JEE Main 2022 Question Paper 28 July Shift 2 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Thursday 28
th
 July, 2022)           TIME : 3 : 00 PM  to  6 : 00 PM 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
SECTION-A 
1. Consider the efficiency of Carnot’s engine is given 
by 
e
x
log ,
sin kT
? ? ?
??
?
 where ? and ? are constants. 
If T is temperature, k is Boltzman constant, ? is 
angular displacement and x has the dimensions of 
length. Then, choose the incorrect option. 
 (A) Dimensions of ? is same as that of force. 
 (B) Dimensions of ?
–1
 x is same as that of energy. 
 (C) Dimensions of ?
–1
 sin ? is same as that of ?? 
 (D) Dimensions of ? is same as that of ? 
 Official Ans. by NTA (D) 
  
Sol. [ ] [ ] [sin ] Dimensionless ? ? ? ? ? ? ? 
 
1
sin [ ] D.L.
?
??
? ? ? ? ? ?
??
 
2. At time t = 0 a particle starts travelling from a 
height 7z cm in a plane keeping z coordinate 
constant. At any instant of time it’s position along 
the x and y directions are defined as 3t and 5t
3
 
respectively. At t = 1s acceleration of the particle 
will be 
 (A) 30y ?  (B) 30y 
 (C) 3x 15y ? (D) 3x 15y 7z ?? 
 Official Ans. by NTA (B) 
  
Sol. 
3
r 3ti 5t j 7k ? ? ? 
 
2
2
dr
30t j
dt
? 
 At  t = 1  
2
2
dr
30j
dt
?? 
3. A pressure-pump has a horizontal tube of  
cross-sectional area 10 cm
2
 for the outflow of 
water at a speed of 20 m/s. The force exerted on 
the vertical wall just in front of the tube which 
stops water horizontally flowing out of the tube, is: 
 [given : density of water = 1000 kg/m
3
] 
 (A) 300 N  (B) 500 N 
 (C) 250 N  (D) 400 N 
 Official Ans. by NTA (D) 
  
Sol. 
2 3 4
F a 10 10 10 20 20
?
? ? ? ? ? ? ? ? 
 F = 400 
4. A uniform metal chain of mass m and length ‘L’ 
passes over a massless and frictionless pulley. It is 
released from rest with a part of its length ‘l’ is 
hanging on one side and rest of its length ‘L – l’ is 
hanging on the other side of the pulley. At a certain 
point of time, when 
L
x
? l , the acceleration of the 
chain is 
g
2
. The value of x is ……… 
 
 (A) 6 (B) 2 (C) 1.5 (D) 4 
 Official Ans. by NTA (D) 
  
Sol.  
 
21
21
(m m )
ag
(m m )
?
?
?
 
 
g ( (L ) )g L L
L
2 L 4 x
? ? ? ?
? ? ? ?
?
 
 x = 4 
Page 2


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Thursday 28
th
 July, 2022)           TIME : 3 : 00 PM  to  6 : 00 PM 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
SECTION-A 
1. Consider the efficiency of Carnot’s engine is given 
by 
e
x
log ,
sin kT
? ? ?
??
?
 where ? and ? are constants. 
If T is temperature, k is Boltzman constant, ? is 
angular displacement and x has the dimensions of 
length. Then, choose the incorrect option. 
 (A) Dimensions of ? is same as that of force. 
 (B) Dimensions of ?
–1
 x is same as that of energy. 
 (C) Dimensions of ?
–1
 sin ? is same as that of ?? 
 (D) Dimensions of ? is same as that of ? 
 Official Ans. by NTA (D) 
  
Sol. [ ] [ ] [sin ] Dimensionless ? ? ? ? ? ? ? 
 
1
sin [ ] D.L.
?
??
? ? ? ? ? ?
??
 
2. At time t = 0 a particle starts travelling from a 
height 7z cm in a plane keeping z coordinate 
constant. At any instant of time it’s position along 
the x and y directions are defined as 3t and 5t
3
 
respectively. At t = 1s acceleration of the particle 
will be 
 (A) 30y ?  (B) 30y 
 (C) 3x 15y ? (D) 3x 15y 7z ?? 
 Official Ans. by NTA (B) 
  
Sol. 
3
r 3ti 5t j 7k ? ? ? 
 
2
2
dr
30t j
dt
? 
 At  t = 1  
2
2
dr
30j
dt
?? 
3. A pressure-pump has a horizontal tube of  
cross-sectional area 10 cm
2
 for the outflow of 
water at a speed of 20 m/s. The force exerted on 
the vertical wall just in front of the tube which 
stops water horizontally flowing out of the tube, is: 
 [given : density of water = 1000 kg/m
3
] 
 (A) 300 N  (B) 500 N 
 (C) 250 N  (D) 400 N 
 Official Ans. by NTA (D) 
  
Sol. 
2 3 4
F a 10 10 10 20 20
?
? ? ? ? ? ? ? ? 
 F = 400 
4. A uniform metal chain of mass m and length ‘L’ 
passes over a massless and frictionless pulley. It is 
released from rest with a part of its length ‘l’ is 
hanging on one side and rest of its length ‘L – l’ is 
hanging on the other side of the pulley. At a certain 
point of time, when 
L
x
? l , the acceleration of the 
chain is 
g
2
. The value of x is ……… 
 
 (A) 6 (B) 2 (C) 1.5 (D) 4 
 Official Ans. by NTA (D) 
  
Sol.  
 
21
21
(m m )
ag
(m m )
?
?
?
 
 
g ( (L ) )g L L
L
2 L 4 x
? ? ? ?
? ? ? ?
?
 
 x = 4 
 
2 
 
5. A bullet of mass 200 g having initial kinetic energy 
90 J is shot inside a long swimming pool as shown 
in the figure. If it’s kinetic energy reduces to 40 J 
within 1s, the minimum length of the pool, the 
bullet has a to travel so that it completely comes to 
rest is 
 
 (A) 45 m  (B) 90 m 
 (C) 125 m  (D) 25 m 
 Official Ans. by NTA (A) 
  
Sol. Using mv 2mk ? 
 
1
u 2 0.2 90 30 m/s
0.2
? ? ? ? 
 
1
v 2 0.2 40 20 m/s
0.2
? ? ? ? 
 
2
20 30
a 10 m/s
1
?
? ? ? 
 
2
u
s 45 m
2a
?
?? 
6. Assume there are two identical simple pendulum 
Clocks-1 is placed on the earth and Clock-2 is 
placed on a space station located at a height h 
above the earth surface. Clock-1 and Clock-2 
operate at time periods 4s and 6s respectively. 
Then the value of h is – 
 (consider radius of earth R
E
 = 6400 km and g on 
earth 10 m/s
2
) 
 (A) 1200 km 
 (B) 1600 km 
 (C) 3200 km 
 (D) 4800 km 
 Official Ans. by NTA (C) 
  
Sol. 
2
11
t and g
g (R h)
??
?
 
 
2
1
2
2
t g' R
tg (R h)
??
?
 
 
1
2
t 4R
h 3200km
t 6 (R h)
? ? ? ?
?
 
7. Consider a cylindrical tank of radius 1m is filled 
with water. The top surface of water is at 15 m 
from the bottom of the cylinder. There is a hole on 
the wall of cylinder at a height of 5m from the 
bottom. A force of 5 × 10
5
 N is applied an the top 
surface of water using a piston. The speed of efflux 
from the hole will be : 
 (given atmospheric pressure P
A
 = 1.01 × 10
5
 Pa, 
density of water ?
w
 = 1000 kg/m
3
 and gravitational 
acceleration g = 10 m/s
2
) 
 
 (A) 11.6 m/s  (B) 10.8 m/s 
 (C) 17.8 m/s  (D) 14.4 m/s 
 Official Ans. by NTA (C) 
  
Sol. Apply Bernoulli’s theorem between Piston and 
hole P
A
 + 
2
0e
1
gh P v
2
? ? ? ? 
 Assuming there is no atmospheric pressure on 
piston  
 
5
3 5 3 2
e
5 10 1
10 10 10 1.01 10 10 v
2
?
? ? ? ? ? ? ? ?
?
 
 v
e
 = 17.8 m/s 
8. A vessel contains 14 g of nitrogen gas at a 
temperature of 27°C. The amount of heat to be 
transferred to the gap to double the r.m.s. speed of 
its molecules will be : (Take R = 8.32 J mol
–1
k
–1
) 
 (A) 2229 J  (B) 5616 J 
 (C) 9360 J  (D) 13,104 J 
 Official Ans. by NTA (C) 
  
Page 3


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Thursday 28
th
 July, 2022)           TIME : 3 : 00 PM  to  6 : 00 PM 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
SECTION-A 
1. Consider the efficiency of Carnot’s engine is given 
by 
e
x
log ,
sin kT
? ? ?
??
?
 where ? and ? are constants. 
If T is temperature, k is Boltzman constant, ? is 
angular displacement and x has the dimensions of 
length. Then, choose the incorrect option. 
 (A) Dimensions of ? is same as that of force. 
 (B) Dimensions of ?
–1
 x is same as that of energy. 
 (C) Dimensions of ?
–1
 sin ? is same as that of ?? 
 (D) Dimensions of ? is same as that of ? 
 Official Ans. by NTA (D) 
  
Sol. [ ] [ ] [sin ] Dimensionless ? ? ? ? ? ? ? 
 
1
sin [ ] D.L.
?
??
? ? ? ? ? ?
??
 
2. At time t = 0 a particle starts travelling from a 
height 7z cm in a plane keeping z coordinate 
constant. At any instant of time it’s position along 
the x and y directions are defined as 3t and 5t
3
 
respectively. At t = 1s acceleration of the particle 
will be 
 (A) 30y ?  (B) 30y 
 (C) 3x 15y ? (D) 3x 15y 7z ?? 
 Official Ans. by NTA (B) 
  
Sol. 
3
r 3ti 5t j 7k ? ? ? 
 
2
2
dr
30t j
dt
? 
 At  t = 1  
2
2
dr
30j
dt
?? 
3. A pressure-pump has a horizontal tube of  
cross-sectional area 10 cm
2
 for the outflow of 
water at a speed of 20 m/s. The force exerted on 
the vertical wall just in front of the tube which 
stops water horizontally flowing out of the tube, is: 
 [given : density of water = 1000 kg/m
3
] 
 (A) 300 N  (B) 500 N 
 (C) 250 N  (D) 400 N 
 Official Ans. by NTA (D) 
  
Sol. 
2 3 4
F a 10 10 10 20 20
?
? ? ? ? ? ? ? ? 
 F = 400 
4. A uniform metal chain of mass m and length ‘L’ 
passes over a massless and frictionless pulley. It is 
released from rest with a part of its length ‘l’ is 
hanging on one side and rest of its length ‘L – l’ is 
hanging on the other side of the pulley. At a certain 
point of time, when 
L
x
? l , the acceleration of the 
chain is 
g
2
. The value of x is ……… 
 
 (A) 6 (B) 2 (C) 1.5 (D) 4 
 Official Ans. by NTA (D) 
  
Sol.  
 
21
21
(m m )
ag
(m m )
?
?
?
 
 
g ( (L ) )g L L
L
2 L 4 x
? ? ? ?
? ? ? ?
?
 
 x = 4 
 
2 
 
5. A bullet of mass 200 g having initial kinetic energy 
90 J is shot inside a long swimming pool as shown 
in the figure. If it’s kinetic energy reduces to 40 J 
within 1s, the minimum length of the pool, the 
bullet has a to travel so that it completely comes to 
rest is 
 
 (A) 45 m  (B) 90 m 
 (C) 125 m  (D) 25 m 
 Official Ans. by NTA (A) 
  
Sol. Using mv 2mk ? 
 
1
u 2 0.2 90 30 m/s
0.2
? ? ? ? 
 
1
v 2 0.2 40 20 m/s
0.2
? ? ? ? 
 
2
20 30
a 10 m/s
1
?
? ? ? 
 
2
u
s 45 m
2a
?
?? 
6. Assume there are two identical simple pendulum 
Clocks-1 is placed on the earth and Clock-2 is 
placed on a space station located at a height h 
above the earth surface. Clock-1 and Clock-2 
operate at time periods 4s and 6s respectively. 
Then the value of h is – 
 (consider radius of earth R
E
 = 6400 km and g on 
earth 10 m/s
2
) 
 (A) 1200 km 
 (B) 1600 km 
 (C) 3200 km 
 (D) 4800 km 
 Official Ans. by NTA (C) 
  
Sol. 
2
11
t and g
g (R h)
??
?
 
 
2
1
2
2
t g' R
tg (R h)
??
?
 
 
1
2
t 4R
h 3200km
t 6 (R h)
? ? ? ?
?
 
7. Consider a cylindrical tank of radius 1m is filled 
with water. The top surface of water is at 15 m 
from the bottom of the cylinder. There is a hole on 
the wall of cylinder at a height of 5m from the 
bottom. A force of 5 × 10
5
 N is applied an the top 
surface of water using a piston. The speed of efflux 
from the hole will be : 
 (given atmospheric pressure P
A
 = 1.01 × 10
5
 Pa, 
density of water ?
w
 = 1000 kg/m
3
 and gravitational 
acceleration g = 10 m/s
2
) 
 
 (A) 11.6 m/s  (B) 10.8 m/s 
 (C) 17.8 m/s  (D) 14.4 m/s 
 Official Ans. by NTA (C) 
  
Sol. Apply Bernoulli’s theorem between Piston and 
hole P
A
 + 
2
0e
1
gh P v
2
? ? ? ? 
 Assuming there is no atmospheric pressure on 
piston  
 
5
3 5 3 2
e
5 10 1
10 10 10 1.01 10 10 v
2
?
? ? ? ? ? ? ? ?
?
 
 v
e
 = 17.8 m/s 
8. A vessel contains 14 g of nitrogen gas at a 
temperature of 27°C. The amount of heat to be 
transferred to the gap to double the r.m.s. speed of 
its molecules will be : (Take R = 8.32 J mol
–1
k
–1
) 
 (A) 2229 J  (B) 5616 J 
 (C) 9360 J  (D) 13,104 J 
 Official Ans. by NTA (C) 
  
 
 
3 
 
Sol. 
rms
vT ? 
 
fi
rms rms rms
v 300K, v 2v ?? 
 
f
rms
v 1200K ? 
 
fi
14 1
T 1200K, T 300K, n
28 2
? ? ? ? 
 
v
1 5R
Q nC T 900
22
? ? ? ? ? 
 Q = 9360 J 
9. A slab of dielectric constant K has the same cross-
sectional area as the plates of a parallel plate 
capacitor and thickness 
3
d
4
, where d is the 
separation of the plates. The capacitance of the 
capacitor when the slab is inserted between the 
plates will be : 
 (Given C
o
 = capacitance of capacitor with air as 
medium between plates.) 
 (A) 
0
4KC
3K ?
  (B) 
0
3KC
3K ?
 
 (C) 
0
3K
4KC
?
  (D) 
K
4K ?
 
 Official Ans. by NTA (A) 
  
Sol. 
 
k
 
 
x
 3d/4
 
y
 
E
 E
 
–Q
 
+Q
 
 
 
3d
x y d
4
? ? ? 
 
d
xy
4
?? 
 
0
0
A
C
d
?
? 
 
E 3d
V Ex Ey
k4
? ? ? ? ? 
 ? ?
3Ed
E x y
4k
? ? ? 
 
3d d
VE
4k 4
??
? ? ?
??
??
 
 
00
3d dk Qd 3 k
V
4k A 4k
? ? ? ? ? ? ?
? ? ?
? ? ? ?
??
? ? ? ?
 
 
00
A 4kC Q 4k
C
V d 3 k k 3
???
? ? ?
??
? ? ?
??
 
10. A uniform electric field E = (8m/e) V/m is created 
between two parallel plates of length 1m as shown 
in figure, (where m = mass of electron and  
e = charge of electron). An electron enters the field 
symmetrically between the plates with a speed of 
2m/s. The angle of the deviation ( ?) of the path of 
the electron as it comes out of the field will be 
………. 
 
 (A) tan
–1
 (4)  (B) tan
–1
 (2) 
 (C) 
1
1
tan
3
?
??
??
??
 (D) tan
–1
 (3) 
 Official Ans. by NTA (B) 
  
Sol. 
 
v
y 
v
x 
 
 
? ?
y 2
y
8m
e
F eE
e
a 8m / s
m m m
??
??
??
? ? ? ? 
 s
x
 = u
x
t 
 1 = 2 × t 
 
1
t
2
? sec 
 v
y
 = u
y
 + a
y
t 
 v
y
 = 0 + 
1
8
2
? 
 v
y
 = 4 m/s 
 ? ?
y 1
x
v
4
tan 2 tan 2
v2
?
? ? ? ? ? ? ?   
 
Page 4


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Thursday 28
th
 July, 2022)           TIME : 3 : 00 PM  to  6 : 00 PM 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
SECTION-A 
1. Consider the efficiency of Carnot’s engine is given 
by 
e
x
log ,
sin kT
? ? ?
??
?
 where ? and ? are constants. 
If T is temperature, k is Boltzman constant, ? is 
angular displacement and x has the dimensions of 
length. Then, choose the incorrect option. 
 (A) Dimensions of ? is same as that of force. 
 (B) Dimensions of ?
–1
 x is same as that of energy. 
 (C) Dimensions of ?
–1
 sin ? is same as that of ?? 
 (D) Dimensions of ? is same as that of ? 
 Official Ans. by NTA (D) 
  
Sol. [ ] [ ] [sin ] Dimensionless ? ? ? ? ? ? ? 
 
1
sin [ ] D.L.
?
??
? ? ? ? ? ?
??
 
2. At time t = 0 a particle starts travelling from a 
height 7z cm in a plane keeping z coordinate 
constant. At any instant of time it’s position along 
the x and y directions are defined as 3t and 5t
3
 
respectively. At t = 1s acceleration of the particle 
will be 
 (A) 30y ?  (B) 30y 
 (C) 3x 15y ? (D) 3x 15y 7z ?? 
 Official Ans. by NTA (B) 
  
Sol. 
3
r 3ti 5t j 7k ? ? ? 
 
2
2
dr
30t j
dt
? 
 At  t = 1  
2
2
dr
30j
dt
?? 
3. A pressure-pump has a horizontal tube of  
cross-sectional area 10 cm
2
 for the outflow of 
water at a speed of 20 m/s. The force exerted on 
the vertical wall just in front of the tube which 
stops water horizontally flowing out of the tube, is: 
 [given : density of water = 1000 kg/m
3
] 
 (A) 300 N  (B) 500 N 
 (C) 250 N  (D) 400 N 
 Official Ans. by NTA (D) 
  
Sol. 
2 3 4
F a 10 10 10 20 20
?
? ? ? ? ? ? ? ? 
 F = 400 
4. A uniform metal chain of mass m and length ‘L’ 
passes over a massless and frictionless pulley. It is 
released from rest with a part of its length ‘l’ is 
hanging on one side and rest of its length ‘L – l’ is 
hanging on the other side of the pulley. At a certain 
point of time, when 
L
x
? l , the acceleration of the 
chain is 
g
2
. The value of x is ……… 
 
 (A) 6 (B) 2 (C) 1.5 (D) 4 
 Official Ans. by NTA (D) 
  
Sol.  
 
21
21
(m m )
ag
(m m )
?
?
?
 
 
g ( (L ) )g L L
L
2 L 4 x
? ? ? ?
? ? ? ?
?
 
 x = 4 
 
2 
 
5. A bullet of mass 200 g having initial kinetic energy 
90 J is shot inside a long swimming pool as shown 
in the figure. If it’s kinetic energy reduces to 40 J 
within 1s, the minimum length of the pool, the 
bullet has a to travel so that it completely comes to 
rest is 
 
 (A) 45 m  (B) 90 m 
 (C) 125 m  (D) 25 m 
 Official Ans. by NTA (A) 
  
Sol. Using mv 2mk ? 
 
1
u 2 0.2 90 30 m/s
0.2
? ? ? ? 
 
1
v 2 0.2 40 20 m/s
0.2
? ? ? ? 
 
2
20 30
a 10 m/s
1
?
? ? ? 
 
2
u
s 45 m
2a
?
?? 
6. Assume there are two identical simple pendulum 
Clocks-1 is placed on the earth and Clock-2 is 
placed on a space station located at a height h 
above the earth surface. Clock-1 and Clock-2 
operate at time periods 4s and 6s respectively. 
Then the value of h is – 
 (consider radius of earth R
E
 = 6400 km and g on 
earth 10 m/s
2
) 
 (A) 1200 km 
 (B) 1600 km 
 (C) 3200 km 
 (D) 4800 km 
 Official Ans. by NTA (C) 
  
Sol. 
2
11
t and g
g (R h)
??
?
 
 
2
1
2
2
t g' R
tg (R h)
??
?
 
 
1
2
t 4R
h 3200km
t 6 (R h)
? ? ? ?
?
 
7. Consider a cylindrical tank of radius 1m is filled 
with water. The top surface of water is at 15 m 
from the bottom of the cylinder. There is a hole on 
the wall of cylinder at a height of 5m from the 
bottom. A force of 5 × 10
5
 N is applied an the top 
surface of water using a piston. The speed of efflux 
from the hole will be : 
 (given atmospheric pressure P
A
 = 1.01 × 10
5
 Pa, 
density of water ?
w
 = 1000 kg/m
3
 and gravitational 
acceleration g = 10 m/s
2
) 
 
 (A) 11.6 m/s  (B) 10.8 m/s 
 (C) 17.8 m/s  (D) 14.4 m/s 
 Official Ans. by NTA (C) 
  
Sol. Apply Bernoulli’s theorem between Piston and 
hole P
A
 + 
2
0e
1
gh P v
2
? ? ? ? 
 Assuming there is no atmospheric pressure on 
piston  
 
5
3 5 3 2
e
5 10 1
10 10 10 1.01 10 10 v
2
?
? ? ? ? ? ? ? ?
?
 
 v
e
 = 17.8 m/s 
8. A vessel contains 14 g of nitrogen gas at a 
temperature of 27°C. The amount of heat to be 
transferred to the gap to double the r.m.s. speed of 
its molecules will be : (Take R = 8.32 J mol
–1
k
–1
) 
 (A) 2229 J  (B) 5616 J 
 (C) 9360 J  (D) 13,104 J 
 Official Ans. by NTA (C) 
  
 
 
3 
 
Sol. 
rms
vT ? 
 
fi
rms rms rms
v 300K, v 2v ?? 
 
f
rms
v 1200K ? 
 
fi
14 1
T 1200K, T 300K, n
28 2
? ? ? ? 
 
v
1 5R
Q nC T 900
22
? ? ? ? ? 
 Q = 9360 J 
9. A slab of dielectric constant K has the same cross-
sectional area as the plates of a parallel plate 
capacitor and thickness 
3
d
4
, where d is the 
separation of the plates. The capacitance of the 
capacitor when the slab is inserted between the 
plates will be : 
 (Given C
o
 = capacitance of capacitor with air as 
medium between plates.) 
 (A) 
0
4KC
3K ?
  (B) 
0
3KC
3K ?
 
 (C) 
0
3K
4KC
?
  (D) 
K
4K ?
 
 Official Ans. by NTA (A) 
  
Sol. 
 
k
 
 
x
 3d/4
 
y
 
E
 E
 
–Q
 
+Q
 
 
 
3d
x y d
4
? ? ? 
 
d
xy
4
?? 
 
0
0
A
C
d
?
? 
 
E 3d
V Ex Ey
k4
? ? ? ? ? 
 ? ?
3Ed
E x y
4k
? ? ? 
 
3d d
VE
4k 4
??
? ? ?
??
??
 
 
00
3d dk Qd 3 k
V
4k A 4k
? ? ? ? ? ? ?
? ? ?
? ? ? ?
??
? ? ? ?
 
 
00
A 4kC Q 4k
C
V d 3 k k 3
???
? ? ?
??
? ? ?
??
 
10. A uniform electric field E = (8m/e) V/m is created 
between two parallel plates of length 1m as shown 
in figure, (where m = mass of electron and  
e = charge of electron). An electron enters the field 
symmetrically between the plates with a speed of 
2m/s. The angle of the deviation ( ?) of the path of 
the electron as it comes out of the field will be 
………. 
 
 (A) tan
–1
 (4)  (B) tan
–1
 (2) 
 (C) 
1
1
tan
3
?
??
??
??
 (D) tan
–1
 (3) 
 Official Ans. by NTA (B) 
  
Sol. 
 
v
y 
v
x 
 
 
? ?
y 2
y
8m
e
F eE
e
a 8m / s
m m m
??
??
??
? ? ? ? 
 s
x
 = u
x
t 
 1 = 2 × t 
 
1
t
2
? sec 
 v
y
 = u
y
 + a
y
t 
 v
y
 = 0 + 
1
8
2
? 
 v
y
 = 4 m/s 
 ? ?
y 1
x
v
4
tan 2 tan 2
v2
?
? ? ? ? ? ? ?   
 
 
4 
 
11. Given below are two statements : 
 Statement I : A uniform wire of resistance 80 ?  is 
cut into four equal parts. These parts are now 
connected in parallel. The equivalent resistance of 
the combination will be 5??. 
 Statement II : Two resistance 2R and 3R are 
connected in parallel in a electric circuit. The value 
of thermal energy developed in 3R and 2R will be 
in the ratio 3 : 2. 
 In the light of the above statements, choose the 
most appropriate answer from the options given 
below 
 (A) Both statement I and statement II are correct 
 (B) Both statement I and statement II are incorrect 
 (C) Statement I is correct but statement II is 
incorrect 
 (D) Statement I is incorrect but statement II is 
correct.  
 Official Ans. by NTA (C) 
  
Sol. Statement 1 - R 80 ?? 
 R
1
 = R
2 
= R
3
 = R
4
 = 20 ? 
 In parallel ? ? ?
eq
20
R5
4
 
 Statement 2 –  
 
R = 3R
1
R = 2R
2
V
 
 
2
th
v
P
R
? 
 
12
21
PR 2
P R 3
??
??
??
??
 (where P is power) 
12. A triangular shaped wire carrying 10A current is 
placed in a uniform magnetic field of 0.5T, as 
shown in figure. The magnetic force on segment 
CD is (Given BC = CD = BD = 5 cm). 
Magnetic
field
5 cm 5 cm
5 cm
A B D E
C
 
 (A) 0.126 N  (B) 0.312 N 
 (C) 0.216 N  (D) 0.245 N 
 Official Ans. by NTA (C) 
  
Sol. ?
M eff
F (CD) BI 
 = 0.5×(10) × (5 sin60 ×10
–2
) 
 = 0.216 N 
13. The magnetic field at the center of current carrying 
circular loop is B
1
. The magnetic field at a distance 
of 3 times radius of the given circular loop from 
the center on its axis is B
2
. The value of B
1
/B
2
 will 
be 
 (A) 9 : 4  (B) 12: 5 
 (C) 8 : 1  (D) 5: 3 
 Official Ans. by NTA (C) 
  
Sol. 
B
1
B
2
 
 
?
?
0
1
I
B
2R
 
 
? ?
?? ??
? ? ?
??
??
?
2
00 1
2 3/2
22
IR I B 1
B
8 2R 8
2 R 3R
 
 ?
1
2
B 8
B1
 
Page 5


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Thursday 28
th
 July, 2022)           TIME : 3 : 00 PM  to  6 : 00 PM 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
SECTION-A 
1. Consider the efficiency of Carnot’s engine is given 
by 
e
x
log ,
sin kT
? ? ?
??
?
 where ? and ? are constants. 
If T is temperature, k is Boltzman constant, ? is 
angular displacement and x has the dimensions of 
length. Then, choose the incorrect option. 
 (A) Dimensions of ? is same as that of force. 
 (B) Dimensions of ?
–1
 x is same as that of energy. 
 (C) Dimensions of ?
–1
 sin ? is same as that of ?? 
 (D) Dimensions of ? is same as that of ? 
 Official Ans. by NTA (D) 
  
Sol. [ ] [ ] [sin ] Dimensionless ? ? ? ? ? ? ? 
 
1
sin [ ] D.L.
?
??
? ? ? ? ? ?
??
 
2. At time t = 0 a particle starts travelling from a 
height 7z cm in a plane keeping z coordinate 
constant. At any instant of time it’s position along 
the x and y directions are defined as 3t and 5t
3
 
respectively. At t = 1s acceleration of the particle 
will be 
 (A) 30y ?  (B) 30y 
 (C) 3x 15y ? (D) 3x 15y 7z ?? 
 Official Ans. by NTA (B) 
  
Sol. 
3
r 3ti 5t j 7k ? ? ? 
 
2
2
dr
30t j
dt
? 
 At  t = 1  
2
2
dr
30j
dt
?? 
3. A pressure-pump has a horizontal tube of  
cross-sectional area 10 cm
2
 for the outflow of 
water at a speed of 20 m/s. The force exerted on 
the vertical wall just in front of the tube which 
stops water horizontally flowing out of the tube, is: 
 [given : density of water = 1000 kg/m
3
] 
 (A) 300 N  (B) 500 N 
 (C) 250 N  (D) 400 N 
 Official Ans. by NTA (D) 
  
Sol. 
2 3 4
F a 10 10 10 20 20
?
? ? ? ? ? ? ? ? 
 F = 400 
4. A uniform metal chain of mass m and length ‘L’ 
passes over a massless and frictionless pulley. It is 
released from rest with a part of its length ‘l’ is 
hanging on one side and rest of its length ‘L – l’ is 
hanging on the other side of the pulley. At a certain 
point of time, when 
L
x
? l , the acceleration of the 
chain is 
g
2
. The value of x is ……… 
 
 (A) 6 (B) 2 (C) 1.5 (D) 4 
 Official Ans. by NTA (D) 
  
Sol.  
 
21
21
(m m )
ag
(m m )
?
?
?
 
 
g ( (L ) )g L L
L
2 L 4 x
? ? ? ?
? ? ? ?
?
 
 x = 4 
 
2 
 
5. A bullet of mass 200 g having initial kinetic energy 
90 J is shot inside a long swimming pool as shown 
in the figure. If it’s kinetic energy reduces to 40 J 
within 1s, the minimum length of the pool, the 
bullet has a to travel so that it completely comes to 
rest is 
 
 (A) 45 m  (B) 90 m 
 (C) 125 m  (D) 25 m 
 Official Ans. by NTA (A) 
  
Sol. Using mv 2mk ? 
 
1
u 2 0.2 90 30 m/s
0.2
? ? ? ? 
 
1
v 2 0.2 40 20 m/s
0.2
? ? ? ? 
 
2
20 30
a 10 m/s
1
?
? ? ? 
 
2
u
s 45 m
2a
?
?? 
6. Assume there are two identical simple pendulum 
Clocks-1 is placed on the earth and Clock-2 is 
placed on a space station located at a height h 
above the earth surface. Clock-1 and Clock-2 
operate at time periods 4s and 6s respectively. 
Then the value of h is – 
 (consider radius of earth R
E
 = 6400 km and g on 
earth 10 m/s
2
) 
 (A) 1200 km 
 (B) 1600 km 
 (C) 3200 km 
 (D) 4800 km 
 Official Ans. by NTA (C) 
  
Sol. 
2
11
t and g
g (R h)
??
?
 
 
2
1
2
2
t g' R
tg (R h)
??
?
 
 
1
2
t 4R
h 3200km
t 6 (R h)
? ? ? ?
?
 
7. Consider a cylindrical tank of radius 1m is filled 
with water. The top surface of water is at 15 m 
from the bottom of the cylinder. There is a hole on 
the wall of cylinder at a height of 5m from the 
bottom. A force of 5 × 10
5
 N is applied an the top 
surface of water using a piston. The speed of efflux 
from the hole will be : 
 (given atmospheric pressure P
A
 = 1.01 × 10
5
 Pa, 
density of water ?
w
 = 1000 kg/m
3
 and gravitational 
acceleration g = 10 m/s
2
) 
 
 (A) 11.6 m/s  (B) 10.8 m/s 
 (C) 17.8 m/s  (D) 14.4 m/s 
 Official Ans. by NTA (C) 
  
Sol. Apply Bernoulli’s theorem between Piston and 
hole P
A
 + 
2
0e
1
gh P v
2
? ? ? ? 
 Assuming there is no atmospheric pressure on 
piston  
 
5
3 5 3 2
e
5 10 1
10 10 10 1.01 10 10 v
2
?
? ? ? ? ? ? ? ?
?
 
 v
e
 = 17.8 m/s 
8. A vessel contains 14 g of nitrogen gas at a 
temperature of 27°C. The amount of heat to be 
transferred to the gap to double the r.m.s. speed of 
its molecules will be : (Take R = 8.32 J mol
–1
k
–1
) 
 (A) 2229 J  (B) 5616 J 
 (C) 9360 J  (D) 13,104 J 
 Official Ans. by NTA (C) 
  
 
 
3 
 
Sol. 
rms
vT ? 
 
fi
rms rms rms
v 300K, v 2v ?? 
 
f
rms
v 1200K ? 
 
fi
14 1
T 1200K, T 300K, n
28 2
? ? ? ? 
 
v
1 5R
Q nC T 900
22
? ? ? ? ? 
 Q = 9360 J 
9. A slab of dielectric constant K has the same cross-
sectional area as the plates of a parallel plate 
capacitor and thickness 
3
d
4
, where d is the 
separation of the plates. The capacitance of the 
capacitor when the slab is inserted between the 
plates will be : 
 (Given C
o
 = capacitance of capacitor with air as 
medium between plates.) 
 (A) 
0
4KC
3K ?
  (B) 
0
3KC
3K ?
 
 (C) 
0
3K
4KC
?
  (D) 
K
4K ?
 
 Official Ans. by NTA (A) 
  
Sol. 
 
k
 
 
x
 3d/4
 
y
 
E
 E
 
–Q
 
+Q
 
 
 
3d
x y d
4
? ? ? 
 
d
xy
4
?? 
 
0
0
A
C
d
?
? 
 
E 3d
V Ex Ey
k4
? ? ? ? ? 
 ? ?
3Ed
E x y
4k
? ? ? 
 
3d d
VE
4k 4
??
? ? ?
??
??
 
 
00
3d dk Qd 3 k
V
4k A 4k
? ? ? ? ? ? ?
? ? ?
? ? ? ?
??
? ? ? ?
 
 
00
A 4kC Q 4k
C
V d 3 k k 3
???
? ? ?
??
? ? ?
??
 
10. A uniform electric field E = (8m/e) V/m is created 
between two parallel plates of length 1m as shown 
in figure, (where m = mass of electron and  
e = charge of electron). An electron enters the field 
symmetrically between the plates with a speed of 
2m/s. The angle of the deviation ( ?) of the path of 
the electron as it comes out of the field will be 
………. 
 
 (A) tan
–1
 (4)  (B) tan
–1
 (2) 
 (C) 
1
1
tan
3
?
??
??
??
 (D) tan
–1
 (3) 
 Official Ans. by NTA (B) 
  
Sol. 
 
v
y 
v
x 
 
 
? ?
y 2
y
8m
e
F eE
e
a 8m / s
m m m
??
??
??
? ? ? ? 
 s
x
 = u
x
t 
 1 = 2 × t 
 
1
t
2
? sec 
 v
y
 = u
y
 + a
y
t 
 v
y
 = 0 + 
1
8
2
? 
 v
y
 = 4 m/s 
 ? ?
y 1
x
v
4
tan 2 tan 2
v2
?
? ? ? ? ? ? ?   
 
 
4 
 
11. Given below are two statements : 
 Statement I : A uniform wire of resistance 80 ?  is 
cut into four equal parts. These parts are now 
connected in parallel. The equivalent resistance of 
the combination will be 5??. 
 Statement II : Two resistance 2R and 3R are 
connected in parallel in a electric circuit. The value 
of thermal energy developed in 3R and 2R will be 
in the ratio 3 : 2. 
 In the light of the above statements, choose the 
most appropriate answer from the options given 
below 
 (A) Both statement I and statement II are correct 
 (B) Both statement I and statement II are incorrect 
 (C) Statement I is correct but statement II is 
incorrect 
 (D) Statement I is incorrect but statement II is 
correct.  
 Official Ans. by NTA (C) 
  
Sol. Statement 1 - R 80 ?? 
 R
1
 = R
2 
= R
3
 = R
4
 = 20 ? 
 In parallel ? ? ?
eq
20
R5
4
 
 Statement 2 –  
 
R = 3R
1
R = 2R
2
V
 
 
2
th
v
P
R
? 
 
12
21
PR 2
P R 3
??
??
??
??
 (where P is power) 
12. A triangular shaped wire carrying 10A current is 
placed in a uniform magnetic field of 0.5T, as 
shown in figure. The magnetic force on segment 
CD is (Given BC = CD = BD = 5 cm). 
Magnetic
field
5 cm 5 cm
5 cm
A B D E
C
 
 (A) 0.126 N  (B) 0.312 N 
 (C) 0.216 N  (D) 0.245 N 
 Official Ans. by NTA (C) 
  
Sol. ?
M eff
F (CD) BI 
 = 0.5×(10) × (5 sin60 ×10
–2
) 
 = 0.216 N 
13. The magnetic field at the center of current carrying 
circular loop is B
1
. The magnetic field at a distance 
of 3 times radius of the given circular loop from 
the center on its axis is B
2
. The value of B
1
/B
2
 will 
be 
 (A) 9 : 4  (B) 12: 5 
 (C) 8 : 1  (D) 5: 3 
 Official Ans. by NTA (C) 
  
Sol. 
B
1
B
2
 
 
?
?
0
1
I
B
2R
 
 
? ?
?? ??
? ? ?
??
??
?
2
00 1
2 3/2
22
IR I B 1
B
8 2R 8
2 R 3R
 
 ?
1
2
B 8
B1
 
 
 
5 
 
14. A transformer operating at primary voltage 8 kV 
and secondary voltage 160 V serves a load of  
80 kW. Assuming the transformer to be ideal with 
purely resistive load and working on unity power 
factor, the loads in the primary and secondary 
circuit would be 
 (A) 800 ? and 1.06?? (B) 10?? and 500?? 
 (C) 800 ? and 0.32 ? (D) 1.06 ? and 500 ? 
 Official Ans. by NTA (C) 
  
Sol. 
? ?
2
3
3
P
8 10
80 10
R
?
?? 
 R
P 
= 800 ? 
 
? ?
??
2
3
S
160
80 10
R
 
 R
S 
= 0.32 ?
?
15. Sun light falls normally on a surface of area 36 cm
2
 
and exerts an average force of 7.2×10
-9
 N within a 
time period of 20 minutes. Considering a case of 
complete absorption, the energy flux of incident 
light is  
 (A) 25.92×10
2
 W/cm
2
 (B) 8.64×10
-6
 W/cm
2
 
 (C) 6.0 W/cm
2
 (D) 0.06 W/cm
2
 
 Official Ans. by NTA (D) 
  
Sol. ??
I
area force
C
 
 
??
? ? ? ?
49
I
36 10 7.2 10
C
 
 
?
?
? ? ?
?
??
98
9
7.2 10 3 10
I
36 10 10
 
 
?
?
?
?
1
3
6 10
10
 
 ??
2
2
w
I 6 10
m
 
 ?
2
w
0.06
cm
 
16. The power of a lens (biconvex) is 1.25 m
-1
 in 
particular medium. Refractive index of the lens is 
1.5 and radii of curvature are 20 cm and 40 cm 
respectively. The refractive index of surrounding 
medium : 
 (A) 1.0  (B) 
9
7
 
 (C) 
3
2
  (D) 
4
3
 
 Official Ans. by NTA (B) 
  
Sol. ? ?
?? ?
? ? ? ? ? ?
??
??
2
12
12
11
P
f R R
 (For this formula 
refer to NCERT Part-2, Chapter-9, Page no. 328, 
solved example 8) 
 (µ
1
 is refractive index of lens and µ
2
 is of 
surrounding medium) 
 ? ?
??
? ? ? ?
??
??
2
11
1.25 1.5
0.2 0.4
  
 ? ?
?
? ? ?
2
1.25 0.08
1.5
0.6
 
 ? ? ?
2
4
3