JEE Main 2020 September 6 Question Paper Shift 1 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


1. Four point masses, each of mass m, are fixed at the corners of a square of side l. The square is
rotating with angular frequency ?, about an axis passing through one of the corners of the square
and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this
axis is :
axis
(1) 4 ml
2
? (2) 2 ml
2
? (3) 3 ml
2
? (4) ml
2
?
Sol. (3)
m
m
m
m
L = I ?
? ?
2
2
a
I m x 2 m 2a
2
? ?
? ?
? ?
? ?
= ma
2
 + 2ma
2
? L = I ? ?= 3ml
2
? (a =|)
2. A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the
pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displace-
ment of 0.5mm is noticed on the pitch scale. The nature of zero error involved and the least
count of the screw gauge, are respectively :
(1) Positive, 0.1 mm (2) Positive, 0.1 ?m
(3) Positive, 10 ?m (4) Negative, 2 ?m
2. (3)
=
5
0.5
L.C mm 1 10 m 10 m
50
?
? ? ? ? ?
Page 2


1. Four point masses, each of mass m, are fixed at the corners of a square of side l. The square is
rotating with angular frequency ?, about an axis passing through one of the corners of the square
and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this
axis is :
axis
(1) 4 ml
2
? (2) 2 ml
2
? (3) 3 ml
2
? (4) ml
2
?
Sol. (3)
m
m
m
m
L = I ?
? ?
2
2
a
I m x 2 m 2a
2
? ?
? ?
? ?
? ?
= ma
2
 + 2ma
2
? L = I ? ?= 3ml
2
? (a =|)
2. A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the
pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displace-
ment of 0.5mm is noticed on the pitch scale. The nature of zero error involved and the least
count of the screw gauge, are respectively :
(1) Positive, 0.1 mm (2) Positive, 0.1 ?m
(3) Positive, 10 ?m (4) Negative, 2 ?m
2. (3)
=
5
0.5
L.C mm 1 10 m 10 m
50
?
? ? ? ? ?
3. An electron, a doubly ionized helium ion (He
++
) and a proton are having the same kinetic energy.
The relation between their respective de-Broglie wavelengths ?
e
, 
He
? ?
? and ?
p
 is :
(1) ?
e
 > ?
P
 > 
He
? ?
? (2) ?
e
 > 
He
? ?
? > ?
P
(3) ?
e
 < ?
P
 < 
He
? ?
? (4) ?
e
 < 
He
? ?
? = ?
P
Sol. (1)
h h
p
2mK E
? ? ?
?
p
d
C
2 27
1 1
C f 55
? ? ? ? ? ? ?
m
He
 > m
P
 > m
e
?
He
 < ?
p
 < ?
e
4. For the given input voltage waveform V
in
(t), the output voltage waveform V
o
(t), across the
capacitor is correctly depicted by :
V (t)
0
0V
0
t
+5V
10 nF
(1) 
V (t)
0
2V
t
(2) 
V (t)
0
2V
t
3V
(3) 
V (t)
0
2V
t
(4) 
V (t)
0
2V
t
Sol. (2)
Answer is (2)  because capacitor is charging then discharging then again charging.
But during discharging not possible to discharge 100%.
Page 3


1. Four point masses, each of mass m, are fixed at the corners of a square of side l. The square is
rotating with angular frequency ?, about an axis passing through one of the corners of the square
and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this
axis is :
axis
(1) 4 ml
2
? (2) 2 ml
2
? (3) 3 ml
2
? (4) ml
2
?
Sol. (3)
m
m
m
m
L = I ?
? ?
2
2
a
I m x 2 m 2a
2
? ?
? ?
? ?
? ?
= ma
2
 + 2ma
2
? L = I ? ?= 3ml
2
? (a =|)
2. A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the
pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displace-
ment of 0.5mm is noticed on the pitch scale. The nature of zero error involved and the least
count of the screw gauge, are respectively :
(1) Positive, 0.1 mm (2) Positive, 0.1 ?m
(3) Positive, 10 ?m (4) Negative, 2 ?m
2. (3)
=
5
0.5
L.C mm 1 10 m 10 m
50
?
? ? ? ? ?
3. An electron, a doubly ionized helium ion (He
++
) and a proton are having the same kinetic energy.
The relation between their respective de-Broglie wavelengths ?
e
, 
He
? ?
? and ?
p
 is :
(1) ?
e
 > ?
P
 > 
He
? ?
? (2) ?
e
 > 
He
? ?
? > ?
P
(3) ?
e
 < ?
P
 < 
He
? ?
? (4) ?
e
 < 
He
? ?
? = ?
P
Sol. (1)
h h
p
2mK E
? ? ?
?
p
d
C
2 27
1 1
C f 55
? ? ? ? ? ? ?
m
He
 > m
P
 > m
e
?
He
 < ?
p
 < ?
e
4. For the given input voltage waveform V
in
(t), the output voltage waveform V
o
(t), across the
capacitor is correctly depicted by :
V (t)
0
0V
0
t
+5V
10 nF
(1) 
V (t)
0
2V
t
(2) 
V (t)
0
2V
t
3V
(3) 
V (t)
0
2V
t
(4) 
V (t)
0
2V
t
Sol. (2)
Answer is (2)  because capacitor is charging then discharging then again charging.
But during discharging not possible to discharge 100%.
5. Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M, radius of its
top, R and height, H, then its moment of inertia about its axis is :
R
H
(1) 
2
2
MR
(2) 
2
3
MR
(3) 
? ?
2 2
4
M R H ?
(4) 
2
3
MH
Sol. (1)
2
mR
I
2
?
Pichka do disk Banege
6. A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite
when it is farthest from the planet is 6 times less than that when it is closest to the planet. The
ratio of distances between the satellite and the planet at closest and farthest points is:
(1) 1 : 2 (2) 1 : 3 (3) 1 : 6 (4) 3 : 4
Sol. (3)
O
v
6v
r
1
r
2
L
i
 = L
f
m ?6vr
1
 = m ?vr
2
6r
1
 = r
2
1
2
r 1
r 6
? ?
Page 4


1. Four point masses, each of mass m, are fixed at the corners of a square of side l. The square is
rotating with angular frequency ?, about an axis passing through one of the corners of the square
and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this
axis is :
axis
(1) 4 ml
2
? (2) 2 ml
2
? (3) 3 ml
2
? (4) ml
2
?
Sol. (3)
m
m
m
m
L = I ?
? ?
2
2
a
I m x 2 m 2a
2
? ?
? ?
? ?
? ?
= ma
2
 + 2ma
2
? L = I ? ?= 3ml
2
? (a =|)
2. A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the
pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displace-
ment of 0.5mm is noticed on the pitch scale. The nature of zero error involved and the least
count of the screw gauge, are respectively :
(1) Positive, 0.1 mm (2) Positive, 0.1 ?m
(3) Positive, 10 ?m (4) Negative, 2 ?m
2. (3)
=
5
0.5
L.C mm 1 10 m 10 m
50
?
? ? ? ? ?
3. An electron, a doubly ionized helium ion (He
++
) and a proton are having the same kinetic energy.
The relation between their respective de-Broglie wavelengths ?
e
, 
He
? ?
? and ?
p
 is :
(1) ?
e
 > ?
P
 > 
He
? ?
? (2) ?
e
 > 
He
? ?
? > ?
P
(3) ?
e
 < ?
P
 < 
He
? ?
? (4) ?
e
 < 
He
? ?
? = ?
P
Sol. (1)
h h
p
2mK E
? ? ?
?
p
d
C
2 27
1 1
C f 55
? ? ? ? ? ? ?
m
He
 > m
P
 > m
e
?
He
 < ?
p
 < ?
e
4. For the given input voltage waveform V
in
(t), the output voltage waveform V
o
(t), across the
capacitor is correctly depicted by :
V (t)
0
0V
0
t
+5V
10 nF
(1) 
V (t)
0
2V
t
(2) 
V (t)
0
2V
t
3V
(3) 
V (t)
0
2V
t
(4) 
V (t)
0
2V
t
Sol. (2)
Answer is (2)  because capacitor is charging then discharging then again charging.
But during discharging not possible to discharge 100%.
5. Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M, radius of its
top, R and height, H, then its moment of inertia about its axis is :
R
H
(1) 
2
2
MR
(2) 
2
3
MR
(3) 
? ?
2 2
4
M R H ?
(4) 
2
3
MH
Sol. (1)
2
mR
I
2
?
Pichka do disk Banege
6. A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite
when it is farthest from the planet is 6 times less than that when it is closest to the planet. The
ratio of distances between the satellite and the planet at closest and farthest points is:
(1) 1 : 2 (2) 1 : 3 (3) 1 : 6 (4) 3 : 4
Sol. (3)
O
v
6v
r
1
r
2
L
i
 = L
f
m ?6vr
1
 = m ?vr
2
6r
1
 = r
2
1
2
r 1
r 6
? ?
7. You are given that Mass of 
7
3
Li 7.0160u ? ,
Mass of 
4
2
He 4.0026u ?
and Mass of 
1
1
H 1.0079u ? .
When 20 g of 
7
3
Li is converted into 
4
2
He by proton capture, the energy liberated, (in kWh), is:
[Mass of nucleon = 1 GeV/c
2
]
(1) 6.82 × 10
5
(2) 4.5 × 10
5
(3) 8 × 10
6
(4) 1.33 × 10
6
Sol. (4)
7 4
3 1 2
Li e 2 He
?
? ?
?m ? [m
Li
 + m
H
] – 2 [M
He
]
?  ? ? m 7.0160 1.0079 2 4.0003 ? ? ? ? ?
= 0.0187
Energy released in 1 reaction ? ?mc
2
In use of 7.016 u Li energy is ?mc
2
In use of 1gm Li energy is 
Li
2
m
mc ?
In use of 20gm energy is ? 
gm 20
m
mc
Li
2
?
?
6 19 23
5
20
0.0187 931.5 10 1.6 10 6.023 10
7
36 10
?
? ? ? ? ? ? ?
?
= 1.33 × 10
6
8. If the potential energy between two molecules is given by U = –
6 12
A B
r r
? , then at equilibrium,
separation between molecules, and the potential energy are :
(1) 
1/6
2B
A
? ?
? ?
? ?
, 
2
A
–
4B
(2) 
1/6
2B
A
? ?
? ?
? ?
, 
2
A
–
2B
(3) 
1/6
B
A
? ?
? ?
? ?
, 0 (4) 
1/6
B
2A
? ?
? ?
? ?
, 
2
A
–
2B
Sol. (1)
6 12
dU d
F ( Ar Br )
dr dr
? ?
? ?
? ? ? ?
for equation  F = 0
7 13
A( 6) B 12
0
r r
? ?
? ? ?
13 7
12B 6A
r r
?
1/6
2B
r
A
? ?
?
? ?
? ?
Page 5


1. Four point masses, each of mass m, are fixed at the corners of a square of side l. The square is
rotating with angular frequency ?, about an axis passing through one of the corners of the square
and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this
axis is :
axis
(1) 4 ml
2
? (2) 2 ml
2
? (3) 3 ml
2
? (4) ml
2
?
Sol. (3)
m
m
m
m
L = I ?
? ?
2
2
a
I m x 2 m 2a
2
? ?
? ?
? ?
? ?
= ma
2
 + 2ma
2
? L = I ? ?= 3ml
2
? (a =|)
2. A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the
pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displace-
ment of 0.5mm is noticed on the pitch scale. The nature of zero error involved and the least
count of the screw gauge, are respectively :
(1) Positive, 0.1 mm (2) Positive, 0.1 ?m
(3) Positive, 10 ?m (4) Negative, 2 ?m
2. (3)
=
5
0.5
L.C mm 1 10 m 10 m
50
?
? ? ? ? ?
3. An electron, a doubly ionized helium ion (He
++
) and a proton are having the same kinetic energy.
The relation between their respective de-Broglie wavelengths ?
e
, 
He
? ?
? and ?
p
 is :
(1) ?
e
 > ?
P
 > 
He
? ?
? (2) ?
e
 > 
He
? ?
? > ?
P
(3) ?
e
 < ?
P
 < 
He
? ?
? (4) ?
e
 < 
He
? ?
? = ?
P
Sol. (1)
h h
p
2mK E
? ? ?
?
p
d
C
2 27
1 1
C f 55
? ? ? ? ? ? ?
m
He
 > m
P
 > m
e
?
He
 < ?
p
 < ?
e
4. For the given input voltage waveform V
in
(t), the output voltage waveform V
o
(t), across the
capacitor is correctly depicted by :
V (t)
0
0V
0
t
+5V
10 nF
(1) 
V (t)
0
2V
t
(2) 
V (t)
0
2V
t
3V
(3) 
V (t)
0
2V
t
(4) 
V (t)
0
2V
t
Sol. (2)
Answer is (2)  because capacitor is charging then discharging then again charging.
But during discharging not possible to discharge 100%.
5. Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M, radius of its
top, R and height, H, then its moment of inertia about its axis is :
R
H
(1) 
2
2
MR
(2) 
2
3
MR
(3) 
? ?
2 2
4
M R H ?
(4) 
2
3
MH
Sol. (1)
2
mR
I
2
?
Pichka do disk Banege
6. A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite
when it is farthest from the planet is 6 times less than that when it is closest to the planet. The
ratio of distances between the satellite and the planet at closest and farthest points is:
(1) 1 : 2 (2) 1 : 3 (3) 1 : 6 (4) 3 : 4
Sol. (3)
O
v
6v
r
1
r
2
L
i
 = L
f
m ?6vr
1
 = m ?vr
2
6r
1
 = r
2
1
2
r 1
r 6
? ?
7. You are given that Mass of 
7
3
Li 7.0160u ? ,
Mass of 
4
2
He 4.0026u ?
and Mass of 
1
1
H 1.0079u ? .
When 20 g of 
7
3
Li is converted into 
4
2
He by proton capture, the energy liberated, (in kWh), is:
[Mass of nucleon = 1 GeV/c
2
]
(1) 6.82 × 10
5
(2) 4.5 × 10
5
(3) 8 × 10
6
(4) 1.33 × 10
6
Sol. (4)
7 4
3 1 2
Li e 2 He
?
? ?
?m ? [m
Li
 + m
H
] – 2 [M
He
]
?  ? ? m 7.0160 1.0079 2 4.0003 ? ? ? ? ?
= 0.0187
Energy released in 1 reaction ? ?mc
2
In use of 7.016 u Li energy is ?mc
2
In use of 1gm Li energy is 
Li
2
m
mc ?
In use of 20gm energy is ? 
gm 20
m
mc
Li
2
?
?
6 19 23
5
20
0.0187 931.5 10 1.6 10 6.023 10
7
36 10
?
? ? ? ? ? ? ?
?
= 1.33 × 10
6
8. If the potential energy between two molecules is given by U = –
6 12
A B
r r
? , then at equilibrium,
separation between molecules, and the potential energy are :
(1) 
1/6
2B
A
? ?
? ?
? ?
, 
2
A
–
4B
(2) 
1/6
2B
A
? ?
? ?
? ?
, 
2
A
–
2B
(3) 
1/6
B
A
? ?
? ?
? ?
, 0 (4) 
1/6
B
2A
? ?
? ?
? ?
, 
2
A
–
2B
Sol. (1)
6 12
dU d
F ( Ar Br )
dr dr
? ?
? ?
? ? ? ?
for equation  F = 0
7 13
A( 6) B 12
0
r r
? ?
? ? ?
13 7
12B 6A
r r
?
1/6
2B
r
A
? ?
?
? ?
? ?
2
A B
U
2B
2B
A
A
?
? ?
? ?
? ?
? ?
2 2 2
A A A
2B 4B 4B
? ?
? ? ?
? Answer (1)
9. A clock has a continuously moving second’s hand of 0.1 m length. The average acceleration of the
tip of the hand (in units of ms
–2
) is of the order of:
(1) 10
–3
(2) 10
–1
(3) 10
–2
(4) 10
–4
Sol. (1)
2
v
a
R
?
2 R
v
60
?
?
? ?
2 2 2
3
2 2 2
4 R 4 R 4
10 0.1 10
(60) (60)
60 R
?
? ? ?
? ? ? ? ? ?
10. Identify the correct output signal Y in the given combination of gates (as shown) for the given
inputs A and B.
B
A
Y
B
t
A
5 10 15 20
(1) (2) 
(3) (4) 
t
5
10 15
20