JEE Main 2020 September 2 Question Paper Shift 1 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


Q.1 The mass density of a spherical galaxy K varies as 
K
r
 over a large distance 'r' from its centre. In
that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on
R as:
(1) 
2
T R ?
(2) 
2 3
T R ?
(3) 
2
3
1
T
R
?
(4) 
T R ?
Sol. (1)
M
R
m
Mass of galaxy = 
R
0
dv ?
?
R
2
0
k
4 r dr
r
? ?
?
R
0
4 k rdr ? ?
?
2
2
1
4 kR
M k R
2
?
? ?
F = m ?
2
R
2
2
GMm
m R
R
? ?
2
2 1
2
Gk R
R
R
? ?
2 2
k
R
? ? ?
2
k
R
? ?
2
2 R
T 2
k
?
? ? ?
?
3
T k R ?
T
2
 ? R
PHYSICS - 2 Sep 2020. - SHIFT - 1
Page 2


Q.1 The mass density of a spherical galaxy K varies as 
K
r
 over a large distance 'r' from its centre. In
that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on
R as:
(1) 
2
T R ?
(2) 
2 3
T R ?
(3) 
2
3
1
T
R
?
(4) 
T R ?
Sol. (1)
M
R
m
Mass of galaxy = 
R
0
dv ?
?
R
2
0
k
4 r dr
r
? ?
?
R
0
4 k rdr ? ?
?
2
2
1
4 kR
M k R
2
?
? ?
F = m ?
2
R
2
2
GMm
m R
R
? ?
2
2 1
2
Gk R
R
R
? ?
2 2
k
R
? ? ?
2
k
R
? ?
2
2 R
T 2
k
?
? ? ?
?
3
T k R ?
T
2
 ? R
PHYSICS - 2 Sep 2020. - SHIFT - 1
Q.2 An amplitude modulated wave is represented by the expression v
m
 = 5(1 + 0.6 cos 6280t)
sin (211 x 10
4
 t) volts. The minimum and maximum amplitudes of the amplitude modulated wave are,
respectively :
(1) 
3
2
V, 5V (2) 5V, 8V (3) 3V, 5V (4) 
5
2
V, 8V
Sol. (4)
m
c
A
0.6
A
?
= (5+3 cos 6280t) sin (211×10
4
 t)
maximum Amp. = 5+3 = 8 V
minimum Amp. = 5–3 = 2 V
from the given option nearest value of minimum Amplitude = 
5
V
2
Q.3 A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is
positioned in front of the minor, what will be the nature and magnification of the image of the
object ? (Figure drawn as schematic and not to scale)
(1) Erect, virtual and unmagnified (2) Inverted, real and magnified
(3) Erect, virtual and magnified (4) Inverted, real and unmagnified
Sol. (4)
Object
12 8 4 16
20
(cm)
C
2R
? beyond C i.e. – ? < u < C
? real, inverted
and unmagnified
Page 3


Q.1 The mass density of a spherical galaxy K varies as 
K
r
 over a large distance 'r' from its centre. In
that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on
R as:
(1) 
2
T R ?
(2) 
2 3
T R ?
(3) 
2
3
1
T
R
?
(4) 
T R ?
Sol. (1)
M
R
m
Mass of galaxy = 
R
0
dv ?
?
R
2
0
k
4 r dr
r
? ?
?
R
0
4 k rdr ? ?
?
2
2
1
4 kR
M k R
2
?
? ?
F = m ?
2
R
2
2
GMm
m R
R
? ?
2
2 1
2
Gk R
R
R
? ?
2 2
k
R
? ? ?
2
k
R
? ?
2
2 R
T 2
k
?
? ? ?
?
3
T k R ?
T
2
 ? R
PHYSICS - 2 Sep 2020. - SHIFT - 1
Q.2 An amplitude modulated wave is represented by the expression v
m
 = 5(1 + 0.6 cos 6280t)
sin (211 x 10
4
 t) volts. The minimum and maximum amplitudes of the amplitude modulated wave are,
respectively :
(1) 
3
2
V, 5V (2) 5V, 8V (3) 3V, 5V (4) 
5
2
V, 8V
Sol. (4)
m
c
A
0.6
A
?
= (5+3 cos 6280t) sin (211×10
4
 t)
maximum Amp. = 5+3 = 8 V
minimum Amp. = 5–3 = 2 V
from the given option nearest value of minimum Amplitude = 
5
V
2
Q.3 A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is
positioned in front of the minor, what will be the nature and magnification of the image of the
object ? (Figure drawn as schematic and not to scale)
(1) Erect, virtual and unmagnified (2) Inverted, real and magnified
(3) Erect, virtual and magnified (4) Inverted, real and unmagnified
Sol. (4)
Object
12 8 4 16
20
(cm)
C
2R
? beyond C i.e. – ? < u < C
? real, inverted
and unmagnified
Q.4 A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as
shown in the figure. The radius of vessel is 5 cm an and the angular speed of rotation is ? rad s
–1
.
The difference in the height, h (in cm) of liquid at the centre of vessel and at the side will be :
(1) 
2
5
2g
?
(2) 
2
2
25g
?
(3) 
2
25
2g
?
(4) 
2
2
5g
?
Sol. (3)
h
10cm
y
2 2
x
y
2g
?
?
at x = 5cm, y=h
2 2 2
(5) 25
h
2g 2g
? ?
? ?
Page 4


Q.1 The mass density of a spherical galaxy K varies as 
K
r
 over a large distance 'r' from its centre. In
that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on
R as:
(1) 
2
T R ?
(2) 
2 3
T R ?
(3) 
2
3
1
T
R
?
(4) 
T R ?
Sol. (1)
M
R
m
Mass of galaxy = 
R
0
dv ?
?
R
2
0
k
4 r dr
r
? ?
?
R
0
4 k rdr ? ?
?
2
2
1
4 kR
M k R
2
?
? ?
F = m ?
2
R
2
2
GMm
m R
R
? ?
2
2 1
2
Gk R
R
R
? ?
2 2
k
R
? ? ?
2
k
R
? ?
2
2 R
T 2
k
?
? ? ?
?
3
T k R ?
T
2
 ? R
PHYSICS - 2 Sep 2020. - SHIFT - 1
Q.2 An amplitude modulated wave is represented by the expression v
m
 = 5(1 + 0.6 cos 6280t)
sin (211 x 10
4
 t) volts. The minimum and maximum amplitudes of the amplitude modulated wave are,
respectively :
(1) 
3
2
V, 5V (2) 5V, 8V (3) 3V, 5V (4) 
5
2
V, 8V
Sol. (4)
m
c
A
0.6
A
?
= (5+3 cos 6280t) sin (211×10
4
 t)
maximum Amp. = 5+3 = 8 V
minimum Amp. = 5–3 = 2 V
from the given option nearest value of minimum Amplitude = 
5
V
2
Q.3 A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is
positioned in front of the minor, what will be the nature and magnification of the image of the
object ? (Figure drawn as schematic and not to scale)
(1) Erect, virtual and unmagnified (2) Inverted, real and magnified
(3) Erect, virtual and magnified (4) Inverted, real and unmagnified
Sol. (4)
Object
12 8 4 16
20
(cm)
C
2R
? beyond C i.e. – ? < u < C
? real, inverted
and unmagnified
Q.4 A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as
shown in the figure. The radius of vessel is 5 cm an and the angular speed of rotation is ? rad s
–1
.
The difference in the height, h (in cm) of liquid at the centre of vessel and at the side will be :
(1) 
2
5
2g
?
(2) 
2
2
25g
?
(3) 
2
25
2g
?
(4) 
2
2
5g
?
Sol. (3)
h
10cm
y
2 2
x
y
2g
?
?
at x = 5cm, y=h
2 2 2
(5) 25
h
2g 2g
? ?
? ?
Q.5 If speed V, area A and force F are chosen as fundamental units, then the dimension of Young's
modulus will be
(1) FA
2
V
–3
(2) FA
2
V
–2
(3) FA
–1
V
0
(4) FA
2
V
–1
Sol. (3)
Y = k [F]
x
 [A]
y
 [V]
z
[ML
1
T
–2
] = [MLT
–2
]
x
 [L
2
]
y
 
 
[LT
–1
]
z
[ML
1
T
–2
] = [M
x
 L
x + 2y + z 
T
–2x – z
]
x = 1, –2x–z = –2, x + 2y + z = –1
? z = 0
? y = –1
Q.6 A bead of mass m stays at point P (a, b) on a wire bent in the shape of a parabola
y = 4Cx
2
 and rotating with angular speed ? (see figure). The value of ? is (neglect friction):
(1) 
2g
C
(2) 2 gC (3) 
2gC
ab
(4) 2 2gC
Sol. (4)
y = 4 cx
2
dy
8cx
dx
?
2
m a
tan
mg
?
? ?
y
0
P(a,b)
x
mg
tan ?=
dy
dx
=8cx
2
a
8cx
g
?
?
(x = a), 
2
a
8 c a
g
?
?
8cg ? ?
2 2gc ? ?
Page 5


Q.1 The mass density of a spherical galaxy K varies as 
K
r
 over a large distance 'r' from its centre. In
that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on
R as:
(1) 
2
T R ?
(2) 
2 3
T R ?
(3) 
2
3
1
T
R
?
(4) 
T R ?
Sol. (1)
M
R
m
Mass of galaxy = 
R
0
dv ?
?
R
2
0
k
4 r dr
r
? ?
?
R
0
4 k rdr ? ?
?
2
2
1
4 kR
M k R
2
?
? ?
F = m ?
2
R
2
2
GMm
m R
R
? ?
2
2 1
2
Gk R
R
R
? ?
2 2
k
R
? ? ?
2
k
R
? ?
2
2 R
T 2
k
?
? ? ?
?
3
T k R ?
T
2
 ? R
PHYSICS - 2 Sep 2020. - SHIFT - 1
Q.2 An amplitude modulated wave is represented by the expression v
m
 = 5(1 + 0.6 cos 6280t)
sin (211 x 10
4
 t) volts. The minimum and maximum amplitudes of the amplitude modulated wave are,
respectively :
(1) 
3
2
V, 5V (2) 5V, 8V (3) 3V, 5V (4) 
5
2
V, 8V
Sol. (4)
m
c
A
0.6
A
?
= (5+3 cos 6280t) sin (211×10
4
 t)
maximum Amp. = 5+3 = 8 V
minimum Amp. = 5–3 = 2 V
from the given option nearest value of minimum Amplitude = 
5
V
2
Q.3 A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is
positioned in front of the minor, what will be the nature and magnification of the image of the
object ? (Figure drawn as schematic and not to scale)
(1) Erect, virtual and unmagnified (2) Inverted, real and magnified
(3) Erect, virtual and magnified (4) Inverted, real and unmagnified
Sol. (4)
Object
12 8 4 16
20
(cm)
C
2R
? beyond C i.e. – ? < u < C
? real, inverted
and unmagnified
Q.4 A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as
shown in the figure. The radius of vessel is 5 cm an and the angular speed of rotation is ? rad s
–1
.
The difference in the height, h (in cm) of liquid at the centre of vessel and at the side will be :
(1) 
2
5
2g
?
(2) 
2
2
25g
?
(3) 
2
25
2g
?
(4) 
2
2
5g
?
Sol. (3)
h
10cm
y
2 2
x
y
2g
?
?
at x = 5cm, y=h
2 2 2
(5) 25
h
2g 2g
? ?
? ?
Q.5 If speed V, area A and force F are chosen as fundamental units, then the dimension of Young's
modulus will be
(1) FA
2
V
–3
(2) FA
2
V
–2
(3) FA
–1
V
0
(4) FA
2
V
–1
Sol. (3)
Y = k [F]
x
 [A]
y
 [V]
z
[ML
1
T
–2
] = [MLT
–2
]
x
 [L
2
]
y
 
 
[LT
–1
]
z
[ML
1
T
–2
] = [M
x
 L
x + 2y + z 
T
–2x – z
]
x = 1, –2x–z = –2, x + 2y + z = –1
? z = 0
? y = –1
Q.6 A bead of mass m stays at point P (a, b) on a wire bent in the shape of a parabola
y = 4Cx
2
 and rotating with angular speed ? (see figure). The value of ? is (neglect friction):
(1) 
2g
C
(2) 2 gC (3) 
2gC
ab
(4) 2 2gC
Sol. (4)
y = 4 cx
2
dy
8cx
dx
?
2
m a
tan
mg
?
? ?
y
0
P(a,b)
x
mg
tan ?=
dy
dx
=8cx
2
a
8cx
g
?
?
(x = a), 
2
a
8 c a
g
?
?
8cg ? ?
2 2gc ? ?
Q.7 Magnetic materials used for making permanent magnets (P) and magnets in a transformer (T) have
different properties of the following, which property best matches for the type of magnet required ?
(1) P : Small retentivity, large coercivity (2) P : Large retentivity, large coercivity
(3) T : Large retentivity, large coercivity (4) T : Large retentivity, small coercivity
Sol. (2)
Permanent magnet must retain for long use and should not be easily demagnetised.
Q. 8 Interference fringes are observed on a screen by illuminating two thin slits 1 mm apart with a light
source ( ? = 632.8 nm). The distance between the screen and the slits is 100 cm. If a bright fringe
is observed on screen at a distance of 1.27 mm from the central bright fringe, then the path
difference between the waves, which are reaching this point from the slits is close to :
(1) 2.05 ?m (2) 2.87 nm (3) 2 nm (4) 1.27 ?m
Sol. (4)
given, d = 1mm
? = 632.8 nm
D = 100cm
y = 1.27 mm
x dsin
( small)
x dtan
? ? ?
? ?
? ? ?
?
3 3
2
dy 1x10 1.27 10
x
D 100 10
? ?
?
? ?
? ? ?
?
= 1.27 × 10
–6 
m
= 1.27 ?m
Q.9 A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the
gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the
mixture is:
(1) 11 (2) 13 (3) 15 (4) 20
Sol. (3)
1 2
1 v 2 v
U n C T n C T ? ?
5 3
3 RT 5x RT
2 2
? ? ?
30
RT 15RT
2
? ?