JEE Main 2023 January 29 Shift 1 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


SECTION - A 
1.  Find the mutual inductance in the arrangement, when a small circular loop of wire of radius 
'?? ' is placed inside a large square loop of wire of side  (?? » ?? ). The loops are coplanar and their centers 
coincide : 
 
 (1) ?? =
v2?? 0
?? 2
??                      (2)?? =
2v2?? 0
?? ?? 2
                         (3) ?? =
v2?? 0
?? ?? 2
                 (4) ?? =
2v2?? 0
?? 2
?? 
Sol. (4) 
 
  
 B 1A 2 = MI 1 
    ….(1) 
 B 1 ? magnetic field due to square frame 
 A 2 ? ? Area of circle 
 I 1 ? ? current in square frame. 
 B 1 ?   
 B 1 = 4. B AB 
  
 
  
 
 
 
(1) 
(2) 
C D 
A 
B 
I L 
L 
 
??
?
??
??
?
? ? ?
L I L
??
2 2µ I 2 2µ R R
M
1
2 2
0 1 0
I
?  
B ·A
M
1
 
12
??
??
??
? ? ?
LL 22
?? µ I µ I 11
B 2 2 2 
0 1 0 1
1
?
??
??
??
?
??
??
2
L
24
µI
4 [sin 45º sin 45] = 
01
I
BA
M
1
 ?
12
21
MI   ??
 ?? MI  
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 29th January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
Page 2


SECTION - A 
1.  Find the mutual inductance in the arrangement, when a small circular loop of wire of radius 
'?? ' is placed inside a large square loop of wire of side  (?? » ?? ). The loops are coplanar and their centers 
coincide : 
 
 (1) ?? =
v2?? 0
?? 2
??                      (2)?? =
2v2?? 0
?? ?? 2
                         (3) ?? =
v2?? 0
?? ?? 2
                 (4) ?? =
2v2?? 0
?? 2
?? 
Sol. (4) 
 
  
 B 1A 2 = MI 1 
    ….(1) 
 B 1 ? magnetic field due to square frame 
 A 2 ? ? Area of circle 
 I 1 ? ? current in square frame. 
 B 1 ?   
 B 1 = 4. B AB 
  
 
  
 
 
 
(1) 
(2) 
C D 
A 
B 
I L 
L 
 
??
?
??
??
?
? ? ?
L I L
??
2 2µ I 2 2µ R R
M
1
2 2
0 1 0
I
?  
B ·A
M
1
 
12
??
??
??
? ? ?
LL 22
?? µ I µ I 11
B 2 2 2 
0 1 0 1
1
?
??
??
??
?
??
??
2
L
24
µI
4 [sin 45º sin 45] = 
01
I
BA
M
1
 ?
12
21
MI   ??
 ?? MI  
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 29th January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
2.  The threshold wavelength for photoelectric emission from a material is 5500A. Photoelectrons will be emitted, 
when this material is illuminated with monochromatic radiation from a  
 (A) 75 W infra –red lamp  (B) 10 W infra-red lamp 
 (C) 75 W ultra – violet lamp (D) 10 W ultra-violet lamp 
 Choose the correct answer from the options given below: 
 (1) B and C only  (2) A and D only   
 (3) C only  (4) C and D Only 
Sol. (4) 
 
00
12400
5500Å 2.25eV
5500
? ? ? ? ? ?  
 
19
3.6 10 J
?
? ? ?  
 
 
 
? P.E.E will occur if wavelength of incidence wave is less then threshold wavelength. So u. v. rays will be 
useful for emission.  
 So both U.V. rays lamps can be used. 
 
 
3.  Match List I with List II: 
 List I (Physical 
 Quantity) 
 
List II (Dimensional Formula) 
A. Pressure gradient I.  [M
0
 L
2
 T
-2
] 
B. Energy density II. [M
1
 L
-1
 T
-2
] 
C. Electric Field III. [M
1
 L
-2
 T
-2
] 
D. Latent heat IV. [M
1
 L
1
 T
-3
 A
-1
] 
 Choose the correct answer from the options given below: 
 (1) A-II, B – III, C-I, D-IV (2) A-II, B – III, C-IV, D-I 
 (3) A-III, B – II, C-IV, D-I (4) A-III, B – II, C-I, D-IV 
Sol. (3) 
 (A) Pressure gradient = 
Pressure Force
Length Area length
?
?
  
 = 
2
22
2
MLT
[ML T ]
L ·L
?
??
?  
 (B) Energy density = 
22
12
3
Energy ML T
[M L T ]
Volume L
?
??
??  
 (C) Electric field = 
2
31
Force MLT
[M LT A ]
Ch arg e AT
?
??
??  
 (D) Latent heat = 
22
22
Heat ML T
[L T ]
Mass M
?
?
??  
 Ans : A-III, B-II, C-IV, D-I 
 Ans. : (3) 
Page 3


SECTION - A 
1.  Find the mutual inductance in the arrangement, when a small circular loop of wire of radius 
'?? ' is placed inside a large square loop of wire of side  (?? » ?? ). The loops are coplanar and their centers 
coincide : 
 
 (1) ?? =
v2?? 0
?? 2
??                      (2)?? =
2v2?? 0
?? ?? 2
                         (3) ?? =
v2?? 0
?? ?? 2
                 (4) ?? =
2v2?? 0
?? 2
?? 
Sol. (4) 
 
  
 B 1A 2 = MI 1 
    ….(1) 
 B 1 ? magnetic field due to square frame 
 A 2 ? ? Area of circle 
 I 1 ? ? current in square frame. 
 B 1 ?   
 B 1 = 4. B AB 
  
 
  
 
 
 
(1) 
(2) 
C D 
A 
B 
I L 
L 
 
??
?
??
??
?
? ? ?
L I L
??
2 2µ I 2 2µ R R
M
1
2 2
0 1 0
I
?  
B ·A
M
1
 
12
??
??
??
? ? ?
LL 22
?? µ I µ I 11
B 2 2 2 
0 1 0 1
1
?
??
??
??
?
??
??
2
L
24
µI
4 [sin 45º sin 45] = 
01
I
BA
M
1
 ?
12
21
MI   ??
 ?? MI  
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 29th January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
2.  The threshold wavelength for photoelectric emission from a material is 5500A. Photoelectrons will be emitted, 
when this material is illuminated with monochromatic radiation from a  
 (A) 75 W infra –red lamp  (B) 10 W infra-red lamp 
 (C) 75 W ultra – violet lamp (D) 10 W ultra-violet lamp 
 Choose the correct answer from the options given below: 
 (1) B and C only  (2) A and D only   
 (3) C only  (4) C and D Only 
Sol. (4) 
 
00
12400
5500Å 2.25eV
5500
? ? ? ? ? ?  
 
19
3.6 10 J
?
? ? ?  
 
 
 
? P.E.E will occur if wavelength of incidence wave is less then threshold wavelength. So u. v. rays will be 
useful for emission.  
 So both U.V. rays lamps can be used. 
 
 
3.  Match List I with List II: 
 List I (Physical 
 Quantity) 
 
List II (Dimensional Formula) 
A. Pressure gradient I.  [M
0
 L
2
 T
-2
] 
B. Energy density II. [M
1
 L
-1
 T
-2
] 
C. Electric Field III. [M
1
 L
-2
 T
-2
] 
D. Latent heat IV. [M
1
 L
1
 T
-3
 A
-1
] 
 Choose the correct answer from the options given below: 
 (1) A-II, B – III, C-I, D-IV (2) A-II, B – III, C-IV, D-I 
 (3) A-III, B – II, C-IV, D-I (4) A-III, B – II, C-I, D-IV 
Sol. (3) 
 (A) Pressure gradient = 
Pressure Force
Length Area length
?
?
  
 = 
2
22
2
MLT
[ML T ]
L ·L
?
??
?  
 (B) Energy density = 
22
12
3
Energy ML T
[M L T ]
Volume L
?
??
??  
 (C) Electric field = 
2
31
Force MLT
[M LT A ]
Ch arg e AT
?
??
??  
 (D) Latent heat = 
22
22
Heat ML T
[L T ]
Mass M
?
?
??  
 Ans : A-III, B-II, C-IV, D-I 
 Ans. : (3) 
 
4.  In a cuboid of dimension 2L × 2L × L, a charge q is placed at the center of the surface ' S ' having area of 4L
2
. 
The flux through the opposite surface to ' S ' is given by 
 (1) 
0
q
12 ?
 (2) 
0
q
6 ?
 (3) 
0
q
3 ?
 (4) 
0
q
2 ?
  
Sol. (2) 
 
 
 
 When smaller box is considered on the given box then charge ‘q’ will be at center.  
 So flux from surface  S’ = 
00
q 1 q
·
66
??
?
??
??
??
 
 
 
 
 Ans : (2) 
 
5. A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of 
30 m/s. If both trains emit sounds with frequency 300 Hz, (Speed of sound:
330 m
s
) approximate difference of 
frequencies heard by the person will be: 
 (1) 55 Hz (2) 80 Hz (3) 33 Hz  (4) 10 Hz 
Sol. (1) 
 A 30m / s ? ,                     Observer                      B 30m / s ? 
 f 0 = 300 Hz 
 V = 330 m/sec. 
 f A = 
0
A
V 330
f 300 330Hz
V V 330 30
??
??
??
??
??
??
??
??
  
 
B0
A
V 330
f f 300 275Hz
V V 360
??
??
? ? ?
??
??
?
??
??
  
 
AB
f f f 330 275 55Hz ? ? ? ? ? ?  
 Ans. : (1) 
 
 
 
 
Page 4


SECTION - A 
1.  Find the mutual inductance in the arrangement, when a small circular loop of wire of radius 
'?? ' is placed inside a large square loop of wire of side  (?? » ?? ). The loops are coplanar and their centers 
coincide : 
 
 (1) ?? =
v2?? 0
?? 2
??                      (2)?? =
2v2?? 0
?? ?? 2
                         (3) ?? =
v2?? 0
?? ?? 2
                 (4) ?? =
2v2?? 0
?? 2
?? 
Sol. (4) 
 
  
 B 1A 2 = MI 1 
    ….(1) 
 B 1 ? magnetic field due to square frame 
 A 2 ? ? Area of circle 
 I 1 ? ? current in square frame. 
 B 1 ?   
 B 1 = 4. B AB 
  
 
  
 
 
 
(1) 
(2) 
C D 
A 
B 
I L 
L 
 
??
?
??
??
?
? ? ?
L I L
??
2 2µ I 2 2µ R R
M
1
2 2
0 1 0
I
?  
B ·A
M
1
 
12
??
??
??
? ? ?
LL 22
?? µ I µ I 11
B 2 2 2 
0 1 0 1
1
?
??
??
??
?
??
??
2
L
24
µI
4 [sin 45º sin 45] = 
01
I
BA
M
1
 ?
12
21
MI   ??
 ?? MI  
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 29th January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
2.  The threshold wavelength for photoelectric emission from a material is 5500A. Photoelectrons will be emitted, 
when this material is illuminated with monochromatic radiation from a  
 (A) 75 W infra –red lamp  (B) 10 W infra-red lamp 
 (C) 75 W ultra – violet lamp (D) 10 W ultra-violet lamp 
 Choose the correct answer from the options given below: 
 (1) B and C only  (2) A and D only   
 (3) C only  (4) C and D Only 
Sol. (4) 
 
00
12400
5500Å 2.25eV
5500
? ? ? ? ? ?  
 
19
3.6 10 J
?
? ? ?  
 
 
 
? P.E.E will occur if wavelength of incidence wave is less then threshold wavelength. So u. v. rays will be 
useful for emission.  
 So both U.V. rays lamps can be used. 
 
 
3.  Match List I with List II: 
 List I (Physical 
 Quantity) 
 
List II (Dimensional Formula) 
A. Pressure gradient I.  [M
0
 L
2
 T
-2
] 
B. Energy density II. [M
1
 L
-1
 T
-2
] 
C. Electric Field III. [M
1
 L
-2
 T
-2
] 
D. Latent heat IV. [M
1
 L
1
 T
-3
 A
-1
] 
 Choose the correct answer from the options given below: 
 (1) A-II, B – III, C-I, D-IV (2) A-II, B – III, C-IV, D-I 
 (3) A-III, B – II, C-IV, D-I (4) A-III, B – II, C-I, D-IV 
Sol. (3) 
 (A) Pressure gradient = 
Pressure Force
Length Area length
?
?
  
 = 
2
22
2
MLT
[ML T ]
L ·L
?
??
?  
 (B) Energy density = 
22
12
3
Energy ML T
[M L T ]
Volume L
?
??
??  
 (C) Electric field = 
2
31
Force MLT
[M LT A ]
Ch arg e AT
?
??
??  
 (D) Latent heat = 
22
22
Heat ML T
[L T ]
Mass M
?
?
??  
 Ans : A-III, B-II, C-IV, D-I 
 Ans. : (3) 
 
4.  In a cuboid of dimension 2L × 2L × L, a charge q is placed at the center of the surface ' S ' having area of 4L
2
. 
The flux through the opposite surface to ' S ' is given by 
 (1) 
0
q
12 ?
 (2) 
0
q
6 ?
 (3) 
0
q
3 ?
 (4) 
0
q
2 ?
  
Sol. (2) 
 
 
 
 When smaller box is considered on the given box then charge ‘q’ will be at center.  
 So flux from surface  S’ = 
00
q 1 q
·
66
??
?
??
??
??
 
 
 
 
 Ans : (2) 
 
5. A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of 
30 m/s. If both trains emit sounds with frequency 300 Hz, (Speed of sound:
330 m
s
) approximate difference of 
frequencies heard by the person will be: 
 (1) 55 Hz (2) 80 Hz (3) 33 Hz  (4) 10 Hz 
Sol. (1) 
 A 30m / s ? ,                     Observer                      B 30m / s ? 
 f 0 = 300 Hz 
 V = 330 m/sec. 
 f A = 
0
A
V 330
f 300 330Hz
V V 330 30
??
??
??
??
??
??
??
??
  
 
B0
A
V 330
f f 300 275Hz
V V 360
??
??
? ? ?
??
??
?
??
??
  
 
AB
f f f 330 275 55Hz ? ? ? ? ? ?  
 Ans. : (1) 
 
 
 
 
 
6.  A block of mass ?? slides down the plane inclined at angle 30
°
 with an acceleration 
?? 4
. The value of 
coefficient of kinetic friction will be: 
 (1) 
1
23
 (2) 
3
2
 (3) 
2 3 1
2
?
 (4) 
2 3 1
2
?
 
Sol. (1) 
 
k
f µN ?  
 N = mg cos ? ?
 f k = µ mg cos ? 
 
mgsin µmg cos
a
m
? ? ?
?  
 a = g sin 30º – µg cos 30º 
 
g 1 3µ
g
4 2 2
??
??
??
??
  
 
1
1 3µ
2
??  
 
1
3µ
2
?  
 
1
µ
23
? 
 Ans. : 1 
 
7.  A bicycle tyre is filled with air having pressure of 270 kPa at 27°C. The approximate pressure of the air in the 
tyre when the temperature increases to 36° C is  
 (1) 270 kPa (2) 262 kPa (3) 360 kPa (4) 278 kPa  
Sol. (4)  
 PV = nRT 
 n ? const.  V = const. 
 P ? T,  
 P 1 = 270 kpa,  
 T 1 = 27ºC = 300 K 
 P 2 = ?,   
 T 2 = 36º = 36 + 273 = 309 K 
 
22
11
PT
PT
?   …(1) 
 
2
P 309
270 KPa 300
?  
 
2
103
P 270KPa 278KPa
100
??  
 Option : (4) 
 
 
 
 
 
Page 5


SECTION - A 
1.  Find the mutual inductance in the arrangement, when a small circular loop of wire of radius 
'?? ' is placed inside a large square loop of wire of side  (?? » ?? ). The loops are coplanar and their centers 
coincide : 
 
 (1) ?? =
v2?? 0
?? 2
??                      (2)?? =
2v2?? 0
?? ?? 2
                         (3) ?? =
v2?? 0
?? ?? 2
                 (4) ?? =
2v2?? 0
?? 2
?? 
Sol. (4) 
 
  
 B 1A 2 = MI 1 
    ….(1) 
 B 1 ? magnetic field due to square frame 
 A 2 ? ? Area of circle 
 I 1 ? ? current in square frame. 
 B 1 ?   
 B 1 = 4. B AB 
  
 
  
 
 
 
(1) 
(2) 
C D 
A 
B 
I L 
L 
 
??
?
??
??
?
? ? ?
L I L
??
2 2µ I 2 2µ R R
M
1
2 2
0 1 0
I
?  
B ·A
M
1
 
12
??
??
??
? ? ?
LL 22
?? µ I µ I 11
B 2 2 2 
0 1 0 1
1
?
??
??
??
?
??
??
2
L
24
µI
4 [sin 45º sin 45] = 
01
I
BA
M
1
 ?
12
21
MI   ??
 ?? MI  
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 29th January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
2.  The threshold wavelength for photoelectric emission from a material is 5500A. Photoelectrons will be emitted, 
when this material is illuminated with monochromatic radiation from a  
 (A) 75 W infra –red lamp  (B) 10 W infra-red lamp 
 (C) 75 W ultra – violet lamp (D) 10 W ultra-violet lamp 
 Choose the correct answer from the options given below: 
 (1) B and C only  (2) A and D only   
 (3) C only  (4) C and D Only 
Sol. (4) 
 
00
12400
5500Å 2.25eV
5500
? ? ? ? ? ?  
 
19
3.6 10 J
?
? ? ?  
 
 
 
? P.E.E will occur if wavelength of incidence wave is less then threshold wavelength. So u. v. rays will be 
useful for emission.  
 So both U.V. rays lamps can be used. 
 
 
3.  Match List I with List II: 
 List I (Physical 
 Quantity) 
 
List II (Dimensional Formula) 
A. Pressure gradient I.  [M
0
 L
2
 T
-2
] 
B. Energy density II. [M
1
 L
-1
 T
-2
] 
C. Electric Field III. [M
1
 L
-2
 T
-2
] 
D. Latent heat IV. [M
1
 L
1
 T
-3
 A
-1
] 
 Choose the correct answer from the options given below: 
 (1) A-II, B – III, C-I, D-IV (2) A-II, B – III, C-IV, D-I 
 (3) A-III, B – II, C-IV, D-I (4) A-III, B – II, C-I, D-IV 
Sol. (3) 
 (A) Pressure gradient = 
Pressure Force
Length Area length
?
?
  
 = 
2
22
2
MLT
[ML T ]
L ·L
?
??
?  
 (B) Energy density = 
22
12
3
Energy ML T
[M L T ]
Volume L
?
??
??  
 (C) Electric field = 
2
31
Force MLT
[M LT A ]
Ch arg e AT
?
??
??  
 (D) Latent heat = 
22
22
Heat ML T
[L T ]
Mass M
?
?
??  
 Ans : A-III, B-II, C-IV, D-I 
 Ans. : (3) 
 
4.  In a cuboid of dimension 2L × 2L × L, a charge q is placed at the center of the surface ' S ' having area of 4L
2
. 
The flux through the opposite surface to ' S ' is given by 
 (1) 
0
q
12 ?
 (2) 
0
q
6 ?
 (3) 
0
q
3 ?
 (4) 
0
q
2 ?
  
Sol. (2) 
 
 
 
 When smaller box is considered on the given box then charge ‘q’ will be at center.  
 So flux from surface  S’ = 
00
q 1 q
·
66
??
?
??
??
??
 
 
 
 
 Ans : (2) 
 
5. A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of 
30 m/s. If both trains emit sounds with frequency 300 Hz, (Speed of sound:
330 m
s
) approximate difference of 
frequencies heard by the person will be: 
 (1) 55 Hz (2) 80 Hz (3) 33 Hz  (4) 10 Hz 
Sol. (1) 
 A 30m / s ? ,                     Observer                      B 30m / s ? 
 f 0 = 300 Hz 
 V = 330 m/sec. 
 f A = 
0
A
V 330
f 300 330Hz
V V 330 30
??
??
??
??
??
??
??
??
  
 
B0
A
V 330
f f 300 275Hz
V V 360
??
??
? ? ?
??
??
?
??
??
  
 
AB
f f f 330 275 55Hz ? ? ? ? ? ?  
 Ans. : (1) 
 
 
 
 
 
6.  A block of mass ?? slides down the plane inclined at angle 30
°
 with an acceleration 
?? 4
. The value of 
coefficient of kinetic friction will be: 
 (1) 
1
23
 (2) 
3
2
 (3) 
2 3 1
2
?
 (4) 
2 3 1
2
?
 
Sol. (1) 
 
k
f µN ?  
 N = mg cos ? ?
 f k = µ mg cos ? 
 
mgsin µmg cos
a
m
? ? ?
?  
 a = g sin 30º – µg cos 30º 
 
g 1 3µ
g
4 2 2
??
??
??
??
  
 
1
1 3µ
2
??  
 
1
3µ
2
?  
 
1
µ
23
? 
 Ans. : 1 
 
7.  A bicycle tyre is filled with air having pressure of 270 kPa at 27°C. The approximate pressure of the air in the 
tyre when the temperature increases to 36° C is  
 (1) 270 kPa (2) 262 kPa (3) 360 kPa (4) 278 kPa  
Sol. (4)  
 PV = nRT 
 n ? const.  V = const. 
 P ? T,  
 P 1 = 270 kpa,  
 T 1 = 27ºC = 300 K 
 P 2 = ?,   
 T 2 = 36º = 36 + 273 = 309 K 
 
22
11
PT
PT
?   …(1) 
 
2
P 309
270 KPa 300
?  
 
2
103
P 270KPa 278KPa
100
??  
 Option : (4) 
 
 
 
 
 
8. A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve 
z direction and lying in ???? plane is shown in figure. The plot of ??ˆ component of magnetic field (By) 
 at a distance ' ?? ' (less than radius of the coil) and on ???? plane vs ?? coordinate looks like 
 
  (1)  (2)    
 (3)     (4)   
Sol. (1) 
 Theory based concept 
 
 
 
9. Surface tension of a soap bubble is 2.0 × 10
–2
 Nm
–1
. Work done to increase the radius of soap bubble from 3.5 
cm to 7 cm will be: 
 Take 
22
7
??
??
??
??
 
 (1) 9.24 × 10
–4
 J (2) 5.76 × 10
–4
 J (3) 0.72 × 10
–4
 J (4) 18.48 × 10
–4
 J 
Sol. (4) 
 T = 2.0 × 10
–2
 Nm
–1
 
 r 1 = 3.5 cm,  r 2 = 7 cm 
? W = T ?A × No. of air – liquid surface  
 
? ?
22
21
W 2T.4 r r ? ? ?  
 
24
49
W 2 2 10 4 49 10
4
??
??
? ? ? ? ? ? ?
??
??
  
 
6
3
W 16 10 49
4
?
? ? ? ? ?  
? W = 1847.26 × 10
–6
 
? W = 18.47 × 10
–4
 J