NEET 2023 Past Year Paper with Detailed Solutions | NEET Past Year Papers PDF Download

 Page 1


   
 
  
Answers & Solutions 
for 
NEET (UG)-2023 
 
 
  
DATE : 07/05/2023 
Time : 3 hrs. 20 Min. M.M. : 720 
Important Instructions :  
1. The test is of 3 hours 20 minutes duration and the Test Booklet contains 200 multiple choice questions (four 
options with a single correct answer) from Physics, Chemistry and Biology (Botany and Zoology). 
50 questions in each subject are divided into two sections (A and B) as per details given below: 
 (a) Section A shall consist of 35 (Thirty-five) Questions in each subject (Question Nos. – 1 to 35, 51 to 85, 
101 to 135 and 151 to 185). All Questions are compulsory. 
 (b) Section B shall consist of 15 (Fifteen) questions in each subject (Question Nos. – 36 to 50, 86 to 100, 
136 to 150 and 186 to 200). In section B, a candidate needs to attempt any 10 (Ten) questions out of  
15 (Fifteen) in each subject.  
 Candidates are advised to read all 15 questions in each subject of Section-B before they start attempting 
the question paper. In the event of a candidate attempting more than ten questions, the first ten questions 
answered by the candidate shall be evaluated. 
2. Each question carries 4 marks. For each correct response, the candidate will get 4 marks. For each incorrect 
response, 1 mark will be deducted from the total scores. The maximum marks are 720. 
3. Use Blue / Black Ball point Pen only for writing particulars on this page / marking responses on Answer 
Sheet. 
4. Rough work is to be done in the space provided for this purpose in the Test Booklet only. 
5. On completion of the test, the candidate must handover the Answer Sheet (ORIGINAL and OFFICE Copy) 
to the Invigilator before leaving the Room/Hall. The candidates are allowed to take away this Test Booklet 
with them. 
6. The CODE for this Booklet is E2. 
7. The candidates should ensure that the Answer Sheet is not folded. Do not make any stray marks on the 
Answer Sheet. Do not write your Roll No. anywhere else except in the specified space in the Test 
Booklet/Answer Sheet. Use of white fluid for correction is NOT permissible on the Answer Sheet. 
8. Each candidate must show on-demand his/her Admit Card to the Invigilator. 
9. No candidate, without special permission of the Centre Superintendent or Invigilator, would leave his/her seat. 
10. Use of Electronic/Manual Calculator is prohibited. 
11. The candidates are governed by all Rules and Regulations of the examination with regard to their conduct in 
the Examination Room/Hall. All cases of unfair means will be dealt with as per Rules and Regulations of this 
examination. 
12. No part of the Test Booklet and Answer Sheet shall be detached under any circumstances. 
13. The candidates will write the Correct Test Booklet Code as given in the Test Booklet / Answer Sheet in the 
Attendance Sheet. 
Test Booklet Code 
E2 
 
Page 2


   
 
  
Answers & Solutions 
for 
NEET (UG)-2023 
 
 
  
DATE : 07/05/2023 
Time : 3 hrs. 20 Min. M.M. : 720 
Important Instructions :  
1. The test is of 3 hours 20 minutes duration and the Test Booklet contains 200 multiple choice questions (four 
options with a single correct answer) from Physics, Chemistry and Biology (Botany and Zoology). 
50 questions in each subject are divided into two sections (A and B) as per details given below: 
 (a) Section A shall consist of 35 (Thirty-five) Questions in each subject (Question Nos. – 1 to 35, 51 to 85, 
101 to 135 and 151 to 185). All Questions are compulsory. 
 (b) Section B shall consist of 15 (Fifteen) questions in each subject (Question Nos. – 36 to 50, 86 to 100, 
136 to 150 and 186 to 200). In section B, a candidate needs to attempt any 10 (Ten) questions out of  
15 (Fifteen) in each subject.  
 Candidates are advised to read all 15 questions in each subject of Section-B before they start attempting 
the question paper. In the event of a candidate attempting more than ten questions, the first ten questions 
answered by the candidate shall be evaluated. 
2. Each question carries 4 marks. For each correct response, the candidate will get 4 marks. For each incorrect 
response, 1 mark will be deducted from the total scores. The maximum marks are 720. 
3. Use Blue / Black Ball point Pen only for writing particulars on this page / marking responses on Answer 
Sheet. 
4. Rough work is to be done in the space provided for this purpose in the Test Booklet only. 
5. On completion of the test, the candidate must handover the Answer Sheet (ORIGINAL and OFFICE Copy) 
to the Invigilator before leaving the Room/Hall. The candidates are allowed to take away this Test Booklet 
with them. 
6. The CODE for this Booklet is E2. 
7. The candidates should ensure that the Answer Sheet is not folded. Do not make any stray marks on the 
Answer Sheet. Do not write your Roll No. anywhere else except in the specified space in the Test 
Booklet/Answer Sheet. Use of white fluid for correction is NOT permissible on the Answer Sheet. 
8. Each candidate must show on-demand his/her Admit Card to the Invigilator. 
9. No candidate, without special permission of the Centre Superintendent or Invigilator, would leave his/her seat. 
10. Use of Electronic/Manual Calculator is prohibited. 
11. The candidates are governed by all Rules and Regulations of the examination with regard to their conduct in 
the Examination Room/Hall. All cases of unfair means will be dealt with as per Rules and Regulations of this 
examination. 
12. No part of the Test Booklet and Answer Sheet shall be detached under any circumstances. 
13. The candidates will write the Correct Test Booklet Code as given in the Test Booklet / Answer Sheet in the 
Attendance Sheet. 
Test Booklet Code 
E2 
 
 
   
  
PHYSICS 
 
SECTION-A 
1. The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of 
V volts is proportional to 
(1) V (2) 
1
V
 
(3) 
1
V
 (4) V
2 
Answer (2) 
Sol. 
min
hc
eV =
?
 
 
min
hc
eV
?= 
 
min
1
V
?? 
2. A Carnot engine has an efficiency of 50% when its source is at a temperature 327°C. The temperature of the 
sink is 
(1) 27°C (2) 15°C 
(3) 100°C (4) 200°C 
Answer (1) 
Sol. Efficiency 
50 1
100 2
? = = 
 Efficiency of Carnot engine  
 
2
1
1 ? = -
T
T
 
 
2
1
600
? = -
T
 
 
2
1
1
2 600
=-
T
 
 
2
2
1
300 K
600 2
= ? =
T
T 
 T2 = 300 – 273 = 27°C 
3. A bullet is fired from a gun at the speed of 280 m s
–1
 in the direction 30° above the horizontal. The maximum 
height attained by the bullet is (g = 9.8 m s
–2
, sin30° = 0.5)  
(1) 2800 m 
(2) 2000 m 
(3) 1000 m 
(4) 3000 m 
Answer (3) 
Page 3


   
 
  
Answers & Solutions 
for 
NEET (UG)-2023 
 
 
  
DATE : 07/05/2023 
Time : 3 hrs. 20 Min. M.M. : 720 
Important Instructions :  
1. The test is of 3 hours 20 minutes duration and the Test Booklet contains 200 multiple choice questions (four 
options with a single correct answer) from Physics, Chemistry and Biology (Botany and Zoology). 
50 questions in each subject are divided into two sections (A and B) as per details given below: 
 (a) Section A shall consist of 35 (Thirty-five) Questions in each subject (Question Nos. – 1 to 35, 51 to 85, 
101 to 135 and 151 to 185). All Questions are compulsory. 
 (b) Section B shall consist of 15 (Fifteen) questions in each subject (Question Nos. – 36 to 50, 86 to 100, 
136 to 150 and 186 to 200). In section B, a candidate needs to attempt any 10 (Ten) questions out of  
15 (Fifteen) in each subject.  
 Candidates are advised to read all 15 questions in each subject of Section-B before they start attempting 
the question paper. In the event of a candidate attempting more than ten questions, the first ten questions 
answered by the candidate shall be evaluated. 
2. Each question carries 4 marks. For each correct response, the candidate will get 4 marks. For each incorrect 
response, 1 mark will be deducted from the total scores. The maximum marks are 720. 
3. Use Blue / Black Ball point Pen only for writing particulars on this page / marking responses on Answer 
Sheet. 
4. Rough work is to be done in the space provided for this purpose in the Test Booklet only. 
5. On completion of the test, the candidate must handover the Answer Sheet (ORIGINAL and OFFICE Copy) 
to the Invigilator before leaving the Room/Hall. The candidates are allowed to take away this Test Booklet 
with them. 
6. The CODE for this Booklet is E2. 
7. The candidates should ensure that the Answer Sheet is not folded. Do not make any stray marks on the 
Answer Sheet. Do not write your Roll No. anywhere else except in the specified space in the Test 
Booklet/Answer Sheet. Use of white fluid for correction is NOT permissible on the Answer Sheet. 
8. Each candidate must show on-demand his/her Admit Card to the Invigilator. 
9. No candidate, without special permission of the Centre Superintendent or Invigilator, would leave his/her seat. 
10. Use of Electronic/Manual Calculator is prohibited. 
11. The candidates are governed by all Rules and Regulations of the examination with regard to their conduct in 
the Examination Room/Hall. All cases of unfair means will be dealt with as per Rules and Regulations of this 
examination. 
12. No part of the Test Booklet and Answer Sheet shall be detached under any circumstances. 
13. The candidates will write the Correct Test Booklet Code as given in the Test Booklet / Answer Sheet in the 
Attendance Sheet. 
Test Booklet Code 
E2 
 
 
   
  
PHYSICS 
 
SECTION-A 
1. The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of 
V volts is proportional to 
(1) V (2) 
1
V
 
(3) 
1
V
 (4) V
2 
Answer (2) 
Sol. 
min
hc
eV =
?
 
 
min
hc
eV
?= 
 
min
1
V
?? 
2. A Carnot engine has an efficiency of 50% when its source is at a temperature 327°C. The temperature of the 
sink is 
(1) 27°C (2) 15°C 
(3) 100°C (4) 200°C 
Answer (1) 
Sol. Efficiency 
50 1
100 2
? = = 
 Efficiency of Carnot engine  
 
2
1
1 ? = -
T
T
 
 
2
1
600
? = -
T
 
 
2
1
1
2 600
=-
T
 
 
2
2
1
300 K
600 2
= ? =
T
T 
 T2 = 300 – 273 = 27°C 
3. A bullet is fired from a gun at the speed of 280 m s
–1
 in the direction 30° above the horizontal. The maximum 
height attained by the bullet is (g = 9.8 m s
–2
, sin30° = 0.5)  
(1) 2800 m 
(2) 2000 m 
(3) 1000 m 
(4) 3000 m 
Answer (3) 
 
   
  
Sol. 
22
sin
2
?
=
u
H
g
 
 
22
(280) (sin 30)
2 9.8
=
?
H 
     
280 280 0.5 0.5
2 9.8
? ? ?
=
?
 
 H = 1000 m  
4. In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 ?F and resistance R is 100 ?. The 
frequency at which resonance occurs is 
(1) 15.9 rad/s (2) 15.9 kHz 
(3) 1.59 rad/s (4) 1.59 kHz 
Answer (4) 
Sol. For resonance frequency = 
1
2? LC
 
 ? 
4
36
1 10
2
2 10 10 1 10
--
==
?
? ?? ? ? ?
f 
    = 1.591 × 10
3 
    = 1.591 kHz 
5. Given below are two statements: 
Statement I: Photovoltaic devices can convert optical radiation into electricity. 
Statement II: Zener diode is designed to operate under reverse bias in breakdown region. 
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) Both Statement I and Statement II are incorrect 
(3) Statement I is correct but Statement II is incorrect 
(4) Statement I is incorrect but Statement II is correct 
Answer (1) 
Sol. Both Statements are correct. 
 I: Photovoltaic devices convert optical radiation into electricity. 
 II: Zener diode is designed to operate under reverse bias in breakdown region. 
 e.g., Zener diode as a voltage regulator. 
6. Light travels a distance x in time t1 in air and 10 x in time t2 in another denser medium. What is the critical angle 
for this medium? 
(1) 
1 2
1
sin
-
??
??
??
t
t
 (2) 
1 2
1
10
sin
-
??
??
??
t
t
 
(3) 
1 1
2
sin
10
-
??
??
??
t
t
 (4) 
1 1
2
10
sin
-
??
??
??
t
t
 
Answer (4) 
Page 4


   
 
  
Answers & Solutions 
for 
NEET (UG)-2023 
 
 
  
DATE : 07/05/2023 
Time : 3 hrs. 20 Min. M.M. : 720 
Important Instructions :  
1. The test is of 3 hours 20 minutes duration and the Test Booklet contains 200 multiple choice questions (four 
options with a single correct answer) from Physics, Chemistry and Biology (Botany and Zoology). 
50 questions in each subject are divided into two sections (A and B) as per details given below: 
 (a) Section A shall consist of 35 (Thirty-five) Questions in each subject (Question Nos. – 1 to 35, 51 to 85, 
101 to 135 and 151 to 185). All Questions are compulsory. 
 (b) Section B shall consist of 15 (Fifteen) questions in each subject (Question Nos. – 36 to 50, 86 to 100, 
136 to 150 and 186 to 200). In section B, a candidate needs to attempt any 10 (Ten) questions out of  
15 (Fifteen) in each subject.  
 Candidates are advised to read all 15 questions in each subject of Section-B before they start attempting 
the question paper. In the event of a candidate attempting more than ten questions, the first ten questions 
answered by the candidate shall be evaluated. 
2. Each question carries 4 marks. For each correct response, the candidate will get 4 marks. For each incorrect 
response, 1 mark will be deducted from the total scores. The maximum marks are 720. 
3. Use Blue / Black Ball point Pen only for writing particulars on this page / marking responses on Answer 
Sheet. 
4. Rough work is to be done in the space provided for this purpose in the Test Booklet only. 
5. On completion of the test, the candidate must handover the Answer Sheet (ORIGINAL and OFFICE Copy) 
to the Invigilator before leaving the Room/Hall. The candidates are allowed to take away this Test Booklet 
with them. 
6. The CODE for this Booklet is E2. 
7. The candidates should ensure that the Answer Sheet is not folded. Do not make any stray marks on the 
Answer Sheet. Do not write your Roll No. anywhere else except in the specified space in the Test 
Booklet/Answer Sheet. Use of white fluid for correction is NOT permissible on the Answer Sheet. 
8. Each candidate must show on-demand his/her Admit Card to the Invigilator. 
9. No candidate, without special permission of the Centre Superintendent or Invigilator, would leave his/her seat. 
10. Use of Electronic/Manual Calculator is prohibited. 
11. The candidates are governed by all Rules and Regulations of the examination with regard to their conduct in 
the Examination Room/Hall. All cases of unfair means will be dealt with as per Rules and Regulations of this 
examination. 
12. No part of the Test Booklet and Answer Sheet shall be detached under any circumstances. 
13. The candidates will write the Correct Test Booklet Code as given in the Test Booklet / Answer Sheet in the 
Attendance Sheet. 
Test Booklet Code 
E2 
 
 
   
  
PHYSICS 
 
SECTION-A 
1. The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of 
V volts is proportional to 
(1) V (2) 
1
V
 
(3) 
1
V
 (4) V
2 
Answer (2) 
Sol. 
min
hc
eV =
?
 
 
min
hc
eV
?= 
 
min
1
V
?? 
2. A Carnot engine has an efficiency of 50% when its source is at a temperature 327°C. The temperature of the 
sink is 
(1) 27°C (2) 15°C 
(3) 100°C (4) 200°C 
Answer (1) 
Sol. Efficiency 
50 1
100 2
? = = 
 Efficiency of Carnot engine  
 
2
1
1 ? = -
T
T
 
 
2
1
600
? = -
T
 
 
2
1
1
2 600
=-
T
 
 
2
2
1
300 K
600 2
= ? =
T
T 
 T2 = 300 – 273 = 27°C 
3. A bullet is fired from a gun at the speed of 280 m s
–1
 in the direction 30° above the horizontal. The maximum 
height attained by the bullet is (g = 9.8 m s
–2
, sin30° = 0.5)  
(1) 2800 m 
(2) 2000 m 
(3) 1000 m 
(4) 3000 m 
Answer (3) 
 
   
  
Sol. 
22
sin
2
?
=
u
H
g
 
 
22
(280) (sin 30)
2 9.8
=
?
H 
     
280 280 0.5 0.5
2 9.8
? ? ?
=
?
 
 H = 1000 m  
4. In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 ?F and resistance R is 100 ?. The 
frequency at which resonance occurs is 
(1) 15.9 rad/s (2) 15.9 kHz 
(3) 1.59 rad/s (4) 1.59 kHz 
Answer (4) 
Sol. For resonance frequency = 
1
2? LC
 
 ? 
4
36
1 10
2
2 10 10 1 10
--
==
?
? ?? ? ? ?
f 
    = 1.591 × 10
3 
    = 1.591 kHz 
5. Given below are two statements: 
Statement I: Photovoltaic devices can convert optical radiation into electricity. 
Statement II: Zener diode is designed to operate under reverse bias in breakdown region. 
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) Both Statement I and Statement II are incorrect 
(3) Statement I is correct but Statement II is incorrect 
(4) Statement I is incorrect but Statement II is correct 
Answer (1) 
Sol. Both Statements are correct. 
 I: Photovoltaic devices convert optical radiation into electricity. 
 II: Zener diode is designed to operate under reverse bias in breakdown region. 
 e.g., Zener diode as a voltage regulator. 
6. Light travels a distance x in time t1 in air and 10 x in time t2 in another denser medium. What is the critical angle 
for this medium? 
(1) 
1 2
1
sin
-
??
??
??
t
t
 (2) 
1 2
1
10
sin
-
??
??
??
t
t
 
(3) 
1 1
2
sin
10
-
??
??
??
t
t
 (4) 
1 1
2
10
sin
-
??
??
??
t
t
 
Answer (4) 
 
   
  
Sol.  
 ?2 sin ic = ?1
  
 sin ic = 
1
2
?
?
 
 ?=
c
V
 
 So 
12
21
sin
?
==
?
c
V
i
V
 
 
1
2
10
sin =
c
xt
i
tx
 
 
1 1
2
10
sin
-
??
=
??
??
c
t
i
t
 
7. In hydrogen spectrum, the shortest wavelength in the Balmer series is ?. The shortest wavelength in the 
Bracket series is 
(1) 2? 
(2) 4? 
(3) 9? 
(4) 16? 
Answer (2) 
Sol. 
22
21
1 1 1
–
??
=
??
?
??
R
nn
  
 For Balmer [n2 = 2, n1 = ?] 
 
1 1 1
–
4
??
=
??
? ? ??
R 
 
4
?=
R
 …(1) 
 For Bracket, (n2 = 4, n1 = ?) 
 
1 1 1
–
16
??
=
??
??? ??
R 
 
16
? ?=
R
 …(2) 
 
n
n
Eq (1)
Eq (2)
 
 ?? = 4?  
Page 5


   
 
  
Answers & Solutions 
for 
NEET (UG)-2023 
 
 
  
DATE : 07/05/2023 
Time : 3 hrs. 20 Min. M.M. : 720 
Important Instructions :  
1. The test is of 3 hours 20 minutes duration and the Test Booklet contains 200 multiple choice questions (four 
options with a single correct answer) from Physics, Chemistry and Biology (Botany and Zoology). 
50 questions in each subject are divided into two sections (A and B) as per details given below: 
 (a) Section A shall consist of 35 (Thirty-five) Questions in each subject (Question Nos. – 1 to 35, 51 to 85, 
101 to 135 and 151 to 185). All Questions are compulsory. 
 (b) Section B shall consist of 15 (Fifteen) questions in each subject (Question Nos. – 36 to 50, 86 to 100, 
136 to 150 and 186 to 200). In section B, a candidate needs to attempt any 10 (Ten) questions out of  
15 (Fifteen) in each subject.  
 Candidates are advised to read all 15 questions in each subject of Section-B before they start attempting 
the question paper. In the event of a candidate attempting more than ten questions, the first ten questions 
answered by the candidate shall be evaluated. 
2. Each question carries 4 marks. For each correct response, the candidate will get 4 marks. For each incorrect 
response, 1 mark will be deducted from the total scores. The maximum marks are 720. 
3. Use Blue / Black Ball point Pen only for writing particulars on this page / marking responses on Answer 
Sheet. 
4. Rough work is to be done in the space provided for this purpose in the Test Booklet only. 
5. On completion of the test, the candidate must handover the Answer Sheet (ORIGINAL and OFFICE Copy) 
to the Invigilator before leaving the Room/Hall. The candidates are allowed to take away this Test Booklet 
with them. 
6. The CODE for this Booklet is E2. 
7. The candidates should ensure that the Answer Sheet is not folded. Do not make any stray marks on the 
Answer Sheet. Do not write your Roll No. anywhere else except in the specified space in the Test 
Booklet/Answer Sheet. Use of white fluid for correction is NOT permissible on the Answer Sheet. 
8. Each candidate must show on-demand his/her Admit Card to the Invigilator. 
9. No candidate, without special permission of the Centre Superintendent or Invigilator, would leave his/her seat. 
10. Use of Electronic/Manual Calculator is prohibited. 
11. The candidates are governed by all Rules and Regulations of the examination with regard to their conduct in 
the Examination Room/Hall. All cases of unfair means will be dealt with as per Rules and Regulations of this 
examination. 
12. No part of the Test Booklet and Answer Sheet shall be detached under any circumstances. 
13. The candidates will write the Correct Test Booklet Code as given in the Test Booklet / Answer Sheet in the 
Attendance Sheet. 
Test Booklet Code 
E2 
 
 
   
  
PHYSICS 
 
SECTION-A 
1. The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of 
V volts is proportional to 
(1) V (2) 
1
V
 
(3) 
1
V
 (4) V
2 
Answer (2) 
Sol. 
min
hc
eV =
?
 
 
min
hc
eV
?= 
 
min
1
V
?? 
2. A Carnot engine has an efficiency of 50% when its source is at a temperature 327°C. The temperature of the 
sink is 
(1) 27°C (2) 15°C 
(3) 100°C (4) 200°C 
Answer (1) 
Sol. Efficiency 
50 1
100 2
? = = 
 Efficiency of Carnot engine  
 
2
1
1 ? = -
T
T
 
 
2
1
600
? = -
T
 
 
2
1
1
2 600
=-
T
 
 
2
2
1
300 K
600 2
= ? =
T
T 
 T2 = 300 – 273 = 27°C 
3. A bullet is fired from a gun at the speed of 280 m s
–1
 in the direction 30° above the horizontal. The maximum 
height attained by the bullet is (g = 9.8 m s
–2
, sin30° = 0.5)  
(1) 2800 m 
(2) 2000 m 
(3) 1000 m 
(4) 3000 m 
Answer (3) 
 
   
  
Sol. 
22
sin
2
?
=
u
H
g
 
 
22
(280) (sin 30)
2 9.8
=
?
H 
     
280 280 0.5 0.5
2 9.8
? ? ?
=
?
 
 H = 1000 m  
4. In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 ?F and resistance R is 100 ?. The 
frequency at which resonance occurs is 
(1) 15.9 rad/s (2) 15.9 kHz 
(3) 1.59 rad/s (4) 1.59 kHz 
Answer (4) 
Sol. For resonance frequency = 
1
2? LC
 
 ? 
4
36
1 10
2
2 10 10 1 10
--
==
?
? ?? ? ? ?
f 
    = 1.591 × 10
3 
    = 1.591 kHz 
5. Given below are two statements: 
Statement I: Photovoltaic devices can convert optical radiation into electricity. 
Statement II: Zener diode is designed to operate under reverse bias in breakdown region. 
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) Both Statement I and Statement II are incorrect 
(3) Statement I is correct but Statement II is incorrect 
(4) Statement I is incorrect but Statement II is correct 
Answer (1) 
Sol. Both Statements are correct. 
 I: Photovoltaic devices convert optical radiation into electricity. 
 II: Zener diode is designed to operate under reverse bias in breakdown region. 
 e.g., Zener diode as a voltage regulator. 
6. Light travels a distance x in time t1 in air and 10 x in time t2 in another denser medium. What is the critical angle 
for this medium? 
(1) 
1 2
1
sin
-
??
??
??
t
t
 (2) 
1 2
1
10
sin
-
??
??
??
t
t
 
(3) 
1 1
2
sin
10
-
??
??
??
t
t
 (4) 
1 1
2
10
sin
-
??
??
??
t
t
 
Answer (4) 
 
   
  
Sol.  
 ?2 sin ic = ?1
  
 sin ic = 
1
2
?
?
 
 ?=
c
V
 
 So 
12
21
sin
?
==
?
c
V
i
V
 
 
1
2
10
sin =
c
xt
i
tx
 
 
1 1
2
10
sin
-
??
=
??
??
c
t
i
t
 
7. In hydrogen spectrum, the shortest wavelength in the Balmer series is ?. The shortest wavelength in the 
Bracket series is 
(1) 2? 
(2) 4? 
(3) 9? 
(4) 16? 
Answer (2) 
Sol. 
22
21
1 1 1
–
??
=
??
?
??
R
nn
  
 For Balmer [n2 = 2, n1 = ?] 
 
1 1 1
–
4
??
=
??
? ? ??
R 
 
4
?=
R
 …(1) 
 For Bracket, (n2 = 4, n1 = ?) 
 
1 1 1
–
16
??
=
??
??? ??
R 
 
16
? ?=
R
 …(2) 
 
n
n
Eq (1)
Eq (2)
 
 ?? = 4?  
 
   
  
8. If the galvanometer G does not show any deflection in the circuit shown, the value of R is given by 
 
(1) 200 ? (2) 50 ? 
(3) 100 ? (4) 400 ? 
Answer (3) 
Sol. Since galvanometer does not show any deflection 
 ?  i g = 0 
  
 
10 2 2 2 400
 100 
400 8
R
R
-?
= ? = = ?  
9. The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly (surface 
tension of soap solution = 0.03 N m
–1
) 
(1) 30.16 × 10
–4
 J (2) 5.06 × 10
–4 
J 
(3) 3.01 × 10
–4
 J (4) 50.1 × 10
–4
 J 
Answer (3) 
Sol. Amount of energy required = [S × ?A] × 2 
 ? Energy required = [0.03 × 4 × ? × 4 × 10
–4
] × 2 
    = 3.015 × 10
–4
 J 
10. The magnetic energy stored in an inductor of inductance 4 ?H carrying a current of 2 A is 
(1) 4 ?J (2) 4 mJ 
(3) 8 mJ (4) 8 ?J 
Answer (4) 
Sol. Magnetic energy stored in an inductor 
 
2
1
2
= U Li 
  
( )
2
6
1
4 10 2
2
-
= ? ? ? 
  = 8 × 10
–6
 J 
 U = 8 ?J