Physics (PH) 2012 GATE Paper with solution GATE Notes | EduRev

GATE Past Year Papers for Practice (All Branches)

GATE : Physics (PH) 2012 GATE Paper with solution GATE Notes | EduRev

 Page 1


2012                                                                                                                                                                                                PHYSICS – PH 
PH 
1/20 
PH : PHYSICS 
 
Duration: Three Hours                          Maximum Marks: 100 
Read the following instructions carefully. 
 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully.   
 
3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble 
corresponding to your test paper code and the appropriate bubble under each digit of your registration 
number and (ii) write your registration number, your name and name of the examination centre and 
put your signature at the specified location.  
 
4. This Question Booklet contains 20 pages including blank pages for rough work. After you are 
permitted to open the seal, please check all pages and report discrepancies, if any, to the invigilator. 
 
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ball point pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
 
6. Since bubbles darkened by the black ink ball point pen cannot be erased, candidates should darken 
the bubbles in the ORS very carefully. 
 
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then 
the answer to the second question in the pair will not be evaluated. 
 
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each.   
 
9. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks.  
For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks questions, 
? mark will be deducted for each wrong answer.  However, in the case of the linked answer question 
pair, there will be negative marks only for wrong answer to the first question and no negative marks 
for wrong answer to the second question.  
 
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 
 
11. Rough work can be done on the question paper itself. Blank pages are provided at the end of the 
question paper for rough work. 
 
12. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ball point pen. 
 
 
Name 
 
 
Registration 
Number 
PH 
      
 
 
Page 2


2012                                                                                                                                                                                                PHYSICS – PH 
PH 
1/20 
PH : PHYSICS 
 
Duration: Three Hours                          Maximum Marks: 100 
Read the following instructions carefully. 
 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully.   
 
3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble 
corresponding to your test paper code and the appropriate bubble under each digit of your registration 
number and (ii) write your registration number, your name and name of the examination centre and 
put your signature at the specified location.  
 
4. This Question Booklet contains 20 pages including blank pages for rough work. After you are 
permitted to open the seal, please check all pages and report discrepancies, if any, to the invigilator. 
 
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ball point pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
 
6. Since bubbles darkened by the black ink ball point pen cannot be erased, candidates should darken 
the bubbles in the ORS very carefully. 
 
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then 
the answer to the second question in the pair will not be evaluated. 
 
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each.   
 
9. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks.  
For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks questions, 
? mark will be deducted for each wrong answer.  However, in the case of the linked answer question 
pair, there will be negative marks only for wrong answer to the first question and no negative marks 
for wrong answer to the second question.  
 
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 
 
11. Rough work can be done on the question paper itself. Blank pages are provided at the end of the 
question paper for rough work. 
 
12. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ball point pen. 
 
 
Name 
 
 
Registration 
Number 
PH 
      
 
 
2012                                                                                                                                                                                                PHYSICS – PH 
PH 
2/20 
Some Useful Constants 
  Speed of light in free space  c = 3 × 10
8
 m/s 
  Boltzmann constant   
B
k = 1.380 × 10
–23
 J/K 
  Planck’s constant   h = 6.626 × 10
–34
 J.s 
  Electron charge    e = 1.602 × 10
-19
 C 
  Permittivity of free space  
0
? = 8.854 × 10
–12
 C
2
/N.m
2
 
  Permeability of free space  
0
? = 4? × 10
–7
 H/m 
NOTE : In numerical problems, the option closest to the correct answer will be given credit. 
  
Q. 1 – Q. 25 carry one mark each. 
Q.1   Identify the CORRECT statement for the following vectors 
ˆˆ
32 a i j ?? and 
ˆˆ
2 b i j ?? 
(A) The vectors a  and  b are linearly independent 
(B) The vectors a  and b are linearly dependent 
(C) The vectors a  and b are orthogonal 
(D) The vectors a  and b are normalized 
  
Q.2   Two uniform thin rods of equal length, L, and masses M
1
 and M
2
 are joined together along the 
length. The moment of inertia of the combined rod of length 2L about an axis passing through the 
mid-point and perpendicular to the length of the rod is, 
(A) ? ?
2
12
12
L
MM ? (B) ? ?
2
12
6
L
MM ? 
(C) ? ?
2
12
3
L
MM ? (D) ? ?
2
12
2
L
MM ? 
  
Q.3   The space-time dependence of the electric field of a linearly polarized light in free space is given by 
0
cos( ) xE t kz ? ? where E
0
, ? and k are the amplitude, the angular frequency and the wavevector, 
respectively. The time averaged energy density associated with the electric field is 
(A) 
2
00
1
4
E ? (B) 
2
00
1
2
E ? 
(C) 
2
00
E ?
 
(D)
  2
00
2 E ?
 
  
Q.4   If the peak output voltage of a full wave rectifier is 10 V, its d.c. voltage is 
(A) 10.0 V (B) 7.07 V (C) 6.36 V (D)  3.18 V 
  
Q.5   A particle of mass m is confined in a two dimensional square well potential of dimension a. This 
potential V(x,y) is given by 
     ( , ) 0 V x y ? for a x a ? ? ? and a y a ? ? ?  
                                                     ?? elsewhere 
The energy of the first excited state for this particle is given by, 
(A) 
22
2
ma
?
 (B) 
22
2
2
ma
?
 (C)  
22
2
5
2ma
?
 (D) 
22
2
4
ma
?
 
Page 3


2012                                                                                                                                                                                                PHYSICS – PH 
PH 
1/20 
PH : PHYSICS 
 
Duration: Three Hours                          Maximum Marks: 100 
Read the following instructions carefully. 
 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully.   
 
3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble 
corresponding to your test paper code and the appropriate bubble under each digit of your registration 
number and (ii) write your registration number, your name and name of the examination centre and 
put your signature at the specified location.  
 
4. This Question Booklet contains 20 pages including blank pages for rough work. After you are 
permitted to open the seal, please check all pages and report discrepancies, if any, to the invigilator. 
 
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ball point pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
 
6. Since bubbles darkened by the black ink ball point pen cannot be erased, candidates should darken 
the bubbles in the ORS very carefully. 
 
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then 
the answer to the second question in the pair will not be evaluated. 
 
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each.   
 
9. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks.  
For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks questions, 
? mark will be deducted for each wrong answer.  However, in the case of the linked answer question 
pair, there will be negative marks only for wrong answer to the first question and no negative marks 
for wrong answer to the second question.  
 
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 
 
11. Rough work can be done on the question paper itself. Blank pages are provided at the end of the 
question paper for rough work. 
 
12. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ball point pen. 
 
 
Name 
 
 
Registration 
Number 
PH 
      
 
 
2012                                                                                                                                                                                                PHYSICS – PH 
PH 
2/20 
Some Useful Constants 
  Speed of light in free space  c = 3 × 10
8
 m/s 
  Boltzmann constant   
B
k = 1.380 × 10
–23
 J/K 
  Planck’s constant   h = 6.626 × 10
–34
 J.s 
  Electron charge    e = 1.602 × 10
-19
 C 
  Permittivity of free space  
0
? = 8.854 × 10
–12
 C
2
/N.m
2
 
  Permeability of free space  
0
? = 4? × 10
–7
 H/m 
NOTE : In numerical problems, the option closest to the correct answer will be given credit. 
  
Q. 1 – Q. 25 carry one mark each. 
Q.1   Identify the CORRECT statement for the following vectors 
ˆˆ
32 a i j ?? and 
ˆˆ
2 b i j ?? 
(A) The vectors a  and  b are linearly independent 
(B) The vectors a  and b are linearly dependent 
(C) The vectors a  and b are orthogonal 
(D) The vectors a  and b are normalized 
  
Q.2   Two uniform thin rods of equal length, L, and masses M
1
 and M
2
 are joined together along the 
length. The moment of inertia of the combined rod of length 2L about an axis passing through the 
mid-point and perpendicular to the length of the rod is, 
(A) ? ?
2
12
12
L
MM ? (B) ? ?
2
12
6
L
MM ? 
(C) ? ?
2
12
3
L
MM ? (D) ? ?
2
12
2
L
MM ? 
  
Q.3   The space-time dependence of the electric field of a linearly polarized light in free space is given by 
0
cos( ) xE t kz ? ? where E
0
, ? and k are the amplitude, the angular frequency and the wavevector, 
respectively. The time averaged energy density associated with the electric field is 
(A) 
2
00
1
4
E ? (B) 
2
00
1
2
E ? 
(C) 
2
00
E ?
 
(D)
  2
00
2 E ?
 
  
Q.4   If the peak output voltage of a full wave rectifier is 10 V, its d.c. voltage is 
(A) 10.0 V (B) 7.07 V (C) 6.36 V (D)  3.18 V 
  
Q.5   A particle of mass m is confined in a two dimensional square well potential of dimension a. This 
potential V(x,y) is given by 
     ( , ) 0 V x y ? for a x a ? ? ? and a y a ? ? ?  
                                                     ?? elsewhere 
The energy of the first excited state for this particle is given by, 
(A) 
22
2
ma
?
 (B) 
22
2
2
ma
?
 (C)  
22
2
5
2ma
?
 (D) 
22
2
4
ma
?
 
2012                                                                                                                                                                                                PHYSICS – PH 
PH 
3/20 
Q.6  
  
The isothermal compressibility, ? of an ideal gas at temperature T
0
 and volume V
0
, is given by 
(A) 
0
0
1
T
V
VP
?
?
?
 (B) 
0
0
1
T
V
VP
?
?
 (C) 
0
0
T
P
V
V
?
?
?
  (D) 
0
0
T
P
V
V
?
?
  
  
Q.7   The ground state of sodium atom (
11
Na) is a 
2
S
1/2
 state. The difference in energy levels arising in the 
presence of a weak external magnetic field B, given in terms of Bohr magneton, µ
B
, is 
(A) µ
B
B (B) 2µ
B
B (C) 4µ
B
B   (D) 6µ
B
B  
  
Q.8   For an ideal Fermi gas in three dimensions, the electron velocity v
F
 at the Fermi surface is related 
to electron concentration n as,  
(A) 
2/3
v
F
n ? (B) v
F
n ? (C) 
1/2
v
F
n ? (D) 
1/3
v
F
n ? 
  
Q.9   Which one of the following sets corresponds to fundamental particles? 
(A) proton, electron and neutron 
(B) proton, electron and photon 
(C) electron, photon and neutrino 
(D) quark, electron and meson 
  
Q.10   In case of a Geiger-Muller (GM) counter, which one of the following statements is CORRECT? 
(A) Multiplication factor of the detector is of the order of 10
10     
 
(B) Type of the particles detected can be identified 
(C) Energy of the particles detected can be distinguished 
(D) Operating voltage of the detector is few tens of  Volts 
  
Q.11   A plane electromagnetic wave traveling in free space is incident normally on a glass plate of 
refractive index 3/2. If there is no absorption by the glass, its reflectivity is 
(A) 4%  (B) 16%  (C) 20%  (D) 50%   
  
Q.12   A Ge semiconductor is doped with acceptor impurity concentration of 10
15
 atoms/cm
3
. For the 
given hole mobility of 1800 cm
2
/V-s, the resistivity of this material is 
(A) 0.288 ? cm (B) 0.694 ? cm (C) 3.472 ? cm   (D) 6.944 ? cm 
  
Q.13   A classical gas of molecules, each of mass m, is in thermal equilibrium at the absolute  
temperature, T. The velocity components of the molecules along the Cartesian axes are 
,
xy
vv and 
z
v . The mean value of 
? ?
2
xy
vv ? is 
(A) 
B
kT
m
 (B) 
3
2
B
kT
m
 (C) 
1
2
B
kT
m
 (D) 
2
B
kT
m
 
  
Q.14   In a central force field, the trajectory of a particle of mass m and angular momentum L in plane 
polar coordinates is given by,  
 
  
  
where, ? is the eccentricity of the particle’s motion. Which one of the following choices for ? gives 
rise to a parabolic trajectory? 
  
(A) 0 ? ? (B) 1 ? ? (C) 01 ? ?? (D) 1 ? ? 
? ?
2
1
1 cos
m
rL
?? ??
Page 4


2012                                                                                                                                                                                                PHYSICS – PH 
PH 
1/20 
PH : PHYSICS 
 
Duration: Three Hours                          Maximum Marks: 100 
Read the following instructions carefully. 
 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully.   
 
3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble 
corresponding to your test paper code and the appropriate bubble under each digit of your registration 
number and (ii) write your registration number, your name and name of the examination centre and 
put your signature at the specified location.  
 
4. This Question Booklet contains 20 pages including blank pages for rough work. After you are 
permitted to open the seal, please check all pages and report discrepancies, if any, to the invigilator. 
 
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ball point pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
 
6. Since bubbles darkened by the black ink ball point pen cannot be erased, candidates should darken 
the bubbles in the ORS very carefully. 
 
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then 
the answer to the second question in the pair will not be evaluated. 
 
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each.   
 
9. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks.  
For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks questions, 
? mark will be deducted for each wrong answer.  However, in the case of the linked answer question 
pair, there will be negative marks only for wrong answer to the first question and no negative marks 
for wrong answer to the second question.  
 
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 
 
11. Rough work can be done on the question paper itself. Blank pages are provided at the end of the 
question paper for rough work. 
 
12. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ball point pen. 
 
 
Name 
 
 
Registration 
Number 
PH 
      
 
 
2012                                                                                                                                                                                                PHYSICS – PH 
PH 
2/20 
Some Useful Constants 
  Speed of light in free space  c = 3 × 10
8
 m/s 
  Boltzmann constant   
B
k = 1.380 × 10
–23
 J/K 
  Planck’s constant   h = 6.626 × 10
–34
 J.s 
  Electron charge    e = 1.602 × 10
-19
 C 
  Permittivity of free space  
0
? = 8.854 × 10
–12
 C
2
/N.m
2
 
  Permeability of free space  
0
? = 4? × 10
–7
 H/m 
NOTE : In numerical problems, the option closest to the correct answer will be given credit. 
  
Q. 1 – Q. 25 carry one mark each. 
Q.1   Identify the CORRECT statement for the following vectors 
ˆˆ
32 a i j ?? and 
ˆˆ
2 b i j ?? 
(A) The vectors a  and  b are linearly independent 
(B) The vectors a  and b are linearly dependent 
(C) The vectors a  and b are orthogonal 
(D) The vectors a  and b are normalized 
  
Q.2   Two uniform thin rods of equal length, L, and masses M
1
 and M
2
 are joined together along the 
length. The moment of inertia of the combined rod of length 2L about an axis passing through the 
mid-point and perpendicular to the length of the rod is, 
(A) ? ?
2
12
12
L
MM ? (B) ? ?
2
12
6
L
MM ? 
(C) ? ?
2
12
3
L
MM ? (D) ? ?
2
12
2
L
MM ? 
  
Q.3   The space-time dependence of the electric field of a linearly polarized light in free space is given by 
0
cos( ) xE t kz ? ? where E
0
, ? and k are the amplitude, the angular frequency and the wavevector, 
respectively. The time averaged energy density associated with the electric field is 
(A) 
2
00
1
4
E ? (B) 
2
00
1
2
E ? 
(C) 
2
00
E ?
 
(D)
  2
00
2 E ?
 
  
Q.4   If the peak output voltage of a full wave rectifier is 10 V, its d.c. voltage is 
(A) 10.0 V (B) 7.07 V (C) 6.36 V (D)  3.18 V 
  
Q.5   A particle of mass m is confined in a two dimensional square well potential of dimension a. This 
potential V(x,y) is given by 
     ( , ) 0 V x y ? for a x a ? ? ? and a y a ? ? ?  
                                                     ?? elsewhere 
The energy of the first excited state for this particle is given by, 
(A) 
22
2
ma
?
 (B) 
22
2
2
ma
?
 (C)  
22
2
5
2ma
?
 (D) 
22
2
4
ma
?
 
2012                                                                                                                                                                                                PHYSICS – PH 
PH 
3/20 
Q.6  
  
The isothermal compressibility, ? of an ideal gas at temperature T
0
 and volume V
0
, is given by 
(A) 
0
0
1
T
V
VP
?
?
?
 (B) 
0
0
1
T
V
VP
?
?
 (C) 
0
0
T
P
V
V
?
?
?
  (D) 
0
0
T
P
V
V
?
?
  
  
Q.7   The ground state of sodium atom (
11
Na) is a 
2
S
1/2
 state. The difference in energy levels arising in the 
presence of a weak external magnetic field B, given in terms of Bohr magneton, µ
B
, is 
(A) µ
B
B (B) 2µ
B
B (C) 4µ
B
B   (D) 6µ
B
B  
  
Q.8   For an ideal Fermi gas in three dimensions, the electron velocity v
F
 at the Fermi surface is related 
to electron concentration n as,  
(A) 
2/3
v
F
n ? (B) v
F
n ? (C) 
1/2
v
F
n ? (D) 
1/3
v
F
n ? 
  
Q.9   Which one of the following sets corresponds to fundamental particles? 
(A) proton, electron and neutron 
(B) proton, electron and photon 
(C) electron, photon and neutrino 
(D) quark, electron and meson 
  
Q.10   In case of a Geiger-Muller (GM) counter, which one of the following statements is CORRECT? 
(A) Multiplication factor of the detector is of the order of 10
10     
 
(B) Type of the particles detected can be identified 
(C) Energy of the particles detected can be distinguished 
(D) Operating voltage of the detector is few tens of  Volts 
  
Q.11   A plane electromagnetic wave traveling in free space is incident normally on a glass plate of 
refractive index 3/2. If there is no absorption by the glass, its reflectivity is 
(A) 4%  (B) 16%  (C) 20%  (D) 50%   
  
Q.12   A Ge semiconductor is doped with acceptor impurity concentration of 10
15
 atoms/cm
3
. For the 
given hole mobility of 1800 cm
2
/V-s, the resistivity of this material is 
(A) 0.288 ? cm (B) 0.694 ? cm (C) 3.472 ? cm   (D) 6.944 ? cm 
  
Q.13   A classical gas of molecules, each of mass m, is in thermal equilibrium at the absolute  
temperature, T. The velocity components of the molecules along the Cartesian axes are 
,
xy
vv and 
z
v . The mean value of 
? ?
2
xy
vv ? is 
(A) 
B
kT
m
 (B) 
3
2
B
kT
m
 (C) 
1
2
B
kT
m
 (D) 
2
B
kT
m
 
  
Q.14   In a central force field, the trajectory of a particle of mass m and angular momentum L in plane 
polar coordinates is given by,  
 
  
  
where, ? is the eccentricity of the particle’s motion. Which one of the following choices for ? gives 
rise to a parabolic trajectory? 
  
(A) 0 ? ? (B) 1 ? ? (C) 01 ? ?? (D) 1 ? ? 
? ?
2
1
1 cos
m
rL
?? ??
2012                                                                                                                                                                                                PHYSICS – PH 
PH 
4/20 
Q.15  
  
Identify the CORRECT energy band diagram for Silicon doped with Arsenic. Here CB, VB, E
D
 and 
E
F
 are conduction band, valence band, impurity level and Fermi level, respectively. 
(A) 
   
  
  
  
  
  
  
 
(B)     
(C) 
  
  
  
  
  
  
  
  
(D)   
  
Q.16   The first Stokes line of a rotational Raman spectrum is observed at 12.96 cm
-1
. Considering the 
rigid rotor approximation, the rotational constant is given by 
(A) 6.48 cm
-1
 (B) 3.24 cm
-1
 (C) 2.16 cm
-1
  (D) 1.62 cm
-1
  
  
Q.17   The total energy, E of an ideal non-relativistic Fermi gas in three dimensions is given by  
5
3
2
3
N
E
V
? where N is the number of particles and V is the volume of the gas. 
Identify the CORRECT equation of state (P being the pressure), 
(A) 
1
3
PV E ? (B) 
2
3
PV E ? 
(C) PV E ? 
(D) 
5
3
PV E ? 
  
Q.18   Consider the wavefunction 
? ?
12
,
s
rr ?? ?? for a fermionic system consisting of two spin-half 
particles. The spatial part of the wavefunction is given by,  
                           
? ? ? ? ? ? ? ? ? ? 1 2 1 1 2 2 2 1 1 2
1
,
2
r r r r r r ? ? ? ? ?
??
??
??
 
where 
12
and ?? are single particle states. The spin part 
s
? of the wavefunction with spin states 
?(+½) and ?(-½) should be  
(A) ? ?
1
2
?? ?? ? (B) ? ?
1
2
?? ?? ? 
 
(C) ??  (D) 
??
   
  
Q.19   The electric and the magnetic fields ( , ) E z t and ( , ) B z t , respectively corresponding to the scalar 
potential ?(z,t) = 0 and vector potential ( , ) A z t itz ? are 
(A) E iz ? and B jt ?? (B) E iz ? and B jt ? 
(C) E iz ?? and B jt ?? (D) E iz ?? and B jt ? 
E 
D 
C B 
V B 
E
F
 
E
D 
C B 
V B    
E
F
 
C B 
V B 
E
F
 
E 
D 
E
D 
C B 
V B 
E 
 
E
F
 
Page 5


2012                                                                                                                                                                                                PHYSICS – PH 
PH 
1/20 
PH : PHYSICS 
 
Duration: Three Hours                          Maximum Marks: 100 
Read the following instructions carefully. 
 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully.   
 
3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble 
corresponding to your test paper code and the appropriate bubble under each digit of your registration 
number and (ii) write your registration number, your name and name of the examination centre and 
put your signature at the specified location.  
 
4. This Question Booklet contains 20 pages including blank pages for rough work. After you are 
permitted to open the seal, please check all pages and report discrepancies, if any, to the invigilator. 
 
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ball point pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
 
6. Since bubbles darkened by the black ink ball point pen cannot be erased, candidates should darken 
the bubbles in the ORS very carefully. 
 
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then 
the answer to the second question in the pair will not be evaluated. 
 
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each.   
 
9. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks.  
For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks questions, 
? mark will be deducted for each wrong answer.  However, in the case of the linked answer question 
pair, there will be negative marks only for wrong answer to the first question and no negative marks 
for wrong answer to the second question.  
 
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 
 
11. Rough work can be done on the question paper itself. Blank pages are provided at the end of the 
question paper for rough work. 
 
12. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ball point pen. 
 
 
Name 
 
 
Registration 
Number 
PH 
      
 
 
2012                                                                                                                                                                                                PHYSICS – PH 
PH 
2/20 
Some Useful Constants 
  Speed of light in free space  c = 3 × 10
8
 m/s 
  Boltzmann constant   
B
k = 1.380 × 10
–23
 J/K 
  Planck’s constant   h = 6.626 × 10
–34
 J.s 
  Electron charge    e = 1.602 × 10
-19
 C 
  Permittivity of free space  
0
? = 8.854 × 10
–12
 C
2
/N.m
2
 
  Permeability of free space  
0
? = 4? × 10
–7
 H/m 
NOTE : In numerical problems, the option closest to the correct answer will be given credit. 
  
Q. 1 – Q. 25 carry one mark each. 
Q.1   Identify the CORRECT statement for the following vectors 
ˆˆ
32 a i j ?? and 
ˆˆ
2 b i j ?? 
(A) The vectors a  and  b are linearly independent 
(B) The vectors a  and b are linearly dependent 
(C) The vectors a  and b are orthogonal 
(D) The vectors a  and b are normalized 
  
Q.2   Two uniform thin rods of equal length, L, and masses M
1
 and M
2
 are joined together along the 
length. The moment of inertia of the combined rod of length 2L about an axis passing through the 
mid-point and perpendicular to the length of the rod is, 
(A) ? ?
2
12
12
L
MM ? (B) ? ?
2
12
6
L
MM ? 
(C) ? ?
2
12
3
L
MM ? (D) ? ?
2
12
2
L
MM ? 
  
Q.3   The space-time dependence of the electric field of a linearly polarized light in free space is given by 
0
cos( ) xE t kz ? ? where E
0
, ? and k are the amplitude, the angular frequency and the wavevector, 
respectively. The time averaged energy density associated with the electric field is 
(A) 
2
00
1
4
E ? (B) 
2
00
1
2
E ? 
(C) 
2
00
E ?
 
(D)
  2
00
2 E ?
 
  
Q.4   If the peak output voltage of a full wave rectifier is 10 V, its d.c. voltage is 
(A) 10.0 V (B) 7.07 V (C) 6.36 V (D)  3.18 V 
  
Q.5   A particle of mass m is confined in a two dimensional square well potential of dimension a. This 
potential V(x,y) is given by 
     ( , ) 0 V x y ? for a x a ? ? ? and a y a ? ? ?  
                                                     ?? elsewhere 
The energy of the first excited state for this particle is given by, 
(A) 
22
2
ma
?
 (B) 
22
2
2
ma
?
 (C)  
22
2
5
2ma
?
 (D) 
22
2
4
ma
?
 
2012                                                                                                                                                                                                PHYSICS – PH 
PH 
3/20 
Q.6  
  
The isothermal compressibility, ? of an ideal gas at temperature T
0
 and volume V
0
, is given by 
(A) 
0
0
1
T
V
VP
?
?
?
 (B) 
0
0
1
T
V
VP
?
?
 (C) 
0
0
T
P
V
V
?
?
?
  (D) 
0
0
T
P
V
V
?
?
  
  
Q.7   The ground state of sodium atom (
11
Na) is a 
2
S
1/2
 state. The difference in energy levels arising in the 
presence of a weak external magnetic field B, given in terms of Bohr magneton, µ
B
, is 
(A) µ
B
B (B) 2µ
B
B (C) 4µ
B
B   (D) 6µ
B
B  
  
Q.8   For an ideal Fermi gas in three dimensions, the electron velocity v
F
 at the Fermi surface is related 
to electron concentration n as,  
(A) 
2/3
v
F
n ? (B) v
F
n ? (C) 
1/2
v
F
n ? (D) 
1/3
v
F
n ? 
  
Q.9   Which one of the following sets corresponds to fundamental particles? 
(A) proton, electron and neutron 
(B) proton, electron and photon 
(C) electron, photon and neutrino 
(D) quark, electron and meson 
  
Q.10   In case of a Geiger-Muller (GM) counter, which one of the following statements is CORRECT? 
(A) Multiplication factor of the detector is of the order of 10
10     
 
(B) Type of the particles detected can be identified 
(C) Energy of the particles detected can be distinguished 
(D) Operating voltage of the detector is few tens of  Volts 
  
Q.11   A plane electromagnetic wave traveling in free space is incident normally on a glass plate of 
refractive index 3/2. If there is no absorption by the glass, its reflectivity is 
(A) 4%  (B) 16%  (C) 20%  (D) 50%   
  
Q.12   A Ge semiconductor is doped with acceptor impurity concentration of 10
15
 atoms/cm
3
. For the 
given hole mobility of 1800 cm
2
/V-s, the resistivity of this material is 
(A) 0.288 ? cm (B) 0.694 ? cm (C) 3.472 ? cm   (D) 6.944 ? cm 
  
Q.13   A classical gas of molecules, each of mass m, is in thermal equilibrium at the absolute  
temperature, T. The velocity components of the molecules along the Cartesian axes are 
,
xy
vv and 
z
v . The mean value of 
? ?
2
xy
vv ? is 
(A) 
B
kT
m
 (B) 
3
2
B
kT
m
 (C) 
1
2
B
kT
m
 (D) 
2
B
kT
m
 
  
Q.14   In a central force field, the trajectory of a particle of mass m and angular momentum L in plane 
polar coordinates is given by,  
 
  
  
where, ? is the eccentricity of the particle’s motion. Which one of the following choices for ? gives 
rise to a parabolic trajectory? 
  
(A) 0 ? ? (B) 1 ? ? (C) 01 ? ?? (D) 1 ? ? 
? ?
2
1
1 cos
m
rL
?? ??
2012                                                                                                                                                                                                PHYSICS – PH 
PH 
4/20 
Q.15  
  
Identify the CORRECT energy band diagram for Silicon doped with Arsenic. Here CB, VB, E
D
 and 
E
F
 are conduction band, valence band, impurity level and Fermi level, respectively. 
(A) 
   
  
  
  
  
  
  
 
(B)     
(C) 
  
  
  
  
  
  
  
  
(D)   
  
Q.16   The first Stokes line of a rotational Raman spectrum is observed at 12.96 cm
-1
. Considering the 
rigid rotor approximation, the rotational constant is given by 
(A) 6.48 cm
-1
 (B) 3.24 cm
-1
 (C) 2.16 cm
-1
  (D) 1.62 cm
-1
  
  
Q.17   The total energy, E of an ideal non-relativistic Fermi gas in three dimensions is given by  
5
3
2
3
N
E
V
? where N is the number of particles and V is the volume of the gas. 
Identify the CORRECT equation of state (P being the pressure), 
(A) 
1
3
PV E ? (B) 
2
3
PV E ? 
(C) PV E ? 
(D) 
5
3
PV E ? 
  
Q.18   Consider the wavefunction 
? ?
12
,
s
rr ?? ?? for a fermionic system consisting of two spin-half 
particles. The spatial part of the wavefunction is given by,  
                           
? ? ? ? ? ? ? ? ? ? 1 2 1 1 2 2 2 1 1 2
1
,
2
r r r r r r ? ? ? ? ?
??
??
??
 
where 
12
and ?? are single particle states. The spin part 
s
? of the wavefunction with spin states 
?(+½) and ?(-½) should be  
(A) ? ?
1
2
?? ?? ? (B) ? ?
1
2
?? ?? ? 
 
(C) ??  (D) 
??
   
  
Q.19   The electric and the magnetic fields ( , ) E z t and ( , ) B z t , respectively corresponding to the scalar 
potential ?(z,t) = 0 and vector potential ( , ) A z t itz ? are 
(A) E iz ? and B jt ?? (B) E iz ? and B jt ? 
(C) E iz ?? and B jt ?? (D) E iz ?? and B jt ? 
E 
D 
C B 
V B 
E
F
 
E
D 
C B 
V B    
E
F
 
C B 
V B 
E
F
 
E 
D 
E
D 
C B 
V B 
E 
 
E
F
 
2012                                                                                                                                                                                                PHYSICS – PH 
PH 
5/20 
Q.20  
  
Consider the following OP-AMP circuit. 
  
                             
V in
+ 5 V
4 k?
1 k?
+
?
+ 10 V
- 10 V
V out
 
Which one of the following correctly represents the output V
out
 corresponding to the input V
in
? 
(A)    
V
in
+ 5 V
V
out
- 10 V
+ 10 V
+ 1 V
t ®
t ®
0 V
 
  
(B) 
V
in
+ 5 V
V
out
- 10 V
+ 10 V
+ 1 V
t ®
t ®
0 V
 
(C) 
V
in
+ 5 V
V
out
- 10 V
+ 10 V
0 V
t ®
t ®
 
  
(D) 
V
in
+ 5 V
V
out
- 10 V
+ 10 V
0 V
t ®
t ®
 
  
Q.21   Deuteron has only one bound state with spin parity 1
+
, isospin 0 and electric quadrupole moment 
0.286 efm
2
. These data suggest that the nuclear forces are having  
(A) only spin and isospin dependence  
(B) no spin dependence and no tensor components 
(C) spin dependence but no tensor components 
(D) spin dependence along with tensor components 
Read More
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