JEE Main 2023 January 25 Shift 1 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


SECTION - A 
1.  Match List I with List II 
List I List II 
A. Surface tension I. kgm
-1
 s
-1
 
B. Pressure II. kgms
-1
 
C. Viscosity III. kgm
-1
 s
-2
 
D. Impulse IV. kgs
-2
 
 
Choose the correct answer from the options given below: 
(1) A-II , B-I , C-III , D-IV (2) A-IV, B-III , C-I , D-II 
(3) A-III , B-IV, C-I , D-II  (4) A-IV , B-III , C-II , D-I 
Sol. 2 
 Surface tension (S) =  ? Kg s
–2
  
  ? N – S 
   ? Kg ms
–2
 . S 
   ? Kg ms
–1
   
Pressure (P) =  ? Kgms
–2
, m
–2
 
? Kg ms
–1
 s
–2
  
 
   ? ?
   ? ?kg m
–1
 s
–1
 
 
2.  The ratio of the density of oxygen nucleus ( 
8
16
O) and helium nucleus ( 
2
4
He) is 
(1) 4:1 (2) 2: 1( 3) 1: 1( 4) 8: 1 
Sol. 3 
 
 ?  
? ? ? ?  
 ? ? ? ? ?
? A M 8 4
? MA 16 2
1
He o He
o o He
A
M
??
?RA
3
M
4
3
0
RA  
0
1
3
3
?? when r = ?? and 
3
4
Vr
V
M
?
 
?
kg ms
m.ms
1
2
6 rv ?
 Viscocity ( ? ) = 
F
A
F
 Impulse (J) = Fdt
?
SM
M1
kg .
l
 ?
2
F
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 25th January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
Page 2


SECTION - A 
1.  Match List I with List II 
List I List II 
A. Surface tension I. kgm
-1
 s
-1
 
B. Pressure II. kgms
-1
 
C. Viscosity III. kgm
-1
 s
-2
 
D. Impulse IV. kgs
-2
 
 
Choose the correct answer from the options given below: 
(1) A-II , B-I , C-III , D-IV (2) A-IV, B-III , C-I , D-II 
(3) A-III , B-IV, C-I , D-II  (4) A-IV , B-III , C-II , D-I 
Sol. 2 
 Surface tension (S) =  ? Kg s
–2
  
  ? N – S 
   ? Kg ms
–2
 . S 
   ? Kg ms
–1
   
Pressure (P) =  ? Kgms
–2
, m
–2
 
? Kg ms
–1
 s
–2
  
 
   ? ?
   ? ?kg m
–1
 s
–1
 
 
2.  The ratio of the density of oxygen nucleus ( 
8
16
O) and helium nucleus ( 
2
4
He) is 
(1) 4:1 (2) 2: 1( 3) 1: 1( 4) 8: 1 
Sol. 3 
 
 ?  
? ? ? ?  
 ? ? ? ? ?
? A M 8 4
? MA 16 2
1
He o He
o o He
A
M
??
?RA
3
M
4
3
0
RA  
0
1
3
3
?? when r = ?? and 
3
4
Vr
V
M
?
 
?
kg ms
m.ms
1
2
6 rv ?
 Viscocity ( ? ) = 
F
A
F
 Impulse (J) = Fdt
?
SM
M1
kg .
l
 ?
2
F
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 25th January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
3. The root mean square velocity of molecules of gas is 
(1) Inversely proportional to square root of temperature (v
1
?? ) 
(2) Proportional to square of temperature ( ?? 2
) 
(3) Proportional to temperature ( ?? ) 
(4) Proportional to square root of temperature ( v ?? ) 
Sol. 4 
rms
0
3RT
V
M
? 
? 
rms
VT ? 
 
4. Match List I with List II 
 
 Choose the correct answer from the options given below : 
 (1) A-III, B-I, C-IV, D-II (2) A-I, B-III, C-IV, D-II 
(3) A-III, B-IV, C-I, D-II  (4) A-II, B-I, C-IV, D-III 
Sol. 1 
 (A) B = 
00
II
2
4 r 2r
??
??
?
 
  = 
I1
1
2r
???
?
??
?
??
 
Page 3


SECTION - A 
1.  Match List I with List II 
List I List II 
A. Surface tension I. kgm
-1
 s
-1
 
B. Pressure II. kgms
-1
 
C. Viscosity III. kgm
-1
 s
-2
 
D. Impulse IV. kgs
-2
 
 
Choose the correct answer from the options given below: 
(1) A-II , B-I , C-III , D-IV (2) A-IV, B-III , C-I , D-II 
(3) A-III , B-IV, C-I , D-II  (4) A-IV , B-III , C-II , D-I 
Sol. 2 
 Surface tension (S) =  ? Kg s
–2
  
  ? N – S 
   ? Kg ms
–2
 . S 
   ? Kg ms
–1
   
Pressure (P) =  ? Kgms
–2
, m
–2
 
? Kg ms
–1
 s
–2
  
 
   ? ?
   ? ?kg m
–1
 s
–1
 
 
2.  The ratio of the density of oxygen nucleus ( 
8
16
O) and helium nucleus ( 
2
4
He) is 
(1) 4:1 (2) 2: 1( 3) 1: 1( 4) 8: 1 
Sol. 3 
 
 ?  
? ? ? ?  
 ? ? ? ? ?
? A M 8 4
? MA 16 2
1
He o He
o o He
A
M
??
?RA
3
M
4
3
0
RA  
0
1
3
3
?? when r = ?? and 
3
4
Vr
V
M
?
 
?
kg ms
m.ms
1
2
6 rv ?
 Viscocity ( ? ) = 
F
A
F
 Impulse (J) = Fdt
?
SM
M1
kg .
l
 ?
2
F
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 25th January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
3. The root mean square velocity of molecules of gas is 
(1) Inversely proportional to square root of temperature (v
1
?? ) 
(2) Proportional to square of temperature ( ?? 2
) 
(3) Proportional to temperature ( ?? ) 
(4) Proportional to square root of temperature ( v ?? ) 
Sol. 4 
rms
0
3RT
V
M
? 
? 
rms
VT ? 
 
4. Match List I with List II 
 
 Choose the correct answer from the options given below : 
 (1) A-III, B-I, C-IV, D-II (2) A-I, B-III, C-IV, D-II 
(3) A-III, B-IV, C-I, D-II  (4) A-II, B-I, C-IV, D-III 
Sol. 1 
 (A) B = 
00
II
2
4 r 2r
??
??
?
 
  = 
I1
1
2r
???
?
??
?
??
 
  = ? ?
I
1
2r
?
??
?
  
  = 
I
( 1)
2r
?
??
?
 ? 
 (B) B = 
00
II
2
4 r 4 r
??
? ? ? ?
??
 
  = 
0
I
( 2)
4r
?
??
?
 
 (C) B = 
00
II
.0
4 r 4 r
??
? ? ?
??
 
  = 
0
I
( 1)
4r
?
??
?
? 
 (D) B = 
0
I
4r
?
 
 
5. A message signal of frequency 5kHz is used to modulate a carrier signal of frequency 2MHz . The bandwidth 
for amplitude modulation is: 
 (1) 20 kHz (2) 5kHz (3) 10kHz (4) 2.5kHz 
Sol. 3 
 Bandwidth = 2 × highest of base band frequency 
   = 2 × 5 = 10 kHZ 
 
6. An object of mass 8 kg hanging from one end of a uniform rod CD of mass 2 kg and length 1m pivoted at its 
end C on a vertical walls as shown in figure. It is supported by a cable AB such that the system is in equilibrium. 
The tension in the cable is:  
 (Take g = 10 m/s
2
) 
 
  (1) 90 N (2) 30 N (3) 300 N (4) 240 N 
Sol. 3 
 The rod is in equilibrium. So, net torque about any point will be zero. 
 
c
? = 0 
 Mg × 50 + 80 × 100 = Tsin30° × 30 
Page 4


SECTION - A 
1.  Match List I with List II 
List I List II 
A. Surface tension I. kgm
-1
 s
-1
 
B. Pressure II. kgms
-1
 
C. Viscosity III. kgm
-1
 s
-2
 
D. Impulse IV. kgs
-2
 
 
Choose the correct answer from the options given below: 
(1) A-II , B-I , C-III , D-IV (2) A-IV, B-III , C-I , D-II 
(3) A-III , B-IV, C-I , D-II  (4) A-IV , B-III , C-II , D-I 
Sol. 2 
 Surface tension (S) =  ? Kg s
–2
  
  ? N – S 
   ? Kg ms
–2
 . S 
   ? Kg ms
–1
   
Pressure (P) =  ? Kgms
–2
, m
–2
 
? Kg ms
–1
 s
–2
  
 
   ? ?
   ? ?kg m
–1
 s
–1
 
 
2.  The ratio of the density of oxygen nucleus ( 
8
16
O) and helium nucleus ( 
2
4
He) is 
(1) 4:1 (2) 2: 1( 3) 1: 1( 4) 8: 1 
Sol. 3 
 
 ?  
? ? ? ?  
 ? ? ? ? ?
? A M 8 4
? MA 16 2
1
He o He
o o He
A
M
??
?RA
3
M
4
3
0
RA  
0
1
3
3
?? when r = ?? and 
3
4
Vr
V
M
?
 
?
kg ms
m.ms
1
2
6 rv ?
 Viscocity ( ? ) = 
F
A
F
 Impulse (J) = Fdt
?
SM
M1
kg .
l
 ?
2
F
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 25th January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
3. The root mean square velocity of molecules of gas is 
(1) Inversely proportional to square root of temperature (v
1
?? ) 
(2) Proportional to square of temperature ( ?? 2
) 
(3) Proportional to temperature ( ?? ) 
(4) Proportional to square root of temperature ( v ?? ) 
Sol. 4 
rms
0
3RT
V
M
? 
? 
rms
VT ? 
 
4. Match List I with List II 
 
 Choose the correct answer from the options given below : 
 (1) A-III, B-I, C-IV, D-II (2) A-I, B-III, C-IV, D-II 
(3) A-III, B-IV, C-I, D-II  (4) A-II, B-I, C-IV, D-III 
Sol. 1 
 (A) B = 
00
II
2
4 r 2r
??
??
?
 
  = 
I1
1
2r
???
?
??
?
??
 
  = ? ?
I
1
2r
?
??
?
  
  = 
I
( 1)
2r
?
??
?
 ? 
 (B) B = 
00
II
2
4 r 4 r
??
? ? ? ?
??
 
  = 
0
I
( 2)
4r
?
??
?
 
 (C) B = 
00
II
.0
4 r 4 r
??
? ? ?
??
 
  = 
0
I
( 1)
4r
?
??
?
? 
 (D) B = 
0
I
4r
?
 
 
5. A message signal of frequency 5kHz is used to modulate a carrier signal of frequency 2MHz . The bandwidth 
for amplitude modulation is: 
 (1) 20 kHz (2) 5kHz (3) 10kHz (4) 2.5kHz 
Sol. 3 
 Bandwidth = 2 × highest of base band frequency 
   = 2 × 5 = 10 kHZ 
 
6. An object of mass 8 kg hanging from one end of a uniform rod CD of mass 2 kg and length 1m pivoted at its 
end C on a vertical walls as shown in figure. It is supported by a cable AB such that the system is in equilibrium. 
The tension in the cable is:  
 (Take g = 10 m/s
2
) 
 
  (1) 90 N (2) 30 N (3) 300 N (4) 240 N 
Sol. 3 
 The rod is in equilibrium. So, net torque about any point will be zero. 
 
c
? = 0 
 Mg × 50 + 80 × 100 = Tsin30° × 30 
 20 × 50 + 80 × 100 = 
T
2
 × 60 
 T = 
900
3
 = 300 N 
 
 
Tsin30° 
A 
C 
Wall 
40cm 
8kg 
60cm 
50 
90° 
30° 
T 
D 
mg 
 
 
7. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R 
 Assertion A: Photodiodes are used in forward bias usually for measuring the light intensity. 
 Reason R: For a p-n junction diode, at applied voltage 
 V the current in the forward bias is more than the current in the reverse bias for |?? ?? | > ±?? =
|?? 0
| where ?? 0
 is the threshold voltage and V
z
 is the breakdown voltage. 
 In the light of the above statements, choose the correct answer from the options given below 
 (1) Both ?? and ?? are true and ?? is correct explanation ?? 
(2) ?? is false but ?? is true 
(3) Both A and R are true but R is NOT the correct explanation A 
 (4) A is true but R is false 
Sol. 2 
 Photo diodes are not used in forward bias. 
 
8. In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then 
the resonant frequency of oscillator becomes ?? times its initial resonant frequency ?? 0
. The value of ?? is: 
 (1) 4 (2) 1/16                       ( 3) 16                               ( 4) ¼ 
Sol. 4 
 
1
LC
?? 
 
1 2 2
2 1 1
LC 2L.8C
4
L C L.C
?
? ? ?
?
  
 
0 1
2
44
? ?
? ? ? 
 
Page 5


SECTION - A 
1.  Match List I with List II 
List I List II 
A. Surface tension I. kgm
-1
 s
-1
 
B. Pressure II. kgms
-1
 
C. Viscosity III. kgm
-1
 s
-2
 
D. Impulse IV. kgs
-2
 
 
Choose the correct answer from the options given below: 
(1) A-II , B-I , C-III , D-IV (2) A-IV, B-III , C-I , D-II 
(3) A-III , B-IV, C-I , D-II  (4) A-IV , B-III , C-II , D-I 
Sol. 2 
 Surface tension (S) =  ? Kg s
–2
  
  ? N – S 
   ? Kg ms
–2
 . S 
   ? Kg ms
–1
   
Pressure (P) =  ? Kgms
–2
, m
–2
 
? Kg ms
–1
 s
–2
  
 
   ? ?
   ? ?kg m
–1
 s
–1
 
 
2.  The ratio of the density of oxygen nucleus ( 
8
16
O) and helium nucleus ( 
2
4
He) is 
(1) 4:1 (2) 2: 1( 3) 1: 1( 4) 8: 1 
Sol. 3 
 
 ?  
? ? ? ?  
 ? ? ? ? ?
? A M 8 4
? MA 16 2
1
He o He
o o He
A
M
??
?RA
3
M
4
3
0
RA  
0
1
3
3
?? when r = ?? and 
3
4
Vr
V
M
?
 
?
kg ms
m.ms
1
2
6 rv ?
 Viscocity ( ? ) = 
F
A
F
 Impulse (J) = Fdt
?
SM
M1
kg .
l
 ?
2
F
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 25th January, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
3. The root mean square velocity of molecules of gas is 
(1) Inversely proportional to square root of temperature (v
1
?? ) 
(2) Proportional to square of temperature ( ?? 2
) 
(3) Proportional to temperature ( ?? ) 
(4) Proportional to square root of temperature ( v ?? ) 
Sol. 4 
rms
0
3RT
V
M
? 
? 
rms
VT ? 
 
4. Match List I with List II 
 
 Choose the correct answer from the options given below : 
 (1) A-III, B-I, C-IV, D-II (2) A-I, B-III, C-IV, D-II 
(3) A-III, B-IV, C-I, D-II  (4) A-II, B-I, C-IV, D-III 
Sol. 1 
 (A) B = 
00
II
2
4 r 2r
??
??
?
 
  = 
I1
1
2r
???
?
??
?
??
 
  = ? ?
I
1
2r
?
??
?
  
  = 
I
( 1)
2r
?
??
?
 ? 
 (B) B = 
00
II
2
4 r 4 r
??
? ? ? ?
??
 
  = 
0
I
( 2)
4r
?
??
?
 
 (C) B = 
00
II
.0
4 r 4 r
??
? ? ?
??
 
  = 
0
I
( 1)
4r
?
??
?
? 
 (D) B = 
0
I
4r
?
 
 
5. A message signal of frequency 5kHz is used to modulate a carrier signal of frequency 2MHz . The bandwidth 
for amplitude modulation is: 
 (1) 20 kHz (2) 5kHz (3) 10kHz (4) 2.5kHz 
Sol. 3 
 Bandwidth = 2 × highest of base band frequency 
   = 2 × 5 = 10 kHZ 
 
6. An object of mass 8 kg hanging from one end of a uniform rod CD of mass 2 kg and length 1m pivoted at its 
end C on a vertical walls as shown in figure. It is supported by a cable AB such that the system is in equilibrium. 
The tension in the cable is:  
 (Take g = 10 m/s
2
) 
 
  (1) 90 N (2) 30 N (3) 300 N (4) 240 N 
Sol. 3 
 The rod is in equilibrium. So, net torque about any point will be zero. 
 
c
? = 0 
 Mg × 50 + 80 × 100 = Tsin30° × 30 
 20 × 50 + 80 × 100 = 
T
2
 × 60 
 T = 
900
3
 = 300 N 
 
 
Tsin30° 
A 
C 
Wall 
40cm 
8kg 
60cm 
50 
90° 
30° 
T 
D 
mg 
 
 
7. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R 
 Assertion A: Photodiodes are used in forward bias usually for measuring the light intensity. 
 Reason R: For a p-n junction diode, at applied voltage 
 V the current in the forward bias is more than the current in the reverse bias for |?? ?? | > ±?? =
|?? 0
| where ?? 0
 is the threshold voltage and V
z
 is the breakdown voltage. 
 In the light of the above statements, choose the correct answer from the options given below 
 (1) Both ?? and ?? are true and ?? is correct explanation ?? 
(2) ?? is false but ?? is true 
(3) Both A and R are true but R is NOT the correct explanation A 
 (4) A is true but R is false 
Sol. 2 
 Photo diodes are not used in forward bias. 
 
8. In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then 
the resonant frequency of oscillator becomes ?? times its initial resonant frequency ?? 0
. The value of ?? is: 
 (1) 4 (2) 1/16                       ( 3) 16                               ( 4) ¼ 
Sol. 4 
 
1
LC
?? 
 
1 2 2
2 1 1
LC 2L.8C
4
L C L.C
?
? ? ?
?
  
 
0 1
2
44
? ?
? ? ? 
 
9. A uniform metallic wire carries a current 2A, when 3.4 V battery is connected across it. The mass of uniform 
metallic wires is 8.92 × 10
–3 
kg density is 8.92 × 10
3
 kg/m
3
 and resistivity is 1.7 × 10
–8
 ? – m. The length of 
wire is: 
 (1) ?? = 10 m                       ( 2) ?? = 100 m                           ( 3) ?? = 5 m                     ( 4) ?? = 6.8 m 
Sol. 1 
 
 
3.4v 
i 
 
 Given,  i = 2A 
 v = 3.4 v 
 v = iR 
 
v 3.4
R 1.7
i2
? ? ? ? 
 
3
3 6 3
3
mass 8.92 10
volume m 10 m
Density 8.92 10
?
?
?
? ? ?
?
 
 ? A ? = 10
–6
 m
3
 ____ (i) 
 
R
A
A
R
?
?
?
??
 
 
8
1.7 10 A
1.7
?
?
? 
 
8
A
10
?
?                     ____ (ii) 
 
eq(i)
eq(ii)
 
 ?
2
 = 10
2
 
 ? = 10 m 
 
10. A car travels a distance of ' ?? ' with speed ?? 1
 and then same distance ' ?? ' with speed ?? 2
 in the same direction. 
The average speed of the car is: 
 (1)  
2?? 1
?? 2
?? 1
+?? 2
                                  ( 2)
2?? ?? 1
+?? 2
                               ( 3)
?? 1
?? 2
2( ?? 1
+?? 2
)
                           ( 4) 
?? 1
+?? 2
2
 
Sol. 1 
 
 
v1 v2 
x x 
 
 
avg
totalDistance
v
TotalTime
?