JEE Main 2021 Physics March 16 Shift 2 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


 
 
16
th
 March. 2021 | Shift 2
SECTION – A 
1. A mosquito is moving with a velocity v
?
 = 0.5 t
2
 
?
i 3tj 9k ? ?
? ?
 m/s and accelerating in uniform 
conditions. What will be the direction of mosquito after 2s? 
 (1) 
1
2
tan fromx axis
3
?
? ?
?
? ?
? ?
  (2) 
1
5
tan fromx axis
2
?
? ?
?
? ?
? ?
   
 (3) 
1
2
tan fromy axis
3
?
? ?
?
? ?
? ?
  (4) 
1
5
tan fromy axis
2
?
? ?
?
? ?
? ?
  
Sol. Bonus  
Given  
2
ˆ ˆ ˆ
v 0.5t i 3tj 9k ? ? ?
?
 
t 2
v
?
?
 = 
ˆ ˆ ˆ
2i 6j 9k ? ? 
 ? angle made by direction of motion of mosquito will be –  
 cos
-1
 
2
11
? ?
? ?
? ?
 from x-axis = tan
-1
 
117
2
? ?
? ?
? ?
? ?
 
 cos
-1
 
6
11
? ?
? ?
? ?
 from y-axis = tan
-1
 
85
9
? ?
? ?
? ?
? ?
 
 cos
-1
 
9
11
? ?
? ?
? ?
 from z-axis = tan
-1
 
40
9
 
 no. option is matching 
 
2. Statement I: A cyclist is moving on an unbanked road with a speed of 7 kmh
–1
 and takes a 
sharp circular turn along a path of radius of 2m without reducing the speed. The static friction 
coefficient is 0.2. The cyclist will not slip and pass the curve. (g = 9.8 m/s
2
) 
 Statement-II: If the road is banked at an angle of 45°, cyclist can cross the curve of 2m radius 
with the speed of 18.5 kmh
-1
 without slipping. 
 In the light of the above statements, choose the correct answer from the options given below. 
 (1) Both statement I and statement II are false  
 (2) Both statement I and statement II are true   
 (3) Statement I is correct and statement II is incorrect  
 (4) Statement I is incorrect and statement II is correct  
Sol. (2) 
 On a horizontal ground, 
 v
max
 = ?Rg = ? ? 0.2 2 9.8 = 1.97 m/s 
 1.97 × 
18
5
 
 = 7.12 km/hr=  7.2 km/hr 
 Statement-2 
 v
max
 = 
? ? ? ? ?
? ?
? ? ?
? ?
tan
gr
1 tan
 = ? ?
12
2 9.8
0.8
 = 19.5 km/hr 
 v
min
 = 
? ? ? ? ?
? ?
? ? ?
? ?
tan
rg
1 tan
 = ? ?
0.8
2 9.8
1.2
 = 12.01 km/hr 
Page 2


 
 
16
th
 March. 2021 | Shift 2
SECTION – A 
1. A mosquito is moving with a velocity v
?
 = 0.5 t
2
 
?
i 3tj 9k ? ?
? ?
 m/s and accelerating in uniform 
conditions. What will be the direction of mosquito after 2s? 
 (1) 
1
2
tan fromx axis
3
?
? ?
?
? ?
? ?
  (2) 
1
5
tan fromx axis
2
?
? ?
?
? ?
? ?
   
 (3) 
1
2
tan fromy axis
3
?
? ?
?
? ?
? ?
  (4) 
1
5
tan fromy axis
2
?
? ?
?
? ?
? ?
  
Sol. Bonus  
Given  
2
ˆ ˆ ˆ
v 0.5t i 3tj 9k ? ? ?
?
 
t 2
v
?
?
 = 
ˆ ˆ ˆ
2i 6j 9k ? ? 
 ? angle made by direction of motion of mosquito will be –  
 cos
-1
 
2
11
? ?
? ?
? ?
 from x-axis = tan
-1
 
117
2
? ?
? ?
? ?
? ?
 
 cos
-1
 
6
11
? ?
? ?
? ?
 from y-axis = tan
-1
 
85
9
? ?
? ?
? ?
? ?
 
 cos
-1
 
9
11
? ?
? ?
? ?
 from z-axis = tan
-1
 
40
9
 
 no. option is matching 
 
2. Statement I: A cyclist is moving on an unbanked road with a speed of 7 kmh
–1
 and takes a 
sharp circular turn along a path of radius of 2m without reducing the speed. The static friction 
coefficient is 0.2. The cyclist will not slip and pass the curve. (g = 9.8 m/s
2
) 
 Statement-II: If the road is banked at an angle of 45°, cyclist can cross the curve of 2m radius 
with the speed of 18.5 kmh
-1
 without slipping. 
 In the light of the above statements, choose the correct answer from the options given below. 
 (1) Both statement I and statement II are false  
 (2) Both statement I and statement II are true   
 (3) Statement I is correct and statement II is incorrect  
 (4) Statement I is incorrect and statement II is correct  
Sol. (2) 
 On a horizontal ground, 
 v
max
 = ?Rg = ? ? 0.2 2 9.8 = 1.97 m/s 
 1.97 × 
18
5
 
 = 7.12 km/hr=  7.2 km/hr 
 Statement-2 
 v
max
 = 
? ? ? ? ?
? ?
? ? ?
? ?
tan
gr
1 tan
 = ? ?
12
2 9.8
0.8
 = 19.5 km/hr 
 v
min
 = 
? ? ? ? ?
? ?
? ? ?
? ?
tan
rg
1 tan
 = ? ?
0.8
2 9.8
1.2
 = 12.01 km/hr 
 
 
3. Calculate the time interval between 33% decay and 67% decay if half-life of a substance is:  
 (1) 40 minutes (2) 20 minutes  (3) 60 minutes  (4) 13 minutes  
Sol. (2) 
 T
1/2
 = 20 min ? 
?
ln2
 = 20 min 
   ? ? ? ? ? ?
ln2
20(min)
?
 ? N
t
 = N
0
e
- ?t
  
 
t
0
N
N
 = 
1
t
e
? ?
 ? 0.67 = 
1
t
e
? ?
 
   ? ln (0.67) = - ?t
1
  
   ? ln 
? ?
? ?
? ?
100
67
 = ?t
1
 ? t
1
 = 
? ?
?
? ?
? ?
100
ln 20(min)
67
(ln2)
 
 Similarly, t
2
 = 
? ?
?
? ?
? ?
100
ln 20(min)
34
(ln2)
 
 t
2
 – t
1
 = 19.57 min ? 20 min. 
 
4. A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of 
mass m = 10 g is fired into the block and gets embedded in it. The (block + bullet) then swing 
upwards, their centre of mass rising a vertical distance h = 9.8 cm before the (block + bullet) 
pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before 
collision is: (take g = 9.8 ms
–2
) 
 
M
m
h
v
 
 (1) 831.4 m/s (2) 841.4 m/s  (3) 811.4 m/s (4) 821.4 m/s  
Sol. (1) 
 P
i
 = 0.01 × u + 0 = P
f
 = 6 × v 
 v = 
0.01u
6
 
 using energy conservation 
 
1
2
 × 6 × 
2
u
600
? ?
? ?
? ?
 = 6 × 9.8 × 9.8 × 10
-2
  
 u = 6 × 98 × 2 = 588 2 m/s 
 
Page 3


 
 
16
th
 March. 2021 | Shift 2
SECTION – A 
1. A mosquito is moving with a velocity v
?
 = 0.5 t
2
 
?
i 3tj 9k ? ?
? ?
 m/s and accelerating in uniform 
conditions. What will be the direction of mosquito after 2s? 
 (1) 
1
2
tan fromx axis
3
?
? ?
?
? ?
? ?
  (2) 
1
5
tan fromx axis
2
?
? ?
?
? ?
? ?
   
 (3) 
1
2
tan fromy axis
3
?
? ?
?
? ?
? ?
  (4) 
1
5
tan fromy axis
2
?
? ?
?
? ?
? ?
  
Sol. Bonus  
Given  
2
ˆ ˆ ˆ
v 0.5t i 3tj 9k ? ? ?
?
 
t 2
v
?
?
 = 
ˆ ˆ ˆ
2i 6j 9k ? ? 
 ? angle made by direction of motion of mosquito will be –  
 cos
-1
 
2
11
? ?
? ?
? ?
 from x-axis = tan
-1
 
117
2
? ?
? ?
? ?
? ?
 
 cos
-1
 
6
11
? ?
? ?
? ?
 from y-axis = tan
-1
 
85
9
? ?
? ?
? ?
? ?
 
 cos
-1
 
9
11
? ?
? ?
? ?
 from z-axis = tan
-1
 
40
9
 
 no. option is matching 
 
2. Statement I: A cyclist is moving on an unbanked road with a speed of 7 kmh
–1
 and takes a 
sharp circular turn along a path of radius of 2m without reducing the speed. The static friction 
coefficient is 0.2. The cyclist will not slip and pass the curve. (g = 9.8 m/s
2
) 
 Statement-II: If the road is banked at an angle of 45°, cyclist can cross the curve of 2m radius 
with the speed of 18.5 kmh
-1
 without slipping. 
 In the light of the above statements, choose the correct answer from the options given below. 
 (1) Both statement I and statement II are false  
 (2) Both statement I and statement II are true   
 (3) Statement I is correct and statement II is incorrect  
 (4) Statement I is incorrect and statement II is correct  
Sol. (2) 
 On a horizontal ground, 
 v
max
 = ?Rg = ? ? 0.2 2 9.8 = 1.97 m/s 
 1.97 × 
18
5
 
 = 7.12 km/hr=  7.2 km/hr 
 Statement-2 
 v
max
 = 
? ? ? ? ?
? ?
? ? ?
? ?
tan
gr
1 tan
 = ? ?
12
2 9.8
0.8
 = 19.5 km/hr 
 v
min
 = 
? ? ? ? ?
? ?
? ? ?
? ?
tan
rg
1 tan
 = ? ?
0.8
2 9.8
1.2
 = 12.01 km/hr 
 
 
3. Calculate the time interval between 33% decay and 67% decay if half-life of a substance is:  
 (1) 40 minutes (2) 20 minutes  (3) 60 minutes  (4) 13 minutes  
Sol. (2) 
 T
1/2
 = 20 min ? 
?
ln2
 = 20 min 
   ? ? ? ? ? ?
ln2
20(min)
?
 ? N
t
 = N
0
e
- ?t
  
 
t
0
N
N
 = 
1
t
e
? ?
 ? 0.67 = 
1
t
e
? ?
 
   ? ln (0.67) = - ?t
1
  
   ? ln 
? ?
? ?
? ?
100
67
 = ?t
1
 ? t
1
 = 
? ?
?
? ?
? ?
100
ln 20(min)
67
(ln2)
 
 Similarly, t
2
 = 
? ?
?
? ?
? ?
100
ln 20(min)
34
(ln2)
 
 t
2
 – t
1
 = 19.57 min ? 20 min. 
 
4. A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of 
mass m = 10 g is fired into the block and gets embedded in it. The (block + bullet) then swing 
upwards, their centre of mass rising a vertical distance h = 9.8 cm before the (block + bullet) 
pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before 
collision is: (take g = 9.8 ms
–2
) 
 
M
m
h
v
 
 (1) 831.4 m/s (2) 841.4 m/s  (3) 811.4 m/s (4) 821.4 m/s  
Sol. (1) 
 P
i
 = 0.01 × u + 0 = P
f
 = 6 × v 
 v = 
0.01u
6
 
 using energy conservation 
 
1
2
 × 6 × 
2
u
600
? ?
? ?
? ?
 = 6 × 9.8 × 9.8 × 10
-2
  
 u = 6 × 98 × 2 = 588 2 m/s 
 
 
 
16
th
 March. 2021 | Shift 2
5. What will be the nature of flow of water from a circular tap, when its flow rate increased from 
0.18 L/min to 0.48 L/min? The radius of the tap and viscosity of water are 0.5 cm and 10
–3
 Pa 
s, respectively. 
 (Density of water: 10
3
 kg/m
3
) 
 (1) Remains steady flow  (2) Unsteady to steady flow  
 (3) Steady flow to unsteady flow  (4) Remains turbulent flow  
Sol. (3) 
 The nature of flow is determined by reynolds no. 
 R
e
 = 
vD ?
?
 
 if R
e
 < 1000 ? flow is steady  
 1000 < R
e
 < 2000 ? flow becomes unsteady 
 R
e
 > 2000 ? flow is turbulent 
 (R
e
)
initial
 = 10
3
 × 
3
2 2
0.18 10
(0.5 10 ) 60
?
?
?
? ? ? ?
 × 
2
3
1 10
10
?
?
?
 = 382.16 
 (R
e
)
final
 = 10
3
 × 
3
2 2
0.48 10
(0.5 10 ) 60
?
?
?
? ? ? ?
 × 
2
3
1 10
10
?
?
?
 
= 1019.09 
 
6. The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is 
placed in a medium of same refractive index? Assume the radii of curvature of the faces of lens 
are R
1
 and R
2
 respectively. 
 (1) Zero (2) 
1 2
1 2
R R
R –R
  (3) Infinite  (4) 1  
Sol. (3) 
 
1
f
 = 
2
1
n
1
n
? ?
?
? ?
? ?
 
1 2
1 1
R R
? ?
?
? ?
? ?
 
 
1
f
 = 0  
 f = infinite. 
 
7. For the given circuit, comment on the type of transformer used. 
 
 
 
 
 
  
P
~
L 
O
A 
D 
S
i
1
i
L
0.11A
60 W V
2
220 V
 
 (1) Step down transformer (2) Auxilliary transformer  
 (3) Step-up transformer  (4) Auto transformer  
Sol. (3) 
 P
s
 = V
s
 × I
s
  
 60 = V
s
 × 0.11 
 V
s
 = 
60
0.11
 = 
6000
11
, V
p
 = 220 volt 
 V
s
 > V
p
 so it is step up transformer 
Page 4


 
 
16
th
 March. 2021 | Shift 2
SECTION – A 
1. A mosquito is moving with a velocity v
?
 = 0.5 t
2
 
?
i 3tj 9k ? ?
? ?
 m/s and accelerating in uniform 
conditions. What will be the direction of mosquito after 2s? 
 (1) 
1
2
tan fromx axis
3
?
? ?
?
? ?
? ?
  (2) 
1
5
tan fromx axis
2
?
? ?
?
? ?
? ?
   
 (3) 
1
2
tan fromy axis
3
?
? ?
?
? ?
? ?
  (4) 
1
5
tan fromy axis
2
?
? ?
?
? ?
? ?
  
Sol. Bonus  
Given  
2
ˆ ˆ ˆ
v 0.5t i 3tj 9k ? ? ?
?
 
t 2
v
?
?
 = 
ˆ ˆ ˆ
2i 6j 9k ? ? 
 ? angle made by direction of motion of mosquito will be –  
 cos
-1
 
2
11
? ?
? ?
? ?
 from x-axis = tan
-1
 
117
2
? ?
? ?
? ?
? ?
 
 cos
-1
 
6
11
? ?
? ?
? ?
 from y-axis = tan
-1
 
85
9
? ?
? ?
? ?
? ?
 
 cos
-1
 
9
11
? ?
? ?
? ?
 from z-axis = tan
-1
 
40
9
 
 no. option is matching 
 
2. Statement I: A cyclist is moving on an unbanked road with a speed of 7 kmh
–1
 and takes a 
sharp circular turn along a path of radius of 2m without reducing the speed. The static friction 
coefficient is 0.2. The cyclist will not slip and pass the curve. (g = 9.8 m/s
2
) 
 Statement-II: If the road is banked at an angle of 45°, cyclist can cross the curve of 2m radius 
with the speed of 18.5 kmh
-1
 without slipping. 
 In the light of the above statements, choose the correct answer from the options given below. 
 (1) Both statement I and statement II are false  
 (2) Both statement I and statement II are true   
 (3) Statement I is correct and statement II is incorrect  
 (4) Statement I is incorrect and statement II is correct  
Sol. (2) 
 On a horizontal ground, 
 v
max
 = ?Rg = ? ? 0.2 2 9.8 = 1.97 m/s 
 1.97 × 
18
5
 
 = 7.12 km/hr=  7.2 km/hr 
 Statement-2 
 v
max
 = 
? ? ? ? ?
? ?
? ? ?
? ?
tan
gr
1 tan
 = ? ?
12
2 9.8
0.8
 = 19.5 km/hr 
 v
min
 = 
? ? ? ? ?
? ?
? ? ?
? ?
tan
rg
1 tan
 = ? ?
0.8
2 9.8
1.2
 = 12.01 km/hr 
 
 
3. Calculate the time interval between 33% decay and 67% decay if half-life of a substance is:  
 (1) 40 minutes (2) 20 minutes  (3) 60 minutes  (4) 13 minutes  
Sol. (2) 
 T
1/2
 = 20 min ? 
?
ln2
 = 20 min 
   ? ? ? ? ? ?
ln2
20(min)
?
 ? N
t
 = N
0
e
- ?t
  
 
t
0
N
N
 = 
1
t
e
? ?
 ? 0.67 = 
1
t
e
? ?
 
   ? ln (0.67) = - ?t
1
  
   ? ln 
? ?
? ?
? ?
100
67
 = ?t
1
 ? t
1
 = 
? ?
?
? ?
? ?
100
ln 20(min)
67
(ln2)
 
 Similarly, t
2
 = 
? ?
?
? ?
? ?
100
ln 20(min)
34
(ln2)
 
 t
2
 – t
1
 = 19.57 min ? 20 min. 
 
4. A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of 
mass m = 10 g is fired into the block and gets embedded in it. The (block + bullet) then swing 
upwards, their centre of mass rising a vertical distance h = 9.8 cm before the (block + bullet) 
pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before 
collision is: (take g = 9.8 ms
–2
) 
 
M
m
h
v
 
 (1) 831.4 m/s (2) 841.4 m/s  (3) 811.4 m/s (4) 821.4 m/s  
Sol. (1) 
 P
i
 = 0.01 × u + 0 = P
f
 = 6 × v 
 v = 
0.01u
6
 
 using energy conservation 
 
1
2
 × 6 × 
2
u
600
? ?
? ?
? ?
 = 6 × 9.8 × 9.8 × 10
-2
  
 u = 6 × 98 × 2 = 588 2 m/s 
 
 
 
16
th
 March. 2021 | Shift 2
5. What will be the nature of flow of water from a circular tap, when its flow rate increased from 
0.18 L/min to 0.48 L/min? The radius of the tap and viscosity of water are 0.5 cm and 10
–3
 Pa 
s, respectively. 
 (Density of water: 10
3
 kg/m
3
) 
 (1) Remains steady flow  (2) Unsteady to steady flow  
 (3) Steady flow to unsteady flow  (4) Remains turbulent flow  
Sol. (3) 
 The nature of flow is determined by reynolds no. 
 R
e
 = 
vD ?
?
 
 if R
e
 < 1000 ? flow is steady  
 1000 < R
e
 < 2000 ? flow becomes unsteady 
 R
e
 > 2000 ? flow is turbulent 
 (R
e
)
initial
 = 10
3
 × 
3
2 2
0.18 10
(0.5 10 ) 60
?
?
?
? ? ? ?
 × 
2
3
1 10
10
?
?
?
 = 382.16 
 (R
e
)
final
 = 10
3
 × 
3
2 2
0.48 10
(0.5 10 ) 60
?
?
?
? ? ? ?
 × 
2
3
1 10
10
?
?
?
 
= 1019.09 
 
6. The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is 
placed in a medium of same refractive index? Assume the radii of curvature of the faces of lens 
are R
1
 and R
2
 respectively. 
 (1) Zero (2) 
1 2
1 2
R R
R –R
  (3) Infinite  (4) 1  
Sol. (3) 
 
1
f
 = 
2
1
n
1
n
? ?
?
? ?
? ?
 
1 2
1 1
R R
? ?
?
? ?
? ?
 
 
1
f
 = 0  
 f = infinite. 
 
7. For the given circuit, comment on the type of transformer used. 
 
 
 
 
 
  
P
~
L 
O
A 
D 
S
i
1
i
L
0.11A
60 W V
2
220 V
 
 (1) Step down transformer (2) Auxilliary transformer  
 (3) Step-up transformer  (4) Auto transformer  
Sol. (3) 
 P
s
 = V
s
 × I
s
  
 60 = V
s
 × 0.11 
 V
s
 = 
60
0.11
 = 
6000
11
, V
p
 = 220 volt 
 V
s
 > V
p
 so it is step up transformer 
 
 
8. Red light differs from blue light as they have: 
 (1) Same frequencies and same wavelengths   
 (2) Different frequencies and different wavelengths  
 (3) Different frequencies and same wavelengths  
 (4) Same frequencies and different wavelengths  
Sol. (2) 
 Red light and blue light have different wavelength and different frequency. 
 
9. The de-Broglie wavelength associated with an electron and a proton were calculated by 
accelerating them through same potential of 100 V. What should nearly be the ratio of their 
wavelengths? (m
p
 = 1.00727u m
e
 = 0.00055u) 
 (1) (1860)
2
 : 1  (2) 43 : 1  (3) 1860 : 1  (4) 41.4 : 1  
Sol. (2) 
 ?
e
 = 
12.27
V
 Å   
 ?
p
 = 
0.286
V
 Å  
 
?
?
e
p
 = 
12.27
0.286
 = 43 
 
10. A charge Q is moving dl
? ? ?
 distance in the magnetic field B
? ?
. Find the value of work done by B
? ?
. 
 (1) Infinite  (2) 1  (3) –1  (4) Zero  
Sol. (4) 
 F qV B ? ?
? ? ?
 
 P = F.V
? ?
 = 0 ? W = 0 
 
11. Amplitude of a mass spring system, which is executing simple harmonic motion decreases with 
time. If mass = 500g, Decay constant = 20 g/s then how much time is required for the 
amplitude of the system to drop to half of its initial value? 
 (ln 2 = 0.693) 
 (1) 15.01 s  (2) 17.32 s  (3) 0.034 s  (4) 34.65 s  
Sol. (4) 
 A = A
0
 
bt
2m
e
?
 
 
bt
2m
 = ln2 = 0.693 
 t = 
2m
b
 × 0.693 
 t = 2× 
500
20
 × 0.693 
 t = 50 × 0.693 = 34.6 sec. 
 
12. A resistor develops 500 J of thermal energy in 20s when a current of 1.5A is passed through it. 
If the current is increased from 1.5A to 3A, what will be the energy developed in 20s. 
 (1) 500 J  (2) 1000 J  (3) 2000 J  (4) 1500 J  
Page 5


 
 
16
th
 March. 2021 | Shift 2
SECTION – A 
1. A mosquito is moving with a velocity v
?
 = 0.5 t
2
 
?
i 3tj 9k ? ?
? ?
 m/s and accelerating in uniform 
conditions. What will be the direction of mosquito after 2s? 
 (1) 
1
2
tan fromx axis
3
?
? ?
?
? ?
? ?
  (2) 
1
5
tan fromx axis
2
?
? ?
?
? ?
? ?
   
 (3) 
1
2
tan fromy axis
3
?
? ?
?
? ?
? ?
  (4) 
1
5
tan fromy axis
2
?
? ?
?
? ?
? ?
  
Sol. Bonus  
Given  
2
ˆ ˆ ˆ
v 0.5t i 3tj 9k ? ? ?
?
 
t 2
v
?
?
 = 
ˆ ˆ ˆ
2i 6j 9k ? ? 
 ? angle made by direction of motion of mosquito will be –  
 cos
-1
 
2
11
? ?
? ?
? ?
 from x-axis = tan
-1
 
117
2
? ?
? ?
? ?
? ?
 
 cos
-1
 
6
11
? ?
? ?
? ?
 from y-axis = tan
-1
 
85
9
? ?
? ?
? ?
? ?
 
 cos
-1
 
9
11
? ?
? ?
? ?
 from z-axis = tan
-1
 
40
9
 
 no. option is matching 
 
2. Statement I: A cyclist is moving on an unbanked road with a speed of 7 kmh
–1
 and takes a 
sharp circular turn along a path of radius of 2m without reducing the speed. The static friction 
coefficient is 0.2. The cyclist will not slip and pass the curve. (g = 9.8 m/s
2
) 
 Statement-II: If the road is banked at an angle of 45°, cyclist can cross the curve of 2m radius 
with the speed of 18.5 kmh
-1
 without slipping. 
 In the light of the above statements, choose the correct answer from the options given below. 
 (1) Both statement I and statement II are false  
 (2) Both statement I and statement II are true   
 (3) Statement I is correct and statement II is incorrect  
 (4) Statement I is incorrect and statement II is correct  
Sol. (2) 
 On a horizontal ground, 
 v
max
 = ?Rg = ? ? 0.2 2 9.8 = 1.97 m/s 
 1.97 × 
18
5
 
 = 7.12 km/hr=  7.2 km/hr 
 Statement-2 
 v
max
 = 
? ? ? ? ?
? ?
? ? ?
? ?
tan
gr
1 tan
 = ? ?
12
2 9.8
0.8
 = 19.5 km/hr 
 v
min
 = 
? ? ? ? ?
? ?
? ? ?
? ?
tan
rg
1 tan
 = ? ?
0.8
2 9.8
1.2
 = 12.01 km/hr 
 
 
3. Calculate the time interval between 33% decay and 67% decay if half-life of a substance is:  
 (1) 40 minutes (2) 20 minutes  (3) 60 minutes  (4) 13 minutes  
Sol. (2) 
 T
1/2
 = 20 min ? 
?
ln2
 = 20 min 
   ? ? ? ? ? ?
ln2
20(min)
?
 ? N
t
 = N
0
e
- ?t
  
 
t
0
N
N
 = 
1
t
e
? ?
 ? 0.67 = 
1
t
e
? ?
 
   ? ln (0.67) = - ?t
1
  
   ? ln 
? ?
? ?
? ?
100
67
 = ?t
1
 ? t
1
 = 
? ?
?
? ?
? ?
100
ln 20(min)
67
(ln2)
 
 Similarly, t
2
 = 
? ?
?
? ?
? ?
100
ln 20(min)
34
(ln2)
 
 t
2
 – t
1
 = 19.57 min ? 20 min. 
 
4. A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of 
mass m = 10 g is fired into the block and gets embedded in it. The (block + bullet) then swing 
upwards, their centre of mass rising a vertical distance h = 9.8 cm before the (block + bullet) 
pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before 
collision is: (take g = 9.8 ms
–2
) 
 
M
m
h
v
 
 (1) 831.4 m/s (2) 841.4 m/s  (3) 811.4 m/s (4) 821.4 m/s  
Sol. (1) 
 P
i
 = 0.01 × u + 0 = P
f
 = 6 × v 
 v = 
0.01u
6
 
 using energy conservation 
 
1
2
 × 6 × 
2
u
600
? ?
? ?
? ?
 = 6 × 9.8 × 9.8 × 10
-2
  
 u = 6 × 98 × 2 = 588 2 m/s 
 
 
 
16
th
 March. 2021 | Shift 2
5. What will be the nature of flow of water from a circular tap, when its flow rate increased from 
0.18 L/min to 0.48 L/min? The radius of the tap and viscosity of water are 0.5 cm and 10
–3
 Pa 
s, respectively. 
 (Density of water: 10
3
 kg/m
3
) 
 (1) Remains steady flow  (2) Unsteady to steady flow  
 (3) Steady flow to unsteady flow  (4) Remains turbulent flow  
Sol. (3) 
 The nature of flow is determined by reynolds no. 
 R
e
 = 
vD ?
?
 
 if R
e
 < 1000 ? flow is steady  
 1000 < R
e
 < 2000 ? flow becomes unsteady 
 R
e
 > 2000 ? flow is turbulent 
 (R
e
)
initial
 = 10
3
 × 
3
2 2
0.18 10
(0.5 10 ) 60
?
?
?
? ? ? ?
 × 
2
3
1 10
10
?
?
?
 = 382.16 
 (R
e
)
final
 = 10
3
 × 
3
2 2
0.48 10
(0.5 10 ) 60
?
?
?
? ? ? ?
 × 
2
3
1 10
10
?
?
?
 
= 1019.09 
 
6. The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is 
placed in a medium of same refractive index? Assume the radii of curvature of the faces of lens 
are R
1
 and R
2
 respectively. 
 (1) Zero (2) 
1 2
1 2
R R
R –R
  (3) Infinite  (4) 1  
Sol. (3) 
 
1
f
 = 
2
1
n
1
n
? ?
?
? ?
? ?
 
1 2
1 1
R R
? ?
?
? ?
? ?
 
 
1
f
 = 0  
 f = infinite. 
 
7. For the given circuit, comment on the type of transformer used. 
 
 
 
 
 
  
P
~
L 
O
A 
D 
S
i
1
i
L
0.11A
60 W V
2
220 V
 
 (1) Step down transformer (2) Auxilliary transformer  
 (3) Step-up transformer  (4) Auto transformer  
Sol. (3) 
 P
s
 = V
s
 × I
s
  
 60 = V
s
 × 0.11 
 V
s
 = 
60
0.11
 = 
6000
11
, V
p
 = 220 volt 
 V
s
 > V
p
 so it is step up transformer 
 
 
8. Red light differs from blue light as they have: 
 (1) Same frequencies and same wavelengths   
 (2) Different frequencies and different wavelengths  
 (3) Different frequencies and same wavelengths  
 (4) Same frequencies and different wavelengths  
Sol. (2) 
 Red light and blue light have different wavelength and different frequency. 
 
9. The de-Broglie wavelength associated with an electron and a proton were calculated by 
accelerating them through same potential of 100 V. What should nearly be the ratio of their 
wavelengths? (m
p
 = 1.00727u m
e
 = 0.00055u) 
 (1) (1860)
2
 : 1  (2) 43 : 1  (3) 1860 : 1  (4) 41.4 : 1  
Sol. (2) 
 ?
e
 = 
12.27
V
 Å   
 ?
p
 = 
0.286
V
 Å  
 
?
?
e
p
 = 
12.27
0.286
 = 43 
 
10. A charge Q is moving dl
? ? ?
 distance in the magnetic field B
? ?
. Find the value of work done by B
? ?
. 
 (1) Infinite  (2) 1  (3) –1  (4) Zero  
Sol. (4) 
 F qV B ? ?
? ? ?
 
 P = F.V
? ?
 = 0 ? W = 0 
 
11. Amplitude of a mass spring system, which is executing simple harmonic motion decreases with 
time. If mass = 500g, Decay constant = 20 g/s then how much time is required for the 
amplitude of the system to drop to half of its initial value? 
 (ln 2 = 0.693) 
 (1) 15.01 s  (2) 17.32 s  (3) 0.034 s  (4) 34.65 s  
Sol. (4) 
 A = A
0
 
bt
2m
e
?
 
 
bt
2m
 = ln2 = 0.693 
 t = 
2m
b
 × 0.693 
 t = 2× 
500
20
 × 0.693 
 t = 50 × 0.693 = 34.6 sec. 
 
12. A resistor develops 500 J of thermal energy in 20s when a current of 1.5A is passed through it. 
If the current is increased from 1.5A to 3A, what will be the energy developed in 20s. 
 (1) 500 J  (2) 1000 J  (3) 2000 J  (4) 1500 J  
 
 
16
th
 March. 2021 | Shift 2
Sol. (3) 
 I
2
RT = H 
 
1
2
H
H
 = 
? ?
? ?
? ?
2
1
2
I
I
 
 ? H
2
 = 500 × 
? ?
? ?
? ?
2
3
3 / 2
 = 2000 J 
 
13. Calculate the value of mean free path ( ?) for oxygen molecules at temperature 27°C and 
pressure 1.01 × 10
5
 Pa. Assume the molecular diameter 0.3nm and the gas is ideal. (k = 1.38 
× 10
–23
 jK
–1
) 
 (1) 102 nm (2) 32 nm  (3) 58 nm  (4) 86 nm  
Sol. (1) 
 Given : P = 1.01 × 10
5
 Pa 
 d = 0.3 nm  
 k = 1.38 × 10
-23
 Jk
-1
  
 T = 27°C 
 ? ? ?
mean
 = 
2
1
N
2 d
V
? ?
?
? ?
? ?
 and PV = nKT 
 ? ? ?
mean
 = 
2
KT
2 d p ?
 
 ? 
23
18 5
1.38 10 300
2 3.14 0.09 10 1.01 10
?
?
? ?
? ? ? ? ?
 
 ? 102 nm 
 
14. A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has 
higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed 
in a cold bath, it will: 
 
A B
 
 (1) Not bend but shrink  (2) Neither bend nor shrink  
 (3) Bend towards the right  (4) Bend towards the left  
Sol. (4) 
 
 
 
 
 
 ?
A
 > ?
B
  
 length of both strips will decrease  
 ?L
A
 > ?L
B