JEE Main 2023 January 31 Shift 1 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


SECTION - A 
1. The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude 
of oscillation. At ?? / 2, the kinetic energy of the block is : 
 (1) 18 . 75 J (2) 9 . 75 J (3) 37 . 5 J (4) 12 . 5 J 
Sol. (1) 
 
2. The drift velocity of electrons for a conductor connected in an electrical circuit is V
d
. The conductor in 
now replaced by another conductor with same material and same length but double the area of cross 
section. The applied voltage remains same. The new drift velocity of electrons will be 
 (1) V
d
 (2) 
V
d
4
 (3) 2 V
d
 (4) 
V
d
2
 
Sol. (1) 
 
 
3. The initial speed of a projectile fired from ground is ?? . At the highest point during its motion, the 
speed of projectile is 
v 3
2
?? . The time of flight of the projectile is : 
 (1) 
2u
g
 (2) 
u
2 g
 (3) 
v 3 ?? ?? (4) 
u
g
 
Sol. (4) 
At highest point - 
 
gg
uu
T??
2 sin
?? 30 
?
u
u cos
2
??
3
I
?
d
V
A
II 
?
d
AneV I 
AA 
? 2
2 ?
A
II 
l
VR
??
??
??
?? ?
4
? ? ? k 
3
25 18.75J
?A km
??
??
??
24
?? 11
1
22
?? k U E 
A
Um ? 
??
??
?
22
??
2
2
1
A
U PE m?x 
22
??
22
1
at ,
2
? ? ?   Total Energy in SHM,
22
1
E m A 25J
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 31st January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
Page 2


SECTION - A 
1. The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude 
of oscillation. At ?? / 2, the kinetic energy of the block is : 
 (1) 18 . 75 J (2) 9 . 75 J (3) 37 . 5 J (4) 12 . 5 J 
Sol. (1) 
 
2. The drift velocity of electrons for a conductor connected in an electrical circuit is V
d
. The conductor in 
now replaced by another conductor with same material and same length but double the area of cross 
section. The applied voltage remains same. The new drift velocity of electrons will be 
 (1) V
d
 (2) 
V
d
4
 (3) 2 V
d
 (4) 
V
d
2
 
Sol. (1) 
 
 
3. The initial speed of a projectile fired from ground is ?? . At the highest point during its motion, the 
speed of projectile is 
v 3
2
?? . The time of flight of the projectile is : 
 (1) 
2u
g
 (2) 
u
2 g
 (3) 
v 3 ?? ?? (4) 
u
g
 
Sol. (4) 
At highest point - 
 
gg
uu
T??
2 sin
?? 30 
?
u
u cos
2
??
3
I
?
d
V
A
II 
?
d
AneV I 
AA 
? 2
2 ?
A
II 
l
VR
??
??
??
?? ?
4
? ? ? k 
3
25 18.75J
?A km
??
??
??
24
?? 11
1
22
?? k U E 
A
Um ? 
??
??
?
22
??
2
2
1
A
U PE m?x 
22
??
22
1
at ,
2
? ? ?   Total Energy in SHM,
22
1
E m A 25J
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 31st January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
4. The correct relation between ?? =
?? ?? ?? ?? and temperature ?? is : 
 (1) ???? ?? 0
 (2) ???? T (3) ????
1
v T
 (4) ????
1
 T
 
Sol. (1) 
 
p
v
C
,
C
?? Independent on T  
 
5. The effect of increase in temperature on the number of electrons in conduction band ( n
e
) and 
resistance of a semiconductor will be as: 
 (1) Both n
e
 and resistance increase (2) Both n
e
 and resistance decrease 
 (3) n
e
 decreases, resistance increases (4) n
e
 increases, resistance decreases 
Sol. (4) 
In semi conductors, 
e
T ,n ? in Conduction Band increases 
T ,R ??  
 
6. The amplitude of 15s i n ? ( 100 0 ???? ) is modulated by 10s i n ? ( 4 ???? ) signal. The amplitude modulated signal 
contains frequency (ies) of 
 A. 500 Hz B. 2 Hz C. 250 Hz D. 498 Hz E. 502 Hz 
 Choose the correct answer from the options given below: 
 (1) A Only (2) B Only (3) A and ?? Only (4) A, D and E Only 
Sol. (4) 
1000
500Hz
2
??
c
p
f
p
 
4
2Hz
2
??
m
p
f
p
 
Upper side Band, 
cm
USB f f ??  
     ? USB 502HZ 
Lower side Band, 
498Hz
??
?
cm
LSB f f
LSB
  
 
7. Two polaroide A and B are placed in such a way that the pass-axis of polaroids are perpendicular to 
each other. Now, another polaroid ?? is placed between ?? and ?? bisecting angle between them. If 
intensity of unpolarized light is I
0
 then intensity of transmitted light after passing through polaroid B 
will be: 
 (1) 
?? 0
4
 (2) 
?? 0
2
 (3) Zero (4) 
?? 0
8
 
Sol. (4) 
After A, ?
2
I
I  
After C, ??
200
cos 45
24
II
I  
After B, ??
200
cos 45
48
II
I  
Page 3


SECTION - A 
1. The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude 
of oscillation. At ?? / 2, the kinetic energy of the block is : 
 (1) 18 . 75 J (2) 9 . 75 J (3) 37 . 5 J (4) 12 . 5 J 
Sol. (1) 
 
2. The drift velocity of electrons for a conductor connected in an electrical circuit is V
d
. The conductor in 
now replaced by another conductor with same material and same length but double the area of cross 
section. The applied voltage remains same. The new drift velocity of electrons will be 
 (1) V
d
 (2) 
V
d
4
 (3) 2 V
d
 (4) 
V
d
2
 
Sol. (1) 
 
 
3. The initial speed of a projectile fired from ground is ?? . At the highest point during its motion, the 
speed of projectile is 
v 3
2
?? . The time of flight of the projectile is : 
 (1) 
2u
g
 (2) 
u
2 g
 (3) 
v 3 ?? ?? (4) 
u
g
 
Sol. (4) 
At highest point - 
 
gg
uu
T??
2 sin
?? 30 
?
u
u cos
2
??
3
I
?
d
V
A
II 
?
d
AneV I 
AA 
? 2
2 ?
A
II 
l
VR
??
??
??
?? ?
4
? ? ? k 
3
25 18.75J
?A km
??
??
??
24
?? 11
1
22
?? k U E 
A
Um ? 
??
??
?
22
??
2
2
1
A
U PE m?x 
22
??
22
1
at ,
2
? ? ?   Total Energy in SHM,
22
1
E m A 25J
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 31st January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
4. The correct relation between ?? =
?? ?? ?? ?? and temperature ?? is : 
 (1) ???? ?? 0
 (2) ???? T (3) ????
1
v T
 (4) ????
1
 T
 
Sol. (1) 
 
p
v
C
,
C
?? Independent on T  
 
5. The effect of increase in temperature on the number of electrons in conduction band ( n
e
) and 
resistance of a semiconductor will be as: 
 (1) Both n
e
 and resistance increase (2) Both n
e
 and resistance decrease 
 (3) n
e
 decreases, resistance increases (4) n
e
 increases, resistance decreases 
Sol. (4) 
In semi conductors, 
e
T ,n ? in Conduction Band increases 
T ,R ??  
 
6. The amplitude of 15s i n ? ( 100 0 ???? ) is modulated by 10s i n ? ( 4 ???? ) signal. The amplitude modulated signal 
contains frequency (ies) of 
 A. 500 Hz B. 2 Hz C. 250 Hz D. 498 Hz E. 502 Hz 
 Choose the correct answer from the options given below: 
 (1) A Only (2) B Only (3) A and ?? Only (4) A, D and E Only 
Sol. (4) 
1000
500Hz
2
??
c
p
f
p
 
4
2Hz
2
??
m
p
f
p
 
Upper side Band, 
cm
USB f f ??  
     ? USB 502HZ 
Lower side Band, 
498Hz
??
?
cm
LSB f f
LSB
  
 
7. Two polaroide A and B are placed in such a way that the pass-axis of polaroids are perpendicular to 
each other. Now, another polaroid ?? is placed between ?? and ?? bisecting angle between them. If 
intensity of unpolarized light is I
0
 then intensity of transmitted light after passing through polaroid B 
will be: 
 (1) 
?? 0
4
 (2) 
?? 0
2
 (3) Zero (4) 
?? 0
8
 
Sol. (4) 
After A, ?
2
I
I  
After C, ??
200
cos 45
24
II
I  
After B, ??
200
cos 45
48
II
I  
8. As shown in figure, a 70 kg garden roller is pushed with a force of ?? ?
= 200 N at an angle of 30
°
 with 
horizontal. The normal reaction on the roller is 
 (Given g = 10 m s
- 2
) 
 
 
 (1) 800 v 2 N (2) 200 v 3 N (3) 600 N (4) 800 N 
Sol. (4) 
FBD of Sphere ? 
 
 
 
9. If 1000 droplets of water of surface tension 0 . 07 N / m, having same radius 1 mm each, combine to 
from a single drop. In the process the released surface energy is- 
 (Take ?? =
22
7
) 
 (1) 8 . 8 × 10
- 5
 J (2) 7 . 92 × 10
- 4
 J (3) 7 . 92 × 10
- 6
 J (4) 9 . 68 × 10
- 4
 J 
Sol. (2) 
12
? VV 
33
44
1000
33
?? pr pR 
?10r R 
12
?? E U U 
? ?
22
1000 4 4 ? ? ? ? T p r T p R 
Page 4


SECTION - A 
1. The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude 
of oscillation. At ?? / 2, the kinetic energy of the block is : 
 (1) 18 . 75 J (2) 9 . 75 J (3) 37 . 5 J (4) 12 . 5 J 
Sol. (1) 
 
2. The drift velocity of electrons for a conductor connected in an electrical circuit is V
d
. The conductor in 
now replaced by another conductor with same material and same length but double the area of cross 
section. The applied voltage remains same. The new drift velocity of electrons will be 
 (1) V
d
 (2) 
V
d
4
 (3) 2 V
d
 (4) 
V
d
2
 
Sol. (1) 
 
 
3. The initial speed of a projectile fired from ground is ?? . At the highest point during its motion, the 
speed of projectile is 
v 3
2
?? . The time of flight of the projectile is : 
 (1) 
2u
g
 (2) 
u
2 g
 (3) 
v 3 ?? ?? (4) 
u
g
 
Sol. (4) 
At highest point - 
 
gg
uu
T??
2 sin
?? 30 
?
u
u cos
2
??
3
I
?
d
V
A
II 
?
d
AneV I 
AA 
? 2
2 ?
A
II 
l
VR
??
??
??
?? ?
4
? ? ? k 
3
25 18.75J
?A km
??
??
??
24
?? 11
1
22
?? k U E 
A
Um ? 
??
??
?
22
??
2
2
1
A
U PE m?x 
22
??
22
1
at ,
2
? ? ?   Total Energy in SHM,
22
1
E m A 25J
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 31st January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
4. The correct relation between ?? =
?? ?? ?? ?? and temperature ?? is : 
 (1) ???? ?? 0
 (2) ???? T (3) ????
1
v T
 (4) ????
1
 T
 
Sol. (1) 
 
p
v
C
,
C
?? Independent on T  
 
5. The effect of increase in temperature on the number of electrons in conduction band ( n
e
) and 
resistance of a semiconductor will be as: 
 (1) Both n
e
 and resistance increase (2) Both n
e
 and resistance decrease 
 (3) n
e
 decreases, resistance increases (4) n
e
 increases, resistance decreases 
Sol. (4) 
In semi conductors, 
e
T ,n ? in Conduction Band increases 
T ,R ??  
 
6. The amplitude of 15s i n ? ( 100 0 ???? ) is modulated by 10s i n ? ( 4 ???? ) signal. The amplitude modulated signal 
contains frequency (ies) of 
 A. 500 Hz B. 2 Hz C. 250 Hz D. 498 Hz E. 502 Hz 
 Choose the correct answer from the options given below: 
 (1) A Only (2) B Only (3) A and ?? Only (4) A, D and E Only 
Sol. (4) 
1000
500Hz
2
??
c
p
f
p
 
4
2Hz
2
??
m
p
f
p
 
Upper side Band, 
cm
USB f f ??  
     ? USB 502HZ 
Lower side Band, 
498Hz
??
?
cm
LSB f f
LSB
  
 
7. Two polaroide A and B are placed in such a way that the pass-axis of polaroids are perpendicular to 
each other. Now, another polaroid ?? is placed between ?? and ?? bisecting angle between them. If 
intensity of unpolarized light is I
0
 then intensity of transmitted light after passing through polaroid B 
will be: 
 (1) 
?? 0
4
 (2) 
?? 0
2
 (3) Zero (4) 
?? 0
8
 
Sol. (4) 
After A, ?
2
I
I  
After C, ??
200
cos 45
24
II
I  
After B, ??
200
cos 45
48
II
I  
8. As shown in figure, a 70 kg garden roller is pushed with a force of ?? ?
= 200 N at an angle of 30
°
 with 
horizontal. The normal reaction on the roller is 
 (Given g = 10 m s
- 2
) 
 
 
 (1) 800 v 2 N (2) 200 v 3 N (3) 600 N (4) 800 N 
Sol. (4) 
FBD of Sphere ? 
 
 
 
9. If 1000 droplets of water of surface tension 0 . 07 N / m, having same radius 1 mm each, combine to 
from a single drop. In the process the released surface energy is- 
 (Take ?? =
22
7
) 
 (1) 8 . 8 × 10
- 5
 J (2) 7 . 92 × 10
- 4
 J (3) 7 . 92 × 10
- 6
 J (4) 9 . 68 × 10
- 4
 J 
Sol. (2) 
12
? VV 
33
44
1000
33
?? pr pR 
?10r R 
12
?? E U U 
? ?
22
1000 4 4 ? ? ? ? T p r T p R 
? ?
? ? ?
22
4 1000 r 100r E pT 
6
22
4 0.07 900 10
7
?
? ? ? ? ? E 
?
??
4
7.92 10 J E 
 
10. The pressure of a gas changes linearly with volume from ?? to ?? as shown in figure. If no heat is 
supplied to or extracted from the gas then change in the internal energy of the gas will be 
 
 (1) –4.5 J (2) zero (3) 4 . 5 J (4) 6 J 
Sol. C 
W = Area of ???? Graph 
36
1
[50 10] 10 150 10
2
?
? ? ? ? ? ? ? W 
??4.5J W 
? ?? Q U W 
0 ? 4 . 5 ?? U 
? 4 . 5 J ?? U 
 
11. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason ?? 
 Assertion A: The beam of electrons show wave nature and exhibit interference and diffraction. 
 Reason R: Davisson Germer Experimentally verified the wave nature of electrons. 
 In the light of the above statements, choose the most appropriate answer from the options given 
below: 
 (1) Both A and R are correct and R is the correct explanation of A 
 (2) A is not correct but R is correct 
 (3) A is correct but R is not correct 
 (4) Both A and R are correct but R is Not the correct explanation of A 
Sol. (1) 
Theoritical 
  
12. A free neutron decays into a proton but a free proton does not decay into neutron. This is because 
 (1) proton is a charged particle 
 (2) neutron is an uncharged particle 
 (3) neutron is a composite particle made of a proton and an electron 
 (4) neutron has larger rest mass than proton 
Sol. (4) 
Rest mass of neutron is greater than proton. 
Page 5


SECTION - A 
1. The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude 
of oscillation. At ?? / 2, the kinetic energy of the block is : 
 (1) 18 . 75 J (2) 9 . 75 J (3) 37 . 5 J (4) 12 . 5 J 
Sol. (1) 
 
2. The drift velocity of electrons for a conductor connected in an electrical circuit is V
d
. The conductor in 
now replaced by another conductor with same material and same length but double the area of cross 
section. The applied voltage remains same. The new drift velocity of electrons will be 
 (1) V
d
 (2) 
V
d
4
 (3) 2 V
d
 (4) 
V
d
2
 
Sol. (1) 
 
 
3. The initial speed of a projectile fired from ground is ?? . At the highest point during its motion, the 
speed of projectile is 
v 3
2
?? . The time of flight of the projectile is : 
 (1) 
2u
g
 (2) 
u
2 g
 (3) 
v 3 ?? ?? (4) 
u
g
 
Sol. (4) 
At highest point - 
 
gg
uu
T??
2 sin
?? 30 
?
u
u cos
2
??
3
I
?
d
V
A
II 
?
d
AneV I 
AA 
? 2
2 ?
A
II 
l
VR
??
??
??
?? ?
4
? ? ? k 
3
25 18.75J
?A km
??
??
??
24
?? 11
1
22
?? k U E 
A
Um ? 
??
??
?
22
??
2
2
1
A
U PE m?x 
22
??
22
1
at ,
2
? ? ?   Total Energy in SHM,
22
1
E m A 25J
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 31st January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
4. The correct relation between ?? =
?? ?? ?? ?? and temperature ?? is : 
 (1) ???? ?? 0
 (2) ???? T (3) ????
1
v T
 (4) ????
1
 T
 
Sol. (1) 
 
p
v
C
,
C
?? Independent on T  
 
5. The effect of increase in temperature on the number of electrons in conduction band ( n
e
) and 
resistance of a semiconductor will be as: 
 (1) Both n
e
 and resistance increase (2) Both n
e
 and resistance decrease 
 (3) n
e
 decreases, resistance increases (4) n
e
 increases, resistance decreases 
Sol. (4) 
In semi conductors, 
e
T ,n ? in Conduction Band increases 
T ,R ??  
 
6. The amplitude of 15s i n ? ( 100 0 ???? ) is modulated by 10s i n ? ( 4 ???? ) signal. The amplitude modulated signal 
contains frequency (ies) of 
 A. 500 Hz B. 2 Hz C. 250 Hz D. 498 Hz E. 502 Hz 
 Choose the correct answer from the options given below: 
 (1) A Only (2) B Only (3) A and ?? Only (4) A, D and E Only 
Sol. (4) 
1000
500Hz
2
??
c
p
f
p
 
4
2Hz
2
??
m
p
f
p
 
Upper side Band, 
cm
USB f f ??  
     ? USB 502HZ 
Lower side Band, 
498Hz
??
?
cm
LSB f f
LSB
  
 
7. Two polaroide A and B are placed in such a way that the pass-axis of polaroids are perpendicular to 
each other. Now, another polaroid ?? is placed between ?? and ?? bisecting angle between them. If 
intensity of unpolarized light is I
0
 then intensity of transmitted light after passing through polaroid B 
will be: 
 (1) 
?? 0
4
 (2) 
?? 0
2
 (3) Zero (4) 
?? 0
8
 
Sol. (4) 
After A, ?
2
I
I  
After C, ??
200
cos 45
24
II
I  
After B, ??
200
cos 45
48
II
I  
8. As shown in figure, a 70 kg garden roller is pushed with a force of ?? ?
= 200 N at an angle of 30
°
 with 
horizontal. The normal reaction on the roller is 
 (Given g = 10 m s
- 2
) 
 
 
 (1) 800 v 2 N (2) 200 v 3 N (3) 600 N (4) 800 N 
Sol. (4) 
FBD of Sphere ? 
 
 
 
9. If 1000 droplets of water of surface tension 0 . 07 N / m, having same radius 1 mm each, combine to 
from a single drop. In the process the released surface energy is- 
 (Take ?? =
22
7
) 
 (1) 8 . 8 × 10
- 5
 J (2) 7 . 92 × 10
- 4
 J (3) 7 . 92 × 10
- 6
 J (4) 9 . 68 × 10
- 4
 J 
Sol. (2) 
12
? VV 
33
44
1000
33
?? pr pR 
?10r R 
12
?? E U U 
? ?
22
1000 4 4 ? ? ? ? T p r T p R 
? ?
? ? ?
22
4 1000 r 100r E pT 
6
22
4 0.07 900 10
7
?
? ? ? ? ? E 
?
??
4
7.92 10 J E 
 
10. The pressure of a gas changes linearly with volume from ?? to ?? as shown in figure. If no heat is 
supplied to or extracted from the gas then change in the internal energy of the gas will be 
 
 (1) –4.5 J (2) zero (3) 4 . 5 J (4) 6 J 
Sol. C 
W = Area of ???? Graph 
36
1
[50 10] 10 150 10
2
?
? ? ? ? ? ? ? W 
??4.5J W 
? ?? Q U W 
0 ? 4 . 5 ?? U 
? 4 . 5 J ?? U 
 
11. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason ?? 
 Assertion A: The beam of electrons show wave nature and exhibit interference and diffraction. 
 Reason R: Davisson Germer Experimentally verified the wave nature of electrons. 
 In the light of the above statements, choose the most appropriate answer from the options given 
below: 
 (1) Both A and R are correct and R is the correct explanation of A 
 (2) A is not correct but R is correct 
 (3) A is correct but R is not correct 
 (4) Both A and R are correct but R is Not the correct explanation of A 
Sol. (1) 
Theoritical 
  
12. A free neutron decays into a proton but a free proton does not decay into neutron. This is because 
 (1) proton is a charged particle 
 (2) neutron is an uncharged particle 
 (3) neutron is a composite particle made of a proton and an electron 
 (4) neutron has larger rest mass than proton 
Sol. (4) 
Rest mass of neutron is greater than proton. 
13. Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the 
same height. Choose the correct statement out of the following Assume negligible air friction} 
 (1) Insulating ball will reach the earth's surface earlier than the metal ball 
 (2) Metal ball will reach the earth's surface earlier than the insulating ball 
 (3) Both will reach the earth's surface simultaneously. 
 (4) Time taken by them to reach the earth's surface will be independent of the properties of their 
materials 
Sol. (1) 
In Conductor, A portion of the Gravitational Potential Energy goes into generating eddy current.  
 
14. If R , X
L
, and X
C
 represent resistance, inductive reactance and capacitive reactance. Then which of the 
following is dimensionless : 
 (1) 
?? ?? ?? ?? ?? (2) 
?? v ?? ?? ?? ?? (3) ?? ?? ?? ?? ?? (4) ?? ?? ?? ? ?? ?? 
Sol. (2) 
LC
R,X ,X have same unit i.e. ohm  
2
LC
R ohm
xx
ohm
?? Dimensionless 
 
15. 100 balls each of mass m moving with speed ?? simultaneously strike a wall normally and reflected 
back with same speed, in time t sec.  The total force exerted by the balls on the wall is 
 (1) 
100 ????
?? (2) 200 ?????? (3) 
????
100 ?? (4) 
200 ????
?? 
Sol. (4) 
 
 
Change in momentum, 
? | ? | 2 p mV 
Average force,   
?
avg
?
N
p
F
t
 
avg
2mV
100
??
?
??
??
F
t
 
 
avg
200mV
? F
t