Electronics and Communication Engineering (EC) 2011 GATE Paper with solution PDF Download

 Page 1


?EC-Paper Code-B? GATE 2011    
1 
Q. No. 1 – 25 Carry One Mark Each 
1. Consider the following statements regarding the complex Poynting vector P


 for
the power radiated by a point source in an infinite homogeneous and lossless
medium.
( )
Re P


 denotes the real part of P


. S denotes a spherical surface whose 
centre is at the point source, and 
?
ndenotes the unit surface normal on S. Which
of the following statements is TRUE?
(A)
( )
Re P


 remains constant at any radial distance from the source 
(B) 
( )
Re P


 increases with increasing radial distance from the source 
(C) 
( )

s
Re P .ndS
??



 remains constant at any radial distance from the source 
(D) 
( )

s
Re P .ndS
??



 decreases with increasing radial distance form the source 
Answer: - (D) 
Exp: - 
( )
S
ˆ Re P .nds
??



gives average power and it decreases with increasing radial 
distance from the source 
2. A transmission line of characteristic impedance 50O is terminated by a 50O load.
When excited by a sinusoidal voltage source at 10GHz, the phase difference
between two points spaced 2mm apart on the line is found to be
4
p
 radians. The 
phase velocity of the wave along the line is
(A) 
8
0.8 10 m /s × (B) 
8
1.2 10 m / s × (C) 
8
1.6 10 m /s × (D) 
8
3 10 m /s × 
Answer: - (C) 
Exp: - 
0
Z 50 = O ; 
L
Z 50 = O
For 
4
p
 radians the distance is 2mm 
The phase velocity 
10
7 8
P
3
2 10
v 16 10 1.6 10 m / s
2
16 10
-
-
? × p ×
= = = × = ×
p ß
×
 
3. An analog signal is band-limited to 4kHz, sampled at the Nyquist rate and the
samples are quantized into 4 levels. The quantized levels are assumed to be
independent and equally probable. If we transmit two quantized samples per
second, the information rate is ________ bits / second.
(A) 1 (B) 2 (C) 3 (D) 4 
Answer: - (D) 
Exp: - Since two samples are transmitted and each sample has 2 bits of information, 
then the information rate is 4 bits/sec. 
Page 2


?EC-Paper Code-B? GATE 2011    
1 
Q. No. 1 – 25 Carry One Mark Each 
1. Consider the following statements regarding the complex Poynting vector P


 for
the power radiated by a point source in an infinite homogeneous and lossless
medium.
( )
Re P


 denotes the real part of P


. S denotes a spherical surface whose 
centre is at the point source, and 
?
ndenotes the unit surface normal on S. Which
of the following statements is TRUE?
(A)
( )
Re P


 remains constant at any radial distance from the source 
(B) 
( )
Re P


 increases with increasing radial distance from the source 
(C) 
( )

s
Re P .ndS
??



 remains constant at any radial distance from the source 
(D) 
( )

s
Re P .ndS
??



 decreases with increasing radial distance form the source 
Answer: - (D) 
Exp: - 
( )
S
ˆ Re P .nds
??



gives average power and it decreases with increasing radial 
distance from the source 
2. A transmission line of characteristic impedance 50O is terminated by a 50O load.
When excited by a sinusoidal voltage source at 10GHz, the phase difference
between two points spaced 2mm apart on the line is found to be
4
p
 radians. The 
phase velocity of the wave along the line is
(A) 
8
0.8 10 m /s × (B) 
8
1.2 10 m / s × (C) 
8
1.6 10 m /s × (D) 
8
3 10 m /s × 
Answer: - (C) 
Exp: - 
0
Z 50 = O ; 
L
Z 50 = O
For 
4
p
 radians the distance is 2mm 
The phase velocity 
10
7 8
P
3
2 10
v 16 10 1.6 10 m / s
2
16 10
-
-
? × p ×
= = = × = ×
p ß
×
 
3. An analog signal is band-limited to 4kHz, sampled at the Nyquist rate and the
samples are quantized into 4 levels. The quantized levels are assumed to be
independent and equally probable. If we transmit two quantized samples per
second, the information rate is ________ bits / second.
(A) 1 (B) 2 (C) 3 (D) 4 
Answer: - (D) 
Exp: - Since two samples are transmitted and each sample has 2 bits of information, 
then the information rate is 4 bits/sec. 
?EC-Paper Code-B? GATE 2011    
4. The root locus plot for a system is given below. The open loop transfer function
corresponding to this plot is given by
(A) ( ) ( )
( )
( ) ( )
s s 1
G s H s k
s 2 s 3
+
=
+ +
(B) ( ) ( )
( )
( ) ( )
2
s 1
G s H s k
s s 2 s 3
+
=
+ +
(C) ( ) ( )
( ) ( ) ( )
1
G s H s k
s s 1 s 2 s 3
=
- + +
(D) ( ) ( )
( )
( ) ( )
s 1
G s H s k
s s 2 s 3
+
=
+ +
Answer: - (B) 
Exp: - 'x' ? indicates pole 
'O' ? indicates zero 
The point on the root locus when the number of poles and zeroes on the real axis 
to the right side of that point must be odd 
5. A system is defined by its impulse response ( ) ( )
n
h n 2 u n 2 = - . The system is 
(A) stable and causal (B) causal but not stable  
(C) stable but not causal (D) unstable and non-causal 
Answer: - (B) 
Exp: - ( ) ( )
n
h n 2 u n 2 = -
( ) h n is existing for n>2 ; so that ( ) h n 0;n 0 = < ? causal
( ) ( )
n n
n n n 2
h n 2 u n 2 2
8 8 8
=-8 =8 =
= - = = 8 ?
? ? ?
 System is unstable
6. If the unit step response of a network is
( )
t
1 e
-a
- , then its unit impulse response
is
(A) 
t
e
-a
a (B) 
1 t
e
- -a
a (C) 
( )
1 t
1 e
- -a
- a (D) ( )
t
1 e
-a
- a
Answer: - (A) 
Exp: - ( ) S t ? step response
Impulse response ( ) ( ) ( ) ( )
t t
d d
h t S t 1 e e
dt dt
a a
= = - = a
7. The output Y in the circuit below is always ‘1’  when
× × × o
j?
s
0 1 - 2 - 3 -
P
Q
R
Y
Page 3


?EC-Paper Code-B? GATE 2011    
1 
Q. No. 1 – 25 Carry One Mark Each 
1. Consider the following statements regarding the complex Poynting vector P


 for
the power radiated by a point source in an infinite homogeneous and lossless
medium.
( )
Re P


 denotes the real part of P


. S denotes a spherical surface whose 
centre is at the point source, and 
?
ndenotes the unit surface normal on S. Which
of the following statements is TRUE?
(A)
( )
Re P


 remains constant at any radial distance from the source 
(B) 
( )
Re P


 increases with increasing radial distance from the source 
(C) 
( )

s
Re P .ndS
??



 remains constant at any radial distance from the source 
(D) 
( )

s
Re P .ndS
??



 decreases with increasing radial distance form the source 
Answer: - (D) 
Exp: - 
( )
S
ˆ Re P .nds
??



gives average power and it decreases with increasing radial 
distance from the source 
2. A transmission line of characteristic impedance 50O is terminated by a 50O load.
When excited by a sinusoidal voltage source at 10GHz, the phase difference
between two points spaced 2mm apart on the line is found to be
4
p
 radians. The 
phase velocity of the wave along the line is
(A) 
8
0.8 10 m /s × (B) 
8
1.2 10 m / s × (C) 
8
1.6 10 m /s × (D) 
8
3 10 m /s × 
Answer: - (C) 
Exp: - 
0
Z 50 = O ; 
L
Z 50 = O
For 
4
p
 radians the distance is 2mm 
The phase velocity 
10
7 8
P
3
2 10
v 16 10 1.6 10 m / s
2
16 10
-
-
? × p ×
= = = × = ×
p ß
×
 
3. An analog signal is band-limited to 4kHz, sampled at the Nyquist rate and the
samples are quantized into 4 levels. The quantized levels are assumed to be
independent and equally probable. If we transmit two quantized samples per
second, the information rate is ________ bits / second.
(A) 1 (B) 2 (C) 3 (D) 4 
Answer: - (D) 
Exp: - Since two samples are transmitted and each sample has 2 bits of information, 
then the information rate is 4 bits/sec. 
?EC-Paper Code-B? GATE 2011    
4. The root locus plot for a system is given below. The open loop transfer function
corresponding to this plot is given by
(A) ( ) ( )
( )
( ) ( )
s s 1
G s H s k
s 2 s 3
+
=
+ +
(B) ( ) ( )
( )
( ) ( )
2
s 1
G s H s k
s s 2 s 3
+
=
+ +
(C) ( ) ( )
( ) ( ) ( )
1
G s H s k
s s 1 s 2 s 3
=
- + +
(D) ( ) ( )
( )
( ) ( )
s 1
G s H s k
s s 2 s 3
+
=
+ +
Answer: - (B) 
Exp: - 'x' ? indicates pole 
'O' ? indicates zero 
The point on the root locus when the number of poles and zeroes on the real axis 
to the right side of that point must be odd 
5. A system is defined by its impulse response ( ) ( )
n
h n 2 u n 2 = - . The system is 
(A) stable and causal (B) causal but not stable  
(C) stable but not causal (D) unstable and non-causal 
Answer: - (B) 
Exp: - ( ) ( )
n
h n 2 u n 2 = -
( ) h n is existing for n>2 ; so that ( ) h n 0;n 0 = < ? causal
( ) ( )
n n
n n n 2
h n 2 u n 2 2
8 8 8
=-8 =8 =
= - = = 8 ?
? ? ?
 System is unstable
6. If the unit step response of a network is
( )
t
1 e
-a
- , then its unit impulse response
is
(A) 
t
e
-a
a (B) 
1 t
e
- -a
a (C) 
( )
1 t
1 e
- -a
- a (D) ( )
t
1 e
-a
- a
Answer: - (A) 
Exp: - ( ) S t ? step response
Impulse response ( ) ( ) ( ) ( )
t t
d d
h t S t 1 e e
dt dt
a a
= = - = a
7. The output Y in the circuit below is always ‘1’  when
× × × o
j?
s
0 1 - 2 - 3 -
P
Q
R
Y
?EC-Paper Code-B? GATE 2011    
(A) two or more of the inputs P,Q,R are ‘0’ 
(B) two or more of the inputs P,Q,R are ‘1’ 
(C) any odd number of the inputs P,Q,R is ‘0’ 
(D) any odd number of the inputs P,Q,R is ‘1’ 
Answer: - (B) 
Exp: - The output Y expression in the Ckt 
Y PQ PR RQ = + +
So that two or more inputs are ‘1’, Y is always ‘1’. 
8. In the circuit shown below, capacitors C
1
 and C
2
 are very large and are shorts at
the input frequency. 
i
v is a small signal input. The gain magnitude 
o
i
v
v
 at 10M 
rad/s is 
(A) maximum (B) minimum (C) unity (D) zero 
Answer: - (A) 
Exp: - In the parallel RLC Ckt 
L 10 H = µ andC 1nF =
7
g
6 9
1 1
10 rad/ s 10Mrad /s
LC
10 10 10
- -
? = = = =
× ×
So that for a tuned amplifier, gain is maximum at resonant frequency 
9. Drift current in the semiconductors depends upon
(A) only the electric field
(B) only the carrier concentration gradient
(C) both the electric field and the carrier concentration
(D) both the electric field and the carrier concentration gradient
Answer: - (C) 
Exp: - Drift current,J E = s 
( )
n P
J n p qE = µ + µ
So that it depends on carrier concentration and electric field. 
~
+
-
+
-
2kO
+
2
C
1
Q
o
v
1
C
2kO
i
v
2.7V
2kO
2kO
10 H µ
5V
Page 4


?EC-Paper Code-B? GATE 2011    
1 
Q. No. 1 – 25 Carry One Mark Each 
1. Consider the following statements regarding the complex Poynting vector P


 for
the power radiated by a point source in an infinite homogeneous and lossless
medium.
( )
Re P


 denotes the real part of P


. S denotes a spherical surface whose 
centre is at the point source, and 
?
ndenotes the unit surface normal on S. Which
of the following statements is TRUE?
(A)
( )
Re P


 remains constant at any radial distance from the source 
(B) 
( )
Re P


 increases with increasing radial distance from the source 
(C) 
( )

s
Re P .ndS
??



 remains constant at any radial distance from the source 
(D) 
( )

s
Re P .ndS
??



 decreases with increasing radial distance form the source 
Answer: - (D) 
Exp: - 
( )
S
ˆ Re P .nds
??



gives average power and it decreases with increasing radial 
distance from the source 
2. A transmission line of characteristic impedance 50O is terminated by a 50O load.
When excited by a sinusoidal voltage source at 10GHz, the phase difference
between two points spaced 2mm apart on the line is found to be
4
p
 radians. The 
phase velocity of the wave along the line is
(A) 
8
0.8 10 m /s × (B) 
8
1.2 10 m / s × (C) 
8
1.6 10 m /s × (D) 
8
3 10 m /s × 
Answer: - (C) 
Exp: - 
0
Z 50 = O ; 
L
Z 50 = O
For 
4
p
 radians the distance is 2mm 
The phase velocity 
10
7 8
P
3
2 10
v 16 10 1.6 10 m / s
2
16 10
-
-
? × p ×
= = = × = ×
p ß
×
 
3. An analog signal is band-limited to 4kHz, sampled at the Nyquist rate and the
samples are quantized into 4 levels. The quantized levels are assumed to be
independent and equally probable. If we transmit two quantized samples per
second, the information rate is ________ bits / second.
(A) 1 (B) 2 (C) 3 (D) 4 
Answer: - (D) 
Exp: - Since two samples are transmitted and each sample has 2 bits of information, 
then the information rate is 4 bits/sec. 
?EC-Paper Code-B? GATE 2011    
4. The root locus plot for a system is given below. The open loop transfer function
corresponding to this plot is given by
(A) ( ) ( )
( )
( ) ( )
s s 1
G s H s k
s 2 s 3
+
=
+ +
(B) ( ) ( )
( )
( ) ( )
2
s 1
G s H s k
s s 2 s 3
+
=
+ +
(C) ( ) ( )
( ) ( ) ( )
1
G s H s k
s s 1 s 2 s 3
=
- + +
(D) ( ) ( )
( )
( ) ( )
s 1
G s H s k
s s 2 s 3
+
=
+ +
Answer: - (B) 
Exp: - 'x' ? indicates pole 
'O' ? indicates zero 
The point on the root locus when the number of poles and zeroes on the real axis 
to the right side of that point must be odd 
5. A system is defined by its impulse response ( ) ( )
n
h n 2 u n 2 = - . The system is 
(A) stable and causal (B) causal but not stable  
(C) stable but not causal (D) unstable and non-causal 
Answer: - (B) 
Exp: - ( ) ( )
n
h n 2 u n 2 = -
( ) h n is existing for n>2 ; so that ( ) h n 0;n 0 = < ? causal
( ) ( )
n n
n n n 2
h n 2 u n 2 2
8 8 8
=-8 =8 =
= - = = 8 ?
? ? ?
 System is unstable
6. If the unit step response of a network is
( )
t
1 e
-a
- , then its unit impulse response
is
(A) 
t
e
-a
a (B) 
1 t
e
- -a
a (C) 
( )
1 t
1 e
- -a
- a (D) ( )
t
1 e
-a
- a
Answer: - (A) 
Exp: - ( ) S t ? step response
Impulse response ( ) ( ) ( ) ( )
t t
d d
h t S t 1 e e
dt dt
a a
= = - = a
7. The output Y in the circuit below is always ‘1’  when
× × × o
j?
s
0 1 - 2 - 3 -
P
Q
R
Y
?EC-Paper Code-B? GATE 2011    
(A) two or more of the inputs P,Q,R are ‘0’ 
(B) two or more of the inputs P,Q,R are ‘1’ 
(C) any odd number of the inputs P,Q,R is ‘0’ 
(D) any odd number of the inputs P,Q,R is ‘1’ 
Answer: - (B) 
Exp: - The output Y expression in the Ckt 
Y PQ PR RQ = + +
So that two or more inputs are ‘1’, Y is always ‘1’. 
8. In the circuit shown below, capacitors C
1
 and C
2
 are very large and are shorts at
the input frequency. 
i
v is a small signal input. The gain magnitude 
o
i
v
v
 at 10M 
rad/s is 
(A) maximum (B) minimum (C) unity (D) zero 
Answer: - (A) 
Exp: - In the parallel RLC Ckt 
L 10 H = µ andC 1nF =
7
g
6 9
1 1
10 rad/ s 10Mrad /s
LC
10 10 10
- -
? = = = =
× ×
So that for a tuned amplifier, gain is maximum at resonant frequency 
9. Drift current in the semiconductors depends upon
(A) only the electric field
(B) only the carrier concentration gradient
(C) both the electric field and the carrier concentration
(D) both the electric field and the carrier concentration gradient
Answer: - (C) 
Exp: - Drift current,J E = s 
( )
n P
J n p qE = µ + µ
So that it depends on carrier concentration and electric field. 
~
+
-
+
-
2kO
+
2
C
1
Q
o
v
1
C
2kO
i
v
2.7V
2kO
2kO
10 H µ
5V
?EC-Paper Code-B? GATE 2011    
10. A Zener diode, when used in voltage stabilization circuits, is biased in
(A) reverse bias region below the breakdown voltage
(B) reverse breakdown region
(C) forward bias region
(D) forward bias constant current mode
Answer: - (B) 
Exp: -  
For Zener diode 
Voltage remains constant in break down region and current carrying capacity in 
high. 
11. The circuit shown below is driven by a sinusoidal input ( )
i p
v V cos t /RC = . The
steady state output v
o is
(A) 
( ) ( )
p
V /3 cos t /RC (B) 
( ) ( )
p
V /3 sin t /RC
(C) 
( ) ( )
p
V /2 cos t /RC (D) 
( ) ( )
p
V /2 sin t /RC
Answer: - (A) 
Exp: - 
0 2
i 1 2
v z
v z z
=
+
 where 
2
1
z R ||
j c
=
?
 and 
1
z R
j c
1
= +
?
( )
2
R
z
R jcw 1
=
+
Given 
i p
1 t
w v v cos
RC RC
? ? ? ?
= =
? ? ? ?
? ? ? ?
?
2
R
z
1 j
? =
+
1
1
z R
j c
= +
?
( )
1
R R 1 j
jR
= + ? -
( )
0
i
R
v 1 1 1 j
R v 1 2 3
R 1 j
1 j
+
= = =
+
+ -
+
~ i
v
R
C
C
R
+
-
o
v
+
-
2
V
Page 5


?EC-Paper Code-B? GATE 2011    
1 
Q. No. 1 – 25 Carry One Mark Each 
1. Consider the following statements regarding the complex Poynting vector P


 for
the power radiated by a point source in an infinite homogeneous and lossless
medium.
( )
Re P


 denotes the real part of P


. S denotes a spherical surface whose 
centre is at the point source, and 
?
ndenotes the unit surface normal on S. Which
of the following statements is TRUE?
(A)
( )
Re P


 remains constant at any radial distance from the source 
(B) 
( )
Re P


 increases with increasing radial distance from the source 
(C) 
( )

s
Re P .ndS
??



 remains constant at any radial distance from the source 
(D) 
( )

s
Re P .ndS
??



 decreases with increasing radial distance form the source 
Answer: - (D) 
Exp: - 
( )
S
ˆ Re P .nds
??



gives average power and it decreases with increasing radial 
distance from the source 
2. A transmission line of characteristic impedance 50O is terminated by a 50O load.
When excited by a sinusoidal voltage source at 10GHz, the phase difference
between two points spaced 2mm apart on the line is found to be
4
p
 radians. The 
phase velocity of the wave along the line is
(A) 
8
0.8 10 m /s × (B) 
8
1.2 10 m / s × (C) 
8
1.6 10 m /s × (D) 
8
3 10 m /s × 
Answer: - (C) 
Exp: - 
0
Z 50 = O ; 
L
Z 50 = O
For 
4
p
 radians the distance is 2mm 
The phase velocity 
10
7 8
P
3
2 10
v 16 10 1.6 10 m / s
2
16 10
-
-
? × p ×
= = = × = ×
p ß
×
 
3. An analog signal is band-limited to 4kHz, sampled at the Nyquist rate and the
samples are quantized into 4 levels. The quantized levels are assumed to be
independent and equally probable. If we transmit two quantized samples per
second, the information rate is ________ bits / second.
(A) 1 (B) 2 (C) 3 (D) 4 
Answer: - (D) 
Exp: - Since two samples are transmitted and each sample has 2 bits of information, 
then the information rate is 4 bits/sec. 
?EC-Paper Code-B? GATE 2011    
4. The root locus plot for a system is given below. The open loop transfer function
corresponding to this plot is given by
(A) ( ) ( )
( )
( ) ( )
s s 1
G s H s k
s 2 s 3
+
=
+ +
(B) ( ) ( )
( )
( ) ( )
2
s 1
G s H s k
s s 2 s 3
+
=
+ +
(C) ( ) ( )
( ) ( ) ( )
1
G s H s k
s s 1 s 2 s 3
=
- + +
(D) ( ) ( )
( )
( ) ( )
s 1
G s H s k
s s 2 s 3
+
=
+ +
Answer: - (B) 
Exp: - 'x' ? indicates pole 
'O' ? indicates zero 
The point on the root locus when the number of poles and zeroes on the real axis 
to the right side of that point must be odd 
5. A system is defined by its impulse response ( ) ( )
n
h n 2 u n 2 = - . The system is 
(A) stable and causal (B) causal but not stable  
(C) stable but not causal (D) unstable and non-causal 
Answer: - (B) 
Exp: - ( ) ( )
n
h n 2 u n 2 = -
( ) h n is existing for n>2 ; so that ( ) h n 0;n 0 = < ? causal
( ) ( )
n n
n n n 2
h n 2 u n 2 2
8 8 8
=-8 =8 =
= - = = 8 ?
? ? ?
 System is unstable
6. If the unit step response of a network is
( )
t
1 e
-a
- , then its unit impulse response
is
(A) 
t
e
-a
a (B) 
1 t
e
- -a
a (C) 
( )
1 t
1 e
- -a
- a (D) ( )
t
1 e
-a
- a
Answer: - (A) 
Exp: - ( ) S t ? step response
Impulse response ( ) ( ) ( ) ( )
t t
d d
h t S t 1 e e
dt dt
a a
= = - = a
7. The output Y in the circuit below is always ‘1’  when
× × × o
j?
s
0 1 - 2 - 3 -
P
Q
R
Y
?EC-Paper Code-B? GATE 2011    
(A) two or more of the inputs P,Q,R are ‘0’ 
(B) two or more of the inputs P,Q,R are ‘1’ 
(C) any odd number of the inputs P,Q,R is ‘0’ 
(D) any odd number of the inputs P,Q,R is ‘1’ 
Answer: - (B) 
Exp: - The output Y expression in the Ckt 
Y PQ PR RQ = + +
So that two or more inputs are ‘1’, Y is always ‘1’. 
8. In the circuit shown below, capacitors C
1
 and C
2
 are very large and are shorts at
the input frequency. 
i
v is a small signal input. The gain magnitude 
o
i
v
v
 at 10M 
rad/s is 
(A) maximum (B) minimum (C) unity (D) zero 
Answer: - (A) 
Exp: - In the parallel RLC Ckt 
L 10 H = µ andC 1nF =
7
g
6 9
1 1
10 rad/ s 10Mrad /s
LC
10 10 10
- -
? = = = =
× ×
So that for a tuned amplifier, gain is maximum at resonant frequency 
9. Drift current in the semiconductors depends upon
(A) only the electric field
(B) only the carrier concentration gradient
(C) both the electric field and the carrier concentration
(D) both the electric field and the carrier concentration gradient
Answer: - (C) 
Exp: - Drift current,J E = s 
( )
n P
J n p qE = µ + µ
So that it depends on carrier concentration and electric field. 
~
+
-
+
-
2kO
+
2
C
1
Q
o
v
1
C
2kO
i
v
2.7V
2kO
2kO
10 H µ
5V
?EC-Paper Code-B? GATE 2011    
10. A Zener diode, when used in voltage stabilization circuits, is biased in
(A) reverse bias region below the breakdown voltage
(B) reverse breakdown region
(C) forward bias region
(D) forward bias constant current mode
Answer: - (B) 
Exp: -  
For Zener diode 
Voltage remains constant in break down region and current carrying capacity in 
high. 
11. The circuit shown below is driven by a sinusoidal input ( )
i p
v V cos t /RC = . The
steady state output v
o is
(A) 
( ) ( )
p
V /3 cos t /RC (B) 
( ) ( )
p
V /3 sin t /RC
(C) 
( ) ( )
p
V /2 cos t /RC (D) 
( ) ( )
p
V /2 sin t /RC
Answer: - (A) 
Exp: - 
0 2
i 1 2
v z
v z z
=
+
 where 
2
1
z R ||
j c
=
?
 and 
1
z R
j c
1
= +
?
( )
2
R
z
R jcw 1
=
+
Given 
i p
1 t
w v v cos
RC RC
? ? ? ?
= =
? ? ? ?
? ? ? ?
?
2
R
z
1 j
? =
+
1
1
z R
j c
= +
?
( )
1
R R 1 j
jR
= + ? -
( )
0
i
R
v 1 1 1 j
R v 1 2 3
R 1 j
1 j
+
= = =
+
+ -
+
~ i
v
R
C
C
R
+
-
o
v
+
-
2
V
?EC-Paper Code-B? GATE 2011    
12. Consider a closed surface S surrounding volume V. If r


 is the position vector of a 
point inside S, with
?
n the unit normal on S, the value of the integral 
s
5r.ndS
??


?

 is 
(A) 3V (B) 5V (C) 10V (D) 15V 
Answer: - (D) 
Exp: - Apply the divergence theorem 
S v
5r.n.dx 5 .rdV = ?
?? ???

 
 


( )
v
5 3 dv =
???
= 15 V ( ) .r 3 and r  is the position vector ? =

 

?
13. The modes in a rectangular waveguide are denoted by
mn
mn
TE
TM
 where m and n are 
the eigen numbers along the larger and smaller dimensions of the waveguide 
respectively. Which one of the following statements is TRUE? 
(A) The TM
10
 mode of the wave does not exist 
(B) The TE
10
 mode of the wave does not exist 
(C) The TM
10 
and the TE
10 
modes both exist and have the same cut-off 
frequencies 
(D) The TM
10 
and TM
01  
modes both exist and have the same cut-off frequencies 
Answer: - (A) 
Exp: - 
10
TM mode doesn’t exist in rectangular waveguide. 
14. The solution of the differential equation ( )
dy
ky, y 0 c
dx
= = is 
(A) 
ky
x ce
-
= (B) 
cy
x ke = (C) 
kx
y ce = (D) 
kx
y ce
-
=
Answer: - (C) 
Exp: - Given ( ) y 0 C = and 
dy
ky,
dx
=
dy
kdx
y
? =
kx c
ln y kx c y e e = + ? =
When ( ) y 0 C = , 
0
1
y k e = ? ( )
kx
1
y c e k C = = ?
15. The Column-I lists the attributes and the Column-II lists the modulation
systems. Match the attribute to the modulation system that best meets it
Column-I Column-II 
P Power efficient transmission of signals 1 Conventional AM 
Q 
Most bandwidth efficient transmission of 
voice signals 
2 FM 
R Simplest receiver structure 3 VSB 
S 
Bandwidth efficient transmission of 
signals with Significant dc component 
4 SSB-SC 
(A) P-4;Q-2;R-1;S-3 (B) P-2;Q-4;R-1;S-3 
(C) P-3;Q-2;R-1;S-4 (D) P-2;Q-4;R-3;S-1