JEE Main 2023 February 1 Shift 2 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


SECTION - A 
1. For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them 
at constant volume, as shown in the figure. 
 
 The temperature corresponding to the point ' K ' is : 
 (1) -273
°
C (2) -100
°
C (3) -40
°
C (4) -373
°
C 
Sol. (1)  
 From ideal gas equation 
 PV = nRT 
   volume is constant 
 It is clear from graph that for all the gases lines of graphs meet at same value. 
 At x-axis (temperature axis) P is zero but temperature is negative and it will be equal to 0 K or –273ºC 
 
2. Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. 
 Assertion A : For measuring the potential difference across a resistance of 600O, the voltmeter with 
resistance 1000O will be preferred over voltmeter with resistance 4000O. 
 Reason R : Voltmeter with higher resistance will draw smaller current than voltmeter with lower 
resistance. 
 In the light of the above statements, choose the most appropriate answer from the options given 
below. 
 (1) Both ?? and ?? are correct and ?? is the correct explanation of ?? 
 (2) Both ?? and ?? are correct but ?? is not the correct explanation of ?? 
 (3) ?? is not correct but ?? is correct 
 (4) ?? is correct but ?? is not correct 
Sol. (3) 
 To measure the potential difference between two point, voltmeter is used. But this voltmeter should be with 
higher resistance so that it cannot draw any current. 
 Now to measure the potential difference across 600 ? voltmeter of 4000 ? is much better than 1000 ? voltmeter.  
 
3. Figures (a), (b), (c) and (d) show variation of force with time. 
 
 The impulse is highest in figure. 
 (1) Fig (c) (2) Fig (b) (3) Fig (d) (4) Fig (a) 
 
 PT ?  
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 1st February, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
Page 2


SECTION - A 
1. For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them 
at constant volume, as shown in the figure. 
 
 The temperature corresponding to the point ' K ' is : 
 (1) -273
°
C (2) -100
°
C (3) -40
°
C (4) -373
°
C 
Sol. (1)  
 From ideal gas equation 
 PV = nRT 
   volume is constant 
 It is clear from graph that for all the gases lines of graphs meet at same value. 
 At x-axis (temperature axis) P is zero but temperature is negative and it will be equal to 0 K or –273ºC 
 
2. Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. 
 Assertion A : For measuring the potential difference across a resistance of 600O, the voltmeter with 
resistance 1000O will be preferred over voltmeter with resistance 4000O. 
 Reason R : Voltmeter with higher resistance will draw smaller current than voltmeter with lower 
resistance. 
 In the light of the above statements, choose the most appropriate answer from the options given 
below. 
 (1) Both ?? and ?? are correct and ?? is the correct explanation of ?? 
 (2) Both ?? and ?? are correct but ?? is not the correct explanation of ?? 
 (3) ?? is not correct but ?? is correct 
 (4) ?? is correct but ?? is not correct 
Sol. (3) 
 To measure the potential difference between two point, voltmeter is used. But this voltmeter should be with 
higher resistance so that it cannot draw any current. 
 Now to measure the potential difference across 600 ? voltmeter of 4000 ? is much better than 1000 ? voltmeter.  
 
3. Figures (a), (b), (c) and (d) show variation of force with time. 
 
 The impulse is highest in figure. 
 (1) Fig (c) (2) Fig (b) (3) Fig (d) (4) Fig (a) 
 
 PT ?  
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 1st February, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
Sol. (2) 
As we know that impulse is given by 
  I P F t ? ? ? ? ? 
 or I = Area of f-t graph 
 For fig (a) ? I =
1
2
 × base × height 
   = 
1
0.5 1 0.25 N sec.
2
? ? ? ? 
 For fig (b) I = length × width 
          = 2 × 0.5 = 1 N-sec 
  For fig (c) I = 
1
2
 × base × height 
             = 
1
2
× 1 × 0.75 = 0.375 N-sec. 
  For fig (d) I = 
1
2
× base × height 
             = 
1
2
× 2 × 0.5 = 0.5 N-sec. 
 Impulse is highest for that figure, whose area under F-t is maximum and i.e. figure(b)  
 Option (2) is correct. 
 
 
4. An electron of a hydrogen like atom, having ?? = 4, jumps from 4
th 
 energy state to 2
nd 
 energy state. 
The energy released in this process, will be : 
 (Given Rch = 13.6eV) 
 Where R = Rydberg constant 
 c = Speed of light in vacuum 
 h = Planck's constant 
 (1) 40.8eV  (2) 3.4eV 
 (3) 10.5eV  (4) 13.6eV 
Sol. (1) 
 
2
22
12
11
E 13.6Z
nn
??
? ? ?
??
??
 
 Z = 4 (hydrogen like atom) 
 n 1 = 2, n 2 = 4 
 
2
11
E 13.6(4)
4 16
??
? ? ?
??
??
 
      
16 4
13.6 16
64
? ??
? ? ?
??
??
 
 
12
E 13.6 16
64
? ? ? ? 
 E 40.8eV ?? 
 
 
5. The ratio of average electric energy density and total average energy density of electromagnetic wave 
is : 
 (1) 3 (2) 
1
2
 (3) 1 (4) 2 
 
Page 3


SECTION - A 
1. For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them 
at constant volume, as shown in the figure. 
 
 The temperature corresponding to the point ' K ' is : 
 (1) -273
°
C (2) -100
°
C (3) -40
°
C (4) -373
°
C 
Sol. (1)  
 From ideal gas equation 
 PV = nRT 
   volume is constant 
 It is clear from graph that for all the gases lines of graphs meet at same value. 
 At x-axis (temperature axis) P is zero but temperature is negative and it will be equal to 0 K or –273ºC 
 
2. Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. 
 Assertion A : For measuring the potential difference across a resistance of 600O, the voltmeter with 
resistance 1000O will be preferred over voltmeter with resistance 4000O. 
 Reason R : Voltmeter with higher resistance will draw smaller current than voltmeter with lower 
resistance. 
 In the light of the above statements, choose the most appropriate answer from the options given 
below. 
 (1) Both ?? and ?? are correct and ?? is the correct explanation of ?? 
 (2) Both ?? and ?? are correct but ?? is not the correct explanation of ?? 
 (3) ?? is not correct but ?? is correct 
 (4) ?? is correct but ?? is not correct 
Sol. (3) 
 To measure the potential difference between two point, voltmeter is used. But this voltmeter should be with 
higher resistance so that it cannot draw any current. 
 Now to measure the potential difference across 600 ? voltmeter of 4000 ? is much better than 1000 ? voltmeter.  
 
3. Figures (a), (b), (c) and (d) show variation of force with time. 
 
 The impulse is highest in figure. 
 (1) Fig (c) (2) Fig (b) (3) Fig (d) (4) Fig (a) 
 
 PT ?  
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 1st February, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
Sol. (2) 
As we know that impulse is given by 
  I P F t ? ? ? ? ? 
 or I = Area of f-t graph 
 For fig (a) ? I =
1
2
 × base × height 
   = 
1
0.5 1 0.25 N sec.
2
? ? ? ? 
 For fig (b) I = length × width 
          = 2 × 0.5 = 1 N-sec 
  For fig (c) I = 
1
2
 × base × height 
             = 
1
2
× 1 × 0.75 = 0.375 N-sec. 
  For fig (d) I = 
1
2
× base × height 
             = 
1
2
× 2 × 0.5 = 0.5 N-sec. 
 Impulse is highest for that figure, whose area under F-t is maximum and i.e. figure(b)  
 Option (2) is correct. 
 
 
4. An electron of a hydrogen like atom, having ?? = 4, jumps from 4
th 
 energy state to 2
nd 
 energy state. 
The energy released in this process, will be : 
 (Given Rch = 13.6eV) 
 Where R = Rydberg constant 
 c = Speed of light in vacuum 
 h = Planck's constant 
 (1) 40.8eV  (2) 3.4eV 
 (3) 10.5eV  (4) 13.6eV 
Sol. (1) 
 
2
22
12
11
E 13.6Z
nn
??
? ? ?
??
??
 
 Z = 4 (hydrogen like atom) 
 n 1 = 2, n 2 = 4 
 
2
11
E 13.6(4)
4 16
??
? ? ?
??
??
 
      
16 4
13.6 16
64
? ??
? ? ?
??
??
 
 
12
E 13.6 16
64
? ? ? ? 
 E 40.8eV ?? 
 
 
5. The ratio of average electric energy density and total average energy density of electromagnetic wave 
is : 
 (1) 3 (2) 
1
2
 (3) 1 (4) 2 
 
Sol. (2) 
Ratio of average electric energy density and total Avg energy density. 
 Avg electric energy density = 
2
00
1
E
4
? 
 Total Avg energy density = 
2
00
1
E
2
? 
 ? 
2
00
2
00
1
E
21
4
1
42
E
2
?
??
?
 
 
6. Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having 
radius of curvature 40 cm. The distance between images formed by the mirror is _______. 
 (1) 100 cm (2) 60 cm (3) 160 cm (4) 40 cm 
Sol. (3) 
 
 
25 cm 
Q 2 
Q 1 
155 cm 
R = 40 cm, f = 20cm 
  
 Using Mirror formula  
 
1 1 1
v u f
?? 
 
1 1 1
v f f
?? 
 
4f
v
uf
?
?
 
 For object A(O 1) u i = –15 cm, f = –20 cm, V 1 = ? 
 
uf
1
v
1
uf
1
?
?
( 15)( 20) 300
( 15) (20) 5
? ? ?
??
??
 
 
1
v 60cm ?? 
 For object B(O 2) u 2 = –25 cm, f = –20cm v 2 = ? 
 
2
2
2
uf ( 25)( 20) 500
v
u f ( 25) ( 20) 5
??
? ? ?
? ? ? ? ?
 
 
2
v 100cm ?? 
 Hence, the distance between images formed by the mirror is 
 d 160cm ? 
 
 
 
 
Page 4


SECTION - A 
1. For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them 
at constant volume, as shown in the figure. 
 
 The temperature corresponding to the point ' K ' is : 
 (1) -273
°
C (2) -100
°
C (3) -40
°
C (4) -373
°
C 
Sol. (1)  
 From ideal gas equation 
 PV = nRT 
   volume is constant 
 It is clear from graph that for all the gases lines of graphs meet at same value. 
 At x-axis (temperature axis) P is zero but temperature is negative and it will be equal to 0 K or –273ºC 
 
2. Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. 
 Assertion A : For measuring the potential difference across a resistance of 600O, the voltmeter with 
resistance 1000O will be preferred over voltmeter with resistance 4000O. 
 Reason R : Voltmeter with higher resistance will draw smaller current than voltmeter with lower 
resistance. 
 In the light of the above statements, choose the most appropriate answer from the options given 
below. 
 (1) Both ?? and ?? are correct and ?? is the correct explanation of ?? 
 (2) Both ?? and ?? are correct but ?? is not the correct explanation of ?? 
 (3) ?? is not correct but ?? is correct 
 (4) ?? is correct but ?? is not correct 
Sol. (3) 
 To measure the potential difference between two point, voltmeter is used. But this voltmeter should be with 
higher resistance so that it cannot draw any current. 
 Now to measure the potential difference across 600 ? voltmeter of 4000 ? is much better than 1000 ? voltmeter.  
 
3. Figures (a), (b), (c) and (d) show variation of force with time. 
 
 The impulse is highest in figure. 
 (1) Fig (c) (2) Fig (b) (3) Fig (d) (4) Fig (a) 
 
 PT ?  
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 1st February, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
Sol. (2) 
As we know that impulse is given by 
  I P F t ? ? ? ? ? 
 or I = Area of f-t graph 
 For fig (a) ? I =
1
2
 × base × height 
   = 
1
0.5 1 0.25 N sec.
2
? ? ? ? 
 For fig (b) I = length × width 
          = 2 × 0.5 = 1 N-sec 
  For fig (c) I = 
1
2
 × base × height 
             = 
1
2
× 1 × 0.75 = 0.375 N-sec. 
  For fig (d) I = 
1
2
× base × height 
             = 
1
2
× 2 × 0.5 = 0.5 N-sec. 
 Impulse is highest for that figure, whose area under F-t is maximum and i.e. figure(b)  
 Option (2) is correct. 
 
 
4. An electron of a hydrogen like atom, having ?? = 4, jumps from 4
th 
 energy state to 2
nd 
 energy state. 
The energy released in this process, will be : 
 (Given Rch = 13.6eV) 
 Where R = Rydberg constant 
 c = Speed of light in vacuum 
 h = Planck's constant 
 (1) 40.8eV  (2) 3.4eV 
 (3) 10.5eV  (4) 13.6eV 
Sol. (1) 
 
2
22
12
11
E 13.6Z
nn
??
? ? ?
??
??
 
 Z = 4 (hydrogen like atom) 
 n 1 = 2, n 2 = 4 
 
2
11
E 13.6(4)
4 16
??
? ? ?
??
??
 
      
16 4
13.6 16
64
? ??
? ? ?
??
??
 
 
12
E 13.6 16
64
? ? ? ? 
 E 40.8eV ?? 
 
 
5. The ratio of average electric energy density and total average energy density of electromagnetic wave 
is : 
 (1) 3 (2) 
1
2
 (3) 1 (4) 2 
 
Sol. (2) 
Ratio of average electric energy density and total Avg energy density. 
 Avg electric energy density = 
2
00
1
E
4
? 
 Total Avg energy density = 
2
00
1
E
2
? 
 ? 
2
00
2
00
1
E
21
4
1
42
E
2
?
??
?
 
 
6. Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having 
radius of curvature 40 cm. The distance between images formed by the mirror is _______. 
 (1) 100 cm (2) 60 cm (3) 160 cm (4) 40 cm 
Sol. (3) 
 
 
25 cm 
Q 2 
Q 1 
155 cm 
R = 40 cm, f = 20cm 
  
 Using Mirror formula  
 
1 1 1
v u f
?? 
 
1 1 1
v f f
?? 
 
4f
v
uf
?
?
 
 For object A(O 1) u i = –15 cm, f = –20 cm, V 1 = ? 
 
uf
1
v
1
uf
1
?
?
( 15)( 20) 300
( 15) (20) 5
? ? ?
??
??
 
 
1
v 60cm ?? 
 For object B(O 2) u 2 = –25 cm, f = –20cm v 2 = ? 
 
2
2
2
uf ( 25)( 20) 500
v
u f ( 25) ( 20) 5
??
? ? ?
? ? ? ? ?
 
 
2
v 100cm ?? 
 Hence, the distance between images formed by the mirror is 
 d 160cm ? 
 
 
 
 
7. Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of 
resistance R would be: 
 (1) 
?? 2
?? ?? -1
 (2) 
(?? -1)?? ?? (3) 
(?? -1)?? ?? 2
 (4) 
(?? -1)?? (2?? -1)
 
Sol. (3) 
When, a uniform wire of resistance R is shaped into a regular n-sided polygon, the resistance of each side will 
be  
 
1
R
R
n
? 
 Let R 1 & R 2 be the resistance between adjacent corners of a regular polygon 
 ?  The resistance of (n –1) side, 
? ?
2
n 1 R
R
n
?
? 
 Since two parts are parallel, therefore R eq 
 R eq = 
12
12
R n 1
R
RR nn
R n 1 RR
R
nn
? ? ? ? ?
? ? ? ?
? ? ? ?
?
? ? ? ? ? ?
?
? ? ? ?
? ? ? ?
 
 R eq = 
2
2
(n 1)R n
n R nR R
?
?
??
 
 
eq 2
(n 1)R
R
n
?
? 
 
 
8. A Carnot engine operating between two reservoirs has efficiency 
1
3
. When the temperature of cold 
reservoir raised by ?? , its efficiency decreases to 
1
6
. The value of ?? , if the temperature of hot reservoir is 
99
°
C, will be : 
 (1) 66 K (2) 62 K (3) 33 K (4) 16.5 K 
Sol. (2) 
 Given   
1
3
?? 
 When ? ?
22
T T x ??  i.e., temp. of cold reservior 
 
1
'
6
?? 
 Temp. of hot reservior (T 1) = 99°C 
  = 99 + 273 = 372ºK 
 As we know, 
 
2
1
T 1
1
T3
? ? ? ?   …( 1) 
 
2
1
(T x) 1
'1
T6
?
? ? ? ?   …( 2) 
 
12
1
T (T x) 1
'
T6
??
? ? ? 
 From equqation (1) 
 
2
T 1
1
3 372
?? 
Page 5


SECTION - A 
1. For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them 
at constant volume, as shown in the figure. 
 
 The temperature corresponding to the point ' K ' is : 
 (1) -273
°
C (2) -100
°
C (3) -40
°
C (4) -373
°
C 
Sol. (1)  
 From ideal gas equation 
 PV = nRT 
   volume is constant 
 It is clear from graph that for all the gases lines of graphs meet at same value. 
 At x-axis (temperature axis) P is zero but temperature is negative and it will be equal to 0 K or –273ºC 
 
2. Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. 
 Assertion A : For measuring the potential difference across a resistance of 600O, the voltmeter with 
resistance 1000O will be preferred over voltmeter with resistance 4000O. 
 Reason R : Voltmeter with higher resistance will draw smaller current than voltmeter with lower 
resistance. 
 In the light of the above statements, choose the most appropriate answer from the options given 
below. 
 (1) Both ?? and ?? are correct and ?? is the correct explanation of ?? 
 (2) Both ?? and ?? are correct but ?? is not the correct explanation of ?? 
 (3) ?? is not correct but ?? is correct 
 (4) ?? is correct but ?? is not correct 
Sol. (3) 
 To measure the potential difference between two point, voltmeter is used. But this voltmeter should be with 
higher resistance so that it cannot draw any current. 
 Now to measure the potential difference across 600 ? voltmeter of 4000 ? is much better than 1000 ? voltmeter.  
 
3. Figures (a), (b), (c) and (d) show variation of force with time. 
 
 The impulse is highest in figure. 
 (1) Fig (c) (2) Fig (b) (3) Fig (d) (4) Fig (a) 
 
 PT ?  
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 1st February, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
Sol. (2) 
As we know that impulse is given by 
  I P F t ? ? ? ? ? 
 or I = Area of f-t graph 
 For fig (a) ? I =
1
2
 × base × height 
   = 
1
0.5 1 0.25 N sec.
2
? ? ? ? 
 For fig (b) I = length × width 
          = 2 × 0.5 = 1 N-sec 
  For fig (c) I = 
1
2
 × base × height 
             = 
1
2
× 1 × 0.75 = 0.375 N-sec. 
  For fig (d) I = 
1
2
× base × height 
             = 
1
2
× 2 × 0.5 = 0.5 N-sec. 
 Impulse is highest for that figure, whose area under F-t is maximum and i.e. figure(b)  
 Option (2) is correct. 
 
 
4. An electron of a hydrogen like atom, having ?? = 4, jumps from 4
th 
 energy state to 2
nd 
 energy state. 
The energy released in this process, will be : 
 (Given Rch = 13.6eV) 
 Where R = Rydberg constant 
 c = Speed of light in vacuum 
 h = Planck's constant 
 (1) 40.8eV  (2) 3.4eV 
 (3) 10.5eV  (4) 13.6eV 
Sol. (1) 
 
2
22
12
11
E 13.6Z
nn
??
? ? ?
??
??
 
 Z = 4 (hydrogen like atom) 
 n 1 = 2, n 2 = 4 
 
2
11
E 13.6(4)
4 16
??
? ? ?
??
??
 
      
16 4
13.6 16
64
? ??
? ? ?
??
??
 
 
12
E 13.6 16
64
? ? ? ? 
 E 40.8eV ?? 
 
 
5. The ratio of average electric energy density and total average energy density of electromagnetic wave 
is : 
 (1) 3 (2) 
1
2
 (3) 1 (4) 2 
 
Sol. (2) 
Ratio of average electric energy density and total Avg energy density. 
 Avg electric energy density = 
2
00
1
E
4
? 
 Total Avg energy density = 
2
00
1
E
2
? 
 ? 
2
00
2
00
1
E
21
4
1
42
E
2
?
??
?
 
 
6. Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having 
radius of curvature 40 cm. The distance between images formed by the mirror is _______. 
 (1) 100 cm (2) 60 cm (3) 160 cm (4) 40 cm 
Sol. (3) 
 
 
25 cm 
Q 2 
Q 1 
155 cm 
R = 40 cm, f = 20cm 
  
 Using Mirror formula  
 
1 1 1
v u f
?? 
 
1 1 1
v f f
?? 
 
4f
v
uf
?
?
 
 For object A(O 1) u i = –15 cm, f = –20 cm, V 1 = ? 
 
uf
1
v
1
uf
1
?
?
( 15)( 20) 300
( 15) (20) 5
? ? ?
??
??
 
 
1
v 60cm ?? 
 For object B(O 2) u 2 = –25 cm, f = –20cm v 2 = ? 
 
2
2
2
uf ( 25)( 20) 500
v
u f ( 25) ( 20) 5
??
? ? ?
? ? ? ? ?
 
 
2
v 100cm ?? 
 Hence, the distance between images formed by the mirror is 
 d 160cm ? 
 
 
 
 
7. Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of 
resistance R would be: 
 (1) 
?? 2
?? ?? -1
 (2) 
(?? -1)?? ?? (3) 
(?? -1)?? ?? 2
 (4) 
(?? -1)?? (2?? -1)
 
Sol. (3) 
When, a uniform wire of resistance R is shaped into a regular n-sided polygon, the resistance of each side will 
be  
 
1
R
R
n
? 
 Let R 1 & R 2 be the resistance between adjacent corners of a regular polygon 
 ?  The resistance of (n –1) side, 
? ?
2
n 1 R
R
n
?
? 
 Since two parts are parallel, therefore R eq 
 R eq = 
12
12
R n 1
R
RR nn
R n 1 RR
R
nn
? ? ? ? ?
? ? ? ?
? ? ? ?
?
? ? ? ? ? ?
?
? ? ? ?
? ? ? ?
 
 R eq = 
2
2
(n 1)R n
n R nR R
?
?
??
 
 
eq 2
(n 1)R
R
n
?
? 
 
 
8. A Carnot engine operating between two reservoirs has efficiency 
1
3
. When the temperature of cold 
reservoir raised by ?? , its efficiency decreases to 
1
6
. The value of ?? , if the temperature of hot reservoir is 
99
°
C, will be : 
 (1) 66 K (2) 62 K (3) 33 K (4) 16.5 K 
Sol. (2) 
 Given   
1
3
?? 
 When ? ?
22
T T x ??  i.e., temp. of cold reservior 
 
1
'
6
?? 
 Temp. of hot reservior (T 1) = 99°C 
  = 99 + 273 = 372ºK 
 As we know, 
 
2
1
T 1
1
T3
? ? ? ?   …( 1) 
 
2
1
(T x) 1
'1
T6
?
? ? ? ?   …( 2) 
 
12
1
T (T x) 1
'
T6
??
? ? ? 
 From equqation (1) 
 
2
T 1
1
3 372
?? 
 
2
372 T 1
3 372
?
? 
 
2
372
372 T
3
?? 
 
2
T 248K ? 
 By putting the value of T 2 in equation (2) 
 
? ?
12
1
T T x
1
T6
??
? 
 
372 (248 x) 1
372 6
??
? 
 
372
372 24 x
6
? ? ? 
 124 x 62 ?? 
 124 62 x ?? 
 x 62K ? 
 
9. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. 
 Assertion A: Two metallic spheres are charged to the same potential. One of them is hollow and 
another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow 
one. 
 Reason R: Capacitance of metallic spheres depend on the radii of spheres. 
 In the light of the above statements, choose the correct answer from the options given below. 
 (1) Both ?? and ?? are true and ?? is the correct explanation of ?? 
 (2) ?? is true but ?? is false 
 (3) ?? is false but ?? is true 4. 
 (4) Both ?? and ?? are true but ?? is not the correct explanation of ?? 
Sol. (3) 
 As we know, capacitance of spherical conductor 
 
0
C 4 R ? ? ?  
 So, capacitance does not depend on its charge, it depends only on the radius of the conductor (R). 
 Therefore, assertion is false, R is true. 
 
10. If the velocity of light c, universal gravitational constant G and Planck's constant h are chosen as 
fundamental quantities. The dimensions of mass in the new system is : 
 (1) [h
1/2
c
-1/2
?? 1
] (2) [h
-1/2
?? 1/2
?? 1/2
] (3) [?? 1/2
?? 1/2
?? -1/2
] (4) [h
1
c
1
G
-1
] 
Sol. (3)  
? ? ? ? ? ? ? ?
x y z
M G h c ? 
 
? ?
x 4 z
1 3 2 2 1 1
M M L T ML T LT
? ? ? ?
? ? ? ? ? ? ?
? ? ? ? ? ?
 
 
2 0 o x y 3x 2y z 2x y z
M L T M L T
? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
 
 y – x = 1   …( 1) 
 3x + 2y + z = 0  …( 2) 
 –2x –y – z = 0  …( 3) 
 On solving, 
1
x
2
?? , 
1
y
2
? , 
1
z
2
? 
 So  
hc
m
G
?