JEE Main 2022 Question Paper 29 July Shift 1 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Friday 29
th
 July, 2022)                TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. Given below are two statements : One is labelled 
as Assertion (A) and other is labelled as 
 Reason (R). 
 Assertion (A) : Time period of oscillation of a 
liquid drop depends on surface tension (S), if 
density of the liquid is p and radius of the drop is r, 
then T = 
3
2
3
pr
k
s
 is dimensionally correct, 
where K is dimensionless. 
 Reason (R) : Using dimensional analysis we get 
R.H.S. having different dimension than that of time 
period. 
 In the light of above statements, choose the correct 
answer from the options given below. 
 (A) Both (A) and (R) are true and (R) is the correct 
explanation of (A)  
  (B) Both (A) and (R) are true but (R) is not the 
correct explanation of (A) 
 (C) (A) is true but (R) is false   
 (D) (A) is false but (R) is true 
 Official Ans. by NTA (D) 
  
Sol. 
3
3
2
r
Tk
s
?
? 
 Dimensions of RHS = 
33 1
2 2 2
13
0
8 2
3
2 4
M L L
M L T
MT
?
?
? ? ? ?
? ? ? ?
? ? ? ?
?
??
??
 
 Dimensions of L.H.S ? Dimensions of R.H.S 
 ? option (D)  
2. A ball is thrown up vertically with a certain 
velocity so that, it reaches a maximum height h. 
Find the ratio of the times in which it is at height 
h
3
 while going up and coming down respectively. 
 (A) 
21
21
?
?
  (B) 
32
32
?
?
  
 (C) 
31
31
?
?
  (D) 
1
3
 
 Official Ans. by NTA (B) 
  
Sol.  
 Max. Height = h = 
2
u
2g
 
 u 2gh ?? 
 S = ut + 
2
1
at
2
 
 
2
h1
2ght ( g)t
32
? ? ? 
 
2
gt h
2ght 0
23
? ? ? (Roots are t
1
 & t
2
) 
 
2
1
g h 4gh
2gh 2gh 4 2gh
t 32
2 3 3
t g h 4gh 3 2
2gh 2gh 4 2gh
2 3 3
? ? ? ? ?
?
? ? ?
?
? ? ? ? ?
 
Page 2


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Friday 29
th
 July, 2022)                TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. Given below are two statements : One is labelled 
as Assertion (A) and other is labelled as 
 Reason (R). 
 Assertion (A) : Time period of oscillation of a 
liquid drop depends on surface tension (S), if 
density of the liquid is p and radius of the drop is r, 
then T = 
3
2
3
pr
k
s
 is dimensionally correct, 
where K is dimensionless. 
 Reason (R) : Using dimensional analysis we get 
R.H.S. having different dimension than that of time 
period. 
 In the light of above statements, choose the correct 
answer from the options given below. 
 (A) Both (A) and (R) are true and (R) is the correct 
explanation of (A)  
  (B) Both (A) and (R) are true but (R) is not the 
correct explanation of (A) 
 (C) (A) is true but (R) is false   
 (D) (A) is false but (R) is true 
 Official Ans. by NTA (D) 
  
Sol. 
3
3
2
r
Tk
s
?
? 
 Dimensions of RHS = 
33 1
2 2 2
13
0
8 2
3
2 4
M L L
M L T
MT
?
?
? ? ? ?
? ? ? ?
? ? ? ?
?
??
??
 
 Dimensions of L.H.S ? Dimensions of R.H.S 
 ? option (D)  
2. A ball is thrown up vertically with a certain 
velocity so that, it reaches a maximum height h. 
Find the ratio of the times in which it is at height 
h
3
 while going up and coming down respectively. 
 (A) 
21
21
?
?
  (B) 
32
32
?
?
  
 (C) 
31
31
?
?
  (D) 
1
3
 
 Official Ans. by NTA (B) 
  
Sol.  
 Max. Height = h = 
2
u
2g
 
 u 2gh ?? 
 S = ut + 
2
1
at
2
 
 
2
h1
2ght ( g)t
32
? ? ? 
 
2
gt h
2ght 0
23
? ? ? (Roots are t
1
 & t
2
) 
 
2
1
g h 4gh
2gh 2gh 4 2gh
t 32
2 3 3
t g h 4gh 3 2
2gh 2gh 4 2gh
2 3 3
? ? ? ? ?
?
? ? ?
?
? ? ? ? ?
 
 
2 
 
3. 
t4
dx
If t x 4,then is:
dt
?
??
??
??
??
 
 (A) 4  (B) Zero  
 (C) 8 (D) 16 
 Official Ans. by NTA (B) 
  
Sol. t x 4 ?? 
 ? x = (t – 4)
2
 = t
2
 – 8t + 16 
 
dx
dt
? = 2t – 8 
 
t4
dx
2 4 8 0
dt
?
? ? ? ? ? 
4. A smooth circular groove has a smooth vertical 
wall as shown in figure. A block of mass m moves 
against the wall with a speed v. Which of the 
following curve represents the correct relation 
between the normal reaction on the block by the 
wall (N) and speed of the block (v) ? 
 
V
 
 
 (A) 
N
v
  
 (B) 
N
v
 
 (C) 
N
v
  
 (D) 
N
v
 
 Official Ans. by NTA (A) 
  
Sol. 
2
mv
N
r
? 
 Curve is parabola 
 Y = kx
2 
 
5. A ball is projected with kinetic energy E, at an 
angle of 60
0
 to the horizontal. The kinetic energy 
of this ball at the highest point of its flight will 
become :
 
 (A) Zero   (B) 
E
2
 
 (C) 
E
4
  (D) E 
 Official Ans. by NTA (C) 
  
Sol. 
60
o
ucos60
o
u
 
 
2
1
E mu
2
? 
 At Highest point, Velocity V = u cos60
o
 = 
u
2
 
 ? K.E at topmost point = 
2
1 u E
m
2 2 4
??
?
??
??
 
6. Two bodies of mass 1 kg and 3 kg have position 
vectors 
ˆ ˆ ˆ
i 2j k ?? and 
ˆ ˆ ˆ
3i 2j k ? ? ? respectively. 
The magnitude of position vector of centre of mass 
of this system will be similar to the magnitude of 
vector : 
 (A) 
ˆ ˆ ˆ
i 2j k ?? (B) 
ˆ ˆ ˆ
3i 2j k ? ? ?
 
 
 (C) 
ˆˆ
2i 2k ?? (D) 
ˆ ˆ ˆ
2i j 2k ? ? ? 
 Official Ans. by NTA (A) 
  
Sol. 
1 1 2 2
com
12
ˆ ˆ ˆ ˆ ˆ ˆ
1(i 2j k) 3( 3i 2j k) m r m r
r
m m 1 3
? ? ? ? ? ? ?
??
??
 
 
ˆ ˆ ˆ
2i j k ? ? ? ? 
 
2 2 2
ˆ ˆ ˆ
|2i j k| (2) (1) (1) 6 ? ? ? ? ? ? 
Page 3


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Friday 29
th
 July, 2022)                TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. Given below are two statements : One is labelled 
as Assertion (A) and other is labelled as 
 Reason (R). 
 Assertion (A) : Time period of oscillation of a 
liquid drop depends on surface tension (S), if 
density of the liquid is p and radius of the drop is r, 
then T = 
3
2
3
pr
k
s
 is dimensionally correct, 
where K is dimensionless. 
 Reason (R) : Using dimensional analysis we get 
R.H.S. having different dimension than that of time 
period. 
 In the light of above statements, choose the correct 
answer from the options given below. 
 (A) Both (A) and (R) are true and (R) is the correct 
explanation of (A)  
  (B) Both (A) and (R) are true but (R) is not the 
correct explanation of (A) 
 (C) (A) is true but (R) is false   
 (D) (A) is false but (R) is true 
 Official Ans. by NTA (D) 
  
Sol. 
3
3
2
r
Tk
s
?
? 
 Dimensions of RHS = 
33 1
2 2 2
13
0
8 2
3
2 4
M L L
M L T
MT
?
?
? ? ? ?
? ? ? ?
? ? ? ?
?
??
??
 
 Dimensions of L.H.S ? Dimensions of R.H.S 
 ? option (D)  
2. A ball is thrown up vertically with a certain 
velocity so that, it reaches a maximum height h. 
Find the ratio of the times in which it is at height 
h
3
 while going up and coming down respectively. 
 (A) 
21
21
?
?
  (B) 
32
32
?
?
  
 (C) 
31
31
?
?
  (D) 
1
3
 
 Official Ans. by NTA (B) 
  
Sol.  
 Max. Height = h = 
2
u
2g
 
 u 2gh ?? 
 S = ut + 
2
1
at
2
 
 
2
h1
2ght ( g)t
32
? ? ? 
 
2
gt h
2ght 0
23
? ? ? (Roots are t
1
 & t
2
) 
 
2
1
g h 4gh
2gh 2gh 4 2gh
t 32
2 3 3
t g h 4gh 3 2
2gh 2gh 4 2gh
2 3 3
? ? ? ? ?
?
? ? ?
?
? ? ? ? ?
 
 
2 
 
3. 
t4
dx
If t x 4,then is:
dt
?
??
??
??
??
 
 (A) 4  (B) Zero  
 (C) 8 (D) 16 
 Official Ans. by NTA (B) 
  
Sol. t x 4 ?? 
 ? x = (t – 4)
2
 = t
2
 – 8t + 16 
 
dx
dt
? = 2t – 8 
 
t4
dx
2 4 8 0
dt
?
? ? ? ? ? 
4. A smooth circular groove has a smooth vertical 
wall as shown in figure. A block of mass m moves 
against the wall with a speed v. Which of the 
following curve represents the correct relation 
between the normal reaction on the block by the 
wall (N) and speed of the block (v) ? 
 
V
 
 
 (A) 
N
v
  
 (B) 
N
v
 
 (C) 
N
v
  
 (D) 
N
v
 
 Official Ans. by NTA (A) 
  
Sol. 
2
mv
N
r
? 
 Curve is parabola 
 Y = kx
2 
 
5. A ball is projected with kinetic energy E, at an 
angle of 60
0
 to the horizontal. The kinetic energy 
of this ball at the highest point of its flight will 
become :
 
 (A) Zero   (B) 
E
2
 
 (C) 
E
4
  (D) E 
 Official Ans. by NTA (C) 
  
Sol. 
60
o
ucos60
o
u
 
 
2
1
E mu
2
? 
 At Highest point, Velocity V = u cos60
o
 = 
u
2
 
 ? K.E at topmost point = 
2
1 u E
m
2 2 4
??
?
??
??
 
6. Two bodies of mass 1 kg and 3 kg have position 
vectors 
ˆ ˆ ˆ
i 2j k ?? and 
ˆ ˆ ˆ
3i 2j k ? ? ? respectively. 
The magnitude of position vector of centre of mass 
of this system will be similar to the magnitude of 
vector : 
 (A) 
ˆ ˆ ˆ
i 2j k ?? (B) 
ˆ ˆ ˆ
3i 2j k ? ? ?
 
 
 (C) 
ˆˆ
2i 2k ?? (D) 
ˆ ˆ ˆ
2i j 2k ? ? ? 
 Official Ans. by NTA (A) 
  
Sol. 
1 1 2 2
com
12
ˆ ˆ ˆ ˆ ˆ ˆ
1(i 2j k) 3( 3i 2j k) m r m r
r
m m 1 3
? ? ? ? ? ? ?
??
??
 
 
ˆ ˆ ˆ
2i j k ? ? ? ? 
 
2 2 2
ˆ ˆ ˆ
|2i j k| (2) (1) (1) 6 ? ? ? ? ? ? 
 
 
3 
 
?  
7. Given below are two statements : One is labelled 
as Assertion (A) and the other is labelled as  
 Reason (R). 
Assertion (A) : Clothes containing oil or grease 
stains cannot be cleaned by water wash. 
Reason (R) : Because the angle of contact between 
the oil/ grease and water is obtuse. In the light of 
the above statements, choose the correct answer 
from the option given below. 
 (A) Both (A) and (R) are true and (R) is the correct 
explanation of (A) 
 (B) Both (A) and (R) are true but (R) is not the 
correct explanation of (A) 
 (C) (A) is true but (R) is false   
 (D) (A) is true but (R) is true 
 Official Ans. by NTA (A) 
  
Sol. 
Water
Oil
?c
 
?c > 90
o
 
 For water oil interface 
8. If the length of a wire is made double and radius is 
halved of its respective values. Then, the Young’s 
modules of the material of the wire will : 
 (A) Remains same 
 (B) Become 8 times its initial value  
 (C) Become 
th
1
4
 of its initial value 
 (D) Become 4 times its initial value 
 Official Ans. by NTA (A) 
  
Sol. Y depends on material of wire 
9. The time period of oscillation of a simple 
pendulum of length L suspended from the roof of a 
vehicle, which moves without friction down an 
inclined plane of inclination ?, is given by : 
 (A) 2 L/(gcos ) ?? (B) 2 L/(gsin ) ??  
 (C) 2 L/g ? (D) 2 L/(gtan ) ?? 
 Official Ans. by NTA (A) 
  
Sol. g
cff
 = gcos ? ?
a = g sin ?
g cos ?
g sin ?
g cos ?
 ?
?
 
L
T2
gcos
??
?
 
10. A spherically symmetric charge distribution is 
considered with charge density varying as 
 
0
3r
for r R
(r) 4R
for r R
Zero
???
?? ?
?
??
??
?? ?
?
?
?
 
 Where, r(r < R) is the distance from the centre O 
(as shown in figure). The electric field at point P 
will be : 
O
P
R
r
(r) ?
 
 (A) 
0
0
r3r
4 4 R
?
??
?
??
?
??
 (B) 
0
0
r3r
3 4 R
?
??
?
??
?
??
 
 
 (C) 
0
0
r r
1
4R
?
??
?
??
?
??
 (D) 
0
0
r r
1
5R
?
??
?
??
?
??
 
 Official Ans. by NTA (C) 
  
Sol. By Gauss law 
O
P
R
r
(r) ?
 
 
in
o
Q
E.ds ?
?
?
 
 
r
2
o
2 0
0
3r
4 r dr
4R
E.4 r
??
? ? ?
??
??
??
?
?
 
 
34
2 o
o
4 3 r r
E4 r
4 3 4R
?? ??
? ? ?
??
?
??
 
 
3
2 o
o
r r
Er 1
4R
?
??
??
??
?
??
 
 
o
o
r r
E1
4R
?
??
??
??
?
??
 
Page 4


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Friday 29
th
 July, 2022)                TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. Given below are two statements : One is labelled 
as Assertion (A) and other is labelled as 
 Reason (R). 
 Assertion (A) : Time period of oscillation of a 
liquid drop depends on surface tension (S), if 
density of the liquid is p and radius of the drop is r, 
then T = 
3
2
3
pr
k
s
 is dimensionally correct, 
where K is dimensionless. 
 Reason (R) : Using dimensional analysis we get 
R.H.S. having different dimension than that of time 
period. 
 In the light of above statements, choose the correct 
answer from the options given below. 
 (A) Both (A) and (R) are true and (R) is the correct 
explanation of (A)  
  (B) Both (A) and (R) are true but (R) is not the 
correct explanation of (A) 
 (C) (A) is true but (R) is false   
 (D) (A) is false but (R) is true 
 Official Ans. by NTA (D) 
  
Sol. 
3
3
2
r
Tk
s
?
? 
 Dimensions of RHS = 
33 1
2 2 2
13
0
8 2
3
2 4
M L L
M L T
MT
?
?
? ? ? ?
? ? ? ?
? ? ? ?
?
??
??
 
 Dimensions of L.H.S ? Dimensions of R.H.S 
 ? option (D)  
2. A ball is thrown up vertically with a certain 
velocity so that, it reaches a maximum height h. 
Find the ratio of the times in which it is at height 
h
3
 while going up and coming down respectively. 
 (A) 
21
21
?
?
  (B) 
32
32
?
?
  
 (C) 
31
31
?
?
  (D) 
1
3
 
 Official Ans. by NTA (B) 
  
Sol.  
 Max. Height = h = 
2
u
2g
 
 u 2gh ?? 
 S = ut + 
2
1
at
2
 
 
2
h1
2ght ( g)t
32
? ? ? 
 
2
gt h
2ght 0
23
? ? ? (Roots are t
1
 & t
2
) 
 
2
1
g h 4gh
2gh 2gh 4 2gh
t 32
2 3 3
t g h 4gh 3 2
2gh 2gh 4 2gh
2 3 3
? ? ? ? ?
?
? ? ?
?
? ? ? ? ?
 
 
2 
 
3. 
t4
dx
If t x 4,then is:
dt
?
??
??
??
??
 
 (A) 4  (B) Zero  
 (C) 8 (D) 16 
 Official Ans. by NTA (B) 
  
Sol. t x 4 ?? 
 ? x = (t – 4)
2
 = t
2
 – 8t + 16 
 
dx
dt
? = 2t – 8 
 
t4
dx
2 4 8 0
dt
?
? ? ? ? ? 
4. A smooth circular groove has a smooth vertical 
wall as shown in figure. A block of mass m moves 
against the wall with a speed v. Which of the 
following curve represents the correct relation 
between the normal reaction on the block by the 
wall (N) and speed of the block (v) ? 
 
V
 
 
 (A) 
N
v
  
 (B) 
N
v
 
 (C) 
N
v
  
 (D) 
N
v
 
 Official Ans. by NTA (A) 
  
Sol. 
2
mv
N
r
? 
 Curve is parabola 
 Y = kx
2 
 
5. A ball is projected with kinetic energy E, at an 
angle of 60
0
 to the horizontal. The kinetic energy 
of this ball at the highest point of its flight will 
become :
 
 (A) Zero   (B) 
E
2
 
 (C) 
E
4
  (D) E 
 Official Ans. by NTA (C) 
  
Sol. 
60
o
ucos60
o
u
 
 
2
1
E mu
2
? 
 At Highest point, Velocity V = u cos60
o
 = 
u
2
 
 ? K.E at topmost point = 
2
1 u E
m
2 2 4
??
?
??
??
 
6. Two bodies of mass 1 kg and 3 kg have position 
vectors 
ˆ ˆ ˆ
i 2j k ?? and 
ˆ ˆ ˆ
3i 2j k ? ? ? respectively. 
The magnitude of position vector of centre of mass 
of this system will be similar to the magnitude of 
vector : 
 (A) 
ˆ ˆ ˆ
i 2j k ?? (B) 
ˆ ˆ ˆ
3i 2j k ? ? ?
 
 
 (C) 
ˆˆ
2i 2k ?? (D) 
ˆ ˆ ˆ
2i j 2k ? ? ? 
 Official Ans. by NTA (A) 
  
Sol. 
1 1 2 2
com
12
ˆ ˆ ˆ ˆ ˆ ˆ
1(i 2j k) 3( 3i 2j k) m r m r
r
m m 1 3
? ? ? ? ? ? ?
??
??
 
 
ˆ ˆ ˆ
2i j k ? ? ? ? 
 
2 2 2
ˆ ˆ ˆ
|2i j k| (2) (1) (1) 6 ? ? ? ? ? ? 
 
 
3 
 
?  
7. Given below are two statements : One is labelled 
as Assertion (A) and the other is labelled as  
 Reason (R). 
Assertion (A) : Clothes containing oil or grease 
stains cannot be cleaned by water wash. 
Reason (R) : Because the angle of contact between 
the oil/ grease and water is obtuse. In the light of 
the above statements, choose the correct answer 
from the option given below. 
 (A) Both (A) and (R) are true and (R) is the correct 
explanation of (A) 
 (B) Both (A) and (R) are true but (R) is not the 
correct explanation of (A) 
 (C) (A) is true but (R) is false   
 (D) (A) is true but (R) is true 
 Official Ans. by NTA (A) 
  
Sol. 
Water
Oil
?c
 
?c > 90
o
 
 For water oil interface 
8. If the length of a wire is made double and radius is 
halved of its respective values. Then, the Young’s 
modules of the material of the wire will : 
 (A) Remains same 
 (B) Become 8 times its initial value  
 (C) Become 
th
1
4
 of its initial value 
 (D) Become 4 times its initial value 
 Official Ans. by NTA (A) 
  
Sol. Y depends on material of wire 
9. The time period of oscillation of a simple 
pendulum of length L suspended from the roof of a 
vehicle, which moves without friction down an 
inclined plane of inclination ?, is given by : 
 (A) 2 L/(gcos ) ?? (B) 2 L/(gsin ) ??  
 (C) 2 L/g ? (D) 2 L/(gtan ) ?? 
 Official Ans. by NTA (A) 
  
Sol. g
cff
 = gcos ? ?
a = g sin ?
g cos ?
g sin ?
g cos ?
 ?
?
 
L
T2
gcos
??
?
 
10. A spherically symmetric charge distribution is 
considered with charge density varying as 
 
0
3r
for r R
(r) 4R
for r R
Zero
???
?? ?
?
??
??
?? ?
?
?
?
 
 Where, r(r < R) is the distance from the centre O 
(as shown in figure). The electric field at point P 
will be : 
O
P
R
r
(r) ?
 
 (A) 
0
0
r3r
4 4 R
?
??
?
??
?
??
 (B) 
0
0
r3r
3 4 R
?
??
?
??
?
??
 
 
 (C) 
0
0
r r
1
4R
?
??
?
??
?
??
 (D) 
0
0
r r
1
5R
?
??
?
??
?
??
 
 Official Ans. by NTA (C) 
  
Sol. By Gauss law 
O
P
R
r
(r) ?
 
 
in
o
Q
E.ds ?
?
?
 
 
r
2
o
2 0
0
3r
4 r dr
4R
E.4 r
??
? ? ?
??
??
??
?
?
 
 
34
2 o
o
4 3 r r
E4 r
4 3 4R
?? ??
? ? ?
??
?
??
 
 
3
2 o
o
r r
Er 1
4R
?
??
??
??
?
??
 
 
o
o
r r
E1
4R
?
??
??
??
?
??
 
 
4 
 
11. Given below are two statements.  
 Statement I : Electric potential is constant within 
and at the surface of each conductor.  
 Statement II : Electric field just outside a charged 
conductor is perpendicular to the surface of the 
conductor at every point.  
 In the light of the above statements, choose the 
most appropriate answer from the options give 
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 and statement II is 
correct 
 Official Ans. by NTA (A) 
  
Sol. (Properties of conductor) 
 Statement – I, true as body of conductor acts as 
equipotential surface. 
 Statement – 2 True, as conductor is equipotential. 
Tangential component of electric field should be 
zero. Therefore electric field should be 
perpendicular to surface.   
12. Two metallic wires of identical dimensions are 
connected is series. If 
1
? and 
2
? are the 
conductivities of the these wires respectively, the 
effective conductivity of the combination is : 
 (A) 
12
12
??
? ? ?
  (B) 
12
12
2??
? ? ?
  
 (C) 
12
12
2
? ? ?
??
  (D) 
12
12
? ? ?
??
 
 Official Ans. by NTA (B) 
  
Sol. 
? ?
A
2 ?
?
A 1
?
2
?
eq
?
Let length of wire be ‘ ’ 
 Area of wire as ‘A’ 
 For equivalent wire length = 2 & area will be A 
 Thermal resistance 
 R
eq
 = R
1 
+ R
2
 
 
eq 1 1
2
A A A
??
? ? ?
 
 
12
eq
eq 1 2 1 2
2 2 ??
? ? ? ? ?
? ? ? ? ? ?
 
13. An alternating emf E = 440 sin 100 ?t is applited to 
a circuit containing an inductance of 
2
?
 H. If an 
a.c. ammeter is connected in the circuit, its reading 
will be : 
 (A) 4.4 A  (B) 1.55 A  
 (C) 2.2 A  (D) 3.11 A 
 Official Ans. by NTA (C) 
  
Sol. E = 440 Sin100?t , L = 
2
H
?
 
 X
L
 = L ? = 100 ? 
2
?
 = 100 2 ? 
 
0
0
L
E 440
PeakcurrentI 2.2 2
X 100 2
? ? ? A 
 AC ammeter reads RMS value therefore reading 
will be I
rms
 
 I
rms
 = 
0
I
2
 = 2.2 A 
14. A coil of inductance 1 H and resistance 100 ? is 
connected to a battery of 6 V. Determine 
approximately :  
 (a) The time elapsed before the current acquires 
half of its steady – state value 
 (b) The energy stored in the magnetic field 
associated with the coil at an instant 15 ms after 
the circuit is switched on. (Given In2 = 0.693,  
e
-3/2 
= 0.25) 
 (A) t = 10 ms; U = 2 mJ 
 (B) t = 10 ms; U = 1 mJ 
 (C) t = 7 ms; U = 1 mJ 
 (D) t = 7 ms; U = 2 mJ 
 Official Ans. by NTA (C) 
  
Page 5


 
    1 
FINAL JEE –MAIN EXAMINATION – JULY, 2022 
(Held On Friday 29
th
 July, 2022)                TIME : 9 : 00 AM  to  12 : 00 NOON 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
 
 
 
 
 
SECTION-A 
1. Given below are two statements : One is labelled 
as Assertion (A) and other is labelled as 
 Reason (R). 
 Assertion (A) : Time period of oscillation of a 
liquid drop depends on surface tension (S), if 
density of the liquid is p and radius of the drop is r, 
then T = 
3
2
3
pr
k
s
 is dimensionally correct, 
where K is dimensionless. 
 Reason (R) : Using dimensional analysis we get 
R.H.S. having different dimension than that of time 
period. 
 In the light of above statements, choose the correct 
answer from the options given below. 
 (A) Both (A) and (R) are true and (R) is the correct 
explanation of (A)  
  (B) Both (A) and (R) are true but (R) is not the 
correct explanation of (A) 
 (C) (A) is true but (R) is false   
 (D) (A) is false but (R) is true 
 Official Ans. by NTA (D) 
  
Sol. 
3
3
2
r
Tk
s
?
? 
 Dimensions of RHS = 
33 1
2 2 2
13
0
8 2
3
2 4
M L L
M L T
MT
?
?
? ? ? ?
? ? ? ?
? ? ? ?
?
??
??
 
 Dimensions of L.H.S ? Dimensions of R.H.S 
 ? option (D)  
2. A ball is thrown up vertically with a certain 
velocity so that, it reaches a maximum height h. 
Find the ratio of the times in which it is at height 
h
3
 while going up and coming down respectively. 
 (A) 
21
21
?
?
  (B) 
32
32
?
?
  
 (C) 
31
31
?
?
  (D) 
1
3
 
 Official Ans. by NTA (B) 
  
Sol.  
 Max. Height = h = 
2
u
2g
 
 u 2gh ?? 
 S = ut + 
2
1
at
2
 
 
2
h1
2ght ( g)t
32
? ? ? 
 
2
gt h
2ght 0
23
? ? ? (Roots are t
1
 & t
2
) 
 
2
1
g h 4gh
2gh 2gh 4 2gh
t 32
2 3 3
t g h 4gh 3 2
2gh 2gh 4 2gh
2 3 3
? ? ? ? ?
?
? ? ?
?
? ? ? ? ?
 
 
2 
 
3. 
t4
dx
If t x 4,then is:
dt
?
??
??
??
??
 
 (A) 4  (B) Zero  
 (C) 8 (D) 16 
 Official Ans. by NTA (B) 
  
Sol. t x 4 ?? 
 ? x = (t – 4)
2
 = t
2
 – 8t + 16 
 
dx
dt
? = 2t – 8 
 
t4
dx
2 4 8 0
dt
?
? ? ? ? ? 
4. A smooth circular groove has a smooth vertical 
wall as shown in figure. A block of mass m moves 
against the wall with a speed v. Which of the 
following curve represents the correct relation 
between the normal reaction on the block by the 
wall (N) and speed of the block (v) ? 
 
V
 
 
 (A) 
N
v
  
 (B) 
N
v
 
 (C) 
N
v
  
 (D) 
N
v
 
 Official Ans. by NTA (A) 
  
Sol. 
2
mv
N
r
? 
 Curve is parabola 
 Y = kx
2 
 
5. A ball is projected with kinetic energy E, at an 
angle of 60
0
 to the horizontal. The kinetic energy 
of this ball at the highest point of its flight will 
become :
 
 (A) Zero   (B) 
E
2
 
 (C) 
E
4
  (D) E 
 Official Ans. by NTA (C) 
  
Sol. 
60
o
ucos60
o
u
 
 
2
1
E mu
2
? 
 At Highest point, Velocity V = u cos60
o
 = 
u
2
 
 ? K.E at topmost point = 
2
1 u E
m
2 2 4
??
?
??
??
 
6. Two bodies of mass 1 kg and 3 kg have position 
vectors 
ˆ ˆ ˆ
i 2j k ?? and 
ˆ ˆ ˆ
3i 2j k ? ? ? respectively. 
The magnitude of position vector of centre of mass 
of this system will be similar to the magnitude of 
vector : 
 (A) 
ˆ ˆ ˆ
i 2j k ?? (B) 
ˆ ˆ ˆ
3i 2j k ? ? ?
 
 
 (C) 
ˆˆ
2i 2k ?? (D) 
ˆ ˆ ˆ
2i j 2k ? ? ? 
 Official Ans. by NTA (A) 
  
Sol. 
1 1 2 2
com
12
ˆ ˆ ˆ ˆ ˆ ˆ
1(i 2j k) 3( 3i 2j k) m r m r
r
m m 1 3
? ? ? ? ? ? ?
??
??
 
 
ˆ ˆ ˆ
2i j k ? ? ? ? 
 
2 2 2
ˆ ˆ ˆ
|2i j k| (2) (1) (1) 6 ? ? ? ? ? ? 
 
 
3 
 
?  
7. Given below are two statements : One is labelled 
as Assertion (A) and the other is labelled as  
 Reason (R). 
Assertion (A) : Clothes containing oil or grease 
stains cannot be cleaned by water wash. 
Reason (R) : Because the angle of contact between 
the oil/ grease and water is obtuse. In the light of 
the above statements, choose the correct answer 
from the option given below. 
 (A) Both (A) and (R) are true and (R) is the correct 
explanation of (A) 
 (B) Both (A) and (R) are true but (R) is not the 
correct explanation of (A) 
 (C) (A) is true but (R) is false   
 (D) (A) is true but (R) is true 
 Official Ans. by NTA (A) 
  
Sol. 
Water
Oil
?c
 
?c > 90
o
 
 For water oil interface 
8. If the length of a wire is made double and radius is 
halved of its respective values. Then, the Young’s 
modules of the material of the wire will : 
 (A) Remains same 
 (B) Become 8 times its initial value  
 (C) Become 
th
1
4
 of its initial value 
 (D) Become 4 times its initial value 
 Official Ans. by NTA (A) 
  
Sol. Y depends on material of wire 
9. The time period of oscillation of a simple 
pendulum of length L suspended from the roof of a 
vehicle, which moves without friction down an 
inclined plane of inclination ?, is given by : 
 (A) 2 L/(gcos ) ?? (B) 2 L/(gsin ) ??  
 (C) 2 L/g ? (D) 2 L/(gtan ) ?? 
 Official Ans. by NTA (A) 
  
Sol. g
cff
 = gcos ? ?
a = g sin ?
g cos ?
g sin ?
g cos ?
 ?
?
 
L
T2
gcos
??
?
 
10. A spherically symmetric charge distribution is 
considered with charge density varying as 
 
0
3r
for r R
(r) 4R
for r R
Zero
???
?? ?
?
??
??
?? ?
?
?
?
 
 Where, r(r < R) is the distance from the centre O 
(as shown in figure). The electric field at point P 
will be : 
O
P
R
r
(r) ?
 
 (A) 
0
0
r3r
4 4 R
?
??
?
??
?
??
 (B) 
0
0
r3r
3 4 R
?
??
?
??
?
??
 
 
 (C) 
0
0
r r
1
4R
?
??
?
??
?
??
 (D) 
0
0
r r
1
5R
?
??
?
??
?
??
 
 Official Ans. by NTA (C) 
  
Sol. By Gauss law 
O
P
R
r
(r) ?
 
 
in
o
Q
E.ds ?
?
?
 
 
r
2
o
2 0
0
3r
4 r dr
4R
E.4 r
??
? ? ?
??
??
??
?
?
 
 
34
2 o
o
4 3 r r
E4 r
4 3 4R
?? ??
? ? ?
??
?
??
 
 
3
2 o
o
r r
Er 1
4R
?
??
??
??
?
??
 
 
o
o
r r
E1
4R
?
??
??
??
?
??
 
 
4 
 
11. Given below are two statements.  
 Statement I : Electric potential is constant within 
and at the surface of each conductor.  
 Statement II : Electric field just outside a charged 
conductor is perpendicular to the surface of the 
conductor at every point.  
 In the light of the above statements, choose the 
most appropriate answer from the options give 
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 and statement II is 
correct 
 Official Ans. by NTA (A) 
  
Sol. (Properties of conductor) 
 Statement – I, true as body of conductor acts as 
equipotential surface. 
 Statement – 2 True, as conductor is equipotential. 
Tangential component of electric field should be 
zero. Therefore electric field should be 
perpendicular to surface.   
12. Two metallic wires of identical dimensions are 
connected is series. If 
1
? and 
2
? are the 
conductivities of the these wires respectively, the 
effective conductivity of the combination is : 
 (A) 
12
12
??
? ? ?
  (B) 
12
12
2??
? ? ?
  
 (C) 
12
12
2
? ? ?
??
  (D) 
12
12
? ? ?
??
 
 Official Ans. by NTA (B) 
  
Sol. 
? ?
A
2 ?
?
A 1
?
2
?
eq
?
Let length of wire be ‘ ’ 
 Area of wire as ‘A’ 
 For equivalent wire length = 2 & area will be A 
 Thermal resistance 
 R
eq
 = R
1 
+ R
2
 
 
eq 1 1
2
A A A
??
? ? ?
 
 
12
eq
eq 1 2 1 2
2 2 ??
? ? ? ? ?
? ? ? ? ? ?
 
13. An alternating emf E = 440 sin 100 ?t is applited to 
a circuit containing an inductance of 
2
?
 H. If an 
a.c. ammeter is connected in the circuit, its reading 
will be : 
 (A) 4.4 A  (B) 1.55 A  
 (C) 2.2 A  (D) 3.11 A 
 Official Ans. by NTA (C) 
  
Sol. E = 440 Sin100?t , L = 
2
H
?
 
 X
L
 = L ? = 100 ? 
2
?
 = 100 2 ? 
 
0
0
L
E 440
PeakcurrentI 2.2 2
X 100 2
? ? ? A 
 AC ammeter reads RMS value therefore reading 
will be I
rms
 
 I
rms
 = 
0
I
2
 = 2.2 A 
14. A coil of inductance 1 H and resistance 100 ? is 
connected to a battery of 6 V. Determine 
approximately :  
 (a) The time elapsed before the current acquires 
half of its steady – state value 
 (b) The energy stored in the magnetic field 
associated with the coil at an instant 15 ms after 
the circuit is switched on. (Given In2 = 0.693,  
e
-3/2 
= 0.25) 
 (A) t = 10 ms; U = 2 mJ 
 (B) t = 10 ms; U = 1 mJ 
 (C) t = 7 ms; U = 1 mJ 
 (D) t = 7 ms; U = 2 mJ 
 Official Ans. by NTA (C) 
  
 
 
5 
 
?  
Sol. Given circuit is R – L growth circuit 
L = 1H
E = 6v
R = 100 ?
 
 i = 
t/
E
(1 e )
R
??
? 
 
t/ )
EE
i (1 e )
2R R
??
? ? ? 
 Solvingt= t l n 2  
 
11
t ln2 0.693 0.00693
R 100
? ? ? 
 = 7 ms 
 
15
10
E
i(15ms) (1 e )
R
?
?? 
 
6 3 6
1
i (1 )
4
100 4 100
? ? ? ? 
 U = 
1
2
LI
2
,  
 by solving we get U = 1 mJ. 
15. Match List – I with List – II 
 List – I List - II 
(a) UV rays (i) Diagnostic tool in 
medicine  
(b) X-rays  (ii) Water purification 
(c) Microwave (iii) Communication, Radar 
(d) Infrared wave (iv) Improving visibility in 
foggy days  
 Choose the correct answer from the options given 
below : 
 (A) (a)–(iii), (b)-(ii), (c)-(i), (d)-(iv) 
 (B) (a)–(ii), (b)-(i), (c)-(iii), (d)-(iv)  
 (C) (a)–(ii), (b)-(iv), (c)-(iii), (d)-(i)   
 (D) (a)–(iii), (b)-(i), (c)-(ii), (d)-(iv) 
 Official Ans. by NTA (B) 
  
Sol. (a) uv rays – used for water purification 
 (b)  x-rays used for diagnosing fracture 
 (c) Microwaves are used for mobile and radar 
communication     
 (d) Infrared waves show less scattering therefore 
used in foggy days  
  (a – ii), (b – i), (c – iii), (d – iv)   
16. The kinetic energy of emitted electron is E when 
the light incident on the metal has wavelength 
? ??To double the kinetic energy, the incident light 
must have wavelength : 
 (A) 
hc
E hc ??
  (B) 
hc
E hc
?
??
  
 (C)
h
E hc
?
??
 (D) 
hc
E hc
?
??
 
 Official Ans. by NTA (B) 
  
Sol. 
hc
E (i) ? ? ? ?
?
 
 
hc
2E (ii)
'
? ? ? ?
?
 
 (ii) – (i) 
 
11
E hc
'
??
??
??
??
??
 
 
hc
'
E hc
?
? ? ?
??
 
17. Find the ratio of energies of photons produced due 
to transition of an election of hydrogen atom from 
its(i) second permitted energy level to the first 
level,  and (ii) the highest permitted energy level to 
the first permitted level.  
 (A) 3 : 4   (B) 4 : 3  
 (C) 1 : 4  (D) 4 : 1 
 Official Ans. by NTA (A) 
  
Sol. 
n 2
13.6
E ev
n
?
? 
 
21
1
1
13.6(1 )
EE 3
4
E E 13.6 4
?
?
?
? ? ?
?
 
18. Find the modulation index of an AM wave having 
8 V variation where maximum amplitude of the 
AM wave is 9 V. 
 (A) 0.8  (B) 0.5  
 (C) 0.2  (D) 0.1 
 Official Ans. by NTA (A) 
  
Sol. Modulation index: 
m
c
A
m
A
? 
 Given 2A
m
 = 8 
 A
m
 + A
c
 = 9 ? A
c
 = 5 
 
4
m 0.8
5
? ? ?