JEE Main 2023 January 30 Shift 2 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


SECTION - A 
1. A current carrying rectangular loop ???????? is made of uniform wire. The length ???? = ???? = 5 cm and 
= ???? = 100 cm. If ammeter current reading changes from ?? to 2?? , the ratio of magnetic forces per unit 
length on the wire ???? due to wire ???? in the two cases respectively (?? ????
?? : ?? ????
2?? ) is: 
 
 (1) 1: 2 (2) 1: 3 (3) 1: 4 (4) 1: 5 
Sol. (3) 
 Ans. (3) 
 
2. The output Y for the inputs A and B of circuit is given by 
 
 Truth table of the shown circuit is: 
 (1)    (2) 
 
 (3)   (4) 
 
Sol.  (3) 
  
  
? 
F 1
F4
2I
1
 
12
F I I ? 
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 30th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
Page 2


SECTION - A 
1. A current carrying rectangular loop ???????? is made of uniform wire. The length ???? = ???? = 5 cm and 
= ???? = 100 cm. If ammeter current reading changes from ?? to 2?? , the ratio of magnetic forces per unit 
length on the wire ???? due to wire ???? in the two cases respectively (?? ????
?? : ?? ????
2?? ) is: 
 
 (1) 1: 2 (2) 1: 3 (3) 1: 4 (4) 1: 5 
Sol. (3) 
 Ans. (3) 
 
2. The output Y for the inputs A and B of circuit is given by 
 
 Truth table of the shown circuit is: 
 (1)    (2) 
 
 (3)   (4) 
 
Sol.  (3) 
  
  
? 
F 1
F4
2I
1
 
12
F I I ? 
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 30th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
 
3. Given below are two statements: one is labelled as Assertion ?? and the other is labelled as Reason R 
 Assertion A: Efficiency of a reversible heat engine will be highest at -273
°
C temperature of cold 
reservoir. 
 Reason R: The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it 
depends on the temperature of hot reservoir too and is given as ?? = (1 -
?? 2
?? 1
). 
 In the light of the above statements, choose the correct answer from the options given below  
 (1) Both ?? and ?? are true but ?? is NOT the correct explanation of ?? 
 (2) Both ?? and ?? are true and ?? is the correct explanation of ?? 
 (3) A is false but ?? is true 
 (4)  A is true but ?? is false 
Sol. (2) 
? ? = 1 – 
L
H
T
?
 = 
HL
H
T
T
??
 
 Efficiently of Carnot’s engine will be highest at – 273º = 0K 
 Ans. (2) 
 
 
4. As shown in the figure, a point charge ?? is placed at the centre of conducting spherical shell of inner radius 
?? and outer radius ?? . The electric field due to charge Q in three different regions I, II and III is given by: 
 (I: ?? < ?? , II: ?? < ?? < ?? , III: ?? > ?? ) 
 
 (1) ?? ?? = 0, ?? ????
= 0, ?? ??????
= 0 (2) ?? ?? = 0, ?? ????
= 0, ?? ??????
? 0 
 (3) ?? ?? ? 0, ?? ????
= 0, ?? ??????
? 0 (4) ?? ?? ? 0, ?? ????
= 0, ?? ??????
= 0 
Sol. Sol. (3) 
 Electric field inside material of conductor is zero 
 Ans. (3) 
 
  
Page 3


SECTION - A 
1. A current carrying rectangular loop ???????? is made of uniform wire. The length ???? = ???? = 5 cm and 
= ???? = 100 cm. If ammeter current reading changes from ?? to 2?? , the ratio of magnetic forces per unit 
length on the wire ???? due to wire ???? in the two cases respectively (?? ????
?? : ?? ????
2?? ) is: 
 
 (1) 1: 2 (2) 1: 3 (3) 1: 4 (4) 1: 5 
Sol. (3) 
 Ans. (3) 
 
2. The output Y for the inputs A and B of circuit is given by 
 
 Truth table of the shown circuit is: 
 (1)    (2) 
 
 (3)   (4) 
 
Sol.  (3) 
  
  
? 
F 1
F4
2I
1
 
12
F I I ? 
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 30th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
 
3. Given below are two statements: one is labelled as Assertion ?? and the other is labelled as Reason R 
 Assertion A: Efficiency of a reversible heat engine will be highest at -273
°
C temperature of cold 
reservoir. 
 Reason R: The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it 
depends on the temperature of hot reservoir too and is given as ?? = (1 -
?? 2
?? 1
). 
 In the light of the above statements, choose the correct answer from the options given below  
 (1) Both ?? and ?? are true but ?? is NOT the correct explanation of ?? 
 (2) Both ?? and ?? are true and ?? is the correct explanation of ?? 
 (3) A is false but ?? is true 
 (4)  A is true but ?? is false 
Sol. (2) 
? ? = 1 – 
L
H
T
?
 = 
HL
H
T
T
??
 
 Efficiently of Carnot’s engine will be highest at – 273º = 0K 
 Ans. (2) 
 
 
4. As shown in the figure, a point charge ?? is placed at the centre of conducting spherical shell of inner radius 
?? and outer radius ?? . The electric field due to charge Q in three different regions I, II and III is given by: 
 (I: ?? < ?? , II: ?? < ?? < ?? , III: ?? > ?? ) 
 
 (1) ?? ?? = 0, ?? ????
= 0, ?? ??????
= 0 (2) ?? ?? = 0, ?? ????
= 0, ?? ??????
? 0 
 (3) ?? ?? ? 0, ?? ????
= 0, ?? ??????
? 0 (4) ?? ?? ? 0, ?? ????
= 0, ?? ??????
= 0 
Sol. Sol. (3) 
 Electric field inside material of conductor is zero 
 Ans. (3) 
 
  
5. The equivalent resistance between ?? and ?? is 
 
 (1) 
1
3
O (2) 
1
2
O (3) 
3
2
O (4) 
2
3
O 
Sol. (4) 
 
 
 
 
eq
1 1 1 1 1 1
R 2 12 4 6 2
? ? ? ? ? 
 
8
12
?
?
3
2
? 
 R eq = 
2
3
 ? 
 Ans. (4) 
 
6. A vehicle travels 4 km with speed of 3 km/h and another 4 km with sped of 5 km/h, then its average 
speed is 
 (1) 3.50 km/h (2) 4.25 km/h (3) 4.00 km/h (4) 3.75 km/h 
Sol. (4) 
 
av
8
V 3 5 15
? ? ?
? ? ? 
 V av = 
5
4
?
 = 3.75 km hr
–1
 
 Ans. (4) 
 
  
Page 4


SECTION - A 
1. A current carrying rectangular loop ???????? is made of uniform wire. The length ???? = ???? = 5 cm and 
= ???? = 100 cm. If ammeter current reading changes from ?? to 2?? , the ratio of magnetic forces per unit 
length on the wire ???? due to wire ???? in the two cases respectively (?? ????
?? : ?? ????
2?? ) is: 
 
 (1) 1: 2 (2) 1: 3 (3) 1: 4 (4) 1: 5 
Sol. (3) 
 Ans. (3) 
 
2. The output Y for the inputs A and B of circuit is given by 
 
 Truth table of the shown circuit is: 
 (1)    (2) 
 
 (3)   (4) 
 
Sol.  (3) 
  
  
? 
F 1
F4
2I
1
 
12
F I I ? 
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 30th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
 
3. Given below are two statements: one is labelled as Assertion ?? and the other is labelled as Reason R 
 Assertion A: Efficiency of a reversible heat engine will be highest at -273
°
C temperature of cold 
reservoir. 
 Reason R: The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it 
depends on the temperature of hot reservoir too and is given as ?? = (1 -
?? 2
?? 1
). 
 In the light of the above statements, choose the correct answer from the options given below  
 (1) Both ?? and ?? are true but ?? is NOT the correct explanation of ?? 
 (2) Both ?? and ?? are true and ?? is the correct explanation of ?? 
 (3) A is false but ?? is true 
 (4)  A is true but ?? is false 
Sol. (2) 
? ? = 1 – 
L
H
T
?
 = 
HL
H
T
T
??
 
 Efficiently of Carnot’s engine will be highest at – 273º = 0K 
 Ans. (2) 
 
 
4. As shown in the figure, a point charge ?? is placed at the centre of conducting spherical shell of inner radius 
?? and outer radius ?? . The electric field due to charge Q in three different regions I, II and III is given by: 
 (I: ?? < ?? , II: ?? < ?? < ?? , III: ?? > ?? ) 
 
 (1) ?? ?? = 0, ?? ????
= 0, ?? ??????
= 0 (2) ?? ?? = 0, ?? ????
= 0, ?? ??????
? 0 
 (3) ?? ?? ? 0, ?? ????
= 0, ?? ??????
? 0 (4) ?? ?? ? 0, ?? ????
= 0, ?? ??????
= 0 
Sol. Sol. (3) 
 Electric field inside material of conductor is zero 
 Ans. (3) 
 
  
5. The equivalent resistance between ?? and ?? is 
 
 (1) 
1
3
O (2) 
1
2
O (3) 
3
2
O (4) 
2
3
O 
Sol. (4) 
 
 
 
 
eq
1 1 1 1 1 1
R 2 12 4 6 2
? ? ? ? ? 
 
8
12
?
?
3
2
? 
 R eq = 
2
3
 ? 
 Ans. (4) 
 
6. A vehicle travels 4 km with speed of 3 km/h and another 4 km with sped of 5 km/h, then its average 
speed is 
 (1) 3.50 km/h (2) 4.25 km/h (3) 4.00 km/h (4) 3.75 km/h 
Sol. (4) 
 
av
8
V 3 5 15
? ? ?
? ? ? 
 V av = 
5
4
?
 = 3.75 km hr
–1
 
 Ans. (4) 
 
  
7. In the given circuit, rms value of current (?? ?????? ) through the resistor ?? is: 
 
 (1)  2v2 A (2) 2 A (3) 20 A (4) 
1
2
 A 
Sol. (2) 
 Z = ? ?
2
2
Le
R X X ?? 
 Z = ? ? ? ?
22
100 200 100 ?? 
 Z = 100 2 ? 
 I rms = 
rms
V 00 2
Z 100 2
?
?  = 2 A 
 
8. A point source of 100 W emits light with 5% efficiency. At a distance of 5 m from the source, the 
intensity produced by the electric field component is: 
 (1) 
1
2?? ?? ?? 2
 (2) 
1
20?? ?? ?? 2
 (3) 
1
10?? ?? ?? 2
 (4) 
1
40?? ?? ?? 2
 
Sol. (4) 
 I EF = 
? ?
2
5
2
45
?
?
?
 
 =
40
?
?
w/m
2
 
 Ans: (4) 
 
9. A block of v3 kg is attached to a string whose other end is attached to the wall. An unknown force F is 
applied so that the string makes an angle of 30
°
 with the wall. The tension T is: (Given g = 10 ms
-2
 ) 
  
 (1) 20 N (2) 10 N (3) 15 N (4) 25 N 
  
Page 5


SECTION - A 
1. A current carrying rectangular loop ???????? is made of uniform wire. The length ???? = ???? = 5 cm and 
= ???? = 100 cm. If ammeter current reading changes from ?? to 2?? , the ratio of magnetic forces per unit 
length on the wire ???? due to wire ???? in the two cases respectively (?? ????
?? : ?? ????
2?? ) is: 
 
 (1) 1: 2 (2) 1: 3 (3) 1: 4 (4) 1: 5 
Sol. (3) 
 Ans. (3) 
 
2. The output Y for the inputs A and B of circuit is given by 
 
 Truth table of the shown circuit is: 
 (1)    (2) 
 
 (3)   (4) 
 
Sol.  (3) 
  
  
? 
F 1
F4
2I
1
 
12
F I I ? 
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 30th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
 
3. Given below are two statements: one is labelled as Assertion ?? and the other is labelled as Reason R 
 Assertion A: Efficiency of a reversible heat engine will be highest at -273
°
C temperature of cold 
reservoir. 
 Reason R: The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it 
depends on the temperature of hot reservoir too and is given as ?? = (1 -
?? 2
?? 1
). 
 In the light of the above statements, choose the correct answer from the options given below  
 (1) Both ?? and ?? are true but ?? is NOT the correct explanation of ?? 
 (2) Both ?? and ?? are true and ?? is the correct explanation of ?? 
 (3) A is false but ?? is true 
 (4)  A is true but ?? is false 
Sol. (2) 
? ? = 1 – 
L
H
T
?
 = 
HL
H
T
T
??
 
 Efficiently of Carnot’s engine will be highest at – 273º = 0K 
 Ans. (2) 
 
 
4. As shown in the figure, a point charge ?? is placed at the centre of conducting spherical shell of inner radius 
?? and outer radius ?? . The electric field due to charge Q in three different regions I, II and III is given by: 
 (I: ?? < ?? , II: ?? < ?? < ?? , III: ?? > ?? ) 
 
 (1) ?? ?? = 0, ?? ????
= 0, ?? ??????
= 0 (2) ?? ?? = 0, ?? ????
= 0, ?? ??????
? 0 
 (3) ?? ?? ? 0, ?? ????
= 0, ?? ??????
? 0 (4) ?? ?? ? 0, ?? ????
= 0, ?? ??????
= 0 
Sol. Sol. (3) 
 Electric field inside material of conductor is zero 
 Ans. (3) 
 
  
5. The equivalent resistance between ?? and ?? is 
 
 (1) 
1
3
O (2) 
1
2
O (3) 
3
2
O (4) 
2
3
O 
Sol. (4) 
 
 
 
 
eq
1 1 1 1 1 1
R 2 12 4 6 2
? ? ? ? ? 
 
8
12
?
?
3
2
? 
 R eq = 
2
3
 ? 
 Ans. (4) 
 
6. A vehicle travels 4 km with speed of 3 km/h and another 4 km with sped of 5 km/h, then its average 
speed is 
 (1) 3.50 km/h (2) 4.25 km/h (3) 4.00 km/h (4) 3.75 km/h 
Sol. (4) 
 
av
8
V 3 5 15
? ? ?
? ? ? 
 V av = 
5
4
?
 = 3.75 km hr
–1
 
 Ans. (4) 
 
  
7. In the given circuit, rms value of current (?? ?????? ) through the resistor ?? is: 
 
 (1)  2v2 A (2) 2 A (3) 20 A (4) 
1
2
 A 
Sol. (2) 
 Z = ? ?
2
2
Le
R X X ?? 
 Z = ? ? ? ?
22
100 200 100 ?? 
 Z = 100 2 ? 
 I rms = 
rms
V 00 2
Z 100 2
?
?  = 2 A 
 
8. A point source of 100 W emits light with 5% efficiency. At a distance of 5 m from the source, the 
intensity produced by the electric field component is: 
 (1) 
1
2?? ?? ?? 2
 (2) 
1
20?? ?? ?? 2
 (3) 
1
10?? ?? ?? 2
 (4) 
1
40?? ?? ?? 2
 
Sol. (4) 
 I EF = 
? ?
2
5
2
45
?
?
?
 
 =
40
?
?
w/m
2
 
 Ans: (4) 
 
9. A block of v3 kg is attached to a string whose other end is attached to the wall. An unknown force F is 
applied so that the string makes an angle of 30
°
 with the wall. The tension T is: (Given g = 10 ms
-2
 ) 
  
 (1) 20 N (2) 10 N (3) 15 N (4) 25 N 
  
Sol. (1) 
 
 
3 kg
 
 F = Tsin 30° 
 3g = T cos 30° 
 tan 30° = 
F
g
3
 
 
1F
3 3g
? 
 F = 10 N 
 T = 
F
sin30 ?
 = 10 × 2 
 T = 10 × 2 = 20 N 
  Ans: (1) 
 
10. Match List I with List II: 
  
 Choose the correct answer from the options given below: 
 (1)  A-IV, B-III, C-I, D-II  (2) A-I, B-II, C-III, D-IV 
 (3) A-IV, B-III, C-II, D-I (4) A-II, B-III, C-IV, D-I 
Sol. (3) 
 Theory 
 
11. An electron accelerated through a potential difference ?? 1
 has a de-Broglie wavelength of ?? . When the 
potential is changed to ?? 2
, its de-Broglie wavelength increases by 50%. The value of (
?? 1
?? 2
) is equal to 
 (1)  3 (2) 
3
2
 (3) 4 (4) 
9
4