JEE Main 2022 Question Paper 28 July Shift 1 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Thursday 28
th
 July, 2022)             TIME : 9 : 00 AM  to 12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTON 
 
 
 
 
 
 
 
SECTION-A 
1. The dimensions of 
2
0
B ??
??
?
??
 will be : 
 (if 
0
? : permeability of free space and  
 B : magnetic field) 
 (A) [M L
2
 T
–2
] (B) [M L T
–2
] 
 (C) [M L
–1
 T
–2
] (D) [M L
2
 T
–2
 A
–1
] 
 Official Ans. by NTA (C) 
  
Sol. 
2
0
B
u
2 ?
? 
 u ? Energy per unit volume 
 
? ?
2
0
B
u
?
??
?
??
??
22
3
MLT
L
?
??
??
?
??
??
 
12
ML T
??
?? ?
??
 
2. A NCC parade is going at a uniform speed of  
9 km/h under a mango tree on which a monkey is 
sitting at a height of 19.6 m. At any particular 
instant, the monkey drops a mango. A cadet will 
receive the mango whose distance from the tree at 
time of drop is : 
 (Given g = 9.8 m/s
2
) 
 (A) 5 m  (B) 10 m   
 (C) 19.8 m  (D) 24.5 m  
 Official Ans. by NTA (A) 
  
Sol. Monkey 
 t = 0 
Vt
tt ?
? ? ?   
 Time taken by mango 
2n
g
? 
    
2 19.6
9.8
?
?? 2 second 
 Distance = vt  
          
5
92
18
? ? ? = 5m 
3. In two different experiments, an object of mass     
5 kg moving with a speed of 25 ms
–1
 hits two 
different walls and comes to rest within  
 (i) 3 second, (ii) 5 seconds, respectively.  
 Choose the correct option out of the following :  
 (A) Impulse and average force acting on the object 
 will be same for both the cases. 
 (B) Impulse will be same for both the cases but the 
 average force will be different.   
 (C) Average force will be same for both the cases  
  but the impulse will be different.  
 (D) Average force and impulse will be different for 
 both the cases. 
 Official Ans. by NTA (B) 
  
Sol. Impulse = change in momentum 
 IP ?? 
 
aug
P
F
t
?
?
?
 
 
1
t3 ?? 
2
t5 ?? 
 
12
PP ? ? ? 
 
12
II ? 
 F
avg
 in case (i) is more than (ii) 
4. A balloon has mass of 10 g in air. The air escapes 
from the balloon at a uniform rate with velocity  
4.5 cm/s. If the balloon shrinks in 5 s completely. 
Then, the average force acting on that balloon will 
be (in dyne). 
 (A) 3 (B) 9 (C) 12 (D) 18 
 Official Ans. by NTA (B) 
  
Sol. 
dm
Fv
dt
? 
 
10g cm
4.5
5s s
??
?
??
??
2
gcm
9
s
? = 9 dyne 
Page 2


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Thursday 28
th
 July, 2022)             TIME : 9 : 00 AM  to 12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTON 
 
 
 
 
 
 
 
SECTION-A 
1. The dimensions of 
2
0
B ??
??
?
??
 will be : 
 (if 
0
? : permeability of free space and  
 B : magnetic field) 
 (A) [M L
2
 T
–2
] (B) [M L T
–2
] 
 (C) [M L
–1
 T
–2
] (D) [M L
2
 T
–2
 A
–1
] 
 Official Ans. by NTA (C) 
  
Sol. 
2
0
B
u
2 ?
? 
 u ? Energy per unit volume 
 
? ?
2
0
B
u
?
??
?
??
??
22
3
MLT
L
?
??
??
?
??
??
 
12
ML T
??
?? ?
??
 
2. A NCC parade is going at a uniform speed of  
9 km/h under a mango tree on which a monkey is 
sitting at a height of 19.6 m. At any particular 
instant, the monkey drops a mango. A cadet will 
receive the mango whose distance from the tree at 
time of drop is : 
 (Given g = 9.8 m/s
2
) 
 (A) 5 m  (B) 10 m   
 (C) 19.8 m  (D) 24.5 m  
 Official Ans. by NTA (A) 
  
Sol. Monkey 
 t = 0 
Vt
tt ?
? ? ?   
 Time taken by mango 
2n
g
? 
    
2 19.6
9.8
?
?? 2 second 
 Distance = vt  
          
5
92
18
? ? ? = 5m 
3. In two different experiments, an object of mass     
5 kg moving with a speed of 25 ms
–1
 hits two 
different walls and comes to rest within  
 (i) 3 second, (ii) 5 seconds, respectively.  
 Choose the correct option out of the following :  
 (A) Impulse and average force acting on the object 
 will be same for both the cases. 
 (B) Impulse will be same for both the cases but the 
 average force will be different.   
 (C) Average force will be same for both the cases  
  but the impulse will be different.  
 (D) Average force and impulse will be different for 
 both the cases. 
 Official Ans. by NTA (B) 
  
Sol. Impulse = change in momentum 
 IP ?? 
 
aug
P
F
t
?
?
?
 
 
1
t3 ?? 
2
t5 ?? 
 
12
PP ? ? ? 
 
12
II ? 
 F
avg
 in case (i) is more than (ii) 
4. A balloon has mass of 10 g in air. The air escapes 
from the balloon at a uniform rate with velocity  
4.5 cm/s. If the balloon shrinks in 5 s completely. 
Then, the average force acting on that balloon will 
be (in dyne). 
 (A) 3 (B) 9 (C) 12 (D) 18 
 Official Ans. by NTA (B) 
  
Sol. 
dm
Fv
dt
? 
 
10g cm
4.5
5s s
??
?
??
??
2
gcm
9
s
? = 9 dyne 
 
2 
 
5. If the radius of earth shrinks by 2% while its mass 
remains same. The acceleration due to gravity on 
the earth’s surface will approximately : 
 (A) decrease by 2%  (B) decrease by 4%  
 (C) increase by 2% (D) increase by 4%  
 Official Ans. by NTA (D) 
  
Sol. 
2
GM
g
R
? 
 M = constant 
2
1
g
R
? 
 100 
gR
2 100
gR
??
?? 
 % change = – 2 (–2)  
 % change in g = 4% 
 increase by 4% 
6. The force required to stretch a wire of cross-
section 1 cm
2
 to double its length will be : 
 (Given Yong’s modulus of the wire = 2 × 10
11
 N/m
2
) 
 (A) 1 × 10
7
 N (B) 1.5 × 10
7
 N
 
 
 (C) 2 × 10
7
 N (D) 2.5 × 10
7
 N   
 Official Ans. by NTA (C) 
  
Sol. FA ?
?
? 
 
11 4
2
2 10 10
?
? ??
? ? ?
??
??
 
 
7
2 10 N ??
 
7. A Carnot engine has efficiency of 50%. If the 
temperature of sink is reduced by 40°C, its 
efficiency increases by 30%. The temperature of 
the source will be : 
 (A) 166.7 K  (B) 255.1 K  
 (C) 266.7 K  (D) 367.7 K 
 Official Ans. by NTA (C) 
  
 
Sol. 
L
H
T
1
T
?? ? 
 
L
H
T 1
1
2T
?? 
 
? ?
L
H
T 40 1
1 3 1
2T
?? ?
? ? ?
??
??
 
 ? ?
H
1 1 40
13
2 2 T
? ? ?    
H
T 266.7K ? 
8. Given below are two statements : 
 Statement I :The average momentum of a 
molecule in a sample of an ideal gas depends on 
temperature. 
 Statement II : The rms speed of oxygen molecules 
in a gas is v. If the temperature is doubled and the 
oxygen molecules dissociate into oxygen atoms, 
the rms speed will become 2v. 
 In the light of the above statements, 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 (D) 
  
Sol. [P
avg
 = 0] (due to random motion) 
 
rms
3RT
v
M
? 
 T
new
 = 2T 
 M
new
 = 
M
2
 
 
new
2T
v
M/2
v
T
M
? 
 v
new 
= 2v 
Page 3


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Thursday 28
th
 July, 2022)             TIME : 9 : 00 AM  to 12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTON 
 
 
 
 
 
 
 
SECTION-A 
1. The dimensions of 
2
0
B ??
??
?
??
 will be : 
 (if 
0
? : permeability of free space and  
 B : magnetic field) 
 (A) [M L
2
 T
–2
] (B) [M L T
–2
] 
 (C) [M L
–1
 T
–2
] (D) [M L
2
 T
–2
 A
–1
] 
 Official Ans. by NTA (C) 
  
Sol. 
2
0
B
u
2 ?
? 
 u ? Energy per unit volume 
 
? ?
2
0
B
u
?
??
?
??
??
22
3
MLT
L
?
??
??
?
??
??
 
12
ML T
??
?? ?
??
 
2. A NCC parade is going at a uniform speed of  
9 km/h under a mango tree on which a monkey is 
sitting at a height of 19.6 m. At any particular 
instant, the monkey drops a mango. A cadet will 
receive the mango whose distance from the tree at 
time of drop is : 
 (Given g = 9.8 m/s
2
) 
 (A) 5 m  (B) 10 m   
 (C) 19.8 m  (D) 24.5 m  
 Official Ans. by NTA (A) 
  
Sol. Monkey 
 t = 0 
Vt
tt ?
? ? ?   
 Time taken by mango 
2n
g
? 
    
2 19.6
9.8
?
?? 2 second 
 Distance = vt  
          
5
92
18
? ? ? = 5m 
3. In two different experiments, an object of mass     
5 kg moving with a speed of 25 ms
–1
 hits two 
different walls and comes to rest within  
 (i) 3 second, (ii) 5 seconds, respectively.  
 Choose the correct option out of the following :  
 (A) Impulse and average force acting on the object 
 will be same for both the cases. 
 (B) Impulse will be same for both the cases but the 
 average force will be different.   
 (C) Average force will be same for both the cases  
  but the impulse will be different.  
 (D) Average force and impulse will be different for 
 both the cases. 
 Official Ans. by NTA (B) 
  
Sol. Impulse = change in momentum 
 IP ?? 
 
aug
P
F
t
?
?
?
 
 
1
t3 ?? 
2
t5 ?? 
 
12
PP ? ? ? 
 
12
II ? 
 F
avg
 in case (i) is more than (ii) 
4. A balloon has mass of 10 g in air. The air escapes 
from the balloon at a uniform rate with velocity  
4.5 cm/s. If the balloon shrinks in 5 s completely. 
Then, the average force acting on that balloon will 
be (in dyne). 
 (A) 3 (B) 9 (C) 12 (D) 18 
 Official Ans. by NTA (B) 
  
Sol. 
dm
Fv
dt
? 
 
10g cm
4.5
5s s
??
?
??
??
2
gcm
9
s
? = 9 dyne 
 
2 
 
5. If the radius of earth shrinks by 2% while its mass 
remains same. The acceleration due to gravity on 
the earth’s surface will approximately : 
 (A) decrease by 2%  (B) decrease by 4%  
 (C) increase by 2% (D) increase by 4%  
 Official Ans. by NTA (D) 
  
Sol. 
2
GM
g
R
? 
 M = constant 
2
1
g
R
? 
 100 
gR
2 100
gR
??
?? 
 % change = – 2 (–2)  
 % change in g = 4% 
 increase by 4% 
6. The force required to stretch a wire of cross-
section 1 cm
2
 to double its length will be : 
 (Given Yong’s modulus of the wire = 2 × 10
11
 N/m
2
) 
 (A) 1 × 10
7
 N (B) 1.5 × 10
7
 N
 
 
 (C) 2 × 10
7
 N (D) 2.5 × 10
7
 N   
 Official Ans. by NTA (C) 
  
Sol. FA ?
?
? 
 
11 4
2
2 10 10
?
? ??
? ? ?
??
??
 
 
7
2 10 N ??
 
7. A Carnot engine has efficiency of 50%. If the 
temperature of sink is reduced by 40°C, its 
efficiency increases by 30%. The temperature of 
the source will be : 
 (A) 166.7 K  (B) 255.1 K  
 (C) 266.7 K  (D) 367.7 K 
 Official Ans. by NTA (C) 
  
 
Sol. 
L
H
T
1
T
?? ? 
 
L
H
T 1
1
2T
?? 
 
? ?
L
H
T 40 1
1 3 1
2T
?? ?
? ? ?
??
??
 
 ? ?
H
1 1 40
13
2 2 T
? ? ?    
H
T 266.7K ? 
8. Given below are two statements : 
 Statement I :The average momentum of a 
molecule in a sample of an ideal gas depends on 
temperature. 
 Statement II : The rms speed of oxygen molecules 
in a gas is v. If the temperature is doubled and the 
oxygen molecules dissociate into oxygen atoms, 
the rms speed will become 2v. 
 In the light of the above statements, 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 (D) 
  
Sol. [P
avg
 = 0] (due to random motion) 
 
rms
3RT
v
M
? 
 T
new
 = 2T 
 M
new
 = 
M
2
 
 
new
2T
v
M/2
v
T
M
? 
 v
new 
= 2v 
 
 
3 
 
?  
9. In the wave equation  
  ? ?
2
y 0.5sin 400 t x m
?
??
?
 
 the velocity of the wave will be : 
 (A) 200 m/s  (B) 200 2 m / s  
 (C) 400 m/s (D) 400 2 m / s 
 Official Ans. by NTA (C) 
  
Sol. 
22
y 0.5sin 400t x
??
??
??
??
??
??
 
 
2
400
?
?
?
? 
 
2
K
?
?
? 
 v
k
?
?  [v = 400 m/s] 
10. Two capacitors, each having capacitance 40 F ? 
are connected in series. The space between one of 
the capacitors is filled with dielectric material of 
dielectric constant K such that the equivalence 
capacitance of the system became 24 F ? . The 
value of K will be : 
 (A) 1.5  (B) 2.5
 
 
 (C) 1.2  (D) 3 
 Official Ans. by NTA (A) 
  
Sol. 
 
C C ?KC 
 
? ?
eq
C KC
KC
C
C KC K 1
??
??
 
 
K40
24
K1
?
?
 
 
? ?
K 1 5 ?? 
11. A wire of resistance R
1
 is drawn out so that its 
length is increased by twice of its original length. 
The ratio of new resistance to original resistance is: 
 (A) 9 : 1 (B) 1 : 9 
 (C) 4 : 1  (D) 3 : 1 
 Official Ans. by NTA (A) 
  
Sol. 
1
1
1
L
R
A
? ? 
 
1
2
1
3L
R
A /3
?
??
?
??
??
1
1
L
9
A
? ? 
 ? 
2
1
R
9
R
? 
12. The current sensitivity of a galvanometer can be 
increased by : 
 (A) decreasing the number of turns   
 (B) increasing the magnetic field  
 (C) decreasing the area of the coil 
 (D) decreasing the torsional constant of the spring  
 Choose the most appropriate answer from the 
options given below : 
 (A) (B) and (C) only (B) (C) and (D) only 
 (C) (A) and (C) only (D) (B) and (D) only 
 Official Ans. by NTA (D) 
  
Sol. 
K
i
NAB
?
??
?
??
??
 
 ? 
d NAB
di K
?
? 
Page 4


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Thursday 28
th
 July, 2022)             TIME : 9 : 00 AM  to 12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTON 
 
 
 
 
 
 
 
SECTION-A 
1. The dimensions of 
2
0
B ??
??
?
??
 will be : 
 (if 
0
? : permeability of free space and  
 B : magnetic field) 
 (A) [M L
2
 T
–2
] (B) [M L T
–2
] 
 (C) [M L
–1
 T
–2
] (D) [M L
2
 T
–2
 A
–1
] 
 Official Ans. by NTA (C) 
  
Sol. 
2
0
B
u
2 ?
? 
 u ? Energy per unit volume 
 
? ?
2
0
B
u
?
??
?
??
??
22
3
MLT
L
?
??
??
?
??
??
 
12
ML T
??
?? ?
??
 
2. A NCC parade is going at a uniform speed of  
9 km/h under a mango tree on which a monkey is 
sitting at a height of 19.6 m. At any particular 
instant, the monkey drops a mango. A cadet will 
receive the mango whose distance from the tree at 
time of drop is : 
 (Given g = 9.8 m/s
2
) 
 (A) 5 m  (B) 10 m   
 (C) 19.8 m  (D) 24.5 m  
 Official Ans. by NTA (A) 
  
Sol. Monkey 
 t = 0 
Vt
tt ?
? ? ?   
 Time taken by mango 
2n
g
? 
    
2 19.6
9.8
?
?? 2 second 
 Distance = vt  
          
5
92
18
? ? ? = 5m 
3. In two different experiments, an object of mass     
5 kg moving with a speed of 25 ms
–1
 hits two 
different walls and comes to rest within  
 (i) 3 second, (ii) 5 seconds, respectively.  
 Choose the correct option out of the following :  
 (A) Impulse and average force acting on the object 
 will be same for both the cases. 
 (B) Impulse will be same for both the cases but the 
 average force will be different.   
 (C) Average force will be same for both the cases  
  but the impulse will be different.  
 (D) Average force and impulse will be different for 
 both the cases. 
 Official Ans. by NTA (B) 
  
Sol. Impulse = change in momentum 
 IP ?? 
 
aug
P
F
t
?
?
?
 
 
1
t3 ?? 
2
t5 ?? 
 
12
PP ? ? ? 
 
12
II ? 
 F
avg
 in case (i) is more than (ii) 
4. A balloon has mass of 10 g in air. The air escapes 
from the balloon at a uniform rate with velocity  
4.5 cm/s. If the balloon shrinks in 5 s completely. 
Then, the average force acting on that balloon will 
be (in dyne). 
 (A) 3 (B) 9 (C) 12 (D) 18 
 Official Ans. by NTA (B) 
  
Sol. 
dm
Fv
dt
? 
 
10g cm
4.5
5s s
??
?
??
??
2
gcm
9
s
? = 9 dyne 
 
2 
 
5. If the radius of earth shrinks by 2% while its mass 
remains same. The acceleration due to gravity on 
the earth’s surface will approximately : 
 (A) decrease by 2%  (B) decrease by 4%  
 (C) increase by 2% (D) increase by 4%  
 Official Ans. by NTA (D) 
  
Sol. 
2
GM
g
R
? 
 M = constant 
2
1
g
R
? 
 100 
gR
2 100
gR
??
?? 
 % change = – 2 (–2)  
 % change in g = 4% 
 increase by 4% 
6. The force required to stretch a wire of cross-
section 1 cm
2
 to double its length will be : 
 (Given Yong’s modulus of the wire = 2 × 10
11
 N/m
2
) 
 (A) 1 × 10
7
 N (B) 1.5 × 10
7
 N
 
 
 (C) 2 × 10
7
 N (D) 2.5 × 10
7
 N   
 Official Ans. by NTA (C) 
  
Sol. FA ?
?
? 
 
11 4
2
2 10 10
?
? ??
? ? ?
??
??
 
 
7
2 10 N ??
 
7. A Carnot engine has efficiency of 50%. If the 
temperature of sink is reduced by 40°C, its 
efficiency increases by 30%. The temperature of 
the source will be : 
 (A) 166.7 K  (B) 255.1 K  
 (C) 266.7 K  (D) 367.7 K 
 Official Ans. by NTA (C) 
  
 
Sol. 
L
H
T
1
T
?? ? 
 
L
H
T 1
1
2T
?? 
 
? ?
L
H
T 40 1
1 3 1
2T
?? ?
? ? ?
??
??
 
 ? ?
H
1 1 40
13
2 2 T
? ? ?    
H
T 266.7K ? 
8. Given below are two statements : 
 Statement I :The average momentum of a 
molecule in a sample of an ideal gas depends on 
temperature. 
 Statement II : The rms speed of oxygen molecules 
in a gas is v. If the temperature is doubled and the 
oxygen molecules dissociate into oxygen atoms, 
the rms speed will become 2v. 
 In the light of the above statements, 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 (D) 
  
Sol. [P
avg
 = 0] (due to random motion) 
 
rms
3RT
v
M
? 
 T
new
 = 2T 
 M
new
 = 
M
2
 
 
new
2T
v
M/2
v
T
M
? 
 v
new 
= 2v 
 
 
3 
 
?  
9. In the wave equation  
  ? ?
2
y 0.5sin 400 t x m
?
??
?
 
 the velocity of the wave will be : 
 (A) 200 m/s  (B) 200 2 m / s  
 (C) 400 m/s (D) 400 2 m / s 
 Official Ans. by NTA (C) 
  
Sol. 
22
y 0.5sin 400t x
??
??
??
??
??
??
 
 
2
400
?
?
?
? 
 
2
K
?
?
? 
 v
k
?
?  [v = 400 m/s] 
10. Two capacitors, each having capacitance 40 F ? 
are connected in series. The space between one of 
the capacitors is filled with dielectric material of 
dielectric constant K such that the equivalence 
capacitance of the system became 24 F ? . The 
value of K will be : 
 (A) 1.5  (B) 2.5
 
 
 (C) 1.2  (D) 3 
 Official Ans. by NTA (A) 
  
Sol. 
 
C C ?KC 
 
? ?
eq
C KC
KC
C
C KC K 1
??
??
 
 
K40
24
K1
?
?
 
 
? ?
K 1 5 ?? 
11. A wire of resistance R
1
 is drawn out so that its 
length is increased by twice of its original length. 
The ratio of new resistance to original resistance is: 
 (A) 9 : 1 (B) 1 : 9 
 (C) 4 : 1  (D) 3 : 1 
 Official Ans. by NTA (A) 
  
Sol. 
1
1
1
L
R
A
? ? 
 
1
2
1
3L
R
A /3
?
??
?
??
??
1
1
L
9
A
? ? 
 ? 
2
1
R
9
R
? 
12. The current sensitivity of a galvanometer can be 
increased by : 
 (A) decreasing the number of turns   
 (B) increasing the magnetic field  
 (C) decreasing the area of the coil 
 (D) decreasing the torsional constant of the spring  
 Choose the most appropriate answer from the 
options given below : 
 (A) (B) and (C) only (B) (C) and (D) only 
 (C) (A) and (C) only (D) (B) and (D) only 
 Official Ans. by NTA (D) 
  
Sol. 
K
i
NAB
?
??
?
??
??
 
 ? 
d NAB
di K
?
? 
 
4 
 
13. As shown in the figure, a metallic rod of linear 
density 0.45 kg m
–1
 is lying horizontally on a 
smooth incline plane which makes an angle of 45° 
with the horizontal. The minimum current flowing 
in the rod required to keep it stationary, when  
0.15 T magnetic field is acting on it in the vertical 
upward direction, will be : 
 {Use g = 10 m/s
2
}  
 
 (A) 30 A  (B) 15 A   
 (C) 10 A  (D) 3 A  
 Official Ans. by NTA (A) 
  
Sol.  
 
 mgsin45 ILBcos45 ? ? ? 
 
mg
I
LB
??
??
??
??
 
 
? ? ? ? 0.45 10
0.15
?
 
30A ? 
14. The equation of current in a purely inductive 
circuit is ? ? 5sin 49 t 30 . ? ? ? If the inductance is  
30 mH then the equation for the voltage across the 
inductor, will be : 
 
22
Let
7
??
??
??
??
  
 (A) 1.47sin(49 t 30 ) ? ? ? (B) 1.47sin(49 t 60 ) ? ? ?  
 (C) 23.1sin(49 t 30 ) ? ? ? (D) 23.1sin(49 t 60 ) ? ? ?  
 Official Ans. by NTA (D) 
  
Sol. 
0 0 L
v i x ? 
 ? ?
0
i wL ? 
 
? ? ? ? ? ?
3
5 49 30 10
?
?? ? 
 23.1 ? 
 Voltage will lead current by 90°. 
 ? V = 23.1 sin (49 ? t + 60°) 
15. As shown in the figure, after passing through the 
medium 1. The speed of light v
2
 in medium 2 will 
be : 
 (Given c = 3 × 10
8
 ms
–1
) 
 
 (A) 1.0 × 10
8
 ms
–1
  (B) 0.5 × 10
8
 ms
–1
  
 (C) 1.5 × 10
8
 ms
–1
 (D) 3.0 × 10
8
 ms
–1 
 Official Ans. by NTA (A) 
  
Sol. 
2
air 2
C
v
?
?
?
 
 ? 
? ?
22
rr
2
C
1v
??
? 
 ? ? ? ? ?
2
C
19
v
? 
 ? 
2
C
v
3
? 
16. In normal adjustment, for a refracting telescope, 
the distance between objective and eye piece is    
30 cm. The focal length of the objective, when the 
angular magnification of the telescope is 2, will be: 
 (A) 20 cm  (B) 30 cm  
 (C) 10 cm (D) 15 cm  
 Official Ans. by NTA (A) 
  
Page 5


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Thursday 28
th
 July, 2022)             TIME : 9 : 00 AM  to 12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTON 
 
 
 
 
 
 
 
SECTION-A 
1. The dimensions of 
2
0
B ??
??
?
??
 will be : 
 (if 
0
? : permeability of free space and  
 B : magnetic field) 
 (A) [M L
2
 T
–2
] (B) [M L T
–2
] 
 (C) [M L
–1
 T
–2
] (D) [M L
2
 T
–2
 A
–1
] 
 Official Ans. by NTA (C) 
  
Sol. 
2
0
B
u
2 ?
? 
 u ? Energy per unit volume 
 
? ?
2
0
B
u
?
??
?
??
??
22
3
MLT
L
?
??
??
?
??
??
 
12
ML T
??
?? ?
??
 
2. A NCC parade is going at a uniform speed of  
9 km/h under a mango tree on which a monkey is 
sitting at a height of 19.6 m. At any particular 
instant, the monkey drops a mango. A cadet will 
receive the mango whose distance from the tree at 
time of drop is : 
 (Given g = 9.8 m/s
2
) 
 (A) 5 m  (B) 10 m   
 (C) 19.8 m  (D) 24.5 m  
 Official Ans. by NTA (A) 
  
Sol. Monkey 
 t = 0 
Vt
tt ?
? ? ?   
 Time taken by mango 
2n
g
? 
    
2 19.6
9.8
?
?? 2 second 
 Distance = vt  
          
5
92
18
? ? ? = 5m 
3. In two different experiments, an object of mass     
5 kg moving with a speed of 25 ms
–1
 hits two 
different walls and comes to rest within  
 (i) 3 second, (ii) 5 seconds, respectively.  
 Choose the correct option out of the following :  
 (A) Impulse and average force acting on the object 
 will be same for both the cases. 
 (B) Impulse will be same for both the cases but the 
 average force will be different.   
 (C) Average force will be same for both the cases  
  but the impulse will be different.  
 (D) Average force and impulse will be different for 
 both the cases. 
 Official Ans. by NTA (B) 
  
Sol. Impulse = change in momentum 
 IP ?? 
 
aug
P
F
t
?
?
?
 
 
1
t3 ?? 
2
t5 ?? 
 
12
PP ? ? ? 
 
12
II ? 
 F
avg
 in case (i) is more than (ii) 
4. A balloon has mass of 10 g in air. The air escapes 
from the balloon at a uniform rate with velocity  
4.5 cm/s. If the balloon shrinks in 5 s completely. 
Then, the average force acting on that balloon will 
be (in dyne). 
 (A) 3 (B) 9 (C) 12 (D) 18 
 Official Ans. by NTA (B) 
  
Sol. 
dm
Fv
dt
? 
 
10g cm
4.5
5s s
??
?
??
??
2
gcm
9
s
? = 9 dyne 
 
2 
 
5. If the radius of earth shrinks by 2% while its mass 
remains same. The acceleration due to gravity on 
the earth’s surface will approximately : 
 (A) decrease by 2%  (B) decrease by 4%  
 (C) increase by 2% (D) increase by 4%  
 Official Ans. by NTA (D) 
  
Sol. 
2
GM
g
R
? 
 M = constant 
2
1
g
R
? 
 100 
gR
2 100
gR
??
?? 
 % change = – 2 (–2)  
 % change in g = 4% 
 increase by 4% 
6. The force required to stretch a wire of cross-
section 1 cm
2
 to double its length will be : 
 (Given Yong’s modulus of the wire = 2 × 10
11
 N/m
2
) 
 (A) 1 × 10
7
 N (B) 1.5 × 10
7
 N
 
 
 (C) 2 × 10
7
 N (D) 2.5 × 10
7
 N   
 Official Ans. by NTA (C) 
  
Sol. FA ?
?
? 
 
11 4
2
2 10 10
?
? ??
? ? ?
??
??
 
 
7
2 10 N ??
 
7. A Carnot engine has efficiency of 50%. If the 
temperature of sink is reduced by 40°C, its 
efficiency increases by 30%. The temperature of 
the source will be : 
 (A) 166.7 K  (B) 255.1 K  
 (C) 266.7 K  (D) 367.7 K 
 Official Ans. by NTA (C) 
  
 
Sol. 
L
H
T
1
T
?? ? 
 
L
H
T 1
1
2T
?? 
 
? ?
L
H
T 40 1
1 3 1
2T
?? ?
? ? ?
??
??
 
 ? ?
H
1 1 40
13
2 2 T
? ? ?    
H
T 266.7K ? 
8. Given below are two statements : 
 Statement I :The average momentum of a 
molecule in a sample of an ideal gas depends on 
temperature. 
 Statement II : The rms speed of oxygen molecules 
in a gas is v. If the temperature is doubled and the 
oxygen molecules dissociate into oxygen atoms, 
the rms speed will become 2v. 
 In the light of the above statements, 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 (D) 
  
Sol. [P
avg
 = 0] (due to random motion) 
 
rms
3RT
v
M
? 
 T
new
 = 2T 
 M
new
 = 
M
2
 
 
new
2T
v
M/2
v
T
M
? 
 v
new 
= 2v 
 
 
3 
 
?  
9. In the wave equation  
  ? ?
2
y 0.5sin 400 t x m
?
??
?
 
 the velocity of the wave will be : 
 (A) 200 m/s  (B) 200 2 m / s  
 (C) 400 m/s (D) 400 2 m / s 
 Official Ans. by NTA (C) 
  
Sol. 
22
y 0.5sin 400t x
??
??
??
??
??
??
 
 
2
400
?
?
?
? 
 
2
K
?
?
? 
 v
k
?
?  [v = 400 m/s] 
10. Two capacitors, each having capacitance 40 F ? 
are connected in series. The space between one of 
the capacitors is filled with dielectric material of 
dielectric constant K such that the equivalence 
capacitance of the system became 24 F ? . The 
value of K will be : 
 (A) 1.5  (B) 2.5
 
 
 (C) 1.2  (D) 3 
 Official Ans. by NTA (A) 
  
Sol. 
 
C C ?KC 
 
? ?
eq
C KC
KC
C
C KC K 1
??
??
 
 
K40
24
K1
?
?
 
 
? ?
K 1 5 ?? 
11. A wire of resistance R
1
 is drawn out so that its 
length is increased by twice of its original length. 
The ratio of new resistance to original resistance is: 
 (A) 9 : 1 (B) 1 : 9 
 (C) 4 : 1  (D) 3 : 1 
 Official Ans. by NTA (A) 
  
Sol. 
1
1
1
L
R
A
? ? 
 
1
2
1
3L
R
A /3
?
??
?
??
??
1
1
L
9
A
? ? 
 ? 
2
1
R
9
R
? 
12. The current sensitivity of a galvanometer can be 
increased by : 
 (A) decreasing the number of turns   
 (B) increasing the magnetic field  
 (C) decreasing the area of the coil 
 (D) decreasing the torsional constant of the spring  
 Choose the most appropriate answer from the 
options given below : 
 (A) (B) and (C) only (B) (C) and (D) only 
 (C) (A) and (C) only (D) (B) and (D) only 
 Official Ans. by NTA (D) 
  
Sol. 
K
i
NAB
?
??
?
??
??
 
 ? 
d NAB
di K
?
? 
 
4 
 
13. As shown in the figure, a metallic rod of linear 
density 0.45 kg m
–1
 is lying horizontally on a 
smooth incline plane which makes an angle of 45° 
with the horizontal. The minimum current flowing 
in the rod required to keep it stationary, when  
0.15 T magnetic field is acting on it in the vertical 
upward direction, will be : 
 {Use g = 10 m/s
2
}  
 
 (A) 30 A  (B) 15 A   
 (C) 10 A  (D) 3 A  
 Official Ans. by NTA (A) 
  
Sol.  
 
 mgsin45 ILBcos45 ? ? ? 
 
mg
I
LB
??
??
??
??
 
 
? ? ? ? 0.45 10
0.15
?
 
30A ? 
14. The equation of current in a purely inductive 
circuit is ? ? 5sin 49 t 30 . ? ? ? If the inductance is  
30 mH then the equation for the voltage across the 
inductor, will be : 
 
22
Let
7
??
??
??
??
  
 (A) 1.47sin(49 t 30 ) ? ? ? (B) 1.47sin(49 t 60 ) ? ? ?  
 (C) 23.1sin(49 t 30 ) ? ? ? (D) 23.1sin(49 t 60 ) ? ? ?  
 Official Ans. by NTA (D) 
  
Sol. 
0 0 L
v i x ? 
 ? ?
0
i wL ? 
 
? ? ? ? ? ?
3
5 49 30 10
?
?? ? 
 23.1 ? 
 Voltage will lead current by 90°. 
 ? V = 23.1 sin (49 ? t + 60°) 
15. As shown in the figure, after passing through the 
medium 1. The speed of light v
2
 in medium 2 will 
be : 
 (Given c = 3 × 10
8
 ms
–1
) 
 
 (A) 1.0 × 10
8
 ms
–1
  (B) 0.5 × 10
8
 ms
–1
  
 (C) 1.5 × 10
8
 ms
–1
 (D) 3.0 × 10
8
 ms
–1 
 Official Ans. by NTA (A) 
  
Sol. 
2
air 2
C
v
?
?
?
 
 ? 
? ?
22
rr
2
C
1v
??
? 
 ? ? ? ? ?
2
C
19
v
? 
 ? 
2
C
v
3
? 
16. In normal adjustment, for a refracting telescope, 
the distance between objective and eye piece is    
30 cm. The focal length of the objective, when the 
angular magnification of the telescope is 2, will be: 
 (A) 20 cm  (B) 30 cm  
 (C) 10 cm (D) 15 cm  
 Official Ans. by NTA (A) 
  
 
 
5 
 
?  
Sol. 
0e
f f 30 ?? 
 
0
e
f
m
f
? 
 
0
0e
e
f
2 f 2f
f
? ? ? 
 So 
0
0
f
f 30
2
?? 
 
0
f 20cm ? 
17. The equation 
1.227
nm
x
?? can be used to find the 
de-Brogli wavelength of an electron. In this 
equation x stands for : 
 Where,  
 m = mass of electron 
 P = momentum of electron 
 K = Kinetic energy of electron 
 V = Accelerating potential in volts for electron   
 (A) mK  (B) P  
 (C) K  (D) V 
 Official Ans. by NTA (D) 
  
Sol. 
h
m
?
?
? (de-Broglie’s wavelength) 
 
? ?
h
2m K E ?
? 
 
h
h
2mqV
? 
 Putting the values of m ; q 
 We get 
1 22
nm
V
?
? ? 
18. The half life period of a radioactive substance is  
60 days. The time taken for 
7
th
8
 of its original 
mass to disintegrate will be : 
 (A) 120 days  (B) 130 days  
 (C) 180 days  (D) 20 days  
 Official Ans. by NTA (C) 
  
Sol. 7/8 disintegrates means 1/8 remains 
 Or 
3
1
2
??
??
??
  
 ? 3 half lives 
  = 180 days 
19. Identify the solar cell characteristics from the 
following options : 
 (A)  (B)   
 (C)  (D)   
 Official Ans. by NTA (B) 
  
Sol. Conceptual / theory 
20. In the case of amplitude modulation to avoid 
distortion the modulation index () ? should be : 
 (A) 1 ??  (B) 1 ??  
 (C) 2 ??  (D) 0 ?? 
 Official Ans. by NTA (A) 
  
Sol. 
m
c
A
A
? ? 
 1 ? ? to avoid distortion 
 because µ > 1 will result in interference between 
career frequency & message frequency.