JEE Main 2020 September 4 Question Paper Shift 1 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


Q.1 Starting from the origin at time t = 0, with initial velocity 
–1
ˆ
5jms , a particle moves in the x-y plane
with a constant acceleration of ? ?
–2
ˆ ˆ
10i 4j ms ?
. At time t, its coordinates are (20 m, y
0
 m). The
values of t and y
0 
are, respectively:
(1) 5s and 25 m (2) 2s and 18 m (3) 2s and 24 m (4) 4s and 52 m
Sol. 2
y = u
y
t + 
1
2
a
y
t
2
y = 5t + 
1
2
(4) t
2
y = 5t + 2t
2
and x = 0 + 
1
2
 (10) (t
2
) = 20
t = 2 s
? y = 10 + 8 = 18m
Q.2 A small bar magnet placed with its axis at 30° with an external field of 0.06 T experiences a torque
of 0.018 Nm. The minimum work required to rotate it from its stable to unstable equilbrium position
is:
(1) 7.2 × 10
–2
 J (2) 6.4 × 10
–2
 J (3) 9.2 × 10
–3
 J (4) 11.7 × 10
–3
 J
Sol. 1
? = MB sin 30º
0.018 = MB
1
2
? ?
? ?
? ?
MB = 0.036
w = ?U = 2MB = 0.072 J
Q.3 Choose the correct option relating wave lengths of different parts of electromagnetic wave spec-
trum:
(1) ?
radio waves
 > ?
micro waves
 > ?
visible
 > ?
x-rays
(2) ?
visible 
> ?
x-rays 
> ?
radio waves 
> ?
micro waves
(3) ?
visible 
< ?
micro waves
 < ?
radio waves
 < ?
x-rays
(4) ?
x-rays
 < ?
micro waves
 < ?
radio waves
 < ?
visible
Sol. 1
By property of electromagnetic wave spectrum.
Q.4 On the x-axis and at a distance x from the origin, the gravitational field due a mass distribution is
given by 
? ?
3/2
2 2
Ax
x a ?
in the x-direction. The magnitude of gravitational potential on the x-axis at a
distance x, taking its value to be zero at infinity, is:
(1) 
? ?
3/2
2 2
A x a ? (2) 
? ?
1/2
2 2
A
x a ?
(3) 
? ?
1/2
2 2
A x a ? (4) 
? ?
3/2
2 2
A
x a ?
PHYSICS _ 4 Sep. _ SHIFT - 1
Page 2


Q.1 Starting from the origin at time t = 0, with initial velocity 
–1
ˆ
5jms , a particle moves in the x-y plane
with a constant acceleration of ? ?
–2
ˆ ˆ
10i 4j ms ?
. At time t, its coordinates are (20 m, y
0
 m). The
values of t and y
0 
are, respectively:
(1) 5s and 25 m (2) 2s and 18 m (3) 2s and 24 m (4) 4s and 52 m
Sol. 2
y = u
y
t + 
1
2
a
y
t
2
y = 5t + 
1
2
(4) t
2
y = 5t + 2t
2
and x = 0 + 
1
2
 (10) (t
2
) = 20
t = 2 s
? y = 10 + 8 = 18m
Q.2 A small bar magnet placed with its axis at 30° with an external field of 0.06 T experiences a torque
of 0.018 Nm. The minimum work required to rotate it from its stable to unstable equilbrium position
is:
(1) 7.2 × 10
–2
 J (2) 6.4 × 10
–2
 J (3) 9.2 × 10
–3
 J (4) 11.7 × 10
–3
 J
Sol. 1
? = MB sin 30º
0.018 = MB
1
2
? ?
? ?
? ?
MB = 0.036
w = ?U = 2MB = 0.072 J
Q.3 Choose the correct option relating wave lengths of different parts of electromagnetic wave spec-
trum:
(1) ?
radio waves
 > ?
micro waves
 > ?
visible
 > ?
x-rays
(2) ?
visible 
> ?
x-rays 
> ?
radio waves 
> ?
micro waves
(3) ?
visible 
< ?
micro waves
 < ?
radio waves
 < ?
x-rays
(4) ?
x-rays
 < ?
micro waves
 < ?
radio waves
 < ?
visible
Sol. 1
By property of electromagnetic wave spectrum.
Q.4 On the x-axis and at a distance x from the origin, the gravitational field due a mass distribution is
given by 
? ?
3/2
2 2
Ax
x a ?
in the x-direction. The magnitude of gravitational potential on the x-axis at a
distance x, taking its value to be zero at infinity, is:
(1) 
? ?
3/2
2 2
A x a ? (2) 
? ?
1/2
2 2
A
x a ?
(3) 
? ?
1/2
2 2
A x a ? (4) 
? ?
3/2
2 2
A
x a ?
PHYSICS _ 4 Sep. _ SHIFT - 1
Sol. 2
E
x
 = 2 2 3/2
(x a )
Ax
?
2 2 3/2
–
(x a )
dv Ax
dx
?
?
2 2 3/2
0
–
(x a )
?
?
?
? ?
V x
Ax
dv dx
V = 2 2 1/2
(x )
A
a ?
Q.5 A small bar magnet is moved through a coil at constant speed from one end to the other. Which of
the following series of observations will be seen on the galvanometer G attached across the coil?
Three positions shown describe: (a) the magnet's entry (b) magnet is completely inside and (c)
magnet's exit.
(1) 
(2) 
(3) 
(4) 
Page 3


Q.1 Starting from the origin at time t = 0, with initial velocity 
–1
ˆ
5jms , a particle moves in the x-y plane
with a constant acceleration of ? ?
–2
ˆ ˆ
10i 4j ms ?
. At time t, its coordinates are (20 m, y
0
 m). The
values of t and y
0 
are, respectively:
(1) 5s and 25 m (2) 2s and 18 m (3) 2s and 24 m (4) 4s and 52 m
Sol. 2
y = u
y
t + 
1
2
a
y
t
2
y = 5t + 
1
2
(4) t
2
y = 5t + 2t
2
and x = 0 + 
1
2
 (10) (t
2
) = 20
t = 2 s
? y = 10 + 8 = 18m
Q.2 A small bar magnet placed with its axis at 30° with an external field of 0.06 T experiences a torque
of 0.018 Nm. The minimum work required to rotate it from its stable to unstable equilbrium position
is:
(1) 7.2 × 10
–2
 J (2) 6.4 × 10
–2
 J (3) 9.2 × 10
–3
 J (4) 11.7 × 10
–3
 J
Sol. 1
? = MB sin 30º
0.018 = MB
1
2
? ?
? ?
? ?
MB = 0.036
w = ?U = 2MB = 0.072 J
Q.3 Choose the correct option relating wave lengths of different parts of electromagnetic wave spec-
trum:
(1) ?
radio waves
 > ?
micro waves
 > ?
visible
 > ?
x-rays
(2) ?
visible 
> ?
x-rays 
> ?
radio waves 
> ?
micro waves
(3) ?
visible 
< ?
micro waves
 < ?
radio waves
 < ?
x-rays
(4) ?
x-rays
 < ?
micro waves
 < ?
radio waves
 < ?
visible
Sol. 1
By property of electromagnetic wave spectrum.
Q.4 On the x-axis and at a distance x from the origin, the gravitational field due a mass distribution is
given by 
? ?
3/2
2 2
Ax
x a ?
in the x-direction. The magnitude of gravitational potential on the x-axis at a
distance x, taking its value to be zero at infinity, is:
(1) 
? ?
3/2
2 2
A x a ? (2) 
? ?
1/2
2 2
A
x a ?
(3) 
? ?
1/2
2 2
A x a ? (4) 
? ?
3/2
2 2
A
x a ?
PHYSICS _ 4 Sep. _ SHIFT - 1
Sol. 2
E
x
 = 2 2 3/2
(x a )
Ax
?
2 2 3/2
–
(x a )
dv Ax
dx
?
?
2 2 3/2
0
–
(x a )
?
?
?
? ?
V x
Ax
dv dx
V = 2 2 1/2
(x )
A
a ?
Q.5 A small bar magnet is moved through a coil at constant speed from one end to the other. Which of
the following series of observations will be seen on the galvanometer G attached across the coil?
Three positions shown describe: (a) the magnet's entry (b) magnet is completely inside and (c)
magnet's exit.
(1) 
(2) 
(3) 
(4) 
Sol. 1
Let N S
? When bar magnet enter
N
? When completely inside
i = 0
? when exit
S
S
N
N
Q.6 A battery of 3.0V is connected to a resistor dissipating 0.5 W of power. If the terminal voltage of
the battery is 2.5V, the power dissipated within the internal resistance is:
(1) 0.072 W (2) 0.10 W (3) 0.125 W (4) 0.50 W
Sol. 2
P
0
 = 0.5 w
i. (2.5) = 0.5
r
R
i
i = 1/5 A
P
r
 = 
1
5
? ?
? ?
? ?
(0.5) = 0.1 W
Q.7 Two charged thin infinite plane sheets of uniform surface charge density ?
+
 and ?
–
, where | ?
+
| > | ?
–
|,
intersect at right angle. Which of the following best represents the electric field lines for this system:
(1) (2) 
(3) (4) 
Page 4


Q.1 Starting from the origin at time t = 0, with initial velocity 
–1
ˆ
5jms , a particle moves in the x-y plane
with a constant acceleration of ? ?
–2
ˆ ˆ
10i 4j ms ?
. At time t, its coordinates are (20 m, y
0
 m). The
values of t and y
0 
are, respectively:
(1) 5s and 25 m (2) 2s and 18 m (3) 2s and 24 m (4) 4s and 52 m
Sol. 2
y = u
y
t + 
1
2
a
y
t
2
y = 5t + 
1
2
(4) t
2
y = 5t + 2t
2
and x = 0 + 
1
2
 (10) (t
2
) = 20
t = 2 s
? y = 10 + 8 = 18m
Q.2 A small bar magnet placed with its axis at 30° with an external field of 0.06 T experiences a torque
of 0.018 Nm. The minimum work required to rotate it from its stable to unstable equilbrium position
is:
(1) 7.2 × 10
–2
 J (2) 6.4 × 10
–2
 J (3) 9.2 × 10
–3
 J (4) 11.7 × 10
–3
 J
Sol. 1
? = MB sin 30º
0.018 = MB
1
2
? ?
? ?
? ?
MB = 0.036
w = ?U = 2MB = 0.072 J
Q.3 Choose the correct option relating wave lengths of different parts of electromagnetic wave spec-
trum:
(1) ?
radio waves
 > ?
micro waves
 > ?
visible
 > ?
x-rays
(2) ?
visible 
> ?
x-rays 
> ?
radio waves 
> ?
micro waves
(3) ?
visible 
< ?
micro waves
 < ?
radio waves
 < ?
x-rays
(4) ?
x-rays
 < ?
micro waves
 < ?
radio waves
 < ?
visible
Sol. 1
By property of electromagnetic wave spectrum.
Q.4 On the x-axis and at a distance x from the origin, the gravitational field due a mass distribution is
given by 
? ?
3/2
2 2
Ax
x a ?
in the x-direction. The magnitude of gravitational potential on the x-axis at a
distance x, taking its value to be zero at infinity, is:
(1) 
? ?
3/2
2 2
A x a ? (2) 
? ?
1/2
2 2
A
x a ?
(3) 
? ?
1/2
2 2
A x a ? (4) 
? ?
3/2
2 2
A
x a ?
PHYSICS _ 4 Sep. _ SHIFT - 1
Sol. 2
E
x
 = 2 2 3/2
(x a )
Ax
?
2 2 3/2
–
(x a )
dv Ax
dx
?
?
2 2 3/2
0
–
(x a )
?
?
?
? ?
V x
Ax
dv dx
V = 2 2 1/2
(x )
A
a ?
Q.5 A small bar magnet is moved through a coil at constant speed from one end to the other. Which of
the following series of observations will be seen on the galvanometer G attached across the coil?
Three positions shown describe: (a) the magnet's entry (b) magnet is completely inside and (c)
magnet's exit.
(1) 
(2) 
(3) 
(4) 
Sol. 1
Let N S
? When bar magnet enter
N
? When completely inside
i = 0
? when exit
S
S
N
N
Q.6 A battery of 3.0V is connected to a resistor dissipating 0.5 W of power. If the terminal voltage of
the battery is 2.5V, the power dissipated within the internal resistance is:
(1) 0.072 W (2) 0.10 W (3) 0.125 W (4) 0.50 W
Sol. 2
P
0
 = 0.5 w
i. (2.5) = 0.5
r
R
i
i = 1/5 A
P
r
 = 
1
5
? ?
? ?
? ?
(0.5) = 0.1 W
Q.7 Two charged thin infinite plane sheets of uniform surface charge density ?
+
 and ?
–
, where | ?
+
| > | ?
–
|,
intersect at right angle. Which of the following best represents the electric field lines for this system:
(1) (2) 
(3) (4) 
Sol. 1
 +
 –
E E 
E 
E 
E
–
E
–
E
+
E
+
E
–
E
+
0
E
+
E
–
s+
– E E ? ?
? > 45°
Q.8 A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s
–2
. The density of water is
1 gm cm
–3
 and water offers negligible drag force on the bubble. The mass of the bubble is (g = 980
cm/s
2
).
(1) 1.52 gm (2) 4.51 gm (3) 3.15 gm (4) 4.15 gm
Sol. 4
F
b
mg
F
b
 –mg = ma ? 
b
F
m
g a
?
?
w
v g
m
g a
? ?
?
?
m =  
3
(4 / 3) r . .
?
w
g
g a
? ?
= 4.15gm
Page 5


Q.1 Starting from the origin at time t = 0, with initial velocity 
–1
ˆ
5jms , a particle moves in the x-y plane
with a constant acceleration of ? ?
–2
ˆ ˆ
10i 4j ms ?
. At time t, its coordinates are (20 m, y
0
 m). The
values of t and y
0 
are, respectively:
(1) 5s and 25 m (2) 2s and 18 m (3) 2s and 24 m (4) 4s and 52 m
Sol. 2
y = u
y
t + 
1
2
a
y
t
2
y = 5t + 
1
2
(4) t
2
y = 5t + 2t
2
and x = 0 + 
1
2
 (10) (t
2
) = 20
t = 2 s
? y = 10 + 8 = 18m
Q.2 A small bar magnet placed with its axis at 30° with an external field of 0.06 T experiences a torque
of 0.018 Nm. The minimum work required to rotate it from its stable to unstable equilbrium position
is:
(1) 7.2 × 10
–2
 J (2) 6.4 × 10
–2
 J (3) 9.2 × 10
–3
 J (4) 11.7 × 10
–3
 J
Sol. 1
? = MB sin 30º
0.018 = MB
1
2
? ?
? ?
? ?
MB = 0.036
w = ?U = 2MB = 0.072 J
Q.3 Choose the correct option relating wave lengths of different parts of electromagnetic wave spec-
trum:
(1) ?
radio waves
 > ?
micro waves
 > ?
visible
 > ?
x-rays
(2) ?
visible 
> ?
x-rays 
> ?
radio waves 
> ?
micro waves
(3) ?
visible 
< ?
micro waves
 < ?
radio waves
 < ?
x-rays
(4) ?
x-rays
 < ?
micro waves
 < ?
radio waves
 < ?
visible
Sol. 1
By property of electromagnetic wave spectrum.
Q.4 On the x-axis and at a distance x from the origin, the gravitational field due a mass distribution is
given by 
? ?
3/2
2 2
Ax
x a ?
in the x-direction. The magnitude of gravitational potential on the x-axis at a
distance x, taking its value to be zero at infinity, is:
(1) 
? ?
3/2
2 2
A x a ? (2) 
? ?
1/2
2 2
A
x a ?
(3) 
? ?
1/2
2 2
A x a ? (4) 
? ?
3/2
2 2
A
x a ?
PHYSICS _ 4 Sep. _ SHIFT - 1
Sol. 2
E
x
 = 2 2 3/2
(x a )
Ax
?
2 2 3/2
–
(x a )
dv Ax
dx
?
?
2 2 3/2
0
–
(x a )
?
?
?
? ?
V x
Ax
dv dx
V = 2 2 1/2
(x )
A
a ?
Q.5 A small bar magnet is moved through a coil at constant speed from one end to the other. Which of
the following series of observations will be seen on the galvanometer G attached across the coil?
Three positions shown describe: (a) the magnet's entry (b) magnet is completely inside and (c)
magnet's exit.
(1) 
(2) 
(3) 
(4) 
Sol. 1
Let N S
? When bar magnet enter
N
? When completely inside
i = 0
? when exit
S
S
N
N
Q.6 A battery of 3.0V is connected to a resistor dissipating 0.5 W of power. If the terminal voltage of
the battery is 2.5V, the power dissipated within the internal resistance is:
(1) 0.072 W (2) 0.10 W (3) 0.125 W (4) 0.50 W
Sol. 2
P
0
 = 0.5 w
i. (2.5) = 0.5
r
R
i
i = 1/5 A
P
r
 = 
1
5
? ?
? ?
? ?
(0.5) = 0.1 W
Q.7 Two charged thin infinite plane sheets of uniform surface charge density ?
+
 and ?
–
, where | ?
+
| > | ?
–
|,
intersect at right angle. Which of the following best represents the electric field lines for this system:
(1) (2) 
(3) (4) 
Sol. 1
 +
 –
E E 
E 
E 
E
–
E
–
E
+
E
+
E
–
E
+
0
E
+
E
–
s+
– E E ? ?
? > 45°
Q.8 A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s
–2
. The density of water is
1 gm cm
–3
 and water offers negligible drag force on the bubble. The mass of the bubble is (g = 980
cm/s
2
).
(1) 1.52 gm (2) 4.51 gm (3) 3.15 gm (4) 4.15 gm
Sol. 4
F
b
mg
F
b
 –mg = ma ? 
b
F
m
g a
?
?
w
v g
m
g a
? ?
?
?
m =  
3
(4 / 3) r . .
?
w
g
g a
? ?
= 4.15gm
Q.9 A wire A, bent in the shape of an arc of a circle, carrying a current of 2A and having  radius 2 cm
and another wire B, also bent in the shape of arc of a circle, carrying a current of 3 A and having
radius of 4 cm, are placed as shown in the figure. The ratio of the magnetic field due to the wires
A and B at the common centre O is:
90°
60°
B
O
A
(1) 2 : 5 (2) 6 : 5 (3) 6 : 4 (4) 4 : 6
Sol. 2
A
3
(2)
2 3
B
2(a)(2 ) 4a
? ? ?
?
? ?
?
? ?
? ?
?
B
5
(3)
3 5
B
2(2a)(2 ) 8a
? ? ?
?
? ?
?
? ?
? ?
?
A
B
B 3 8a
6:5
B 4a 5
?
? ? ?
?
Q.10 Particle A of mass m
A
 = 
m
2
 moving along the x-axis with velocity v
0
 collides elastically with another
particle B at rest having mass 
B
m
m
3
?
. If both particles move along the x-axis after the collision,
the change ? ? in de-Broglie wavlength of particle A, in terms of its de-Broglie wavelength ( ?
0
)
before collision is:
(1) 
0
5
2
? ? ? ? (2) 
0
2 ? ? ? ? (3) 
0
4 ? ? ? ? (4) 
0
3
2
? ? ? ?
Sol. 3
V
1
 = 
1 2
1 2
– m m
m m ?
. u
1
 + 
2
1 2
2m
m m ?
. u
2
V
1
 = 
– / 3
2
/ 3
2
m
m
m
m ?
 V
0
 = V
0 
/5
?
’
 = 
0
.
2 5
h
V m
= 5.
0
.
2
h
m
V
= 5 ?
0
? ? = 4 ?
0