JEE Main 2022 Question Paper 27 July Shift 1 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
 (Held On Wednesday 27
th
 July, 2022)          TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. A torque meter is calibrated to reference standards  
of mass, length and time each with 5% accuracy. 
After calibration, the measured torque with this 
torque meter will have net accuracy of : 
 (A) 15% (B) 25% (C) 75% (D) 5% 
 Official Ans. by NTA (B) 
  
Sol. Dimensional formula for Torque 
 [] ? = [ML
2
T
–2
] 
  Now 
 Percentage error in torque = % ? = % M + 2 % L  
2 % T 
 % ? = 25% 
2. A bullet is shot vertically downwards with an 
initial velocity of 100 m/s from a certain height. 
Within 10 s, the bullet reaches the ground and 
instantaneously comes to rest due to the perfectly 
inelastic collision. The velocity-time curve for total 
time t = 20 s will be : (Take g = 10 m/s
2
) 
 (A)
 
 
 (B)
  
  
 (C) 
 
 
 (D)
 
 
 Official Ans. by NTA (A) 
  
Sol. V = –100 –10t 
 
3. Sand is being dropped from a stationary dropper at 
a rate of 0.5 kgs
–1
 on a conveyor belt moving with 
a velocity of 5 ms
–1
. The power needed to keep belt 
moving with the same velocity will be : 
 (A) 1.25 W (B) 2.5 W 
 (C) 6.25 W  (D) 12.5 W 
 Official Ans. by NTA (D) 
  
Sol. Thrust = 
rel
V ? 
 = 2.5 N 
 Now, Power =F × V = 12.5 W 
4. A bag is gently dropped on a conveyor belt moving 
at a speed of 2 m/s. The coefficient of friction 
between the conveyor belt and bag is 0.4 Initially, 
the bag slips on the belt before it stops due to 
friction. The distance travelled by the bag on the 
belt during slipping motion is : [Take g = 10 m/s
–2
] 
 (A) 2 m (B) 0.5 m 
 (C) 3.2 m  (D) 0.8 ms 
 Official Ans. by NTA (B) 
  
Sol. In frame of belt 
 a = ? g = 4 m/s
2
 , v = 2m/s , u = 0 
 v
2
 = u
2
 + 2as 
 ? s = 0.5 m  
5. Two cylindrical vessels of equal cross-sectional 
area 16 cm
2
 contain water upto heights 100 cm and 
150 cm respectively. The vessels are 
interconnected so that the water levels in them 
become equal. The work done by the force of 
gravity during the process, is [Take density of 
water = 10
3
 kg/m
3
 and g = 10 ms
–2
] 
 (A) 0.25 J (B) 1 J 
 (C) 8 J  (D) 12 J 
 Official Ans. by NTA (B) 
  
Page 2


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
 (Held On Wednesday 27
th
 July, 2022)          TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. A torque meter is calibrated to reference standards  
of mass, length and time each with 5% accuracy. 
After calibration, the measured torque with this 
torque meter will have net accuracy of : 
 (A) 15% (B) 25% (C) 75% (D) 5% 
 Official Ans. by NTA (B) 
  
Sol. Dimensional formula for Torque 
 [] ? = [ML
2
T
–2
] 
  Now 
 Percentage error in torque = % ? = % M + 2 % L  
2 % T 
 % ? = 25% 
2. A bullet is shot vertically downwards with an 
initial velocity of 100 m/s from a certain height. 
Within 10 s, the bullet reaches the ground and 
instantaneously comes to rest due to the perfectly 
inelastic collision. The velocity-time curve for total 
time t = 20 s will be : (Take g = 10 m/s
2
) 
 (A)
 
 
 (B)
  
  
 (C) 
 
 
 (D)
 
 
 Official Ans. by NTA (A) 
  
Sol. V = –100 –10t 
 
3. Sand is being dropped from a stationary dropper at 
a rate of 0.5 kgs
–1
 on a conveyor belt moving with 
a velocity of 5 ms
–1
. The power needed to keep belt 
moving with the same velocity will be : 
 (A) 1.25 W (B) 2.5 W 
 (C) 6.25 W  (D) 12.5 W 
 Official Ans. by NTA (D) 
  
Sol. Thrust = 
rel
V ? 
 = 2.5 N 
 Now, Power =F × V = 12.5 W 
4. A bag is gently dropped on a conveyor belt moving 
at a speed of 2 m/s. The coefficient of friction 
between the conveyor belt and bag is 0.4 Initially, 
the bag slips on the belt before it stops due to 
friction. The distance travelled by the bag on the 
belt during slipping motion is : [Take g = 10 m/s
–2
] 
 (A) 2 m (B) 0.5 m 
 (C) 3.2 m  (D) 0.8 ms 
 Official Ans. by NTA (B) 
  
Sol. In frame of belt 
 a = ? g = 4 m/s
2
 , v = 2m/s , u = 0 
 v
2
 = u
2
 + 2as 
 ? s = 0.5 m  
5. Two cylindrical vessels of equal cross-sectional 
area 16 cm
2
 contain water upto heights 100 cm and 
150 cm respectively. The vessels are 
interconnected so that the water levels in them 
become equal. The work done by the force of 
gravity during the process, is [Take density of 
water = 10
3
 kg/m
3
 and g = 10 ms
–2
] 
 (A) 0.25 J (B) 1 J 
 (C) 8 J  (D) 12 J 
 Official Ans. by NTA (B) 
  
 
2 
 
Sol. 
 
h
2
=
h
 
 
12
hh
h
2
?
? 
 Now, 
 W = U
i
–U
f
 
 W = ( ?Ah
1
) g 
1
h
2
+( ? Ah
2
)g
2
h
2
–?? A(h
1
+h
2
)g
12
hh
4
?? ?
??
??
 
 W = 
2
22 12
12
(h h ) Ag
h h –
22
?? ? ?
?
??
??
 
 W = 1 J  
6. Two satellites A and B having masses in the ratio 
4:3 are revolving in circular orbits of radii 3r and  
4 r respectively around the earth. The ratio of total 
mechanical energy of A to B is : 
 (A) 9 : 16 (B) 16 : 9 
 (C) 1 : 1  (D) 4 : 3 
 Official Ans. by NTA (B) 
  
Sol. Given that 
1
2
m 4
3 m
? , 
1
2
r 3
4 r
? 
 Now TE = 
1
2
 mv
2
+
–GMm
r
??
??
??
 
 but 
2
2
2
mv GMm GMm
mv
rr r
? ? ? 
 
GMm m
TE –
2r r
? ? ? 
 
1 1 2
2 2 1
TE m r 4 4 16
.
3 3 9 TE m r
? ? ? ? 
7. If K
1
 and K
2
 are the thermal conductivities L
1
 and 
L
2
 are the lengths and A
1
 and A
2
 are the cross 
sectional areas of steel and copper rods 
respectively such that 
2 1 1
1 2 2
9, 2, 2
K A L
K A L
? ? ? . 
Then, for the arrangement as shown in the figure. 
The value of temperature T of the steel – copper 
junction in the steady state will be : 
  
 (A) 18ºC (B) 14 ºC 
 (C) 45 ºC  (D) 150 ºC 
 Official Ans. by NTA (C) 
  
Sol. 
A
1
l
1
K
1
Steel
Copper K
2
l
1
A
2
T =0ºC
2
1 1 2 2
12
12
K A K A d
(T – T) (T – T )
dtll
?
?? 
 
2 2 1
1 1 2
K A l 450 – T 1
92
T – 0 2 K A l
? ? ? ? ? 
 ? 450 – T = 9T ? T = 45ºC 
8. Read the following statements : 
 A. When small temperature difference between a 
liquid and its surrounding is doubled the rate of 
loss of heat of the liquid becomes twice. 
 B. Two bodies P and Q having equal surface areas 
are maintained at temperature 10ºC and 20 ºC. The 
thermal radiation emitted in a given time by P and 
Q are in the ratio 1 : 1.15 
 C. A carnot Engine working between 100 K and 
400 K has an efficiency of 75% 
 D. When small temperature difference between a 
liquid and its surrounding is quadrupled, the rate of 
loss of heat of the liquid becomes twice. 
 Choose the correct answer from the options given 
below : 
 (A) A, B, C only (B) A, B only 
 (C) A, C only (D) B, C, D only 
 Official Ans. by NTA (A) 
  
Page 3


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
 (Held On Wednesday 27
th
 July, 2022)          TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. A torque meter is calibrated to reference standards  
of mass, length and time each with 5% accuracy. 
After calibration, the measured torque with this 
torque meter will have net accuracy of : 
 (A) 15% (B) 25% (C) 75% (D) 5% 
 Official Ans. by NTA (B) 
  
Sol. Dimensional formula for Torque 
 [] ? = [ML
2
T
–2
] 
  Now 
 Percentage error in torque = % ? = % M + 2 % L  
2 % T 
 % ? = 25% 
2. A bullet is shot vertically downwards with an 
initial velocity of 100 m/s from a certain height. 
Within 10 s, the bullet reaches the ground and 
instantaneously comes to rest due to the perfectly 
inelastic collision. The velocity-time curve for total 
time t = 20 s will be : (Take g = 10 m/s
2
) 
 (A)
 
 
 (B)
  
  
 (C) 
 
 
 (D)
 
 
 Official Ans. by NTA (A) 
  
Sol. V = –100 –10t 
 
3. Sand is being dropped from a stationary dropper at 
a rate of 0.5 kgs
–1
 on a conveyor belt moving with 
a velocity of 5 ms
–1
. The power needed to keep belt 
moving with the same velocity will be : 
 (A) 1.25 W (B) 2.5 W 
 (C) 6.25 W  (D) 12.5 W 
 Official Ans. by NTA (D) 
  
Sol. Thrust = 
rel
V ? 
 = 2.5 N 
 Now, Power =F × V = 12.5 W 
4. A bag is gently dropped on a conveyor belt moving 
at a speed of 2 m/s. The coefficient of friction 
between the conveyor belt and bag is 0.4 Initially, 
the bag slips on the belt before it stops due to 
friction. The distance travelled by the bag on the 
belt during slipping motion is : [Take g = 10 m/s
–2
] 
 (A) 2 m (B) 0.5 m 
 (C) 3.2 m  (D) 0.8 ms 
 Official Ans. by NTA (B) 
  
Sol. In frame of belt 
 a = ? g = 4 m/s
2
 , v = 2m/s , u = 0 
 v
2
 = u
2
 + 2as 
 ? s = 0.5 m  
5. Two cylindrical vessels of equal cross-sectional 
area 16 cm
2
 contain water upto heights 100 cm and 
150 cm respectively. The vessels are 
interconnected so that the water levels in them 
become equal. The work done by the force of 
gravity during the process, is [Take density of 
water = 10
3
 kg/m
3
 and g = 10 ms
–2
] 
 (A) 0.25 J (B) 1 J 
 (C) 8 J  (D) 12 J 
 Official Ans. by NTA (B) 
  
 
2 
 
Sol. 
 
h
2
=
h
 
 
12
hh
h
2
?
? 
 Now, 
 W = U
i
–U
f
 
 W = ( ?Ah
1
) g 
1
h
2
+( ? Ah
2
)g
2
h
2
–?? A(h
1
+h
2
)g
12
hh
4
?? ?
??
??
 
 W = 
2
22 12
12
(h h ) Ag
h h –
22
?? ? ?
?
??
??
 
 W = 1 J  
6. Two satellites A and B having masses in the ratio 
4:3 are revolving in circular orbits of radii 3r and  
4 r respectively around the earth. The ratio of total 
mechanical energy of A to B is : 
 (A) 9 : 16 (B) 16 : 9 
 (C) 1 : 1  (D) 4 : 3 
 Official Ans. by NTA (B) 
  
Sol. Given that 
1
2
m 4
3 m
? , 
1
2
r 3
4 r
? 
 Now TE = 
1
2
 mv
2
+
–GMm
r
??
??
??
 
 but 
2
2
2
mv GMm GMm
mv
rr r
? ? ? 
 
GMm m
TE –
2r r
? ? ? 
 
1 1 2
2 2 1
TE m r 4 4 16
.
3 3 9 TE m r
? ? ? ? 
7. If K
1
 and K
2
 are the thermal conductivities L
1
 and 
L
2
 are the lengths and A
1
 and A
2
 are the cross 
sectional areas of steel and copper rods 
respectively such that 
2 1 1
1 2 2
9, 2, 2
K A L
K A L
? ? ? . 
Then, for the arrangement as shown in the figure. 
The value of temperature T of the steel – copper 
junction in the steady state will be : 
  
 (A) 18ºC (B) 14 ºC 
 (C) 45 ºC  (D) 150 ºC 
 Official Ans. by NTA (C) 
  
Sol. 
A
1
l
1
K
1
Steel
Copper K
2
l
1
A
2
T =0ºC
2
1 1 2 2
12
12
K A K A d
(T – T) (T – T )
dtll
?
?? 
 
2 2 1
1 1 2
K A l 450 – T 1
92
T – 0 2 K A l
? ? ? ? ? 
 ? 450 – T = 9T ? T = 45ºC 
8. Read the following statements : 
 A. When small temperature difference between a 
liquid and its surrounding is doubled the rate of 
loss of heat of the liquid becomes twice. 
 B. Two bodies P and Q having equal surface areas 
are maintained at temperature 10ºC and 20 ºC. The 
thermal radiation emitted in a given time by P and 
Q are in the ratio 1 : 1.15 
 C. A carnot Engine working between 100 K and 
400 K has an efficiency of 75% 
 D. When small temperature difference between a 
liquid and its surrounding is quadrupled, the rate of 
loss of heat of the liquid becomes twice. 
 Choose the correct answer from the options given 
below : 
 (A) A, B, C only (B) A, B only 
 (C) A, C only (D) B, C, D only 
 Official Ans. by NTA (A) 
  
 
 
3 
 
Sol. Heat Transfer 
 A. by Newton’s low of colling 
d
T
dt
?
? ? ? 
 B. 
4
4
4 PP
QQ
HT d 283
H eAT
dt 293 HT
??
? ??
? ? ? ? ? ? ??
??
??
??
??
 
 H
P
 : H
Q
 = 1 (1.03)
4
 = 1 : (1.03)
4
 = 1 : 1.15 
 ? B is correct 
 C. ? = 1 – 
100 3
75%
400 4
?? 
 D. is wrong as 
d
T
dt
?
?? 
9. Same gas is filled in two vessels of the same 
volume at the same temperature. If the ratio of the 
number of molecules is 1:4, then 
 A. The r.m.s. velocity of gas molecules in two 
vessels will be the same. 
 B. The ratio of pressure in these vessels will  
be 1 : 4 
 C. The ratio of pressure will be 1 : 1 
 D. The r.m.s. velocity of gas molecules in two 
vessels will be in the ratio of 1 : 4 
 (A) A and C only (B) B and D only 
 (C) A and B only (D) C and D only 
 Official Ans. by NTA (C) 
  
Sol. KTG 
 A. V
Rms
 = 
w
3RT
M
? V
Rms
 is same 
 B. 
11
22
PN
PN
?? B is correct 
 Ans [A & B only are correct] 
10. Two identical positive charges Q each are fixed at 
a distance of ‘2a’ apart from each other. Another 
point charge q
0
 with mass ‘m’ is placed at 
midpoint between two fixed charges. For a small 
displacement along the line joining the fixed 
charges, the charge q
0 
executes SHM. The time 
period of oscillation of charge q
0  
will be : 
 (A) 
33
0
0
4 ma
qQ
??
 (B) 
0
33
0
4
qQ
ma ??
 
 (C) 
??
23
0
0
2 ma
qQ
 (D) 
33
0
0
8 ma
qQ
??
 
 Official Ans. by NTA (A) 
  
Sol. Electrostatics 
  
 F = m acc
n 
= 
00
22
KQq KQq
–
(a – x) (a x) ?
 
 m acc
n 
=
0
2 2 2
KQq [2a][2x]
(a – x )
 
 
n 0
3
4kQq
acc x
ma
??
??
??
??
 
 T = 
3
0
0
ma
2
Qq
??
? 
 T = 
33
0
0
4 ma
Qq
??
 
11. Two sources of equal emfs are connected in series. 
This combination is connected to an external 
resistance R. The internal resistances of the two 
sources are r
1
 and r
2
 (r
1
 > r
2
). If the potential 
difference across the source of internal resistance r
1 
is zero then the value of R will be 
 (A) r
1
 – r
2
 (B) 
?
12
12
r
r
r
r
 
 (C) 
?
12
r
2
r
 (D) r
2
 – r
1
 
 Official Ans. by NTA (A) 
  
Sol. 
I R
r
1
r
2
E
V = 0
 
 
12
2E
I
rrR
?
??
 
 IR = E – Ir
2 
 
I (R+ r
2
)= E 
 
2
E
I
Rr
?
?
 
 
1 2 2
2E E
r r R R r
?
? ? ?
 
 2R + 2r
2
 = r
1
 + r
2
 + R 
 R = r
1
 – r
2
 
Page 4


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
 (Held On Wednesday 27
th
 July, 2022)          TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. A torque meter is calibrated to reference standards  
of mass, length and time each with 5% accuracy. 
After calibration, the measured torque with this 
torque meter will have net accuracy of : 
 (A) 15% (B) 25% (C) 75% (D) 5% 
 Official Ans. by NTA (B) 
  
Sol. Dimensional formula for Torque 
 [] ? = [ML
2
T
–2
] 
  Now 
 Percentage error in torque = % ? = % M + 2 % L  
2 % T 
 % ? = 25% 
2. A bullet is shot vertically downwards with an 
initial velocity of 100 m/s from a certain height. 
Within 10 s, the bullet reaches the ground and 
instantaneously comes to rest due to the perfectly 
inelastic collision. The velocity-time curve for total 
time t = 20 s will be : (Take g = 10 m/s
2
) 
 (A)
 
 
 (B)
  
  
 (C) 
 
 
 (D)
 
 
 Official Ans. by NTA (A) 
  
Sol. V = –100 –10t 
 
3. Sand is being dropped from a stationary dropper at 
a rate of 0.5 kgs
–1
 on a conveyor belt moving with 
a velocity of 5 ms
–1
. The power needed to keep belt 
moving with the same velocity will be : 
 (A) 1.25 W (B) 2.5 W 
 (C) 6.25 W  (D) 12.5 W 
 Official Ans. by NTA (D) 
  
Sol. Thrust = 
rel
V ? 
 = 2.5 N 
 Now, Power =F × V = 12.5 W 
4. A bag is gently dropped on a conveyor belt moving 
at a speed of 2 m/s. The coefficient of friction 
between the conveyor belt and bag is 0.4 Initially, 
the bag slips on the belt before it stops due to 
friction. The distance travelled by the bag on the 
belt during slipping motion is : [Take g = 10 m/s
–2
] 
 (A) 2 m (B) 0.5 m 
 (C) 3.2 m  (D) 0.8 ms 
 Official Ans. by NTA (B) 
  
Sol. In frame of belt 
 a = ? g = 4 m/s
2
 , v = 2m/s , u = 0 
 v
2
 = u
2
 + 2as 
 ? s = 0.5 m  
5. Two cylindrical vessels of equal cross-sectional 
area 16 cm
2
 contain water upto heights 100 cm and 
150 cm respectively. The vessels are 
interconnected so that the water levels in them 
become equal. The work done by the force of 
gravity during the process, is [Take density of 
water = 10
3
 kg/m
3
 and g = 10 ms
–2
] 
 (A) 0.25 J (B) 1 J 
 (C) 8 J  (D) 12 J 
 Official Ans. by NTA (B) 
  
 
2 
 
Sol. 
 
h
2
=
h
 
 
12
hh
h
2
?
? 
 Now, 
 W = U
i
–U
f
 
 W = ( ?Ah
1
) g 
1
h
2
+( ? Ah
2
)g
2
h
2
–?? A(h
1
+h
2
)g
12
hh
4
?? ?
??
??
 
 W = 
2
22 12
12
(h h ) Ag
h h –
22
?? ? ?
?
??
??
 
 W = 1 J  
6. Two satellites A and B having masses in the ratio 
4:3 are revolving in circular orbits of radii 3r and  
4 r respectively around the earth. The ratio of total 
mechanical energy of A to B is : 
 (A) 9 : 16 (B) 16 : 9 
 (C) 1 : 1  (D) 4 : 3 
 Official Ans. by NTA (B) 
  
Sol. Given that 
1
2
m 4
3 m
? , 
1
2
r 3
4 r
? 
 Now TE = 
1
2
 mv
2
+
–GMm
r
??
??
??
 
 but 
2
2
2
mv GMm GMm
mv
rr r
? ? ? 
 
GMm m
TE –
2r r
? ? ? 
 
1 1 2
2 2 1
TE m r 4 4 16
.
3 3 9 TE m r
? ? ? ? 
7. If K
1
 and K
2
 are the thermal conductivities L
1
 and 
L
2
 are the lengths and A
1
 and A
2
 are the cross 
sectional areas of steel and copper rods 
respectively such that 
2 1 1
1 2 2
9, 2, 2
K A L
K A L
? ? ? . 
Then, for the arrangement as shown in the figure. 
The value of temperature T of the steel – copper 
junction in the steady state will be : 
  
 (A) 18ºC (B) 14 ºC 
 (C) 45 ºC  (D) 150 ºC 
 Official Ans. by NTA (C) 
  
Sol. 
A
1
l
1
K
1
Steel
Copper K
2
l
1
A
2
T =0ºC
2
1 1 2 2
12
12
K A K A d
(T – T) (T – T )
dtll
?
?? 
 
2 2 1
1 1 2
K A l 450 – T 1
92
T – 0 2 K A l
? ? ? ? ? 
 ? 450 – T = 9T ? T = 45ºC 
8. Read the following statements : 
 A. When small temperature difference between a 
liquid and its surrounding is doubled the rate of 
loss of heat of the liquid becomes twice. 
 B. Two bodies P and Q having equal surface areas 
are maintained at temperature 10ºC and 20 ºC. The 
thermal radiation emitted in a given time by P and 
Q are in the ratio 1 : 1.15 
 C. A carnot Engine working between 100 K and 
400 K has an efficiency of 75% 
 D. When small temperature difference between a 
liquid and its surrounding is quadrupled, the rate of 
loss of heat of the liquid becomes twice. 
 Choose the correct answer from the options given 
below : 
 (A) A, B, C only (B) A, B only 
 (C) A, C only (D) B, C, D only 
 Official Ans. by NTA (A) 
  
 
 
3 
 
Sol. Heat Transfer 
 A. by Newton’s low of colling 
d
T
dt
?
? ? ? 
 B. 
4
4
4 PP
QQ
HT d 283
H eAT
dt 293 HT
??
? ??
? ? ? ? ? ? ??
??
??
??
??
 
 H
P
 : H
Q
 = 1 (1.03)
4
 = 1 : (1.03)
4
 = 1 : 1.15 
 ? B is correct 
 C. ? = 1 – 
100 3
75%
400 4
?? 
 D. is wrong as 
d
T
dt
?
?? 
9. Same gas is filled in two vessels of the same 
volume at the same temperature. If the ratio of the 
number of molecules is 1:4, then 
 A. The r.m.s. velocity of gas molecules in two 
vessels will be the same. 
 B. The ratio of pressure in these vessels will  
be 1 : 4 
 C. The ratio of pressure will be 1 : 1 
 D. The r.m.s. velocity of gas molecules in two 
vessels will be in the ratio of 1 : 4 
 (A) A and C only (B) B and D only 
 (C) A and B only (D) C and D only 
 Official Ans. by NTA (C) 
  
Sol. KTG 
 A. V
Rms
 = 
w
3RT
M
? V
Rms
 is same 
 B. 
11
22
PN
PN
?? B is correct 
 Ans [A & B only are correct] 
10. Two identical positive charges Q each are fixed at 
a distance of ‘2a’ apart from each other. Another 
point charge q
0
 with mass ‘m’ is placed at 
midpoint between two fixed charges. For a small 
displacement along the line joining the fixed 
charges, the charge q
0 
executes SHM. The time 
period of oscillation of charge q
0  
will be : 
 (A) 
33
0
0
4 ma
qQ
??
 (B) 
0
33
0
4
qQ
ma ??
 
 (C) 
??
23
0
0
2 ma
qQ
 (D) 
33
0
0
8 ma
qQ
??
 
 Official Ans. by NTA (A) 
  
Sol. Electrostatics 
  
 F = m acc
n 
= 
00
22
KQq KQq
–
(a – x) (a x) ?
 
 m acc
n 
=
0
2 2 2
KQq [2a][2x]
(a – x )
 
 
n 0
3
4kQq
acc x
ma
??
??
??
??
 
 T = 
3
0
0
ma
2
Qq
??
? 
 T = 
33
0
0
4 ma
Qq
??
 
11. Two sources of equal emfs are connected in series. 
This combination is connected to an external 
resistance R. The internal resistances of the two 
sources are r
1
 and r
2
 (r
1
 > r
2
). If the potential 
difference across the source of internal resistance r
1 
is zero then the value of R will be 
 (A) r
1
 – r
2
 (B) 
?
12
12
r
r
r
r
 
 (C) 
?
12
r
2
r
 (D) r
2
 – r
1
 
 Official Ans. by NTA (A) 
  
Sol. 
I R
r
1
r
2
E
V = 0
 
 
12
2E
I
rrR
?
??
 
 IR = E – Ir
2 
 
I (R+ r
2
)= E 
 
2
E
I
Rr
?
?
 
 
1 2 2
2E E
r r R R r
?
? ? ?
 
 2R + 2r
2
 = r
1
 + r
2
 + R 
 R = r
1
 – r
2
 
 
4 
 
12. Two bar magnets oscillate in a horizontal plane in 
earth’s magnetic field with time periods of 3 s and 
4 s respectively. If their moments of inertia are in 
the ratio of 3 : 2 then the ratio of their magnetic 
moments will e : 
 (A) 2 : 1 (B) 8 : 3 
 (C) 1 : 3  (D) 27 : 16 
 Official Ans. by NTA (B) 
  
Sol. T = 
H
I
2
MB
? 
 
1
1H 1
2
2
2H
I
2
MB T
T
I
2
MB
?
?
?
=
3
4
 
 
12
21
IM 3
4 IM
?? 
 
12
21
IM 3
4 IM
?? 
 
2
1
M 33
24 M
?? 
 
2
1
M 39
2 16 M
?? 
 
1
2
M 8
3 M
?  
13. A magnet hung at 45º with magnetic meridian 
makes an angle of 60º with the horizontal. The 
actual value of the angle of dip is 
 (A) 
–1
3
tan
2
??
??
??
??
 (B) 
? ?
–1
tan 6 
 (C) 
–1
2
tan
3
??
??
??
??
 (D) 
–1
1
tan
2
??
??
??
??
 
 Official Ans. by NTA (A) 
  
Sol. 
tan
tan '
cos
?
??
?
 
 ? ’ = 60º 
 ? = 45º 
 
tan
3
1
2
?
? 
 
3
tan
2
?? 
 
–1
3
tan
2
??
 
14. A direct current of 4 A and an alternating current 
of peak value 4 A flow through resistance of 3 ? 
and 2 ? respectively. The ratio of heat produced 
in the two resistances in same interval of time will 
be : 
 (A) 3 : 2 (B) 3 : 1 
 (C) 3 : 4  (D) 4 : 3 
 Official Ans. by NTA (B) 
  
Sol.  
 
?
4A
DC
i =4A
0
AC
2 ?
 
 H
1 
= i
2
R
1
t            H
2 
= 
2 0
rms 2 rms
i
i R t i
2
??
??
?
??
??
??
 
 H
1 
= 16(3)t         H
2 
= 
2
0
2
i
Rt
2
 
                            H
2 
= 16t 
  H
1 
: H
2
 = 3 : 1 
15. A beam of light travelling along X-axis  
is described by the electric field  
E
y
 = 900 sin ? (t–x/c). The ratio of electric force to 
magnetic force on a charge q moving along Y-axis 
with a speed of 3 × 10
7
 ms
–1
 will be :  
 [Given speed of light = 3 × 10
8
 ms
–1
] 
 (A) 1 : 1 (B) 1 : 10 
 (C) 10 : 1  (D) 1 : 2 
 Official Ans. by NTA (C) 
  
Page 5


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
 (Held On Wednesday 27
th
 July, 2022)          TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. A torque meter is calibrated to reference standards  
of mass, length and time each with 5% accuracy. 
After calibration, the measured torque with this 
torque meter will have net accuracy of : 
 (A) 15% (B) 25% (C) 75% (D) 5% 
 Official Ans. by NTA (B) 
  
Sol. Dimensional formula for Torque 
 [] ? = [ML
2
T
–2
] 
  Now 
 Percentage error in torque = % ? = % M + 2 % L  
2 % T 
 % ? = 25% 
2. A bullet is shot vertically downwards with an 
initial velocity of 100 m/s from a certain height. 
Within 10 s, the bullet reaches the ground and 
instantaneously comes to rest due to the perfectly 
inelastic collision. The velocity-time curve for total 
time t = 20 s will be : (Take g = 10 m/s
2
) 
 (A)
 
 
 (B)
  
  
 (C) 
 
 
 (D)
 
 
 Official Ans. by NTA (A) 
  
Sol. V = –100 –10t 
 
3. Sand is being dropped from a stationary dropper at 
a rate of 0.5 kgs
–1
 on a conveyor belt moving with 
a velocity of 5 ms
–1
. The power needed to keep belt 
moving with the same velocity will be : 
 (A) 1.25 W (B) 2.5 W 
 (C) 6.25 W  (D) 12.5 W 
 Official Ans. by NTA (D) 
  
Sol. Thrust = 
rel
V ? 
 = 2.5 N 
 Now, Power =F × V = 12.5 W 
4. A bag is gently dropped on a conveyor belt moving 
at a speed of 2 m/s. The coefficient of friction 
between the conveyor belt and bag is 0.4 Initially, 
the bag slips on the belt before it stops due to 
friction. The distance travelled by the bag on the 
belt during slipping motion is : [Take g = 10 m/s
–2
] 
 (A) 2 m (B) 0.5 m 
 (C) 3.2 m  (D) 0.8 ms 
 Official Ans. by NTA (B) 
  
Sol. In frame of belt 
 a = ? g = 4 m/s
2
 , v = 2m/s , u = 0 
 v
2
 = u
2
 + 2as 
 ? s = 0.5 m  
5. Two cylindrical vessels of equal cross-sectional 
area 16 cm
2
 contain water upto heights 100 cm and 
150 cm respectively. The vessels are 
interconnected so that the water levels in them 
become equal. The work done by the force of 
gravity during the process, is [Take density of 
water = 10
3
 kg/m
3
 and g = 10 ms
–2
] 
 (A) 0.25 J (B) 1 J 
 (C) 8 J  (D) 12 J 
 Official Ans. by NTA (B) 
  
 
2 
 
Sol. 
 
h
2
=
h
 
 
12
hh
h
2
?
? 
 Now, 
 W = U
i
–U
f
 
 W = ( ?Ah
1
) g 
1
h
2
+( ? Ah
2
)g
2
h
2
–?? A(h
1
+h
2
)g
12
hh
4
?? ?
??
??
 
 W = 
2
22 12
12
(h h ) Ag
h h –
22
?? ? ?
?
??
??
 
 W = 1 J  
6. Two satellites A and B having masses in the ratio 
4:3 are revolving in circular orbits of radii 3r and  
4 r respectively around the earth. The ratio of total 
mechanical energy of A to B is : 
 (A) 9 : 16 (B) 16 : 9 
 (C) 1 : 1  (D) 4 : 3 
 Official Ans. by NTA (B) 
  
Sol. Given that 
1
2
m 4
3 m
? , 
1
2
r 3
4 r
? 
 Now TE = 
1
2
 mv
2
+
–GMm
r
??
??
??
 
 but 
2
2
2
mv GMm GMm
mv
rr r
? ? ? 
 
GMm m
TE –
2r r
? ? ? 
 
1 1 2
2 2 1
TE m r 4 4 16
.
3 3 9 TE m r
? ? ? ? 
7. If K
1
 and K
2
 are the thermal conductivities L
1
 and 
L
2
 are the lengths and A
1
 and A
2
 are the cross 
sectional areas of steel and copper rods 
respectively such that 
2 1 1
1 2 2
9, 2, 2
K A L
K A L
? ? ? . 
Then, for the arrangement as shown in the figure. 
The value of temperature T of the steel – copper 
junction in the steady state will be : 
  
 (A) 18ºC (B) 14 ºC 
 (C) 45 ºC  (D) 150 ºC 
 Official Ans. by NTA (C) 
  
Sol. 
A
1
l
1
K
1
Steel
Copper K
2
l
1
A
2
T =0ºC
2
1 1 2 2
12
12
K A K A d
(T – T) (T – T )
dtll
?
?? 
 
2 2 1
1 1 2
K A l 450 – T 1
92
T – 0 2 K A l
? ? ? ? ? 
 ? 450 – T = 9T ? T = 45ºC 
8. Read the following statements : 
 A. When small temperature difference between a 
liquid and its surrounding is doubled the rate of 
loss of heat of the liquid becomes twice. 
 B. Two bodies P and Q having equal surface areas 
are maintained at temperature 10ºC and 20 ºC. The 
thermal radiation emitted in a given time by P and 
Q are in the ratio 1 : 1.15 
 C. A carnot Engine working between 100 K and 
400 K has an efficiency of 75% 
 D. When small temperature difference between a 
liquid and its surrounding is quadrupled, the rate of 
loss of heat of the liquid becomes twice. 
 Choose the correct answer from the options given 
below : 
 (A) A, B, C only (B) A, B only 
 (C) A, C only (D) B, C, D only 
 Official Ans. by NTA (A) 
  
 
 
3 
 
Sol. Heat Transfer 
 A. by Newton’s low of colling 
d
T
dt
?
? ? ? 
 B. 
4
4
4 PP
QQ
HT d 283
H eAT
dt 293 HT
??
? ??
? ? ? ? ? ? ??
??
??
??
??
 
 H
P
 : H
Q
 = 1 (1.03)
4
 = 1 : (1.03)
4
 = 1 : 1.15 
 ? B is correct 
 C. ? = 1 – 
100 3
75%
400 4
?? 
 D. is wrong as 
d
T
dt
?
?? 
9. Same gas is filled in two vessels of the same 
volume at the same temperature. If the ratio of the 
number of molecules is 1:4, then 
 A. The r.m.s. velocity of gas molecules in two 
vessels will be the same. 
 B. The ratio of pressure in these vessels will  
be 1 : 4 
 C. The ratio of pressure will be 1 : 1 
 D. The r.m.s. velocity of gas molecules in two 
vessels will be in the ratio of 1 : 4 
 (A) A and C only (B) B and D only 
 (C) A and B only (D) C and D only 
 Official Ans. by NTA (C) 
  
Sol. KTG 
 A. V
Rms
 = 
w
3RT
M
? V
Rms
 is same 
 B. 
11
22
PN
PN
?? B is correct 
 Ans [A & B only are correct] 
10. Two identical positive charges Q each are fixed at 
a distance of ‘2a’ apart from each other. Another 
point charge q
0
 with mass ‘m’ is placed at 
midpoint between two fixed charges. For a small 
displacement along the line joining the fixed 
charges, the charge q
0 
executes SHM. The time 
period of oscillation of charge q
0  
will be : 
 (A) 
33
0
0
4 ma
qQ
??
 (B) 
0
33
0
4
qQ
ma ??
 
 (C) 
??
23
0
0
2 ma
qQ
 (D) 
33
0
0
8 ma
qQ
??
 
 Official Ans. by NTA (A) 
  
Sol. Electrostatics 
  
 F = m acc
n 
= 
00
22
KQq KQq
–
(a – x) (a x) ?
 
 m acc
n 
=
0
2 2 2
KQq [2a][2x]
(a – x )
 
 
n 0
3
4kQq
acc x
ma
??
??
??
??
 
 T = 
3
0
0
ma
2
Qq
??
? 
 T = 
33
0
0
4 ma
Qq
??
 
11. Two sources of equal emfs are connected in series. 
This combination is connected to an external 
resistance R. The internal resistances of the two 
sources are r
1
 and r
2
 (r
1
 > r
2
). If the potential 
difference across the source of internal resistance r
1 
is zero then the value of R will be 
 (A) r
1
 – r
2
 (B) 
?
12
12
r
r
r
r
 
 (C) 
?
12
r
2
r
 (D) r
2
 – r
1
 
 Official Ans. by NTA (A) 
  
Sol. 
I R
r
1
r
2
E
V = 0
 
 
12
2E
I
rrR
?
??
 
 IR = E – Ir
2 
 
I (R+ r
2
)= E 
 
2
E
I
Rr
?
?
 
 
1 2 2
2E E
r r R R r
?
? ? ?
 
 2R + 2r
2
 = r
1
 + r
2
 + R 
 R = r
1
 – r
2
 
 
4 
 
12. Two bar magnets oscillate in a horizontal plane in 
earth’s magnetic field with time periods of 3 s and 
4 s respectively. If their moments of inertia are in 
the ratio of 3 : 2 then the ratio of their magnetic 
moments will e : 
 (A) 2 : 1 (B) 8 : 3 
 (C) 1 : 3  (D) 27 : 16 
 Official Ans. by NTA (B) 
  
Sol. T = 
H
I
2
MB
? 
 
1
1H 1
2
2
2H
I
2
MB T
T
I
2
MB
?
?
?
=
3
4
 
 
12
21
IM 3
4 IM
?? 
 
12
21
IM 3
4 IM
?? 
 
2
1
M 33
24 M
?? 
 
2
1
M 39
2 16 M
?? 
 
1
2
M 8
3 M
?  
13. A magnet hung at 45º with magnetic meridian 
makes an angle of 60º with the horizontal. The 
actual value of the angle of dip is 
 (A) 
–1
3
tan
2
??
??
??
??
 (B) 
? ?
–1
tan 6 
 (C) 
–1
2
tan
3
??
??
??
??
 (D) 
–1
1
tan
2
??
??
??
??
 
 Official Ans. by NTA (A) 
  
Sol. 
tan
tan '
cos
?
??
?
 
 ? ’ = 60º 
 ? = 45º 
 
tan
3
1
2
?
? 
 
3
tan
2
?? 
 
–1
3
tan
2
??
 
14. A direct current of 4 A and an alternating current 
of peak value 4 A flow through resistance of 3 ? 
and 2 ? respectively. The ratio of heat produced 
in the two resistances in same interval of time will 
be : 
 (A) 3 : 2 (B) 3 : 1 
 (C) 3 : 4  (D) 4 : 3 
 Official Ans. by NTA (B) 
  
Sol.  
 
?
4A
DC
i =4A
0
AC
2 ?
 
 H
1 
= i
2
R
1
t            H
2 
= 
2 0
rms 2 rms
i
i R t i
2
??
??
?
??
??
??
 
 H
1 
= 16(3)t         H
2 
= 
2
0
2
i
Rt
2
 
                            H
2 
= 16t 
  H
1 
: H
2
 = 3 : 1 
15. A beam of light travelling along X-axis  
is described by the electric field  
E
y
 = 900 sin ? (t–x/c). The ratio of electric force to 
magnetic force on a charge q moving along Y-axis 
with a speed of 3 × 10
7
 ms
–1
 will be :  
 [Given speed of light = 3 × 10
8
 ms
–1
] 
 (A) 1 : 1 (B) 1 : 10 
 (C) 10 : 1  (D) 1 : 2 
 Official Ans. by NTA (C) 
  
 
 
5 
 
Sol. 
y
x
E 900sin t –
c
? ??
??
??
??
 
 E
0
 = 900 
 
B
V
y
z
x
 
 F
E
 = qE
0
 
 F
B
 = qvB
0 
 
8
0 E
7
B0
E F c 3 10
10:1
v F vB 3 10
?
? ? ? ?
?
 
16. A microscope was initially placed in air (refractive 
index 1). It is then immersed in oil (refractive 
index 2). For a light whose wavelength in air is ? , 
calculate the change of microscope’s resolving 
power due to oil and choose the correct option 
 (A) Resolving power will be 
1
4
 in the oil than it 
was in the air 
 (B) Resolving power will be twice in the oil than it 
was in the air. 
 (C) Resolving power will be four times in the oil 
than it was in the air. 
 (D) Resolving power will be 
1
2
 in the oil than it 
was in the air. 
 Official Ans. by NTA (C)  
  
Sol. (R.P)
air 
= 
2sin
1.22
?
?
 
 
oil
oil
2sin 2sin
(R.P)
1.22 1.22
? ? ? ?
??
? ?
 
 
(R.P)
oil 
= (R.P)
air 
× 2 
 
17. An electron (mass m) with an initial velocity 
00
v v i(v 0) ?? is moving in an electric field 
00
E –E i(E 0) ?? where E
0
 is constant. If at t = 0 
de Broglie wavelength is 
0
0
h
mv
?? , then its de 
Broglie wavelength after time t is given by 
 (A) 
0
? (B) 
0
0
0
eE t
1
mv
??
??
??
??
 
 (C) 
0
t ?  (D) 
0
0
0
eE t
1
mv
?
??
?
??
??
 
 Official Ans. by NTA (D) 
  
Sol. 
V
0
 
 
0
ˆ
E –E i ? 
 
0
0
h
mv
?? 
 v = v
0
 + 
0
eE t
m
 
 
0
0
hh
mv
eE
m v t
m
? ? ?
??
?
??
??
 
 
0
0
0
h
'
eE
mv 1 t
mv
??
??
?
??
??
 
 
0
0
0
'
eE
1t
mv
?
??
??
?
??
??
 
18. What is the half-life period of a radioactive 
material if its activity drops to 1/16
th
 of its initial 
value of 30 years ? 
 (A) 9.5 years (B) 8.5 years 
 (C) 7.5 years (D) 10.5 years 
 Official Ans. by NTA (C) 
  
Sol. 
t
0
A A e
??
? 
 
0
A
tn
A
??
? ? ? ?
??
??
 
 
1/2
n2 1
30 n
t 16
??
? ? ? ?
??
??
 
 
1/2
n2
30 4 n2
t
? ? ? ? ? 
 
1/2
30
t 7.5
4
? ? ? yrs