JEE Main 2020 September 5 Question Paper Shift 1 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


1. Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V
diagram. The paths are labelled as A ? B, A ? C and A ? D. The change in internal energies during
these process are taken as E
AB
 , E
AC
 and E
AD
 and the workdone as W
AB
, W
AC
 and E
AD
. The correct
relation between these parameters are :
(1) E
AB
 = E
AC
 < E
AD
, W
AB 
> 0, W
AC
 = 0, W
AD
 < 0
(2) E
AB
 > E
AC
 > E
AD
, W
AB 
< W
AC
 < W
AD
(3) E
AB
 < E
AC
 < E
AD
, W
AB 
> 0, W
AC
 > W
AD
(4) E
AB
 = E
AC
 = E
AD
, W
AB 
> 0, W
AC
 = 0, W
AD
 > 0
Sol. 1 (Bonus)
E
AB
 = E
AC
 = E
AD
dU = 
nfR
2
 (T
f
 – T
i
)
w
AB
 > 0 (+) V ?
w
AC
 = 0 V const.
w
AD
 < 0 (–) V ?
2. With increasing biasing voltage of a photodiode, the photocurrent magnitude :
(1) increases initially and saturates finally
(2) remains constant
(3) increases linearly
(4) increases initially and after attaining certain value, it decreases
Sol. 1
By theory
Page 2


1. Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V
diagram. The paths are labelled as A ? B, A ? C and A ? D. The change in internal energies during
these process are taken as E
AB
 , E
AC
 and E
AD
 and the workdone as W
AB
, W
AC
 and E
AD
. The correct
relation between these parameters are :
(1) E
AB
 = E
AC
 < E
AD
, W
AB 
> 0, W
AC
 = 0, W
AD
 < 0
(2) E
AB
 > E
AC
 > E
AD
, W
AB 
< W
AC
 < W
AD
(3) E
AB
 < E
AC
 < E
AD
, W
AB 
> 0, W
AC
 > W
AD
(4) E
AB
 = E
AC
 = E
AD
, W
AB 
> 0, W
AC
 = 0, W
AD
 > 0
Sol. 1 (Bonus)
E
AB
 = E
AC
 = E
AD
dU = 
nfR
2
 (T
f
 – T
i
)
w
AB
 > 0 (+) V ?
w
AC
 = 0 V const.
w
AD
 < 0 (–) V ?
2. With increasing biasing voltage of a photodiode, the photocurrent magnitude :
(1) increases initially and saturates finally
(2) remains constant
(3) increases linearly
(4) increases initially and after attaining certain value, it decreases
Sol. 1
By theory
3. A square loop of side 2a, and carrying current I, is kept in XZ plane with its centre at origin. A long
wire carrying the same current I is placed parallel to the z-axis and passing through the point (0, b,
0), (b > > a). The magnitude of the torque on the loop about z-axis is given by :
(1) 
2 3
0
2
2 I a
b
?
?
(2) 
2 3
0
2
I a
2 b
?
?
(3)
2 2
0
2 I a
b
?
?
(4)
2 2
0
I a
2 b
?
?
Sol. 3
M = I
2
 (2a)
2
 = 4a
2
I
2
(magnetic moment)
B = 
0 2
I
2 b
?
?
? = MB sin ?
? angle between B and M [ ? = 90°]
? ?= 4 (a
2
I
2
) 
0 1
I
2 b
?
?
? = 
2
0 1 2
2 I I a
b
?
?
 = 
2 2
0
2 I a
b
?
?
Page 3


1. Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V
diagram. The paths are labelled as A ? B, A ? C and A ? D. The change in internal energies during
these process are taken as E
AB
 , E
AC
 and E
AD
 and the workdone as W
AB
, W
AC
 and E
AD
. The correct
relation between these parameters are :
(1) E
AB
 = E
AC
 < E
AD
, W
AB 
> 0, W
AC
 = 0, W
AD
 < 0
(2) E
AB
 > E
AC
 > E
AD
, W
AB 
< W
AC
 < W
AD
(3) E
AB
 < E
AC
 < E
AD
, W
AB 
> 0, W
AC
 > W
AD
(4) E
AB
 = E
AC
 = E
AD
, W
AB 
> 0, W
AC
 = 0, W
AD
 > 0
Sol. 1 (Bonus)
E
AB
 = E
AC
 = E
AD
dU = 
nfR
2
 (T
f
 – T
i
)
w
AB
 > 0 (+) V ?
w
AC
 = 0 V const.
w
AD
 < 0 (–) V ?
2. With increasing biasing voltage of a photodiode, the photocurrent magnitude :
(1) increases initially and saturates finally
(2) remains constant
(3) increases linearly
(4) increases initially and after attaining certain value, it decreases
Sol. 1
By theory
3. A square loop of side 2a, and carrying current I, is kept in XZ plane with its centre at origin. A long
wire carrying the same current I is placed parallel to the z-axis and passing through the point (0, b,
0), (b > > a). The magnitude of the torque on the loop about z-axis is given by :
(1) 
2 3
0
2
2 I a
b
?
?
(2) 
2 3
0
2
I a
2 b
?
?
(3)
2 2
0
2 I a
b
?
?
(4)
2 2
0
I a
2 b
?
?
Sol. 3
M = I
2
 (2a)
2
 = 4a
2
I
2
(magnetic moment)
B = 
0 2
I
2 b
?
?
? = MB sin ?
? angle between B and M [ ? = 90°]
? ?= 4 (a
2
I
2
) 
0 1
I
2 b
?
?
? = 
2
0 1 2
2 I I a
b
?
?
 = 
2 2
0
2 I a
b
?
?
4. Assume that the displacement (s) of air is proportional to the pressure difference ( ?p) created by
a sound wave. Displacement(s) further depends on the speed of sound ( ?), density of air ( ?) and
the frequency (f). If ?p ? 10Pa, ? ? 300 m/s , ? ? 1 kg/m
3
 and f ? 1000 Hz, then s will be of the order
of (take the multiplicative constant to be 1)
(1) 1 mm (2) 10 mm (3) 
1
10
mm (4) 
3
100
 mm
Ans. 4
S
0
 = 
f 2 v
P
v
P
v
v
P
k
P
2 ? ?
?
?
? ?
?
?
?
?
?
?
?
?
? Proportionally constant = 1
S
0
= 
vf
P
?
?
= 
10
1 300 1000 ? ?
m
= 
300
10
mm
= 
90
3
~ 
100
3
mm
5. Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respec-
tively. These are then connected in parallel in such a manner that the positive terminal of one is
connected to the negative terminal of the other. The final energy of this configuration is :
(1) zero (2) 
9
2
 CV
2
(3) 
25
6
 CV
2
(4) 
3
2
CV
2
Sol. 4
U
i
 = 
1
2
 Cv
2
 + 
1
2
 (2C) (2v)
2
= 
9
2
 Cv
2
q
1
 + q
2
 = q
1
'
 
+ q
2
'
–CV + (2C(2V) = (C + 2C)V'
V' = 
3CV
3C
 = V
U
f
 = 
1
2
 CV
2
 + 
1
2
 (2C)V
2
U
f
 = 
3
2
 CV
2
Page 4


1. Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V
diagram. The paths are labelled as A ? B, A ? C and A ? D. The change in internal energies during
these process are taken as E
AB
 , E
AC
 and E
AD
 and the workdone as W
AB
, W
AC
 and E
AD
. The correct
relation between these parameters are :
(1) E
AB
 = E
AC
 < E
AD
, W
AB 
> 0, W
AC
 = 0, W
AD
 < 0
(2) E
AB
 > E
AC
 > E
AD
, W
AB 
< W
AC
 < W
AD
(3) E
AB
 < E
AC
 < E
AD
, W
AB 
> 0, W
AC
 > W
AD
(4) E
AB
 = E
AC
 = E
AD
, W
AB 
> 0, W
AC
 = 0, W
AD
 > 0
Sol. 1 (Bonus)
E
AB
 = E
AC
 = E
AD
dU = 
nfR
2
 (T
f
 – T
i
)
w
AB
 > 0 (+) V ?
w
AC
 = 0 V const.
w
AD
 < 0 (–) V ?
2. With increasing biasing voltage of a photodiode, the photocurrent magnitude :
(1) increases initially and saturates finally
(2) remains constant
(3) increases linearly
(4) increases initially and after attaining certain value, it decreases
Sol. 1
By theory
3. A square loop of side 2a, and carrying current I, is kept in XZ plane with its centre at origin. A long
wire carrying the same current I is placed parallel to the z-axis and passing through the point (0, b,
0), (b > > a). The magnitude of the torque on the loop about z-axis is given by :
(1) 
2 3
0
2
2 I a
b
?
?
(2) 
2 3
0
2
I a
2 b
?
?
(3)
2 2
0
2 I a
b
?
?
(4)
2 2
0
I a
2 b
?
?
Sol. 3
M = I
2
 (2a)
2
 = 4a
2
I
2
(magnetic moment)
B = 
0 2
I
2 b
?
?
? = MB sin ?
? angle between B and M [ ? = 90°]
? ?= 4 (a
2
I
2
) 
0 1
I
2 b
?
?
? = 
2
0 1 2
2 I I a
b
?
?
 = 
2 2
0
2 I a
b
?
?
4. Assume that the displacement (s) of air is proportional to the pressure difference ( ?p) created by
a sound wave. Displacement(s) further depends on the speed of sound ( ?), density of air ( ?) and
the frequency (f). If ?p ? 10Pa, ? ? 300 m/s , ? ? 1 kg/m
3
 and f ? 1000 Hz, then s will be of the order
of (take the multiplicative constant to be 1)
(1) 1 mm (2) 10 mm (3) 
1
10
mm (4) 
3
100
 mm
Ans. 4
S
0
 = 
f 2 v
P
v
P
v
v
P
k
P
2 ? ?
?
?
? ?
?
?
?
?
?
?
?
?
? Proportionally constant = 1
S
0
= 
vf
P
?
?
= 
10
1 300 1000 ? ?
m
= 
300
10
mm
= 
90
3
~ 
100
3
mm
5. Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respec-
tively. These are then connected in parallel in such a manner that the positive terminal of one is
connected to the negative terminal of the other. The final energy of this configuration is :
(1) zero (2) 
9
2
 CV
2
(3) 
25
6
 CV
2
(4) 
3
2
CV
2
Sol. 4
U
i
 = 
1
2
 Cv
2
 + 
1
2
 (2C) (2v)
2
= 
9
2
 Cv
2
q
1
 + q
2
 = q
1
'
 
+ q
2
'
–CV + (2C(2V) = (C + 2C)V'
V' = 
3CV
3C
 = V
U
f
 = 
1
2
 CV
2
 + 
1
2
 (2C)V
2
U
f
 = 
3
2
 CV
2
6. A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food
packet is dropped from the helicopter when it is at a height h. The time taken by the packet to
reach the ground is close to [g is the acceleration due to gravity] :
(1) t = 3.4 
h
g
? ?
? ?
? ?
(2) t =
2h
3g
(3) t =
2
3
h
g
? ?
? ?
? ?
(4) t = 1.8 
h
g
Sol. 1
V
B
2
 = 0
2
 + 2gh
V
B
 = 2gh
–h = (V
B
)t – 
1
2
 gt
2
–h = 2ght – 
1
2
 gt
2
gt
2
 – 2 2ght – 2h = 0
t = 
2ght 8gh 8gh
2g
? ?
 = 
2 2gh 16gh
2g
?
 = 
2gh 2 gh
g
?
t = 
2h
g
 + 
h
2
g
 = 
h
g
 ? ?
2 2 ?
 = 3.4 
h
g
7. A bullet of mass 5 g, travelling with a speed of 210 m/s, strikes a fixed wooden target. One half of
its kinetic energy is converted into heat in the bullet while the other half is converted into heat in
the wood. The rise of temperature of the bullet if the specific heat of its material is
0.030 cal/(g – °C) (1 cal = 4.2 × 10
7
 ergs) close to :
(1) 38.4°C (2) 87.5°C (3) 83.3°C (4)119.2°C
Sol. 2
2
1
m
2
? ?
?
? ?
? ?
 × 
1
2
 = ms ?T s = 0.03 cal/y°C
Page 5


1. Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V
diagram. The paths are labelled as A ? B, A ? C and A ? D. The change in internal energies during
these process are taken as E
AB
 , E
AC
 and E
AD
 and the workdone as W
AB
, W
AC
 and E
AD
. The correct
relation between these parameters are :
(1) E
AB
 = E
AC
 < E
AD
, W
AB 
> 0, W
AC
 = 0, W
AD
 < 0
(2) E
AB
 > E
AC
 > E
AD
, W
AB 
< W
AC
 < W
AD
(3) E
AB
 < E
AC
 < E
AD
, W
AB 
> 0, W
AC
 > W
AD
(4) E
AB
 = E
AC
 = E
AD
, W
AB 
> 0, W
AC
 = 0, W
AD
 > 0
Sol. 1 (Bonus)
E
AB
 = E
AC
 = E
AD
dU = 
nfR
2
 (T
f
 – T
i
)
w
AB
 > 0 (+) V ?
w
AC
 = 0 V const.
w
AD
 < 0 (–) V ?
2. With increasing biasing voltage of a photodiode, the photocurrent magnitude :
(1) increases initially and saturates finally
(2) remains constant
(3) increases linearly
(4) increases initially and after attaining certain value, it decreases
Sol. 1
By theory
3. A square loop of side 2a, and carrying current I, is kept in XZ plane with its centre at origin. A long
wire carrying the same current I is placed parallel to the z-axis and passing through the point (0, b,
0), (b > > a). The magnitude of the torque on the loop about z-axis is given by :
(1) 
2 3
0
2
2 I a
b
?
?
(2) 
2 3
0
2
I a
2 b
?
?
(3)
2 2
0
2 I a
b
?
?
(4)
2 2
0
I a
2 b
?
?
Sol. 3
M = I
2
 (2a)
2
 = 4a
2
I
2
(magnetic moment)
B = 
0 2
I
2 b
?
?
? = MB sin ?
? angle between B and M [ ? = 90°]
? ?= 4 (a
2
I
2
) 
0 1
I
2 b
?
?
? = 
2
0 1 2
2 I I a
b
?
?
 = 
2 2
0
2 I a
b
?
?
4. Assume that the displacement (s) of air is proportional to the pressure difference ( ?p) created by
a sound wave. Displacement(s) further depends on the speed of sound ( ?), density of air ( ?) and
the frequency (f). If ?p ? 10Pa, ? ? 300 m/s , ? ? 1 kg/m
3
 and f ? 1000 Hz, then s will be of the order
of (take the multiplicative constant to be 1)
(1) 1 mm (2) 10 mm (3) 
1
10
mm (4) 
3
100
 mm
Ans. 4
S
0
 = 
f 2 v
P
v
P
v
v
P
k
P
2 ? ?
?
?
? ?
?
?
?
?
?
?
?
?
? Proportionally constant = 1
S
0
= 
vf
P
?
?
= 
10
1 300 1000 ? ?
m
= 
300
10
mm
= 
90
3
~ 
100
3
mm
5. Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respec-
tively. These are then connected in parallel in such a manner that the positive terminal of one is
connected to the negative terminal of the other. The final energy of this configuration is :
(1) zero (2) 
9
2
 CV
2
(3) 
25
6
 CV
2
(4) 
3
2
CV
2
Sol. 4
U
i
 = 
1
2
 Cv
2
 + 
1
2
 (2C) (2v)
2
= 
9
2
 Cv
2
q
1
 + q
2
 = q
1
'
 
+ q
2
'
–CV + (2C(2V) = (C + 2C)V'
V' = 
3CV
3C
 = V
U
f
 = 
1
2
 CV
2
 + 
1
2
 (2C)V
2
U
f
 = 
3
2
 CV
2
6. A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food
packet is dropped from the helicopter when it is at a height h. The time taken by the packet to
reach the ground is close to [g is the acceleration due to gravity] :
(1) t = 3.4 
h
g
? ?
? ?
? ?
(2) t =
2h
3g
(3) t =
2
3
h
g
? ?
? ?
? ?
(4) t = 1.8 
h
g
Sol. 1
V
B
2
 = 0
2
 + 2gh
V
B
 = 2gh
–h = (V
B
)t – 
1
2
 gt
2
–h = 2ght – 
1
2
 gt
2
gt
2
 – 2 2ght – 2h = 0
t = 
2ght 8gh 8gh
2g
? ?
 = 
2 2gh 16gh
2g
?
 = 
2gh 2 gh
g
?
t = 
2h
g
 + 
h
2
g
 = 
h
g
 ? ?
2 2 ?
 = 3.4 
h
g
7. A bullet of mass 5 g, travelling with a speed of 210 m/s, strikes a fixed wooden target. One half of
its kinetic energy is converted into heat in the bullet while the other half is converted into heat in
the wood. The rise of temperature of the bullet if the specific heat of its material is
0.030 cal/(g – °C) (1 cal = 4.2 × 10
7
 ergs) close to :
(1) 38.4°C (2) 87.5°C (3) 83.3°C (4)119.2°C
Sol. 2
2
1
m
2
? ?
?
? ?
? ?
 × 
1
2
 = ms ?T s = 0.03 cal/y°C
2
4
?
 = 126 × ?T = ?
?
3
0.03 4.2J
10 kgC
?
2
 = 4 × 126 × ?T = 126 J/kgC
(210)
2
 = 4 × 126 × ?T
210 × 210 = 4 × 126 × ?T
44100 = 504 × ?T
?T = 
504
44100
 = 87.5°C
8. A wheel is rotating freely with an angular speed ? on a shaft. The moment of inertia of the wheel is
I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially
at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of
the system is :
(1) 
3
4
(2) 0 (3) 
5
6
(4)
1
4
Sol. 1
k
i
 = 
1
2
 I ?
2
k
f
 = 
1
2
 (4I) ( ?')
2
= 2I 
2
4
? ? ?
? ?
? ?
 = 
1
8
 I ?
2
A.M.C
I ? = (I+3I) ?'
?' = 
I
4I
?
 = 
4
?
= 
i f
i
K K
K
?
 ? 
2 2
2
1 1
I I
2 8
1
I
2
? ? ?
?
2
2
I
2
1
I
8
3
?
?
 = 
4
3