JEE Main 2021 Physics March 17 Shift 2 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


 
 
17
th
 Mar. 2021 | Shift 2
SECTION – A 
 
1. Two identical blocks A and B each of mass m resting on the smooth horizontal floor are 
connected by a light spring of natural length L and spring constant K. A third block C of mass m 
moving with a speed v along the line joining A and B collides with A. The maximum compression 
in the spring is  
 
C A B
m m 
m
 
(1) 
mv
2K
  (2) 
m
2K
 (3) 
mv
K
 (4) 
m
v
2K
 
Sol. (4) 
 
 
C A ?V
1
B ?V
1
m m
m
v 
 
 From conservation of momentum 
 mv = mv
1
 + mv
1
 
 V
1
 = 
V
2
 
 
 
A ?V/2 B ? V/2
m m
 
 & from energy conservation 
 
2
2 2
1 1 V 1
mv m 2 Kx
2 2 2 2
? ?
? ?
? ? ? ? ? ?
? ?
? ?
? ?
? ?
 
 
2 2
2
mv mv 1
kx
2 4 2
? ? 
 
2
2
mv 1
kx
4 2
? 
 Then the maximum compression in the spring is  
 
2
mv
x
2K
? 
 
m
x v
2K
? 
- 
2. A sphere of mass 2 kg radius 0.5m is rolling with an initial speed of 1 ms
-1
 goes up an inclined 
plane which makes an angle of 30
0
 with the horizontal plane, without slipping. How long will the 
sphere take to return to the starting point A ? 
 
30
0
A
 
(1) 0.80 s  (2) 0.60 s  (3) 0.52 s  (4) 0.57 s  
 
 
Sol. (4) 
Page 2


 
 
17
th
 Mar. 2021 | Shift 2
SECTION – A 
 
1. Two identical blocks A and B each of mass m resting on the smooth horizontal floor are 
connected by a light spring of natural length L and spring constant K. A third block C of mass m 
moving with a speed v along the line joining A and B collides with A. The maximum compression 
in the spring is  
 
C A B
m m 
m
 
(1) 
mv
2K
  (2) 
m
2K
 (3) 
mv
K
 (4) 
m
v
2K
 
Sol. (4) 
 
 
C A ?V
1
B ?V
1
m m
m
v 
 
 From conservation of momentum 
 mv = mv
1
 + mv
1
 
 V
1
 = 
V
2
 
 
 
A ?V/2 B ? V/2
m m
 
 & from energy conservation 
 
2
2 2
1 1 V 1
mv m 2 Kx
2 2 2 2
? ?
? ?
? ? ? ? ? ?
? ?
? ?
? ?
? ?
 
 
2 2
2
mv mv 1
kx
2 4 2
? ? 
 
2
2
mv 1
kx
4 2
? 
 Then the maximum compression in the spring is  
 
2
mv
x
2K
? 
 
m
x v
2K
? 
- 
2. A sphere of mass 2 kg radius 0.5m is rolling with an initial speed of 1 ms
-1
 goes up an inclined 
plane which makes an angle of 30
0
 with the horizontal plane, without slipping. How long will the 
sphere take to return to the starting point A ? 
 
30
0
A
 
(1) 0.80 s  (2) 0.60 s  (3) 0.52 s  (4) 0.57 s  
 
 
Sol. (4) 
 
 
 
 
mg sin ? 
f 
30
0
 
A 
 
 
gsin
a
1 c
?
?
?
 
 
9.8sin30º
a
2
1
5
?
?
 
 a = 3.5 m/sec
2
 
 Time of accent 
 V = u + at  
 0 = 1 –3.5 t 
 t =
1
3.5
sec. 
 Time of decent 
 t = 
1
3.5
sec. 
 Total time 
2
T
3.5
? =0.57 sec. 
 
3. If one mole of the polyatomic gas is having two vibrational modes and ? is the ratio of molar 
specific heats for polyatomic gas p
v
C
C
? ?
? ?
? ?
? ?
then the value of ? is : 
 (1) 1.35 (2) 1.02  (3) 1.25  (4) 1.2 
Sol. (NTA answer is 4) our answer is (3) 
 Degree of freedom of polyatomic gas 
 f = T + R + V 
 f = 3 + 3 + 2 = 8 
 ? = 1 + 
2
f
=
2
1
8
? 
 
10 5
1.25
8 4
? ? ? ?
 
 
4. Two cells of emf 2E and E with internal resistance r
1
 and r
2
 respectively are connected in series 
to an external resistor R (see figure). The value of R, at which the potential difference across 
the terminals of the first cell becomes zero is  
 
R
E 2E
 
 (1) 
1 2
r r ?  (2) 
1 2
r r ? (3) 
1
2
r
r
2
?  (4) 
1
2
r
r
2
? 
Page 3


 
 
17
th
 Mar. 2021 | Shift 2
SECTION – A 
 
1. Two identical blocks A and B each of mass m resting on the smooth horizontal floor are 
connected by a light spring of natural length L and spring constant K. A third block C of mass m 
moving with a speed v along the line joining A and B collides with A. The maximum compression 
in the spring is  
 
C A B
m m 
m
 
(1) 
mv
2K
  (2) 
m
2K
 (3) 
mv
K
 (4) 
m
v
2K
 
Sol. (4) 
 
 
C A ?V
1
B ?V
1
m m
m
v 
 
 From conservation of momentum 
 mv = mv
1
 + mv
1
 
 V
1
 = 
V
2
 
 
 
A ?V/2 B ? V/2
m m
 
 & from energy conservation 
 
2
2 2
1 1 V 1
mv m 2 Kx
2 2 2 2
? ?
? ?
? ? ? ? ? ?
? ?
? ?
? ?
? ?
 
 
2 2
2
mv mv 1
kx
2 4 2
? ? 
 
2
2
mv 1
kx
4 2
? 
 Then the maximum compression in the spring is  
 
2
mv
x
2K
? 
 
m
x v
2K
? 
- 
2. A sphere of mass 2 kg radius 0.5m is rolling with an initial speed of 1 ms
-1
 goes up an inclined 
plane which makes an angle of 30
0
 with the horizontal plane, without slipping. How long will the 
sphere take to return to the starting point A ? 
 
30
0
A
 
(1) 0.80 s  (2) 0.60 s  (3) 0.52 s  (4) 0.57 s  
 
 
Sol. (4) 
 
 
 
 
mg sin ? 
f 
30
0
 
A 
 
 
gsin
a
1 c
?
?
?
 
 
9.8sin30º
a
2
1
5
?
?
 
 a = 3.5 m/sec
2
 
 Time of accent 
 V = u + at  
 0 = 1 –3.5 t 
 t =
1
3.5
sec. 
 Time of decent 
 t = 
1
3.5
sec. 
 Total time 
2
T
3.5
? =0.57 sec. 
 
3. If one mole of the polyatomic gas is having two vibrational modes and ? is the ratio of molar 
specific heats for polyatomic gas p
v
C
C
? ?
? ?
? ?
? ?
then the value of ? is : 
 (1) 1.35 (2) 1.02  (3) 1.25  (4) 1.2 
Sol. (NTA answer is 4) our answer is (3) 
 Degree of freedom of polyatomic gas 
 f = T + R + V 
 f = 3 + 3 + 2 = 8 
 ? = 1 + 
2
f
=
2
1
8
? 
 
10 5
1.25
8 4
? ? ? ?
 
 
4. Two cells of emf 2E and E with internal resistance r
1
 and r
2
 respectively are connected in series 
to an external resistor R (see figure). The value of R, at which the potential difference across 
the terminals of the first cell becomes zero is  
 
R
E 2E
 
 (1) 
1 2
r r ?  (2) 
1 2
r r ? (3) 
1
2
r
r
2
?  (4) 
1
2
r
r
2
? 
 
 
17
th
 Mar. 2021 | Shift 2
Sol. (4) 
 
 
R
E 2E
A B
r
2
r
1
 
 
1 2
3E
R r r
?
? ?
? 
 
 
2E
r
1
B A
i
 
 V
A
 = V
B
 
 2 E = i r
1
 
 2E =
1 2
3E
R r r ? ?
r
1
 
 2R + 2r
1
 + 2r
2
 = 3r
1
 
 R =
1
2
r
r
2
? 
 
5. A sound wave of frequency 245 Hz travels with the speed of 300 ms
-1
 along the positive x-axis. 
Each point of the wave move to and fro through a total distance of 6 cm. What will be the 
mathematical expression of the travelling wave ? 
 (1) 
? ?
3
Y(x,t) 0.03 sin5.1x 0.2 10 t
? ?
? ? ?
? ?
 
 (2) 
? ?
3
Y(x,t) 0.06 sin5.1x 1.5 10 t
? ?
? ? ?
? ?
 
  (3) 
? ?
3
Y(x,t) 0.06 sin0.8x 0.5 10 t
? ?
? ? ?
? ?
  
 (4) 
? ?
3
Y(x,t) 0.03 sin5.1x 1.5 10 t
? ?
? ? ?
? ?
  
Sol. (4) 
 Y = A sin (kx - ?t) 
 A = 
6
2
= 3cm = 0.03 m 
 ? = 2 ? f = 2 ? ×245 
 ? = 1.5 ×10
3
 
 k = 
3
1.5 10
v 300
? ?
? 
 k = 5.1 
 y = 0.03 sin (5.1x – 1.5 × 10
3
t) 
 
Page 4


 
 
17
th
 Mar. 2021 | Shift 2
SECTION – A 
 
1. Two identical blocks A and B each of mass m resting on the smooth horizontal floor are 
connected by a light spring of natural length L and spring constant K. A third block C of mass m 
moving with a speed v along the line joining A and B collides with A. The maximum compression 
in the spring is  
 
C A B
m m 
m
 
(1) 
mv
2K
  (2) 
m
2K
 (3) 
mv
K
 (4) 
m
v
2K
 
Sol. (4) 
 
 
C A ?V
1
B ?V
1
m m
m
v 
 
 From conservation of momentum 
 mv = mv
1
 + mv
1
 
 V
1
 = 
V
2
 
 
 
A ?V/2 B ? V/2
m m
 
 & from energy conservation 
 
2
2 2
1 1 V 1
mv m 2 Kx
2 2 2 2
? ?
? ?
? ? ? ? ? ?
? ?
? ?
? ?
? ?
 
 
2 2
2
mv mv 1
kx
2 4 2
? ? 
 
2
2
mv 1
kx
4 2
? 
 Then the maximum compression in the spring is  
 
2
mv
x
2K
? 
 
m
x v
2K
? 
- 
2. A sphere of mass 2 kg radius 0.5m is rolling with an initial speed of 1 ms
-1
 goes up an inclined 
plane which makes an angle of 30
0
 with the horizontal plane, without slipping. How long will the 
sphere take to return to the starting point A ? 
 
30
0
A
 
(1) 0.80 s  (2) 0.60 s  (3) 0.52 s  (4) 0.57 s  
 
 
Sol. (4) 
 
 
 
 
mg sin ? 
f 
30
0
 
A 
 
 
gsin
a
1 c
?
?
?
 
 
9.8sin30º
a
2
1
5
?
?
 
 a = 3.5 m/sec
2
 
 Time of accent 
 V = u + at  
 0 = 1 –3.5 t 
 t =
1
3.5
sec. 
 Time of decent 
 t = 
1
3.5
sec. 
 Total time 
2
T
3.5
? =0.57 sec. 
 
3. If one mole of the polyatomic gas is having two vibrational modes and ? is the ratio of molar 
specific heats for polyatomic gas p
v
C
C
? ?
? ?
? ?
? ?
then the value of ? is : 
 (1) 1.35 (2) 1.02  (3) 1.25  (4) 1.2 
Sol. (NTA answer is 4) our answer is (3) 
 Degree of freedom of polyatomic gas 
 f = T + R + V 
 f = 3 + 3 + 2 = 8 
 ? = 1 + 
2
f
=
2
1
8
? 
 
10 5
1.25
8 4
? ? ? ?
 
 
4. Two cells of emf 2E and E with internal resistance r
1
 and r
2
 respectively are connected in series 
to an external resistor R (see figure). The value of R, at which the potential difference across 
the terminals of the first cell becomes zero is  
 
R
E 2E
 
 (1) 
1 2
r r ?  (2) 
1 2
r r ? (3) 
1
2
r
r
2
?  (4) 
1
2
r
r
2
? 
 
 
17
th
 Mar. 2021 | Shift 2
Sol. (4) 
 
 
R
E 2E
A B
r
2
r
1
 
 
1 2
3E
R r r
?
? ?
? 
 
 
2E
r
1
B A
i
 
 V
A
 = V
B
 
 2 E = i r
1
 
 2E =
1 2
3E
R r r ? ?
r
1
 
 2R + 2r
1
 + 2r
2
 = 3r
1
 
 R =
1
2
r
r
2
? 
 
5. A sound wave of frequency 245 Hz travels with the speed of 300 ms
-1
 along the positive x-axis. 
Each point of the wave move to and fro through a total distance of 6 cm. What will be the 
mathematical expression of the travelling wave ? 
 (1) 
? ?
3
Y(x,t) 0.03 sin5.1x 0.2 10 t
? ?
? ? ?
? ?
 
 (2) 
? ?
3
Y(x,t) 0.06 sin5.1x 1.5 10 t
? ?
? ? ?
? ?
 
  (3) 
? ?
3
Y(x,t) 0.06 sin0.8x 0.5 10 t
? ?
? ? ?
? ?
  
 (4) 
? ?
3
Y(x,t) 0.03 sin5.1x 1.5 10 t
? ?
? ? ?
? ?
  
Sol. (4) 
 Y = A sin (kx - ?t) 
 A = 
6
2
= 3cm = 0.03 m 
 ? = 2 ? f = 2 ? ×245 
 ? = 1.5 ×10
3
 
 k = 
3
1.5 10
v 300
? ?
? 
 k = 5.1 
 y = 0.03 sin (5.1x – 1.5 × 10
3
t) 
 
 
 
6. A carrier signal C(t) = 25 sin (2.512×10
10
t) is amplitude modulated by a message signal 
m(t)=5 sin (1.57×10
8
t) and transmitted through an antenna. What will be bandwith of the 
modulated signal ? 
 (1) 1987.5 MHz (2) 2.01 GHz (3) 50 MHz (4) 8 GHz 
Sol. (3) 
 ? = 2f
m(t)
 
 ? = 2×
8
1.57 10
2
?
?
 
 ? = 50 MHz 
 
7. Two particles A and B of equal masses are suspended from two massless springs of spring 
constants K
1
 and K
2
 respectively. If the maximum velocities during osciliations are equal, the 
ratio of the amplitude of A and B is : 
 (1) 
1
2
K
K
 (2) 
1
2
K
K
 (3) 
2
1
K
K
 (4) 
2
1
K
K
 
Sol. (3) 
 ? V
max
 = A ? 
 Given         ?
1
A
1
 = ?
2
 A
2
 
 We know that ? = 
K
m
 
 
1 2
1 2
k k
A A
m m
? 
 
1 2
2 1
A k
A k
? 
 
 
8. Match List I with List II 
 List I   List II 
 (a) Phase difference between current and voltage (i) 
2
?
; current leads voltage 
 in a purely resistive AC circuit  
 (b) Phase difference between current and voltage in (ii) zero 
 a pure inductive AC circuit 
 (c) Phase difference between current and voltage in (iii) 
2
?
; current lags voltage 
 a pure capacitive AC circuit 
 (d) Phase difference between current and voltage in  (iv) 
1 C L
X X
tan
R
?
? ? ?
? ?
? ?
 
 an LCR series circuit 
 Choose the most appropriate answer from the options given below : 
(1) (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)  (2) (a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)  
(3) (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)  (4) (a)-(ii), (b)-(iii), (c)-(i), (d)-(iv)  
 
 
Page 5


 
 
17
th
 Mar. 2021 | Shift 2
SECTION – A 
 
1. Two identical blocks A and B each of mass m resting on the smooth horizontal floor are 
connected by a light spring of natural length L and spring constant K. A third block C of mass m 
moving with a speed v along the line joining A and B collides with A. The maximum compression 
in the spring is  
 
C A B
m m 
m
 
(1) 
mv
2K
  (2) 
m
2K
 (3) 
mv
K
 (4) 
m
v
2K
 
Sol. (4) 
 
 
C A ?V
1
B ?V
1
m m
m
v 
 
 From conservation of momentum 
 mv = mv
1
 + mv
1
 
 V
1
 = 
V
2
 
 
 
A ?V/2 B ? V/2
m m
 
 & from energy conservation 
 
2
2 2
1 1 V 1
mv m 2 Kx
2 2 2 2
? ?
? ?
? ? ? ? ? ?
? ?
? ?
? ?
? ?
 
 
2 2
2
mv mv 1
kx
2 4 2
? ? 
 
2
2
mv 1
kx
4 2
? 
 Then the maximum compression in the spring is  
 
2
mv
x
2K
? 
 
m
x v
2K
? 
- 
2. A sphere of mass 2 kg radius 0.5m is rolling with an initial speed of 1 ms
-1
 goes up an inclined 
plane which makes an angle of 30
0
 with the horizontal plane, without slipping. How long will the 
sphere take to return to the starting point A ? 
 
30
0
A
 
(1) 0.80 s  (2) 0.60 s  (3) 0.52 s  (4) 0.57 s  
 
 
Sol. (4) 
 
 
 
 
mg sin ? 
f 
30
0
 
A 
 
 
gsin
a
1 c
?
?
?
 
 
9.8sin30º
a
2
1
5
?
?
 
 a = 3.5 m/sec
2
 
 Time of accent 
 V = u + at  
 0 = 1 –3.5 t 
 t =
1
3.5
sec. 
 Time of decent 
 t = 
1
3.5
sec. 
 Total time 
2
T
3.5
? =0.57 sec. 
 
3. If one mole of the polyatomic gas is having two vibrational modes and ? is the ratio of molar 
specific heats for polyatomic gas p
v
C
C
? ?
? ?
? ?
? ?
then the value of ? is : 
 (1) 1.35 (2) 1.02  (3) 1.25  (4) 1.2 
Sol. (NTA answer is 4) our answer is (3) 
 Degree of freedom of polyatomic gas 
 f = T + R + V 
 f = 3 + 3 + 2 = 8 
 ? = 1 + 
2
f
=
2
1
8
? 
 
10 5
1.25
8 4
? ? ? ?
 
 
4. Two cells of emf 2E and E with internal resistance r
1
 and r
2
 respectively are connected in series 
to an external resistor R (see figure). The value of R, at which the potential difference across 
the terminals of the first cell becomes zero is  
 
R
E 2E
 
 (1) 
1 2
r r ?  (2) 
1 2
r r ? (3) 
1
2
r
r
2
?  (4) 
1
2
r
r
2
? 
 
 
17
th
 Mar. 2021 | Shift 2
Sol. (4) 
 
 
R
E 2E
A B
r
2
r
1
 
 
1 2
3E
R r r
?
? ?
? 
 
 
2E
r
1
B A
i
 
 V
A
 = V
B
 
 2 E = i r
1
 
 2E =
1 2
3E
R r r ? ?
r
1
 
 2R + 2r
1
 + 2r
2
 = 3r
1
 
 R =
1
2
r
r
2
? 
 
5. A sound wave of frequency 245 Hz travels with the speed of 300 ms
-1
 along the positive x-axis. 
Each point of the wave move to and fro through a total distance of 6 cm. What will be the 
mathematical expression of the travelling wave ? 
 (1) 
? ?
3
Y(x,t) 0.03 sin5.1x 0.2 10 t
? ?
? ? ?
? ?
 
 (2) 
? ?
3
Y(x,t) 0.06 sin5.1x 1.5 10 t
? ?
? ? ?
? ?
 
  (3) 
? ?
3
Y(x,t) 0.06 sin0.8x 0.5 10 t
? ?
? ? ?
? ?
  
 (4) 
? ?
3
Y(x,t) 0.03 sin5.1x 1.5 10 t
? ?
? ? ?
? ?
  
Sol. (4) 
 Y = A sin (kx - ?t) 
 A = 
6
2
= 3cm = 0.03 m 
 ? = 2 ? f = 2 ? ×245 
 ? = 1.5 ×10
3
 
 k = 
3
1.5 10
v 300
? ?
? 
 k = 5.1 
 y = 0.03 sin (5.1x – 1.5 × 10
3
t) 
 
 
 
6. A carrier signal C(t) = 25 sin (2.512×10
10
t) is amplitude modulated by a message signal 
m(t)=5 sin (1.57×10
8
t) and transmitted through an antenna. What will be bandwith of the 
modulated signal ? 
 (1) 1987.5 MHz (2) 2.01 GHz (3) 50 MHz (4) 8 GHz 
Sol. (3) 
 ? = 2f
m(t)
 
 ? = 2×
8
1.57 10
2
?
?
 
 ? = 50 MHz 
 
7. Two particles A and B of equal masses are suspended from two massless springs of spring 
constants K
1
 and K
2
 respectively. If the maximum velocities during osciliations are equal, the 
ratio of the amplitude of A and B is : 
 (1) 
1
2
K
K
 (2) 
1
2
K
K
 (3) 
2
1
K
K
 (4) 
2
1
K
K
 
Sol. (3) 
 ? V
max
 = A ? 
 Given         ?
1
A
1
 = ?
2
 A
2
 
 We know that ? = 
K
m
 
 
1 2
1 2
k k
A A
m m
? 
 
1 2
2 1
A k
A k
? 
 
 
8. Match List I with List II 
 List I   List II 
 (a) Phase difference between current and voltage (i) 
2
?
; current leads voltage 
 in a purely resistive AC circuit  
 (b) Phase difference between current and voltage in (ii) zero 
 a pure inductive AC circuit 
 (c) Phase difference between current and voltage in (iii) 
2
?
; current lags voltage 
 a pure capacitive AC circuit 
 (d) Phase difference between current and voltage in  (iv) 
1 C L
X X
tan
R
?
? ? ?
? ?
? ?
 
 an LCR series circuit 
 Choose the most appropriate answer from the options given below : 
(1) (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)  (2) (a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)  
(3) (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)  (4) (a)-(ii), (b)-(iii), (c)-(i), (d)-(iv)  
 
 
 
 
17
th
 Mar. 2021 | Shift 2
Sol. (4) 
 
 
I
R
V
L
V
C
V
R
 
(a) phase difference b/w current & voltage in a purely resistive AC circuit is zero 
(b)  phase difference b/w current & voltage in a pure inductive AC circuit is 
2
?
; current lags voltage. 
(c) phase different b/w current & voltage in a pure capacitive AC circuit is  
2
?
; current lead voltage. 
(d) phase difference b/w current & voltage in an LCR series circuit is = 
1 C L
X X
tan
R
?
? ? ?
? ?
? ?
 
 
 
9. A geostationary satellite is orbiting around an arbitary planet ‘P’ at a height of 11R above the 
surface of ‘P’, R being the radius of ‘P’. The time period of another satellite in hours at a height 
of 2R from the surface of ‘P’ is _____. ‘P’ has the time period of 24 hours. 
 (1) 
6
2
 (2) 3 (3) 6 2 (4) 5 
Sol. (2) 
 
 
2R
11R
R
R
 
 From Kepler’s law 
 T
2
  ? R
3
 
 
2 3
24 12R
T 3R
? ? ? ?
?
? ? ? ?
? ? ? ?
 
 T = 3 sec 
 
10. The velocity of a particle is v=v
0
+gt+Ft
2
. Its position is x=0 at t=0; then its displacement after 
time (t = 1) is : 
 (1) 
0
g
v F
2
? ? (2) v
0
+2g+3F (3) v
0
+g+F (4) 
0
g F
v
2 3
? ?