JEE Main 2022 Question Paper 27 June Shift 2 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
 (Held On Monday 27
th
 June, 2022)   TIME : 3 : 00 PM  to  6 : 00 PM 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. The SI unit of a physical quantity is pascal-second.
The dimensional formula of this quantity will be
(A) [ML
–1
T
–1
] (B) [ML
–1
T
–2
]
(C) [ML
2
T
–1
] (D) [M
–1
L
3
T
0
]
Official Ans. by NTA (A) 
 
Sol. Pascal second 
?
?
2
2
F MLT
tT
A
L
 = ML
–1
T
–1
 
2. The distance of the Sun from earth is 1.5 × 10
11
 m
and its angular diameter is (2000) s when observed
from the earth. The diameter of the Sun will be :
(A) 2.45 × 10
10
 m (B) 1.45 × 10
10
 m
(C) 1.45 × 10
9
 m (D) 0.14 × 10
9
 m
Official Ans. by NTA (C) 
 
Sol. 
??
d
r
?
??
?? ??
2000 d
60 60 180 1.5 10
? ? ?
?
? ? ? ? ??
?
2000
d 1.5 10
60 60 180
= 
??
? ??
??
1.5
10
3 6 18
 = 1.45 × 10
9
 
3. When a ball is dropped into a lake from a height
4.9 m above the water level, it hits the water with a
velocity v and then sinks to the bottom with the
constant velocity v. It reaches the bottom of the
lake 4.0 s after it is dropped. The approximate
depth of the lake is :
(A) 19.6 m (B) 29.4 m
(C) 39.2 m (D) 73.5 m
Official Ans. by NTA (B) 
 
Sol. V
2
 = 2 × 9.8 × 4.9 
V = 9.8 m/s 
Depth = distance travelled in 3 seconds 
          = 9.8 × 3 = 29.4 m 
4. One end of a massless spring of spring constant k
and natural length l
0
 is fixed while the other end is
connected to a small object of mass m lying on a
frictionless table. The spring remains horizontal on
the table. If the object is made to rotate at an
angular velocity ? about an axis passing through
fixed end, then the elongation of the spring will be:
(A) 
??
?
2
0
2
km
m
l
(B) 
?
??
0
2
m
km
l
(C) 
?
??
2
0
2
m
km
l
(D) 
??
?
2
0
2
km
m
l
Official Ans. by NTA (C)
Page 2


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
 (Held On Monday 27
th
 June, 2022)   TIME : 3 : 00 PM  to  6 : 00 PM 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. The SI unit of a physical quantity is pascal-second.
The dimensional formula of this quantity will be
(A) [ML
–1
T
–1
] (B) [ML
–1
T
–2
]
(C) [ML
2
T
–1
] (D) [M
–1
L
3
T
0
]
Official Ans. by NTA (A) 
 
Sol. Pascal second 
?
?
2
2
F MLT
tT
A
L
 = ML
–1
T
–1
 
2. The distance of the Sun from earth is 1.5 × 10
11
 m
and its angular diameter is (2000) s when observed
from the earth. The diameter of the Sun will be :
(A) 2.45 × 10
10
 m (B) 1.45 × 10
10
 m
(C) 1.45 × 10
9
 m (D) 0.14 × 10
9
 m
Official Ans. by NTA (C) 
 
Sol. 
??
d
r
?
??
?? ??
2000 d
60 60 180 1.5 10
? ? ?
?
? ? ? ? ??
?
2000
d 1.5 10
60 60 180
= 
??
? ??
??
1.5
10
3 6 18
 = 1.45 × 10
9
 
3. When a ball is dropped into a lake from a height
4.9 m above the water level, it hits the water with a
velocity v and then sinks to the bottom with the
constant velocity v. It reaches the bottom of the
lake 4.0 s after it is dropped. The approximate
depth of the lake is :
(A) 19.6 m (B) 29.4 m
(C) 39.2 m (D) 73.5 m
Official Ans. by NTA (B) 
 
Sol. V
2
 = 2 × 9.8 × 4.9 
V = 9.8 m/s 
Depth = distance travelled in 3 seconds 
          = 9.8 × 3 = 29.4 m 
4. One end of a massless spring of spring constant k
and natural length l
0
 is fixed while the other end is
connected to a small object of mass m lying on a
frictionless table. The spring remains horizontal on
the table. If the object is made to rotate at an
angular velocity ? about an axis passing through
fixed end, then the elongation of the spring will be:
(A) 
??
?
2
0
2
km
m
l
(B) 
?
??
0
2
m
km
l
(C) 
?
??
2
0
2
m
km
l
(D) 
??
?
2
0
2
km
m
l
Official Ans. by NTA (C)
2 
Sol. 
K ? x = m( ?
0
 + ?x)w
2
K ? x = m ?
0
 w
2
 + mw
2
 ?x
??
?
2
0
2
mw
x
k mw
5. A stone tide to a string of length L is whirled in a
vertical circle with the other end of the string at the 
centre. At a certain instant of time, the stone is at 
its lowest position and has a speed u. The 
magnitude of change in its velocity, as it reaches a 
position where the string is horizontal, is 
?
2
x(u gL) . The value of x is   
(A) 3 (B) 2
(C) 1 (D) 5
Official Ans. by NTA (B) 
 
Sol. ??
2
v u 2gL
? ? ?
22
v u v
? ? ? ?
22
v u v 2gL
? ? ?
2
v 2u 2gL
? ?
? ? ?
2
v 2 u gL x = 2 
6. Four spheres each of mass m form a square of side
d (as shown in figure). A fifth sphere of mass M is 
situated at the centre of square. The total 
gravitational potential energy of the system is : 
(A)
??
? ? ?
??
Gm
(4 2)m 4 2M
d
(B)
??
? ? ?
??
Gm
(4 2)M 4 2m
d
(C)
??
??
??
2
Gm
3m 4 2M
d
(D) 
2
Gm
6m 4 2M
d
??
??
??
Official Ans. by NTA (A) 
 
Sol. 
? ? ?
22
Gm Gm GMm
– 4 – 2 – 4 2
dd
2d
??
??
??
Gm
– ( 4 2 ) m 4 2 M
d
Page 3


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
 (Held On Monday 27
th
 June, 2022)   TIME : 3 : 00 PM  to  6 : 00 PM 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. The SI unit of a physical quantity is pascal-second.
The dimensional formula of this quantity will be
(A) [ML
–1
T
–1
] (B) [ML
–1
T
–2
]
(C) [ML
2
T
–1
] (D) [M
–1
L
3
T
0
]
Official Ans. by NTA (A) 
 
Sol. Pascal second 
?
?
2
2
F MLT
tT
A
L
 = ML
–1
T
–1
 
2. The distance of the Sun from earth is 1.5 × 10
11
 m
and its angular diameter is (2000) s when observed
from the earth. The diameter of the Sun will be :
(A) 2.45 × 10
10
 m (B) 1.45 × 10
10
 m
(C) 1.45 × 10
9
 m (D) 0.14 × 10
9
 m
Official Ans. by NTA (C) 
 
Sol. 
??
d
r
?
??
?? ??
2000 d
60 60 180 1.5 10
? ? ?
?
? ? ? ? ??
?
2000
d 1.5 10
60 60 180
= 
??
? ??
??
1.5
10
3 6 18
 = 1.45 × 10
9
 
3. When a ball is dropped into a lake from a height
4.9 m above the water level, it hits the water with a
velocity v and then sinks to the bottom with the
constant velocity v. It reaches the bottom of the
lake 4.0 s after it is dropped. The approximate
depth of the lake is :
(A) 19.6 m (B) 29.4 m
(C) 39.2 m (D) 73.5 m
Official Ans. by NTA (B) 
 
Sol. V
2
 = 2 × 9.8 × 4.9 
V = 9.8 m/s 
Depth = distance travelled in 3 seconds 
          = 9.8 × 3 = 29.4 m 
4. One end of a massless spring of spring constant k
and natural length l
0
 is fixed while the other end is
connected to a small object of mass m lying on a
frictionless table. The spring remains horizontal on
the table. If the object is made to rotate at an
angular velocity ? about an axis passing through
fixed end, then the elongation of the spring will be:
(A) 
??
?
2
0
2
km
m
l
(B) 
?
??
0
2
m
km
l
(C) 
?
??
2
0
2
m
km
l
(D) 
??
?
2
0
2
km
m
l
Official Ans. by NTA (C)
2 
Sol. 
K ? x = m( ?
0
 + ?x)w
2
K ? x = m ?
0
 w
2
 + mw
2
 ?x
??
?
2
0
2
mw
x
k mw
5. A stone tide to a string of length L is whirled in a
vertical circle with the other end of the string at the 
centre. At a certain instant of time, the stone is at 
its lowest position and has a speed u. The 
magnitude of change in its velocity, as it reaches a 
position where the string is horizontal, is 
?
2
x(u gL) . The value of x is   
(A) 3 (B) 2
(C) 1 (D) 5
Official Ans. by NTA (B) 
 
Sol. ??
2
v u 2gL
? ? ?
22
v u v
? ? ? ?
22
v u v 2gL
? ? ?
2
v 2u 2gL
? ?
? ? ?
2
v 2 u gL x = 2 
6. Four spheres each of mass m form a square of side
d (as shown in figure). A fifth sphere of mass M is 
situated at the centre of square. The total 
gravitational potential energy of the system is : 
(A)
??
? ? ?
??
Gm
(4 2)m 4 2M
d
(B)
??
? ? ?
??
Gm
(4 2)M 4 2m
d
(C)
??
??
??
2
Gm
3m 4 2M
d
(D) 
2
Gm
6m 4 2M
d
??
??
??
Official Ans. by NTA (A) 
 
Sol. 
? ? ?
22
Gm Gm GMm
– 4 – 2 – 4 2
dd
2d
??
??
??
Gm
– ( 4 2 ) m 4 2 M
d
 
 
3 
 
7. For a perfect gas, two pressures P
1
 and P
2
 are 
shown in figure. The graph shows: 
 
 (A) P
1
 > P
2
 
 (B) P
1
 < P
2
 
 (C) P
1
 = P
2
  
 (D) Insufficient data to draw any conclusion  
  Official Ans. by NTA (A) 
  
Sol. PV = nRT 
 ?
V nR
TP
 
 ?
12
nR nR
PP
 
 ?
21
PP 
8. According to kinetic theory of gases, 
 A. The motion of the gas molecules freezes at 0ºC 
 B. The mean free path of gas molecules decreases 
if the density of molecules is increased. 
 C. The mean free path of gas molecules increases 
if temperature is increased keeping pressure 
constant. 
 D. Average kinetic energy per molecule per degree 
of freedom is 
B
3
kT
2
 (for monoatomic gases) 
 Choose the most appropriate answer from the 
options given below: 
 (A) A and C only (B) B and C only 
 (C) A and B only (D) C and D only 
  Official Ans. by NTA (B) 
  
Sol. ??
?
2
kT
2 d P
 
 
9.  A lead bullet penetrates into a solid object and 
melts. Assuming that 40% of its kinetic energy is 
used to heat it, the initial speed of bullet is: 
 (Given, initial temperature of the bullet = 127ºC, 
Melting point of the bullet = 327ºC, 
 Latent heat of fusion of lead = 2.5 × 10
4
J Kg
–1
, 
 Specific heat capacity of lead = 125J/kg K) 
 (A) 125 ms
–1
 (B) 500 ms
–1
 
 (C) 250 ms
–1
 (D) 600 ms
–1
 
 Official Ans. by NTA (B) 
  
Sol. ? ? ? ? ? ? ?
42
1 40
m 125 200 m 2.5 10 mv
2 100
 
 V = 500 m/s 
 
10. The equation of a particle executing simple 
harmonic motion is given by 
??
? ? ?
??
??
1
x sin t m
3
. 
At t = 1s, the speed of particle will be  
 (Given : ? = 3.14) 
 (A) 0 cm s
–1
  (B) 157 cm s
–1
  
 (C) 272 cm s
–1
  (D) 314 cm s
–1
  
 Official Ans. by NTA (B) 
  
Sol. 
??
? ? ?
??
??
1
x sin t
3
 
 
? ??
? ? ?
??
??
x sin t
3
 
 
dx
V cos t
dt 3
? ??
? ? ? ? ?
??
??
 
 ? ? ?
1
–
2
 = 157 cm/s 
Page 4


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
 (Held On Monday 27
th
 June, 2022)   TIME : 3 : 00 PM  to  6 : 00 PM 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. The SI unit of a physical quantity is pascal-second.
The dimensional formula of this quantity will be
(A) [ML
–1
T
–1
] (B) [ML
–1
T
–2
]
(C) [ML
2
T
–1
] (D) [M
–1
L
3
T
0
]
Official Ans. by NTA (A) 
 
Sol. Pascal second 
?
?
2
2
F MLT
tT
A
L
 = ML
–1
T
–1
 
2. The distance of the Sun from earth is 1.5 × 10
11
 m
and its angular diameter is (2000) s when observed
from the earth. The diameter of the Sun will be :
(A) 2.45 × 10
10
 m (B) 1.45 × 10
10
 m
(C) 1.45 × 10
9
 m (D) 0.14 × 10
9
 m
Official Ans. by NTA (C) 
 
Sol. 
??
d
r
?
??
?? ??
2000 d
60 60 180 1.5 10
? ? ?
?
? ? ? ? ??
?
2000
d 1.5 10
60 60 180
= 
??
? ??
??
1.5
10
3 6 18
 = 1.45 × 10
9
 
3. When a ball is dropped into a lake from a height
4.9 m above the water level, it hits the water with a
velocity v and then sinks to the bottom with the
constant velocity v. It reaches the bottom of the
lake 4.0 s after it is dropped. The approximate
depth of the lake is :
(A) 19.6 m (B) 29.4 m
(C) 39.2 m (D) 73.5 m
Official Ans. by NTA (B) 
 
Sol. V
2
 = 2 × 9.8 × 4.9 
V = 9.8 m/s 
Depth = distance travelled in 3 seconds 
          = 9.8 × 3 = 29.4 m 
4. One end of a massless spring of spring constant k
and natural length l
0
 is fixed while the other end is
connected to a small object of mass m lying on a
frictionless table. The spring remains horizontal on
the table. If the object is made to rotate at an
angular velocity ? about an axis passing through
fixed end, then the elongation of the spring will be:
(A) 
??
?
2
0
2
km
m
l
(B) 
?
??
0
2
m
km
l
(C) 
?
??
2
0
2
m
km
l
(D) 
??
?
2
0
2
km
m
l
Official Ans. by NTA (C)
2 
Sol. 
K ? x = m( ?
0
 + ?x)w
2
K ? x = m ?
0
 w
2
 + mw
2
 ?x
??
?
2
0
2
mw
x
k mw
5. A stone tide to a string of length L is whirled in a
vertical circle with the other end of the string at the 
centre. At a certain instant of time, the stone is at 
its lowest position and has a speed u. The 
magnitude of change in its velocity, as it reaches a 
position where the string is horizontal, is 
?
2
x(u gL) . The value of x is   
(A) 3 (B) 2
(C) 1 (D) 5
Official Ans. by NTA (B) 
 
Sol. ??
2
v u 2gL
? ? ?
22
v u v
? ? ? ?
22
v u v 2gL
? ? ?
2
v 2u 2gL
? ?
? ? ?
2
v 2 u gL x = 2 
6. Four spheres each of mass m form a square of side
d (as shown in figure). A fifth sphere of mass M is 
situated at the centre of square. The total 
gravitational potential energy of the system is : 
(A)
??
? ? ?
??
Gm
(4 2)m 4 2M
d
(B)
??
? ? ?
??
Gm
(4 2)M 4 2m
d
(C)
??
??
??
2
Gm
3m 4 2M
d
(D) 
2
Gm
6m 4 2M
d
??
??
??
Official Ans. by NTA (A) 
 
Sol. 
? ? ?
22
Gm Gm GMm
– 4 – 2 – 4 2
dd
2d
??
??
??
Gm
– ( 4 2 ) m 4 2 M
d
 
 
3 
 
7. For a perfect gas, two pressures P
1
 and P
2
 are 
shown in figure. The graph shows: 
 
 (A) P
1
 > P
2
 
 (B) P
1
 < P
2
 
 (C) P
1
 = P
2
  
 (D) Insufficient data to draw any conclusion  
  Official Ans. by NTA (A) 
  
Sol. PV = nRT 
 ?
V nR
TP
 
 ?
12
nR nR
PP
 
 ?
21
PP 
8. According to kinetic theory of gases, 
 A. The motion of the gas molecules freezes at 0ºC 
 B. The mean free path of gas molecules decreases 
if the density of molecules is increased. 
 C. The mean free path of gas molecules increases 
if temperature is increased keeping pressure 
constant. 
 D. Average kinetic energy per molecule per degree 
of freedom is 
B
3
kT
2
 (for monoatomic gases) 
 Choose the most appropriate answer from the 
options given below: 
 (A) A and C only (B) B and C only 
 (C) A and B only (D) C and D only 
  Official Ans. by NTA (B) 
  
Sol. ??
?
2
kT
2 d P
 
 
9.  A lead bullet penetrates into a solid object and 
melts. Assuming that 40% of its kinetic energy is 
used to heat it, the initial speed of bullet is: 
 (Given, initial temperature of the bullet = 127ºC, 
Melting point of the bullet = 327ºC, 
 Latent heat of fusion of lead = 2.5 × 10
4
J Kg
–1
, 
 Specific heat capacity of lead = 125J/kg K) 
 (A) 125 ms
–1
 (B) 500 ms
–1
 
 (C) 250 ms
–1
 (D) 600 ms
–1
 
 Official Ans. by NTA (B) 
  
Sol. ? ? ? ? ? ? ?
42
1 40
m 125 200 m 2.5 10 mv
2 100
 
 V = 500 m/s 
 
10. The equation of a particle executing simple 
harmonic motion is given by 
??
? ? ?
??
??
1
x sin t m
3
. 
At t = 1s, the speed of particle will be  
 (Given : ? = 3.14) 
 (A) 0 cm s
–1
  (B) 157 cm s
–1
  
 (C) 272 cm s
–1
  (D) 314 cm s
–1
  
 Official Ans. by NTA (B) 
  
Sol. 
??
? ? ?
??
??
1
x sin t
3
 
 
? ??
? ? ?
??
??
x sin t
3
 
 
dx
V cos t
dt 3
? ??
? ? ? ? ?
??
??
 
 ? ? ?
1
–
2
 = 157 cm/s 
 
4 
 
11. If a charge q is placed at the centre of a closed 
hemispherical non-conducting surface, the total 
flux passing through the flat surface would be : 
 
 (A) 
?
0
q
 (B) 
?
0
q
2
 
 (C) 
?
0
q
4
 (D) 
??
0
q
2
 
 Official Ans. by NTA (B) 
  
 
Sol.  
  
 Total flux through complete spherical surface is 
0
q
?
. 
 So the flux through curved surface will be 
?
0
q
2
. 
The flux through flat surface will be zero. 
 Remark : Electric flux through flat surface is zero 
but no option is given, option is available for 
electric flux passing through curved surface. 
12. Three identical charged balls each of charge 2C are 
suspended from a common point P by silk threads 
of 2m each (as shown in figure). They form an 
equilateral triangle of side 1m. 
 The ratio of net force on a charged ball to the force 
between any two charged balls will be : 
 
 (A) 1 : 1 (B) 1 : 4 
 (C) 3 : 2 (D) 3 :1 
 Official Ans. by NTA (D) 
  
Sol.  
  
 
? ? ? ?
? ?
?
2
k 2 2
F
1
  
 (F = Force between two charges).
 
 F = 4k 
 F
net
 = 2F cos 30º = 
3
2 F F 3
2
? ? ?
 
 (F
net
 = Net electrostatic force on one charged ball)
 
 
? ?
??
net
F 3F
3
FF
 
 Remark: Net force on any one of the ball is zero. 
But no option given in options.
 
Page 5


 1 
FINAL JEE –MAIN EXAMINATION – JUNE, 2022 
 (Held On Monday 27
th
 June, 2022)   TIME : 3 : 00 PM  to  6 : 00 PM 
PHYSICS TEST PAPER WITH SOLUTION 
 
 
SECTION-A 
1. The SI unit of a physical quantity is pascal-second.
The dimensional formula of this quantity will be
(A) [ML
–1
T
–1
] (B) [ML
–1
T
–2
]
(C) [ML
2
T
–1
] (D) [M
–1
L
3
T
0
]
Official Ans. by NTA (A) 
 
Sol. Pascal second 
?
?
2
2
F MLT
tT
A
L
 = ML
–1
T
–1
 
2. The distance of the Sun from earth is 1.5 × 10
11
 m
and its angular diameter is (2000) s when observed
from the earth. The diameter of the Sun will be :
(A) 2.45 × 10
10
 m (B) 1.45 × 10
10
 m
(C) 1.45 × 10
9
 m (D) 0.14 × 10
9
 m
Official Ans. by NTA (C) 
 
Sol. 
??
d
r
?
??
?? ??
2000 d
60 60 180 1.5 10
? ? ?
?
? ? ? ? ??
?
2000
d 1.5 10
60 60 180
= 
??
? ??
??
1.5
10
3 6 18
 = 1.45 × 10
9
 
3. When a ball is dropped into a lake from a height
4.9 m above the water level, it hits the water with a
velocity v and then sinks to the bottom with the
constant velocity v. It reaches the bottom of the
lake 4.0 s after it is dropped. The approximate
depth of the lake is :
(A) 19.6 m (B) 29.4 m
(C) 39.2 m (D) 73.5 m
Official Ans. by NTA (B) 
 
Sol. V
2
 = 2 × 9.8 × 4.9 
V = 9.8 m/s 
Depth = distance travelled in 3 seconds 
          = 9.8 × 3 = 29.4 m 
4. One end of a massless spring of spring constant k
and natural length l
0
 is fixed while the other end is
connected to a small object of mass m lying on a
frictionless table. The spring remains horizontal on
the table. If the object is made to rotate at an
angular velocity ? about an axis passing through
fixed end, then the elongation of the spring will be:
(A) 
??
?
2
0
2
km
m
l
(B) 
?
??
0
2
m
km
l
(C) 
?
??
2
0
2
m
km
l
(D) 
??
?
2
0
2
km
m
l
Official Ans. by NTA (C)
2 
Sol. 
K ? x = m( ?
0
 + ?x)w
2
K ? x = m ?
0
 w
2
 + mw
2
 ?x
??
?
2
0
2
mw
x
k mw
5. A stone tide to a string of length L is whirled in a
vertical circle with the other end of the string at the 
centre. At a certain instant of time, the stone is at 
its lowest position and has a speed u. The 
magnitude of change in its velocity, as it reaches a 
position where the string is horizontal, is 
?
2
x(u gL) . The value of x is   
(A) 3 (B) 2
(C) 1 (D) 5
Official Ans. by NTA (B) 
 
Sol. ??
2
v u 2gL
? ? ?
22
v u v
? ? ? ?
22
v u v 2gL
? ? ?
2
v 2u 2gL
? ?
? ? ?
2
v 2 u gL x = 2 
6. Four spheres each of mass m form a square of side
d (as shown in figure). A fifth sphere of mass M is 
situated at the centre of square. The total 
gravitational potential energy of the system is : 
(A)
??
? ? ?
??
Gm
(4 2)m 4 2M
d
(B)
??
? ? ?
??
Gm
(4 2)M 4 2m
d
(C)
??
??
??
2
Gm
3m 4 2M
d
(D) 
2
Gm
6m 4 2M
d
??
??
??
Official Ans. by NTA (A) 
 
Sol. 
? ? ?
22
Gm Gm GMm
– 4 – 2 – 4 2
dd
2d
??
??
??
Gm
– ( 4 2 ) m 4 2 M
d
 
 
3 
 
7. For a perfect gas, two pressures P
1
 and P
2
 are 
shown in figure. The graph shows: 
 
 (A) P
1
 > P
2
 
 (B) P
1
 < P
2
 
 (C) P
1
 = P
2
  
 (D) Insufficient data to draw any conclusion  
  Official Ans. by NTA (A) 
  
Sol. PV = nRT 
 ?
V nR
TP
 
 ?
12
nR nR
PP
 
 ?
21
PP 
8. According to kinetic theory of gases, 
 A. The motion of the gas molecules freezes at 0ºC 
 B. The mean free path of gas molecules decreases 
if the density of molecules is increased. 
 C. The mean free path of gas molecules increases 
if temperature is increased keeping pressure 
constant. 
 D. Average kinetic energy per molecule per degree 
of freedom is 
B
3
kT
2
 (for monoatomic gases) 
 Choose the most appropriate answer from the 
options given below: 
 (A) A and C only (B) B and C only 
 (C) A and B only (D) C and D only 
  Official Ans. by NTA (B) 
  
Sol. ??
?
2
kT
2 d P
 
 
9.  A lead bullet penetrates into a solid object and 
melts. Assuming that 40% of its kinetic energy is 
used to heat it, the initial speed of bullet is: 
 (Given, initial temperature of the bullet = 127ºC, 
Melting point of the bullet = 327ºC, 
 Latent heat of fusion of lead = 2.5 × 10
4
J Kg
–1
, 
 Specific heat capacity of lead = 125J/kg K) 
 (A) 125 ms
–1
 (B) 500 ms
–1
 
 (C) 250 ms
–1
 (D) 600 ms
–1
 
 Official Ans. by NTA (B) 
  
Sol. ? ? ? ? ? ? ?
42
1 40
m 125 200 m 2.5 10 mv
2 100
 
 V = 500 m/s 
 
10. The equation of a particle executing simple 
harmonic motion is given by 
??
? ? ?
??
??
1
x sin t m
3
. 
At t = 1s, the speed of particle will be  
 (Given : ? = 3.14) 
 (A) 0 cm s
–1
  (B) 157 cm s
–1
  
 (C) 272 cm s
–1
  (D) 314 cm s
–1
  
 Official Ans. by NTA (B) 
  
Sol. 
??
? ? ?
??
??
1
x sin t
3
 
 
? ??
? ? ?
??
??
x sin t
3
 
 
dx
V cos t
dt 3
? ??
? ? ? ? ?
??
??
 
 ? ? ?
1
–
2
 = 157 cm/s 
 
4 
 
11. If a charge q is placed at the centre of a closed 
hemispherical non-conducting surface, the total 
flux passing through the flat surface would be : 
 
 (A) 
?
0
q
 (B) 
?
0
q
2
 
 (C) 
?
0
q
4
 (D) 
??
0
q
2
 
 Official Ans. by NTA (B) 
  
 
Sol.  
  
 Total flux through complete spherical surface is 
0
q
?
. 
 So the flux through curved surface will be 
?
0
q
2
. 
The flux through flat surface will be zero. 
 Remark : Electric flux through flat surface is zero 
but no option is given, option is available for 
electric flux passing through curved surface. 
12. Three identical charged balls each of charge 2C are 
suspended from a common point P by silk threads 
of 2m each (as shown in figure). They form an 
equilateral triangle of side 1m. 
 The ratio of net force on a charged ball to the force 
between any two charged balls will be : 
 
 (A) 1 : 1 (B) 1 : 4 
 (C) 3 : 2 (D) 3 :1 
 Official Ans. by NTA (D) 
  
Sol.  
  
 
? ? ? ?
? ?
?
2
k 2 2
F
1
  
 (F = Force between two charges).
 
 F = 4k 
 F
net
 = 2F cos 30º = 
3
2 F F 3
2
? ? ?
 
 (F
net
 = Net electrostatic force on one charged ball)
 
 
? ?
??
net
F 3F
3
FF
 
 Remark: Net force on any one of the ball is zero. 
But no option given in options.
 
 
 
5 
 
13. Two long parallel conductors S
1
 and S
2
 are 
separated by a distance 10 cm and carrying 
currents of 4A and 2A respectively. The 
conductors are placed along x-axis in X-Y plane. 
There is a point P located between the conductors 
(as shown in figure). 
 A charge particle of 3 ? coulomb is passing through 
the point P with velocity  
 
?
??
ˆ ˆ ˆ ˆ
v (2i 3j)m / s; where i & j represents unit 
vector along x & y axis respectively. 
 The force acting on the charge particle is 
5
ˆˆ
4 10 ( xi 2 j)N.
?
? ? ? ?  The value of x is : 
 
(A) 2 (B) 1 
(C) 3 (D) –3 
 Official Ans. by NTA (C) 
  
Sol.  
  
 ??
net 1 2
B B B = 
? ? ? ?
? ? ? ?
?
??
00
42
2 .04 2 .06
 
 
? ?
?
??
??
??
?
??
0
net
200
ˆ
Bk
23
 
 ?? ??
??
F q v B 
 = 
? ? ? ?
?? ? ????
? ? ? ?
?? ?? ??
?? ?? ?
??
0
200
ˆ ˆ ˆ
3 2i 3j k
23
 
 = 
? ?
0
200
ˆˆ
3 2 j 3 i
23
?
??
??
? ? ? ?
??
??
?? ?
 
 = 
? ?
? ?
? ?
?
? ? ? ?
7
ˆˆ
4 10 100 3i 2j 
 = 
?
??
? ? ? ? ?
??
5
ˆˆ
4 10 3i 2j 
14. If L, C and R are the self inductance, capacitance 
and resistance respectively, which of the following 
does not have the dimension of time ? 
 (A) RC (B) 
L
R
 
 (C) LC (D) 
L
C
 
 Official Ans. by NTA (D) 
  
Sol. 
??
??
??
L
C
 does not have dimension of time. 
RC, 
L
R
 are time constant while LC is reciprocal 
of angular frequency or having dimension of time. 
15. Given below are two statements: 
 Statement I : A time varying electric field is a 
source of changing magnetic field and vice-versa. 
Thus a disturbance in electric or magnetic field 
creates EM waves.  
 Statement II : In a material medium. The EM 
wave travels with speed ?
??
00
1
v . 
 In the light of the above statements, choose the 
correct answer from the options given below: 
 (A) Both statement I and statement II are true. 
(B) Both statement I and statement II are false. 
(C) Statement I is correct but statement II is false. 
(D) Statement I is incorrect but statement II is true. 
 Official Ans. by NTA (C) 
  
Sol. The statement II is wrong as the velocity of ?m 
wave in a medium is 
0 r 0 r
11
?
? ? ? ? ? ?
.