JEE Main 2022 Physics June 29 Shift 1 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


 
  
PHYSICS 
SECTION - A 
Multiple Choice Questions: This section contains 20 
multiple choice questions. Each question has 4 choices 
(1), (2), (3) and (4), out of which ONLY ONE is correct. 
Choose the correct answer : 
1. Two balls A and B are placed at the top of 180 m 
tall tower. Ball A is released from the top at t = 0 s. 
Ball B is thrown vertically down with an initial 
velocity u at t = 2 s. After a certain time, both balls 
meet 100 m above the ground. Find the value of u 
in ms
–1
 [use g = 10 ms
–2
]  
 (A) 10 
 (B) 15 
 (C) 20 
 (D) 30 
Answer (D) 
Sol. Let us assume that they meet at t = t0 
 
2
0
1
: 80
2
A gt =   …(i) 
 
2
00
1
: 80 ( 2) ( 2)
2
B ut g t = -+ -  …(ii) 
 From (i), t0 = 4 
 ? 80 = 2u + 5(2)
2 
 ? u = 30 m/s 
2. A body of mass M at rest explodes into three 
pieces, in the ratio of masses 1 : 1 : 2. Two smaller 
pieces fly off perpendicular to each other with 
velocities of 30 ms
–1
 and 40 ms
–1
 respectively. The 
velocity of the third piece will be 
 (A) 15 ms
–1 
 (B) 25 ms
–1
 
 (C) 35 ms
–1 
 (D) 50 ms
–1
 
Answer (B) 
Sol. Conserving momentum: 
 
ˆˆ
(30 ) (40 ) 2 ( ) 0 m i m j mv + +=
?
?
 
 ?  
ˆˆ
15 20 v ij = --
?
 
 ? | | 25 m/s v =
?
 
3. The activity of a radioactive material is 2.56 × 10
–3
 Ci. 
If the half life of the material is 5 days, after how 
many days the activity will become 2 × 10
–5
 Ci? 
 (A) 30 days 
 (B) 35 days 
 (C) 40 days 
 (D) 25 days 
Answer (B) 
Sol. 
0
t
A Ae
-?
= 
 ? 2 × 10
–5
 = 2.56 × 10
–3
 e
–?t 
 ? 
7
11
128 2
t
e
-?
??
= =
??
??
 
 ? 
1
2
7 35 days tt = = 
4. A spherical shell of 1 kg mass and radius R is rolling 
with angular speed ? on horizontal plane (as shown 
in figure). The magnitude of angular momentum of 
the shell about the origin O is 
2
3
a
R ? . The value of 
a will be 
 
 (A) 2 
 (B) 3 
 (C) 5 
 (D) 4 
Answer (C) 
Sol. 
0 of cm about cm
LL L = +
?? ?
 
 ? 
2 22
25
3 33
a
R mvR mR mR ?= + ?= ? 
 ? a = 5 
Page 2


 
  
PHYSICS 
SECTION - A 
Multiple Choice Questions: This section contains 20 
multiple choice questions. Each question has 4 choices 
(1), (2), (3) and (4), out of which ONLY ONE is correct. 
Choose the correct answer : 
1. Two balls A and B are placed at the top of 180 m 
tall tower. Ball A is released from the top at t = 0 s. 
Ball B is thrown vertically down with an initial 
velocity u at t = 2 s. After a certain time, both balls 
meet 100 m above the ground. Find the value of u 
in ms
–1
 [use g = 10 ms
–2
]  
 (A) 10 
 (B) 15 
 (C) 20 
 (D) 30 
Answer (D) 
Sol. Let us assume that they meet at t = t0 
 
2
0
1
: 80
2
A gt =   …(i) 
 
2
00
1
: 80 ( 2) ( 2)
2
B ut g t = -+ -  …(ii) 
 From (i), t0 = 4 
 ? 80 = 2u + 5(2)
2 
 ? u = 30 m/s 
2. A body of mass M at rest explodes into three 
pieces, in the ratio of masses 1 : 1 : 2. Two smaller 
pieces fly off perpendicular to each other with 
velocities of 30 ms
–1
 and 40 ms
–1
 respectively. The 
velocity of the third piece will be 
 (A) 15 ms
–1 
 (B) 25 ms
–1
 
 (C) 35 ms
–1 
 (D) 50 ms
–1
 
Answer (B) 
Sol. Conserving momentum: 
 
ˆˆ
(30 ) (40 ) 2 ( ) 0 m i m j mv + +=
?
?
 
 ?  
ˆˆ
15 20 v ij = --
?
 
 ? | | 25 m/s v =
?
 
3. The activity of a radioactive material is 2.56 × 10
–3
 Ci. 
If the half life of the material is 5 days, after how 
many days the activity will become 2 × 10
–5
 Ci? 
 (A) 30 days 
 (B) 35 days 
 (C) 40 days 
 (D) 25 days 
Answer (B) 
Sol. 
0
t
A Ae
-?
= 
 ? 2 × 10
–5
 = 2.56 × 10
–3
 e
–?t 
 ? 
7
11
128 2
t
e
-?
??
= =
??
??
 
 ? 
1
2
7 35 days tt = = 
4. A spherical shell of 1 kg mass and radius R is rolling 
with angular speed ? on horizontal plane (as shown 
in figure). The magnitude of angular momentum of 
the shell about the origin O is 
2
3
a
R ? . The value of 
a will be 
 
 (A) 2 
 (B) 3 
 (C) 5 
 (D) 4 
Answer (C) 
Sol. 
0 of cm about cm
LL L = +
?? ?
 
 ? 
2 22
25
3 33
a
R mvR mR mR ?= + ?= ? 
 ? a = 5 
 
  
5. A cylinder of fixed capacity of 44.8 litres contains 
helium gas at standard temperature and pressure. 
The amount of heat needed to raise the 
temperature of gas in the cylinder by 20.0°C will be 
 (Given gas constant R = 8.3 JK
–1
-mol
–1
) 
 (A) 249 J 
 (B) 415 J 
 (C) 498 J 
 (D) 830 J 
Answer (C) 
Sol. ?Q = nC v?T (Isochoric process) 
       
3
2 20
2
R
= ×× 
  = 498 J 
6. A wire of length L is hanging from a fixed support. 
The length changes to L1 and L2 when masses 1 kg 
and 2 kg are suspended respectively from its free 
end. Then the value of L is equal to 
 (A) 
12
LL 
 (B) 
12
2
+ LL
 
 (C) 2L1 – L2 
 (D) 3L1 – 2L2 
Answer (C) 
Sol. 
FL
y
AL
=
?
 
 ? 
FL
L
Ay
? = 
 ? 
1
(1 ) gL
LL
Ay
= + …(i) 
 and 
2
(2 ) gL
LL
Ay
= + …(ii)  
 ? L = 2L1 – L2  
7. Given below are two statements : one is labelled as 
Assertion A and the other is labelled as Reason 
R. 
 Assertion A : The photoelectric effect does not 
takes place, if the energy of the incident radiation is 
less than the work function of a metal. 
 Reason R : Kinetic energy of the photoelectrons is 
zero, if the energy of the incident radiation is equal 
to the work function of a metal. 
 In the light of the above statements, choose the 
most appropriate answer from the options given 
below. 
 (A) Both A and R are correct and R is the correct 
explanation of A 
 (B) Both A and R are correct but R is not the 
correct explanation of A 
 (C) A is correct but R is not correct 
 (D) A is not correct but R is correct 
Answer (B) 
Sol. When energy of incident radiation is equal to the 
work function of the metal, then the KE of 
photoelectrons would be zero. But this statement 
does not comment on the situation when energy is 
less than the work function. 
8. A particle of mass 500 gm is moving in a straight 
line with velocity v = bx
5/2
. The work done by the net 
force during its displacement from x = 0 to x = 4 m 
is : (Take b = 0.25 m
–3/2
s
–1
). 
 (A) 2 J (B) 4 J 
 (C) 8 J (D) 16 J 
Answer (D) 
Sol. Wtotal = ?K 
 
5/2 2
11
{ (4) } – 0
22
b
? ?
??
=
? ?
??
? ?
 
 
2
5
4
4
b
= × 
 ? Wtotal = 16 J 
9. A charge particle moves along circular path in a 
uniform magnetic field in a cyclotron. The kinetic 
energy of the charge particle increases to 4 times 
its initial value. What will be the ratio of new radius 
to the original radius of circular path of the charge 
particle 
 (A) 1 : 1 
 (B) 1 : 2 
 (C) 2 : 1 
 (D) 1 : 4 
Answer (C) 
Sol. 
2 mv mK
R
Bq Bq
= = 
 ? RK ? 
 ? ratio = 2 : 1 
Page 3


 
  
PHYSICS 
SECTION - A 
Multiple Choice Questions: This section contains 20 
multiple choice questions. Each question has 4 choices 
(1), (2), (3) and (4), out of which ONLY ONE is correct. 
Choose the correct answer : 
1. Two balls A and B are placed at the top of 180 m 
tall tower. Ball A is released from the top at t = 0 s. 
Ball B is thrown vertically down with an initial 
velocity u at t = 2 s. After a certain time, both balls 
meet 100 m above the ground. Find the value of u 
in ms
–1
 [use g = 10 ms
–2
]  
 (A) 10 
 (B) 15 
 (C) 20 
 (D) 30 
Answer (D) 
Sol. Let us assume that they meet at t = t0 
 
2
0
1
: 80
2
A gt =   …(i) 
 
2
00
1
: 80 ( 2) ( 2)
2
B ut g t = -+ -  …(ii) 
 From (i), t0 = 4 
 ? 80 = 2u + 5(2)
2 
 ? u = 30 m/s 
2. A body of mass M at rest explodes into three 
pieces, in the ratio of masses 1 : 1 : 2. Two smaller 
pieces fly off perpendicular to each other with 
velocities of 30 ms
–1
 and 40 ms
–1
 respectively. The 
velocity of the third piece will be 
 (A) 15 ms
–1 
 (B) 25 ms
–1
 
 (C) 35 ms
–1 
 (D) 50 ms
–1
 
Answer (B) 
Sol. Conserving momentum: 
 
ˆˆ
(30 ) (40 ) 2 ( ) 0 m i m j mv + +=
?
?
 
 ?  
ˆˆ
15 20 v ij = --
?
 
 ? | | 25 m/s v =
?
 
3. The activity of a radioactive material is 2.56 × 10
–3
 Ci. 
If the half life of the material is 5 days, after how 
many days the activity will become 2 × 10
–5
 Ci? 
 (A) 30 days 
 (B) 35 days 
 (C) 40 days 
 (D) 25 days 
Answer (B) 
Sol. 
0
t
A Ae
-?
= 
 ? 2 × 10
–5
 = 2.56 × 10
–3
 e
–?t 
 ? 
7
11
128 2
t
e
-?
??
= =
??
??
 
 ? 
1
2
7 35 days tt = = 
4. A spherical shell of 1 kg mass and radius R is rolling 
with angular speed ? on horizontal plane (as shown 
in figure). The magnitude of angular momentum of 
the shell about the origin O is 
2
3
a
R ? . The value of 
a will be 
 
 (A) 2 
 (B) 3 
 (C) 5 
 (D) 4 
Answer (C) 
Sol. 
0 of cm about cm
LL L = +
?? ?
 
 ? 
2 22
25
3 33
a
R mvR mR mR ?= + ?= ? 
 ? a = 5 
 
  
5. A cylinder of fixed capacity of 44.8 litres contains 
helium gas at standard temperature and pressure. 
The amount of heat needed to raise the 
temperature of gas in the cylinder by 20.0°C will be 
 (Given gas constant R = 8.3 JK
–1
-mol
–1
) 
 (A) 249 J 
 (B) 415 J 
 (C) 498 J 
 (D) 830 J 
Answer (C) 
Sol. ?Q = nC v?T (Isochoric process) 
       
3
2 20
2
R
= ×× 
  = 498 J 
6. A wire of length L is hanging from a fixed support. 
The length changes to L1 and L2 when masses 1 kg 
and 2 kg are suspended respectively from its free 
end. Then the value of L is equal to 
 (A) 
12
LL 
 (B) 
12
2
+ LL
 
 (C) 2L1 – L2 
 (D) 3L1 – 2L2 
Answer (C) 
Sol. 
FL
y
AL
=
?
 
 ? 
FL
L
Ay
? = 
 ? 
1
(1 ) gL
LL
Ay
= + …(i) 
 and 
2
(2 ) gL
LL
Ay
= + …(ii)  
 ? L = 2L1 – L2  
7. Given below are two statements : one is labelled as 
Assertion A and the other is labelled as Reason 
R. 
 Assertion A : The photoelectric effect does not 
takes place, if the energy of the incident radiation is 
less than the work function of a metal. 
 Reason R : Kinetic energy of the photoelectrons is 
zero, if the energy of the incident radiation is equal 
to the work function of a metal. 
 In the light of the above statements, choose the 
most appropriate answer from the options given 
below. 
 (A) Both A and R are correct and R is the correct 
explanation of A 
 (B) Both A and R are correct but R is not the 
correct explanation of A 
 (C) A is correct but R is not correct 
 (D) A is not correct but R is correct 
Answer (B) 
Sol. When energy of incident radiation is equal to the 
work function of the metal, then the KE of 
photoelectrons would be zero. But this statement 
does not comment on the situation when energy is 
less than the work function. 
8. A particle of mass 500 gm is moving in a straight 
line with velocity v = bx
5/2
. The work done by the net 
force during its displacement from x = 0 to x = 4 m 
is : (Take b = 0.25 m
–3/2
s
–1
). 
 (A) 2 J (B) 4 J 
 (C) 8 J (D) 16 J 
Answer (D) 
Sol. Wtotal = ?K 
 
5/2 2
11
{ (4) } – 0
22
b
? ?
??
=
? ?
??
? ?
 
 
2
5
4
4
b
= × 
 ? Wtotal = 16 J 
9. A charge particle moves along circular path in a 
uniform magnetic field in a cyclotron. The kinetic 
energy of the charge particle increases to 4 times 
its initial value. What will be the ratio of new radius 
to the original radius of circular path of the charge 
particle 
 (A) 1 : 1 
 (B) 1 : 2 
 (C) 2 : 1 
 (D) 1 : 4 
Answer (C) 
Sol. 
2 mv mK
R
Bq Bq
= = 
 ? RK ? 
 ? ratio = 2 : 1 
 
  
10. For a series LCR circuit, I vs ? curve is shown : 
 (a) To the left of ? r, the circuit is mainly capacitive. 
 (b) To the left of ? r, the circuit is mainly inductive. 
 (c) At ? r, impedance of the circuit is equal to the 
resistance of the circuit. 
 (d) At ? r, impedance of the circuit is 0. 
 
 Choose the most appropriate answer from the 
options given below 
 (A) (a) and (d) only (B) (b) and (d) only 
 (C) (a) and (c) only (D) (b) and (c) only 
Answer (C) 
Sol. We know that
1
C
X
C
=
?
and XL = ?L  
 Also, at ? = ? r : X L = X C 
 ? For ? < ? r : capacitive 
 and At 
22
: (– )
r LC
z R XX R ?= ? = + = 
11. A block of metal weighing 2 kg is resting on a 
frictionless plane (as shown in figure). It is struck by 
a jet releasing water at a rate of 1 kgs
–1
 and at a 
speed of 10 ms
–1
. Then, the initial acceleration of 
the block, in ms
–2
, will be:  
 
 (A) 3 
 (B) 6 
 (C) 5 
 (D) 4 
Answer (C) 
Sol. F = ?v
2
a 
 ? 10 × 1 = 2 × acceleration  
 ? Acc. = 5 m/s
2
 
12. In van der Wall equation 
2
[] ;
??
+ -=
??
??
a
P V b RT P
V
 
is pressure, V is volume, R is universal gas 
constant and T is temperature. The ratio of 
constants 
a
b
 is dimensionally equal to:  
 (A) 
P
V
 
 (B) 
V
P
 
 (C) PV 
 (D) PV
3
 
Answer (C) 
Sol. From the equation  
 [a] = [PV
2
] 
 [b] = [V] 
 [ ]
a
PV
b
? ?
?=
? ?
? ?
 
13. Two vectors 
?
A and 
?
B have equal magnitudes. If 
magnitude of +
??
AB is equal to two times the 
magnitude of , -
??
AB then the angle between 
?
A and 
?
B will be:  
 (A) 
1
3
sin
5
-
? ?
? ?
? ?
 
 (B) 
1
1
sin
3
-
? ?
? ?
? ?
 
 (C)
1
3
cos
5
-
? ?
? ?
? ?
 
 (D) 
1
1
cos
3
-
? ?
? ?
? ?
 
Answer (C) 
Sol. 
22 2 22 2
2 cos 2 2 ( cos ) AA A AA A ++ ?= ++ - ? 
 ? 2A
2
 + 2A
2
cos? = 8A
2
 + 8A
2
(–cos?) 
 ? 5cos? = 3 
 
1
3
cos
5
-
? ?
? ?=
? ?
? ?
 
Page 4


 
  
PHYSICS 
SECTION - A 
Multiple Choice Questions: This section contains 20 
multiple choice questions. Each question has 4 choices 
(1), (2), (3) and (4), out of which ONLY ONE is correct. 
Choose the correct answer : 
1. Two balls A and B are placed at the top of 180 m 
tall tower. Ball A is released from the top at t = 0 s. 
Ball B is thrown vertically down with an initial 
velocity u at t = 2 s. After a certain time, both balls 
meet 100 m above the ground. Find the value of u 
in ms
–1
 [use g = 10 ms
–2
]  
 (A) 10 
 (B) 15 
 (C) 20 
 (D) 30 
Answer (D) 
Sol. Let us assume that they meet at t = t0 
 
2
0
1
: 80
2
A gt =   …(i) 
 
2
00
1
: 80 ( 2) ( 2)
2
B ut g t = -+ -  …(ii) 
 From (i), t0 = 4 
 ? 80 = 2u + 5(2)
2 
 ? u = 30 m/s 
2. A body of mass M at rest explodes into three 
pieces, in the ratio of masses 1 : 1 : 2. Two smaller 
pieces fly off perpendicular to each other with 
velocities of 30 ms
–1
 and 40 ms
–1
 respectively. The 
velocity of the third piece will be 
 (A) 15 ms
–1 
 (B) 25 ms
–1
 
 (C) 35 ms
–1 
 (D) 50 ms
–1
 
Answer (B) 
Sol. Conserving momentum: 
 
ˆˆ
(30 ) (40 ) 2 ( ) 0 m i m j mv + +=
?
?
 
 ?  
ˆˆ
15 20 v ij = --
?
 
 ? | | 25 m/s v =
?
 
3. The activity of a radioactive material is 2.56 × 10
–3
 Ci. 
If the half life of the material is 5 days, after how 
many days the activity will become 2 × 10
–5
 Ci? 
 (A) 30 days 
 (B) 35 days 
 (C) 40 days 
 (D) 25 days 
Answer (B) 
Sol. 
0
t
A Ae
-?
= 
 ? 2 × 10
–5
 = 2.56 × 10
–3
 e
–?t 
 ? 
7
11
128 2
t
e
-?
??
= =
??
??
 
 ? 
1
2
7 35 days tt = = 
4. A spherical shell of 1 kg mass and radius R is rolling 
with angular speed ? on horizontal plane (as shown 
in figure). The magnitude of angular momentum of 
the shell about the origin O is 
2
3
a
R ? . The value of 
a will be 
 
 (A) 2 
 (B) 3 
 (C) 5 
 (D) 4 
Answer (C) 
Sol. 
0 of cm about cm
LL L = +
?? ?
 
 ? 
2 22
25
3 33
a
R mvR mR mR ?= + ?= ? 
 ? a = 5 
 
  
5. A cylinder of fixed capacity of 44.8 litres contains 
helium gas at standard temperature and pressure. 
The amount of heat needed to raise the 
temperature of gas in the cylinder by 20.0°C will be 
 (Given gas constant R = 8.3 JK
–1
-mol
–1
) 
 (A) 249 J 
 (B) 415 J 
 (C) 498 J 
 (D) 830 J 
Answer (C) 
Sol. ?Q = nC v?T (Isochoric process) 
       
3
2 20
2
R
= ×× 
  = 498 J 
6. A wire of length L is hanging from a fixed support. 
The length changes to L1 and L2 when masses 1 kg 
and 2 kg are suspended respectively from its free 
end. Then the value of L is equal to 
 (A) 
12
LL 
 (B) 
12
2
+ LL
 
 (C) 2L1 – L2 
 (D) 3L1 – 2L2 
Answer (C) 
Sol. 
FL
y
AL
=
?
 
 ? 
FL
L
Ay
? = 
 ? 
1
(1 ) gL
LL
Ay
= + …(i) 
 and 
2
(2 ) gL
LL
Ay
= + …(ii)  
 ? L = 2L1 – L2  
7. Given below are two statements : one is labelled as 
Assertion A and the other is labelled as Reason 
R. 
 Assertion A : The photoelectric effect does not 
takes place, if the energy of the incident radiation is 
less than the work function of a metal. 
 Reason R : Kinetic energy of the photoelectrons is 
zero, if the energy of the incident radiation is equal 
to the work function of a metal. 
 In the light of the above statements, choose the 
most appropriate answer from the options given 
below. 
 (A) Both A and R are correct and R is the correct 
explanation of A 
 (B) Both A and R are correct but R is not the 
correct explanation of A 
 (C) A is correct but R is not correct 
 (D) A is not correct but R is correct 
Answer (B) 
Sol. When energy of incident radiation is equal to the 
work function of the metal, then the KE of 
photoelectrons would be zero. But this statement 
does not comment on the situation when energy is 
less than the work function. 
8. A particle of mass 500 gm is moving in a straight 
line with velocity v = bx
5/2
. The work done by the net 
force during its displacement from x = 0 to x = 4 m 
is : (Take b = 0.25 m
–3/2
s
–1
). 
 (A) 2 J (B) 4 J 
 (C) 8 J (D) 16 J 
Answer (D) 
Sol. Wtotal = ?K 
 
5/2 2
11
{ (4) } – 0
22
b
? ?
??
=
? ?
??
? ?
 
 
2
5
4
4
b
= × 
 ? Wtotal = 16 J 
9. A charge particle moves along circular path in a 
uniform magnetic field in a cyclotron. The kinetic 
energy of the charge particle increases to 4 times 
its initial value. What will be the ratio of new radius 
to the original radius of circular path of the charge 
particle 
 (A) 1 : 1 
 (B) 1 : 2 
 (C) 2 : 1 
 (D) 1 : 4 
Answer (C) 
Sol. 
2 mv mK
R
Bq Bq
= = 
 ? RK ? 
 ? ratio = 2 : 1 
 
  
10. For a series LCR circuit, I vs ? curve is shown : 
 (a) To the left of ? r, the circuit is mainly capacitive. 
 (b) To the left of ? r, the circuit is mainly inductive. 
 (c) At ? r, impedance of the circuit is equal to the 
resistance of the circuit. 
 (d) At ? r, impedance of the circuit is 0. 
 
 Choose the most appropriate answer from the 
options given below 
 (A) (a) and (d) only (B) (b) and (d) only 
 (C) (a) and (c) only (D) (b) and (c) only 
Answer (C) 
Sol. We know that
1
C
X
C
=
?
and XL = ?L  
 Also, at ? = ? r : X L = X C 
 ? For ? < ? r : capacitive 
 and At 
22
: (– )
r LC
z R XX R ?= ? = + = 
11. A block of metal weighing 2 kg is resting on a 
frictionless plane (as shown in figure). It is struck by 
a jet releasing water at a rate of 1 kgs
–1
 and at a 
speed of 10 ms
–1
. Then, the initial acceleration of 
the block, in ms
–2
, will be:  
 
 (A) 3 
 (B) 6 
 (C) 5 
 (D) 4 
Answer (C) 
Sol. F = ?v
2
a 
 ? 10 × 1 = 2 × acceleration  
 ? Acc. = 5 m/s
2
 
12. In van der Wall equation 
2
[] ;
??
+ -=
??
??
a
P V b RT P
V
 
is pressure, V is volume, R is universal gas 
constant and T is temperature. The ratio of 
constants 
a
b
 is dimensionally equal to:  
 (A) 
P
V
 
 (B) 
V
P
 
 (C) PV 
 (D) PV
3
 
Answer (C) 
Sol. From the equation  
 [a] = [PV
2
] 
 [b] = [V] 
 [ ]
a
PV
b
? ?
?=
? ?
? ?
 
13. Two vectors 
?
A and 
?
B have equal magnitudes. If 
magnitude of +
??
AB is equal to two times the 
magnitude of , -
??
AB then the angle between 
?
A and 
?
B will be:  
 (A) 
1
3
sin
5
-
? ?
? ?
? ?
 
 (B) 
1
1
sin
3
-
? ?
? ?
? ?
 
 (C)
1
3
cos
5
-
? ?
? ?
? ?
 
 (D) 
1
1
cos
3
-
? ?
? ?
? ?
 
Answer (C) 
Sol. 
22 2 22 2
2 cos 2 2 ( cos ) AA A AA A ++ ?= ++ - ? 
 ? 2A
2
 + 2A
2
cos? = 8A
2
 + 8A
2
(–cos?) 
 ? 5cos? = 3 
 
1
3
cos
5
-
? ?
? ?=
? ?
? ?
 
 
  
14. The escape velocity of a body on a planet ‘A’ is  
12 kms
–1
. The escape velocity of the body on 
another planet ‘B’, whose density is four times and 
radius is half of the planet ‘A’, is: 
 (A) 12 kms
–1 
 (B) 24 kms
–1
 
 (C) 36 kms
–1 
 (D) 6 kms
–1
 
Answer (A) 
Sol. 
3
esc
2 24
3
GM G
vR
RR
= = ×?×p 
 
esc
vR ? ?? 
 
esc
esc
()
1
()
B
A
v
v
?= 
 ? (vesc) B = 12 km/s 
15. At a certain place the angle of dip is 30° and the 
horizontal component of earth’s magnetic field is 
0.5 G. The earth’s total magnetic field (in G), at that 
certain place, is : 
 (A) 
1
3
 
 (B) 
1
2
 
 (C) 3 
 (D) 1 
Answer (A) 
Sol. BH = Bcos30° 
 
1
3
BG ?= 
16. A longitudinal wave is represented by 
x
x 10sin2 nt cm
? ?
= p-
? ?
? ? ?
. The maximum particle 
velocity will be four times the wave velocity if the 
determined value of wavelength is equal to : 
 (A) 2p 
 (B) 5p 
 (C) p 
 (D) 
5
2
p
 
Answer (B) 
Sol. Particle velocity 
x
t
?
=
?
 
 ? Maximum particle velocity = (2pn) (10) 
 ? (2pn) (10) = (n?) (4) 
 ? ? = 5p 
17. A parallel plate capacitor filled with a medium of 
dielectric constant 10, is connected across a battery 
and is charged. The dielectric slab is replaced by 
another slab of dielectric constant 15. Then the 
energy of capacitor will : 
 (A) increased by 50% 
 (B) decrease by 15% 
 (C) increase by 25% 
 (D) increase by 33% 
Answer (A) 
Sol. ( ) U kC V
2
0
1
2
= 
 
U
U
1.5
'
? = 
 ? Energy increases by 50% 
18. A positive charge particle of 100 mg is thrown in 
opposite direction to a uniform electric field of 
strength 1 × 10
5
 NC
–1
. If the charge on the particle 
is 40 µC and the initial velocity is 200 ms
–1
, how 
much distance it will travel before coming to the rest 
momentarily? 
 (A) 1 m 
 (B) 5 m 
 (C) 10 m 
 (D) 0.5 m 
Answer (D) 
Sol. v u aS
22
2 -= 
 
qE
S
m
22
0 200 2 ( )
- ? ?
?- =
? ?
? ?
 
 S
6 5
2
6
40 10 10
200 2 [ ]
100 10
-
-
??
- × ×
? - =
??
× ??
??
 
 S  
4
m 0.5 m
24
?= =
×
 
Page 5


 
  
PHYSICS 
SECTION - A 
Multiple Choice Questions: This section contains 20 
multiple choice questions. Each question has 4 choices 
(1), (2), (3) and (4), out of which ONLY ONE is correct. 
Choose the correct answer : 
1. Two balls A and B are placed at the top of 180 m 
tall tower. Ball A is released from the top at t = 0 s. 
Ball B is thrown vertically down with an initial 
velocity u at t = 2 s. After a certain time, both balls 
meet 100 m above the ground. Find the value of u 
in ms
–1
 [use g = 10 ms
–2
]  
 (A) 10 
 (B) 15 
 (C) 20 
 (D) 30 
Answer (D) 
Sol. Let us assume that they meet at t = t0 
 
2
0
1
: 80
2
A gt =   …(i) 
 
2
00
1
: 80 ( 2) ( 2)
2
B ut g t = -+ -  …(ii) 
 From (i), t0 = 4 
 ? 80 = 2u + 5(2)
2 
 ? u = 30 m/s 
2. A body of mass M at rest explodes into three 
pieces, in the ratio of masses 1 : 1 : 2. Two smaller 
pieces fly off perpendicular to each other with 
velocities of 30 ms
–1
 and 40 ms
–1
 respectively. The 
velocity of the third piece will be 
 (A) 15 ms
–1 
 (B) 25 ms
–1
 
 (C) 35 ms
–1 
 (D) 50 ms
–1
 
Answer (B) 
Sol. Conserving momentum: 
 
ˆˆ
(30 ) (40 ) 2 ( ) 0 m i m j mv + +=
?
?
 
 ?  
ˆˆ
15 20 v ij = --
?
 
 ? | | 25 m/s v =
?
 
3. The activity of a radioactive material is 2.56 × 10
–3
 Ci. 
If the half life of the material is 5 days, after how 
many days the activity will become 2 × 10
–5
 Ci? 
 (A) 30 days 
 (B) 35 days 
 (C) 40 days 
 (D) 25 days 
Answer (B) 
Sol. 
0
t
A Ae
-?
= 
 ? 2 × 10
–5
 = 2.56 × 10
–3
 e
–?t 
 ? 
7
11
128 2
t
e
-?
??
= =
??
??
 
 ? 
1
2
7 35 days tt = = 
4. A spherical shell of 1 kg mass and radius R is rolling 
with angular speed ? on horizontal plane (as shown 
in figure). The magnitude of angular momentum of 
the shell about the origin O is 
2
3
a
R ? . The value of 
a will be 
 
 (A) 2 
 (B) 3 
 (C) 5 
 (D) 4 
Answer (C) 
Sol. 
0 of cm about cm
LL L = +
?? ?
 
 ? 
2 22
25
3 33
a
R mvR mR mR ?= + ?= ? 
 ? a = 5 
 
  
5. A cylinder of fixed capacity of 44.8 litres contains 
helium gas at standard temperature and pressure. 
The amount of heat needed to raise the 
temperature of gas in the cylinder by 20.0°C will be 
 (Given gas constant R = 8.3 JK
–1
-mol
–1
) 
 (A) 249 J 
 (B) 415 J 
 (C) 498 J 
 (D) 830 J 
Answer (C) 
Sol. ?Q = nC v?T (Isochoric process) 
       
3
2 20
2
R
= ×× 
  = 498 J 
6. A wire of length L is hanging from a fixed support. 
The length changes to L1 and L2 when masses 1 kg 
and 2 kg are suspended respectively from its free 
end. Then the value of L is equal to 
 (A) 
12
LL 
 (B) 
12
2
+ LL
 
 (C) 2L1 – L2 
 (D) 3L1 – 2L2 
Answer (C) 
Sol. 
FL
y
AL
=
?
 
 ? 
FL
L
Ay
? = 
 ? 
1
(1 ) gL
LL
Ay
= + …(i) 
 and 
2
(2 ) gL
LL
Ay
= + …(ii)  
 ? L = 2L1 – L2  
7. Given below are two statements : one is labelled as 
Assertion A and the other is labelled as Reason 
R. 
 Assertion A : The photoelectric effect does not 
takes place, if the energy of the incident radiation is 
less than the work function of a metal. 
 Reason R : Kinetic energy of the photoelectrons is 
zero, if the energy of the incident radiation is equal 
to the work function of a metal. 
 In the light of the above statements, choose the 
most appropriate answer from the options given 
below. 
 (A) Both A and R are correct and R is the correct 
explanation of A 
 (B) Both A and R are correct but R is not the 
correct explanation of A 
 (C) A is correct but R is not correct 
 (D) A is not correct but R is correct 
Answer (B) 
Sol. When energy of incident radiation is equal to the 
work function of the metal, then the KE of 
photoelectrons would be zero. But this statement 
does not comment on the situation when energy is 
less than the work function. 
8. A particle of mass 500 gm is moving in a straight 
line with velocity v = bx
5/2
. The work done by the net 
force during its displacement from x = 0 to x = 4 m 
is : (Take b = 0.25 m
–3/2
s
–1
). 
 (A) 2 J (B) 4 J 
 (C) 8 J (D) 16 J 
Answer (D) 
Sol. Wtotal = ?K 
 
5/2 2
11
{ (4) } – 0
22
b
? ?
??
=
? ?
??
? ?
 
 
2
5
4
4
b
= × 
 ? Wtotal = 16 J 
9. A charge particle moves along circular path in a 
uniform magnetic field in a cyclotron. The kinetic 
energy of the charge particle increases to 4 times 
its initial value. What will be the ratio of new radius 
to the original radius of circular path of the charge 
particle 
 (A) 1 : 1 
 (B) 1 : 2 
 (C) 2 : 1 
 (D) 1 : 4 
Answer (C) 
Sol. 
2 mv mK
R
Bq Bq
= = 
 ? RK ? 
 ? ratio = 2 : 1 
 
  
10. For a series LCR circuit, I vs ? curve is shown : 
 (a) To the left of ? r, the circuit is mainly capacitive. 
 (b) To the left of ? r, the circuit is mainly inductive. 
 (c) At ? r, impedance of the circuit is equal to the 
resistance of the circuit. 
 (d) At ? r, impedance of the circuit is 0. 
 
 Choose the most appropriate answer from the 
options given below 
 (A) (a) and (d) only (B) (b) and (d) only 
 (C) (a) and (c) only (D) (b) and (c) only 
Answer (C) 
Sol. We know that
1
C
X
C
=
?
and XL = ?L  
 Also, at ? = ? r : X L = X C 
 ? For ? < ? r : capacitive 
 and At 
22
: (– )
r LC
z R XX R ?= ? = + = 
11. A block of metal weighing 2 kg is resting on a 
frictionless plane (as shown in figure). It is struck by 
a jet releasing water at a rate of 1 kgs
–1
 and at a 
speed of 10 ms
–1
. Then, the initial acceleration of 
the block, in ms
–2
, will be:  
 
 (A) 3 
 (B) 6 
 (C) 5 
 (D) 4 
Answer (C) 
Sol. F = ?v
2
a 
 ? 10 × 1 = 2 × acceleration  
 ? Acc. = 5 m/s
2
 
12. In van der Wall equation 
2
[] ;
??
+ -=
??
??
a
P V b RT P
V
 
is pressure, V is volume, R is universal gas 
constant and T is temperature. The ratio of 
constants 
a
b
 is dimensionally equal to:  
 (A) 
P
V
 
 (B) 
V
P
 
 (C) PV 
 (D) PV
3
 
Answer (C) 
Sol. From the equation  
 [a] = [PV
2
] 
 [b] = [V] 
 [ ]
a
PV
b
? ?
?=
? ?
? ?
 
13. Two vectors 
?
A and 
?
B have equal magnitudes. If 
magnitude of +
??
AB is equal to two times the 
magnitude of , -
??
AB then the angle between 
?
A and 
?
B will be:  
 (A) 
1
3
sin
5
-
? ?
? ?
? ?
 
 (B) 
1
1
sin
3
-
? ?
? ?
? ?
 
 (C)
1
3
cos
5
-
? ?
? ?
? ?
 
 (D) 
1
1
cos
3
-
? ?
? ?
? ?
 
Answer (C) 
Sol. 
22 2 22 2
2 cos 2 2 ( cos ) AA A AA A ++ ?= ++ - ? 
 ? 2A
2
 + 2A
2
cos? = 8A
2
 + 8A
2
(–cos?) 
 ? 5cos? = 3 
 
1
3
cos
5
-
? ?
? ?=
? ?
? ?
 
 
  
14. The escape velocity of a body on a planet ‘A’ is  
12 kms
–1
. The escape velocity of the body on 
another planet ‘B’, whose density is four times and 
radius is half of the planet ‘A’, is: 
 (A) 12 kms
–1 
 (B) 24 kms
–1
 
 (C) 36 kms
–1 
 (D) 6 kms
–1
 
Answer (A) 
Sol. 
3
esc
2 24
3
GM G
vR
RR
= = ×?×p 
 
esc
vR ? ?? 
 
esc
esc
()
1
()
B
A
v
v
?= 
 ? (vesc) B = 12 km/s 
15. At a certain place the angle of dip is 30° and the 
horizontal component of earth’s magnetic field is 
0.5 G. The earth’s total magnetic field (in G), at that 
certain place, is : 
 (A) 
1
3
 
 (B) 
1
2
 
 (C) 3 
 (D) 1 
Answer (A) 
Sol. BH = Bcos30° 
 
1
3
BG ?= 
16. A longitudinal wave is represented by 
x
x 10sin2 nt cm
? ?
= p-
? ?
? ? ?
. The maximum particle 
velocity will be four times the wave velocity if the 
determined value of wavelength is equal to : 
 (A) 2p 
 (B) 5p 
 (C) p 
 (D) 
5
2
p
 
Answer (B) 
Sol. Particle velocity 
x
t
?
=
?
 
 ? Maximum particle velocity = (2pn) (10) 
 ? (2pn) (10) = (n?) (4) 
 ? ? = 5p 
17. A parallel plate capacitor filled with a medium of 
dielectric constant 10, is connected across a battery 
and is charged. The dielectric slab is replaced by 
another slab of dielectric constant 15. Then the 
energy of capacitor will : 
 (A) increased by 50% 
 (B) decrease by 15% 
 (C) increase by 25% 
 (D) increase by 33% 
Answer (A) 
Sol. ( ) U kC V
2
0
1
2
= 
 
U
U
1.5
'
? = 
 ? Energy increases by 50% 
18. A positive charge particle of 100 mg is thrown in 
opposite direction to a uniform electric field of 
strength 1 × 10
5
 NC
–1
. If the charge on the particle 
is 40 µC and the initial velocity is 200 ms
–1
, how 
much distance it will travel before coming to the rest 
momentarily? 
 (A) 1 m 
 (B) 5 m 
 (C) 10 m 
 (D) 0.5 m 
Answer (D) 
Sol. v u aS
22
2 -= 
 
qE
S
m
22
0 200 2 ( )
- ? ?
?- =
? ?
? ?
 
 S
6 5
2
6
40 10 10
200 2 [ ]
100 10
-
-
??
- × ×
? - =
??
× ??
??
 
 S  
4
m 0.5 m
24
?= =
×
 
 
  
19. Using Young’s double slit experiment, a 
monochromatic light of wavelength 5000 Å 
produces fringes of fringe width 0.5 mm. If another 
monochromatic light of wavelength 6000 Å is used 
and the separation between the slits is doubled, 
then the new fringe width will be : 
 (A) 0.5 mm (B) 1.0 mm 
 (C) 0.6 mm (D) 0.3 mm 
Answer (D) 
Sol. Fringe width 
D
d
?
= 
 ? Fringe width 
d
?
? 
 ? New fringe width = 
1.2
0.5 mm 0.3 mm
2
×= 
20. Only 2% of the optical source frequency is the 
available channel bandwidth for an optical 
communicating system operating at 1000 nm. If an 
audio signal requires a bandwidth of 8 kHz, how 
many channels can be accommodated for 
transmission? 
 (A) 375 × 10
7 
 (B) 75 × 10
7
 
 (C) 375 × 10
8 
 (D) 75 × 10
9
 
Answer (B) 
Sol. vf = ? 
 
v
f
8
14
9
3 10
 Hz 3 10 Hz
1000 10
-
×
?= = = ×
? ×
 
 ? Channels 
14
7
3
2
3 10
100
75 10
8 10
××
= = ×
×
 
SECTION - B 
Numerical Value Type Questions: This section 
contains 10 questions. In Section B, attempt any five 
questions out of 10. The answer to each question is a 
NUMERICAL VALUE. For each question, enter the 
correct numerical value (in decimal notation, 
truncated/rounded-off to the second decimal place; e.g. 
06.25, 07.00, –00.33, –00.30, 30.27, –27.30) using the 
mouse and the on-screen virtual numeric keypad in the 
place designated to enter the answer. 
1. Two coils require 20 minutes and 60 minutes 
respectively to produce same amount of heat 
energy when connected separately to the same 
source. If they are connected in parallel 
arrangement to the same source; the time required 
to produce same amount of heat by the 
combination of coils, will be ___ min. 
Answer (15) 
Sol. 
2
V
Ht
R
= ·? 
 ? 
22
12
20 60
VV
H
RR
= ·= · …(i) 
 Also, 
2
12
12
V
Ht
RR
RR
= ·?
? ?
? ?
+
? ?
 
  
2
1
4
3
V
t
R
= · ·? [ ? R2 = 3R1] 
 ?  ?t = 15 
2. The intensity of the light from a bulb incident on a 
surface is 0.22 W/m
2
. The amplitude of the 
magnetic field in this light-wave is ___ × 10
–9
 T. 
 (Given : Permittivity of vacuum e0 = 8.85 × 10
–12 
C
2
N
–1 
–m
–2
, speed of light in vacuum c = 3 × 10
8
 
ms
–1
) 
Answer (43) 
Sol. ( )
2
2
00 0 0
11
22
I E c cB c = e ·= e 
 ? 
32
00
1
2
I cB = e 
 ? 
( )( )
3
–12 8 2
0
1
0.22 8.85 10 3 10
2
B = × × 
 ? 
–9
0
43 10 BT × ?