JEE Main 2022 Question Paper 29 July Shift 2 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Friday 29
th
 July, 2022)                 TIME : 3 : 00 PM  to  06 : 00 PM 
 
PHYSICS 
 
TEST PAPER WITH SOLUTION 
 
 
 
  
 
 
 
SECTION-A 
1. Two identical metallic spheres A and B when 
placed at certain distance in air repel each other 
with a force of F. Another identical uncharged 
sphere C is first placed in contact with A and then 
in contact with B and finally placed at midpoint 
between spheres A and B. The force experienced 
by sphere C will be : 
 (A) 3F/2 (B) 3F/4 
 (C) F  (D) 2F 
 Official Ans. by NTA (B) 
  
Sol. Let q
A
 = q
B 
= q 
 
A B
r
 
2
2
Kq
F
r
? 
 When C is placed in contact with A, charge on A 
& C will be = 
q
2
 
 Now C is placed in contact with B, charge on B & 
C will be = 
q
q
3q
2
24
?
? 
 Now, 
 
A B
F
1
C
F
2
r
2
r
2
3q
4
3q
4
q
2
 
 
21
2
3q q
KK
42
F' F F
r
4
??
?
??
??
? ? ? .
3q
4
 
 
2
2
3Kq 3F
4 4r
??   (B) 
2. Match List I with List II. 
List I List II 
A. Torque I. Nms
–1
 
B. Stress II. J kg
–1
 
C. 
Latent 
Heat III. Nm 
D. Power IV. Nm
–2
 
 Choose the correct answer from the options given 
below: 
 (A) A-III, B-II, C-I, D-IV 
 (B) A-III, B-IV, C-II, D-I 
 (C) A-IV, B-I, C-III, D-II 
 (D) A-II, B-III, C-I, D-IV 
 Official Ans. by NTA (B) 
  
Sol. Torque = Fr
?
?     Nm 
 Stress = 
Force
Area
     N/m
2 
 
Latent heat = 
Energy
Mass
  J Kg
–1 
 
Power = 
Work
Time
  N ms
–1
  
 A-III, B-IV, C-II, D-I 
3. Two identical thin metal plates has charge q
1
and q
2
 
respectively such that q
1
 > q
2
. The plates were 
brought close to each other to form a parallel plate 
capacitor of capacitance C. The potential 
difference between them is : 
 (A) 
? ?
12
qq
C
?
 (B) 
? ?
12
qq
C
?
   
 (C) 
? ?
12
qq
2C
?
 (D) 
? ?
12
2 q q
C
?
 
 Official Ans. by NTA (C) 
  
Sol. Electric field between plates 
12
0
qq
E
2A
?
?
?
 
 V = Ed = 
12
0
qq
d
2A
?
?
 
 V = 
12
qq
2C
?
 
Page 2


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Friday 29
th
 July, 2022)                 TIME : 3 : 00 PM  to  06 : 00 PM 
 
PHYSICS 
 
TEST PAPER WITH SOLUTION 
 
 
 
  
 
 
 
SECTION-A 
1. Two identical metallic spheres A and B when 
placed at certain distance in air repel each other 
with a force of F. Another identical uncharged 
sphere C is first placed in contact with A and then 
in contact with B and finally placed at midpoint 
between spheres A and B. The force experienced 
by sphere C will be : 
 (A) 3F/2 (B) 3F/4 
 (C) F  (D) 2F 
 Official Ans. by NTA (B) 
  
Sol. Let q
A
 = q
B 
= q 
 
A B
r
 
2
2
Kq
F
r
? 
 When C is placed in contact with A, charge on A 
& C will be = 
q
2
 
 Now C is placed in contact with B, charge on B & 
C will be = 
q
q
3q
2
24
?
? 
 Now, 
 
A B
F
1
C
F
2
r
2
r
2
3q
4
3q
4
q
2
 
 
21
2
3q q
KK
42
F' F F
r
4
??
?
??
??
? ? ? .
3q
4
 
 
2
2
3Kq 3F
4 4r
??   (B) 
2. Match List I with List II. 
List I List II 
A. Torque I. Nms
–1
 
B. Stress II. J kg
–1
 
C. 
Latent 
Heat III. Nm 
D. Power IV. Nm
–2
 
 Choose the correct answer from the options given 
below: 
 (A) A-III, B-II, C-I, D-IV 
 (B) A-III, B-IV, C-II, D-I 
 (C) A-IV, B-I, C-III, D-II 
 (D) A-II, B-III, C-I, D-IV 
 Official Ans. by NTA (B) 
  
Sol. Torque = Fr
?
?     Nm 
 Stress = 
Force
Area
     N/m
2 
 
Latent heat = 
Energy
Mass
  J Kg
–1 
 
Power = 
Work
Time
  N ms
–1
  
 A-III, B-IV, C-II, D-I 
3. Two identical thin metal plates has charge q
1
and q
2
 
respectively such that q
1
 > q
2
. The plates were 
brought close to each other to form a parallel plate 
capacitor of capacitance C. The potential 
difference between them is : 
 (A) 
? ?
12
qq
C
?
 (B) 
? ?
12
qq
C
?
   
 (C) 
? ?
12
qq
2C
?
 (D) 
? ?
12
2 q q
C
?
 
 Official Ans. by NTA (C) 
  
Sol. Electric field between plates 
12
0
qq
E
2A
?
?
?
 
 V = Ed = 
12
0
qq
d
2A
?
?
 
 V = 
12
qq
2C
?
 
 
2 
 
 
4. Given below are two statements: one is labelled as 
Assertion A and the other is labelled as Reason R. 
 Assertion A: Alloys such as constantan and 
manganin are used in making standard resistance 
coils. 
 Reason R: Constantan and manganin have very 
small value of temperature coefficient of 
resistance. 
 In the light of the above statements, choose the 
correct answer from the options given below. 
 (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. Theory based 
5. A 1 m long wire is broken into two unequal parts  
X and Y The X part of the wire is streched into 
another wire W. Length of W is twice the length of 
X and the resistance of W is twice that of Y. Find 
the ratio of length of X and Y. 
 (A) 1 : 4   (B) 1 : 2 
 (C) 4 :1  (D) 2 : 1 
 Official Ans. by NTA (B) 
  
Sol. 
Y X
? 1– ?
 
 
W
2 ?
 
 
XX
YY
R
R
? 
 When wire is stretched to double of its length, then 
resistance becomes 4 times 
 R
W
 = 4R
X
 = 2R
Y 
 
X
Y
R 1
R2
? 
 
X
y
1
So.
2
? 
6. A wire X of length 50 cm carrying a current of 2 A 
is placed parallel to a long wire Y of length 5 m. 
The wire Y carries a current of 3 A. The distance 
between two wires is 5 cm and currents flow in the 
same direction. The force acting on the wire Y is : 
X
2A 3A
5cm
Y
 
 (A) 1.2 × 10
–5
 N directed towards wire X. 
 (B) 1.2 × 10
–4
 N directed away from wire X.
 
 
 (C) 1.2 × 10
–4
 N directed towards wire X.  
 (D) 2.4 × 10
–5
 N directed towards wire X. 
 Official Ans. by NTA (A) 
  
Sol. Force of interaction = I
1
 ?
1
 B
12 
 
0 1 2
1
II
2r
?
?
?
 
 
7
2
4 10 6 0.5
2 5 10
?
?
? ? ? ?
?
? ? ?
 
 = 1.2 × 10
–5
 towards X 
7. A juggler throws balls vertically upwards with  
same initial velocity in air. When the first ball 
reaches its highest position, he throws the next 
ball. Assuming the juggler throws n balls per 
second, the maximum height the balls can reach is 
 (A) g/2n  (B) g/n 
 (C) 2gn  (D) g/2n
2
 
 Official Ans. by NTA (D) 
  
Sol. Time taken by ball to reach highest point = 
u
g
 
 Frequency of throw = 
g
n
u
? 
 
g
u
n
?? 
 
2
2
max
g
u n
H
2g 2g
??
??
??
?? 
 
2
g
2n
 
Page 3


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Friday 29
th
 July, 2022)                 TIME : 3 : 00 PM  to  06 : 00 PM 
 
PHYSICS 
 
TEST PAPER WITH SOLUTION 
 
 
 
  
 
 
 
SECTION-A 
1. Two identical metallic spheres A and B when 
placed at certain distance in air repel each other 
with a force of F. Another identical uncharged 
sphere C is first placed in contact with A and then 
in contact with B and finally placed at midpoint 
between spheres A and B. The force experienced 
by sphere C will be : 
 (A) 3F/2 (B) 3F/4 
 (C) F  (D) 2F 
 Official Ans. by NTA (B) 
  
Sol. Let q
A
 = q
B 
= q 
 
A B
r
 
2
2
Kq
F
r
? 
 When C is placed in contact with A, charge on A 
& C will be = 
q
2
 
 Now C is placed in contact with B, charge on B & 
C will be = 
q
q
3q
2
24
?
? 
 Now, 
 
A B
F
1
C
F
2
r
2
r
2
3q
4
3q
4
q
2
 
 
21
2
3q q
KK
42
F' F F
r
4
??
?
??
??
? ? ? .
3q
4
 
 
2
2
3Kq 3F
4 4r
??   (B) 
2. Match List I with List II. 
List I List II 
A. Torque I. Nms
–1
 
B. Stress II. J kg
–1
 
C. 
Latent 
Heat III. Nm 
D. Power IV. Nm
–2
 
 Choose the correct answer from the options given 
below: 
 (A) A-III, B-II, C-I, D-IV 
 (B) A-III, B-IV, C-II, D-I 
 (C) A-IV, B-I, C-III, D-II 
 (D) A-II, B-III, C-I, D-IV 
 Official Ans. by NTA (B) 
  
Sol. Torque = Fr
?
?     Nm 
 Stress = 
Force
Area
     N/m
2 
 
Latent heat = 
Energy
Mass
  J Kg
–1 
 
Power = 
Work
Time
  N ms
–1
  
 A-III, B-IV, C-II, D-I 
3. Two identical thin metal plates has charge q
1
and q
2
 
respectively such that q
1
 > q
2
. The plates were 
brought close to each other to form a parallel plate 
capacitor of capacitance C. The potential 
difference between them is : 
 (A) 
? ?
12
qq
C
?
 (B) 
? ?
12
qq
C
?
   
 (C) 
? ?
12
qq
2C
?
 (D) 
? ?
12
2 q q
C
?
 
 Official Ans. by NTA (C) 
  
Sol. Electric field between plates 
12
0
qq
E
2A
?
?
?
 
 V = Ed = 
12
0
qq
d
2A
?
?
 
 V = 
12
qq
2C
?
 
 
2 
 
 
4. Given below are two statements: one is labelled as 
Assertion A and the other is labelled as Reason R. 
 Assertion A: Alloys such as constantan and 
manganin are used in making standard resistance 
coils. 
 Reason R: Constantan and manganin have very 
small value of temperature coefficient of 
resistance. 
 In the light of the above statements, choose the 
correct answer from the options given below. 
 (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. Theory based 
5. A 1 m long wire is broken into two unequal parts  
X and Y The X part of the wire is streched into 
another wire W. Length of W is twice the length of 
X and the resistance of W is twice that of Y. Find 
the ratio of length of X and Y. 
 (A) 1 : 4   (B) 1 : 2 
 (C) 4 :1  (D) 2 : 1 
 Official Ans. by NTA (B) 
  
Sol. 
Y X
? 1– ?
 
 
W
2 ?
 
 
XX
YY
R
R
? 
 When wire is stretched to double of its length, then 
resistance becomes 4 times 
 R
W
 = 4R
X
 = 2R
Y 
 
X
Y
R 1
R2
? 
 
X
y
1
So.
2
? 
6. A wire X of length 50 cm carrying a current of 2 A 
is placed parallel to a long wire Y of length 5 m. 
The wire Y carries a current of 3 A. The distance 
between two wires is 5 cm and currents flow in the 
same direction. The force acting on the wire Y is : 
X
2A 3A
5cm
Y
 
 (A) 1.2 × 10
–5
 N directed towards wire X. 
 (B) 1.2 × 10
–4
 N directed away from wire X.
 
 
 (C) 1.2 × 10
–4
 N directed towards wire X.  
 (D) 2.4 × 10
–5
 N directed towards wire X. 
 Official Ans. by NTA (A) 
  
Sol. Force of interaction = I
1
 ?
1
 B
12 
 
0 1 2
1
II
2r
?
?
?
 
 
7
2
4 10 6 0.5
2 5 10
?
?
? ? ? ?
?
? ? ?
 
 = 1.2 × 10
–5
 towards X 
7. A juggler throws balls vertically upwards with  
same initial velocity in air. When the first ball 
reaches its highest position, he throws the next 
ball. Assuming the juggler throws n balls per 
second, the maximum height the balls can reach is 
 (A) g/2n  (B) g/n 
 (C) 2gn  (D) g/2n
2
 
 Official Ans. by NTA (D) 
  
Sol. Time taken by ball to reach highest point = 
u
g
 
 Frequency of throw = 
g
n
u
? 
 
g
u
n
?? 
 
2
2
max
g
u n
H
2g 2g
??
??
??
?? 
 
2
g
2n
 
 
 
3 
 
 
8. A circuit element X when connected to an a.c. 
supply of peak voltage 100 V gives a peak current 
of 5 A which is in phase with the voltage. A 
second element Y when connected to the same a.c. 
supply also gives the same value of peak current 
which lags behind the voltage by 
2
?
. If X and Y 
are connected in series to the same supply, what 
will be the rms value of the current in ampere ? 
 (A) 
10
2
 (B) 
5
2
 (C) 52 (D) 
5
2
 
 Official Ans. by NTA (D) 
  
Sol. Element X should be resistive with R = 20 ? 
 Element Y should be inductive with X
L
 = 20 ? ? 
 When X and Y are connector in series 
 
22
L
Z X R 20 2 ? ? ? 
 
0
0
E 100 5
IA
Z 20 2 2
? ? ? 
 
0
rms
I 5
IA
2 2
??  
9. An unpolarised light beam of intensity 2I
0
 is 
passed through a polaroid P and then through 
another polaroid Q which is oriented in such a way 
that its passing axis makes an angle of 30° relative 
to that of P. The intensity of the emergent light is 
 (A) 
0
I
4
 (B) 
0
I
2
 (C) 
0
3I
4
 (D) 
0
3I
2
 
 Official Ans. by NTA (C) 
  
Sol. 
I
1
I
2
2I
0
 
 ? ?
1 0 0
1
I 2I I
2
?? 
 I
2
 = I
1
 cos
2
30º 
 
0
0
3I 3
I.
44
?? 
10. An ? particle and a proton are accelerated from 
rest through the same potential difference. The 
ratio of linear momenta acquired by above two 
particals will be : 
 (A) 2 :1  (B) 2 2 :1 
 (C) 4 2 : 1  (D) 8 : 1 
 Official Ans. by NTA (B) 
  
Sol. p 2mE 2mqV ?? 
 
p p p
p m q 42
p m q 1 1
? ? ?
? ? ? 
 
22
1
? 
11. Read the following statements: 
 (A) Volume of the nucleus is directly proportional 
 to the mass number. 
 (B) Volume of the nucleus is independent of mass 
 number. 
 (C) Density of the nucleus is directly proportional 
 to the mass number. 
 (D) Density of the nucleus is directly proportional 
 to the cube root of the mass number. 
 (E) Density of the nucleus is independent of the 
 mass number. 
 Choose the correct option from the following 
options. 
 (A) (A) and (D) only. (B) (A) and (E) only. 
 (C) (B) and (E) only. (D) (A) and (C) only 
 Official Ans. by NTA (B) 
  
Sol. R ? A
1/3
 
 
3
4
V R A
3
? ? ? 
 Mass ? A 
 So density is independent of A. 
Page 4


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Friday 29
th
 July, 2022)                 TIME : 3 : 00 PM  to  06 : 00 PM 
 
PHYSICS 
 
TEST PAPER WITH SOLUTION 
 
 
 
  
 
 
 
SECTION-A 
1. Two identical metallic spheres A and B when 
placed at certain distance in air repel each other 
with a force of F. Another identical uncharged 
sphere C is first placed in contact with A and then 
in contact with B and finally placed at midpoint 
between spheres A and B. The force experienced 
by sphere C will be : 
 (A) 3F/2 (B) 3F/4 
 (C) F  (D) 2F 
 Official Ans. by NTA (B) 
  
Sol. Let q
A
 = q
B 
= q 
 
A B
r
 
2
2
Kq
F
r
? 
 When C is placed in contact with A, charge on A 
& C will be = 
q
2
 
 Now C is placed in contact with B, charge on B & 
C will be = 
q
q
3q
2
24
?
? 
 Now, 
 
A B
F
1
C
F
2
r
2
r
2
3q
4
3q
4
q
2
 
 
21
2
3q q
KK
42
F' F F
r
4
??
?
??
??
? ? ? .
3q
4
 
 
2
2
3Kq 3F
4 4r
??   (B) 
2. Match List I with List II. 
List I List II 
A. Torque I. Nms
–1
 
B. Stress II. J kg
–1
 
C. 
Latent 
Heat III. Nm 
D. Power IV. Nm
–2
 
 Choose the correct answer from the options given 
below: 
 (A) A-III, B-II, C-I, D-IV 
 (B) A-III, B-IV, C-II, D-I 
 (C) A-IV, B-I, C-III, D-II 
 (D) A-II, B-III, C-I, D-IV 
 Official Ans. by NTA (B) 
  
Sol. Torque = Fr
?
?     Nm 
 Stress = 
Force
Area
     N/m
2 
 
Latent heat = 
Energy
Mass
  J Kg
–1 
 
Power = 
Work
Time
  N ms
–1
  
 A-III, B-IV, C-II, D-I 
3. Two identical thin metal plates has charge q
1
and q
2
 
respectively such that q
1
 > q
2
. The plates were 
brought close to each other to form a parallel plate 
capacitor of capacitance C. The potential 
difference between them is : 
 (A) 
? ?
12
qq
C
?
 (B) 
? ?
12
qq
C
?
   
 (C) 
? ?
12
qq
2C
?
 (D) 
? ?
12
2 q q
C
?
 
 Official Ans. by NTA (C) 
  
Sol. Electric field between plates 
12
0
qq
E
2A
?
?
?
 
 V = Ed = 
12
0
qq
d
2A
?
?
 
 V = 
12
qq
2C
?
 
 
2 
 
 
4. Given below are two statements: one is labelled as 
Assertion A and the other is labelled as Reason R. 
 Assertion A: Alloys such as constantan and 
manganin are used in making standard resistance 
coils. 
 Reason R: Constantan and manganin have very 
small value of temperature coefficient of 
resistance. 
 In the light of the above statements, choose the 
correct answer from the options given below. 
 (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. Theory based 
5. A 1 m long wire is broken into two unequal parts  
X and Y The X part of the wire is streched into 
another wire W. Length of W is twice the length of 
X and the resistance of W is twice that of Y. Find 
the ratio of length of X and Y. 
 (A) 1 : 4   (B) 1 : 2 
 (C) 4 :1  (D) 2 : 1 
 Official Ans. by NTA (B) 
  
Sol. 
Y X
? 1– ?
 
 
W
2 ?
 
 
XX
YY
R
R
? 
 When wire is stretched to double of its length, then 
resistance becomes 4 times 
 R
W
 = 4R
X
 = 2R
Y 
 
X
Y
R 1
R2
? 
 
X
y
1
So.
2
? 
6. A wire X of length 50 cm carrying a current of 2 A 
is placed parallel to a long wire Y of length 5 m. 
The wire Y carries a current of 3 A. The distance 
between two wires is 5 cm and currents flow in the 
same direction. The force acting on the wire Y is : 
X
2A 3A
5cm
Y
 
 (A) 1.2 × 10
–5
 N directed towards wire X. 
 (B) 1.2 × 10
–4
 N directed away from wire X.
 
 
 (C) 1.2 × 10
–4
 N directed towards wire X.  
 (D) 2.4 × 10
–5
 N directed towards wire X. 
 Official Ans. by NTA (A) 
  
Sol. Force of interaction = I
1
 ?
1
 B
12 
 
0 1 2
1
II
2r
?
?
?
 
 
7
2
4 10 6 0.5
2 5 10
?
?
? ? ? ?
?
? ? ?
 
 = 1.2 × 10
–5
 towards X 
7. A juggler throws balls vertically upwards with  
same initial velocity in air. When the first ball 
reaches its highest position, he throws the next 
ball. Assuming the juggler throws n balls per 
second, the maximum height the balls can reach is 
 (A) g/2n  (B) g/n 
 (C) 2gn  (D) g/2n
2
 
 Official Ans. by NTA (D) 
  
Sol. Time taken by ball to reach highest point = 
u
g
 
 Frequency of throw = 
g
n
u
? 
 
g
u
n
?? 
 
2
2
max
g
u n
H
2g 2g
??
??
??
?? 
 
2
g
2n
 
 
 
3 
 
 
8. A circuit element X when connected to an a.c. 
supply of peak voltage 100 V gives a peak current 
of 5 A which is in phase with the voltage. A 
second element Y when connected to the same a.c. 
supply also gives the same value of peak current 
which lags behind the voltage by 
2
?
. If X and Y 
are connected in series to the same supply, what 
will be the rms value of the current in ampere ? 
 (A) 
10
2
 (B) 
5
2
 (C) 52 (D) 
5
2
 
 Official Ans. by NTA (D) 
  
Sol. Element X should be resistive with R = 20 ? 
 Element Y should be inductive with X
L
 = 20 ? ? 
 When X and Y are connector in series 
 
22
L
Z X R 20 2 ? ? ? 
 
0
0
E 100 5
IA
Z 20 2 2
? ? ? 
 
0
rms
I 5
IA
2 2
??  
9. An unpolarised light beam of intensity 2I
0
 is 
passed through a polaroid P and then through 
another polaroid Q which is oriented in such a way 
that its passing axis makes an angle of 30° relative 
to that of P. The intensity of the emergent light is 
 (A) 
0
I
4
 (B) 
0
I
2
 (C) 
0
3I
4
 (D) 
0
3I
2
 
 Official Ans. by NTA (C) 
  
Sol. 
I
1
I
2
2I
0
 
 ? ?
1 0 0
1
I 2I I
2
?? 
 I
2
 = I
1
 cos
2
30º 
 
0
0
3I 3
I.
44
?? 
10. An ? particle and a proton are accelerated from 
rest through the same potential difference. The 
ratio of linear momenta acquired by above two 
particals will be : 
 (A) 2 :1  (B) 2 2 :1 
 (C) 4 2 : 1  (D) 8 : 1 
 Official Ans. by NTA (B) 
  
Sol. p 2mE 2mqV ?? 
 
p p p
p m q 42
p m q 1 1
? ? ?
? ? ? 
 
22
1
? 
11. Read the following statements: 
 (A) Volume of the nucleus is directly proportional 
 to the mass number. 
 (B) Volume of the nucleus is independent of mass 
 number. 
 (C) Density of the nucleus is directly proportional 
 to the mass number. 
 (D) Density of the nucleus is directly proportional 
 to the cube root of the mass number. 
 (E) Density of the nucleus is independent of the 
 mass number. 
 Choose the correct option from the following 
options. 
 (A) (A) and (D) only. (B) (A) and (E) only. 
 (C) (B) and (E) only. (D) (A) and (C) only 
 Official Ans. by NTA (B) 
  
Sol. R ? A
1/3
 
 
3
4
V R A
3
? ? ? 
 Mass ? A 
 So density is independent of A. 
 
4 
 
 
12. An object of mass 1 kg is taken to a height from 
the surface of earth which is equal to three times 
the radius of earth. The gain in potential energy of 
the object will be  
 [If, g=10ms
–2
 and radius of earth = 6400 km] 
 (A) 48 MJ  (B) 24 MJ 
 (C) 36 MJ  (D) 12 MJ 
 Official Ans. by NTA (A) 
  
Sol. 
i
GMm
U
R
?
? 
 
f
GMm
U
4R
?? 
 
fi
3GMm
U U U
4R
? ? ? ? 
 
3
mgR
4
? 
 
5
3
1 10 64 10
4
? ? ? ? ? 
 = 48 MJ 
13. A ball is released from a height h. If t
1
 and t
2
 be the 
time required to complete first half and second half 
of the distance respectively. Then, choose the 
correct relation between t
1
 and t
2
.  
 (A) 
? ?
12
t 2 t ? (B) 
? ?
12
t 2 1 t ?? 
 (C) 
? ?
21
t 2 1 t ?? (D) 
? ?
21
t 2 1 t ?? 
 Official Ans. by NTA (D) 
  
Sol. For first 
h
2
 
 
2
1
h1
gt
22
? 
 For total height h 
 ? ?
2
12
1
h g t t
2
?? 
 
1
12
t 1
tt 2
?
?
 
 
2
1
t
12
t
?? 
 
1
2
t 1
t 21
?
?
 
 
? ? 21
t 2 1 t ?? 
14. Two bodies of masses m
1
 = 5 kg and m
2
 = 3 kg are 
connected by a light string going over a smooth 
light pulley on a smooth inclined plane as shown in 
the figure. The system is at rest. The force exerted 
by the inclined plane on the body of mass m
1
 will 
be :[Take g = 10 ms
–2
] 
 
?
m
1
m
2
 
 (A) 30 N  (B) 40 N 
 (C) 50 N  (D) 60 N 
 Official Ans. by NTA (B) 
  
Sol. For equilibrium m
2
g = m
1
g sin ? 
 
2
1
m 3
sin
m5
? ? ? 
 
4
cos
5
?? 
 Normal force on m
1
 = 5g cos ? 
 
4
5 10 40 N
5
? ? ? ? 
15. If momentum of a body is increased by 20%, then 
its kinetic energy increases by : 
 (A) 36% (B) 40% 
 (C) 44%  (D) 48% 
 Official Ans. by NTA (C) 
  
Sol. 
20
P' P P 1.2 P
100
? ? ? 
 % change in KE = 
K' K
100
K
?
? 
 
22
2
P' P
2m 2m
100
P
2m
??
?
??
?? ??
??
??
??
 
 = [(1.2)
2
 – 1] × 100 
 = 44 % 
Page 5


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Friday 29
th
 July, 2022)                 TIME : 3 : 00 PM  to  06 : 00 PM 
 
PHYSICS 
 
TEST PAPER WITH SOLUTION 
 
 
 
  
 
 
 
SECTION-A 
1. Two identical metallic spheres A and B when 
placed at certain distance in air repel each other 
with a force of F. Another identical uncharged 
sphere C is first placed in contact with A and then 
in contact with B and finally placed at midpoint 
between spheres A and B. The force experienced 
by sphere C will be : 
 (A) 3F/2 (B) 3F/4 
 (C) F  (D) 2F 
 Official Ans. by NTA (B) 
  
Sol. Let q
A
 = q
B 
= q 
 
A B
r
 
2
2
Kq
F
r
? 
 When C is placed in contact with A, charge on A 
& C will be = 
q
2
 
 Now C is placed in contact with B, charge on B & 
C will be = 
q
q
3q
2
24
?
? 
 Now, 
 
A B
F
1
C
F
2
r
2
r
2
3q
4
3q
4
q
2
 
 
21
2
3q q
KK
42
F' F F
r
4
??
?
??
??
? ? ? .
3q
4
 
 
2
2
3Kq 3F
4 4r
??   (B) 
2. Match List I with List II. 
List I List II 
A. Torque I. Nms
–1
 
B. Stress II. J kg
–1
 
C. 
Latent 
Heat III. Nm 
D. Power IV. Nm
–2
 
 Choose the correct answer from the options given 
below: 
 (A) A-III, B-II, C-I, D-IV 
 (B) A-III, B-IV, C-II, D-I 
 (C) A-IV, B-I, C-III, D-II 
 (D) A-II, B-III, C-I, D-IV 
 Official Ans. by NTA (B) 
  
Sol. Torque = Fr
?
?     Nm 
 Stress = 
Force
Area
     N/m
2 
 
Latent heat = 
Energy
Mass
  J Kg
–1 
 
Power = 
Work
Time
  N ms
–1
  
 A-III, B-IV, C-II, D-I 
3. Two identical thin metal plates has charge q
1
and q
2
 
respectively such that q
1
 > q
2
. The plates were 
brought close to each other to form a parallel plate 
capacitor of capacitance C. The potential 
difference between them is : 
 (A) 
? ?
12
qq
C
?
 (B) 
? ?
12
qq
C
?
   
 (C) 
? ?
12
qq
2C
?
 (D) 
? ?
12
2 q q
C
?
 
 Official Ans. by NTA (C) 
  
Sol. Electric field between plates 
12
0
qq
E
2A
?
?
?
 
 V = Ed = 
12
0
qq
d
2A
?
?
 
 V = 
12
qq
2C
?
 
 
2 
 
 
4. Given below are two statements: one is labelled as 
Assertion A and the other is labelled as Reason R. 
 Assertion A: Alloys such as constantan and 
manganin are used in making standard resistance 
coils. 
 Reason R: Constantan and manganin have very 
small value of temperature coefficient of 
resistance. 
 In the light of the above statements, choose the 
correct answer from the options given below. 
 (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. Theory based 
5. A 1 m long wire is broken into two unequal parts  
X and Y The X part of the wire is streched into 
another wire W. Length of W is twice the length of 
X and the resistance of W is twice that of Y. Find 
the ratio of length of X and Y. 
 (A) 1 : 4   (B) 1 : 2 
 (C) 4 :1  (D) 2 : 1 
 Official Ans. by NTA (B) 
  
Sol. 
Y X
? 1– ?
 
 
W
2 ?
 
 
XX
YY
R
R
? 
 When wire is stretched to double of its length, then 
resistance becomes 4 times 
 R
W
 = 4R
X
 = 2R
Y 
 
X
Y
R 1
R2
? 
 
X
y
1
So.
2
? 
6. A wire X of length 50 cm carrying a current of 2 A 
is placed parallel to a long wire Y of length 5 m. 
The wire Y carries a current of 3 A. The distance 
between two wires is 5 cm and currents flow in the 
same direction. The force acting on the wire Y is : 
X
2A 3A
5cm
Y
 
 (A) 1.2 × 10
–5
 N directed towards wire X. 
 (B) 1.2 × 10
–4
 N directed away from wire X.
 
 
 (C) 1.2 × 10
–4
 N directed towards wire X.  
 (D) 2.4 × 10
–5
 N directed towards wire X. 
 Official Ans. by NTA (A) 
  
Sol. Force of interaction = I
1
 ?
1
 B
12 
 
0 1 2
1
II
2r
?
?
?
 
 
7
2
4 10 6 0.5
2 5 10
?
?
? ? ? ?
?
? ? ?
 
 = 1.2 × 10
–5
 towards X 
7. A juggler throws balls vertically upwards with  
same initial velocity in air. When the first ball 
reaches its highest position, he throws the next 
ball. Assuming the juggler throws n balls per 
second, the maximum height the balls can reach is 
 (A) g/2n  (B) g/n 
 (C) 2gn  (D) g/2n
2
 
 Official Ans. by NTA (D) 
  
Sol. Time taken by ball to reach highest point = 
u
g
 
 Frequency of throw = 
g
n
u
? 
 
g
u
n
?? 
 
2
2
max
g
u n
H
2g 2g
??
??
??
?? 
 
2
g
2n
 
 
 
3 
 
 
8. A circuit element X when connected to an a.c. 
supply of peak voltage 100 V gives a peak current 
of 5 A which is in phase with the voltage. A 
second element Y when connected to the same a.c. 
supply also gives the same value of peak current 
which lags behind the voltage by 
2
?
. If X and Y 
are connected in series to the same supply, what 
will be the rms value of the current in ampere ? 
 (A) 
10
2
 (B) 
5
2
 (C) 52 (D) 
5
2
 
 Official Ans. by NTA (D) 
  
Sol. Element X should be resistive with R = 20 ? 
 Element Y should be inductive with X
L
 = 20 ? ? 
 When X and Y are connector in series 
 
22
L
Z X R 20 2 ? ? ? 
 
0
0
E 100 5
IA
Z 20 2 2
? ? ? 
 
0
rms
I 5
IA
2 2
??  
9. An unpolarised light beam of intensity 2I
0
 is 
passed through a polaroid P and then through 
another polaroid Q which is oriented in such a way 
that its passing axis makes an angle of 30° relative 
to that of P. The intensity of the emergent light is 
 (A) 
0
I
4
 (B) 
0
I
2
 (C) 
0
3I
4
 (D) 
0
3I
2
 
 Official Ans. by NTA (C) 
  
Sol. 
I
1
I
2
2I
0
 
 ? ?
1 0 0
1
I 2I I
2
?? 
 I
2
 = I
1
 cos
2
30º 
 
0
0
3I 3
I.
44
?? 
10. An ? particle and a proton are accelerated from 
rest through the same potential difference. The 
ratio of linear momenta acquired by above two 
particals will be : 
 (A) 2 :1  (B) 2 2 :1 
 (C) 4 2 : 1  (D) 8 : 1 
 Official Ans. by NTA (B) 
  
Sol. p 2mE 2mqV ?? 
 
p p p
p m q 42
p m q 1 1
? ? ?
? ? ? 
 
22
1
? 
11. Read the following statements: 
 (A) Volume of the nucleus is directly proportional 
 to the mass number. 
 (B) Volume of the nucleus is independent of mass 
 number. 
 (C) Density of the nucleus is directly proportional 
 to the mass number. 
 (D) Density of the nucleus is directly proportional 
 to the cube root of the mass number. 
 (E) Density of the nucleus is independent of the 
 mass number. 
 Choose the correct option from the following 
options. 
 (A) (A) and (D) only. (B) (A) and (E) only. 
 (C) (B) and (E) only. (D) (A) and (C) only 
 Official Ans. by NTA (B) 
  
Sol. R ? A
1/3
 
 
3
4
V R A
3
? ? ? 
 Mass ? A 
 So density is independent of A. 
 
4 
 
 
12. An object of mass 1 kg is taken to a height from 
the surface of earth which is equal to three times 
the radius of earth. The gain in potential energy of 
the object will be  
 [If, g=10ms
–2
 and radius of earth = 6400 km] 
 (A) 48 MJ  (B) 24 MJ 
 (C) 36 MJ  (D) 12 MJ 
 Official Ans. by NTA (A) 
  
Sol. 
i
GMm
U
R
?
? 
 
f
GMm
U
4R
?? 
 
fi
3GMm
U U U
4R
? ? ? ? 
 
3
mgR
4
? 
 
5
3
1 10 64 10
4
? ? ? ? ? 
 = 48 MJ 
13. A ball is released from a height h. If t
1
 and t
2
 be the 
time required to complete first half and second half 
of the distance respectively. Then, choose the 
correct relation between t
1
 and t
2
.  
 (A) 
? ?
12
t 2 t ? (B) 
? ?
12
t 2 1 t ?? 
 (C) 
? ?
21
t 2 1 t ?? (D) 
? ?
21
t 2 1 t ?? 
 Official Ans. by NTA (D) 
  
Sol. For first 
h
2
 
 
2
1
h1
gt
22
? 
 For total height h 
 ? ?
2
12
1
h g t t
2
?? 
 
1
12
t 1
tt 2
?
?
 
 
2
1
t
12
t
?? 
 
1
2
t 1
t 21
?
?
 
 
? ? 21
t 2 1 t ?? 
14. Two bodies of masses m
1
 = 5 kg and m
2
 = 3 kg are 
connected by a light string going over a smooth 
light pulley on a smooth inclined plane as shown in 
the figure. The system is at rest. The force exerted 
by the inclined plane on the body of mass m
1
 will 
be :[Take g = 10 ms
–2
] 
 
?
m
1
m
2
 
 (A) 30 N  (B) 40 N 
 (C) 50 N  (D) 60 N 
 Official Ans. by NTA (B) 
  
Sol. For equilibrium m
2
g = m
1
g sin ? 
 
2
1
m 3
sin
m5
? ? ? 
 
4
cos
5
?? 
 Normal force on m
1
 = 5g cos ? 
 
4
5 10 40 N
5
? ? ? ? 
15. If momentum of a body is increased by 20%, then 
its kinetic energy increases by : 
 (A) 36% (B) 40% 
 (C) 44%  (D) 48% 
 Official Ans. by NTA (C) 
  
Sol. 
20
P' P P 1.2 P
100
? ? ? 
 % change in KE = 
K' K
100
K
?
? 
 
22
2
P' P
2m 2m
100
P
2m
??
?
??
?? ??
??
??
??
 
 = [(1.2)
2
 – 1] × 100 
 = 44 % 
 
 
5 
 
 
16. The torque of a force 
ˆˆ ˆ
5i 3j 7k ?? about the origin 
is ?. If the force acts on a particle whose position 
vector is 
ˆˆ ˆ
2i 2j k ?? , then the value of ? will be : 
 (A) 
ˆˆ ˆ
11i 19j 4k ?? (B) 
ˆˆ ˆ
11i 9j 16k ? ? ? 
 (C)
ˆˆ ˆ
17i 19j 4k ? ? ? (D) 
ˆˆ ˆ
17i 9j 16k ?? 
 Official Ans. by NTA (C) 
  
Sol. 
i j k
r F 2 2 1
5 3 7
? ? ? ?
?
 
 ? ? ? ? ? ?
ˆ
i 14 3 j 14 5 k 6 10 ? ? ? ? ? ? ? ? 
 
ˆ ˆ ˆ
17i 19j 4k ? ? ? ? 
17. A thermodynamic system is taken from an original 
state D to an intermediate state E by the linear 
process shown in the figure. Its volume is then 
reduced to the original volume from E to F by an 
isobaric process. The total work done by the gas 
from D to E to F will be  
 
E
F
300
0 2.0 5.0
D
600
Volume V,(m )
3
Pressure-P(N/m )
2
 
 (A) –450 J  (B) 450 J 
 (C) 900 J  (D) 1350 J 
 Official Ans. by NTA (B) 
  
Sol. ? ?
DE
1
W 600 300 3
2
?? J 
 = 1350 J 
 
EF
W 3 0 0 3 – 9 0 0 J ? ? ? ? 
 
DEF
W 450J ? 
18. The vertical component of the earth's magnetic 
field is 6 × 10
–5
 T at any place where the angle of 
dip is 37º. The earth's resultant magnetic field at 
that place will be (Given tan 37º = 
3
4
) 
 (A) 8 × 10
–5
 T (B) 6 × 10
–5
 T  
 (C) 5 × 10
–4
 T (D) 1 × 10
–4
 T 
 Official Ans. by NTA (D) 
  
Sol. 
B
?
 
 ( ? = 37°) 
 B
V
 = B sin ? 
 6 × 10
–5
 =
3
B
5
 
 B = 10 × 10
–5
 T 
 = 10
–4
 T 
19. The root mean square speed of smoke particles of 
mass 5 × 10
–17
 kg in their Brownian motion in air at 
NTP is approximately. [Given k = 1.38 × 10
–23
 JK
–1
] 
 (A) 60 mm s
–1
 (B) 12 mm s
–1
 
 (C) 15 mm s
–1
 (D) 36 mm s
–1
 
 Official Ans. by NTA (C) 
  
Sol. 
23
rms
17
3kT 3 1.38 10 293
V
m 5 10
?
?
? ? ?
??
?
 
 15mm / s ? 
20. Light enters from air into a given medium at an 
angle of 45° with interface of the air-medium 
surface. After refraction, the light ray is deviated 
through an angle of 15° from its original direction. 
The refractive index of the medium is : 
 (A) 1.732  (B) 1.333 
 (C) 1.414  (D) 2.732 
 Official Ans. by NTA (C)