JEE Main 2022 Question Paper 28 June Shift 2

 Page 1


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
(Held On Tuesday 28
th
 June, 2022)  TIME : 3 : 00 PM  to  6 : 00 PM
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. Velocity (v) and acceleration (a) in two systems of
units 1 and 2 are related as ?
21 2
n
vv
m
and 
1
2
a
a
mn
? respectively. Here m and n are 
constants. The relations for distance and time in 
two systems respectively are: 
(A) 
32
1 2 1 2 3
nn
L L and T T
mm
??
(B) 
42
1 2 1 2 2
nn
L L andT T
mm
??
(C) 
24
1 2 1 2 2
nn
L L and T T
mm
??
(D) 
24
1 2 1 2 2
nn
L L and T T
mm
??
Official Ans. by NTA (A) 
 
Sol. 
21
2
21
LL n
TT m
?
21
22
21
LL
T T mn
?
?
2
22
22
1 1
TT n
T m T mn
??
?
2
2
1
T n
mT
?
4
2
2
1
L n1
L mn m
??
3
2
3
1
L n
L m
?
2. A ball is spun with angular acceleration
? ? ?
2
6t 2t where t is in second and ? is in 
rads
–2
. At t = 0, the ball has angular velocity of 10 
rads
–1
 and angular position of 4 rad. The most 
appropriate expression for the angular position of 
the ball is: 
(A) 
42
3
t t 10t
2
??
(B) 
43
tt
10t 4
23
? ? ?
(C) 
43
2t t
10t 12
36
? ? ?
(D) 
3
4
t
2t 5t 4
2
? ? ?
Official Ans. by NTA (B) 
 
Sol. 
2
dw
6t 2t
dt
??
w
32
10
dw 2t t ??
?
32
w 10 2t t ? ? ?
32
d
10 2t t
dt
?
? ? ?
32
4
d 10 2t t
?
? ? ? ?
?
?
? ? ? ?
?
43
4
tt
d 10t
23
43
tt
4 10t
23
? ? ? ? ?
Page 2


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
(Held On Tuesday 28
th
 June, 2022)  TIME : 3 : 00 PM  to  6 : 00 PM
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. Velocity (v) and acceleration (a) in two systems of
units 1 and 2 are related as ?
21 2
n
vv
m
and 
1
2
a
a
mn
? respectively. Here m and n are 
constants. The relations for distance and time in 
two systems respectively are: 
(A) 
32
1 2 1 2 3
nn
L L and T T
mm
??
(B) 
42
1 2 1 2 2
nn
L L andT T
mm
??
(C) 
24
1 2 1 2 2
nn
L L and T T
mm
??
(D) 
24
1 2 1 2 2
nn
L L and T T
mm
??
Official Ans. by NTA (A) 
 
Sol. 
21
2
21
LL n
TT m
?
21
22
21
LL
T T mn
?
?
2
22
22
1 1
TT n
T m T mn
??
?
2
2
1
T n
mT
?
4
2
2
1
L n1
L mn m
??
3
2
3
1
L n
L m
?
2. A ball is spun with angular acceleration
? ? ?
2
6t 2t where t is in second and ? is in 
rads
–2
. At t = 0, the ball has angular velocity of 10 
rads
–1
 and angular position of 4 rad. The most 
appropriate expression for the angular position of 
the ball is: 
(A) 
42
3
t t 10t
2
??
(B) 
43
tt
10t 4
23
? ? ?
(C) 
43
2t t
10t 12
36
? ? ?
(D) 
3
4
t
2t 5t 4
2
? ? ?
Official Ans. by NTA (B) 
 
Sol. 
2
dw
6t 2t
dt
??
w
32
10
dw 2t t ??
?
32
w 10 2t t ? ? ?
32
d
10 2t t
dt
?
? ? ?
32
4
d 10 2t t
?
? ? ? ?
?
?
? ? ? ?
?
43
4
tt
d 10t
23
43
tt
4 10t
23
? ? ? ? ?
 
2 
 
3. A block of mass 2 kg moving on a horizontal 
surface with speed of 4 ms
-1
 enters a rough surface 
ranging from x = 0.5 m to x = 1.5 m. The retarding 
force in this range of rough surface is related to 
distance by F kx ?? where k = 12 Nm
-1
. The 
speed of the block as it just crosses the rough 
surface will be: 
 (A) Zero  (B) 1.5 ms
-1 
 (C) 2.0 ms
-1
 (D) 2.5 ms
-1 
 Official Ans. by NTA (C) 
  
Sol. 
kx 12x
a 6x
22
??
? ? ? ? 
 
vdv
6x
dx
?? 
 
v 3/2
1 4
2
vdv 6xdx ??
??
 
 
22
22
v 4 6 3 1
2 2 2 2
??
? ? ? ? ?
? ? ? ??
? ? ? ?
? ? ? ? ??
??
 
 
2
91
v 16 6
44
??
? ? ? ?
??
??
 
 
2
v 16 6 2 4 ? ? ? ? 
 V = 2 m/s 
4. A 34 m long ladder weighing 10 kg leans on a 
frictionless wall. Its feet rest on the floor 3 m away 
from the wall as shown in the figure. If F
f
 and F
w
 
are the reaction forces of the floor and the wall, 
then ratio of F
w
/F
f
 will be: 
 (Use g = 10 m/s
2
) 
 
 (A) 
6
110
  (B) 
3
113
  
 (C) 
3
109
  (D) 
2
109
 
 Official Ans. by NTA (C) 
  
Sol. 
 
34m
N
2
S
3m
mg
N
1
f
?
 
 ?
2
fN 
 
1
N mg ? 
 
2
N sin mg cos
2
? ? ? ? 
 
2
mg
N cot
2
?? 
 
? ?
w
2
f
2
mg
cot
F
2
F
mg
mg cot
2
?
?
??
??
??
??
 
 
2
1
4
1
cot
?
?
?
 
 
3
109
? 
5. Water fall from a 40 m high dam at the rate of 
?
4
9 10 kg per hour. Fifty percentage of 
gravitational potential energy can be converted into 
electrical energy. Using this hydroelectric energy 
number of 100W lamps, that can be lit, is: 
 (Take g = 10 ms
-2
) 
 (A) 25   (B) 50 
 (C) 100  (D) 18 
 Official Ans. by NTA (B) 
  
Sol. 
4
9 10 g 40
0.5 n 100
3600
? ? ?
? ? ? 
 
4
10 0.5
n
100
?
? 
 100 × 0.5 = n 
 n = 50 
Page 3


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
(Held On Tuesday 28
th
 June, 2022)  TIME : 3 : 00 PM  to  6 : 00 PM
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. Velocity (v) and acceleration (a) in two systems of
units 1 and 2 are related as ?
21 2
n
vv
m
and 
1
2
a
a
mn
? respectively. Here m and n are 
constants. The relations for distance and time in 
two systems respectively are: 
(A) 
32
1 2 1 2 3
nn
L L and T T
mm
??
(B) 
42
1 2 1 2 2
nn
L L andT T
mm
??
(C) 
24
1 2 1 2 2
nn
L L and T T
mm
??
(D) 
24
1 2 1 2 2
nn
L L and T T
mm
??
Official Ans. by NTA (A) 
 
Sol. 
21
2
21
LL n
TT m
?
21
22
21
LL
T T mn
?
?
2
22
22
1 1
TT n
T m T mn
??
?
2
2
1
T n
mT
?
4
2
2
1
L n1
L mn m
??
3
2
3
1
L n
L m
?
2. A ball is spun with angular acceleration
? ? ?
2
6t 2t where t is in second and ? is in 
rads
–2
. At t = 0, the ball has angular velocity of 10 
rads
–1
 and angular position of 4 rad. The most 
appropriate expression for the angular position of 
the ball is: 
(A) 
42
3
t t 10t
2
??
(B) 
43
tt
10t 4
23
? ? ?
(C) 
43
2t t
10t 12
36
? ? ?
(D) 
3
4
t
2t 5t 4
2
? ? ?
Official Ans. by NTA (B) 
 
Sol. 
2
dw
6t 2t
dt
??
w
32
10
dw 2t t ??
?
32
w 10 2t t ? ? ?
32
d
10 2t t
dt
?
? ? ?
32
4
d 10 2t t
?
? ? ? ?
?
?
? ? ? ?
?
43
4
tt
d 10t
23
43
tt
4 10t
23
? ? ? ? ?
 
2 
 
3. A block of mass 2 kg moving on a horizontal 
surface with speed of 4 ms
-1
 enters a rough surface 
ranging from x = 0.5 m to x = 1.5 m. The retarding 
force in this range of rough surface is related to 
distance by F kx ?? where k = 12 Nm
-1
. The 
speed of the block as it just crosses the rough 
surface will be: 
 (A) Zero  (B) 1.5 ms
-1 
 (C) 2.0 ms
-1
 (D) 2.5 ms
-1 
 Official Ans. by NTA (C) 
  
Sol. 
kx 12x
a 6x
22
??
? ? ? ? 
 
vdv
6x
dx
?? 
 
v 3/2
1 4
2
vdv 6xdx ??
??
 
 
22
22
v 4 6 3 1
2 2 2 2
??
? ? ? ? ?
? ? ? ??
? ? ? ?
? ? ? ? ??
??
 
 
2
91
v 16 6
44
??
? ? ? ?
??
??
 
 
2
v 16 6 2 4 ? ? ? ? 
 V = 2 m/s 
4. A 34 m long ladder weighing 10 kg leans on a 
frictionless wall. Its feet rest on the floor 3 m away 
from the wall as shown in the figure. If F
f
 and F
w
 
are the reaction forces of the floor and the wall, 
then ratio of F
w
/F
f
 will be: 
 (Use g = 10 m/s
2
) 
 
 (A) 
6
110
  (B) 
3
113
  
 (C) 
3
109
  (D) 
2
109
 
 Official Ans. by NTA (C) 
  
Sol. 
 
34m
N
2
S
3m
mg
N
1
f
?
 
 ?
2
fN 
 
1
N mg ? 
 
2
N sin mg cos
2
? ? ? ? 
 
2
mg
N cot
2
?? 
 
? ?
w
2
f
2
mg
cot
F
2
F
mg
mg cot
2
?
?
??
??
??
??
 
 
2
1
4
1
cot
?
?
?
 
 
3
109
? 
5. Water fall from a 40 m high dam at the rate of 
?
4
9 10 kg per hour. Fifty percentage of 
gravitational potential energy can be converted into 
electrical energy. Using this hydroelectric energy 
number of 100W lamps, that can be lit, is: 
 (Take g = 10 ms
-2
) 
 (A) 25   (B) 50 
 (C) 100  (D) 18 
 Official Ans. by NTA (B) 
  
Sol. 
4
9 10 g 40
0.5 n 100
3600
? ? ?
? ? ? 
 
4
10 0.5
n
100
?
? 
 100 × 0.5 = n 
 n = 50 
 
 
3 
 
6. Two objects of equal masses placed at certain 
distance from each other attracts each other with a 
force of F. If one-third mass of one object is 
transferred to the other object, then the new force 
will be :  
 (A)  
2
F
9
  (B) 
16
F
9
 
 
 (C)  
8
F
9
  (D) F 
 Official Ans. by NTA (C) 
  
Sol. 
2
2
Gm
F
r
? 
 
2
4m 2m
G
33
F'
r
? ? ? ?
?
? ? ? ?
? ? ? ?
? 
 
8
F' F
9
? 
7. A water drop of radius ? 1m falls in a situation 
where the effect of buoyant force is negligible. Co-
efficient of viscosity of air is 
??
?
52
1.8 10 Nsm and 
its density is negligible as compared to that of 
water 
? 63
10 gm . Terminal velocity of the water 
drop is: 
 (Take acceleration due to gravity = 10 ms
–2
) 
 (A) 
??
?
61
145.4 10 ms (B) 
??
?
61
118.0 10 ms 
 (C) 
??
?
61
132.6 10 ms (D) 
??
?
61
123.4 10 ms 
 Official Ans. by NTA (D) 
  
Sol.  
 
F = 6 rv
vt
??
4
mg
3
=
?? rg
3
v
t
 
 
3
t
4
6 rv r g
3
? ? ? ? ? 
 
3
t
4 r g
v
3 6 r
??
??
??
 
 
3 12 3
t –5
4 r g 2 10 10 10
v
3 6 r 9 1.8 10
?
? ? ? ? ?
? ? ?
?? ??
 
 = 123.4 × 10
–6 
m/s
 
8. A sample of an ideal gas is taken through the 
cyclic process ABCA as shown in figure. It 
absorbs, 40 J of heat during the part AB, no heat 
during BC and rejects 60J of heat during CA. A 
work 50J is done on the gas during the part BC. 
The internal energy of the gas at A is 1560J. The 
work done by the gas during the part CA is: 
 
 (A) 20 J  (B) 30 J  
 (C) –30J  (D) –60 J 
 Official Ans. by NTA (B) 
  
Sol.  
  
 
cycle
Q 40 60 W ? ? ? ? ? 
 
BC CA
W – 2 0J W W ? ? ? ? ? 
 
CA BC
W – 2 0 J W ? ? ? 
 = –20 – (–50) 
 = 30 J 
9. What will be the effect on the root mean square 
velocity of oxygen molecules if the temperature is 
doubled and oxygen molecule dissociates into 
atomic oxygen? 
 (A) The velocity of atomic oxygen remains same 
 (B) The velocity of atomic oxygen doubles 
 (C) The velocity of atomic oxygen becomes half  
 (D) The velocity of atomic oxygen becomes four 
times 
 Official Ans. by NTA (B) 
  
Page 4


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
(Held On Tuesday 28
th
 June, 2022)  TIME : 3 : 00 PM  to  6 : 00 PM
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. Velocity (v) and acceleration (a) in two systems of
units 1 and 2 are related as ?
21 2
n
vv
m
and 
1
2
a
a
mn
? respectively. Here m and n are 
constants. The relations for distance and time in 
two systems respectively are: 
(A) 
32
1 2 1 2 3
nn
L L and T T
mm
??
(B) 
42
1 2 1 2 2
nn
L L andT T
mm
??
(C) 
24
1 2 1 2 2
nn
L L and T T
mm
??
(D) 
24
1 2 1 2 2
nn
L L and T T
mm
??
Official Ans. by NTA (A) 
 
Sol. 
21
2
21
LL n
TT m
?
21
22
21
LL
T T mn
?
?
2
22
22
1 1
TT n
T m T mn
??
?
2
2
1
T n
mT
?
4
2
2
1
L n1
L mn m
??
3
2
3
1
L n
L m
?
2. A ball is spun with angular acceleration
? ? ?
2
6t 2t where t is in second and ? is in 
rads
–2
. At t = 0, the ball has angular velocity of 10 
rads
–1
 and angular position of 4 rad. The most 
appropriate expression for the angular position of 
the ball is: 
(A) 
42
3
t t 10t
2
??
(B) 
43
tt
10t 4
23
? ? ?
(C) 
43
2t t
10t 12
36
? ? ?
(D) 
3
4
t
2t 5t 4
2
? ? ?
Official Ans. by NTA (B) 
 
Sol. 
2
dw
6t 2t
dt
??
w
32
10
dw 2t t ??
?
32
w 10 2t t ? ? ?
32
d
10 2t t
dt
?
? ? ?
32
4
d 10 2t t
?
? ? ? ?
?
?
? ? ? ?
?
43
4
tt
d 10t
23
43
tt
4 10t
23
? ? ? ? ?
 
2 
 
3. A block of mass 2 kg moving on a horizontal 
surface with speed of 4 ms
-1
 enters a rough surface 
ranging from x = 0.5 m to x = 1.5 m. The retarding 
force in this range of rough surface is related to 
distance by F kx ?? where k = 12 Nm
-1
. The 
speed of the block as it just crosses the rough 
surface will be: 
 (A) Zero  (B) 1.5 ms
-1 
 (C) 2.0 ms
-1
 (D) 2.5 ms
-1 
 Official Ans. by NTA (C) 
  
Sol. 
kx 12x
a 6x
22
??
? ? ? ? 
 
vdv
6x
dx
?? 
 
v 3/2
1 4
2
vdv 6xdx ??
??
 
 
22
22
v 4 6 3 1
2 2 2 2
??
? ? ? ? ?
? ? ? ??
? ? ? ?
? ? ? ? ??
??
 
 
2
91
v 16 6
44
??
? ? ? ?
??
??
 
 
2
v 16 6 2 4 ? ? ? ? 
 V = 2 m/s 
4. A 34 m long ladder weighing 10 kg leans on a 
frictionless wall. Its feet rest on the floor 3 m away 
from the wall as shown in the figure. If F
f
 and F
w
 
are the reaction forces of the floor and the wall, 
then ratio of F
w
/F
f
 will be: 
 (Use g = 10 m/s
2
) 
 
 (A) 
6
110
  (B) 
3
113
  
 (C) 
3
109
  (D) 
2
109
 
 Official Ans. by NTA (C) 
  
Sol. 
 
34m
N
2
S
3m
mg
N
1
f
?
 
 ?
2
fN 
 
1
N mg ? 
 
2
N sin mg cos
2
? ? ? ? 
 
2
mg
N cot
2
?? 
 
? ?
w
2
f
2
mg
cot
F
2
F
mg
mg cot
2
?
?
??
??
??
??
 
 
2
1
4
1
cot
?
?
?
 
 
3
109
? 
5. Water fall from a 40 m high dam at the rate of 
?
4
9 10 kg per hour. Fifty percentage of 
gravitational potential energy can be converted into 
electrical energy. Using this hydroelectric energy 
number of 100W lamps, that can be lit, is: 
 (Take g = 10 ms
-2
) 
 (A) 25   (B) 50 
 (C) 100  (D) 18 
 Official Ans. by NTA (B) 
  
Sol. 
4
9 10 g 40
0.5 n 100
3600
? ? ?
? ? ? 
 
4
10 0.5
n
100
?
? 
 100 × 0.5 = n 
 n = 50 
 
 
3 
 
6. Two objects of equal masses placed at certain 
distance from each other attracts each other with a 
force of F. If one-third mass of one object is 
transferred to the other object, then the new force 
will be :  
 (A)  
2
F
9
  (B) 
16
F
9
 
 
 (C)  
8
F
9
  (D) F 
 Official Ans. by NTA (C) 
  
Sol. 
2
2
Gm
F
r
? 
 
2
4m 2m
G
33
F'
r
? ? ? ?
?
? ? ? ?
? ? ? ?
? 
 
8
F' F
9
? 
7. A water drop of radius ? 1m falls in a situation 
where the effect of buoyant force is negligible. Co-
efficient of viscosity of air is 
??
?
52
1.8 10 Nsm and 
its density is negligible as compared to that of 
water 
? 63
10 gm . Terminal velocity of the water 
drop is: 
 (Take acceleration due to gravity = 10 ms
–2
) 
 (A) 
??
?
61
145.4 10 ms (B) 
??
?
61
118.0 10 ms 
 (C) 
??
?
61
132.6 10 ms (D) 
??
?
61
123.4 10 ms 
 Official Ans. by NTA (D) 
  
Sol.  
 
F = 6 rv
vt
??
4
mg
3
=
?? rg
3
v
t
 
 
3
t
4
6 rv r g
3
? ? ? ? ? 
 
3
t
4 r g
v
3 6 r
??
??
??
 
 
3 12 3
t –5
4 r g 2 10 10 10
v
3 6 r 9 1.8 10
?
? ? ? ? ?
? ? ?
?? ??
 
 = 123.4 × 10
–6 
m/s
 
8. A sample of an ideal gas is taken through the 
cyclic process ABCA as shown in figure. It 
absorbs, 40 J of heat during the part AB, no heat 
during BC and rejects 60J of heat during CA. A 
work 50J is done on the gas during the part BC. 
The internal energy of the gas at A is 1560J. The 
work done by the gas during the part CA is: 
 
 (A) 20 J  (B) 30 J  
 (C) –30J  (D) –60 J 
 Official Ans. by NTA (B) 
  
Sol.  
  
 
cycle
Q 40 60 W ? ? ? ? ? 
 
BC CA
W – 2 0J W W ? ? ? ? ? 
 
CA BC
W – 2 0 J W ? ? ? 
 = –20 – (–50) 
 = 30 J 
9. What will be the effect on the root mean square 
velocity of oxygen molecules if the temperature is 
doubled and oxygen molecule dissociates into 
atomic oxygen? 
 (A) The velocity of atomic oxygen remains same 
 (B) The velocity of atomic oxygen doubles 
 (C) The velocity of atomic oxygen becomes half  
 (D) The velocity of atomic oxygen becomes four 
times 
 Official Ans. by NTA (B) 
  
 
4 
 
Sol. 
rms
3RT
V
M
? 
 T ? 2T 
 
M
M
2
? 
 
rms
T
V
M
? 
? ? ? ? ? ?
rms rms rms
atomic molecular molecular
2
V V 2 V
1 / 2
? ? ? ? 
10. Two point charges A and B of magnitude 
?
??
6
8 10 C and 
?
??
6
8 10 C respectively are 
placed at a distance d apart. The electric field at the 
middle point O between the charges is 
?
?
41
6.4 10 NC . The distance ‘d’ between the point 
charges A and B is: 
 (A) 2.0 m  (B) 3.0 m
 
 
 (C) 1.0 m  (D) 4.0 m 
 Official Ans. by NTA (B) 
  
Sol.  
 
–q +q
O
E
–
E
+
 
 
? ?
0 2
Kq
E2
d / 2
?? 
 
0 2
Kq
E8
d
?? 
 
96
2
4
8 9 10 8 10
d
6.4 10
?
? ? ? ?
??
?
 
 d = 3 m 
11. Resistance of the wire is measured as ? 2 and ? 3 
at 10°C and 30°C respectively. Temperature co–
coefficient of resistance of the material of the wire is : 
 (A) 0.033°C
–1
 (B) –0.033°C
–1 
 (C) 0.011°C
–1
 (D) 0.055°C
–1 
 Official Ans. by NTA (A) 
  
Sol. ? ?
0
R R 1 T ? ? ? ? 
 
? ? ? ?
0
3 R 1 3 0 – 0 ? ? ? 
 
? ? ? ?
0
2 R 1 1 0 – 0 ? ? ? 
 
3 1 30
2 1 10
??
?
??
 
 
1
0.033
30
? ? ? 
12. The space inside a straight current carrying solenoid 
is filled with a magnetic material having magnetic 
susceptibility equal to 
?
?
5
1.2 10 . What is fractional 
increase in the magnetic field inside solenoid with 
respect to air as medium inside the solenoid? 
 (A) 
?
?
5
1.2 10 (B) 
?
?
3
1.2 10 
 (C) 
?
?
3
1.8 10 (D) 
?
?
5
2.4 10 
 Official Ans. by NTA (A) 
  
Sol. 
5
1.2 10
?
? ? ? 
 
5
r
1 1 1.2 10
?
? ? ? ? ? ? ? 
 Fractional Change 
 ? ?
0 r 0
r
0
ni ni B
1
B ni
? ? ? ? ?
? ? ? ? ?
?
 
 = 1.2 × 10
–5
 
13. Two parallel, long wires are kept 0.20 m apart in 
vacuum, each carrying current of x A in the same 
direction. If the force of attraction per meter of 
each wire is 
?
?
6
2 10 N , then the value of x is 
approximately: 
 (A) 1  (B) 2.4 
 (C) 1.4  (D) 2 
 Official Ans. by NTA (C) 
  
Page 5


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
(Held On Tuesday 28
th
 June, 2022)  TIME : 3 : 00 PM  to  6 : 00 PM
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. Velocity (v) and acceleration (a) in two systems of
units 1 and 2 are related as ?
21 2
n
vv
m
and 
1
2
a
a
mn
? respectively. Here m and n are 
constants. The relations for distance and time in 
two systems respectively are: 
(A) 
32
1 2 1 2 3
nn
L L and T T
mm
??
(B) 
42
1 2 1 2 2
nn
L L andT T
mm
??
(C) 
24
1 2 1 2 2
nn
L L and T T
mm
??
(D) 
24
1 2 1 2 2
nn
L L and T T
mm
??
Official Ans. by NTA (A) 
 
Sol. 
21
2
21
LL n
TT m
?
21
22
21
LL
T T mn
?
?
2
22
22
1 1
TT n
T m T mn
??
?
2
2
1
T n
mT
?
4
2
2
1
L n1
L mn m
??
3
2
3
1
L n
L m
?
2. A ball is spun with angular acceleration
? ? ?
2
6t 2t where t is in second and ? is in 
rads
–2
. At t = 0, the ball has angular velocity of 10 
rads
–1
 and angular position of 4 rad. The most 
appropriate expression for the angular position of 
the ball is: 
(A) 
42
3
t t 10t
2
??
(B) 
43
tt
10t 4
23
? ? ?
(C) 
43
2t t
10t 12
36
? ? ?
(D) 
3
4
t
2t 5t 4
2
? ? ?
Official Ans. by NTA (B) 
 
Sol. 
2
dw
6t 2t
dt
??
w
32
10
dw 2t t ??
?
32
w 10 2t t ? ? ?
32
d
10 2t t
dt
?
? ? ?
32
4
d 10 2t t
?
? ? ? ?
?
?
? ? ? ?
?
43
4
tt
d 10t
23
43
tt
4 10t
23
? ? ? ? ?
 
2 
 
3. A block of mass 2 kg moving on a horizontal 
surface with speed of 4 ms
-1
 enters a rough surface 
ranging from x = 0.5 m to x = 1.5 m. The retarding 
force in this range of rough surface is related to 
distance by F kx ?? where k = 12 Nm
-1
. The 
speed of the block as it just crosses the rough 
surface will be: 
 (A) Zero  (B) 1.5 ms
-1 
 (C) 2.0 ms
-1
 (D) 2.5 ms
-1 
 Official Ans. by NTA (C) 
  
Sol. 
kx 12x
a 6x
22
??
? ? ? ? 
 
vdv
6x
dx
?? 
 
v 3/2
1 4
2
vdv 6xdx ??
??
 
 
22
22
v 4 6 3 1
2 2 2 2
??
? ? ? ? ?
? ? ? ??
? ? ? ?
? ? ? ? ??
??
 
 
2
91
v 16 6
44
??
? ? ? ?
??
??
 
 
2
v 16 6 2 4 ? ? ? ? 
 V = 2 m/s 
4. A 34 m long ladder weighing 10 kg leans on a 
frictionless wall. Its feet rest on the floor 3 m away 
from the wall as shown in the figure. If F
f
 and F
w
 
are the reaction forces of the floor and the wall, 
then ratio of F
w
/F
f
 will be: 
 (Use g = 10 m/s
2
) 
 
 (A) 
6
110
  (B) 
3
113
  
 (C) 
3
109
  (D) 
2
109
 
 Official Ans. by NTA (C) 
  
Sol. 
 
34m
N
2
S
3m
mg
N
1
f
?
 
 ?
2
fN 
 
1
N mg ? 
 
2
N sin mg cos
2
? ? ? ? 
 
2
mg
N cot
2
?? 
 
? ?
w
2
f
2
mg
cot
F
2
F
mg
mg cot
2
?
?
??
??
??
??
 
 
2
1
4
1
cot
?
?
?
 
 
3
109
? 
5. Water fall from a 40 m high dam at the rate of 
?
4
9 10 kg per hour. Fifty percentage of 
gravitational potential energy can be converted into 
electrical energy. Using this hydroelectric energy 
number of 100W lamps, that can be lit, is: 
 (Take g = 10 ms
-2
) 
 (A) 25   (B) 50 
 (C) 100  (D) 18 
 Official Ans. by NTA (B) 
  
Sol. 
4
9 10 g 40
0.5 n 100
3600
? ? ?
? ? ? 
 
4
10 0.5
n
100
?
? 
 100 × 0.5 = n 
 n = 50 
 
 
3 
 
6. Two objects of equal masses placed at certain 
distance from each other attracts each other with a 
force of F. If one-third mass of one object is 
transferred to the other object, then the new force 
will be :  
 (A)  
2
F
9
  (B) 
16
F
9
 
 
 (C)  
8
F
9
  (D) F 
 Official Ans. by NTA (C) 
  
Sol. 
2
2
Gm
F
r
? 
 
2
4m 2m
G
33
F'
r
? ? ? ?
?
? ? ? ?
? ? ? ?
? 
 
8
F' F
9
? 
7. A water drop of radius ? 1m falls in a situation 
where the effect of buoyant force is negligible. Co-
efficient of viscosity of air is 
??
?
52
1.8 10 Nsm and 
its density is negligible as compared to that of 
water 
? 63
10 gm . Terminal velocity of the water 
drop is: 
 (Take acceleration due to gravity = 10 ms
–2
) 
 (A) 
??
?
61
145.4 10 ms (B) 
??
?
61
118.0 10 ms 
 (C) 
??
?
61
132.6 10 ms (D) 
??
?
61
123.4 10 ms 
 Official Ans. by NTA (D) 
  
Sol.  
 
F = 6 rv
vt
??
4
mg
3
=
?? rg
3
v
t
 
 
3
t
4
6 rv r g
3
? ? ? ? ? 
 
3
t
4 r g
v
3 6 r
??
??
??
 
 
3 12 3
t –5
4 r g 2 10 10 10
v
3 6 r 9 1.8 10
?
? ? ? ? ?
? ? ?
?? ??
 
 = 123.4 × 10
–6 
m/s
 
8. A sample of an ideal gas is taken through the 
cyclic process ABCA as shown in figure. It 
absorbs, 40 J of heat during the part AB, no heat 
during BC and rejects 60J of heat during CA. A 
work 50J is done on the gas during the part BC. 
The internal energy of the gas at A is 1560J. The 
work done by the gas during the part CA is: 
 
 (A) 20 J  (B) 30 J  
 (C) –30J  (D) –60 J 
 Official Ans. by NTA (B) 
  
Sol.  
  
 
cycle
Q 40 60 W ? ? ? ? ? 
 
BC CA
W – 2 0J W W ? ? ? ? ? 
 
CA BC
W – 2 0 J W ? ? ? 
 = –20 – (–50) 
 = 30 J 
9. What will be the effect on the root mean square 
velocity of oxygen molecules if the temperature is 
doubled and oxygen molecule dissociates into 
atomic oxygen? 
 (A) The velocity of atomic oxygen remains same 
 (B) The velocity of atomic oxygen doubles 
 (C) The velocity of atomic oxygen becomes half  
 (D) The velocity of atomic oxygen becomes four 
times 
 Official Ans. by NTA (B) 
  
 
4 
 
Sol. 
rms
3RT
V
M
? 
 T ? 2T 
 
M
M
2
? 
 
rms
T
V
M
? 
? ? ? ? ? ?
rms rms rms
atomic molecular molecular
2
V V 2 V
1 / 2
? ? ? ? 
10. Two point charges A and B of magnitude 
?
??
6
8 10 C and 
?
??
6
8 10 C respectively are 
placed at a distance d apart. The electric field at the 
middle point O between the charges is 
?
?
41
6.4 10 NC . The distance ‘d’ between the point 
charges A and B is: 
 (A) 2.0 m  (B) 3.0 m
 
 
 (C) 1.0 m  (D) 4.0 m 
 Official Ans. by NTA (B) 
  
Sol.  
 
–q +q
O
E
–
E
+
 
 
? ?
0 2
Kq
E2
d / 2
?? 
 
0 2
Kq
E8
d
?? 
 
96
2
4
8 9 10 8 10
d
6.4 10
?
? ? ? ?
??
?
 
 d = 3 m 
11. Resistance of the wire is measured as ? 2 and ? 3 
at 10°C and 30°C respectively. Temperature co–
coefficient of resistance of the material of the wire is : 
 (A) 0.033°C
–1
 (B) –0.033°C
–1 
 (C) 0.011°C
–1
 (D) 0.055°C
–1 
 Official Ans. by NTA (A) 
  
Sol. ? ?
0
R R 1 T ? ? ? ? 
 
? ? ? ?
0
3 R 1 3 0 – 0 ? ? ? 
 
? ? ? ?
0
2 R 1 1 0 – 0 ? ? ? 
 
3 1 30
2 1 10
??
?
??
 
 
1
0.033
30
? ? ? 
12. The space inside a straight current carrying solenoid 
is filled with a magnetic material having magnetic 
susceptibility equal to 
?
?
5
1.2 10 . What is fractional 
increase in the magnetic field inside solenoid with 
respect to air as medium inside the solenoid? 
 (A) 
?
?
5
1.2 10 (B) 
?
?
3
1.2 10 
 (C) 
?
?
3
1.8 10 (D) 
?
?
5
2.4 10 
 Official Ans. by NTA (A) 
  
Sol. 
5
1.2 10
?
? ? ? 
 
5
r
1 1 1.2 10
?
? ? ? ? ? ? ? 
 Fractional Change 
 ? ?
0 r 0
r
0
ni ni B
1
B ni
? ? ? ? ?
? ? ? ? ?
?
 
 = 1.2 × 10
–5
 
13. Two parallel, long wires are kept 0.20 m apart in 
vacuum, each carrying current of x A in the same 
direction. If the force of attraction per meter of 
each wire is 
?
?
6
2 10 N , then the value of x is 
approximately: 
 (A) 1  (B) 2.4 
 (C) 1.4  (D) 2 
 Official Ans. by NTA (C) 
  
 
 
5 
 
Sol.
 
 
 Force per unit length = 
?
?
0 1 2
ii
2d
 
 
??
?
??
2
0
x
2 0.2
 
 F = 2 × 10
–6
 = 
?
? ? ?
??
72
4 10 x
2 0.2
 
 
??
??
2
67
x
10 10
0.2
 
 ? ? ?
2
x 10 0.2 
       =  2 
 ? ? ? x 2 1.4 Amp. 
14. A coil is placed in a time varying magnetic field. If 
the number of turns in the coil were to be halved 
and the radius of wire doubled, the electrical power 
dissipated due to the current induced in the coil 
would be: 
 (Assume the coil to be short circuited.) 
 (A) Halved   
 (B) Quadrupled 
 (C) The same  
 (D) Doubled 
 Official Ans. by NTA (D) 
  
Sol. P = 
2
R
?
 = 
2
C
dB
NA A
dt
??
?
??
??
?
 
 P' = 
2
C
NA dB
4A
2 dt
/2
??
?
??
??
?
 
 ? P' = 2P     
15. An EM wave propagating in x-direction has a 
wavelength of 8 mm. The electric field vibrating y-
direction has maximum magnitude of 60 Vm
–1
. 
Choose the correct equations for electric and 
magnetic fields if the EM wave is propagating in 
vacuum : 
 (A) 
? ?
?
???
? ? ? ?
??
??
3 8 1
y
ˆ
E 60sin 10 x 3 10 t jVm
4
 
? ?
???
? ? ? ?
??
??
38
z
ˆ
B 2sin 10 x 3 10 t kT
4
 
 (B) 
? ?
?
???
? ? ? ?
??
??
3 8 1
y
ˆ
E 60sin 10 x 3 10 t jVm
4
 
? ?
?
???
? ? ? ? ?
??
??
7 3 8
z
ˆ
B 2 10 sin 10 x 3 10 t kT
4
  
 (C) 
? ?
??
???
? ? ? ? ?
??
??
7 3 8 1
y
ˆ
E 2 10 sin 10 x 3 10 t jVm
4
 
? ?
???
? ? ? ?
??
??
38
z
ˆ
B 60sin 10 x 3 10 t kT
4
 
 (D) 
? ?
??
???
? ? ? ? ?
??
??
7 4 8 1
y
ˆ
E 2 10 sin 10 x 4 10 t jVm
4
 
? ?
???
? ? ? ?
??
??
48
z
ˆ
B 60sin 10 x 4 10 t kT
4
 
 Official Ans. by NTA (B) 
  
Sol. 
?
? ? ? ?
?
7 0
0
8
E 60
B 2 10 T
c 3 10
 
 ? EB must be direction of propagation. 
 So, ? B z-axis 
 
?
??
? ? ?
?
31
2
k 10 m
4
 
 
?
???
? ? ? ?
??
??
3 8 1
y
E 60sin 10 (x 3 10 t) j Vm
4
 
 
?
???
? ? ? ? ?
??
??
7 3 8
z
B 2 10 sin 10 (x 3 10 t) k T
4