mass 100 g to the end of a 2 
m long string and whirls it around in a horizontal 
plane. The string can withstand the maximum 
tension of 80 N. If the maximum speed with which 
the stone can revolve is 
K
rev. / min
?
. The value of 
K is : (Assume the string is massless and 
unstretchable)  
 (A) 400  (B) 300 
 (C) 600  (D) 800 
 Official Ans. by NTA (C) 
  
Sol. T = M ?
 2
R 
 T = 80 N    M = 0.1    ? = ?     R = 2m 
 80 = 0.1 ?
2
(2) 
 ?
2
 = 400 
 ?
 
= 20 
 2 ?f = 20 
 
10 rev
f
s
?
?
 
 
600 rev
min
?
?
 
Page 3


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
(Held On Friday 24
th
 June, 2022)  TIME : 9 : 00 AM  to  12 : 00 PM 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. The bulk modulus of a liquid is 3 × 10
10
 Nm
-2
. The
pressure required to reduce the volume of liquid by
2% is :
(A) 3 × 10
8
 Nm
-2
(B) 9 × 10
8
 Nm
-2
(C) 6 × 10
8
 Nm
-2
(D) 12 × 10
8
 Nm
-2
Official Ans. by NTA (C) 
 
Sol. B = 3 × 10
10
 
V
0.02
V
?
??
?? ??
? ? ? ? ?
??
?
??
?
PV
B P B
V
V
v
10
(3 10 )(0.02) ??
82
6 10 N / m ??
2. Given below are two statements : One is labelled
as Assertion (A) and the other is labelled as
Reason (R).
Assertion (A) : In an uniform magnetic field,
speed and energy remains the same for a moving
charged particle.
Reason (R) : Moving charged particle experiences
magnetic force perpendicular to its direction of
motion.
(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. F q(v B) ?? 
Fv ?
Work done ?? FS 
Work done = 0 
3. Two identical cells each of emf 1.5 V are
connected in parallel across a parallel combination 
of two resistors each of resistance 20?. A 
voltmeter connected in the circuit measures 1.2 V. 
The internal resistance of each cell is 
(A) 2.5 ? (B) 4 ?
(C) 5? (D) 10 ?
Official Ans. by NTA (C) 
 
Sol. 
1.5V
1.5V
r/2
1.5V
r
10 ?
20 ?
20 ?
r
V = E – ir/2 
1.2 = 1.5 – i 
r
2
??
??
??
r
i 0.3
2
?
1.5 ir
i 10i 1.5
r
2
10
2
? ? ? ?
?
10i = 1.5 – 0.3 
i = 0.12 A 
0.6
r5
0.12
? ? ? ?
 
2 
 
4. Identify the pair of physical quantities which have 
different dimensions :  
 (A) Wave number and Rydberg’s constant   
 (B) Stress and Coefficient of elasticity 
 (C) Coercivity and Magnetisation   
 (D) Specific heat capacity and Latent heat  
 Official Ans. by NTA (D) 
  
Sol. ??
??
QJ
S
m T Kg C
 
 
QJ
L
m Kg
??  
5. A projectile is projected with velocity of 25 m/s at 
an angle ? ?with the horizontal. After t seconds its 
inclination with horizontal becomes zero. If R 
represents horizontal range of the projectile, the 
value of ? will be : [use g = 10 m/s
2
] 
 (A) 
2
1
1 5t
sin
2 4R
?
??
??
??
 (B) 
?
??
??
??
1
2
1 4R
sin
2 5t
  
 (C) 
2
1
4t
tan
5R
?
??
??
??
 (D) 
1
2
R
cot
20t
?
??
??
??
 
 Official Ans. by NTA (D) 
  
Sol. 
2
V (2sin cos )
R
g
??
? 
 
?
? ? ?
?
Vsin gt
tV
g sin
 
 
22
2
g t 2sin cos
R.
g sin
??
??
?
 
 
2
2gt
tan
R
?? 
2
20t
R
? 
 
2
R
cot
20t
?? 
6. A block of mass 10 kg starts sliding on a surface 
with an initial velocity of 9.8 ms
-1
. The coefficient 
of friction between the surface and bock is 0.5. The 
distance covered by the block before coming to 
rest is : [use g = 9.8 ms
-2
]  
 (A) 4.9 m  (B) 9.8 m
 
 
 (C) 12.5 m  (D) 19.6 m  
 Official Ans. by NTA (B) 
  
Sol. 
2
a g 0.5 9.8 4.9m / s ? ? ? ? ? ? ? ? 
 
2
v 9.8 9.8
d
2a 2(4.9)
?
?? 
 = 9.8 m 
7. A boy ties a stone of mass 100 g to the end of a 2 
m long string and whirls it around in a horizontal 
plane. The string can withstand the maximum 
tension of 80 N. If the maximum speed with which 
the stone can revolve is 
K
rev. / min
?
. The value of 
K is : (Assume the string is massless and 
unstretchable)  
 (A) 400  (B) 300 
 (C) 600  (D) 800 
 Official Ans. by NTA (C) 
  
Sol. T = M ?
 2
R 
 T = 80 N    M = 0.1    ? = ?     R = 2m 
 80 = 0.1 ?
2
(2) 
 ?
2
 = 400 
 ?
 
= 20 
 2 ?f = 20 
 
10 rev
f
s
?
?
 
 
600 rev
min
?
?
 
 
 
3 
 
8. A vertical electric field of magnitude 4.9 × 10
5
 N/C 
just prevents a water droplet of a mass 0.1 g from 
falling. The value of charge on the droplet will be : 
(Given g = 9.8 m/s
2
) 
 (A) 1.6 × 10
-9
 C (B) 2.0 × 10
-9
 C 
 (C) 3.2 × 10
-9
 C (D) 0.5 × 10
-9
 C 
 Official Ans. by NTA (B) 
  
Sol. Mg = qE 
 
35
(0.1 10 )(9.8) 4.9 10 q
?
? ? ? 
 
4
5
2 10
q
10
?
?
? 
 
9
q 2 10 C
?
??  
9. A particle experiences a variable force 
2
ˆˆ
F (4xi 3y j) ?? in a horizontal x-y plane. Assume 
distance in meters and force is newton. If the 
particle moves from point (1, 2) to point (2, 3) in 
the x-y plane, the Kinetic Energy changes by  
 (A) 50.0 J  (B) 12.5 J  
 (C) 25.0 J (D) 0 J 
 Official Ans. by NTA (C) 
  
Sol. 
2
ˆˆ
F 4xi 3y j ?? 
 WD = ?KE 
 
ˆˆ
W F.(dxi dyj) ??
?
 
 
23
2
12
4xdx 3y dx ??
??
 
 
2 2 3 3
12
(2x ) (y ) ?? 
 (8 2) (27 8) ? ? ? ? 
 6 19 25J ? ? ? 
10. The approximate height from the surface of earth 
at which the weight of the body becomes 
1
3
 of its 
weight on the surface of earth is : [Radius of earth 
R = 6400 km and 3 1.732 ? ] 
 (A) 3840 km (B)
 
4685 km 
 (C) 2133 km  (D) 4267 km 
 Official Ans. by NTA (B) 
  
Sol. 
M
Mg' g
3
? 
 
g
g'
3
? 
 
2
Rg
g' g
R h 3
??
??
??
?
??
 
 
R1
.
Rh
3
?
?
 
 h ( 3 1)R ?? 
 (1.732 1)6400 ?? 
 h 4685km ? 
11. A resistance of 40 ? is connected to a source of 
alternating current rated 220 V, 50 Hz. Find the 
time taken by the current to change from its 
maximum value to rms value :   
 (A) 2.5 ms (B) 1.25 ms 
 (C) 2.5 s  (D) 0.25 s 
 Official Ans. by NTA (A) 
  
Sol. Considering sinusoidal AC. 
 Phase at maximum value 
?
?
2
 
 Phase at rms value = 
? 3
4
 
 Thus phase change 
? ? ?
? ? ?
3
4 2 4
 
 Now ? = 2 ?f 
 = 2 ? × 50 
 = 100 ? 
 time taken t = 
??
??
??
/ 4 1
s
100 400
 
 t = 2.5 × 10
–3
 = 2.5 ms  
Page 4


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
(Held On Friday 24
th
 June, 2022)  TIME : 9 : 00 AM  to  12 : 00 PM 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. The bulk modulus of a liquid is 3 × 10
10
 Nm
-2
. The
pressure required to reduce the volume of liquid by
2% is :
(A) 3 × 10
8
 Nm
-2
(B) 9 × 10
8
 Nm
-2
(C) 6 × 10
8
 Nm
-2
(D) 12 × 10
8
 Nm
-2
Official Ans. by NTA (C) 
 
Sol. B = 3 × 10
10
 
V
0.02
V
?
??
?? ??
? ? ? ? ?
??
?
??
?
PV
B P B
V
V
v
10
(3 10 )(0.02) ??
82
6 10 N / m ??
2. Given below are two statements : One is labelled
as Assertion (A) and the other is labelled as
Reason (R).
Assertion (A) : In an uniform magnetic field,
speed and energy remains the same for a moving
charged particle.
Reason (R) : Moving charged particle experiences
magnetic force perpendicular to its direction of
motion.
(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. F q(v B) ?? 
Fv ?
Work done ?? FS 
Work done = 0 
3. Two identical cells each of emf 1.5 V are
connected in parallel across a parallel combination 
of two resistors each of resistance 20?. A 
voltmeter connected in the circuit measures 1.2 V. 
The internal resistance of each cell is 
(A) 2.5 ? (B) 4 ?
(C) 5? (D) 10 ?
Official Ans. by NTA (C) 
 
Sol. 
1.5V
1.5V
r/2
1.5V
r
10 ?
20 ?
20 ?
r
V = E – ir/2 
1.2 = 1.5 – i 
r
2
??
??
??
r
i 0.3
2
?
1.5 ir
i 10i 1.5
r
2
10
2
? ? ? ?
?
10i = 1.5 – 0.3 
i = 0.12 A 
0.6
r5
0.12
? ? ? ?
 
2 
 
4. Identify the pair of physical quantities which have 
different dimensions :  
 (A) Wave number and Rydberg’s constant   
 (B) Stress and Coefficient of elasticity 
 (C) Coercivity and Magnetisation   
 (D) Specific heat capacity and Latent heat  
 Official Ans. by NTA (D) 
  
Sol. ??
??
QJ
S
m T Kg C
 
 
QJ
L
m Kg
??  
5. A projectile is projected with velocity of 25 m/s at 
an angle ? ?with the horizontal. After t seconds its 
inclination with horizontal becomes zero. If R 
represents horizontal range of the projectile, the 
value of ? will be : [use g = 10 m/s
2
] 
 (A) 
2
1
1 5t
sin
2 4R
?
??
??
??
 (B) 
?
??
??
??
1
2
1 4R
sin
2 5t
  
 (C) 
2
1
4t
tan
5R
?
??
??
??
 (D) 
1
2
R
cot
20t
?
??
??
??
 
 Official Ans. by NTA (D) 
  
Sol. 
2
V (2sin cos )
R
g
??
? 
 
?
? ? ?
?
Vsin gt
tV
g sin
 
 
22
2
g t 2sin cos
R.
g sin
??
??
?
 
 
2
2gt
tan
R
?? 
2
20t
R
? 
 
2
R
cot
20t
?? 
6. A block of mass 10 kg starts sliding on a surface 
with an initial velocity of 9.8 ms
-1
. The coefficient 
of friction between the surface and bock is 0.5. The 
distance covered by the block before coming to 
rest is : [use g = 9.8 ms
-2
]  
 (A) 4.9 m  (B) 9.8 m
 
 
 (C) 12.5 m  (D) 19.6 m  
 Official Ans. by NTA (B) 
  
Sol. 
2
a g 0.5 9.8 4.9m / s ? ? ? ? ? ? ? ? 
 
2
v 9.8 9.8
d
2a 2(4.9)
?
?? 
 = 9.8 m 
7. A boy ties a stone of mass 100 g to the end of a 2 
m long string and whirls it around in a horizontal 
plane. The string can withstand the maximum 
tension of 80 N. If the maximum speed with which 
the stone can revolve is 
K
rev. / min
?
. The value of 
K is : (Assume the string is massless and 
unstretchable)  
 (A) 400  (B) 300 
 (C) 600  (D) 800 
 Official Ans. by NTA (C) 
  
Sol. T = M ?
 2
R 
 T = 80 N    M = 0.1    ? = ?     R = 2m 
 80 = 0.1 ?
2
(2) 
 ?
2
 = 400 
 ?
 
= 20 
 2 ?f = 20 
 
10 rev
f
s
?
?
 
 
600 rev
min
?
?
 
 
 
3 
 
8. A vertical electric field of magnitude 4.9 × 10
5
 N/C 
just prevents a water droplet of a mass 0.1 g from 
falling. The value of charge on the droplet will be : 
(Given g = 9.8 m/s
2
) 
 (A) 1.6 × 10
-9
 C (B) 2.0 × 10
-9
 C 
 (C) 3.2 × 10
-9
 C (D) 0.5 × 10
-9
 C 
 Official Ans. by NTA (B) 
  
Sol. Mg = qE 
 
35
(0.1 10 )(9.8) 4.9 10 q
?
? ? ? 
 
4
5
2 10
q
10
?
?
? 
 
9
q 2 10 C
?
??  
9. A particle experiences a variable force 
2
ˆˆ
F (4xi 3y j) ?? in a horizontal x-y plane. Assume 
distance in meters and force is newton. If the 
particle moves from point (1, 2) to point (2, 3) in 
the x-y plane, the Kinetic Energy changes by  
 (A) 50.0 J  (B) 12.5 J  
 (C) 25.0 J (D) 0 J 
 Official Ans. by NTA (C) 
  
Sol. 
2
ˆˆ
F 4xi 3y j ?? 
 WD = ?KE 
 
ˆˆ
W F.(dxi dyj) ??
?
 
 
23
2
12
4xdx 3y dx ??
??
 
 
2 2 3 3
12
(2x ) (y ) ?? 
 (8 2) (27 8) ? ? ? ? 
 6 19 25J ? ? ? 
10. The approximate height from the surface of earth 
at which the weight of the body becomes 
1
3
 of its 
weight on the surface of earth is : [Radius of earth 
R = 6400 km and 3 1.732 ? ] 
 (A) 3840 km (B)
 
4685 km 
 (C) 2133 km  (D) 4267 km 
 Official Ans. by NTA (B) 
  
Sol. 
M
Mg' g
3
? 
 
g
g'
3
? 
 
2
Rg
g' g
R h 3
??
??
??
?
??
 
 
R1
.
Rh
3
?
?
 
 h ( 3 1)R ?? 
 (1.732 1)6400 ?? 
 h 4685km ? 
11. A resistance of 40 ? is connected to a source of 
alternating current rated 220 V, 50 Hz. Find the 
time taken by the current to change from its 
maximum value to rms value :   
 (A) 2.5 ms (B) 1.25 ms 
 (C) 2.5 s  (D) 0.25 s 
 Official Ans. by NTA (A) 
  
Sol. Considering sinusoidal AC. 
 Phase at maximum value 
?
?
2
 
 Phase at rms value = 
? 3
4
 
 Thus phase change 
? ? ?
? ? ?
3
4 2 4
 
 Now ? = 2 ?f 
 = 2 ? × 50 
 = 100 ? 
 time taken t = 
??
??
??
/ 4 1
s
100 400
 
 t = 2.5 × 10
–3
 = 2.5 ms  
 
4 
 
12. The equations of two waves are given by : 
  
1
y 5sin2 (x vt)cm ? ? ? 
  
2
y 3sin2 (x vt 1.5)cm ? ? ? ? 
 These waves are simultaneously passing through a 
string. The amplitude of the resulting wave is  
 (A) 2 cm  (B) 4 cm 
 (C) 5.8 cm  (D) 8 cm 
 Official Ans. by NTA (A) 
  
Sol. 
12
A 5 A 3 ?? 
 2 (1.5) 3 ? ? ? ? ? ? 
 
22
net 1 2 1 2
A A A 2A A cos(3 ) ? ? ? ? 
 
12
AA ?? 
 = 2cm 
13. A plane electromagnetic wave travels in a medium 
of relative permeability 1.61 and relative 
permittivity 6.44. If magnitude of magnetic 
intensity is 4.5 × 10
-2
 Am
-1
 at a point, what will be 
the approximate magnitude of electric field 
intensity at that point ? 
 (Given : permeability of free space ?
0
 = 4 ? × 10
-7
 
NA
-2
, speed of light in vacuum c = 3 × 10
8
 ms
-1
) 
 (A) 16.96 Vm
-1
 (B) 2.25 × 10
-2
 Vm
-1
  
 (C) 8.48 Vm
-1
 (D) 6.75 × 10
6
 Vm
-1
 
 Official Ans. by NTA (C) 
 
Sol. 
r
1.61 ?? 
r
6.44 ?? 
 
2
B 4.5 10
?
?? 
 E = ? 
 
00
11
CV ??
? ? ? ?
 
 
rr
C
1.61 6.44
V
? ? ? ? ? 
 
8
7
3 10
V 9.32 10 m / s
B
1.61 6.44
??
? ? ? ?
?
 
 
27
E 4.5 10 9.32 10
?
? ? ? ? 
 
6
4.2 10 ?? 
14. Choose the correct option from the following 
options given below :  
 (A) In the ground state of Rutherford's model 
electrons are in stable equilibrium. While in 
Thomson's model electrons always 
experience a net-force. 
 (B) An atom has a nearly continuous mass 
distribution in a Rutherford's model but has a 
highly non-uniform mass distribution in 
Thomson's model 
 (C) A classical atom based on Rutherford's model 
is doomed to collapse. 
 (D) The positively charged part of the atom 
possesses most of the mass in Rutherford's 
model but not in Thomson's model.  
 Official Ans. by NTA (C) 
  
Sol. According to Rutherford, e
–
 revolves around 
nucleus in circular orbit. Thus e
–
 is always 
accelerating (centripetal acceleration). An 
accelerating change emits EM radiation and thus e
–
 
should loose energy and finally should collapse in 
the nucleus. 
15. Nucleus A is having mass number 220 and its 
binding energy per nucleon is 5.6 MeV. It 
splits in two fragments 'B' and 'C' of mass numbers 
105 and 115. The binding energy of nucleons  in 
'B' and 'C' is 6.4 MeV per nucleon. The energy Q 
released per fission will be : 
 (A) 0.8 MeV  (B) 275 MeV 
 (C) 220 MeV (D) 176 MeV 
 Official Ans. by NTA (D) 
  
Sol. 
PR
Q (B.E) (B.E) ?? 
 (105 115)(6.4) (220)(5.6) ? ? ? 
 = 176 MeV 
16. A baseband signal of 3.5 MHz frequency is 
modulated with a carrier signal of 3.5 GHz 
frequency using amplitude modulation method. 
What should be the minimum size of antenna 
required to transmit the modulated signal ? 
 (A) 42.8 m  (B) 42.8 mm 
 (C) 21.4 mm (D) 21.4 m 
 Official Ans. by NTA (C) 
  
Page 5


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
(Held On Friday 24
th
 June, 2022)  TIME : 9 : 00 AM  to  12 : 00 PM 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. The bulk modulus of a liquid is 3 × 10
10
 Nm
-2
. The
pressure required to reduce the volume of liquid by
2% is :
(A) 3 × 10
8
 Nm
-2
(B) 9 × 10
8
 Nm
-2
(C) 6 × 10
8
 Nm
-2
(D) 12 × 10
8
 Nm
-2
Official Ans. by NTA (C) 
 
Sol. B = 3 × 10
10
 
V
0.02
V
?
??
?? ??
? ? ? ? ?
??
?
??
?
PV
B P B
V
V
v
10
(3 10 )(0.02) ??
82
6 10 N / m ??
2. Given below are two statements : One is labelled
as Assertion (A) and the other is labelled as
Reason (R).
Assertion (A) : In an uniform magnetic field,
speed and energy remains the same for a moving
charged particle.
Reason (R) : Moving charged particle experiences
magnetic force perpendicular to its direction of
motion.
(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. F q(v B) ?? 
Fv ?
Work done ?? FS 
Work done = 0 
3. Two identical cells each of emf 1.5 V are
connected in parallel across a parallel combination 
of two resistors each of resistance 20?. A 
voltmeter connected in the circuit measures 1.2 V. 
The internal resistance of each cell is 
(A) 2.5 ? (B) 4 ?
(C) 5? (D) 10 ?
Official Ans. by NTA (C) 
 
Sol. 
1.5V
1.5V
r/2
1.5V
r
10 ?
20 ?
20 ?
r
V = E – ir/2 
1.2 = 1.5 – i 
r
2
??
??
??
r
i 0.3
2
?
1.5 ir
i 10i 1.5
r
2
10
2
? ? ? ?
?
10i = 1.5 – 0.3 
i = 0.12 A 
0.6
r5
0.12
? ? ? ?
 
2 
 
4. Identify the pair of physical quantities which have 
different dimensions :  
 (A) Wave number and Rydberg’s constant   
 (B) Stress and Coefficient of elasticity 
 (C) Coercivity and Magnetisation   
 (D) Specific heat capacity and Latent heat  
 Official Ans. by NTA (D) 
  
Sol. ??
??
QJ
S
m T Kg C
 
 
QJ
L
m Kg
??  
5. A projectile is projected with velocity of 25 m/s at 
an angle ? ?with the horizontal. After t seconds its 
inclination with horizontal becomes zero. If R 
represents horizontal range of the projectile, the 
value of ? will be : [use g = 10 m/s
2
] 
 (A) 
2
1
1 5t
sin
2 4R
?
??
??
??
 (B) 
?
??
??
??
1
2
1 4R
sin
2 5t
  
 (C) 
2
1
4t
tan
5R
?
??
??
??
 (D) 
1
2
R
cot
20t
?
??
??
??
 
 Official Ans. by NTA (D) 
  
Sol. 
2
V (2sin cos )
R
g
??
? 
 
?
? ? ?
?
Vsin gt
tV
g sin
 
 
22
2
g t 2sin cos
R.
g sin
??
??
?
 
 
2
2gt
tan
R
?? 
2
20t
R
? 
 
2
R
cot
20t
?? 
6. A block of mass 10 kg starts sliding on a surface 
with an initial velocity of 9.8 ms
-1
. The coefficient 
of friction between the surface and bock is 0.5. The 
distance covered by the block before coming to 
rest is : [use g = 9.8 ms
-2
]  
 (A) 4.9 m  (B) 9.8 m
 
 
 (C) 12.5 m  (D) 19.6 m  
 Official Ans. by NTA (B) 
  
Sol. 
2
a g 0.5 9.8 4.9m / s ? ? ? ? ? ? ? ? 
 
2
v 9.8 9.8
d
2a 2(4.9)
?
?? 
 = 9.8 m 
7. A boy ties a stone of mass 100 g to the end of a 2 
m long string and whirls it around in a horizontal 
plane. The string can withstand the maximum 
tension of 80 N. If the maximum speed with which 
the stone can revolve is 
K
rev. / min
?
. The value of 
K is : (Assume the string is massless and 
unstretchable)  
 (A) 400  (B) 300 
 (C) 600  (D) 800 
 Official Ans. by NTA (C) 
  
Sol. T = M ?
 2
R 
 T = 80 N    M = 0.1    ? = ?     R = 2m 
 80 = 0.1 ?
2
(2) 
 ?
2
 = 400 
 ?
 
= 20 
 2 ?f = 20 
 
10 rev
f
s
?
?
 
 
600 rev
min
?
?
 
 
 
3 
 
8. A vertical electric field of magnitude 4.9 × 10
5
 N/C 
just prevents a water droplet of a mass 0.1 g from 
falling. The value of charge on the droplet will be : 
(Given g = 9.8 m/s
2
) 
 (A) 1.6 × 10
-9
 C (B) 2.0 × 10
-9
 C 
 (C) 3.2 × 10
-9
 C (D) 0.5 × 10
-9
 C 
 Official Ans. by NTA (B) 
  
Sol. Mg = qE 
 
35
(0.1 10 )(9.8) 4.9 10 q
?
? ? ? 
 
4
5
2 10
q
10
?
?
? 
 
9
q 2 10 C
?
??  
9. A particle experiences a variable force 
2
ˆˆ
F (4xi 3y j) ?? in a horizontal x-y plane. Assume 
distance in meters and force is newton. If the 
particle moves from point (1, 2) to point (2, 3) in 
the x-y plane, the Kinetic Energy changes by  
 (A) 50.0 J  (B) 12.5 J  
 (C) 25.0 J (D) 0 J 
 Official Ans. by NTA (C) 
  
Sol. 
2
ˆˆ
F 4xi 3y j ?? 
 WD = ?KE 
 
ˆˆ
W F.(dxi dyj) ??
?
 
 
23
2
12
4xdx 3y dx ??
??
 
 
2 2 3 3
12
(2x ) (y ) ?? 
 (8 2) (27 8) ? ? ? ? 
 6 19 25J ? ? ? 
10. The approximate height from the surface of earth 
at which the weight of the body becomes 
1
3
 of its 
weight on the surface of earth is : [Radius of earth 
R = 6400 km and 3 1.732 ? ] 
 (A) 3840 km (B)
 
4685 km 
 (C) 2133 km  (D) 4267 km 
 Official Ans. by NTA (B) 
  
Sol. 
M
Mg' g
3
? 
 
g
g'
3
? 
 
2
Rg
g' g
R h 3
??
??
??
?
??
 
 
R1
.
Rh
3
?
?
 
 h ( 3 1)R ?? 
 (1.732 1)6400 ?? 
 h 4685km ? 
11. A resistance of 40 ? is connected to a source of 
alternating current rated 220 V, 50 Hz. Find the 
time taken by the current to change from its 
maximum value to rms value :   
 (A) 2.5 ms (B) 1.25 ms 
 (C) 2.5 s  (D) 0.25 s 
 Official Ans. by NTA (A) 
  
Sol. Considering sinusoidal AC. 
 Phase at maximum value 
?
?
2
 
 Phase at rms value = 
? 3
4
 
 Thus phase change 
? ? ?
? ? ?
3
4 2 4
 
 Now ? = 2 ?f 
 = 2 ? × 50 
 = 100 ? 
 time taken t = 
??
??
??
/ 4 1
s
100 400
 
 t = 2.5 × 10
–3
 = 2.5 ms  
 
4 
 
12. The equations of two waves are given by : 
  
1
y 5sin2 (x vt)cm ? ? ? 
  
2
y 3sin2 (x vt 1.5)cm ? ? ? ? 
 These waves are simultaneously passing through a 
string. The amplitude of the resulting wave is  
 (A) 2 cm  (B) 4 cm 
 (C) 5.8 cm  (D) 8 cm 
 Official Ans. by NTA (A) 
  
Sol. 
12
A 5 A 3 ?? 
 2 (1.5) 3 ? ? ? ? ? ? 
 
22
net 1 2 1 2
A A A 2A A cos(3 ) ? ? ? ? 
 
12
AA ?? 
 = 2cm 
13. A plane electromagnetic wave travels in a medium 
of relative permeability 1.61 and relative 
permittivity 6.44. If magnitude of magnetic 
intensity is 4.5 × 10
-2
 Am
-1
 at a point, what will be 
the approximate magnitude of electric field 
intensity at that point ? 
 (Given : permeability of free space ?
0
 = 4 ? × 10
-7
 
NA
-2
, speed of light in vacuum c = 3 × 10
8
 ms
-1
) 
 (A) 16.96 Vm
-1
 (B) 2.25 × 10
-2
 Vm
-1
  
 (C) 8.48 Vm
-1
 (D) 6.75 × 10
6
 Vm
-1
 
 Official Ans. by NTA (C) 
 
Sol. 
r
1.61 ?? 
r
6.44 ?? 
 
2
B 4.5 10
?
?? 
 E = ? 
 
00
11
CV ??
? ? ? ?
 
 
rr
C
1.61 6.44
V
? ? ? ? ? 
 
8
7
3 10
V 9.32 10 m / s
B
1.61 6.44
??
? ? ? ?
?
 
 
27
E 4.5 10 9.32 10
?
? ? ? ? 
 
6
4.2 10 ?? 
14. Choose the correct option from the following 
options given below :  
 (A) In the ground state of Rutherford's model 
electrons are in stable equilibrium. While in 
Thomson's model electrons always 
experience a net-force. 
 (B) An atom has a nearly continuous mass 
distribution in a Rutherford's model but has a 
highly non-uniform mass distribution in 
Thomson's model 
 (C) A classical atom based on Rutherford's model 
is doomed to collapse. 
 (D) The positively charged part of the atom 
possesses most of the mass in Rutherford's 
model but not in Thomson's model.  
 Official Ans. by NTA (C) 
  
Sol. According to Rutherford, e
–
 revolves around 
nucleus in circular orbit. Thus e
–
 is always 
accelerating (centripetal acceleration). An 
accelerating change emits EM radiation and thus e
–
 
should loose energy and finally should collapse in 
the nucleus. 
15. Nucleus A is having mass number 220 and its 
binding energy per nucleon is 5.6 MeV. It 
splits in two fragments 'B' and 'C' of mass numbers 
105 and 115. The binding energy of nucleons  in 
'B' and 'C' is 6.4 MeV per nucleon. The energy Q 
released per fission will be : 
 (A) 0.8 MeV  (B) 275 MeV 
 (C) 220 MeV (D) 176 MeV 
 Official Ans. by NTA (D) 
  
Sol. 
PR
Q (B.E) (B.E) ?? 
 (105 115)(6.4) (220)(5.6) ? ? ? 
 = 176 MeV 
16. A baseband signal of 3.5 MHz frequency is 
modulated with a carrier signal of 3.5 GHz 
frequency using amplitude modulation method. 
What should be the minimum size of antenna 
required to transmit the modulated signal ? 
 (A) 42.8 m  (B) 42.8 mm 
 (C) 21.4 mm (D) 21.4 m 
 Official Ans. by NTA (C) 
  
 
 
5 
 
Sol. 
cm
f 3.5GHz f 3.5MHz ?? 
 Side band frequencies are f
c
 – f
m
 & f
c
 + f
m
. which 
are almost f
c
 
 
c
c
f
?? 
 Minimum length of antenna = 
  
8
9
c
c 3 10
f 4 4 3.5 10 4
??
??
??
 
 = 21.4 mm 
17. A Carnot engine whose heat sinks at 27°C, has an 
efficiency of 25%. By how many degrees 
should the temperature of the source be changed to 
increase the efficiency by 100% of the 
original efficiency ? 
 (A) Increases by 18°C (B) Increase by 200°C  
 (C) Increase by 120°C (D) Increase by 73° 
 Official Ans. by NTA (B)  
  
Sol.  
 
Source 
T
T=273+ 27
  =300K
n=25%
 
 
300
1 0.25
T
?? 
 
300
0.75
T
? 
 T = 400K 
 If efficiency increased by 100% then new 
efficiency ? n’ = 50%  
 
300
1 0.5
T'
?? 
 T' 600K ? 
 Increase in temp = 600 – 400 
          = 200 K    or    200°C 
18. A parallel plate capacitor is formed by two plates 
each of area 30 ? ?cm
2
 separated by 1 mm. A 
material of dielectric strength 3.6 × 10
7
 Vm
-1
 is 
filled between the plates. If the maximum charge 
that can be stored on the capacitor without causing 
any dielectric breakdown is 7 × 10
-6
 C, the value of 
dielectric constant of the material is : 
 
?
??
??
??
??
??
??
??
9 2 2
0
1
Use : 9 10 Nm C
4
 
 (A) 1.66  (B) 1.75 
 (C) 2.25  (D) 2.33 
 Official Ans. by NTA (D) 
  
Sol. 
6
47
0
9
q 7 10
K
1
AE
30 10 3.6 10
4 9 10
?
?
?
??
?
? ? ? ? ?
? ? ?
 
 
36 7
K 2.33
30 3.6
?
??
?
 
19. The magnetic field at the centre of a circular coil of 
radius r, due to current I flowing through it, is B.  
The magnetic field at a point along the axis at a 
distance 
r
2
 from the centre is : 
 (A) B/2 (B) 2B 
 (C) 
3
2
B
5
??
??
??
 (D) 
3
2
B
3
??
??
??
 
 Official Ans. by NTA (C) 
  
Sol. 
2
00
Ca 2 2 3/2
I Ir
B ,B
2r 2(x r )
??
??
?
 
 At  
r
x
2
? 
 
2
0
a 3/2
2
2
Ir
B
r
2r
4
?
?
??
?
??
??
 
 
3/2
2
00
3/2
2
Ir I 4
2r 5
5
2r
4
?? ??
??
??
??
??
??
??
 
 
3
0
I 2
2r
5
? ??
?
??
??