JEE Main 2023 January 30 Shift 1 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


SECTION - A 
1.  The magnetic moments associated with two closely wound circular coils A and B of radius r
A
= 10 cm 
and r
B
= 20 cm respectively are equal if : (Where N
A
, I
A
 and N
B
, I
B
 are number of turn and current of 
A and B respectively) 
 (1) 4 N
A
I
A
= N
B
I
B
 (2) N
A
= 2 N
B
 (3) N
A
I
A
= 4 N
B
I
B
 (4) 2 N
A
I
A
= N
B
I
B
 
Sol. (3) 
  Magnetic moment m = IAN 
 Magnetic moment of coil A ? 
  
  
 Magnetic moment of coil B ? 
  
  
 Now  
  
 
 
2.  The figure represents the momentum time (p-t) curve for a particle moving along an axis under the 
influence of the force. Identify the regions on the graph where the magnitude of the force is maximum 
and minimum respectively ? 
 If (?? 3
- ?? 2
) < ?? 1
 
 
 (1) c and b (2) b and c (3) ?? and ?? (4) c and a 
Sol. (1) 
 Slope of curve P-t will represent the force so 
  
 Maximum slope ? (c)  
 Minimum slope ? ?(b) 
 
3.  Two isolated metallic solid spheres of radii ?? and 2R are charged such that both have same charge 
density ?? . The spheres are then connected by a thin conducting wire. If the new charge density of the 
bigger sphere is ?? '
. The ratio 
?? '
?? is : 
 (1)  (2)  (3)  (4)  
 
4
9
6
5
3
5
3
4
??   F slope
dt
dP
A A B B
I . N (100) I N 400 ? ? ? 
  
A A B B
I N 4I N ? 
mm ? 
AB
B B B
m I N (20) ??  …(2) 
2
B B B B
m I N r ?? 
2
A A A
m I N (10) ??  ...(1) 
2
A A A A
m I r N ?? 
2
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 30th January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
Page 2


SECTION - A 
1.  The magnetic moments associated with two closely wound circular coils A and B of radius r
A
= 10 cm 
and r
B
= 20 cm respectively are equal if : (Where N
A
, I
A
 and N
B
, I
B
 are number of turn and current of 
A and B respectively) 
 (1) 4 N
A
I
A
= N
B
I
B
 (2) N
A
= 2 N
B
 (3) N
A
I
A
= 4 N
B
I
B
 (4) 2 N
A
I
A
= N
B
I
B
 
Sol. (3) 
  Magnetic moment m = IAN 
 Magnetic moment of coil A ? 
  
  
 Magnetic moment of coil B ? 
  
  
 Now  
  
 
 
2.  The figure represents the momentum time (p-t) curve for a particle moving along an axis under the 
influence of the force. Identify the regions on the graph where the magnitude of the force is maximum 
and minimum respectively ? 
 If (?? 3
- ?? 2
) < ?? 1
 
 
 (1) c and b (2) b and c (3) ?? and ?? (4) c and a 
Sol. (1) 
 Slope of curve P-t will represent the force so 
  
 Maximum slope ? (c)  
 Minimum slope ? ?(b) 
 
3.  Two isolated metallic solid spheres of radii ?? and 2R are charged such that both have same charge 
density ?? . The spheres are then connected by a thin conducting wire. If the new charge density of the 
bigger sphere is ?? '
. The ratio 
?? '
?? is : 
 (1)  (2)  (3)  (4)  
 
4
9
6
5
3
5
3
4
??   F slope
dt
dP
A A B B
I . N (100) I N 400 ? ? ? 
  
A A B B
I N 4I N ? 
mm ? 
AB
B B B
m I N (20) ??  …(2) 
2
B B B B
m I N r ?? 
2
A A A
m I N (10) ??  ...(1) 
2
A A A A
m I r N ?? 
2
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 30th January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
Sol. (3) 
 
 
R 
Q 1= ?4 ?R
2
 
2R Q 2 = ?4 ? ? ?R)
2
 
Q 2 = ? ? ? ?R
2
 
 
 Now 
 
 
1
1
Q 
1
2
Q 
 
 Charge will flow until voltage of both sphere become equal so 
  
0
c 4 R ? ?? 
  
11
12
vv ? 
  
12
12
QQ
cc
?
   
?
  
12
00
Q ' Q '
4 R 4 (2R)
?
? ? ? ?
 
 
?
  
12
2Q ' Q ' ?        …(1) 
  
1 2 1 2
Q Q Q ' Q ' ? ? ? 
  
2 2
22
Q' 3
20 R Q ' Q '
22
? ? ? ? ? 
?
  
2
2
40 R
Q'
3
??
?  …(2) 
 
2
2
40 R
Q'
3
??
? 
 Now   
2
2
40 R
'4 (2R)
3
??
? ? ? 
  
2
2
40 R
'16 R
3
??
? ? ? 
  
' 40 1 5
3 16 6
?
? ? ?
?
   
 
 
4.  A person has been using spectacles of power -1.0 dioptre for distant vision and a separate reading 
glass of power 2.0 dioptres. What is the least distance of distinct vision for this person : 
 (1) 40 cm (2) 30 cm (3) 10 cm (4) 50 cm 
Sol. (4) 
Power convex lens = 2.0 D 
 Power of concave lens = –1.0 D 
 
 
Obj Image 
  x 
25 cm 
 
 x ? least distance of distinct vision 
Page 3


SECTION - A 
1.  The magnetic moments associated with two closely wound circular coils A and B of radius r
A
= 10 cm 
and r
B
= 20 cm respectively are equal if : (Where N
A
, I
A
 and N
B
, I
B
 are number of turn and current of 
A and B respectively) 
 (1) 4 N
A
I
A
= N
B
I
B
 (2) N
A
= 2 N
B
 (3) N
A
I
A
= 4 N
B
I
B
 (4) 2 N
A
I
A
= N
B
I
B
 
Sol. (3) 
  Magnetic moment m = IAN 
 Magnetic moment of coil A ? 
  
  
 Magnetic moment of coil B ? 
  
  
 Now  
  
 
 
2.  The figure represents the momentum time (p-t) curve for a particle moving along an axis under the 
influence of the force. Identify the regions on the graph where the magnitude of the force is maximum 
and minimum respectively ? 
 If (?? 3
- ?? 2
) < ?? 1
 
 
 (1) c and b (2) b and c (3) ?? and ?? (4) c and a 
Sol. (1) 
 Slope of curve P-t will represent the force so 
  
 Maximum slope ? (c)  
 Minimum slope ? ?(b) 
 
3.  Two isolated metallic solid spheres of radii ?? and 2R are charged such that both have same charge 
density ?? . The spheres are then connected by a thin conducting wire. If the new charge density of the 
bigger sphere is ?? '
. The ratio 
?? '
?? is : 
 (1)  (2)  (3)  (4)  
 
4
9
6
5
3
5
3
4
??   F slope
dt
dP
A A B B
I . N (100) I N 400 ? ? ? 
  
A A B B
I N 4I N ? 
mm ? 
AB
B B B
m I N (20) ??  …(2) 
2
B B B B
m I N r ?? 
2
A A A
m I N (10) ??  ...(1) 
2
A A A A
m I r N ?? 
2
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 30th January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
Sol. (3) 
 
 
R 
Q 1= ?4 ?R
2
 
2R Q 2 = ?4 ? ? ?R)
2
 
Q 2 = ? ? ? ?R
2
 
 
 Now 
 
 
1
1
Q 
1
2
Q 
 
 Charge will flow until voltage of both sphere become equal so 
  
0
c 4 R ? ?? 
  
11
12
vv ? 
  
12
12
QQ
cc
?
   
?
  
12
00
Q ' Q '
4 R 4 (2R)
?
? ? ? ?
 
 
?
  
12
2Q ' Q ' ?        …(1) 
  
1 2 1 2
Q Q Q ' Q ' ? ? ? 
  
2 2
22
Q' 3
20 R Q ' Q '
22
? ? ? ? ? 
?
  
2
2
40 R
Q'
3
??
?  …(2) 
 
2
2
40 R
Q'
3
??
? 
 Now   
2
2
40 R
'4 (2R)
3
??
? ? ? 
  
2
2
40 R
'16 R
3
??
? ? ? 
  
' 40 1 5
3 16 6
?
? ? ?
?
   
 
 
4.  A person has been using spectacles of power -1.0 dioptre for distant vision and a separate reading 
glass of power 2.0 dioptres. What is the least distance of distinct vision for this person : 
 (1) 40 cm (2) 30 cm (3) 10 cm (4) 50 cm 
Sol. (4) 
Power convex lens = 2.0 D 
 Power of concave lens = –1.0 D 
 
 
Obj Image 
  x 
25 cm 
 
 x ? least distance of distinct vision 
 
1
f 100 50cm
2
? ? ? 
  
1 1 1
f v u
?? 
  
1 1 1
50 ( x) 25
??
??
  
?
 
1 1 1
50 25 ( x)
??
?
 
 
?
 
1 2 1
50 x
??
? 
 
?
 x 50cm ? 
 
 
5. A small object at rest, absorbs a light pulse of power 20 mW and duration 300 ns. Assuming speed 
 of light as 3 × 10
8
 m/s, the momentum of the object becomes equal to : 
 (1) 3 × 10
– 17
 kg m/s (2) 2 × 10
– 17
 kg m/s (3) 1 × 10
– 17
 kg m/s (4) 0.5 × 10
– 17
 kg m/s 
Sol. (2) 
Power = 20 mw 
 t = 300 nsec 
 energy absorbed 
93
300 10 20 10
??
? ? ? ? 
3 12 9
6 10 10 6 10 J
??
? ? ? ? ? 
 
light 
 
 Pressure = 
Intensity Power
=
C Area×C
 
 Pressure × Area = 
Power
C
 
 Force = 
3
8
Power 20 10
C 3 10
?
?
?
?
 
 
11
20
F 10 N
3
?
?? 
 F t P ? ? ? (momentum) 
 
11 9
fi
20
10 300 10 P P
3
??
? ? ? ? ? 
 
20
f
20 10 100 P
?
? ? ? 
 
17
f
2 10 P
?
?? 
  
 
 
 
 
 
 
Page 4


SECTION - A 
1.  The magnetic moments associated with two closely wound circular coils A and B of radius r
A
= 10 cm 
and r
B
= 20 cm respectively are equal if : (Where N
A
, I
A
 and N
B
, I
B
 are number of turn and current of 
A and B respectively) 
 (1) 4 N
A
I
A
= N
B
I
B
 (2) N
A
= 2 N
B
 (3) N
A
I
A
= 4 N
B
I
B
 (4) 2 N
A
I
A
= N
B
I
B
 
Sol. (3) 
  Magnetic moment m = IAN 
 Magnetic moment of coil A ? 
  
  
 Magnetic moment of coil B ? 
  
  
 Now  
  
 
 
2.  The figure represents the momentum time (p-t) curve for a particle moving along an axis under the 
influence of the force. Identify the regions on the graph where the magnitude of the force is maximum 
and minimum respectively ? 
 If (?? 3
- ?? 2
) < ?? 1
 
 
 (1) c and b (2) b and c (3) ?? and ?? (4) c and a 
Sol. (1) 
 Slope of curve P-t will represent the force so 
  
 Maximum slope ? (c)  
 Minimum slope ? ?(b) 
 
3.  Two isolated metallic solid spheres of radii ?? and 2R are charged such that both have same charge 
density ?? . The spheres are then connected by a thin conducting wire. If the new charge density of the 
bigger sphere is ?? '
. The ratio 
?? '
?? is : 
 (1)  (2)  (3)  (4)  
 
4
9
6
5
3
5
3
4
??   F slope
dt
dP
A A B B
I . N (100) I N 400 ? ? ? 
  
A A B B
I N 4I N ? 
mm ? 
AB
B B B
m I N (20) ??  …(2) 
2
B B B B
m I N r ?? 
2
A A A
m I N (10) ??  ...(1) 
2
A A A A
m I r N ?? 
2
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 30th January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
Sol. (3) 
 
 
R 
Q 1= ?4 ?R
2
 
2R Q 2 = ?4 ? ? ?R)
2
 
Q 2 = ? ? ? ?R
2
 
 
 Now 
 
 
1
1
Q 
1
2
Q 
 
 Charge will flow until voltage of both sphere become equal so 
  
0
c 4 R ? ?? 
  
11
12
vv ? 
  
12
12
QQ
cc
?
   
?
  
12
00
Q ' Q '
4 R 4 (2R)
?
? ? ? ?
 
 
?
  
12
2Q ' Q ' ?        …(1) 
  
1 2 1 2
Q Q Q ' Q ' ? ? ? 
  
2 2
22
Q' 3
20 R Q ' Q '
22
? ? ? ? ? 
?
  
2
2
40 R
Q'
3
??
?  …(2) 
 
2
2
40 R
Q'
3
??
? 
 Now   
2
2
40 R
'4 (2R)
3
??
? ? ? 
  
2
2
40 R
'16 R
3
??
? ? ? 
  
' 40 1 5
3 16 6
?
? ? ?
?
   
 
 
4.  A person has been using spectacles of power -1.0 dioptre for distant vision and a separate reading 
glass of power 2.0 dioptres. What is the least distance of distinct vision for this person : 
 (1) 40 cm (2) 30 cm (3) 10 cm (4) 50 cm 
Sol. (4) 
Power convex lens = 2.0 D 
 Power of concave lens = –1.0 D 
 
 
Obj Image 
  x 
25 cm 
 
 x ? least distance of distinct vision 
 
1
f 100 50cm
2
? ? ? 
  
1 1 1
f v u
?? 
  
1 1 1
50 ( x) 25
??
??
  
?
 
1 1 1
50 25 ( x)
??
?
 
 
?
 
1 2 1
50 x
??
? 
 
?
 x 50cm ? 
 
 
5. A small object at rest, absorbs a light pulse of power 20 mW and duration 300 ns. Assuming speed 
 of light as 3 × 10
8
 m/s, the momentum of the object becomes equal to : 
 (1) 3 × 10
– 17
 kg m/s (2) 2 × 10
– 17
 kg m/s (3) 1 × 10
– 17
 kg m/s (4) 0.5 × 10
– 17
 kg m/s 
Sol. (2) 
Power = 20 mw 
 t = 300 nsec 
 energy absorbed 
93
300 10 20 10
??
? ? ? ? 
3 12 9
6 10 10 6 10 J
??
? ? ? ? ? 
 
light 
 
 Pressure = 
Intensity Power
=
C Area×C
 
 Pressure × Area = 
Power
C
 
 Force = 
3
8
Power 20 10
C 3 10
?
?
?
?
 
 
11
20
F 10 N
3
?
?? 
 F t P ? ? ? (momentum) 
 
11 9
fi
20
10 300 10 P P
3
??
? ? ? ? ? 
 
20
f
20 10 100 P
?
? ? ? 
 
17
f
2 10 P
?
?? 
  
 
 
 
 
 
 
6.  Match Column-I with Column-II : 
  
 Choose the correct answer from the options given below:  
 (1) A- I, B-II, C-III, D-IV 
 (2) A- II, B-III, C-IV, D-I 
 (3) A- I, B-III, C-IV, D-II 
 (4) A- II, B-IV, C-III, D-I 
Sol. (4) 
 (A) 
2
xt ? 
  
dx
2t
dt
?
?
  Vt ?  A
?
II 
 (B) 
t
0
x x e
??
? 
  
tt
00
dx
x e ( ) (x e )
dt
? ? ? ?
? ? ? ? ? ? 
  
t
0
V x e
??
? ? ?   B
?
IV 
 (C) 
xt ?
 
?
 V const ? 
  xt ??  
?
  V const ?? C
?
III 
 (D)  xt ? 
?
 V const ?  D
?
I 
 
7. The pressure (P) and temperature (T) relationship of an ideal gas obeys the equation PT
2
= constant. 
The volume expansion coefficient of the gas will be : 
 (1) 
3
 T
3
 (2) 
3
 T
2
 (3) 3 T
2
 (4) 
3
 T
 
Page 5


SECTION - A 
1.  The magnetic moments associated with two closely wound circular coils A and B of radius r
A
= 10 cm 
and r
B
= 20 cm respectively are equal if : (Where N
A
, I
A
 and N
B
, I
B
 are number of turn and current of 
A and B respectively) 
 (1) 4 N
A
I
A
= N
B
I
B
 (2) N
A
= 2 N
B
 (3) N
A
I
A
= 4 N
B
I
B
 (4) 2 N
A
I
A
= N
B
I
B
 
Sol. (3) 
  Magnetic moment m = IAN 
 Magnetic moment of coil A ? 
  
  
 Magnetic moment of coil B ? 
  
  
 Now  
  
 
 
2.  The figure represents the momentum time (p-t) curve for a particle moving along an axis under the 
influence of the force. Identify the regions on the graph where the magnitude of the force is maximum 
and minimum respectively ? 
 If (?? 3
- ?? 2
) < ?? 1
 
 
 (1) c and b (2) b and c (3) ?? and ?? (4) c and a 
Sol. (1) 
 Slope of curve P-t will represent the force so 
  
 Maximum slope ? (c)  
 Minimum slope ? ?(b) 
 
3.  Two isolated metallic solid spheres of radii ?? and 2R are charged such that both have same charge 
density ?? . The spheres are then connected by a thin conducting wire. If the new charge density of the 
bigger sphere is ?? '
. The ratio 
?? '
?? is : 
 (1)  (2)  (3)  (4)  
 
4
9
6
5
3
5
3
4
??   F slope
dt
dP
A A B B
I . N (100) I N 400 ? ? ? 
  
A A B B
I N 4I N ? 
mm ? 
AB
B B B
m I N (20) ??  …(2) 
2
B B B B
m I N r ?? 
2
A A A
m I N (10) ??  ...(1) 
2
A A A A
m I r N ?? 
2
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 30th January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
Sol. (3) 
 
 
R 
Q 1= ?4 ?R
2
 
2R Q 2 = ?4 ? ? ?R)
2
 
Q 2 = ? ? ? ?R
2
 
 
 Now 
 
 
1
1
Q 
1
2
Q 
 
 Charge will flow until voltage of both sphere become equal so 
  
0
c 4 R ? ?? 
  
11
12
vv ? 
  
12
12
QQ
cc
?
   
?
  
12
00
Q ' Q '
4 R 4 (2R)
?
? ? ? ?
 
 
?
  
12
2Q ' Q ' ?        …(1) 
  
1 2 1 2
Q Q Q ' Q ' ? ? ? 
  
2 2
22
Q' 3
20 R Q ' Q '
22
? ? ? ? ? 
?
  
2
2
40 R
Q'
3
??
?  …(2) 
 
2
2
40 R
Q'
3
??
? 
 Now   
2
2
40 R
'4 (2R)
3
??
? ? ? 
  
2
2
40 R
'16 R
3
??
? ? ? 
  
' 40 1 5
3 16 6
?
? ? ?
?
   
 
 
4.  A person has been using spectacles of power -1.0 dioptre for distant vision and a separate reading 
glass of power 2.0 dioptres. What is the least distance of distinct vision for this person : 
 (1) 40 cm (2) 30 cm (3) 10 cm (4) 50 cm 
Sol. (4) 
Power convex lens = 2.0 D 
 Power of concave lens = –1.0 D 
 
 
Obj Image 
  x 
25 cm 
 
 x ? least distance of distinct vision 
 
1
f 100 50cm
2
? ? ? 
  
1 1 1
f v u
?? 
  
1 1 1
50 ( x) 25
??
??
  
?
 
1 1 1
50 25 ( x)
??
?
 
 
?
 
1 2 1
50 x
??
? 
 
?
 x 50cm ? 
 
 
5. A small object at rest, absorbs a light pulse of power 20 mW and duration 300 ns. Assuming speed 
 of light as 3 × 10
8
 m/s, the momentum of the object becomes equal to : 
 (1) 3 × 10
– 17
 kg m/s (2) 2 × 10
– 17
 kg m/s (3) 1 × 10
– 17
 kg m/s (4) 0.5 × 10
– 17
 kg m/s 
Sol. (2) 
Power = 20 mw 
 t = 300 nsec 
 energy absorbed 
93
300 10 20 10
??
? ? ? ? 
3 12 9
6 10 10 6 10 J
??
? ? ? ? ? 
 
light 
 
 Pressure = 
Intensity Power
=
C Area×C
 
 Pressure × Area = 
Power
C
 
 Force = 
3
8
Power 20 10
C 3 10
?
?
?
?
 
 
11
20
F 10 N
3
?
?? 
 F t P ? ? ? (momentum) 
 
11 9
fi
20
10 300 10 P P
3
??
? ? ? ? ? 
 
20
f
20 10 100 P
?
? ? ? 
 
17
f
2 10 P
?
?? 
  
 
 
 
 
 
 
6.  Match Column-I with Column-II : 
  
 Choose the correct answer from the options given below:  
 (1) A- I, B-II, C-III, D-IV 
 (2) A- II, B-III, C-IV, D-I 
 (3) A- I, B-III, C-IV, D-II 
 (4) A- II, B-IV, C-III, D-I 
Sol. (4) 
 (A) 
2
xt ? 
  
dx
2t
dt
?
?
  Vt ?  A
?
II 
 (B) 
t
0
x x e
??
? 
  
tt
00
dx
x e ( ) (x e )
dt
? ? ? ?
? ? ? ? ? ? 
  
t
0
V x e
??
? ? ?   B
?
IV 
 (C) 
xt ?
 
?
 V const ? 
  xt ??  
?
  V const ?? C
?
III 
 (D)  xt ? 
?
 V const ?  D
?
I 
 
7. The pressure (P) and temperature (T) relationship of an ideal gas obeys the equation PT
2
= constant. 
The volume expansion coefficient of the gas will be : 
 (1) 
3
 T
3
 (2) 
3
 T
2
 (3) 3 T
2
 (4) 
3
 T
 
Sol. (4) 
 
2
PT const. ? 
 dV V dT ?? 
 
1 dV
V dT
??  …(1) 
 Using PV = nRT and PT
2
 = cont. 
 
2
nRT
.T const
V
? 
 
3
VT ? 
?
  
3
V KT ?  …(2) 
 Now put in (1) 
 
2
3
13
3KT
KT T
? ? ? ?    
?
  
3
T
?? 
 
8.  Heat is given to an ideal gas in an isothermal process.  
 A. Internal energy of the gas will decrease. 
 B. Internal energy of the gas will increase. 
 C. Internal energy of the gas will not change. 
 D. The gas will do positive work. 
 E. The gas will do negative work. 
 Choose the correct answer from the options given below : 
 (1) C and D only (2) C and E only (3) A and E only (4) B and D only 
Sol. (1) 
In isothermal process 
  T0 ?? 
 So  U0 ?? 
  QU ? ? ? ? ? 
  Q ? ? ?   
 So heat will be used to do positive work 
 
 
9. If the gravitational field in the space is given as (-
K
r
2
). Taking the reference point to be at r = 2 cm 
with gravitational potential V = 10 J/kg. Find the gravitational potential at r = 3 cm in SI unit (Given, 
that K = 6Jcm/kg ) 
 (1) 9 (2) 10 (3) 11 (4) 12 
Sol. (3) 
3
2
V E.dr ? ? ?
?
 
 
3
2
2
K
V(3) V(2) .dr
r
?
? ? ?
?
 
 
3
2
1
V(3) 10 K
r
??
? ? ?
??
??
 
 
11
V(3) 10 6
32
??
? ? ? ?
??
??
 
 
23
V 10 6 1
6
? ??
? ? ? ?
??
??
 
 V 11 ?