JEE Main 2023 January 31 Shift 2 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


SECTION - A 
1. Given below are two statements: 
 Statement I: In a typical transistor, all three regions emitter, base and collector have same doping 
level. 
 Statement II: In a transistor, collector is the thickest and base is the thinnest segment. 
 In the light of the above statements, choose the most appropriate answer from the options given below. 
 (1) Both Statement I and Statement II are correct 
 (2) Statement I is incorrect but Statement II is correct 
 (3) Statement I is correct but Statement II is incorrect 
 (4) Both Statement I and Statement II are incorrect 
Sol. (2) 
  
Emitter Base Collector 
Moderate Size Thin Thick 
Maximum 
Doping 
Minimum 
Doping 
Moderate Doping 
 
 
2. If the two metals ?? and ?? are exposed to radiation of wavelength 350 nm. The work functions of 
metals A and B are 4 . 8eV and 2 . 2eV. Then choose the correct option. 
 (1) Both metals A and B will emit photo-electrons 
 (2) Metal ?? will not emit photo-electrons 
 (3) Metal B will not emit photo-electrons 
 (4) Both metals A and B will not emit photo-electrons 
Sol. (2) 
  
 If E > ?, photo electrons will emit. 
 A will not emit and B will emit. 
 
3. Heat energy of 735 J is given to a diatomic gas allowing the gas to expand at constant pressure. Each 
gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy 
of the gas will be : 
 (1) 525 J (2) 441 J (3) 572 J (4) 735 J 
Sol. (1) 
 At constant Pressure, 
 Q = nCpdT = 735J 
 
 
 
 
 
? ? ? 
7
5
735
U 525J
? ?
? ? ? ?  
Cp 8
Cv
735 735
U nCvdT
? ?
? ? ?
?
E 3.54eV
350
hc 1240
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 31st January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
Page 2


SECTION - A 
1. Given below are two statements: 
 Statement I: In a typical transistor, all three regions emitter, base and collector have same doping 
level. 
 Statement II: In a transistor, collector is the thickest and base is the thinnest segment. 
 In the light of the above statements, choose the most appropriate answer from the options given below. 
 (1) Both Statement I and Statement II are correct 
 (2) Statement I is incorrect but Statement II is correct 
 (3) Statement I is correct but Statement II is incorrect 
 (4) Both Statement I and Statement II are incorrect 
Sol. (2) 
  
Emitter Base Collector 
Moderate Size Thin Thick 
Maximum 
Doping 
Minimum 
Doping 
Moderate Doping 
 
 
2. If the two metals ?? and ?? are exposed to radiation of wavelength 350 nm. The work functions of 
metals A and B are 4 . 8eV and 2 . 2eV. Then choose the correct option. 
 (1) Both metals A and B will emit photo-electrons 
 (2) Metal ?? will not emit photo-electrons 
 (3) Metal B will not emit photo-electrons 
 (4) Both metals A and B will not emit photo-electrons 
Sol. (2) 
  
 If E > ?, photo electrons will emit. 
 A will not emit and B will emit. 
 
3. Heat energy of 735 J is given to a diatomic gas allowing the gas to expand at constant pressure. Each 
gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy 
of the gas will be : 
 (1) 525 J (2) 441 J (3) 572 J (4) 735 J 
Sol. (1) 
 At constant Pressure, 
 Q = nCpdT = 735J 
 
 
 
 
 
? ? ? 
7
5
735
U 525J
? ?
? ? ? ?  
Cp 8
Cv
735 735
U nCvdT
? ?
? ? ?
?
E 3.54eV
350
hc 1240
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 31st January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
4. Match List I with List II 
LIST I LIST II 
A. Angular momentum I. [ ML
2
 T
- 2
] 
B. Torque II. [ ML
- 2
 T
- 2
] 
C. Stress III. [ ML
2
 T
- 1
] 
D. Pressure gradient IV. [ ML
- 1
 T
- 2
] 
 
 Choose the correct answer from the options given below: 
 (1) A - III, B - I, C - IV, D – II (2) A - II, B - III, C - IV, D – I 
 (3) A - IV, B - II, C - I, D – III (4) A - I, B - IV, C - III, D – II 
Sol. (1) 
 L = mvr = [M
1
L
2
T
–1
] 
 ? = rF = [M
1
L
2
T
–2
] 
 Stress = 
F
A
= [M
1
L
–1
T
–2
] 
 Pressure Gradient = 
dp
dx
 = [M
1
L
–2
T
–2
] 
 
5. A stone of mass 1 kg is tied to end of a massless string of length 1 m. If the breaking tension of the 
string is 400 N, then maximum linear velocity, the stone can have without breaking the string, while 
rotating in horizontal plane, is : 
 (1) 40 ms
- 1
 (2) 400 ms
- 1
 (3) 20 ms
- 1
 (4) 10 ms
- 1
 
Sol. (3) 
 
 
 
T = 
2
mv
 
 400 = 
2
1v
1
?
 
 V = 20 m/s 
 
6. A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index 
5
3
 is 
poured inside the bucket, then microscope have to be raised by 30 cm to focus the object again. The 
height of the liquid in the bucket is : 
 (1) 12 cm (2) 50 cm (3) 18 cm (4) 75 cm 
Sol. (4) 
 d app = 
? ?
dh
5
3
?
?
 
Page 3


SECTION - A 
1. Given below are two statements: 
 Statement I: In a typical transistor, all three regions emitter, base and collector have same doping 
level. 
 Statement II: In a transistor, collector is the thickest and base is the thinnest segment. 
 In the light of the above statements, choose the most appropriate answer from the options given below. 
 (1) Both Statement I and Statement II are correct 
 (2) Statement I is incorrect but Statement II is correct 
 (3) Statement I is correct but Statement II is incorrect 
 (4) Both Statement I and Statement II are incorrect 
Sol. (2) 
  
Emitter Base Collector 
Moderate Size Thin Thick 
Maximum 
Doping 
Minimum 
Doping 
Moderate Doping 
 
 
2. If the two metals ?? and ?? are exposed to radiation of wavelength 350 nm. The work functions of 
metals A and B are 4 . 8eV and 2 . 2eV. Then choose the correct option. 
 (1) Both metals A and B will emit photo-electrons 
 (2) Metal ?? will not emit photo-electrons 
 (3) Metal B will not emit photo-electrons 
 (4) Both metals A and B will not emit photo-electrons 
Sol. (2) 
  
 If E > ?, photo electrons will emit. 
 A will not emit and B will emit. 
 
3. Heat energy of 735 J is given to a diatomic gas allowing the gas to expand at constant pressure. Each 
gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy 
of the gas will be : 
 (1) 525 J (2) 441 J (3) 572 J (4) 735 J 
Sol. (1) 
 At constant Pressure, 
 Q = nCpdT = 735J 
 
 
 
 
 
? ? ? 
7
5
735
U 525J
? ?
? ? ? ?  
Cp 8
Cv
735 735
U nCvdT
? ?
? ? ?
?
E 3.54eV
350
hc 1240
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 31st January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
4. Match List I with List II 
LIST I LIST II 
A. Angular momentum I. [ ML
2
 T
- 2
] 
B. Torque II. [ ML
- 2
 T
- 2
] 
C. Stress III. [ ML
2
 T
- 1
] 
D. Pressure gradient IV. [ ML
- 1
 T
- 2
] 
 
 Choose the correct answer from the options given below: 
 (1) A - III, B - I, C - IV, D – II (2) A - II, B - III, C - IV, D – I 
 (3) A - IV, B - II, C - I, D – III (4) A - I, B - IV, C - III, D – II 
Sol. (1) 
 L = mvr = [M
1
L
2
T
–1
] 
 ? = rF = [M
1
L
2
T
–2
] 
 Stress = 
F
A
= [M
1
L
–1
T
–2
] 
 Pressure Gradient = 
dp
dx
 = [M
1
L
–2
T
–2
] 
 
5. A stone of mass 1 kg is tied to end of a massless string of length 1 m. If the breaking tension of the 
string is 400 N, then maximum linear velocity, the stone can have without breaking the string, while 
rotating in horizontal plane, is : 
 (1) 40 ms
- 1
 (2) 400 ms
- 1
 (3) 20 ms
- 1
 (4) 10 ms
- 1
 
Sol. (3) 
 
 
 
T = 
2
mv
 
 400 = 
2
1v
1
?
 
 V = 20 m/s 
 
6. A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index 
5
3
 is 
poured inside the bucket, then microscope have to be raised by 30 cm to focus the object again. The 
height of the liquid in the bucket is : 
 (1) 12 cm (2) 50 cm (3) 18 cm (4) 75 cm 
Sol. (4) 
 d app = 
? ?
dh
5
3
?
?
 
 Shift = h 
–3h
5
 = 30 
 h = 75 cm 
 
7. The number of turns of the coil of a moving coil galvanometer is increased in order to increase current 
sensitivity by 50%. The percentage change in voltage sensitivity of the galvanometer will be : 
 (1) 0% (2) 75% (3) 50% (4) 100% 
Sol. (1) 
 
V
NAB N
KR R
? ? ? 
 
I
NAB
N
K
? ? ? 
 
I
N
N , ,
R
? ? ? ? Constant 
 
V
0 ? ? ? 
 
8. A body is moving with constant speed, in a circle of radius 10 m. The body completes one revolution 
in 4s. At the end of 3
rd
 second, the displacement of body (in m) from its starting point is: 
 (1) 15 ? ? (2) 10 2 (3) 30 (4) 5 ?  
Sol. (2) 
 
22
rad
w
s
T 4 2
? ? ?
??? 
 ? = wt 
 ? = 3
2
?
? 
 ? =
3
2
?
 rad 
 
+ 
R 
R 
+ 
Displacement = 2R 10 2m ? 
 
 
9. The H amount of thermal energy is developed by a resistor in 10 s when a current of 4 A is passed 
through it. If the current is increased to 16 A, the thermal energy developed by the resistor in 10 s will 
be : 
 (1) 
H
4
 (2) 16H (3) 4H (4) H 
Sol. (2) 
 H = I
2
Rt 
 
2
2
11
22
HI 4
H I 16
??
??
??
?? ??
??
??
 
 H 2 = 16H 1 
Page 4


SECTION - A 
1. Given below are two statements: 
 Statement I: In a typical transistor, all three regions emitter, base and collector have same doping 
level. 
 Statement II: In a transistor, collector is the thickest and base is the thinnest segment. 
 In the light of the above statements, choose the most appropriate answer from the options given below. 
 (1) Both Statement I and Statement II are correct 
 (2) Statement I is incorrect but Statement II is correct 
 (3) Statement I is correct but Statement II is incorrect 
 (4) Both Statement I and Statement II are incorrect 
Sol. (2) 
  
Emitter Base Collector 
Moderate Size Thin Thick 
Maximum 
Doping 
Minimum 
Doping 
Moderate Doping 
 
 
2. If the two metals ?? and ?? are exposed to radiation of wavelength 350 nm. The work functions of 
metals A and B are 4 . 8eV and 2 . 2eV. Then choose the correct option. 
 (1) Both metals A and B will emit photo-electrons 
 (2) Metal ?? will not emit photo-electrons 
 (3) Metal B will not emit photo-electrons 
 (4) Both metals A and B will not emit photo-electrons 
Sol. (2) 
  
 If E > ?, photo electrons will emit. 
 A will not emit and B will emit. 
 
3. Heat energy of 735 J is given to a diatomic gas allowing the gas to expand at constant pressure. Each 
gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy 
of the gas will be : 
 (1) 525 J (2) 441 J (3) 572 J (4) 735 J 
Sol. (1) 
 At constant Pressure, 
 Q = nCpdT = 735J 
 
 
 
 
 
? ? ? 
7
5
735
U 525J
? ?
? ? ? ?  
Cp 8
Cv
735 735
U nCvdT
? ?
? ? ?
?
E 3.54eV
350
hc 1240
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 31st January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
4. Match List I with List II 
LIST I LIST II 
A. Angular momentum I. [ ML
2
 T
- 2
] 
B. Torque II. [ ML
- 2
 T
- 2
] 
C. Stress III. [ ML
2
 T
- 1
] 
D. Pressure gradient IV. [ ML
- 1
 T
- 2
] 
 
 Choose the correct answer from the options given below: 
 (1) A - III, B - I, C - IV, D – II (2) A - II, B - III, C - IV, D – I 
 (3) A - IV, B - II, C - I, D – III (4) A - I, B - IV, C - III, D – II 
Sol. (1) 
 L = mvr = [M
1
L
2
T
–1
] 
 ? = rF = [M
1
L
2
T
–2
] 
 Stress = 
F
A
= [M
1
L
–1
T
–2
] 
 Pressure Gradient = 
dp
dx
 = [M
1
L
–2
T
–2
] 
 
5. A stone of mass 1 kg is tied to end of a massless string of length 1 m. If the breaking tension of the 
string is 400 N, then maximum linear velocity, the stone can have without breaking the string, while 
rotating in horizontal plane, is : 
 (1) 40 ms
- 1
 (2) 400 ms
- 1
 (3) 20 ms
- 1
 (4) 10 ms
- 1
 
Sol. (3) 
 
 
 
T = 
2
mv
 
 400 = 
2
1v
1
?
 
 V = 20 m/s 
 
6. A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index 
5
3
 is 
poured inside the bucket, then microscope have to be raised by 30 cm to focus the object again. The 
height of the liquid in the bucket is : 
 (1) 12 cm (2) 50 cm (3) 18 cm (4) 75 cm 
Sol. (4) 
 d app = 
? ?
dh
5
3
?
?
 
 Shift = h 
–3h
5
 = 30 
 h = 75 cm 
 
7. The number of turns of the coil of a moving coil galvanometer is increased in order to increase current 
sensitivity by 50%. The percentage change in voltage sensitivity of the galvanometer will be : 
 (1) 0% (2) 75% (3) 50% (4) 100% 
Sol. (1) 
 
V
NAB N
KR R
? ? ? 
 
I
NAB
N
K
? ? ? 
 
I
N
N , ,
R
? ? ? ? Constant 
 
V
0 ? ? ? 
 
8. A body is moving with constant speed, in a circle of radius 10 m. The body completes one revolution 
in 4s. At the end of 3
rd
 second, the displacement of body (in m) from its starting point is: 
 (1) 15 ? ? (2) 10 2 (3) 30 (4) 5 ?  
Sol. (2) 
 
22
rad
w
s
T 4 2
? ? ?
??? 
 ? = wt 
 ? = 3
2
?
? 
 ? =
3
2
?
 rad 
 
+ 
R 
R 
+ 
Displacement = 2R 10 2m ? 
 
 
9. The H amount of thermal energy is developed by a resistor in 10 s when a current of 4 A is passed 
through it. If the current is increased to 16 A, the thermal energy developed by the resistor in 10 s will 
be : 
 (1) 
H
4
 (2) 16H (3) 4H (4) H 
Sol. (2) 
 H = I
2
Rt 
 
2
2
11
22
HI 4
H I 16
??
??
??
?? ??
??
??
 
 H 2 = 16H 1 
10. A long conducting wire having a current I flowing through it, is bent into a circular coil of N turns. 
Then it is bent into a circular coil of n turns. The magnetic field is calculated at the centre of coils in 
both the cases. The ratio of the magnetic field in first case to that of second case is: 
 (1) n : N (2) ?? 2
: N
2
 (3) ?? 2
: ?? 2
 (4) N : n 
Sol. (3) 
 Length Remains Same. 
 
? ? ? ?
12
N 2 r n 2 r ? ? ? ? 
 
0
1 12
21 0
2
I
N
2r Br N N N
B n r n n I
n
2r
?? ?
??
??
??
??
? ? ?
?? ??
?? ? ??
??
??
??
 
 
2
1
2
B N
Bn
??
?
??
??
 
 
11. A body weight W, is projected vertically upwards from earth's surface to reach a height above the earth 
which is equal to nine times the radius of earth. The weight of the body at that height will be : 
 (1) 
W
100
 (2) 
?? 91
 (3) 
W
3
 (4) 
?? 9
 
Sol. (1) 
 
h 2
g
g
h
1
R
?
??
?
??
??
 
 h = 9R 
 
? ?
h 2
gg
g
100
19
??
?
 
 
h
mg w
w
100 100
?? 
 
12. The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be 
 (1) 
R
3
 (2) 3R (3) 2 . 25R (4) 9R 
Sol. (3) 
 
2
n
R
z
? 
 
2
2
11
22
Rn 2
R n 3
??
??
??
?? ??
??
??
 
 
2
9R
R 2.25R
4
?? 
 
 
 
13. A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the 
ratio of final pressure of the gas to initial pressure of the gas is 
16
81
. Then the ratio of 
Cp
Cv
 will be. 
 (1) 
1
2
 (2) 
4
3
 (3) 
3
2
 (4) 
3
1
 
Page 5


SECTION - A 
1. Given below are two statements: 
 Statement I: In a typical transistor, all three regions emitter, base and collector have same doping 
level. 
 Statement II: In a transistor, collector is the thickest and base is the thinnest segment. 
 In the light of the above statements, choose the most appropriate answer from the options given below. 
 (1) Both Statement I and Statement II are correct 
 (2) Statement I is incorrect but Statement II is correct 
 (3) Statement I is correct but Statement II is incorrect 
 (4) Both Statement I and Statement II are incorrect 
Sol. (2) 
  
Emitter Base Collector 
Moderate Size Thin Thick 
Maximum 
Doping 
Minimum 
Doping 
Moderate Doping 
 
 
2. If the two metals ?? and ?? are exposed to radiation of wavelength 350 nm. The work functions of 
metals A and B are 4 . 8eV and 2 . 2eV. Then choose the correct option. 
 (1) Both metals A and B will emit photo-electrons 
 (2) Metal ?? will not emit photo-electrons 
 (3) Metal B will not emit photo-electrons 
 (4) Both metals A and B will not emit photo-electrons 
Sol. (2) 
  
 If E > ?, photo electrons will emit. 
 A will not emit and B will emit. 
 
3. Heat energy of 735 J is given to a diatomic gas allowing the gas to expand at constant pressure. Each 
gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy 
of the gas will be : 
 (1) 525 J (2) 441 J (3) 572 J (4) 735 J 
Sol. (1) 
 At constant Pressure, 
 Q = nCpdT = 735J 
 
 
 
 
 
? ? ? 
7
5
735
U 525J
? ?
? ? ? ?  
Cp 8
Cv
735 735
U nCvdT
? ?
? ? ?
?
E 3.54eV
350
hc 1240
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 31st January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
4. Match List I with List II 
LIST I LIST II 
A. Angular momentum I. [ ML
2
 T
- 2
] 
B. Torque II. [ ML
- 2
 T
- 2
] 
C. Stress III. [ ML
2
 T
- 1
] 
D. Pressure gradient IV. [ ML
- 1
 T
- 2
] 
 
 Choose the correct answer from the options given below: 
 (1) A - III, B - I, C - IV, D – II (2) A - II, B - III, C - IV, D – I 
 (3) A - IV, B - II, C - I, D – III (4) A - I, B - IV, C - III, D – II 
Sol. (1) 
 L = mvr = [M
1
L
2
T
–1
] 
 ? = rF = [M
1
L
2
T
–2
] 
 Stress = 
F
A
= [M
1
L
–1
T
–2
] 
 Pressure Gradient = 
dp
dx
 = [M
1
L
–2
T
–2
] 
 
5. A stone of mass 1 kg is tied to end of a massless string of length 1 m. If the breaking tension of the 
string is 400 N, then maximum linear velocity, the stone can have without breaking the string, while 
rotating in horizontal plane, is : 
 (1) 40 ms
- 1
 (2) 400 ms
- 1
 (3) 20 ms
- 1
 (4) 10 ms
- 1
 
Sol. (3) 
 
 
 
T = 
2
mv
 
 400 = 
2
1v
1
?
 
 V = 20 m/s 
 
6. A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index 
5
3
 is 
poured inside the bucket, then microscope have to be raised by 30 cm to focus the object again. The 
height of the liquid in the bucket is : 
 (1) 12 cm (2) 50 cm (3) 18 cm (4) 75 cm 
Sol. (4) 
 d app = 
? ?
dh
5
3
?
?
 
 Shift = h 
–3h
5
 = 30 
 h = 75 cm 
 
7. The number of turns of the coil of a moving coil galvanometer is increased in order to increase current 
sensitivity by 50%. The percentage change in voltage sensitivity of the galvanometer will be : 
 (1) 0% (2) 75% (3) 50% (4) 100% 
Sol. (1) 
 
V
NAB N
KR R
? ? ? 
 
I
NAB
N
K
? ? ? 
 
I
N
N , ,
R
? ? ? ? Constant 
 
V
0 ? ? ? 
 
8. A body is moving with constant speed, in a circle of radius 10 m. The body completes one revolution 
in 4s. At the end of 3
rd
 second, the displacement of body (in m) from its starting point is: 
 (1) 15 ? ? (2) 10 2 (3) 30 (4) 5 ?  
Sol. (2) 
 
22
rad
w
s
T 4 2
? ? ?
??? 
 ? = wt 
 ? = 3
2
?
? 
 ? =
3
2
?
 rad 
 
+ 
R 
R 
+ 
Displacement = 2R 10 2m ? 
 
 
9. The H amount of thermal energy is developed by a resistor in 10 s when a current of 4 A is passed 
through it. If the current is increased to 16 A, the thermal energy developed by the resistor in 10 s will 
be : 
 (1) 
H
4
 (2) 16H (3) 4H (4) H 
Sol. (2) 
 H = I
2
Rt 
 
2
2
11
22
HI 4
H I 16
??
??
??
?? ??
??
??
 
 H 2 = 16H 1 
10. A long conducting wire having a current I flowing through it, is bent into a circular coil of N turns. 
Then it is bent into a circular coil of n turns. The magnetic field is calculated at the centre of coils in 
both the cases. The ratio of the magnetic field in first case to that of second case is: 
 (1) n : N (2) ?? 2
: N
2
 (3) ?? 2
: ?? 2
 (4) N : n 
Sol. (3) 
 Length Remains Same. 
 
? ? ? ?
12
N 2 r n 2 r ? ? ? ? 
 
0
1 12
21 0
2
I
N
2r Br N N N
B n r n n I
n
2r
?? ?
??
??
??
??
? ? ?
?? ??
?? ? ??
??
??
??
 
 
2
1
2
B N
Bn
??
?
??
??
 
 
11. A body weight W, is projected vertically upwards from earth's surface to reach a height above the earth 
which is equal to nine times the radius of earth. The weight of the body at that height will be : 
 (1) 
W
100
 (2) 
?? 91
 (3) 
W
3
 (4) 
?? 9
 
Sol. (1) 
 
h 2
g
g
h
1
R
?
??
?
??
??
 
 h = 9R 
 
? ?
h 2
gg
g
100
19
??
?
 
 
h
mg w
w
100 100
?? 
 
12. The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be 
 (1) 
R
3
 (2) 3R (3) 2 . 25R (4) 9R 
Sol. (3) 
 
2
n
R
z
? 
 
2
2
11
22
Rn 2
R n 3
??
??
??
?? ??
??
??
 
 
2
9R
R 2.25R
4
?? 
 
 
 
13. A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the 
ratio of final pressure of the gas to initial pressure of the gas is 
16
81
. Then the ratio of 
Cp
Cv
 will be. 
 (1) 
1
2
 (2) 
4
3
 (3) 
3
2
 (4) 
3
1
 
Sol. (2) 
 For Adiabatic process, 
  
1 1 2 2
P V P V
??
? 
  
8 16
27 81
?
??
?
??
??
 
  
34
22
33
?
? ? ? ?
?
? ? ? ?
? ? ? ?
 
  34 ?? 
  
4 Cp
3 Cv
? ? ? 
 
 
14. For a solid rod, the Young's modulus of elasticity is 3 . 2 × 10
11
Nm
- 2
 and density is 8 × 10
3
 kg m
- 3
. The 
velocity of longitudinal wave in the rod will be. 
 (1) 145 . 75 × 10
3
 ms
- 1
  (2) 18 . 96 × 10
3
 ms
- 1
 
 (3) 3 . 65 × 10
3
 ms
- 1
  (4) 6 . 32 × 10
3
 ms
- 1
 
Sol. (4) 
 
Y
V ?
?
 
  
11
8
3
3.2 10
V 0.4 10
8 10
?
? ? ?
?
 
  
6
V 40 10 ?? 
  
3
m
V 6.32 10
s
?? 
 
15. A body of mass 10 kg is moving with an initial speed of 20 m / s. The body stops after 5 s due to friction 
between body and the floor. The value of the coefficient of friction is: (Take acceleration due to gravity 
?? = 10 ms
- 2
 ) 
 (1) 0.3 (2) 0 . 5 (3) 0 . 2 (4) 0 . 4 
Sol. (4) 
 v = u + at 
  0 = 20 – ?g(5) 
  
2
0.4
5
? ? ? 
16. Given below are two statements : 
 Statement I : For transmitting a signal, size of antenna (l) should be comparable to wavelength of 
signal (at least ?? =
?? 4
 in dimension) 
 Statement II : In amplitude modulation, amplitude of carrier wave remains constant (unchanged). 
 In the light of the above statements, choose the most appropriate answer from the options given 
below. 
 (1) Statement ?? is correct but Statement II is incorrect 
 (2) Both Statement I and Statement II are correct 
 (3) Statement I is incorrect but Statement II is correct 
 (4) Both Statement I and Statement II are incorrect