Electronics and Communication Engineering (EC) 2012 GATE Paper with solution Electronics and Communication Engineering (ECE) Notes | EduRev

Mock Tests Electronics & Communication Engineering GATE 2020

Electronics and Communication Engineering (ECE) : Electronics and Communication Engineering (EC) 2012 GATE Paper with solution Electronics and Communication Engineering (ECE) Notes | EduRev

 Page 1


2012                                                                                                                           Question Booklet Code                                                                            
 
EC-A 
 
1/20 
EC : ELECTRONICS AND COMMUNICATION ENGINEERING 
 
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. If you find that the Question Booklet Code 
printed at the right hand top corner of this page does not match with the Booklet Code on the ORS, 
exchange the booklet immediately with a new sealed Question Booklet.  
 
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 EC 
       
 
A 
Page 2


2012                                                                                                                           Question Booklet Code                                                                            
 
EC-A 
 
1/20 
EC : ELECTRONICS AND COMMUNICATION ENGINEERING 
 
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. If you find that the Question Booklet Code 
printed at the right hand top corner of this page does not match with the Booklet Code on the ORS, 
exchange the booklet immediately with a new sealed Question Booklet.  
 
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 EC 
       
 
A 2012                                                                                                                                  ELECTRONICS & COMMN. ENGG. - EC                                                                                                                        
 
EC-A 2/20 
Q. 1 – Q. 25 carry one mark each. 
Q.1  The current i
b
 through the base of a silicon npn transistor is mA ) 10000 ( cos 1 . 0 1 t ? ? . At 300 K, 
the r
?
  in the small signal model of the transistor is 
i
b
r
?
r
0
B C
E
 
(A)  250 ?   (B)  27.5 ? (C)  25 ? (D)  22.5 ? 
 
Q.2  The power spectral density of a real process X(t) for positive frequencies is shown below. The 
values of E[X
2
(t)] and )] ( [ t X E , respectively, are 
                                       
S
X
(?)
400 d( w-10
4
)
? (10
3
 rad/s) 10 11 9
6
0
 
(A)  6000/p, 0 (B)  6400/p, 0 
(C)  6400/p, ) 2 /( 20 ? (D)  6000/p, ) 2 /( 20 ? 
 
Q.3  In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a 
raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum 
possible signaling rate in symbols per second is 
(A)  1750 (B)  2625 (C)  4000 (D)  5250 
 
Q.4  A plane wave propagating in air with V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a E
? ?
? ? ?
w
?
 is incident on a 
perfectly conducting slab positioned at 0 ? x . The E
?
 field of the reflected wave is  
(A)  V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
(B) V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
(C)  V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
(D)  V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
 
Q.5  The electric field of a uniform plane electromagnetic wave in free space, along the positive  
x direction, is given by ? ?
x j
z y
e a j a E
25
ˆ ˆ 10
?
? ?
?
. The frequency and polarization of the wave, 
respectively, are 
(A)  1.2 GHz and left circular (B)  4 Hz and left circular 
(C)  1.2 GHz and right circular (D)  4 Hz and right circular 
 
Page 3


2012                                                                                                                           Question Booklet Code                                                                            
 
EC-A 
 
1/20 
EC : ELECTRONICS AND COMMUNICATION ENGINEERING 
 
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. If you find that the Question Booklet Code 
printed at the right hand top corner of this page does not match with the Booklet Code on the ORS, 
exchange the booklet immediately with a new sealed Question Booklet.  
 
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 EC 
       
 
A 2012                                                                                                                                  ELECTRONICS & COMMN. ENGG. - EC                                                                                                                        
 
EC-A 2/20 
Q. 1 – Q. 25 carry one mark each. 
Q.1  The current i
b
 through the base of a silicon npn transistor is mA ) 10000 ( cos 1 . 0 1 t ? ? . At 300 K, 
the r
?
  in the small signal model of the transistor is 
i
b
r
?
r
0
B C
E
 
(A)  250 ?   (B)  27.5 ? (C)  25 ? (D)  22.5 ? 
 
Q.2  The power spectral density of a real process X(t) for positive frequencies is shown below. The 
values of E[X
2
(t)] and )] ( [ t X E , respectively, are 
                                       
S
X
(?)
400 d( w-10
4
)
? (10
3
 rad/s) 10 11 9
6
0
 
(A)  6000/p, 0 (B)  6400/p, 0 
(C)  6400/p, ) 2 /( 20 ? (D)  6000/p, ) 2 /( 20 ? 
 
Q.3  In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a 
raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum 
possible signaling rate in symbols per second is 
(A)  1750 (B)  2625 (C)  4000 (D)  5250 
 
Q.4  A plane wave propagating in air with V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a E
? ?
? ? ?
w
?
 is incident on a 
perfectly conducting slab positioned at 0 ? x . The E
?
 field of the reflected wave is  
(A)  V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
(B) V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
(C)  V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
(D)  V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
 
Q.5  The electric field of a uniform plane electromagnetic wave in free space, along the positive  
x direction, is given by ? ?
x j
z y
e a j a E
25
ˆ ˆ 10
?
? ?
?
. The frequency and polarization of the wave, 
respectively, are 
(A)  1.2 GHz and left circular (B)  4 Hz and left circular 
(C)  1.2 GHz and right circular (D)  4 Hz and right circular 
 
2012                                                                                                                                  ELECTRONICS & COMMN. ENGG. - EC                                                                                                                        
 
EC-A 3/20 
Q.6  Consider the given circuit. 
A
B
CLK
 
In this circuit, the race around 
(A)  does not occur (B)  occurs when CLK = 0 
(C)  occurs when CLK = 1 and A = B = 1 (D)  occurs when CLK = 1 and A = B = 0 
 
 
Q.7  The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit 
input B. The number of combinations for which the output is logic 1, is 
(A)  4 (B)  6 (C)   8 (D)   10 
 
Q.8  The i-v characteristics of the diode in the circuit given below are  
 
?
?
?
?
?
?
?
?
?
V 7 . 0 , A 0
V 7 . 0 , A
500
7 . 0
v
v
v
i 
                                              
+
1k ?
10V
-
i
+
-
v
 
The current in the circuit is 
(A)  10 mA  (B)  9.3 mA  (C)  6.67 mA (D)  6.2 mA 
 
Q.9  In the following figure, C
1 
 and C
2
 are ideal capacitors. C
1
 has been charged to 12 V before the ideal 
switch S is closed at t = 0. The current i(t) for all t is  
C
1
t = 0
C
2
i(t)
S
 
(A)  zero  (B)  a step function 
(C)  an exponentially decaying function (D)  an impulse function 
 
Q.10  The average power delivered to an impedance ) 3 4 ( j ? ??by a current ) 100 100 ( cos 5 ? t ? A is 
(A)  44.2 W (B)  50 W (C)  62.5 W (D)  125 W 
 
Q.11  The unilateral Laplace transform of  f (t) is 
1
1
2
? ? s s
. The unilateral Laplace transform of ) (t f t is 
(A)  
2 2
) 1 ( ? ?
?
s s
s
 (B)  
2 2
) 1 (
1 2
? ?
?
?
s s
s
 
(C)   
2 2
) 1 ( ? ? s s
s
 (D)  
2 2
) 1 (
1 2
? ?
?
s s
s
 
 
Page 4


2012                                                                                                                           Question Booklet Code                                                                            
 
EC-A 
 
1/20 
EC : ELECTRONICS AND COMMUNICATION ENGINEERING 
 
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. If you find that the Question Booklet Code 
printed at the right hand top corner of this page does not match with the Booklet Code on the ORS, 
exchange the booklet immediately with a new sealed Question Booklet.  
 
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 EC 
       
 
A 2012                                                                                                                                  ELECTRONICS & COMMN. ENGG. - EC                                                                                                                        
 
EC-A 2/20 
Q. 1 – Q. 25 carry one mark each. 
Q.1  The current i
b
 through the base of a silicon npn transistor is mA ) 10000 ( cos 1 . 0 1 t ? ? . At 300 K, 
the r
?
  in the small signal model of the transistor is 
i
b
r
?
r
0
B C
E
 
(A)  250 ?   (B)  27.5 ? (C)  25 ? (D)  22.5 ? 
 
Q.2  The power spectral density of a real process X(t) for positive frequencies is shown below. The 
values of E[X
2
(t)] and )] ( [ t X E , respectively, are 
                                       
S
X
(?)
400 d( w-10
4
)
? (10
3
 rad/s) 10 11 9
6
0
 
(A)  6000/p, 0 (B)  6400/p, 0 
(C)  6400/p, ) 2 /( 20 ? (D)  6000/p, ) 2 /( 20 ? 
 
Q.3  In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a 
raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum 
possible signaling rate in symbols per second is 
(A)  1750 (B)  2625 (C)  4000 (D)  5250 
 
Q.4  A plane wave propagating in air with V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a E
? ?
? ? ?
w
?
 is incident on a 
perfectly conducting slab positioned at 0 ? x . The E
?
 field of the reflected wave is  
(A)  V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
(B) V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
(C)  V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
(D)  V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
 
Q.5  The electric field of a uniform plane electromagnetic wave in free space, along the positive  
x direction, is given by ? ?
x j
z y
e a j a E
25
ˆ ˆ 10
?
? ?
?
. The frequency and polarization of the wave, 
respectively, are 
(A)  1.2 GHz and left circular (B)  4 Hz and left circular 
(C)  1.2 GHz and right circular (D)  4 Hz and right circular 
 
2012                                                                                                                                  ELECTRONICS & COMMN. ENGG. - EC                                                                                                                        
 
EC-A 3/20 
Q.6  Consider the given circuit. 
A
B
CLK
 
In this circuit, the race around 
(A)  does not occur (B)  occurs when CLK = 0 
(C)  occurs when CLK = 1 and A = B = 1 (D)  occurs when CLK = 1 and A = B = 0 
 
 
Q.7  The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit 
input B. The number of combinations for which the output is logic 1, is 
(A)  4 (B)  6 (C)   8 (D)   10 
 
Q.8  The i-v characteristics of the diode in the circuit given below are  
 
?
?
?
?
?
?
?
?
?
V 7 . 0 , A 0
V 7 . 0 , A
500
7 . 0
v
v
v
i 
                                              
+
1k ?
10V
-
i
+
-
v
 
The current in the circuit is 
(A)  10 mA  (B)  9.3 mA  (C)  6.67 mA (D)  6.2 mA 
 
Q.9  In the following figure, C
1 
 and C
2
 are ideal capacitors. C
1
 has been charged to 12 V before the ideal 
switch S is closed at t = 0. The current i(t) for all t is  
C
1
t = 0
C
2
i(t)
S
 
(A)  zero  (B)  a step function 
(C)  an exponentially decaying function (D)  an impulse function 
 
Q.10  The average power delivered to an impedance ) 3 4 ( j ? ??by a current ) 100 100 ( cos 5 ? t ? A is 
(A)  44.2 W (B)  50 W (C)  62.5 W (D)  125 W 
 
Q.11  The unilateral Laplace transform of  f (t) is 
1
1
2
? ? s s
. The unilateral Laplace transform of ) (t f t is 
(A)  
2 2
) 1 ( ? ?
?
s s
s
 (B)  
2 2
) 1 (
1 2
? ?
?
?
s s
s
 
(C)   
2 2
) 1 ( ? ? s s
s
 (D)  
2 2
) 1 (
1 2
? ?
?
s s
s
 
 
2012                                                                                                                                  ELECTRONICS & COMMN. ENGG. - EC                                                                                                                        
 
EC-A 4/20 
Q.12  With initial condition 5 . 0 ) 1 ( ? x , the solution of the differential equation, 
t x
dt
dx
t ? ? is 
(A)  
2
1
? ? t x (B)  
2
1
2
? ? t x 
(C)  
2
2
t
x ? 
(D)  
2
t
x ? 
 
Q.13  The diodes and capacitors in the circuit shown are ideal. The voltage v(t) across the diode D1 is 
 
                                     
v(t)
cos( wt)
+
-
D2 C1
C2 D1
 
(A)  1 ) ( cos ? t w (B)  ) ( sin t w  (C)  ) ( cos 1 t w ? (D)  ) ( sin 1 t w ?  
 
Q.14  In the circuit shown 
                                                    
5 Volts
A
A B
B
C
C
Y
 
(A)  C B A Y ? ? 
(B)  C B A Y ) ( ? ? 
(C)  C B A Y ) ( ? ? 
(D)  C B A Y ? ? 
 
Q.15  A source alphabet consists of N symbols with the probability of the first two symbols being the 
same. A source encoder increases the probability of the first symbol by a small amount ? and 
decreases that of the second by ? . After encoding, the entropy of the source 
(A)  increases (B)  remains the same 
(C)  increases only if N = 2 (D)  decreases 
 
Q.16  A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm is filled with a 
dielectric of relative permittivity 10.89. Given m H 10 4
7
0
?
? ? ? ? , m F
36
10
9
0
?
?
?
? , the 
characteristic impedance of the cable is  
(A)  330 ? (B)  100 ? (C)  143.3 ? (D)  43.4 ? 
 
Q.17  The radiation pattern of an antenna in spherical co-ordinates is given by 
? ?
4
cos ) ( ? F ; 2 / 0 ? ? ? ? 
The directivity of the antenna is  
(A)  10 dB (B)  12.6 dB  (C)  11.5 dB  (D)  18 dB   
 
Page 5


2012                                                                                                                           Question Booklet Code                                                                            
 
EC-A 
 
1/20 
EC : ELECTRONICS AND COMMUNICATION ENGINEERING 
 
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. If you find that the Question Booklet Code 
printed at the right hand top corner of this page does not match with the Booklet Code on the ORS, 
exchange the booklet immediately with a new sealed Question Booklet.  
 
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 EC 
       
 
A 2012                                                                                                                                  ELECTRONICS & COMMN. ENGG. - EC                                                                                                                        
 
EC-A 2/20 
Q. 1 – Q. 25 carry one mark each. 
Q.1  The current i
b
 through the base of a silicon npn transistor is mA ) 10000 ( cos 1 . 0 1 t ? ? . At 300 K, 
the r
?
  in the small signal model of the transistor is 
i
b
r
?
r
0
B C
E
 
(A)  250 ?   (B)  27.5 ? (C)  25 ? (D)  22.5 ? 
 
Q.2  The power spectral density of a real process X(t) for positive frequencies is shown below. The 
values of E[X
2
(t)] and )] ( [ t X E , respectively, are 
                                       
S
X
(?)
400 d( w-10
4
)
? (10
3
 rad/s) 10 11 9
6
0
 
(A)  6000/p, 0 (B)  6400/p, 0 
(C)  6400/p, ) 2 /( 20 ? (D)  6000/p, ) 2 /( 20 ? 
 
Q.3  In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a 
raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum 
possible signaling rate in symbols per second is 
(A)  1750 (B)  2625 (C)  4000 (D)  5250 
 
Q.4  A plane wave propagating in air with V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a E
? ?
? ? ?
w
?
 is incident on a 
perfectly conducting slab positioned at 0 ? x . The E
?
 field of the reflected wave is  
(A)  V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
(B) V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
(C)  V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
(D)  V/m ) ˆ 5 ˆ 6 ˆ 8 (
) 4 3 ( y x t j
z y x
e a a a
? ?
? ? ?
w
 
 
Q.5  The electric field of a uniform plane electromagnetic wave in free space, along the positive  
x direction, is given by ? ?
x j
z y
e a j a E
25
ˆ ˆ 10
?
? ?
?
. The frequency and polarization of the wave, 
respectively, are 
(A)  1.2 GHz and left circular (B)  4 Hz and left circular 
(C)  1.2 GHz and right circular (D)  4 Hz and right circular 
 
2012                                                                                                                                  ELECTRONICS & COMMN. ENGG. - EC                                                                                                                        
 
EC-A 3/20 
Q.6  Consider the given circuit. 
A
B
CLK
 
In this circuit, the race around 
(A)  does not occur (B)  occurs when CLK = 0 
(C)  occurs when CLK = 1 and A = B = 1 (D)  occurs when CLK = 1 and A = B = 0 
 
 
Q.7  The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit 
input B. The number of combinations for which the output is logic 1, is 
(A)  4 (B)  6 (C)   8 (D)   10 
 
Q.8  The i-v characteristics of the diode in the circuit given below are  
 
?
?
?
?
?
?
?
?
?
V 7 . 0 , A 0
V 7 . 0 , A
500
7 . 0
v
v
v
i 
                                              
+
1k ?
10V
-
i
+
-
v
 
The current in the circuit is 
(A)  10 mA  (B)  9.3 mA  (C)  6.67 mA (D)  6.2 mA 
 
Q.9  In the following figure, C
1 
 and C
2
 are ideal capacitors. C
1
 has been charged to 12 V before the ideal 
switch S is closed at t = 0. The current i(t) for all t is  
C
1
t = 0
C
2
i(t)
S
 
(A)  zero  (B)  a step function 
(C)  an exponentially decaying function (D)  an impulse function 
 
Q.10  The average power delivered to an impedance ) 3 4 ( j ? ??by a current ) 100 100 ( cos 5 ? t ? A is 
(A)  44.2 W (B)  50 W (C)  62.5 W (D)  125 W 
 
Q.11  The unilateral Laplace transform of  f (t) is 
1
1
2
? ? s s
. The unilateral Laplace transform of ) (t f t is 
(A)  
2 2
) 1 ( ? ?
?
s s
s
 (B)  
2 2
) 1 (
1 2
? ?
?
?
s s
s
 
(C)   
2 2
) 1 ( ? ? s s
s
 (D)  
2 2
) 1 (
1 2
? ?
?
s s
s
 
 
2012                                                                                                                                  ELECTRONICS & COMMN. ENGG. - EC                                                                                                                        
 
EC-A 4/20 
Q.12  With initial condition 5 . 0 ) 1 ( ? x , the solution of the differential equation, 
t x
dt
dx
t ? ? is 
(A)  
2
1
? ? t x (B)  
2
1
2
? ? t x 
(C)  
2
2
t
x ? 
(D)  
2
t
x ? 
 
Q.13  The diodes and capacitors in the circuit shown are ideal. The voltage v(t) across the diode D1 is 
 
                                     
v(t)
cos( wt)
+
-
D2 C1
C2 D1
 
(A)  1 ) ( cos ? t w (B)  ) ( sin t w  (C)  ) ( cos 1 t w ? (D)  ) ( sin 1 t w ?  
 
Q.14  In the circuit shown 
                                                    
5 Volts
A
A B
B
C
C
Y
 
(A)  C B A Y ? ? 
(B)  C B A Y ) ( ? ? 
(C)  C B A Y ) ( ? ? 
(D)  C B A Y ? ? 
 
Q.15  A source alphabet consists of N symbols with the probability of the first two symbols being the 
same. A source encoder increases the probability of the first symbol by a small amount ? and 
decreases that of the second by ? . After encoding, the entropy of the source 
(A)  increases (B)  remains the same 
(C)  increases only if N = 2 (D)  decreases 
 
Q.16  A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm is filled with a 
dielectric of relative permittivity 10.89. Given m H 10 4
7
0
?
? ? ? ? , m F
36
10
9
0
?
?
?
? , the 
characteristic impedance of the cable is  
(A)  330 ? (B)  100 ? (C)  143.3 ? (D)  43.4 ? 
 
Q.17  The radiation pattern of an antenna in spherical co-ordinates is given by 
? ?
4
cos ) ( ? F ; 2 / 0 ? ? ? ? 
The directivity of the antenna is  
(A)  10 dB (B)  12.6 dB  (C)  11.5 dB  (D)  18 dB   
 
2012                                                                                                                                  ELECTRONICS & COMMN. ENGG. - EC                                                                                                                        
 
EC-A 5/20 
Q.18  If ] [ ) 2 / 1 ( ) 3 / 1 ( ] [ n u n x
n n
? ? , then the region of convergence (ROC) of its Z-transform in the  
Z-plane will be 
(A)  3
3
1
? ? z (B)  
2
1
3
1
? ? z (C)  3
2
1
? ? z (D)  z ?
3
1
 
 
Q.19  In the sum of products function  
?
? ) 5 , 4 , 3 , 2 ( ) , , ( Z Y X f , the prime implicants are 
(A)  Y X Y X , (B)   Z Y X Z Y X Y X , , 
(C)  Y X Z Y X Z Y X , , (D)  Z Y X Z Y X Z Y X Z Y X , , , 
 
Q.20  A system with transfer function 
                                                     
) 4 ( ) 3 ( ) 1 (
) 2 ( ) 9 (
) (
2
? ? ?
? ?
?
s s s
s s
s G  
is excited by ) ( sin t w . The steady-state output of the system is zero at 
(A)   rad/s 1 ? w  (B)  rad/s 2 ? w 
(C)   rad/s 3 ? w (D)  rad/s 4 ? w 
 
Q.21  The impedance looking into nodes 1 and 2 in the given circuit is 
i
b
99i
b
9k ?
100 ?
1k ?
1
2
 
(A)  50 ?  (B)  100 ? (C)  5 k ? (D)  10.1 k ? 
 
Q.22  In the circuit shown below, the current through the inductor is 
1 ? 
1 ? 
j1 ? 
- j1 ? 
A
A
V
+           - -        +
V 1 0
1 0
1 0
1 0
 
(A)  A
1
2
j ?
 (B)  A
1
1
j ?
?
 (C)  A
1
1
j ?
 (D)  0 A 
 
Q.23  Given  
3
2
1
1
) (
?
?
?
?
z z
z f . If C is a counterclockwise path in the z-plane such that 1 1 ? ? z , the value of  
?
C
dz z f
j
) (
2
1
?
 is 
(A)  –2 (B)  –1 (C)  1 (D)    2 
 
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