JEE  >  JEE Advance 2022 Question Paper - 1 with Solutions

# JEE Advance 2022 Question Paper - 1 with Solutions | JEE Main & Advanced Mock Test Series

``` Page 1

[Paper-1]

Physics

Question: Two spherical stars A and B have densities
A
? and ,
B
? respectively. A and B
have the same radius, and their masses MA and MB are related by MB = 2MA. Due to an
interaction process, star A loses some of its mass, so that its radius is halved, while its
spherical shape is retained and its density remains .
A
? The entire mass lost by A is deposited
as a thick spheric shell on B with the density the shell being .
A
? If
A
v and
B
v are the escape
velocities from A and B after the interaction process, the ratio
1/3
10
.
15
B
A
v n
v
= The value of n is
________
Solution:
0
2
2
8
A
A
v GM
v
R
A
= =
??
×
??
??

For, B,
( )
33 3
4 47
3 38
rR R p p -= ×
1
3
15
8
rR
??
?=
??
??

Therefore,
( ) ( )
0 11
33
7
22
23 2 8
15 8 15
2
AA
B
GM M
vv
R
? ?
× +
? ?
×
? ?
= = ×
×

Therefore,
( ) ( )
11
33
23 2.30 10
15 15
B
A
v
v
×
= =
Therefore, n = 2.30

Question: The minimum kinetic energy needed by an alpha particle to cause the nuclear
reaction
16 4 1 19
7 2 18
N He H + ?+ O in a laboratory frame is n (in MeV). Assume that
16
7
N is at
Page 2

[Paper-1]

Physics

Question: Two spherical stars A and B have densities
A
? and ,
B
? respectively. A and B
have the same radius, and their masses MA and MB are related by MB = 2MA. Due to an
interaction process, star A loses some of its mass, so that its radius is halved, while its
spherical shape is retained and its density remains .
A
? The entire mass lost by A is deposited
as a thick spheric shell on B with the density the shell being .
A
? If
A
v and
B
v are the escape
velocities from A and B after the interaction process, the ratio
1/3
10
.
15
B
A
v n
v
= The value of n is
________
Solution:
0
2
2
8
A
A
v GM
v
R
A
= =
??
×
??
??

For, B,
( )
33 3
4 47
3 38
rR R p p -= ×
1
3
15
8
rR
??
?=
??
??

Therefore,
( ) ( )
0 11
33
7
22
23 2 8
15 8 15
2
AA
B
GM M
vv
R
? ?
× +
? ?
×
? ?
= = ×
×

Therefore,
( ) ( )
11
33
23 2.30 10
15 15
B
A
v
v
×
= =
Therefore, n = 2.30

Question: The minimum kinetic energy needed by an alpha particle to cause the nuclear
reaction
16 4 1 19
7 2 18
N He H + ?+ O in a laboratory frame is n (in MeV). Assume that
16
7
N is at

rest in the laboratory frame. The masses of
16
7
, N
1 19
18
and HO can be taken to be 16.006 u,
4.003 u, 1008 u and 19.003 u, respectively, where 1 u = 930 MeV c
-2
. The value of n is
_______.
Solution:
( )
2
N He H O
Qm m m m c = + -- ×

( ) 16.006 4.003 1.008 19.003 930MeV = + -- ×

1.86MeV = -

1.86 energy absorbed. MeV =

And,
2
14
max loss in kinetic energy
2 5
mm
v
m
×
× ×=
2
15
24
mv Q ?=×

( )
5
1.86 2.325
4
MeV MeV =× =

Therefore, 2.33 n =

Question: In the following circuit
1 23
12 , 4 C FC C F µµ = = = and C4 = C5 = 2 µF. The charge
stored in C3 is ______µC

Solution:
From circuit given, Potential difference across C3 is 2 V (constant)
Therefore,
3
24 8 Q C C µµ =×=

Question: A rod of length 2 cm makes an angle
2
3
p
rad with the principal axis of a thin
convex lens. The lens has a focal length of 10 cm and placed at a distance of
40
3
cm from the
Page 3

[Paper-1]

Physics

Question: Two spherical stars A and B have densities
A
? and ,
B
? respectively. A and B
have the same radius, and their masses MA and MB are related by MB = 2MA. Due to an
interaction process, star A loses some of its mass, so that its radius is halved, while its
spherical shape is retained and its density remains .
A
? The entire mass lost by A is deposited
as a thick spheric shell on B with the density the shell being .
A
? If
A
v and
B
v are the escape
velocities from A and B after the interaction process, the ratio
1/3
10
.
15
B
A
v n
v
= The value of n is
________
Solution:
0
2
2
8
A
A
v GM
v
R
A
= =
??
×
??
??

For, B,
( )
33 3
4 47
3 38
rR R p p -= ×
1
3
15
8
rR
??
?=
??
??

Therefore,
( ) ( )
0 11
33
7
22
23 2 8
15 8 15
2
AA
B
GM M
vv
R
? ?
× +
? ?
×
? ?
= = ×
×

Therefore,
( ) ( )
11
33
23 2.30 10
15 15
B
A
v
v
×
= =
Therefore, n = 2.30

Question: The minimum kinetic energy needed by an alpha particle to cause the nuclear
reaction
16 4 1 19
7 2 18
N He H + ?+ O in a laboratory frame is n (in MeV). Assume that
16
7
N is at

rest in the laboratory frame. The masses of
16
7
, N
1 19
18
and HO can be taken to be 16.006 u,
4.003 u, 1008 u and 19.003 u, respectively, where 1 u = 930 MeV c
-2
. The value of n is
_______.
Solution:
( )
2
N He H O
Qm m m m c = + -- ×

( ) 16.006 4.003 1.008 19.003 930MeV = + -- ×

1.86MeV = -

1.86 energy absorbed. MeV =

And,
2
14
max loss in kinetic energy
2 5
mm
v
m
×
× ×=
2
15
24
mv Q ?=×

( )
5
1.86 2.325
4
MeV MeV =× =

Therefore, 2.33 n =

Question: In the following circuit
1 23
12 , 4 C FC C F µµ = = = and C4 = C5 = 2 µF. The charge
stored in C3 is ______µC

Solution:
From circuit given, Potential difference across C3 is 2 V (constant)
Therefore,
3
24 8 Q C C µµ =×=

Question: A rod of length 2 cm makes an angle
2
3
p
rad with the principal axis of a thin
convex lens. The lens has a focal length of 10 cm and placed at a distance of
40
3
cm from the

object as shown in the figure. The height of the image is
30 3
13
cm and the angle made by it
with respect to the principal axis is a rad. The value of a is
n
p

Solution:

40
10
3
' 40
43
10
3
OA cm
×
= =
-

43
10
430
3
'
43
13
10
3
OB cm
×
= =
-

Therefore,
430 90
' ' 40
13 13
A B cm = -=
Therefore,
30 3 1
tan
90
3
13
13
a = =
??
??
??

6
p
a ? =

Therefore, 6.00 n =

Question: At time t = 0, a disk of radius 1 m starts to roll without slipping on a horizontal
plane with an angular acceleration of
2
2
.
3
-
= A small stone A stuck to the disk. At t =
0, it is at the contact point of the disk and the plane. Later, at time , ts p = the stone detaches
Page 4

[Paper-1]

Physics

Question: Two spherical stars A and B have densities
A
? and ,
B
? respectively. A and B
have the same radius, and their masses MA and MB are related by MB = 2MA. Due to an
interaction process, star A loses some of its mass, so that its radius is halved, while its
spherical shape is retained and its density remains .
A
? The entire mass lost by A is deposited
as a thick spheric shell on B with the density the shell being .
A
? If
A
v and
B
v are the escape
velocities from A and B after the interaction process, the ratio
1/3
10
.
15
B
A
v n
v
= The value of n is
________
Solution:
0
2
2
8
A
A
v GM
v
R
A
= =
??
×
??
??

For, B,
( )
33 3
4 47
3 38
rR R p p -= ×
1
3
15
8
rR
??
?=
??
??

Therefore,
( ) ( )
0 11
33
7
22
23 2 8
15 8 15
2
AA
B
GM M
vv
R
? ?
× +
? ?
×
? ?
= = ×
×

Therefore,
( ) ( )
11
33
23 2.30 10
15 15
B
A
v
v
×
= =
Therefore, n = 2.30

Question: The minimum kinetic energy needed by an alpha particle to cause the nuclear
reaction
16 4 1 19
7 2 18
N He H + ?+ O in a laboratory frame is n (in MeV). Assume that
16
7
N is at

rest in the laboratory frame. The masses of
16
7
, N
1 19
18
and HO can be taken to be 16.006 u,
4.003 u, 1008 u and 19.003 u, respectively, where 1 u = 930 MeV c
-2
. The value of n is
_______.
Solution:
( )
2
N He H O
Qm m m m c = + -- ×

( ) 16.006 4.003 1.008 19.003 930MeV = + -- ×

1.86MeV = -

1.86 energy absorbed. MeV =

And,
2
14
max loss in kinetic energy
2 5
mm
v
m
×
× ×=
2
15
24
mv Q ?=×

( )
5
1.86 2.325
4
MeV MeV =× =

Therefore, 2.33 n =

Question: In the following circuit
1 23
12 , 4 C FC C F µµ = = = and C4 = C5 = 2 µF. The charge
stored in C3 is ______µC

Solution:
From circuit given, Potential difference across C3 is 2 V (constant)
Therefore,
3
24 8 Q C C µµ =×=

Question: A rod of length 2 cm makes an angle
2
3
p
rad with the principal axis of a thin
convex lens. The lens has a focal length of 10 cm and placed at a distance of
40
3
cm from the

object as shown in the figure. The height of the image is
30 3
13
cm and the angle made by it
with respect to the principal axis is a rad. The value of a is
n
p

Solution:

40
10
3
' 40
43
10
3
OA cm
×
= =
-

43
10
430
3
'
43
13
10
3
OB cm
×
= =
-

Therefore,
430 90
' ' 40
13 13
A B cm = -=
Therefore,
30 3 1
tan
90
3
13
13
a = =
??
??
??

6
p
a ? =

Therefore, 6.00 n =

Question: At time t = 0, a disk of radius 1 m starts to roll without slipping on a horizontal
plane with an angular acceleration of
2
2
.
3
-
= A small stone A stuck to the disk. At t =
0, it is at the contact point of the disk and the plane. Later, at time , ts p = the stone detaches

itself and flies off tangentially from the disk. The maximum height (in m) reached by the
stone measured from the plane is
1
.
2 10
x
+ The value of x is ___________       [Take g = 10
ms
-2
]
Solution:
The angle rotated by disc in ts p = is
( )
2
0
2
1
2
12
2 3
3
tt
?? a
?p
p
= +
?= ×
=

and the angular velocity of disc is
0
2
/
3
t
? ? a
p
= +
=

And
2
1
3
cm
vR
p
? = = ×
2
/
3
ms
p
=
So, at the moment it detaches the situation is

( ) ( )
2
2
2 cos120
cm cm
v R v Rv ?? = ++ °
2
/
3
sin120
and tan
cos120
cm
cm
v ms
R
vR
p
?
?
?
= =
°
=
+°

Page 5

[Paper-1]

Physics

Question: Two spherical stars A and B have densities
A
? and ,
B
? respectively. A and B
have the same radius, and their masses MA and MB are related by MB = 2MA. Due to an
interaction process, star A loses some of its mass, so that its radius is halved, while its
spherical shape is retained and its density remains .
A
? The entire mass lost by A is deposited
as a thick spheric shell on B with the density the shell being .
A
? If
A
v and
B
v are the escape
velocities from A and B after the interaction process, the ratio
1/3
10
.
15
B
A
v n
v
= The value of n is
________
Solution:
0
2
2
8
A
A
v GM
v
R
A
= =
??
×
??
??

For, B,
( )
33 3
4 47
3 38
rR R p p -= ×
1
3
15
8
rR
??
?=
??
??

Therefore,
( ) ( )
0 11
33
7
22
23 2 8
15 8 15
2
AA
B
GM M
vv
R
? ?
× +
? ?
×
? ?
= = ×
×

Therefore,
( ) ( )
11
33
23 2.30 10
15 15
B
A
v
v
×
= =
Therefore, n = 2.30

Question: The minimum kinetic energy needed by an alpha particle to cause the nuclear
reaction
16 4 1 19
7 2 18
N He H + ?+ O in a laboratory frame is n (in MeV). Assume that
16
7
N is at

rest in the laboratory frame. The masses of
16
7
, N
1 19
18
and HO can be taken to be 16.006 u,
4.003 u, 1008 u and 19.003 u, respectively, where 1 u = 930 MeV c
-2
. The value of n is
_______.
Solution:
( )
2
N He H O
Qm m m m c = + -- ×

( ) 16.006 4.003 1.008 19.003 930MeV = + -- ×

1.86MeV = -

1.86 energy absorbed. MeV =

And,
2
14
max loss in kinetic energy
2 5
mm
v
m
×
× ×=
2
15
24
mv Q ?=×

( )
5
1.86 2.325
4
MeV MeV =× =

Therefore, 2.33 n =

Question: In the following circuit
1 23
12 , 4 C FC C F µµ = = = and C4 = C5 = 2 µF. The charge
stored in C3 is ______µC

Solution:
From circuit given, Potential difference across C3 is 2 V (constant)
Therefore,
3
24 8 Q C C µµ =×=

Question: A rod of length 2 cm makes an angle
2
3
p
rad with the principal axis of a thin
convex lens. The lens has a focal length of 10 cm and placed at a distance of
40
3
cm from the

object as shown in the figure. The height of the image is
30 3
13
cm and the angle made by it
with respect to the principal axis is a rad. The value of a is
n
p

Solution:

40
10
3
' 40
43
10
3
OA cm
×
= =
-

43
10
430
3
'
43
13
10
3
OB cm
×
= =
-

Therefore,
430 90
' ' 40
13 13
A B cm = -=
Therefore,
30 3 1
tan
90
3
13
13
a = =
??
??
??

6
p
a ? =

Therefore, 6.00 n =

Question: At time t = 0, a disk of radius 1 m starts to roll without slipping on a horizontal
plane with an angular acceleration of
2
2
.
3
-
= A small stone A stuck to the disk. At t =
0, it is at the contact point of the disk and the plane. Later, at time , ts p = the stone detaches

itself and flies off tangentially from the disk. The maximum height (in m) reached by the
stone measured from the plane is
1
.
2 10
x
+ The value of x is ___________       [Take g = 10
ms
-2
]
Solution:
The angle rotated by disc in ts p = is
( )
2
0
2
1
2
12
2 3
3
tt
?? a
?p
p
= +
?= ×
=

and the angular velocity of disc is
0
2
/
3
t
? ? a
p
= +
=

And
2
1
3
cm
vR
p
? = = ×
2
/
3
ms
p
=
So, at the moment it detaches the situation is

( ) ( )
2
2
2 cos120
cm cm
v R v Rv ?? = ++ °
2
/
3
sin120
and tan
cos120
cm
cm
v ms
R
vR
p
?
?
?
= =
°
=
+°

tan 3
3
?
p
?
?=
?=

So,
2 2
max
sin
2
u
H
g
?
=
2
2
2
sin 60
3
2 10
p
? ?
×°
? ?
? ?
=
×

43
92 104
60
m
p
p
×
=
×× ×
=

So, height from ground will be
( )
1
1 cos 60
60 2 10
0.52
6
x
R
x
p
p
- °+ = +
?= =

Question: A solid sphere of mass I kg and radius 1 m rolls without slipping on a fixed
inclined plane with an angle of inclination ? = 30
o
from the horizontal. Two forces of
magnitude 1 N each, parallel to the incline, act on the sphere, both at distance r = 0.5 m from
the center of the sphere, as shown in the figure. The acceleration of the sphere down the plane
is _____ms
-2
(Take g = 10 ms
-2
)

Solution:
```

## JEE Main & Advanced Mock Test Series

2 videos|327 docs|203 tests

## JEE Main & Advanced Mock Test Series

2 videos|327 docs|203 tests

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