JEE Main 2020 September 4 Question Paper Shift 2 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


1. A circular coil has moment of inertia 0.8 kg m
2
 around any diameter and is carrying current to
produce a magnetic moment of 20 Am
2
. The coil is kept initially in a vertical position and it can
rotate freely around a horizontal diameter . When a uniform magnetic field of 4 T is applied along the
vertical,it starts rotating around its horizontal diameter. The angular speed the coil acquires after
rotating by 60° will be:
(1) 10 ? rad s
–1
(2) 20 rad s
–1
(3) 20 ? rad s
–1
(4) 10 rad s
–1
Sol. 4
By energy conservation
i i f f
U K U K ? ? ?
2
1
MBcos60 0 MBcos 0 I
2
? ? ? ? ? ? ? ?
2
MB 1
MB I
2 2
? ? ? ?
2
MB 1
I
2 2
? ?
MB 20 4
100
I 0.8
?
? ? ? ? = 10 rad/s
2. A person pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a
distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with
distance to 100 N. The total distance through which the box has been moved is 30 m. What is the
work done by the person during the total movement of the box?
(1) 5690 J (2) 5250 J (3) 2780 J (4) 3280 J
Sol. 2
A
B
C
30 15
O
D
100
Force 
disp (in m) (in N)
200
E
Work done = area of ABCEO
= area of trap. ABCD + area of rect. ODCE
= 
1
45 30 100 30 5250J
2
? ? ? ? ?
PHYSICS _ 4 Sep. _ SHIFT - 2
Page 2


1. A circular coil has moment of inertia 0.8 kg m
2
 around any diameter and is carrying current to
produce a magnetic moment of 20 Am
2
. The coil is kept initially in a vertical position and it can
rotate freely around a horizontal diameter . When a uniform magnetic field of 4 T is applied along the
vertical,it starts rotating around its horizontal diameter. The angular speed the coil acquires after
rotating by 60° will be:
(1) 10 ? rad s
–1
(2) 20 rad s
–1
(3) 20 ? rad s
–1
(4) 10 rad s
–1
Sol. 4
By energy conservation
i i f f
U K U K ? ? ?
2
1
MBcos60 0 MBcos 0 I
2
? ? ? ? ? ? ? ?
2
MB 1
MB I
2 2
? ? ? ?
2
MB 1
I
2 2
? ?
MB 20 4
100
I 0.8
?
? ? ? ? = 10 rad/s
2. A person pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a
distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with
distance to 100 N. The total distance through which the box has been moved is 30 m. What is the
work done by the person during the total movement of the box?
(1) 5690 J (2) 5250 J (3) 2780 J (4) 3280 J
Sol. 2
A
B
C
30 15
O
D
100
Force 
disp (in m) (in N)
200
E
Work done = area of ABCEO
= area of trap. ABCD + area of rect. ODCE
= 
1
45 30 100 30 5250J
2
? ? ? ? ?
PHYSICS _ 4 Sep. _ SHIFT - 2
3. Match the thermodynamic processes taking place in a system with the correct conditions. In the
table : ?Q is the heat supplied, ?W is the work done and ?U is change in internal energy of the
system.
     Process Condition
(I) Adiabatic (1) ?W = 0
(II) Isothermal (2) ?Q = 0
(III) Isochoric (3) ?U ? ?0, ?W ? 0,
      ?Q ? 0
(IV) Isobaric (4) ?U = 0
(1) (I) - (1), (II) - (1), (III) - (2), (IV) - (3)
(2) (I) - (1), (II) - (2), (III) - (4), (IV) - (4)
(3) (I) - (2), (II) - (4), (III) - (1), (IV) - (3)
(4) (I) - (2), (II) - (1), (III) - (4), (IV) - (3)
Sol. 3
adiabatic, ?Q = 0
Isothermal, ?U = 0
Isochoric, pdV 0 ?
?
W 0 ? ?
Isobaric, Q 0, U 0, W 0 ? ? ? ? ? ?
4. The driver of a bus approaching a big wall notices that the frequency of his bus’s horn changes
from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the
bus if speed of the sound is 330 ms
–1
.
(1) 81 kmh
–1
(2) 91 kmh
–1
(3) 71 kmh
–1
(4) 61 kmh
–1
Sol. 2
Freq received by wall,
w 0
330
f f
330 v
? ?
?
? ?
? ? ?
freq. after reflection, w
330 v
f ' f
330
? ? ?
?
? ?
? ?
= 0
330 v 330
f
330 330 v
? ? ? ? ?
?
? ? ? ?
? ? ? ? ?
330 v
490 420
330 v
? ? ?
?
? ?
? ? ?
v 25.2m/s ? ?
= 91 km/h
Page 3


1. A circular coil has moment of inertia 0.8 kg m
2
 around any diameter and is carrying current to
produce a magnetic moment of 20 Am
2
. The coil is kept initially in a vertical position and it can
rotate freely around a horizontal diameter . When a uniform magnetic field of 4 T is applied along the
vertical,it starts rotating around its horizontal diameter. The angular speed the coil acquires after
rotating by 60° will be:
(1) 10 ? rad s
–1
(2) 20 rad s
–1
(3) 20 ? rad s
–1
(4) 10 rad s
–1
Sol. 4
By energy conservation
i i f f
U K U K ? ? ?
2
1
MBcos60 0 MBcos 0 I
2
? ? ? ? ? ? ? ?
2
MB 1
MB I
2 2
? ? ? ?
2
MB 1
I
2 2
? ?
MB 20 4
100
I 0.8
?
? ? ? ? = 10 rad/s
2. A person pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a
distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with
distance to 100 N. The total distance through which the box has been moved is 30 m. What is the
work done by the person during the total movement of the box?
(1) 5690 J (2) 5250 J (3) 2780 J (4) 3280 J
Sol. 2
A
B
C
30 15
O
D
100
Force 
disp (in m) (in N)
200
E
Work done = area of ABCEO
= area of trap. ABCD + area of rect. ODCE
= 
1
45 30 100 30 5250J
2
? ? ? ? ?
PHYSICS _ 4 Sep. _ SHIFT - 2
3. Match the thermodynamic processes taking place in a system with the correct conditions. In the
table : ?Q is the heat supplied, ?W is the work done and ?U is change in internal energy of the
system.
     Process Condition
(I) Adiabatic (1) ?W = 0
(II) Isothermal (2) ?Q = 0
(III) Isochoric (3) ?U ? ?0, ?W ? 0,
      ?Q ? 0
(IV) Isobaric (4) ?U = 0
(1) (I) - (1), (II) - (1), (III) - (2), (IV) - (3)
(2) (I) - (1), (II) - (2), (III) - (4), (IV) - (4)
(3) (I) - (2), (II) - (4), (III) - (1), (IV) - (3)
(4) (I) - (2), (II) - (1), (III) - (4), (IV) - (3)
Sol. 3
adiabatic, ?Q = 0
Isothermal, ?U = 0
Isochoric, pdV 0 ?
?
W 0 ? ?
Isobaric, Q 0, U 0, W 0 ? ? ? ? ? ?
4. The driver of a bus approaching a big wall notices that the frequency of his bus’s horn changes
from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the
bus if speed of the sound is 330 ms
–1
.
(1) 81 kmh
–1
(2) 91 kmh
–1
(3) 71 kmh
–1
(4) 61 kmh
–1
Sol. 2
Freq received by wall,
w 0
330
f f
330 v
? ?
?
? ?
? ? ?
freq. after reflection, w
330 v
f ' f
330
? ? ?
?
? ?
? ?
= 0
330 v 330
f
330 330 v
? ? ? ? ?
?
? ? ? ?
? ? ? ? ?
330 v
490 420
330 v
? ? ?
?
? ?
? ? ?
v 25.2m/s ? ?
= 91 km/h
5. A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a
resistive force mkv
2
 where v is its speed. The maximum height attained by the ball is:
(1)
–1
1 ku
tan
k 2g
?
(2) 
1 ku
ln 1
2k g
?
? ?
?
? ?
? ?
(3) 
1 ku
ln 1
k 2g
?
? ?
?
? ?
? ?
(4) 
2
1
1 ku
tan
2k g
?
Sol. 2
v
mg mkv
2
 at H
m
 , V = 0
F
net
 = ma
2
dv
mg mKv mv
ds
? ? ?
? ?
H v 0
2
S 0 v u
vdv
ds 1
g kv
?
? ?
? ?
?
? ?
       
2
xdx
a bx ?
?
2
max
1 g ku
H n
2K g
? ? ?
?
? ?
? ?
?
2
m
1 Ku
H n 1
2K g
? ?
? ?
? ?
? ?
?
6. Consider two uniform discs of the same thickness and different radii R
1
 = R and R
2
 = ?R made of
the same material. If the ratio of their moments of inertia I
1
 and I
2
, respectively, about their axes
is I
1
 : I
2
 = 1 : 16 then the value of ? is :
(1) 
2
(2) 2 (3) 
2 2
(4) 4
Page 4


1. A circular coil has moment of inertia 0.8 kg m
2
 around any diameter and is carrying current to
produce a magnetic moment of 20 Am
2
. The coil is kept initially in a vertical position and it can
rotate freely around a horizontal diameter . When a uniform magnetic field of 4 T is applied along the
vertical,it starts rotating around its horizontal diameter. The angular speed the coil acquires after
rotating by 60° will be:
(1) 10 ? rad s
–1
(2) 20 rad s
–1
(3) 20 ? rad s
–1
(4) 10 rad s
–1
Sol. 4
By energy conservation
i i f f
U K U K ? ? ?
2
1
MBcos60 0 MBcos 0 I
2
? ? ? ? ? ? ? ?
2
MB 1
MB I
2 2
? ? ? ?
2
MB 1
I
2 2
? ?
MB 20 4
100
I 0.8
?
? ? ? ? = 10 rad/s
2. A person pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a
distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with
distance to 100 N. The total distance through which the box has been moved is 30 m. What is the
work done by the person during the total movement of the box?
(1) 5690 J (2) 5250 J (3) 2780 J (4) 3280 J
Sol. 2
A
B
C
30 15
O
D
100
Force 
disp (in m) (in N)
200
E
Work done = area of ABCEO
= area of trap. ABCD + area of rect. ODCE
= 
1
45 30 100 30 5250J
2
? ? ? ? ?
PHYSICS _ 4 Sep. _ SHIFT - 2
3. Match the thermodynamic processes taking place in a system with the correct conditions. In the
table : ?Q is the heat supplied, ?W is the work done and ?U is change in internal energy of the
system.
     Process Condition
(I) Adiabatic (1) ?W = 0
(II) Isothermal (2) ?Q = 0
(III) Isochoric (3) ?U ? ?0, ?W ? 0,
      ?Q ? 0
(IV) Isobaric (4) ?U = 0
(1) (I) - (1), (II) - (1), (III) - (2), (IV) - (3)
(2) (I) - (1), (II) - (2), (III) - (4), (IV) - (4)
(3) (I) - (2), (II) - (4), (III) - (1), (IV) - (3)
(4) (I) - (2), (II) - (1), (III) - (4), (IV) - (3)
Sol. 3
adiabatic, ?Q = 0
Isothermal, ?U = 0
Isochoric, pdV 0 ?
?
W 0 ? ?
Isobaric, Q 0, U 0, W 0 ? ? ? ? ? ?
4. The driver of a bus approaching a big wall notices that the frequency of his bus’s horn changes
from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the
bus if speed of the sound is 330 ms
–1
.
(1) 81 kmh
–1
(2) 91 kmh
–1
(3) 71 kmh
–1
(4) 61 kmh
–1
Sol. 2
Freq received by wall,
w 0
330
f f
330 v
? ?
?
? ?
? ? ?
freq. after reflection, w
330 v
f ' f
330
? ? ?
?
? ?
? ?
= 0
330 v 330
f
330 330 v
? ? ? ? ?
?
? ? ? ?
? ? ? ? ?
330 v
490 420
330 v
? ? ?
?
? ?
? ? ?
v 25.2m/s ? ?
= 91 km/h
5. A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a
resistive force mkv
2
 where v is its speed. The maximum height attained by the ball is:
(1)
–1
1 ku
tan
k 2g
?
(2) 
1 ku
ln 1
2k g
?
? ?
?
? ?
? ?
(3) 
1 ku
ln 1
k 2g
?
? ?
?
? ?
? ?
(4) 
2
1
1 ku
tan
2k g
?
Sol. 2
v
mg mkv
2
 at H
m
 , V = 0
F
net
 = ma
2
dv
mg mKv mv
ds
? ? ?
? ?
H v 0
2
S 0 v u
vdv
ds 1
g kv
?
? ?
? ?
?
? ?
       
2
xdx
a bx ?
?
2
max
1 g ku
H n
2K g
? ? ?
?
? ?
? ?
?
2
m
1 Ku
H n 1
2K g
? ?
? ?
? ?
? ?
?
6. Consider two uniform discs of the same thickness and different radii R
1
 = R and R
2
 = ?R made of
the same material. If the ratio of their moments of inertia I
1
 and I
2
, respectively, about their axes
is I
1
 : I
2
 = 1 : 16 then the value of ? is :
(1) 
2
(2) 2 (3) 
2 2
(4) 4
Sol. 2
Moment of inertia of disc, 
? ?
2 2
2
R t R
MR
I
2 2
? ?
? ?
? ?
? ?
I = KR
4
4
1 1
2 2
I R
I R
? ?
?
? ?
? ?
? ?
4
1
4
1 R
16 2
16 R
? ?
? ? ? ? ?
? ?
? ? ?
7. A series L-R circuit is connected to a battery of emf V. If the circuit is switched on at t = 0, then
the time at which the energy stored in the inductor reaches 
1
n
? ?
? ?
? ?
 times of its maximum value, is :
(1) 
L n
ln
R
n 1
? ?
? ?
? ?
?
? ?
(2) 
L n
ln
R
n –1
? ?
? ?
? ?
? ?
(3) 
L n 1
ln
R
n –1
? ?
?
? ?
? ?
? ?
(4) 
L n –1
ln
R
n
? ?
? ?
? ?
? ?
Sol. 2
L
R
V
P.E. in inductor, 
2
1
U LI
2
?
2
U I ?
2
0 0
U I
U I
? ?
?
? ?
? ?
2
0
1 I
n I
? ?
?
? ?
? ?
0
I
I
n
?
Page 5


1. A circular coil has moment of inertia 0.8 kg m
2
 around any diameter and is carrying current to
produce a magnetic moment of 20 Am
2
. The coil is kept initially in a vertical position and it can
rotate freely around a horizontal diameter . When a uniform magnetic field of 4 T is applied along the
vertical,it starts rotating around its horizontal diameter. The angular speed the coil acquires after
rotating by 60° will be:
(1) 10 ? rad s
–1
(2) 20 rad s
–1
(3) 20 ? rad s
–1
(4) 10 rad s
–1
Sol. 4
By energy conservation
i i f f
U K U K ? ? ?
2
1
MBcos60 0 MBcos 0 I
2
? ? ? ? ? ? ? ?
2
MB 1
MB I
2 2
? ? ? ?
2
MB 1
I
2 2
? ?
MB 20 4
100
I 0.8
?
? ? ? ? = 10 rad/s
2. A person pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a
distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with
distance to 100 N. The total distance through which the box has been moved is 30 m. What is the
work done by the person during the total movement of the box?
(1) 5690 J (2) 5250 J (3) 2780 J (4) 3280 J
Sol. 2
A
B
C
30 15
O
D
100
Force 
disp (in m) (in N)
200
E
Work done = area of ABCEO
= area of trap. ABCD + area of rect. ODCE
= 
1
45 30 100 30 5250J
2
? ? ? ? ?
PHYSICS _ 4 Sep. _ SHIFT - 2
3. Match the thermodynamic processes taking place in a system with the correct conditions. In the
table : ?Q is the heat supplied, ?W is the work done and ?U is change in internal energy of the
system.
     Process Condition
(I) Adiabatic (1) ?W = 0
(II) Isothermal (2) ?Q = 0
(III) Isochoric (3) ?U ? ?0, ?W ? 0,
      ?Q ? 0
(IV) Isobaric (4) ?U = 0
(1) (I) - (1), (II) - (1), (III) - (2), (IV) - (3)
(2) (I) - (1), (II) - (2), (III) - (4), (IV) - (4)
(3) (I) - (2), (II) - (4), (III) - (1), (IV) - (3)
(4) (I) - (2), (II) - (1), (III) - (4), (IV) - (3)
Sol. 3
adiabatic, ?Q = 0
Isothermal, ?U = 0
Isochoric, pdV 0 ?
?
W 0 ? ?
Isobaric, Q 0, U 0, W 0 ? ? ? ? ? ?
4. The driver of a bus approaching a big wall notices that the frequency of his bus’s horn changes
from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the
bus if speed of the sound is 330 ms
–1
.
(1) 81 kmh
–1
(2) 91 kmh
–1
(3) 71 kmh
–1
(4) 61 kmh
–1
Sol. 2
Freq received by wall,
w 0
330
f f
330 v
? ?
?
? ?
? ? ?
freq. after reflection, w
330 v
f ' f
330
? ? ?
?
? ?
? ?
= 0
330 v 330
f
330 330 v
? ? ? ? ?
?
? ? ? ?
? ? ? ? ?
330 v
490 420
330 v
? ? ?
?
? ?
? ? ?
v 25.2m/s ? ?
= 91 km/h
5. A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a
resistive force mkv
2
 where v is its speed. The maximum height attained by the ball is:
(1)
–1
1 ku
tan
k 2g
?
(2) 
1 ku
ln 1
2k g
?
? ?
?
? ?
? ?
(3) 
1 ku
ln 1
k 2g
?
? ?
?
? ?
? ?
(4) 
2
1
1 ku
tan
2k g
?
Sol. 2
v
mg mkv
2
 at H
m
 , V = 0
F
net
 = ma
2
dv
mg mKv mv
ds
? ? ?
? ?
H v 0
2
S 0 v u
vdv
ds 1
g kv
?
? ?
? ?
?
? ?
       
2
xdx
a bx ?
?
2
max
1 g ku
H n
2K g
? ? ?
?
? ?
? ?
?
2
m
1 Ku
H n 1
2K g
? ?
? ?
? ?
? ?
?
6. Consider two uniform discs of the same thickness and different radii R
1
 = R and R
2
 = ?R made of
the same material. If the ratio of their moments of inertia I
1
 and I
2
, respectively, about their axes
is I
1
 : I
2
 = 1 : 16 then the value of ? is :
(1) 
2
(2) 2 (3) 
2 2
(4) 4
Sol. 2
Moment of inertia of disc, 
? ?
2 2
2
R t R
MR
I
2 2
? ?
? ?
? ?
? ?
I = KR
4
4
1 1
2 2
I R
I R
? ?
?
? ?
? ?
? ?
4
1
4
1 R
16 2
16 R
? ?
? ? ? ? ?
? ?
? ? ?
7. A series L-R circuit is connected to a battery of emf V. If the circuit is switched on at t = 0, then
the time at which the energy stored in the inductor reaches 
1
n
? ?
? ?
? ?
 times of its maximum value, is :
(1) 
L n
ln
R
n 1
? ?
? ?
? ?
?
? ?
(2) 
L n
ln
R
n –1
? ?
? ?
? ?
? ?
(3) 
L n 1
ln
R
n –1
? ?
?
? ?
? ?
? ?
(4) 
L n –1
ln
R
n
? ?
? ?
? ?
? ?
Sol. 2
L
R
V
P.E. in inductor, 
2
1
U LI
2
?
2
U I ?
2
0 0
U I
U I
? ?
?
? ?
? ?
2
0
1 I
n I
? ?
?
? ?
? ?
0
I
I
n
?
R
t
L
0
I I 1 e
? ? ?
? ?
? ?
? ?
R
t
0 L
0
I
I 1 e
n
? ? ?
? ?
? ?
? ?
taking ?n  & solving we get,
L n
t n
R n 1
? ?
?
? ?
? ?
?
? ?
?
8. The electric field of a plane electromagnetic wave is given by
? ?
? ?
? ?
0
E E x y sin kz – t ? ? ?
?
Its magnetic field will be given by :
(1) 
? ?
? ?
? ?
0
E
x y sin kz – t
c
? ? (2) 
? ?
? ?
? ?
0
E
x – y sin kz – t
c
?
(3) 
? ?
? ?
? ?
0
E
x – y cos kz – t
c
? (4) 
? ?
? ?
? ?
0
E
–x y sin kz – t
c
? ?
Sol. (4)
E B ?
? ?
 should be in direction of 
v
?
? ? ? ?
0
E
ˆ ˆ B x y sin Kz t
C
? ? ? ? ? ?
?
9. A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the
length of the side of the cube is close to :
(Given bulk modulus of metal, B = 8 × 10
10
 Pa)
(1) 0.6 (2) 20 (3) 1.67 (4) 5
Sol. (3)
? ?
P
B
V
v
?
? ?
?
V
P .B
V
? ? ?
? ?
? ?
? ?
= 
3 L
B
L
?
?
L P
L 3B
? ?
? ?
% ? we get, 
L
100%
L
?
?
Putting values we get = 1.67