JEE Main 2023 January 24 Shift 2 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


SECTION - A 
1. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. 
 Assertion A: A pendulum clock when taken to Mount Everest becomes fast. 
 Reason: The value of g (acceleration due to gravity) is less at Mount Everest than its value on the 
surface of earth. 
 In the light of the above statements, choose the most appropriate answer from the options given below 
 (1) Both ?? and ?? are correct but ?? is NOT the correct explanation of ?? 
 (2) A is correct but ?? is not correct 
 (3) Both ?? and ?? are correct and ?? is the correct explanation of ?? 
 (4) ?? is not correct but ?? is correct 
Sol. 4 
 
 on Everest g decreases, so T increases, so moves slow. 
 
2. The frequency (?? ) of an oscillating liquid drop may depend upon radius (?? ) of the drop, density (?? ) of 
liquid and the surface tension (s) of the liquid as : ?? = ?? a
?? b
s
c
. The values of a,b and c respectively are 
 (1) (-
3
2
,
1
2
,
1
2
) (2) (
3
2
,-
1
2
,
1
2
) (3) (-
3
2
,-
1
2
,
1
2
) (4) (
3
2
,
1
2
,-
1
2
) 
Sol. 3 
 
 
 
 –2c = –1 ……. (1) 
 c = ½ 
 b + c = 0 … … ….(2) 
 b = –½ 
 a – 3b = 0 ………(3) 
 a = 3b =  
 
3. Given below are two statements: 
 Statement I : Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. 
 Statement II : Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's 
surface, if h = d. 
 In the light of above statements, choose the most appropriate answer form the options given below 
 (1) Both Statement I and Statement II are incorrect 
 (2) Statement I is incorrect but statement II is correct 
 (3) Both Statement I and II are correct 
 (4) Statement I is correct but statement II is incorrect 
Sol. 4 
  =  
 
 
R 
g 
r 
2
? 
d
h
??
??
?
R
?? d
g1
??
??
?
R
?? 2h
g1
?3
2
1 a 3b b c 2c
T L , M T
? ? ? ?
? 
? ? ? ?
a
1 3 2
T L M L MT
? ? ?
? ? ? ? ?
bc
?? 
 ? ?
a b c
f r s
g
? 
1
T
??  T2
g
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 24th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
Page 2


SECTION - A 
1. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. 
 Assertion A: A pendulum clock when taken to Mount Everest becomes fast. 
 Reason: The value of g (acceleration due to gravity) is less at Mount Everest than its value on the 
surface of earth. 
 In the light of the above statements, choose the most appropriate answer from the options given below 
 (1) Both ?? and ?? are correct but ?? is NOT the correct explanation of ?? 
 (2) A is correct but ?? is not correct 
 (3) Both ?? and ?? are correct and ?? is the correct explanation of ?? 
 (4) ?? is not correct but ?? is correct 
Sol. 4 
 
 on Everest g decreases, so T increases, so moves slow. 
 
2. The frequency (?? ) of an oscillating liquid drop may depend upon radius (?? ) of the drop, density (?? ) of 
liquid and the surface tension (s) of the liquid as : ?? = ?? a
?? b
s
c
. The values of a,b and c respectively are 
 (1) (-
3
2
,
1
2
,
1
2
) (2) (
3
2
,-
1
2
,
1
2
) (3) (-
3
2
,-
1
2
,
1
2
) (4) (
3
2
,
1
2
,-
1
2
) 
Sol. 3 
 
 
 
 –2c = –1 ……. (1) 
 c = ½ 
 b + c = 0 … … ….(2) 
 b = –½ 
 a – 3b = 0 ………(3) 
 a = 3b =  
 
3. Given below are two statements: 
 Statement I : Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. 
 Statement II : Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's 
surface, if h = d. 
 In the light of above statements, choose the most appropriate answer form the options given below 
 (1) Both Statement I and Statement II are incorrect 
 (2) Statement I is incorrect but statement II is correct 
 (3) Both Statement I and II are correct 
 (4) Statement I is correct but statement II is incorrect 
Sol. 4 
  =  
 
 
R 
g 
r 
2
? 
d
h
??
??
?
R
?? d
g1
??
??
?
R
?? 2h
g1
?3
2
1 a 3b b c 2c
T L , M T
? ? ? ?
? 
? ? ? ?
a
1 3 2
T L M L MT
? ? ?
? ? ? ? ?
bc
?? 
 ? ?
a b c
f r s
g
? 
1
T
??  T2
g
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 24th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
4. A long solenoid is formed by winding 70 turns cm
– 1
. If 2.0 A current flows, then the magnetic field 
produced inside the solenoid is __________
? ?
71
0
4 10 TmA
??
? ? ? ? 
 (1) 88 × 10
– 4
 T (2) 352 × 10
– 4
 T (3) 176 × 10
– 4
 T (4) 1232 × 10
– 4
 T 
Sol. 3 
 
0
B ni ?? 
 = 
7
22
4 10 70 100 2
7
?
? ? ? ? ? 
 = 176 × 10
– 4
  
 
5. The electric potential at the centre of two concentric half rings of radii ?? 1
 and ?? 2
, having same linear 
charge density ?? is : 
 
 (1) 
0
2
?
?
 (2) 
0
4
?
?
 (3) 
0
2 ?
?
 (4) 
0
?
?
 
Sol. 1 
 
2
C1
12
kq K
Vq
RR
?? 
 = 
12
0 1 0 2
RR 11
4 R 4 R
? ? ? ?
? ? ?
? ? ? ?
 
 = 
0
2
?
?
 
 
 
6. If the distance of the earth from Sun is 1.5× 10
6
 km. Then the distance of an imaginary planet from 
Sun, if its period of revolution is 2.83 years is : 
 (1) 6 × 10
6
 km (2) 3 × 10
6
 km (3) 3 × 10
7
 km (4) 6 × 10
7
 km 
Sol. 2 
 
23
TR ? 
 
2
3
EE
pp
TR
TR
? ? ? ?
? ? ? ? ?
? ? ? ?
? ? ? ?
 
 
2
3
1
2.83
??
??
??
 = 
6
1.5 10
R
?
 
 R = 1.5 × 10
6
 × ? ?
2
3
2.83 
 1.5 × 10
6
 × ? ?
2
3
1.41 2 ? 
 1.5 × 10
6
 × 
? ?
2
3
22 
 1.5 × 10
6
 × 
? ?
2
3
8 
 3 × 10
6
 KM 
 
 
Page 3


SECTION - A 
1. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. 
 Assertion A: A pendulum clock when taken to Mount Everest becomes fast. 
 Reason: The value of g (acceleration due to gravity) is less at Mount Everest than its value on the 
surface of earth. 
 In the light of the above statements, choose the most appropriate answer from the options given below 
 (1) Both ?? and ?? are correct but ?? is NOT the correct explanation of ?? 
 (2) A is correct but ?? is not correct 
 (3) Both ?? and ?? are correct and ?? is the correct explanation of ?? 
 (4) ?? is not correct but ?? is correct 
Sol. 4 
 
 on Everest g decreases, so T increases, so moves slow. 
 
2. The frequency (?? ) of an oscillating liquid drop may depend upon radius (?? ) of the drop, density (?? ) of 
liquid and the surface tension (s) of the liquid as : ?? = ?? a
?? b
s
c
. The values of a,b and c respectively are 
 (1) (-
3
2
,
1
2
,
1
2
) (2) (
3
2
,-
1
2
,
1
2
) (3) (-
3
2
,-
1
2
,
1
2
) (4) (
3
2
,
1
2
,-
1
2
) 
Sol. 3 
 
 
 
 –2c = –1 ……. (1) 
 c = ½ 
 b + c = 0 … … ….(2) 
 b = –½ 
 a – 3b = 0 ………(3) 
 a = 3b =  
 
3. Given below are two statements: 
 Statement I : Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. 
 Statement II : Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's 
surface, if h = d. 
 In the light of above statements, choose the most appropriate answer form the options given below 
 (1) Both Statement I and Statement II are incorrect 
 (2) Statement I is incorrect but statement II is correct 
 (3) Both Statement I and II are correct 
 (4) Statement I is correct but statement II is incorrect 
Sol. 4 
  =  
 
 
R 
g 
r 
2
? 
d
h
??
??
?
R
?? d
g1
??
??
?
R
?? 2h
g1
?3
2
1 a 3b b c 2c
T L , M T
? ? ? ?
? 
? ? ? ?
a
1 3 2
T L M L MT
? ? ?
? ? ? ? ?
bc
?? 
 ? ?
a b c
f r s
g
? 
1
T
??  T2
g
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 24th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
4. A long solenoid is formed by winding 70 turns cm
– 1
. If 2.0 A current flows, then the magnetic field 
produced inside the solenoid is __________
? ?
71
0
4 10 TmA
??
? ? ? ? 
 (1) 88 × 10
– 4
 T (2) 352 × 10
– 4
 T (3) 176 × 10
– 4
 T (4) 1232 × 10
– 4
 T 
Sol. 3 
 
0
B ni ?? 
 = 
7
22
4 10 70 100 2
7
?
? ? ? ? ? 
 = 176 × 10
– 4
  
 
5. The electric potential at the centre of two concentric half rings of radii ?? 1
 and ?? 2
, having same linear 
charge density ?? is : 
 
 (1) 
0
2
?
?
 (2) 
0
4
?
?
 (3) 
0
2 ?
?
 (4) 
0
?
?
 
Sol. 1 
 
2
C1
12
kq K
Vq
RR
?? 
 = 
12
0 1 0 2
RR 11
4 R 4 R
? ? ? ?
? ? ?
? ? ? ?
 
 = 
0
2
?
?
 
 
 
6. If the distance of the earth from Sun is 1.5× 10
6
 km. Then the distance of an imaginary planet from 
Sun, if its period of revolution is 2.83 years is : 
 (1) 6 × 10
6
 km (2) 3 × 10
6
 km (3) 3 × 10
7
 km (4) 6 × 10
7
 km 
Sol. 2 
 
23
TR ? 
 
2
3
EE
pp
TR
TR
? ? ? ?
? ? ? ? ?
? ? ? ?
? ? ? ?
 
 
2
3
1
2.83
??
??
??
 = 
6
1.5 10
R
?
 
 R = 1.5 × 10
6
 × ? ?
2
3
2.83 
 1.5 × 10
6
 × ? ?
2
3
1.41 2 ? 
 1.5 × 10
6
 × 
? ?
2
3
22 
 1.5 × 10
6
 × 
? ?
2
3
8 
 3 × 10
6
 KM 
 
 
 
7. A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding 
wavelength for this transition is (given, h = 4 × 10
-15
eVs ) : 
 (1) 99.3 nm (2) 941 nm (3) 974 nm (4) 94.1 nm 
Sol. 4 
? ?E = E 4 – E 1 
 
hc
?
= –0.85 – ( –13.6) 
 
? ?
15 17
nm
4 10 3 10 nm
s
?
? ? ?
?
 = 12.75 
 
1200
12.75
?? nm 
 = 94.1 nm 
 
8. A cell of emf 90 V is connected across series combination of two resistors each of 100O resistance. A 
voltmeter of resistance 400O is used to measure the potential difference across each resistor. The 
reading of the voltmeter will be: 
 (1) 90 V (2) 45 V (3) 80 V (4) 40 V 
Sol. 2 
 
 
90 V 
100 100 
V V 
400 400 
 
 as Resistance are same so equal division of potential. 
 ? 
90
2
 = 45 V 
  
9. If two vectors P
? ? 
= ??ˆ + 2?? ??ˆ + ?? ?? ˆ
 and ?? ? 
= 4??ˆ - 2??ˆ + ?? ?? ˆ
 are perpendicular to each other. Then, the 
value of m will be: 
 (1) -1 (2) 3 (3) 2 (4) 1 
Sol. 3 
 P. Q = 0 
 4 × 1 + 2mx – 2 + m
2
 = 0 
 m
2
 – 4m + 4 = 0 
 (m – 2)
2
 = 0 
 m = 2 
 
10. The electric field and magnetic field components of an electromagnetic wave going through vacuum 
is described by 
 E
?? = E
0
sin? (kz - ?? t) 
 B
?? = B
o
sin? (kz - ?? t) 
 Then the correct relation between E
o
 and B
o
 is given by 
 (1) E
0
 B
0
= ???? (2) E
0
= kB
0
 (3) kE
o
= ?? B
o
 (4) ?? E
O
= kB
O
 
Sol. 3 
 by theory of EM wave 
 
0
0
E
v
BK
?
?? 
Page 4


SECTION - A 
1. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. 
 Assertion A: A pendulum clock when taken to Mount Everest becomes fast. 
 Reason: The value of g (acceleration due to gravity) is less at Mount Everest than its value on the 
surface of earth. 
 In the light of the above statements, choose the most appropriate answer from the options given below 
 (1) Both ?? and ?? are correct but ?? is NOT the correct explanation of ?? 
 (2) A is correct but ?? is not correct 
 (3) Both ?? and ?? are correct and ?? is the correct explanation of ?? 
 (4) ?? is not correct but ?? is correct 
Sol. 4 
 
 on Everest g decreases, so T increases, so moves slow. 
 
2. The frequency (?? ) of an oscillating liquid drop may depend upon radius (?? ) of the drop, density (?? ) of 
liquid and the surface tension (s) of the liquid as : ?? = ?? a
?? b
s
c
. The values of a,b and c respectively are 
 (1) (-
3
2
,
1
2
,
1
2
) (2) (
3
2
,-
1
2
,
1
2
) (3) (-
3
2
,-
1
2
,
1
2
) (4) (
3
2
,
1
2
,-
1
2
) 
Sol. 3 
 
 
 
 –2c = –1 ……. (1) 
 c = ½ 
 b + c = 0 … … ….(2) 
 b = –½ 
 a – 3b = 0 ………(3) 
 a = 3b =  
 
3. Given below are two statements: 
 Statement I : Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. 
 Statement II : Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's 
surface, if h = d. 
 In the light of above statements, choose the most appropriate answer form the options given below 
 (1) Both Statement I and Statement II are incorrect 
 (2) Statement I is incorrect but statement II is correct 
 (3) Both Statement I and II are correct 
 (4) Statement I is correct but statement II is incorrect 
Sol. 4 
  =  
 
 
R 
g 
r 
2
? 
d
h
??
??
?
R
?? d
g1
??
??
?
R
?? 2h
g1
?3
2
1 a 3b b c 2c
T L , M T
? ? ? ?
? 
? ? ? ?
a
1 3 2
T L M L MT
? ? ?
? ? ? ? ?
bc
?? 
 ? ?
a b c
f r s
g
? 
1
T
??  T2
g
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 24th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
4. A long solenoid is formed by winding 70 turns cm
– 1
. If 2.0 A current flows, then the magnetic field 
produced inside the solenoid is __________
? ?
71
0
4 10 TmA
??
? ? ? ? 
 (1) 88 × 10
– 4
 T (2) 352 × 10
– 4
 T (3) 176 × 10
– 4
 T (4) 1232 × 10
– 4
 T 
Sol. 3 
 
0
B ni ?? 
 = 
7
22
4 10 70 100 2
7
?
? ? ? ? ? 
 = 176 × 10
– 4
  
 
5. The electric potential at the centre of two concentric half rings of radii ?? 1
 and ?? 2
, having same linear 
charge density ?? is : 
 
 (1) 
0
2
?
?
 (2) 
0
4
?
?
 (3) 
0
2 ?
?
 (4) 
0
?
?
 
Sol. 1 
 
2
C1
12
kq K
Vq
RR
?? 
 = 
12
0 1 0 2
RR 11
4 R 4 R
? ? ? ?
? ? ?
? ? ? ?
 
 = 
0
2
?
?
 
 
 
6. If the distance of the earth from Sun is 1.5× 10
6
 km. Then the distance of an imaginary planet from 
Sun, if its period of revolution is 2.83 years is : 
 (1) 6 × 10
6
 km (2) 3 × 10
6
 km (3) 3 × 10
7
 km (4) 6 × 10
7
 km 
Sol. 2 
 
23
TR ? 
 
2
3
EE
pp
TR
TR
? ? ? ?
? ? ? ? ?
? ? ? ?
? ? ? ?
 
 
2
3
1
2.83
??
??
??
 = 
6
1.5 10
R
?
 
 R = 1.5 × 10
6
 × ? ?
2
3
2.83 
 1.5 × 10
6
 × ? ?
2
3
1.41 2 ? 
 1.5 × 10
6
 × 
? ?
2
3
22 
 1.5 × 10
6
 × 
? ?
2
3
8 
 3 × 10
6
 KM 
 
 
 
7. A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding 
wavelength for this transition is (given, h = 4 × 10
-15
eVs ) : 
 (1) 99.3 nm (2) 941 nm (3) 974 nm (4) 94.1 nm 
Sol. 4 
? ?E = E 4 – E 1 
 
hc
?
= –0.85 – ( –13.6) 
 
? ?
15 17
nm
4 10 3 10 nm
s
?
? ? ?
?
 = 12.75 
 
1200
12.75
?? nm 
 = 94.1 nm 
 
8. A cell of emf 90 V is connected across series combination of two resistors each of 100O resistance. A 
voltmeter of resistance 400O is used to measure the potential difference across each resistor. The 
reading of the voltmeter will be: 
 (1) 90 V (2) 45 V (3) 80 V (4) 40 V 
Sol. 2 
 
 
90 V 
100 100 
V V 
400 400 
 
 as Resistance are same so equal division of potential. 
 ? 
90
2
 = 45 V 
  
9. If two vectors P
? ? 
= ??ˆ + 2?? ??ˆ + ?? ?? ˆ
 and ?? ? 
= 4??ˆ - 2??ˆ + ?? ?? ˆ
 are perpendicular to each other. Then, the 
value of m will be: 
 (1) -1 (2) 3 (3) 2 (4) 1 
Sol. 3 
 P. Q = 0 
 4 × 1 + 2mx – 2 + m
2
 = 0 
 m
2
 – 4m + 4 = 0 
 (m – 2)
2
 = 0 
 m = 2 
 
10. The electric field and magnetic field components of an electromagnetic wave going through vacuum 
is described by 
 E
?? = E
0
sin? (kz - ?? t) 
 B
?? = B
o
sin? (kz - ?? t) 
 Then the correct relation between E
o
 and B
o
 is given by 
 (1) E
0
 B
0
= ???? (2) E
0
= kB
0
 (3) kE
o
= ?? B
o
 (4) ?? E
O
= kB
O
 
Sol. 3 
 by theory of EM wave 
 
0
0
E
v
BK
?
?? 
 
11. The logic gate equivalent to the given circuit diagram is : 
  
 (1) NAND (2) OR (3) AND (4) NOR 
Sol. 1 
 by truth table 
A 1 B 1 V 1 
0 
0 
1 
1 
0 
1 
0 
1 
1 
1 
1 
0 
 NAND gate 
 
12. Let ?? 1
 be the ratio of molar specific heat at constant pressure and molar specific heat at constant 
volume of a monoatomic gas and ?? 2
 be the similar ratio of diatomic gas. Considering the diatomic gas 
molecule as a rigid rotator, the ratio, 
?? 1
?? 2
 is : 
 (1) 
25
21
 (2) 
35
27
 (3) 
21
25
 (4) 
27
35
 
Sol. 1 
 
1
2
5
r 25
3
7
r 21
5
?? 
 
13. When a beam of white light is allowed to pass through convex lens parallel to principal axis, the 
different colours of light converge at different point on the principle axis after refraction. This is called: 
 (1) Spherical aberration (2) Polarisation 
 (3) Chromatic aberration (4) Scattering 
Sol. Theory : Colors are due to chromatic aberration.  
 
14. A metallic rod of length ' ?? ' is rotated with an angular speed of ' ?? ' normal to a uniform magnetic 
field ' B ' about an axis passing through one end of rod as shown in figure. The induced emf will be: 
 
 (1) 
1
4
BL
2
?? (2) 
1
2
?? 2
?? 2
?? (3) 
1
4
 B
2
 L?? (4) 
1
2
BL
2
?? 
Sol. 4 
 
L
0
B x dx ? ? ?
?
 
 = 
2
1
BL
2
? 
 
Page 5


SECTION - A 
1. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. 
 Assertion A: A pendulum clock when taken to Mount Everest becomes fast. 
 Reason: The value of g (acceleration due to gravity) is less at Mount Everest than its value on the 
surface of earth. 
 In the light of the above statements, choose the most appropriate answer from the options given below 
 (1) Both ?? and ?? are correct but ?? is NOT the correct explanation of ?? 
 (2) A is correct but ?? is not correct 
 (3) Both ?? and ?? are correct and ?? is the correct explanation of ?? 
 (4) ?? is not correct but ?? is correct 
Sol. 4 
 
 on Everest g decreases, so T increases, so moves slow. 
 
2. The frequency (?? ) of an oscillating liquid drop may depend upon radius (?? ) of the drop, density (?? ) of 
liquid and the surface tension (s) of the liquid as : ?? = ?? a
?? b
s
c
. The values of a,b and c respectively are 
 (1) (-
3
2
,
1
2
,
1
2
) (2) (
3
2
,-
1
2
,
1
2
) (3) (-
3
2
,-
1
2
,
1
2
) (4) (
3
2
,
1
2
,-
1
2
) 
Sol. 3 
 
 
 
 –2c = –1 ……. (1) 
 c = ½ 
 b + c = 0 … … ….(2) 
 b = –½ 
 a – 3b = 0 ………(3) 
 a = 3b =  
 
3. Given below are two statements: 
 Statement I : Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. 
 Statement II : Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's 
surface, if h = d. 
 In the light of above statements, choose the most appropriate answer form the options given below 
 (1) Both Statement I and Statement II are incorrect 
 (2) Statement I is incorrect but statement II is correct 
 (3) Both Statement I and II are correct 
 (4) Statement I is correct but statement II is incorrect 
Sol. 4 
  =  
 
 
R 
g 
r 
2
? 
d
h
??
??
?
R
?? d
g1
??
??
?
R
?? 2h
g1
?3
2
1 a 3b b c 2c
T L , M T
? ? ? ?
? 
? ? ? ?
a
1 3 2
T L M L MT
? ? ?
? ? ? ? ?
bc
?? 
 ? ?
a b c
f r s
g
? 
1
T
??  T2
g
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 24th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
4. A long solenoid is formed by winding 70 turns cm
– 1
. If 2.0 A current flows, then the magnetic field 
produced inside the solenoid is __________
? ?
71
0
4 10 TmA
??
? ? ? ? 
 (1) 88 × 10
– 4
 T (2) 352 × 10
– 4
 T (3) 176 × 10
– 4
 T (4) 1232 × 10
– 4
 T 
Sol. 3 
 
0
B ni ?? 
 = 
7
22
4 10 70 100 2
7
?
? ? ? ? ? 
 = 176 × 10
– 4
  
 
5. The electric potential at the centre of two concentric half rings of radii ?? 1
 and ?? 2
, having same linear 
charge density ?? is : 
 
 (1) 
0
2
?
?
 (2) 
0
4
?
?
 (3) 
0
2 ?
?
 (4) 
0
?
?
 
Sol. 1 
 
2
C1
12
kq K
Vq
RR
?? 
 = 
12
0 1 0 2
RR 11
4 R 4 R
? ? ? ?
? ? ?
? ? ? ?
 
 = 
0
2
?
?
 
 
 
6. If the distance of the earth from Sun is 1.5× 10
6
 km. Then the distance of an imaginary planet from 
Sun, if its period of revolution is 2.83 years is : 
 (1) 6 × 10
6
 km (2) 3 × 10
6
 km (3) 3 × 10
7
 km (4) 6 × 10
7
 km 
Sol. 2 
 
23
TR ? 
 
2
3
EE
pp
TR
TR
? ? ? ?
? ? ? ? ?
? ? ? ?
? ? ? ?
 
 
2
3
1
2.83
??
??
??
 = 
6
1.5 10
R
?
 
 R = 1.5 × 10
6
 × ? ?
2
3
2.83 
 1.5 × 10
6
 × ? ?
2
3
1.41 2 ? 
 1.5 × 10
6
 × 
? ?
2
3
22 
 1.5 × 10
6
 × 
? ?
2
3
8 
 3 × 10
6
 KM 
 
 
 
7. A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding 
wavelength for this transition is (given, h = 4 × 10
-15
eVs ) : 
 (1) 99.3 nm (2) 941 nm (3) 974 nm (4) 94.1 nm 
Sol. 4 
? ?E = E 4 – E 1 
 
hc
?
= –0.85 – ( –13.6) 
 
? ?
15 17
nm
4 10 3 10 nm
s
?
? ? ?
?
 = 12.75 
 
1200
12.75
?? nm 
 = 94.1 nm 
 
8. A cell of emf 90 V is connected across series combination of two resistors each of 100O resistance. A 
voltmeter of resistance 400O is used to measure the potential difference across each resistor. The 
reading of the voltmeter will be: 
 (1) 90 V (2) 45 V (3) 80 V (4) 40 V 
Sol. 2 
 
 
90 V 
100 100 
V V 
400 400 
 
 as Resistance are same so equal division of potential. 
 ? 
90
2
 = 45 V 
  
9. If two vectors P
? ? 
= ??ˆ + 2?? ??ˆ + ?? ?? ˆ
 and ?? ? 
= 4??ˆ - 2??ˆ + ?? ?? ˆ
 are perpendicular to each other. Then, the 
value of m will be: 
 (1) -1 (2) 3 (3) 2 (4) 1 
Sol. 3 
 P. Q = 0 
 4 × 1 + 2mx – 2 + m
2
 = 0 
 m
2
 – 4m + 4 = 0 
 (m – 2)
2
 = 0 
 m = 2 
 
10. The electric field and magnetic field components of an electromagnetic wave going through vacuum 
is described by 
 E
?? = E
0
sin? (kz - ?? t) 
 B
?? = B
o
sin? (kz - ?? t) 
 Then the correct relation between E
o
 and B
o
 is given by 
 (1) E
0
 B
0
= ???? (2) E
0
= kB
0
 (3) kE
o
= ?? B
o
 (4) ?? E
O
= kB
O
 
Sol. 3 
 by theory of EM wave 
 
0
0
E
v
BK
?
?? 
 
11. The logic gate equivalent to the given circuit diagram is : 
  
 (1) NAND (2) OR (3) AND (4) NOR 
Sol. 1 
 by truth table 
A 1 B 1 V 1 
0 
0 
1 
1 
0 
1 
0 
1 
1 
1 
1 
0 
 NAND gate 
 
12. Let ?? 1
 be the ratio of molar specific heat at constant pressure and molar specific heat at constant 
volume of a monoatomic gas and ?? 2
 be the similar ratio of diatomic gas. Considering the diatomic gas 
molecule as a rigid rotator, the ratio, 
?? 1
?? 2
 is : 
 (1) 
25
21
 (2) 
35
27
 (3) 
21
25
 (4) 
27
35
 
Sol. 1 
 
1
2
5
r 25
3
7
r 21
5
?? 
 
13. When a beam of white light is allowed to pass through convex lens parallel to principal axis, the 
different colours of light converge at different point on the principle axis after refraction. This is called: 
 (1) Spherical aberration (2) Polarisation 
 (3) Chromatic aberration (4) Scattering 
Sol. Theory : Colors are due to chromatic aberration.  
 
14. A metallic rod of length ' ?? ' is rotated with an angular speed of ' ?? ' normal to a uniform magnetic 
field ' B ' about an axis passing through one end of rod as shown in figure. The induced emf will be: 
 
 (1) 
1
4
BL
2
?? (2) 
1
2
?? 2
?? 2
?? (3) 
1
4
 B
2
 L?? (4) 
1
2
BL
2
?? 
Sol. 4 
 
L
0
B x dx ? ? ?
?
 
 = 
2
1
BL
2
? 
 
 
15. An a-particle, a proton and an electron have the same kinetic energy. Which one of the following is 
correct in case of their de-Broglie wavelength: 
 (1) ??? ?? < ?? ?? < ?? ?? (2) ?? ?? = ?? ?? = ?? ?? (3) ?? ?? > ?? ?? > ?? ?? (4) ?? ?? > ?? ?? < ?? ?? 
Sol. 1 
 
h1
2mkE m
? ? ? 
 
a p e
m m m ?? 
 ? 
pe ?
? ? ? ? ? 
 
16. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason 
 Assertion A : Steel is used in the construction of buildings and bridges. 
 Reason R : Steel is more elastic and its elastic limit is high. 
 In the light of 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) A is correct but ?? is not correct 
 (4) A is not correct but ?? is correct 
Sol. 1 
 Steel is more elastic. 
 
17. In an Isothermal change, the change in pressure and volume of a gas can be represented for three 
different temperature; T
3
> T
2
> T
1
 as: 
 (1)  (2) 
 (3)   (4)  
Sol. 3 
 PV = nRT const. 
  
 
1
P
V
?