JEE Main 2023 January 29 Shift 2 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


SECTION - A 
1. Substance A has atomic mass number 16 and half-life of 1 day. Another substance ?? has atomic mass 
number 32 and half life of 
1
2
 day. If both ?? and ?? simultaneously start undergo radio activity at the 
same time with initial mass 320 g each, how many total atoms of A and B combined would be left after 
2 days. 
 (1) 3 . 38 × 10
24
 (2) 1 . 69 × 10
24
 (3) 6 . 76 × 10
24
 (4) 6 . 76 × 10
23
 
Sol. (1) 
 
 
Total N = 5.625 moles 
 =5.625 × 6.023 × 10
23
 = (3.38 × 10
24
) 
 
2. For the given logic gates combination, the correct truth table will be 
 
 (1)   (2)  (3)  (4)  
Sol. (3) 
  
 From Bodean Algebra : 
 The correct truth table will be  
  
 
??  X AB AB
 
A B X
0 0 1
0 1 0
1 0 1
1 1 0
A B X
0 0 0
0 1 1
1 0 1
1 1 0
A B X
0 0 0
0 1 1
1 0 1
1 1 1
A B X
0 0 1
0 1 0
1 0 0
1 1 0
NN ? 
A
 No. of  atoms ? ? ? ?
? ? ? ? 
22
(2)
10 10
N 0.625
N
2 n 4
0.5
B
B
0
2
? ?
24
? ? ? 
20
N5
N
n
A
A
0
1
? ?
32
?? moles 
320
N 10
B
0
 ? ?
16
?? moles 
320
N 20
A
0
? ?
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 29th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
Page 2


SECTION - A 
1. Substance A has atomic mass number 16 and half-life of 1 day. Another substance ?? has atomic mass 
number 32 and half life of 
1
2
 day. If both ?? and ?? simultaneously start undergo radio activity at the 
same time with initial mass 320 g each, how many total atoms of A and B combined would be left after 
2 days. 
 (1) 3 . 38 × 10
24
 (2) 1 . 69 × 10
24
 (3) 6 . 76 × 10
24
 (4) 6 . 76 × 10
23
 
Sol. (1) 
 
 
Total N = 5.625 moles 
 =5.625 × 6.023 × 10
23
 = (3.38 × 10
24
) 
 
2. For the given logic gates combination, the correct truth table will be 
 
 (1)   (2)  (3)  (4)  
Sol. (3) 
  
 From Bodean Algebra : 
 The correct truth table will be  
  
 
??  X AB AB
 
A B X
0 0 1
0 1 0
1 0 1
1 1 0
A B X
0 0 0
0 1 1
1 0 1
1 1 0
A B X
0 0 0
0 1 1
1 0 1
1 1 1
A B X
0 0 1
0 1 0
1 0 0
1 1 0
NN ? 
A
 No. of  atoms ? ? ? ?
? ? ? ? 
22
(2)
10 10
N 0.625
N
2 n 4
0.5
B
B
0
2
? ?
24
? ? ? 
20
N5
N
n
A
A
0
1
? ?
32
?? moles 
320
N 10
B
0
 ? ?
16
?? moles 
320
N 20
A
0
? ?
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 29th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
  
3. The time taken by an object to slide down 45
°
 rough inclined plane is n times as it takes to slide down 
a perfectly smooth 45
°
 incline plane. The coefficient of kinetic friction between the object and the 
incline plane is: 
 (1) v 1 -
1
?? 2
 (2) 1 +
1
?? 2
 (3) 1 -
1
?? 2
 (4) v
1
1 - ?? 2
 
Sol. (3) 
 Acceleration on the smooth inclined plane 
 
1
g
a g sin
2
? ? ? 
 Acceleration on the rough inclined plane 
 ? ?
2
g Kg
a g sin g cos K
22
? ? ? ? ? ? ? ? ? 
 Given that: 
 
21
t nt ?   and   
22
1 2 2
11
a t a t
22
?
1
 
 
22
1 1 2 2
a t a t ? 
 
? ?
2 2 2
11
g g Kg
t n t
2 2 2
??
??
??
??
 
 
2
g g Kg
n
2 2 2
??
??
??
??
 
 
2
1
K1
n
?? 
 
4. Heat energy of 184 kJ is given to ice of mass 600 g at - 12
°
C. Specific heat of ice is 2222 . 3 J kg
- 1
C
- 1
 
and latent heat of ice in 336 kJkg
- 1
  
 A. Final temperature of system will be 0
°
C. 
 B. Final temperature of the system will be greater than 0
°
C. 
 C. The final system will have a mixture of ice and water in the ratio of 5 : 1. 
 D. The final system will have a mixture of ice and water in the ratio of 1:5. 
 E. The final system will have water only. 
 Choose the correct answer from the options given below: 
 (1) A and D Only (2) A and E Only (3) A and C Only (4) B and D Only 
Sol. (1) 
 Heat energy given 
3
184KJ 184 10 J ? ? ? 
 Amount of heat required to raise the temperature 
 
1 ice
ms T 0.6 2222.3 12 ? ? ? ? ? ? 
          =16000.56 J 
 Remaining heat 
2
184000 16000.56 ? ? ? = 167999.44 J  
 For melting at 0°C heat required = mL f 
                                                      = 0.6 × 336000 
                                                      = (201600) J needed 
 ? 100% ice is not melted 
 Amount of ice melted 
 167999.44 = m × 336000 
 m = mass of water = 0.4999 Kg 
 Mass of ice = 0.1001 
 Ratio 
0.1001
1:5
0.4999
??  
Page 3


SECTION - A 
1. Substance A has atomic mass number 16 and half-life of 1 day. Another substance ?? has atomic mass 
number 32 and half life of 
1
2
 day. If both ?? and ?? simultaneously start undergo radio activity at the 
same time with initial mass 320 g each, how many total atoms of A and B combined would be left after 
2 days. 
 (1) 3 . 38 × 10
24
 (2) 1 . 69 × 10
24
 (3) 6 . 76 × 10
24
 (4) 6 . 76 × 10
23
 
Sol. (1) 
 
 
Total N = 5.625 moles 
 =5.625 × 6.023 × 10
23
 = (3.38 × 10
24
) 
 
2. For the given logic gates combination, the correct truth table will be 
 
 (1)   (2)  (3)  (4)  
Sol. (3) 
  
 From Bodean Algebra : 
 The correct truth table will be  
  
 
??  X AB AB
 
A B X
0 0 1
0 1 0
1 0 1
1 1 0
A B X
0 0 0
0 1 1
1 0 1
1 1 0
A B X
0 0 0
0 1 1
1 0 1
1 1 1
A B X
0 0 1
0 1 0
1 0 0
1 1 0
NN ? 
A
 No. of  atoms ? ? ? ?
? ? ? ? 
22
(2)
10 10
N 0.625
N
2 n 4
0.5
B
B
0
2
? ?
24
? ? ? 
20
N5
N
n
A
A
0
1
? ?
32
?? moles 
320
N 10
B
0
 ? ?
16
?? moles 
320
N 20
A
0
? ?
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 29th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
  
3. The time taken by an object to slide down 45
°
 rough inclined plane is n times as it takes to slide down 
a perfectly smooth 45
°
 incline plane. The coefficient of kinetic friction between the object and the 
incline plane is: 
 (1) v 1 -
1
?? 2
 (2) 1 +
1
?? 2
 (3) 1 -
1
?? 2
 (4) v
1
1 - ?? 2
 
Sol. (3) 
 Acceleration on the smooth inclined plane 
 
1
g
a g sin
2
? ? ? 
 Acceleration on the rough inclined plane 
 ? ?
2
g Kg
a g sin g cos K
22
? ? ? ? ? ? ? ? ? 
 Given that: 
 
21
t nt ?   and   
22
1 2 2
11
a t a t
22
?
1
 
 
22
1 1 2 2
a t a t ? 
 
? ?
2 2 2
11
g g Kg
t n t
2 2 2
??
??
??
??
 
 
2
g g Kg
n
2 2 2
??
??
??
??
 
 
2
1
K1
n
?? 
 
4. Heat energy of 184 kJ is given to ice of mass 600 g at - 12
°
C. Specific heat of ice is 2222 . 3 J kg
- 1
C
- 1
 
and latent heat of ice in 336 kJkg
- 1
  
 A. Final temperature of system will be 0
°
C. 
 B. Final temperature of the system will be greater than 0
°
C. 
 C. The final system will have a mixture of ice and water in the ratio of 5 : 1. 
 D. The final system will have a mixture of ice and water in the ratio of 1:5. 
 E. The final system will have water only. 
 Choose the correct answer from the options given below: 
 (1) A and D Only (2) A and E Only (3) A and C Only (4) B and D Only 
Sol. (1) 
 Heat energy given 
3
184KJ 184 10 J ? ? ? 
 Amount of heat required to raise the temperature 
 
1 ice
ms T 0.6 2222.3 12 ? ? ? ? ? ? 
          =16000.56 J 
 Remaining heat 
2
184000 16000.56 ? ? ? = 167999.44 J  
 For melting at 0°C heat required = mL f 
                                                      = 0.6 × 336000 
                                                      = (201600) J needed 
 ? 100% ice is not melted 
 Amount of ice melted 
 167999.44 = m × 336000 
 m = mass of water = 0.4999 Kg 
 Mass of ice = 0.1001 
 Ratio 
0.1001
1:5
0.4999
??  
5. Identify the correct statements from the following: 
 A. Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative. 
 B. Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is 
negative. 
 C. Work done by friction on a body sliding down an inclined plane is positive. 
 D. Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity 
in zero. 
 E. Work done by the air resistance on an oscillating pendulum in negative. 
 Choose the correct answer from the options given below: 
 (1) B, D and E only (2) A and C Only (3) ?? and ?? only (4) ?? and ?? only 
Sol. (4) 
 ? Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is positive 
 ? Work done by friction on a body sliding down an inclined plane is negative 
? Work done by a applied force on a body moving on a rough horizontal plane with uniform velocity is positive 
 
6. A scientist is observing a bacteria through a compound microscope. For better analysis and to improve 
its resolving power he should. (Select the best option) 
 (1) Increase the refractive index of the medium between the object and objective lens 
 (2) Decrease the diameter of the objective lens 
 (3) Increase the wave length of the light 
 (4) Decrease the focal length of the eye piece. 
Sol. (1) 
 
2 sin
R.P
1.22
??
?
?
 
 , R.P ? ? ? 
 D , ,R.P ? ? ? ? 
 ,R.P ? ? ? 
 R.P is independent of focal length of eye piece  
 
7. With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of 
the potentiometer is 
 (A) directly proportional to the length of the potentiometer wire 
(B) directly proportional to the potential gradient of the wire 
(C) inversely proportional to the potential gradient of the wire 
(D) inversely proportional to the length of the potentiometer wire 
 Choose the correct option for the above statements: 
 (1) A only (2) C only (3) A and ?? only (4) ?? and ?? only 
Sol. (3) 
If on displacing the jockey slightly from the null point position, the galvanometer shows a large deflection, than 
the potentiometer is said to be sensitive. The sensitivity of the potentiometer depends upon the potential gradient 
along the wire. The smaller potential gradient greater will be sensitivity. 
Sensitivity ?, potential gradient ?, length ? 
Sensitivity ? length 
Sensitivity 
1
Potential gradient
? 
 
 
Page 4


SECTION - A 
1. Substance A has atomic mass number 16 and half-life of 1 day. Another substance ?? has atomic mass 
number 32 and half life of 
1
2
 day. If both ?? and ?? simultaneously start undergo radio activity at the 
same time with initial mass 320 g each, how many total atoms of A and B combined would be left after 
2 days. 
 (1) 3 . 38 × 10
24
 (2) 1 . 69 × 10
24
 (3) 6 . 76 × 10
24
 (4) 6 . 76 × 10
23
 
Sol. (1) 
 
 
Total N = 5.625 moles 
 =5.625 × 6.023 × 10
23
 = (3.38 × 10
24
) 
 
2. For the given logic gates combination, the correct truth table will be 
 
 (1)   (2)  (3)  (4)  
Sol. (3) 
  
 From Bodean Algebra : 
 The correct truth table will be  
  
 
??  X AB AB
 
A B X
0 0 1
0 1 0
1 0 1
1 1 0
A B X
0 0 0
0 1 1
1 0 1
1 1 0
A B X
0 0 0
0 1 1
1 0 1
1 1 1
A B X
0 0 1
0 1 0
1 0 0
1 1 0
NN ? 
A
 No. of  atoms ? ? ? ?
? ? ? ? 
22
(2)
10 10
N 0.625
N
2 n 4
0.5
B
B
0
2
? ?
24
? ? ? 
20
N5
N
n
A
A
0
1
? ?
32
?? moles 
320
N 10
B
0
 ? ?
16
?? moles 
320
N 20
A
0
? ?
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 29th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
  
3. The time taken by an object to slide down 45
°
 rough inclined plane is n times as it takes to slide down 
a perfectly smooth 45
°
 incline plane. The coefficient of kinetic friction between the object and the 
incline plane is: 
 (1) v 1 -
1
?? 2
 (2) 1 +
1
?? 2
 (3) 1 -
1
?? 2
 (4) v
1
1 - ?? 2
 
Sol. (3) 
 Acceleration on the smooth inclined plane 
 
1
g
a g sin
2
? ? ? 
 Acceleration on the rough inclined plane 
 ? ?
2
g Kg
a g sin g cos K
22
? ? ? ? ? ? ? ? ? 
 Given that: 
 
21
t nt ?   and   
22
1 2 2
11
a t a t
22
?
1
 
 
22
1 1 2 2
a t a t ? 
 
? ?
2 2 2
11
g g Kg
t n t
2 2 2
??
??
??
??
 
 
2
g g Kg
n
2 2 2
??
??
??
??
 
 
2
1
K1
n
?? 
 
4. Heat energy of 184 kJ is given to ice of mass 600 g at - 12
°
C. Specific heat of ice is 2222 . 3 J kg
- 1
C
- 1
 
and latent heat of ice in 336 kJkg
- 1
  
 A. Final temperature of system will be 0
°
C. 
 B. Final temperature of the system will be greater than 0
°
C. 
 C. The final system will have a mixture of ice and water in the ratio of 5 : 1. 
 D. The final system will have a mixture of ice and water in the ratio of 1:5. 
 E. The final system will have water only. 
 Choose the correct answer from the options given below: 
 (1) A and D Only (2) A and E Only (3) A and C Only (4) B and D Only 
Sol. (1) 
 Heat energy given 
3
184KJ 184 10 J ? ? ? 
 Amount of heat required to raise the temperature 
 
1 ice
ms T 0.6 2222.3 12 ? ? ? ? ? ? 
          =16000.56 J 
 Remaining heat 
2
184000 16000.56 ? ? ? = 167999.44 J  
 For melting at 0°C heat required = mL f 
                                                      = 0.6 × 336000 
                                                      = (201600) J needed 
 ? 100% ice is not melted 
 Amount of ice melted 
 167999.44 = m × 336000 
 m = mass of water = 0.4999 Kg 
 Mass of ice = 0.1001 
 Ratio 
0.1001
1:5
0.4999
??  
5. Identify the correct statements from the following: 
 A. Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative. 
 B. Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is 
negative. 
 C. Work done by friction on a body sliding down an inclined plane is positive. 
 D. Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity 
in zero. 
 E. Work done by the air resistance on an oscillating pendulum in negative. 
 Choose the correct answer from the options given below: 
 (1) B, D and E only (2) A and C Only (3) ?? and ?? only (4) ?? and ?? only 
Sol. (4) 
 ? Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is positive 
 ? Work done by friction on a body sliding down an inclined plane is negative 
? Work done by a applied force on a body moving on a rough horizontal plane with uniform velocity is positive 
 
6. A scientist is observing a bacteria through a compound microscope. For better analysis and to improve 
its resolving power he should. (Select the best option) 
 (1) Increase the refractive index of the medium between the object and objective lens 
 (2) Decrease the diameter of the objective lens 
 (3) Increase the wave length of the light 
 (4) Decrease the focal length of the eye piece. 
Sol. (1) 
 
2 sin
R.P
1.22
??
?
?
 
 , R.P ? ? ? 
 D , ,R.P ? ? ? ? 
 ,R.P ? ? ? 
 R.P is independent of focal length of eye piece  
 
7. With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of 
the potentiometer is 
 (A) directly proportional to the length of the potentiometer wire 
(B) directly proportional to the potential gradient of the wire 
(C) inversely proportional to the potential gradient of the wire 
(D) inversely proportional to the length of the potentiometer wire 
 Choose the correct option for the above statements: 
 (1) A only (2) C only (3) A and ?? only (4) ?? and ?? only 
Sol. (3) 
If on displacing the jockey slightly from the null point position, the galvanometer shows a large deflection, than 
the potentiometer is said to be sensitive. The sensitivity of the potentiometer depends upon the potential gradient 
along the wire. The smaller potential gradient greater will be sensitivity. 
Sensitivity ?, potential gradient ?, length ? 
Sensitivity ? length 
Sensitivity 
1
Potential gradient
? 
 
 
 
8. A force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then 
body describes 50 m in the next 10 s. The value of force will be: 
 (1) 40 N (2) 5 N (3) 20 N (4) 10 N 
Sol. (2) 
 
 
 
 50 = V×10 
 V=5 ms
–1 
 
V= 0 + a × 20 
 5= a × 20 
 
2
1
a ms
4
?
? 
 
1
F ma 20 5N
4
? ? ? ? 
 
9. The modulation index for an A.M. wave having maximum and minimum peak-to-peak voltages of 14 
mV and 6 mV respectively is: 
 (1) 0.4 (2) 0.6 (3) 0.2 (4) 1.4 
Sol. (1) 
 ?? Modulating index 
max min
max min
AA
AA
?
?
?
 
       
14 6
14 6
?
?
?
 
        = 0.4 
 
10. Given below are two statements: 
 Statement I: Electromagnetic waves are not deflected by electric and magnetic field. 
 Statement II: The amplitude of electric field and the magnetic field in electromagnetic waves are 
related to each other as ?? 0
=
v
?? 0
?? 0
?? 0
. 
 In the light of the above statements, choose the correct answer from the options given below : 
 (1) Statement I is true but statement II is false 
 (2) Both Statement I and Statement II are false 
 (3) Statement I is false but statement II is true 
 (4) Both Statement I and Statement II are true 
Sol. (1) 
 Statement -I     is correct as 
             EMW are neutral 
 Statement – II  is wrong 
 
00
00
1
EB ?
??
 
 
 
Page 5


SECTION - A 
1. Substance A has atomic mass number 16 and half-life of 1 day. Another substance ?? has atomic mass 
number 32 and half life of 
1
2
 day. If both ?? and ?? simultaneously start undergo radio activity at the 
same time with initial mass 320 g each, how many total atoms of A and B combined would be left after 
2 days. 
 (1) 3 . 38 × 10
24
 (2) 1 . 69 × 10
24
 (3) 6 . 76 × 10
24
 (4) 6 . 76 × 10
23
 
Sol. (1) 
 
 
Total N = 5.625 moles 
 =5.625 × 6.023 × 10
23
 = (3.38 × 10
24
) 
 
2. For the given logic gates combination, the correct truth table will be 
 
 (1)   (2)  (3)  (4)  
Sol. (3) 
  
 From Bodean Algebra : 
 The correct truth table will be  
  
 
??  X AB AB
 
A B X
0 0 1
0 1 0
1 0 1
1 1 0
A B X
0 0 0
0 1 1
1 0 1
1 1 0
A B X
0 0 0
0 1 1
1 0 1
1 1 1
A B X
0 0 1
0 1 0
1 0 0
1 1 0
NN ? 
A
 No. of  atoms ? ? ? ?
? ? ? ? 
22
(2)
10 10
N 0.625
N
2 n 4
0.5
B
B
0
2
? ?
24
? ? ? 
20
N5
N
n
A
A
0
1
? ?
32
?? moles 
320
N 10
B
0
 ? ?
16
?? moles 
320
N 20
A
0
? ?
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 29th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
  
3. The time taken by an object to slide down 45
°
 rough inclined plane is n times as it takes to slide down 
a perfectly smooth 45
°
 incline plane. The coefficient of kinetic friction between the object and the 
incline plane is: 
 (1) v 1 -
1
?? 2
 (2) 1 +
1
?? 2
 (3) 1 -
1
?? 2
 (4) v
1
1 - ?? 2
 
Sol. (3) 
 Acceleration on the smooth inclined plane 
 
1
g
a g sin
2
? ? ? 
 Acceleration on the rough inclined plane 
 ? ?
2
g Kg
a g sin g cos K
22
? ? ? ? ? ? ? ? ? 
 Given that: 
 
21
t nt ?   and   
22
1 2 2
11
a t a t
22
?
1
 
 
22
1 1 2 2
a t a t ? 
 
? ?
2 2 2
11
g g Kg
t n t
2 2 2
??
??
??
??
 
 
2
g g Kg
n
2 2 2
??
??
??
??
 
 
2
1
K1
n
?? 
 
4. Heat energy of 184 kJ is given to ice of mass 600 g at - 12
°
C. Specific heat of ice is 2222 . 3 J kg
- 1
C
- 1
 
and latent heat of ice in 336 kJkg
- 1
  
 A. Final temperature of system will be 0
°
C. 
 B. Final temperature of the system will be greater than 0
°
C. 
 C. The final system will have a mixture of ice and water in the ratio of 5 : 1. 
 D. The final system will have a mixture of ice and water in the ratio of 1:5. 
 E. The final system will have water only. 
 Choose the correct answer from the options given below: 
 (1) A and D Only (2) A and E Only (3) A and C Only (4) B and D Only 
Sol. (1) 
 Heat energy given 
3
184KJ 184 10 J ? ? ? 
 Amount of heat required to raise the temperature 
 
1 ice
ms T 0.6 2222.3 12 ? ? ? ? ? ? 
          =16000.56 J 
 Remaining heat 
2
184000 16000.56 ? ? ? = 167999.44 J  
 For melting at 0°C heat required = mL f 
                                                      = 0.6 × 336000 
                                                      = (201600) J needed 
 ? 100% ice is not melted 
 Amount of ice melted 
 167999.44 = m × 336000 
 m = mass of water = 0.4999 Kg 
 Mass of ice = 0.1001 
 Ratio 
0.1001
1:5
0.4999
??  
5. Identify the correct statements from the following: 
 A. Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative. 
 B. Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is 
negative. 
 C. Work done by friction on a body sliding down an inclined plane is positive. 
 D. Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity 
in zero. 
 E. Work done by the air resistance on an oscillating pendulum in negative. 
 Choose the correct answer from the options given below: 
 (1) B, D and E only (2) A and C Only (3) ?? and ?? only (4) ?? and ?? only 
Sol. (4) 
 ? Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is positive 
 ? Work done by friction on a body sliding down an inclined plane is negative 
? Work done by a applied force on a body moving on a rough horizontal plane with uniform velocity is positive 
 
6. A scientist is observing a bacteria through a compound microscope. For better analysis and to improve 
its resolving power he should. (Select the best option) 
 (1) Increase the refractive index of the medium between the object and objective lens 
 (2) Decrease the diameter of the objective lens 
 (3) Increase the wave length of the light 
 (4) Decrease the focal length of the eye piece. 
Sol. (1) 
 
2 sin
R.P
1.22
??
?
?
 
 , R.P ? ? ? 
 D , ,R.P ? ? ? ? 
 ,R.P ? ? ? 
 R.P is independent of focal length of eye piece  
 
7. With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of 
the potentiometer is 
 (A) directly proportional to the length of the potentiometer wire 
(B) directly proportional to the potential gradient of the wire 
(C) inversely proportional to the potential gradient of the wire 
(D) inversely proportional to the length of the potentiometer wire 
 Choose the correct option for the above statements: 
 (1) A only (2) C only (3) A and ?? only (4) ?? and ?? only 
Sol. (3) 
If on displacing the jockey slightly from the null point position, the galvanometer shows a large deflection, than 
the potentiometer is said to be sensitive. The sensitivity of the potentiometer depends upon the potential gradient 
along the wire. The smaller potential gradient greater will be sensitivity. 
Sensitivity ?, potential gradient ?, length ? 
Sensitivity ? length 
Sensitivity 
1
Potential gradient
? 
 
 
 
8. A force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then 
body describes 50 m in the next 10 s. The value of force will be: 
 (1) 40 N (2) 5 N (3) 20 N (4) 10 N 
Sol. (2) 
 
 
 
 50 = V×10 
 V=5 ms
–1 
 
V= 0 + a × 20 
 5= a × 20 
 
2
1
a ms
4
?
? 
 
1
F ma 20 5N
4
? ? ? ? 
 
9. The modulation index for an A.M. wave having maximum and minimum peak-to-peak voltages of 14 
mV and 6 mV respectively is: 
 (1) 0.4 (2) 0.6 (3) 0.2 (4) 1.4 
Sol. (1) 
 ?? Modulating index 
max min
max min
AA
AA
?
?
?
 
       
14 6
14 6
?
?
?
 
        = 0.4 
 
10. Given below are two statements: 
 Statement I: Electromagnetic waves are not deflected by electric and magnetic field. 
 Statement II: The amplitude of electric field and the magnetic field in electromagnetic waves are 
related to each other as ?? 0
=
v
?? 0
?? 0
?? 0
. 
 In the light of the above statements, choose the correct answer from the options given below : 
 (1) Statement I is true but statement II is false 
 (2) Both Statement I and Statement II are false 
 (3) Statement I is false but statement II is true 
 (4) Both Statement I and Statement II are true 
Sol. (1) 
 Statement -I     is correct as 
             EMW are neutral 
 Statement – II  is wrong 
 
00
00
1
EB ?
??
 
 
 
 
11. A square loop of area 25 cm
2
 has a resistance of 10O. The loop is placed in uniform magnetic field of 
magnitude 40 . 0 T. The plane of loop is perpendicular to the magnetic field. The work done in pulling 
the loop out of the magnetic field slowly and uniformly in 1 . 0s ec, will be 
 (1) 1 . 0 × 10
- 3
 J (2) 2 . 5 × 10
- 3
 J (3) 5 × 10
- 3
 J (4) 1 . 0 × 10
- 4
 J 
Sol. (1) 
 l = 5 cm 
 t = 1 sec 
 
1
0.05
V 0.05ms
1
?
?? 
 
40 0.05 0.05 BLV
I 0.01A
10 R
??
? ? ? 
F BIL 40 0.010.05 0.02N ? ? ? ? 
 
3
W F 0.02 0.05 1 10 J
?
? ? ? ? ? 
 
12. For the given figures, choose the correct options: 
 
 (1) At resonance, current in (b) is less than that in (a) 
 (2) The rms current in circuit (b) can never be larger than that in (a) 
 (3) The rms current in figure(a) is always equal to that in figure (b) 
 (4) The rms current in circuit (b) can be larger than that in (a) 
Sol. (2) 
 
 
 
 
rms
220
I 5.5A
40
?? 
 X L is not equal to X C, so rms current 
 In (b) can never be large than (a)