JEE Main 2022 Question Paper 25 July Shift 1 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Monday 25
th
 July, 2022)                 TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. If momentum [P], area [A] and time [T] are taken 
as fundamental quantities, then the dimensional 
formula for coefficient of viscosity is : 
 (A) [P A
-1
 T
0
] (B) [P A T
-1
]   
 (C) [P A
-1
 T]  (D) [P A
-1
 T
-1
] 
 Official Ans. by NTA (A) 
  
Sol. Viscosity =  pascal.second 
 P
x
 A
y
 T
z
 = [M
1
 L
-1
 T
-1
] 
 [M
1
 L
+1
 T
-1
]
x
 [L
2
]
y
[T
1
]
z
 = M
1
L
-1
 T
-1
 
 M
x
L
+x+2y
 T
-x+z
 = M
1
 L
-1
 T
-1 
 
x = 1     x + 2y = -1     -x + z = -1 
 y = -1 
 z = 0 
 Viscosity = P
1
 A
-1
 T
0
  
2. Which of the following physical quantities have 
the same dimensions ?  
 (A) Electric displacement (D) and surface charge 
density     
 (B) Displacement current and electric field 
 (C) Current density and surface charge density 
 (D) Electric potential and energy 
 Official Ans. by NTA (A) 
  
Sol. Electric displacement  
 
0
DE ?? 
 ? ? ? ?
00
0
DE
?? ?
? ? ? ?
??
?
??
 
 [D] = [ ?] 
 ? Surface change density = ?. 
3. A person moved from A to B on a circular path as 
shown in figure. If the distance travelled by him is 
60 m, then the magnitude of displacement would 
be : (Given cos135° = - 0.7)  
 
 (A) 42 m  (B) 47 m   
 (C) 19 m (D) 40 m 
 Official Ans. by NTA (B) 
  
Sol. d = R ? 
 
3
60 R
4
? ??
?
??
??
 
 
60 4 80
Rm
3
?
??
??
 
 Displacement 
2 2 2
R R 2R cos135 ? ? ? 
 
? ?
22
2R 2R 0.7 ? ? ? 
 
2
2
80
3.4R 3.4
??
??
??
?
??
 
 ? 47 m 
4. A body of mass 0.5 kg travels on straight line path 
with velocity v = (3x
2
 + 4)m/s. The net workdone 
by the force during its displacement from x = 0 to 
x = 2 m is :  
 (A) 64 J  (B) 60 J  
 (C) 120 J  (D) 128 J  
 Official Ans. by NTA (B) 
  
Sol. v
i
 = 3(0
2
) + 4 = 4       ?    x = 0 
 v
F
 = 3(2)
2
 + 4            ?    x = 2 
 = 16 
 
? ?
22
1
W K m 16 4
2
? ? ? ? 
 
11
(256 16)
22
? ? ? 
 
240
60J
4
?? 
Page 2


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Monday 25
th
 July, 2022)                 TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. If momentum [P], area [A] and time [T] are taken 
as fundamental quantities, then the dimensional 
formula for coefficient of viscosity is : 
 (A) [P A
-1
 T
0
] (B) [P A T
-1
]   
 (C) [P A
-1
 T]  (D) [P A
-1
 T
-1
] 
 Official Ans. by NTA (A) 
  
Sol. Viscosity =  pascal.second 
 P
x
 A
y
 T
z
 = [M
1
 L
-1
 T
-1
] 
 [M
1
 L
+1
 T
-1
]
x
 [L
2
]
y
[T
1
]
z
 = M
1
L
-1
 T
-1
 
 M
x
L
+x+2y
 T
-x+z
 = M
1
 L
-1
 T
-1 
 
x = 1     x + 2y = -1     -x + z = -1 
 y = -1 
 z = 0 
 Viscosity = P
1
 A
-1
 T
0
  
2. Which of the following physical quantities have 
the same dimensions ?  
 (A) Electric displacement (D) and surface charge 
density     
 (B) Displacement current and electric field 
 (C) Current density and surface charge density 
 (D) Electric potential and energy 
 Official Ans. by NTA (A) 
  
Sol. Electric displacement  
 
0
DE ?? 
 ? ? ? ?
00
0
DE
?? ?
? ? ? ?
??
?
??
 
 [D] = [ ?] 
 ? Surface change density = ?. 
3. A person moved from A to B on a circular path as 
shown in figure. If the distance travelled by him is 
60 m, then the magnitude of displacement would 
be : (Given cos135° = - 0.7)  
 
 (A) 42 m  (B) 47 m   
 (C) 19 m (D) 40 m 
 Official Ans. by NTA (B) 
  
Sol. d = R ? 
 
3
60 R
4
? ??
?
??
??
 
 
60 4 80
Rm
3
?
??
??
 
 Displacement 
2 2 2
R R 2R cos135 ? ? ? 
 
? ?
22
2R 2R 0.7 ? ? ? 
 
2
2
80
3.4R 3.4
??
??
??
?
??
 
 ? 47 m 
4. A body of mass 0.5 kg travels on straight line path 
with velocity v = (3x
2
 + 4)m/s. The net workdone 
by the force during its displacement from x = 0 to 
x = 2 m is :  
 (A) 64 J  (B) 60 J  
 (C) 120 J  (D) 128 J  
 Official Ans. by NTA (B) 
  
Sol. v
i
 = 3(0
2
) + 4 = 4       ?    x = 0 
 v
F
 = 3(2)
2
 + 4            ?    x = 2 
 = 16 
 
? ?
22
1
W K m 16 4
2
? ? ? ? 
 
11
(256 16)
22
? ? ? 
 
240
60J
4
?? 
 
2 
 
 
5. A solid cylinder and a solid sphere, having same 
mass M and radius R, roll down the same inclined 
plane from top without slipping. They start from 
rest. The ratio of velocity of the solid cylinder to 
that of the solid sphere, with which they reach the 
ground, will be :  
 (A) 
5
3
  (B) 
4
5
 
 
 (C) 
3
5
  (D) 
14
15
  
 Official Ans. by NTA (D) 
  
Sol. 
22
2gH
V
1 k / R
?
?
 
 
22
cylinder sphere
22
sphere cylinder
V (1 k / R )
V (1 k / R )
?
?
?
 
 
1 2 / 5 7 2
1 1/ 2 5 3
?
? ? ?
?
 
14
15
? 
6. Three identical particle A, B and C of mass 100 kg 
each are placed in a straight line with  
AB = BC = 13 m. The gravitational force on a 
fourth particle P of the same mass is F, when 
placed at a distance 13 m from the particle B on the 
perpendicular bisector of the line AC. The value of 
F will be approximately :  
 (A) 21 G  (B) 100 G
 
 
 (C) 59 G   (D) 42 G 
 Official Ans. by NTA (B) 
  
Sol.  
 
2 2
GMM GMM
F2
r ( 2r)
?? 
 
2
GMM 1
1
r 2
??
??
??
??
 
 
4
2
G 10 1
1
13 2
?? ?
??
??
??
 
 F 100G 
7. A certain amount of gas of volume V at 27°C 
temperature and pressure 2 × 10
7
 Nm
-2
 expands 
isothermally until its volume gets doubled. Later it 
expands adiabatically until its volume gets 
redoubled. The final pressure of the gas will be 
(Use ? = 1.5)  
 (A) 3.536 × 10
5
 Pa (B) 3.536 × 10
6
 Pa   
 (C) 1.25 × 10
6
 Pa  (D) 1.25 × 10
5
 Pa   
 Official Ans. by NTA (B) 
  
Sol. 
7
1
P 2 10 Pa ?? 
 P
1
V
1
 = P
2
V
2
 
 Since V
2
 = 2V
1
 Hence P
2
 = P
1
/2 (isothermal 
expansion) 
 
7
2
P 1 10 Pa ?? 
 
2 2 3 2
P (V ) P (2V )
??
? 
 
7
6
3
1.5
1 10
P 3.536 10
2
?
? ? ? 
8. Following statements are given : 
 (1) The average kinetic energy of a gas molecule 
decreases when the temperature is reduced.   
 (2) The average kinetic energy of a gas molecule 
increases with increase in pressure at constant 
temperature.    
 (3) The average kinetic energy of a gas molecule 
decreases with increases in volume.    
 (4) Pressure of a gas increases with increase in 
temperature at constant pressure.  
 (5) The volume of gas decreases with increase in 
temperature.  
 Choose the correct answer from the options given 
below :   
 (A) (1) and (4) only (B) (1), (2) and (4) only
 (C) (2) and (4) only (D) (1), (2) and (5) only 
 Official Ans. by NTA (A) 
  
Sol. 
avg
3
KE KT
2
? 
 
2
rms
1
PV
3
?? 
 Note : Statement (4) is correct only if we 
consider it at constant volume and not constant 
pressure. Ideally, this question must be bonus 
but most appropriate answer is option (A) 
Page 3


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Monday 25
th
 July, 2022)                 TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. If momentum [P], area [A] and time [T] are taken 
as fundamental quantities, then the dimensional 
formula for coefficient of viscosity is : 
 (A) [P A
-1
 T
0
] (B) [P A T
-1
]   
 (C) [P A
-1
 T]  (D) [P A
-1
 T
-1
] 
 Official Ans. by NTA (A) 
  
Sol. Viscosity =  pascal.second 
 P
x
 A
y
 T
z
 = [M
1
 L
-1
 T
-1
] 
 [M
1
 L
+1
 T
-1
]
x
 [L
2
]
y
[T
1
]
z
 = M
1
L
-1
 T
-1
 
 M
x
L
+x+2y
 T
-x+z
 = M
1
 L
-1
 T
-1 
 
x = 1     x + 2y = -1     -x + z = -1 
 y = -1 
 z = 0 
 Viscosity = P
1
 A
-1
 T
0
  
2. Which of the following physical quantities have 
the same dimensions ?  
 (A) Electric displacement (D) and surface charge 
density     
 (B) Displacement current and electric field 
 (C) Current density and surface charge density 
 (D) Electric potential and energy 
 Official Ans. by NTA (A) 
  
Sol. Electric displacement  
 
0
DE ?? 
 ? ? ? ?
00
0
DE
?? ?
? ? ? ?
??
?
??
 
 [D] = [ ?] 
 ? Surface change density = ?. 
3. A person moved from A to B on a circular path as 
shown in figure. If the distance travelled by him is 
60 m, then the magnitude of displacement would 
be : (Given cos135° = - 0.7)  
 
 (A) 42 m  (B) 47 m   
 (C) 19 m (D) 40 m 
 Official Ans. by NTA (B) 
  
Sol. d = R ? 
 
3
60 R
4
? ??
?
??
??
 
 
60 4 80
Rm
3
?
??
??
 
 Displacement 
2 2 2
R R 2R cos135 ? ? ? 
 
? ?
22
2R 2R 0.7 ? ? ? 
 
2
2
80
3.4R 3.4
??
??
??
?
??
 
 ? 47 m 
4. A body of mass 0.5 kg travels on straight line path 
with velocity v = (3x
2
 + 4)m/s. The net workdone 
by the force during its displacement from x = 0 to 
x = 2 m is :  
 (A) 64 J  (B) 60 J  
 (C) 120 J  (D) 128 J  
 Official Ans. by NTA (B) 
  
Sol. v
i
 = 3(0
2
) + 4 = 4       ?    x = 0 
 v
F
 = 3(2)
2
 + 4            ?    x = 2 
 = 16 
 
? ?
22
1
W K m 16 4
2
? ? ? ? 
 
11
(256 16)
22
? ? ? 
 
240
60J
4
?? 
 
2 
 
 
5. A solid cylinder and a solid sphere, having same 
mass M and radius R, roll down the same inclined 
plane from top without slipping. They start from 
rest. The ratio of velocity of the solid cylinder to 
that of the solid sphere, with which they reach the 
ground, will be :  
 (A) 
5
3
  (B) 
4
5
 
 
 (C) 
3
5
  (D) 
14
15
  
 Official Ans. by NTA (D) 
  
Sol. 
22
2gH
V
1 k / R
?
?
 
 
22
cylinder sphere
22
sphere cylinder
V (1 k / R )
V (1 k / R )
?
?
?
 
 
1 2 / 5 7 2
1 1/ 2 5 3
?
? ? ?
?
 
14
15
? 
6. Three identical particle A, B and C of mass 100 kg 
each are placed in a straight line with  
AB = BC = 13 m. The gravitational force on a 
fourth particle P of the same mass is F, when 
placed at a distance 13 m from the particle B on the 
perpendicular bisector of the line AC. The value of 
F will be approximately :  
 (A) 21 G  (B) 100 G
 
 
 (C) 59 G   (D) 42 G 
 Official Ans. by NTA (B) 
  
Sol.  
 
2 2
GMM GMM
F2
r ( 2r)
?? 
 
2
GMM 1
1
r 2
??
??
??
??
 
 
4
2
G 10 1
1
13 2
?? ?
??
??
??
 
 F 100G 
7. A certain amount of gas of volume V at 27°C 
temperature and pressure 2 × 10
7
 Nm
-2
 expands 
isothermally until its volume gets doubled. Later it 
expands adiabatically until its volume gets 
redoubled. The final pressure of the gas will be 
(Use ? = 1.5)  
 (A) 3.536 × 10
5
 Pa (B) 3.536 × 10
6
 Pa   
 (C) 1.25 × 10
6
 Pa  (D) 1.25 × 10
5
 Pa   
 Official Ans. by NTA (B) 
  
Sol. 
7
1
P 2 10 Pa ?? 
 P
1
V
1
 = P
2
V
2
 
 Since V
2
 = 2V
1
 Hence P
2
 = P
1
/2 (isothermal 
expansion) 
 
7
2
P 1 10 Pa ?? 
 
2 2 3 2
P (V ) P (2V )
??
? 
 
7
6
3
1.5
1 10
P 3.536 10
2
?
? ? ? 
8. Following statements are given : 
 (1) The average kinetic energy of a gas molecule 
decreases when the temperature is reduced.   
 (2) The average kinetic energy of a gas molecule 
increases with increase in pressure at constant 
temperature.    
 (3) The average kinetic energy of a gas molecule 
decreases with increases in volume.    
 (4) Pressure of a gas increases with increase in 
temperature at constant pressure.  
 (5) The volume of gas decreases with increase in 
temperature.  
 Choose the correct answer from the options given 
below :   
 (A) (1) and (4) only (B) (1), (2) and (4) only
 (C) (2) and (4) only (D) (1), (2) and (5) only 
 Official Ans. by NTA (A) 
  
Sol. 
avg
3
KE KT
2
? 
 
2
rms
1
PV
3
?? 
 Note : Statement (4) is correct only if we 
consider it at constant volume and not constant 
pressure. Ideally, this question must be bonus 
but most appropriate answer is option (A) 
 
 
3 
 
 
9. In figure (A), mass ‘2 m’ is fixed on mass ‘m’ 
which is attached to two springs of spring constant 
k. In figure (B), mass ‘m’ is attached to two spring 
of spring constant ‘k’ and ‘2k’. If mass ‘m’ in (A) 
and (B) are displaced by distance ‘x’ horizontally 
and then released, then time period T
1
 and T
2
 
corresponding to (A) and (B) respectively follow 
the relation.   
 
 (A) 
1
2
T 3
T
2
? (B) 
1
2
T 3
T2
?  
 (C) 
1
2
T 2
T3
? (D) 
1
2
T 2
T3
? 
 Official Ans. by NTA (A) 
  
Sol. 
1
3m
T2
2k
?? 
 
2
m
T2
3k
?? 
 
1
2
3m
2
T 3
2k
T
m2
2
3k
?
??
?
 
10. A condenser of 2 ?F capacitance is charged 
steadily from 0 to 5C. Which of the following 
graph represents correctly the variation of potential 
difference (V) across it’s plates with respect to the 
charge (Q) on the condenser ?  
 (A)  (B) 
 
 
 (C)  (D)   
 Official Ans. by NTA (A) 
  
 
Sol. Q = CV 
 
1
VQ
C
? 
 Straight line with slope = 
1
C
 
 Slope 
5
6
11
5 10
C 2 10
?
? ? ? ?
?
 
11. Two charged particles, having same kinetic energy, 
are allowed to pass through a uniform magnetic 
field perpendicular to the direction of motion. If 
the ratio of radii of their circular paths is 6 : 5 and 
their respective masses ratio is 9 : 4. Then, the ratio 
of their charges will be :  
 (A) 8 : 5 (B) 5 : 4  
 (C) 5 : 3  (D) 8 : 7 
 Official Ans. by NTA (B) 
  
Sol. Radius of circular path 
2mk
R
qB
? 
 
2mk
q
RB
? 
 
1 1 2
2 2 1
q m R 9 5 5
q m R 4 6 4
? ? ? ? ? 
12. To increase the resonant frequency in series LCR 
circuit,  
 (A) Source frequency should be increased  
 (B) Another resistance should be added in series 
with the first resistance.   
 (C) Another capacitor should be added in series 
with the first capacitor    
 (D) The source frequency should be decreased  
 Official Ans. by NTA (C) 
  
Sol. 
1
f
2 LC
?
?
  
 To increase the resonating frequency product of L 
and C should decrease. 
 By joining capacitor in series, capacitor will 
decrease  
Page 4


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Monday 25
th
 July, 2022)                 TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. If momentum [P], area [A] and time [T] are taken 
as fundamental quantities, then the dimensional 
formula for coefficient of viscosity is : 
 (A) [P A
-1
 T
0
] (B) [P A T
-1
]   
 (C) [P A
-1
 T]  (D) [P A
-1
 T
-1
] 
 Official Ans. by NTA (A) 
  
Sol. Viscosity =  pascal.second 
 P
x
 A
y
 T
z
 = [M
1
 L
-1
 T
-1
] 
 [M
1
 L
+1
 T
-1
]
x
 [L
2
]
y
[T
1
]
z
 = M
1
L
-1
 T
-1
 
 M
x
L
+x+2y
 T
-x+z
 = M
1
 L
-1
 T
-1 
 
x = 1     x + 2y = -1     -x + z = -1 
 y = -1 
 z = 0 
 Viscosity = P
1
 A
-1
 T
0
  
2. Which of the following physical quantities have 
the same dimensions ?  
 (A) Electric displacement (D) and surface charge 
density     
 (B) Displacement current and electric field 
 (C) Current density and surface charge density 
 (D) Electric potential and energy 
 Official Ans. by NTA (A) 
  
Sol. Electric displacement  
 
0
DE ?? 
 ? ? ? ?
00
0
DE
?? ?
? ? ? ?
??
?
??
 
 [D] = [ ?] 
 ? Surface change density = ?. 
3. A person moved from A to B on a circular path as 
shown in figure. If the distance travelled by him is 
60 m, then the magnitude of displacement would 
be : (Given cos135° = - 0.7)  
 
 (A) 42 m  (B) 47 m   
 (C) 19 m (D) 40 m 
 Official Ans. by NTA (B) 
  
Sol. d = R ? 
 
3
60 R
4
? ??
?
??
??
 
 
60 4 80
Rm
3
?
??
??
 
 Displacement 
2 2 2
R R 2R cos135 ? ? ? 
 
? ?
22
2R 2R 0.7 ? ? ? 
 
2
2
80
3.4R 3.4
??
??
??
?
??
 
 ? 47 m 
4. A body of mass 0.5 kg travels on straight line path 
with velocity v = (3x
2
 + 4)m/s. The net workdone 
by the force during its displacement from x = 0 to 
x = 2 m is :  
 (A) 64 J  (B) 60 J  
 (C) 120 J  (D) 128 J  
 Official Ans. by NTA (B) 
  
Sol. v
i
 = 3(0
2
) + 4 = 4       ?    x = 0 
 v
F
 = 3(2)
2
 + 4            ?    x = 2 
 = 16 
 
? ?
22
1
W K m 16 4
2
? ? ? ? 
 
11
(256 16)
22
? ? ? 
 
240
60J
4
?? 
 
2 
 
 
5. A solid cylinder and a solid sphere, having same 
mass M and radius R, roll down the same inclined 
plane from top without slipping. They start from 
rest. The ratio of velocity of the solid cylinder to 
that of the solid sphere, with which they reach the 
ground, will be :  
 (A) 
5
3
  (B) 
4
5
 
 
 (C) 
3
5
  (D) 
14
15
  
 Official Ans. by NTA (D) 
  
Sol. 
22
2gH
V
1 k / R
?
?
 
 
22
cylinder sphere
22
sphere cylinder
V (1 k / R )
V (1 k / R )
?
?
?
 
 
1 2 / 5 7 2
1 1/ 2 5 3
?
? ? ?
?
 
14
15
? 
6. Three identical particle A, B and C of mass 100 kg 
each are placed in a straight line with  
AB = BC = 13 m. The gravitational force on a 
fourth particle P of the same mass is F, when 
placed at a distance 13 m from the particle B on the 
perpendicular bisector of the line AC. The value of 
F will be approximately :  
 (A) 21 G  (B) 100 G
 
 
 (C) 59 G   (D) 42 G 
 Official Ans. by NTA (B) 
  
Sol.  
 
2 2
GMM GMM
F2
r ( 2r)
?? 
 
2
GMM 1
1
r 2
??
??
??
??
 
 
4
2
G 10 1
1
13 2
?? ?
??
??
??
 
 F 100G 
7. A certain amount of gas of volume V at 27°C 
temperature and pressure 2 × 10
7
 Nm
-2
 expands 
isothermally until its volume gets doubled. Later it 
expands adiabatically until its volume gets 
redoubled. The final pressure of the gas will be 
(Use ? = 1.5)  
 (A) 3.536 × 10
5
 Pa (B) 3.536 × 10
6
 Pa   
 (C) 1.25 × 10
6
 Pa  (D) 1.25 × 10
5
 Pa   
 Official Ans. by NTA (B) 
  
Sol. 
7
1
P 2 10 Pa ?? 
 P
1
V
1
 = P
2
V
2
 
 Since V
2
 = 2V
1
 Hence P
2
 = P
1
/2 (isothermal 
expansion) 
 
7
2
P 1 10 Pa ?? 
 
2 2 3 2
P (V ) P (2V )
??
? 
 
7
6
3
1.5
1 10
P 3.536 10
2
?
? ? ? 
8. Following statements are given : 
 (1) The average kinetic energy of a gas molecule 
decreases when the temperature is reduced.   
 (2) The average kinetic energy of a gas molecule 
increases with increase in pressure at constant 
temperature.    
 (3) The average kinetic energy of a gas molecule 
decreases with increases in volume.    
 (4) Pressure of a gas increases with increase in 
temperature at constant pressure.  
 (5) The volume of gas decreases with increase in 
temperature.  
 Choose the correct answer from the options given 
below :   
 (A) (1) and (4) only (B) (1), (2) and (4) only
 (C) (2) and (4) only (D) (1), (2) and (5) only 
 Official Ans. by NTA (A) 
  
Sol. 
avg
3
KE KT
2
? 
 
2
rms
1
PV
3
?? 
 Note : Statement (4) is correct only if we 
consider it at constant volume and not constant 
pressure. Ideally, this question must be bonus 
but most appropriate answer is option (A) 
 
 
3 
 
 
9. In figure (A), mass ‘2 m’ is fixed on mass ‘m’ 
which is attached to two springs of spring constant 
k. In figure (B), mass ‘m’ is attached to two spring 
of spring constant ‘k’ and ‘2k’. If mass ‘m’ in (A) 
and (B) are displaced by distance ‘x’ horizontally 
and then released, then time period T
1
 and T
2
 
corresponding to (A) and (B) respectively follow 
the relation.   
 
 (A) 
1
2
T 3
T
2
? (B) 
1
2
T 3
T2
?  
 (C) 
1
2
T 2
T3
? (D) 
1
2
T 2
T3
? 
 Official Ans. by NTA (A) 
  
Sol. 
1
3m
T2
2k
?? 
 
2
m
T2
3k
?? 
 
1
2
3m
2
T 3
2k
T
m2
2
3k
?
??
?
 
10. A condenser of 2 ?F capacitance is charged 
steadily from 0 to 5C. Which of the following 
graph represents correctly the variation of potential 
difference (V) across it’s plates with respect to the 
charge (Q) on the condenser ?  
 (A)  (B) 
 
 
 (C)  (D)   
 Official Ans. by NTA (A) 
  
 
Sol. Q = CV 
 
1
VQ
C
? 
 Straight line with slope = 
1
C
 
 Slope 
5
6
11
5 10
C 2 10
?
? ? ? ?
?
 
11. Two charged particles, having same kinetic energy, 
are allowed to pass through a uniform magnetic 
field perpendicular to the direction of motion. If 
the ratio of radii of their circular paths is 6 : 5 and 
their respective masses ratio is 9 : 4. Then, the ratio 
of their charges will be :  
 (A) 8 : 5 (B) 5 : 4  
 (C) 5 : 3  (D) 8 : 7 
 Official Ans. by NTA (B) 
  
Sol. Radius of circular path 
2mk
R
qB
? 
 
2mk
q
RB
? 
 
1 1 2
2 2 1
q m R 9 5 5
q m R 4 6 4
? ? ? ? ? 
12. To increase the resonant frequency in series LCR 
circuit,  
 (A) Source frequency should be increased  
 (B) Another resistance should be added in series 
with the first resistance.   
 (C) Another capacitor should be added in series 
with the first capacitor    
 (D) The source frequency should be decreased  
 Official Ans. by NTA (C) 
  
Sol. 
1
f
2 LC
?
?
  
 To increase the resonating frequency product of L 
and C should decrease. 
 By joining capacitor in series, capacitor will 
decrease  
 
4 
 
 
13. A small square loop of wire of side l is placed 
inside a large square loop of wire L (L >> l). Both 
loops are coplanar and their centres coincide at 
point O as shown in figure. The mutual inductance 
of the system is :  
 
 (A) 
2
0
2 2 L ?
?
 (B) 
2
0
2 2 L
?
?
   
 (C) 
2
0
22
L
?
?
 (D) 
2
0
L
22
?
?
  
 Official Ans. by NTA (C) 
  
Sol. Assuming current I in outer loop magnetic field at 
centre 
00
i 2 2 i
4 (2sin45 )
L
L
4
2
??
? ? ? ? ?
?
??
 
l
l
 
 
Flux through inner loop
M
i
? 
 
2
0
22
M
L
?
?
?
 
14. The rms value of conduction current in a parallel 
plate capacitor is 6.9 ?A. The capacity of this 
capacitor, if it is connected to 230 V ac supply with 
an angular frequency of 600 rad/s, will be : 
 (A) 5 pF  (B) 50 pF  
 (C) 100 pF  (D) 200 pF 
 Official Ans. by NTA (B) 
  
Sol. Current in capacitor 
C
V
I
X
? 
 ? ? ? ? I V C ? ? ? 
 
6
I 6.9 10
C 50pF
V 230 600
?
?
? ? ?
??
  
15. Which of the following statement is correct ?  
 (A) In primary rainbow, observer sees red colour 
on the top and violet on the bottom  
 (B) In primary rainbow, observer sees violet colour 
on the top and red on the bottom  
 (C) In primary rainbow, light wave suffers total 
internal reflection twice before coming out of 
water drops   
 (D) Primary rainbow is less bright than secondary 
rainbow.   
 Official Ans. by NTA (A) 
  
Sol. In primary rainbow, red colour is at top and violet 
is at bottom.  
 Intensity of secondary rainbow is less in 
comparison to primary rainbow.  
16. Time taken by light to travel in two different 
materials A and B of refractive indices ?
A
 and ?
B
 
of same thickness is t
1
 and t
2
 respectively. If  
t
2
 – t
1
 = 5 × 10
-10
 s and the ratio of ?
A
 to ?
B
 is 1 : 2. 
Then the thickness of material, in meter is : (Given 
v
A
 and v
B
 are velocities of light in A and B 
materials respectively).  
 (A) 5 × 10
-10
 v
a 
m (B) 5 × 10
-10
 m  
 (C) (D) 5 × 10
-10
 v
B
 m  
 Official Ans. by NTA (A) 
  
Sol.  
A A B
B B A
c / V V 1
c / V V 2
?
? ? ?
?
 
 Let the thickness is d  
 
10
BA
dd
5 10
vv
?
? ? ? 
 
10
AB
AB
5 10 v v
d
vv
?
??
?
?
 
 As v
A
 = 2v
B
 ? d = 5 × 10
-10
 × 2v
B
 
 Or  d = 5 × 10
-10
 × v
A
 
Page 5


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Monday 25
th
 July, 2022)                 TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. If momentum [P], area [A] and time [T] are taken 
as fundamental quantities, then the dimensional 
formula for coefficient of viscosity is : 
 (A) [P A
-1
 T
0
] (B) [P A T
-1
]   
 (C) [P A
-1
 T]  (D) [P A
-1
 T
-1
] 
 Official Ans. by NTA (A) 
  
Sol. Viscosity =  pascal.second 
 P
x
 A
y
 T
z
 = [M
1
 L
-1
 T
-1
] 
 [M
1
 L
+1
 T
-1
]
x
 [L
2
]
y
[T
1
]
z
 = M
1
L
-1
 T
-1
 
 M
x
L
+x+2y
 T
-x+z
 = M
1
 L
-1
 T
-1 
 
x = 1     x + 2y = -1     -x + z = -1 
 y = -1 
 z = 0 
 Viscosity = P
1
 A
-1
 T
0
  
2. Which of the following physical quantities have 
the same dimensions ?  
 (A) Electric displacement (D) and surface charge 
density     
 (B) Displacement current and electric field 
 (C) Current density and surface charge density 
 (D) Electric potential and energy 
 Official Ans. by NTA (A) 
  
Sol. Electric displacement  
 
0
DE ?? 
 ? ? ? ?
00
0
DE
?? ?
? ? ? ?
??
?
??
 
 [D] = [ ?] 
 ? Surface change density = ?. 
3. A person moved from A to B on a circular path as 
shown in figure. If the distance travelled by him is 
60 m, then the magnitude of displacement would 
be : (Given cos135° = - 0.7)  
 
 (A) 42 m  (B) 47 m   
 (C) 19 m (D) 40 m 
 Official Ans. by NTA (B) 
  
Sol. d = R ? 
 
3
60 R
4
? ??
?
??
??
 
 
60 4 80
Rm
3
?
??
??
 
 Displacement 
2 2 2
R R 2R cos135 ? ? ? 
 
? ?
22
2R 2R 0.7 ? ? ? 
 
2
2
80
3.4R 3.4
??
??
??
?
??
 
 ? 47 m 
4. A body of mass 0.5 kg travels on straight line path 
with velocity v = (3x
2
 + 4)m/s. The net workdone 
by the force during its displacement from x = 0 to 
x = 2 m is :  
 (A) 64 J  (B) 60 J  
 (C) 120 J  (D) 128 J  
 Official Ans. by NTA (B) 
  
Sol. v
i
 = 3(0
2
) + 4 = 4       ?    x = 0 
 v
F
 = 3(2)
2
 + 4            ?    x = 2 
 = 16 
 
? ?
22
1
W K m 16 4
2
? ? ? ? 
 
11
(256 16)
22
? ? ? 
 
240
60J
4
?? 
 
2 
 
 
5. A solid cylinder and a solid sphere, having same 
mass M and radius R, roll down the same inclined 
plane from top without slipping. They start from 
rest. The ratio of velocity of the solid cylinder to 
that of the solid sphere, with which they reach the 
ground, will be :  
 (A) 
5
3
  (B) 
4
5
 
 
 (C) 
3
5
  (D) 
14
15
  
 Official Ans. by NTA (D) 
  
Sol. 
22
2gH
V
1 k / R
?
?
 
 
22
cylinder sphere
22
sphere cylinder
V (1 k / R )
V (1 k / R )
?
?
?
 
 
1 2 / 5 7 2
1 1/ 2 5 3
?
? ? ?
?
 
14
15
? 
6. Three identical particle A, B and C of mass 100 kg 
each are placed in a straight line with  
AB = BC = 13 m. The gravitational force on a 
fourth particle P of the same mass is F, when 
placed at a distance 13 m from the particle B on the 
perpendicular bisector of the line AC. The value of 
F will be approximately :  
 (A) 21 G  (B) 100 G
 
 
 (C) 59 G   (D) 42 G 
 Official Ans. by NTA (B) 
  
Sol.  
 
2 2
GMM GMM
F2
r ( 2r)
?? 
 
2
GMM 1
1
r 2
??
??
??
??
 
 
4
2
G 10 1
1
13 2
?? ?
??
??
??
 
 F 100G 
7. A certain amount of gas of volume V at 27°C 
temperature and pressure 2 × 10
7
 Nm
-2
 expands 
isothermally until its volume gets doubled. Later it 
expands adiabatically until its volume gets 
redoubled. The final pressure of the gas will be 
(Use ? = 1.5)  
 (A) 3.536 × 10
5
 Pa (B) 3.536 × 10
6
 Pa   
 (C) 1.25 × 10
6
 Pa  (D) 1.25 × 10
5
 Pa   
 Official Ans. by NTA (B) 
  
Sol. 
7
1
P 2 10 Pa ?? 
 P
1
V
1
 = P
2
V
2
 
 Since V
2
 = 2V
1
 Hence P
2
 = P
1
/2 (isothermal 
expansion) 
 
7
2
P 1 10 Pa ?? 
 
2 2 3 2
P (V ) P (2V )
??
? 
 
7
6
3
1.5
1 10
P 3.536 10
2
?
? ? ? 
8. Following statements are given : 
 (1) The average kinetic energy of a gas molecule 
decreases when the temperature is reduced.   
 (2) The average kinetic energy of a gas molecule 
increases with increase in pressure at constant 
temperature.    
 (3) The average kinetic energy of a gas molecule 
decreases with increases in volume.    
 (4) Pressure of a gas increases with increase in 
temperature at constant pressure.  
 (5) The volume of gas decreases with increase in 
temperature.  
 Choose the correct answer from the options given 
below :   
 (A) (1) and (4) only (B) (1), (2) and (4) only
 (C) (2) and (4) only (D) (1), (2) and (5) only 
 Official Ans. by NTA (A) 
  
Sol. 
avg
3
KE KT
2
? 
 
2
rms
1
PV
3
?? 
 Note : Statement (4) is correct only if we 
consider it at constant volume and not constant 
pressure. Ideally, this question must be bonus 
but most appropriate answer is option (A) 
 
 
3 
 
 
9. In figure (A), mass ‘2 m’ is fixed on mass ‘m’ 
which is attached to two springs of spring constant 
k. In figure (B), mass ‘m’ is attached to two spring 
of spring constant ‘k’ and ‘2k’. If mass ‘m’ in (A) 
and (B) are displaced by distance ‘x’ horizontally 
and then released, then time period T
1
 and T
2
 
corresponding to (A) and (B) respectively follow 
the relation.   
 
 (A) 
1
2
T 3
T
2
? (B) 
1
2
T 3
T2
?  
 (C) 
1
2
T 2
T3
? (D) 
1
2
T 2
T3
? 
 Official Ans. by NTA (A) 
  
Sol. 
1
3m
T2
2k
?? 
 
2
m
T2
3k
?? 
 
1
2
3m
2
T 3
2k
T
m2
2
3k
?
??
?
 
10. A condenser of 2 ?F capacitance is charged 
steadily from 0 to 5C. Which of the following 
graph represents correctly the variation of potential 
difference (V) across it’s plates with respect to the 
charge (Q) on the condenser ?  
 (A)  (B) 
 
 
 (C)  (D)   
 Official Ans. by NTA (A) 
  
 
Sol. Q = CV 
 
1
VQ
C
? 
 Straight line with slope = 
1
C
 
 Slope 
5
6
11
5 10
C 2 10
?
? ? ? ?
?
 
11. Two charged particles, having same kinetic energy, 
are allowed to pass through a uniform magnetic 
field perpendicular to the direction of motion. If 
the ratio of radii of their circular paths is 6 : 5 and 
their respective masses ratio is 9 : 4. Then, the ratio 
of their charges will be :  
 (A) 8 : 5 (B) 5 : 4  
 (C) 5 : 3  (D) 8 : 7 
 Official Ans. by NTA (B) 
  
Sol. Radius of circular path 
2mk
R
qB
? 
 
2mk
q
RB
? 
 
1 1 2
2 2 1
q m R 9 5 5
q m R 4 6 4
? ? ? ? ? 
12. To increase the resonant frequency in series LCR 
circuit,  
 (A) Source frequency should be increased  
 (B) Another resistance should be added in series 
with the first resistance.   
 (C) Another capacitor should be added in series 
with the first capacitor    
 (D) The source frequency should be decreased  
 Official Ans. by NTA (C) 
  
Sol. 
1
f
2 LC
?
?
  
 To increase the resonating frequency product of L 
and C should decrease. 
 By joining capacitor in series, capacitor will 
decrease  
 
4 
 
 
13. A small square loop of wire of side l is placed 
inside a large square loop of wire L (L >> l). Both 
loops are coplanar and their centres coincide at 
point O as shown in figure. The mutual inductance 
of the system is :  
 
 (A) 
2
0
2 2 L ?
?
 (B) 
2
0
2 2 L
?
?
   
 (C) 
2
0
22
L
?
?
 (D) 
2
0
L
22
?
?
  
 Official Ans. by NTA (C) 
  
Sol. Assuming current I in outer loop magnetic field at 
centre 
00
i 2 2 i
4 (2sin45 )
L
L
4
2
??
? ? ? ? ?
?
??
 
l
l
 
 
Flux through inner loop
M
i
? 
 
2
0
22
M
L
?
?
?
 
14. The rms value of conduction current in a parallel 
plate capacitor is 6.9 ?A. The capacity of this 
capacitor, if it is connected to 230 V ac supply with 
an angular frequency of 600 rad/s, will be : 
 (A) 5 pF  (B) 50 pF  
 (C) 100 pF  (D) 200 pF 
 Official Ans. by NTA (B) 
  
Sol. Current in capacitor 
C
V
I
X
? 
 ? ? ? ? I V C ? ? ? 
 
6
I 6.9 10
C 50pF
V 230 600
?
?
? ? ?
??
  
15. Which of the following statement is correct ?  
 (A) In primary rainbow, observer sees red colour 
on the top and violet on the bottom  
 (B) In primary rainbow, observer sees violet colour 
on the top and red on the bottom  
 (C) In primary rainbow, light wave suffers total 
internal reflection twice before coming out of 
water drops   
 (D) Primary rainbow is less bright than secondary 
rainbow.   
 Official Ans. by NTA (A) 
  
Sol. In primary rainbow, red colour is at top and violet 
is at bottom.  
 Intensity of secondary rainbow is less in 
comparison to primary rainbow.  
16. Time taken by light to travel in two different 
materials A and B of refractive indices ?
A
 and ?
B
 
of same thickness is t
1
 and t
2
 respectively. If  
t
2
 – t
1
 = 5 × 10
-10
 s and the ratio of ?
A
 to ?
B
 is 1 : 2. 
Then the thickness of material, in meter is : (Given 
v
A
 and v
B
 are velocities of light in A and B 
materials respectively).  
 (A) 5 × 10
-10
 v
a 
m (B) 5 × 10
-10
 m  
 (C) (D) 5 × 10
-10
 v
B
 m  
 Official Ans. by NTA (A) 
  
Sol.  
A A B
B B A
c / V V 1
c / V V 2
?
? ? ?
?
 
 Let the thickness is d  
 
10
BA
dd
5 10
vv
?
? ? ? 
 
10
AB
AB
5 10 v v
d
vv
?
??
?
?
 
 As v
A
 = 2v
B
 ? d = 5 × 10
-10
 × 2v
B
 
 Or  d = 5 × 10
-10
 × v
A
 
 
 
5 
 
 
17. A metal exposed to light of wavelength 800 nm 
and emits photoelectrons with a certain kinetic 
energy. The maximum kinetic energy of  
photo-electron doubles when light of wavelength 
500 nm is used. The work function of the metal is 
(Take hc = 1230 eV-nm). 
 (A) 1.537 eV (B) 2.46 eV  
 (C) 0.615 eV (D) 1.23 eV  
 Official Ans. by NTA (C) 
  
Sol. 
1
1230
k
800
? ? ?          …(1)    
 
21
1230
k 2k
500
?? - ?      …(2)  
 Eliminating k
1
 from (1) and (2) we get 
1230 1230
0
500 400
? ? ? ? 
  0.615eV ?? 
18. The momentum of an electron revolving in n
th
 orbit 
is given by : (Symbols have their usual meanings) 
 (A) 
nh
2r ?
  (B) 
nh
2r
  
 (C) 
nh
2 ?
  (D) 
2r
nh
?
  
 Official Ans. by NTA (A) 
  
Sol. Angular momentum is integral multiple of 
h
2 ?
 
mvr = 
nh
2 ?
 
 So momentum mv = 
nh
2r ?
  
19. The magnetic moment of an electron (e) revolving 
in an orbit around nucleus with an orbital angular 
momentum is given by :  
 (A) 
L
eL
2m
?? (B) 
L
eL
2m
? ? ?  
 (C) 
l
eL
m
? ? ? (D) 
l
2eL
m
??  
 Official Ans. by NTA (B) 
  
Sol. Ratio of magnetic moment and angular momentum 
q
2m L
?
? 
 For e
–
  
 
e
L
2m
? ? ? 
20. In the circuit, the logical value of A = 1 or B = 1 
when potential at A or B is 5V and the logical value 
of A = 0 or B = 0 when potential at A or B is 0 V. 
 
 The truth table of the given circuit will be : 
 (A) 
A B Y
000
1 0 0
0 1 0
111
 (B) 
A B Y
000
1 0 1
0 1 1
111
  
 (C) 
A B Y
000
1 0 0
0 1 0
1 1 0
 (D) 
A B Y
0 0 1
1 0 1
0 1 1
1 1 0
  
 Official Ans. by NTA (A) 
  
Sol. When both A and B have logical value ‘1’ both 
diode are reverse bias and current will flow in 
resistor hence output will be 5 volt i.e. logical 
value ‘1’.  
 In all other case conduction will take place, hence 
output will be zero volt i.e. logical value ‘0’. 
 So truth table is  
 
A B Y
000
0 1 0
1 0 0
111
 (AND gate)