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

 Page 1


SECTION - A 
1.  A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an 
initial speed of 5 ms
-1
. Neglecting the air resistance, the speed with which the stone hits the ground 
will be __ ms
-1
 (given, ?? = 10 ms
-2
 ). 
 (1) 15 (2) 20 (3) 30 (4) 25 
Sol. (1) 
 Along vertical direction 
 sy = 10 m 
 = 15 m/s 
 
 
2. Let ?? be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the 
electric fields in three different region ?? ?? ,?? ????
 and ?? ??????
 are: 
 
 (1) ?? ? 
?? =
2?? ?? 0
?? ˆ,?? ? 
????
= 0,?? ? 
??????
=
2?? ?? 0
?? ˆ (2) ?? ? 
?? =
?? 2?? 0
?? ˆ,?? ? 
????
= 0,?? ? 
??????
=
?? 2?? 0
?? ˆ 
 (3) ?? ? 
?? = -
?? ?? 0
?? ˆ,?? ? 
????
= 0,?? ? 
??????
=
?? ?? 0
?? ˆ (4) ?? ? 
?? = 0,?? ? 
????
=
?? ?? 0
?? ˆ,?? ??????
= 0 
 
 
5m/s 
v 
g 
10m  
 
 = 25 200 ?  = 225   
?? 
xy
v v v ?   
22
y
v 200 ?  
2
y
v 200 ?  
y
v ? ?     
2
??         =
2
(0) 2 10 10 ? ? ? ag 
y
?? 
y y y y
v u 2a g u0 ?   
22
 
y
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 1st February, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
Page 2


SECTION - A 
1.  A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an 
initial speed of 5 ms
-1
. Neglecting the air resistance, the speed with which the stone hits the ground 
will be __ ms
-1
 (given, ?? = 10 ms
-2
 ). 
 (1) 15 (2) 20 (3) 30 (4) 25 
Sol. (1) 
 Along vertical direction 
 sy = 10 m 
 = 15 m/s 
 
 
2. Let ?? be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the 
electric fields in three different region ?? ?? ,?? ????
 and ?? ??????
 are: 
 
 (1) ?? ? 
?? =
2?? ?? 0
?? ˆ,?? ? 
????
= 0,?? ? 
??????
=
2?? ?? 0
?? ˆ (2) ?? ? 
?? =
?? 2?? 0
?? ˆ,?? ? 
????
= 0,?? ? 
??????
=
?? 2?? 0
?? ˆ 
 (3) ?? ? 
?? = -
?? ?? 0
?? ˆ,?? ? 
????
= 0,?? ? 
??????
=
?? ?? 0
?? ˆ (4) ?? ? 
?? = 0,?? ? 
????
=
?? ?? 0
?? ˆ,?? ??????
= 0 
 
 
5m/s 
v 
g 
10m  
 
 = 25 200 ?  = 225   
?? 
xy
v v v ?   
22
y
v 200 ?  
2
y
v 200 ?  
y
v ? ?     
2
??         =
2
(0) 2 10 10 ? ? ? ag 
y
?? 
y y y y
v u 2a g u0 ?   
22
 
y
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 1st February, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
 
Sol. (3) 
   
 
I
0
ˆ En
E
?
? ? ? 
 
II
E0 ?? 
 
III
0
ˆ En
E
?
? ? ? 
 
3. A mercury drop of radius 10
-3
 m is broken into 125 equal size droplets. 
 Surface tension of mercury is 0.45Nm
-1
. The gain in surface energy is: 
 (1) 28× 10
-5
 J (2) 17.5 × 10
-5
 J (3) 5 × 10
-5
 J (4) 2.26× 10
-5
 J 
Sol. (4) 
 [Volume of bigger drop] = [volume of smaller drop] × 125 
 
33
44
R 125 r
33
? ? ? ? 
 
33
R 125r ? 
 R 5 r ? ? ? 
 ?  Gain in sinface energy = TdA 
  
? ?
21
0.45 A A ? ? ? 
  
22
0.45 125 4 r 4 R ?? ? ? ? ? ? ?
??
 
  
2
2
R
0.45 125 4 4 R
5
??
??
? ? ? ? ? ?
??
??
??
??
??
 
  
22
0.45 20 R 4 R ?? ? ? ? ? ?
??
 
  
2
0.45 16 R ? ? ? 
  
? ?
2
3
0.45 16 3.14 10
?
? ? ? ? 
  
5
2.26 10 J
?
?? 
 
4. If earth has a mass nine times and radius twice to that of a planet P. Then 
?? ?? 3
v?? ms
-1
 will be the 
minimum velocity required by a rocket to pull out of gravitational force of P, where ?? ?? is escape 
velocity on earth. The value of ?? is 
 (1) 1 (2) 3 (3) 18 (4) 2 
 
E 1 
(I) 
(II) 
(III) 
E 1 
E 2 
E 2 
E 1 
E 2 
E 1 
 d    
+ ? 
+ ? 
Page 3


SECTION - A 
1.  A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an 
initial speed of 5 ms
-1
. Neglecting the air resistance, the speed with which the stone hits the ground 
will be __ ms
-1
 (given, ?? = 10 ms
-2
 ). 
 (1) 15 (2) 20 (3) 30 (4) 25 
Sol. (1) 
 Along vertical direction 
 sy = 10 m 
 = 15 m/s 
 
 
2. Let ?? be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the 
electric fields in three different region ?? ?? ,?? ????
 and ?? ??????
 are: 
 
 (1) ?? ? 
?? =
2?? ?? 0
?? ˆ,?? ? 
????
= 0,?? ? 
??????
=
2?? ?? 0
?? ˆ (2) ?? ? 
?? =
?? 2?? 0
?? ˆ,?? ? 
????
= 0,?? ? 
??????
=
?? 2?? 0
?? ˆ 
 (3) ?? ? 
?? = -
?? ?? 0
?? ˆ,?? ? 
????
= 0,?? ? 
??????
=
?? ?? 0
?? ˆ (4) ?? ? 
?? = 0,?? ? 
????
=
?? ?? 0
?? ˆ,?? ??????
= 0 
 
 
5m/s 
v 
g 
10m  
 
 = 25 200 ?  = 225   
?? 
xy
v v v ?   
22
y
v 200 ?  
2
y
v 200 ?  
y
v ? ?     
2
??         =
2
(0) 2 10 10 ? ? ? ag 
y
?? 
y y y y
v u 2a g u0 ?   
22
 
y
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 1st February, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
 
Sol. (3) 
   
 
I
0
ˆ En
E
?
? ? ? 
 
II
E0 ?? 
 
III
0
ˆ En
E
?
? ? ? 
 
3. A mercury drop of radius 10
-3
 m is broken into 125 equal size droplets. 
 Surface tension of mercury is 0.45Nm
-1
. The gain in surface energy is: 
 (1) 28× 10
-5
 J (2) 17.5 × 10
-5
 J (3) 5 × 10
-5
 J (4) 2.26× 10
-5
 J 
Sol. (4) 
 [Volume of bigger drop] = [volume of smaller drop] × 125 
 
33
44
R 125 r
33
? ? ? ? 
 
33
R 125r ? 
 R 5 r ? ? ? 
 ?  Gain in sinface energy = TdA 
  
? ?
21
0.45 A A ? ? ? 
  
22
0.45 125 4 r 4 R ?? ? ? ? ? ? ?
??
 
  
2
2
R
0.45 125 4 4 R
5
??
??
? ? ? ? ? ?
??
??
??
??
??
 
  
22
0.45 20 R 4 R ?? ? ? ? ? ?
??
 
  
2
0.45 16 R ? ? ? 
  
? ?
2
3
0.45 16 3.14 10
?
? ? ? ? 
  
5
2.26 10 J
?
?? 
 
4. If earth has a mass nine times and radius twice to that of a planet P. Then 
?? ?? 3
v?? ms
-1
 will be the 
minimum velocity required by a rocket to pull out of gravitational force of P, where ?? ?? is escape 
velocity on earth. The value of ?? is 
 (1) 1 (2) 3 (3) 18 (4) 2 
 
E 1 
(I) 
(II) 
(III) 
E 1 
E 2 
E 2 
E 1 
E 2 
E 1 
 d    
+ ? 
+ ? 
Sol. (4) 
 
EP
M 9M ? 
 
EP
R 2R ? 
 
E
1 P
c
E
P
M
2G
2GM
9
V
R
R
2
?? 
     
E
E
2GM 2
R9
??  
  
1 e
c
V
V2
3
? 
 
 
5. A sample of gas at temperature ?? is adiabatically expanded to double its volume. The work done by 
the gas in the process is 
3
given, ?
2
 : 
 (1) ?? =
?? ?? [v2- 2] (2) ?? = ???? [2- v2] (3) ?? = ???? [v2- 2] (4) ?? =
?? ?? [2- v2] 
Sol. (2) 
 Work done in the process is given by 
 
12
R
W (T T )
1
??
??
 
 For adiabatic process: 
 
11
1 1 2 2
T V T V
? ? ? ?
? 
 
33
11
22
2
TV T (2V)
??
? 
 
11
22
2
TV T (2V) ? 
 
22
2
T V T 2V ?? 
 
2
T
T
2
?? 
 
RT
WT
1 2
??
? ? ? ?
??
??
??
 
 = 
1
2RT 1
2
??
?
??
??
 
 = 
2
RT 2
2
??
?
??
??
 
 = RT[2 2] ? 
 W RT 2 2
??
??
??
 
 
 
Page 4


SECTION - A 
1.  A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an 
initial speed of 5 ms
-1
. Neglecting the air resistance, the speed with which the stone hits the ground 
will be __ ms
-1
 (given, ?? = 10 ms
-2
 ). 
 (1) 15 (2) 20 (3) 30 (4) 25 
Sol. (1) 
 Along vertical direction 
 sy = 10 m 
 = 15 m/s 
 
 
2. Let ?? be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the 
electric fields in three different region ?? ?? ,?? ????
 and ?? ??????
 are: 
 
 (1) ?? ? 
?? =
2?? ?? 0
?? ˆ,?? ? 
????
= 0,?? ? 
??????
=
2?? ?? 0
?? ˆ (2) ?? ? 
?? =
?? 2?? 0
?? ˆ,?? ? 
????
= 0,?? ? 
??????
=
?? 2?? 0
?? ˆ 
 (3) ?? ? 
?? = -
?? ?? 0
?? ˆ,?? ? 
????
= 0,?? ? 
??????
=
?? ?? 0
?? ˆ (4) ?? ? 
?? = 0,?? ? 
????
=
?? ?? 0
?? ˆ,?? ??????
= 0 
 
 
5m/s 
v 
g 
10m  
 
 = 25 200 ?  = 225   
?? 
xy
v v v ?   
22
y
v 200 ?  
2
y
v 200 ?  
y
v ? ?     
2
??         =
2
(0) 2 10 10 ? ? ? ag 
y
?? 
y y y y
v u 2a g u0 ?   
22
 
y
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 1st February, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
 
Sol. (3) 
   
 
I
0
ˆ En
E
?
? ? ? 
 
II
E0 ?? 
 
III
0
ˆ En
E
?
? ? ? 
 
3. A mercury drop of radius 10
-3
 m is broken into 125 equal size droplets. 
 Surface tension of mercury is 0.45Nm
-1
. The gain in surface energy is: 
 (1) 28× 10
-5
 J (2) 17.5 × 10
-5
 J (3) 5 × 10
-5
 J (4) 2.26× 10
-5
 J 
Sol. (4) 
 [Volume of bigger drop] = [volume of smaller drop] × 125 
 
33
44
R 125 r
33
? ? ? ? 
 
33
R 125r ? 
 R 5 r ? ? ? 
 ?  Gain in sinface energy = TdA 
  
? ?
21
0.45 A A ? ? ? 
  
22
0.45 125 4 r 4 R ?? ? ? ? ? ? ?
??
 
  
2
2
R
0.45 125 4 4 R
5
??
??
? ? ? ? ? ?
??
??
??
??
??
 
  
22
0.45 20 R 4 R ?? ? ? ? ? ?
??
 
  
2
0.45 16 R ? ? ? 
  
? ?
2
3
0.45 16 3.14 10
?
? ? ? ? 
  
5
2.26 10 J
?
?? 
 
4. If earth has a mass nine times and radius twice to that of a planet P. Then 
?? ?? 3
v?? ms
-1
 will be the 
minimum velocity required by a rocket to pull out of gravitational force of P, where ?? ?? is escape 
velocity on earth. The value of ?? is 
 (1) 1 (2) 3 (3) 18 (4) 2 
 
E 1 
(I) 
(II) 
(III) 
E 1 
E 2 
E 2 
E 1 
E 2 
E 1 
 d    
+ ? 
+ ? 
Sol. (4) 
 
EP
M 9M ? 
 
EP
R 2R ? 
 
E
1 P
c
E
P
M
2G
2GM
9
V
R
R
2
?? 
     
E
E
2GM 2
R9
??  
  
1 e
c
V
V2
3
? 
 
 
5. A sample of gas at temperature ?? is adiabatically expanded to double its volume. The work done by 
the gas in the process is 
3
given, ?
2
 : 
 (1) ?? =
?? ?? [v2- 2] (2) ?? = ???? [2- v2] (3) ?? = ???? [v2- 2] (4) ?? =
?? ?? [2- v2] 
Sol. (2) 
 Work done in the process is given by 
 
12
R
W (T T )
1
??
??
 
 For adiabatic process: 
 
11
1 1 2 2
T V T V
? ? ? ?
? 
 
33
11
22
2
TV T (2V)
??
? 
 
11
22
2
TV T (2V) ? 
 
22
2
T V T 2V ?? 
 
2
T
T
2
?? 
 
RT
WT
1 2
??
? ? ? ?
??
??
??
 
 = 
1
2RT 1
2
??
?
??
??
 
 = 
2
RT 2
2
??
?
??
??
 
 = RT[2 2] ? 
 W RT 2 2
??
??
??
 
 
 
6. 
2
a
P (V– b) RT
V
 represents the equation of state of some gases. Where P is the pressure, ?? is the 
volume, ?? is the temperature and ?? ,?? ,?? are the constants. The physical quantity, which has 
dimensional formula as that of 
?? 2
?? , will be: 
 (1) Compressibility  (2) Energy density  
 (3) Modulus of rigidity (4) Bulk modulus 
Sol. (1) 
 ? ?
3
bL ?? ?
??
 
 ? ?
2
a PV ?? ?
??
 
        = 
1 2 6
ML T L
??
? ? ? ?
? ? ? ?
 
        = 
52
ML T
?
??
??
 
 
? ?
26
1 1 2
52
bL
M L T
a ML T
?
?
? ? ? ?
? ? ? ?
?? ??
??
??
??
 
 
 
7. The equivalent resistance between ?? and ?? of the network shown in figure: 
 
 (1) 
8
3
R (2) 21R (3) 14R (4) 11
2
3
R 
Sol. (1) 
  The given network is wheat-stone network 
  
 ?  
eq
4R 8R
R
4R 8R
?
?
?
 
  
4R 8R
12R
?
? 
      
eq
8
RR
3
?  
 
  
R 
2R 
6R 
3R 
Page 5


SECTION - A 
1.  A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an 
initial speed of 5 ms
-1
. Neglecting the air resistance, the speed with which the stone hits the ground 
will be __ ms
-1
 (given, ?? = 10 ms
-2
 ). 
 (1) 15 (2) 20 (3) 30 (4) 25 
Sol. (1) 
 Along vertical direction 
 sy = 10 m 
 = 15 m/s 
 
 
2. Let ?? be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the 
electric fields in three different region ?? ?? ,?? ????
 and ?? ??????
 are: 
 
 (1) ?? ? 
?? =
2?? ?? 0
?? ˆ,?? ? 
????
= 0,?? ? 
??????
=
2?? ?? 0
?? ˆ (2) ?? ? 
?? =
?? 2?? 0
?? ˆ,?? ? 
????
= 0,?? ? 
??????
=
?? 2?? 0
?? ˆ 
 (3) ?? ? 
?? = -
?? ?? 0
?? ˆ,?? ? 
????
= 0,?? ? 
??????
=
?? ?? 0
?? ˆ (4) ?? ? 
?? = 0,?? ? 
????
=
?? ?? 0
?? ˆ,?? ??????
= 0 
 
 
5m/s 
v 
g 
10m  
 
 = 25 200 ?  = 225   
?? 
xy
v v v ?   
22
y
v 200 ?  
2
y
v 200 ?  
y
v ? ?     
2
??         =
2
(0) 2 10 10 ? ? ? ag 
y
?? 
y y y y
v u 2a g u0 ?   
22
 
y
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 1st February, 2023) TIME : 9 : 00 AM to 12 : 00 NOON 
 
 
Sol. (3) 
   
 
I
0
ˆ En
E
?
? ? ? 
 
II
E0 ?? 
 
III
0
ˆ En
E
?
? ? ? 
 
3. A mercury drop of radius 10
-3
 m is broken into 125 equal size droplets. 
 Surface tension of mercury is 0.45Nm
-1
. The gain in surface energy is: 
 (1) 28× 10
-5
 J (2) 17.5 × 10
-5
 J (3) 5 × 10
-5
 J (4) 2.26× 10
-5
 J 
Sol. (4) 
 [Volume of bigger drop] = [volume of smaller drop] × 125 
 
33
44
R 125 r
33
? ? ? ? 
 
33
R 125r ? 
 R 5 r ? ? ? 
 ?  Gain in sinface energy = TdA 
  
? ?
21
0.45 A A ? ? ? 
  
22
0.45 125 4 r 4 R ?? ? ? ? ? ? ?
??
 
  
2
2
R
0.45 125 4 4 R
5
??
??
? ? ? ? ? ?
??
??
??
??
??
 
  
22
0.45 20 R 4 R ?? ? ? ? ? ?
??
 
  
2
0.45 16 R ? ? ? 
  
? ?
2
3
0.45 16 3.14 10
?
? ? ? ? 
  
5
2.26 10 J
?
?? 
 
4. If earth has a mass nine times and radius twice to that of a planet P. Then 
?? ?? 3
v?? ms
-1
 will be the 
minimum velocity required by a rocket to pull out of gravitational force of P, where ?? ?? is escape 
velocity on earth. The value of ?? is 
 (1) 1 (2) 3 (3) 18 (4) 2 
 
E 1 
(I) 
(II) 
(III) 
E 1 
E 2 
E 2 
E 1 
E 2 
E 1 
 d    
+ ? 
+ ? 
Sol. (4) 
 
EP
M 9M ? 
 
EP
R 2R ? 
 
E
1 P
c
E
P
M
2G
2GM
9
V
R
R
2
?? 
     
E
E
2GM 2
R9
??  
  
1 e
c
V
V2
3
? 
 
 
5. A sample of gas at temperature ?? is adiabatically expanded to double its volume. The work done by 
the gas in the process is 
3
given, ?
2
 : 
 (1) ?? =
?? ?? [v2- 2] (2) ?? = ???? [2- v2] (3) ?? = ???? [v2- 2] (4) ?? =
?? ?? [2- v2] 
Sol. (2) 
 Work done in the process is given by 
 
12
R
W (T T )
1
??
??
 
 For adiabatic process: 
 
11
1 1 2 2
T V T V
? ? ? ?
? 
 
33
11
22
2
TV T (2V)
??
? 
 
11
22
2
TV T (2V) ? 
 
22
2
T V T 2V ?? 
 
2
T
T
2
?? 
 
RT
WT
1 2
??
? ? ? ?
??
??
??
 
 = 
1
2RT 1
2
??
?
??
??
 
 = 
2
RT 2
2
??
?
??
??
 
 = RT[2 2] ? 
 W RT 2 2
??
??
??
 
 
 
6. 
2
a
P (V– b) RT
V
 represents the equation of state of some gases. Where P is the pressure, ?? is the 
volume, ?? is the temperature and ?? ,?? ,?? are the constants. The physical quantity, which has 
dimensional formula as that of 
?? 2
?? , will be: 
 (1) Compressibility  (2) Energy density  
 (3) Modulus of rigidity (4) Bulk modulus 
Sol. (1) 
 ? ?
3
bL ?? ?
??
 
 ? ?
2
a PV ?? ?
??
 
        = 
1 2 6
ML T L
??
? ? ? ?
? ? ? ?
 
        = 
52
ML T
?
??
??
 
 
? ?
26
1 1 2
52
bL
M L T
a ML T
?
?
? ? ? ?
? ? ? ?
?? ??
??
??
??
 
 
 
7. The equivalent resistance between ?? and ?? of the network shown in figure: 
 
 (1) 
8
3
R (2) 21R (3) 14R (4) 11
2
3
R 
Sol. (1) 
  The given network is wheat-stone network 
  
 ?  
eq
4R 8R
R
4R 8R
?
?
?
 
  
4R 8R
12R
?
? 
      
eq
8
RR
3
?  
 
  
R 
2R 
6R 
3R 
 
8. Match List I with List II: 
List I List II 
A. AC generator I. Presence of both L and C 
B. Transformer II. Electromagnetic Induction 
C. Resonance phenomenon to occur III. Quality factor 
D. Sharpness of resonance IV. Mutual Induction 
 
 Choose the correct answer from the options given below: 
 (1) A-IV, B-III, C-I, D-II (2) A-IV, B-II, C-I, D-III 
 (3) A-II, B-IV, C-I, D-III (4) A-II, B-I, C-III, D-IV 
Sol. (3) 
 (A) A.C. generator ? II. Electro-magnetic induction 
 (B) transformer  ? IV Mutual induction 
 (C) Resonance phenomenon to occur ?  (I) presence of both L and C 
 (D) Sharpness of resonance ? (III) Quality factor 
 
 
9. An object moves with speed ?? 1
,?? 2
 and ?? 3
 along a line segment AB,BC and CD respectively as shown 
in figure. Where AB = BC and AD = 3AB, then average speed of the object will be: 
 
 (1) 
(?? 1
+?? 2
+?? 3
)
3?? 1
?? 2
?? 3
 (2) 
(?? 1
+?? 2
+?? 3
)
3
 (3) 
3?? 1
?? 2
?? 3
(?? 1
?? 2
+?? 2
?? 3
+?? 3
?? 1
)
 (4) 
?? 1
?? 2
?? 3
3(?? 1
?? 2
+?? 2
?? 3
+?? 3
?? 1
)
 
Sol. (3) 
  
 <v> = 
Total distance
Total time
 
         
1 2 3
3x
x x x
v v v
?
??
 
       
2 3 1 3 1 2
1 2 3 1 2 3
33
v v v v v v 1 1 1
v v v v v v
??
? ? ? ? ??
??
? ? ? ?
? ? ? ?
 
 <v> = 
? ?
1 2 3
3 2 1 2 1 2
3v v v
v v v v v v ??
 
 
 
 
 
x 
A 
v 1 v 2 
v 3 B C D 
x x