Download Graduate Aptitude Test in Engineering (GATE) 2015 ECE Electronics and Communication Engg. SET 3 Question Paper
EC 1/15
Q. 1 ? Q. 25 carry one mark each.
Q.1
The bilateral Laplace transform of a function
1 if
()
0 otherwise
at b
ft
?? ?
=
?
?
is
(A)
ab
s
?
(B)
()
s
ea b
s
?
(C)
as bs
ee
s
??
?
(D)
() s ab
e
s
?
Q.2 The value of for which all the eigen-values of the matrix given below are real is
10 5 + 4
20 2
42 ?10
(A) 5+ j (B) 5? (C) 1?5 (D) 1+5
Q.3
Let ( ) =
. If ( ) = ( ) for all ?
, = 2, = 4 a nd = 5, then should be
equal to _______.
Q.4
The general solution of the differential equation
1cos2
1cos2
dy y
dx x
+
=
?
is
(A) tan cot yxc ?= ( c is a constant) (B) tan cot x yc ?= ( c is a constant)
(C) tan cot yxc += ( c is a constant) (D) tan cot x yc += ( c is a constant)
Q.5 The magnitude and phase of the complex Fourier series coefficients of a periodic signal () are
shown in the figure. Choose the correct statement from the four choices given. Notation: is the
set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary
numbers.
(A) ( ) ?
(B) ( ) ?
(C) ( ) ?( ?)
(D) the information given is not sufficient to draw any conclusion about ( )
01
1
k
2 3 -3 -2 -1
|a
k
|
2
3
2
3
-5 4 -4
k
-4 -5 -3 -2 -1
0
1 23 4
? ?
a
k
?
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GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/15
Q. 1 ? Q. 25 carry one mark each.
Q.1
The bilateral Laplace transform of a function
1 if
()
0 otherwise
at b
ft
?? ?
=
?
?
is
(A)
ab
s
?
(B)
()
s
ea b
s
?
(C)
as bs
ee
s
??
?
(D)
() s ab
e
s
?
Q.2 The value of for which all the eigen-values of the matrix given below are real is
10 5 + 4
20 2
42 ?10
(A) 5+ j (B) 5? (C) 1?5 (D) 1+5
Q.3
Let ( ) =
. If ( ) = ( ) for all ?
, = 2, = 4 a nd = 5, then should be
equal to _______.
Q.4
The general solution of the differential equation
1cos2
1cos2
dy y
dx x
+
=
?
is
(A) tan cot yxc ?= ( c is a constant) (B) tan cot x yc ?= ( c is a constant)
(C) tan cot yxc += ( c is a constant) (D) tan cot x yc += ( c is a constant)
Q.5 The magnitude and phase of the complex Fourier series coefficients of a periodic signal () are
shown in the figure. Choose the correct statement from the four choices given. Notation: is the
set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary
numbers.
(A) ( ) ?
(B) ( ) ?
(C) ( ) ?( ?)
(D) the information given is not sufficient to draw any conclusion about ( )
01
1
k
2 3 -3 -2 -1
|a
k
|
2
3
2
3
-5 4 -4
k
-4 -5 -3 -2 -1
0
1 23 4
? ?
a
k
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/15
Q.6 The voltage ( ) across the capacitor (in Volts) in the network shown is ______ .
Q.7 In the circuit shown, the average value of the voltage V
ab
(in Volts) in steady state condition is
________.
Q.8 The 2-port admittance matrix of the circuit shown is given by
(A) 0.3 0 .2
0.2 0 .3
(B) 15 5
515
(C) 3.3 3 5
53.33
(D) 0.3 0 .4
0.4 0 .3
Q.9 An n-type silicon sample is uniformly illuminated with light which generates 10
20
electron-hole
pairs per cm
3
per second. The minority carrier lifetime in the sample is 1 ?s. In the steady state, the
hole concentration in the sample is approximately 10
x
, where x is an integer. The value of x is ___.
5? sin(5000t)
1 k? 2 k? 1 ?F
1 mH
5 V
a b
+
V
ab
80 V 40 V
~
100 V,
50 Hz
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GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/15
Q. 1 ? Q. 25 carry one mark each.
Q.1
The bilateral Laplace transform of a function
1 if
()
0 otherwise
at b
ft
?? ?
=
?
?
is
(A)
ab
s
?
(B)
()
s
ea b
s
?
(C)
as bs
ee
s
??
?
(D)
() s ab
e
s
?
Q.2 The value of for which all the eigen-values of the matrix given below are real is
10 5 + 4
20 2
42 ?10
(A) 5+ j (B) 5? (C) 1?5 (D) 1+5
Q.3
Let ( ) =
. If ( ) = ( ) for all ?
, = 2, = 4 a nd = 5, then should be
equal to _______.
Q.4
The general solution of the differential equation
1cos2
1cos2
dy y
dx x
+
=
?
is
(A) tan cot yxc ?= ( c is a constant) (B) tan cot x yc ?= ( c is a constant)
(C) tan cot yxc += ( c is a constant) (D) tan cot x yc += ( c is a constant)
Q.5 The magnitude and phase of the complex Fourier series coefficients of a periodic signal () are
shown in the figure. Choose the correct statement from the four choices given. Notation: is the
set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary
numbers.
(A) ( ) ?
(B) ( ) ?
(C) ( ) ?( ?)
(D) the information given is not sufficient to draw any conclusion about ( )
01
1
k
2 3 -3 -2 -1
|a
k
|
2
3
2
3
-5 4 -4
k
-4 -5 -3 -2 -1
0
1 23 4
? ?
a
k
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/15
Q.6 The voltage ( ) across the capacitor (in Volts) in the network shown is ______ .
Q.7 In the circuit shown, the average value of the voltage V
ab
(in Volts) in steady state condition is
________.
Q.8 The 2-port admittance matrix of the circuit shown is given by
(A) 0.3 0 .2
0.2 0 .3
(B) 15 5
515
(C) 3.3 3 5
53.33
(D) 0.3 0 .4
0.4 0 .3
Q.9 An n-type silicon sample is uniformly illuminated with light which generates 10
20
electron-hole
pairs per cm
3
per second. The minority carrier lifetime in the sample is 1 ?s. In the steady state, the
hole concentration in the sample is approximately 10
x
, where x is an integer. The value of x is ___.
5? sin(5000t)
1 k? 2 k? 1 ?F
1 mH
5 V
a b
+
V
ab
80 V 40 V
~
100 V,
50 Hz
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/15
Q.10 A piece of silicon is doped uniformly with phosphorous with a doping concentration of
10
16
/cm
3
. The expected value of mobility versus doping concentration for silicon assuming full
dopant ionization is shown below. The charge of an electron is 1.6 ?10
-19
C. The conductivity
(in
1
S cm
?
) of the silicon sample at 300
K is _______.
Q.11 If the circuit shown has to function as a clamping circuit, then which one of the following
conditions should be satisfied for the sinusoidal signal of period T ?
(A) RC << T (B) RC = 0.35 T (C) RC ? T (D) RC >> T
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GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/15
Q. 1 ? Q. 25 carry one mark each.
Q.1
The bilateral Laplace transform of a function
1 if
()
0 otherwise
at b
ft
?? ?
=
?
?
is
(A)
ab
s
?
(B)
()
s
ea b
s
?
(C)
as bs
ee
s
??
?
(D)
() s ab
e
s
?
Q.2 The value of for which all the eigen-values of the matrix given below are real is
10 5 + 4
20 2
42 ?10
(A) 5+ j (B) 5? (C) 1?5 (D) 1+5
Q.3
Let ( ) =
. If ( ) = ( ) for all ?
, = 2, = 4 a nd = 5, then should be
equal to _______.
Q.4
The general solution of the differential equation
1cos2
1cos2
dy y
dx x
+
=
?
is
(A) tan cot yxc ?= ( c is a constant) (B) tan cot x yc ?= ( c is a constant)
(C) tan cot yxc += ( c is a constant) (D) tan cot x yc += ( c is a constant)
Q.5 The magnitude and phase of the complex Fourier series coefficients of a periodic signal () are
shown in the figure. Choose the correct statement from the four choices given. Notation: is the
set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary
numbers.
(A) ( ) ?
(B) ( ) ?
(C) ( ) ?( ?)
(D) the information given is not sufficient to draw any conclusion about ( )
01
1
k
2 3 -3 -2 -1
|a
k
|
2
3
2
3
-5 4 -4
k
-4 -5 -3 -2 -1
0
1 23 4
? ?
a
k
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/15
Q.6 The voltage ( ) across the capacitor (in Volts) in the network shown is ______ .
Q.7 In the circuit shown, the average value of the voltage V
ab
(in Volts) in steady state condition is
________.
Q.8 The 2-port admittance matrix of the circuit shown is given by
(A) 0.3 0 .2
0.2 0 .3
(B) 15 5
515
(C) 3.3 3 5
53.33
(D) 0.3 0 .4
0.4 0 .3
Q.9 An n-type silicon sample is uniformly illuminated with light which generates 10
20
electron-hole
pairs per cm
3
per second. The minority carrier lifetime in the sample is 1 ?s. In the steady state, the
hole concentration in the sample is approximately 10
x
, where x is an integer. The value of x is ___.
5? sin(5000t)
1 k? 2 k? 1 ?F
1 mH
5 V
a b
+
V
ab
80 V 40 V
~
100 V,
50 Hz
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/15
Q.10 A piece of silicon is doped uniformly with phosphorous with a doping concentration of
10
16
/cm
3
. The expected value of mobility versus doping concentration for silicon assuming full
dopant ionization is shown below. The charge of an electron is 1.6 ?10
-19
C. The conductivity
(in
1
S cm
?
) of the silicon sample at 300
K is _______.
Q.11 If the circuit shown has to function as a clamping circuit, then which one of the following
conditions should be satisfied for the sinusoidal signal of period T ?
(A) RC << T (B) RC = 0.35 T (C) RC ? T (D) RC >> T
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/15
Q.12 In the circuit shown, V
0
= V
0A
for switch SW in position A and V
0
= V
0B
for SW in position B.
Assume that the opamp is ideal. The value of
0
0
B
A
V
V
is ___________.
Q.13 In the bistable circuit shown, the ideal opamp has saturation levels of ? 5 V. The value of R
1
(in
k ?) that gives a hysteresis width of 500 mV is ________.
Q.14 In the figure shown, the output is required to be = + ? . The gates G1
and G2 must be,
respectively,
(A) NOR, OR (B) OR, NAND
(C) NAND, OR (D) AND, NAND
Q.15 In an 8085 microprocessor, which one of the following instructions changes the content of the
accumulator?
(A) MOV B,M (B) PCHL (C) RNZ (D) SBI BEH
5 V
V
0
1 V
B A
1 k?
SW
1 k?
1 k?
1 k?
1 k?
+
?
+
?
R
2
= 20 k ?
R
1
v
out
v
in
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/15
Q. 1 ? Q. 25 carry one mark each.
Q.1
The bilateral Laplace transform of a function
1 if
()
0 otherwise
at b
ft
?? ?
=
?
?
is
(A)
ab
s
?
(B)
()
s
ea b
s
?
(C)
as bs
ee
s
??
?
(D)
() s ab
e
s
?
Q.2 The value of for which all the eigen-values of the matrix given below are real is
10 5 + 4
20 2
42 ?10
(A) 5+ j (B) 5? (C) 1?5 (D) 1+5
Q.3
Let ( ) =
. If ( ) = ( ) for all ?
, = 2, = 4 a nd = 5, then should be
equal to _______.
Q.4
The general solution of the differential equation
1cos2
1cos2
dy y
dx x
+
=
?
is
(A) tan cot yxc ?= ( c is a constant) (B) tan cot x yc ?= ( c is a constant)
(C) tan cot yxc += ( c is a constant) (D) tan cot x yc += ( c is a constant)
Q.5 The magnitude and phase of the complex Fourier series coefficients of a periodic signal () are
shown in the figure. Choose the correct statement from the four choices given. Notation: is the
set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary
numbers.
(A) ( ) ?
(B) ( ) ?
(C) ( ) ?( ?)
(D) the information given is not sufficient to draw any conclusion about ( )
01
1
k
2 3 -3 -2 -1
|a
k
|
2
3
2
3
-5 4 -4
k
-4 -5 -3 -2 -1
0
1 23 4
? ?
a
k
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/15
Q.6 The voltage ( ) across the capacitor (in Volts) in the network shown is ______ .
Q.7 In the circuit shown, the average value of the voltage V
ab
(in Volts) in steady state condition is
________.
Q.8 The 2-port admittance matrix of the circuit shown is given by
(A) 0.3 0 .2
0.2 0 .3
(B) 15 5
515
(C) 3.3 3 5
53.33
(D) 0.3 0 .4
0.4 0 .3
Q.9 An n-type silicon sample is uniformly illuminated with light which generates 10
20
electron-hole
pairs per cm
3
per second. The minority carrier lifetime in the sample is 1 ?s. In the steady state, the
hole concentration in the sample is approximately 10
x
, where x is an integer. The value of x is ___.
5? sin(5000t)
1 k? 2 k? 1 ?F
1 mH
5 V
a b
+
V
ab
80 V 40 V
~
100 V,
50 Hz
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/15
Q.10 A piece of silicon is doped uniformly with phosphorous with a doping concentration of
10
16
/cm
3
. The expected value of mobility versus doping concentration for silicon assuming full
dopant ionization is shown below. The charge of an electron is 1.6 ?10
-19
C. The conductivity
(in
1
S cm
?
) of the silicon sample at 300
K is _______.
Q.11 If the circuit shown has to function as a clamping circuit, then which one of the following
conditions should be satisfied for the sinusoidal signal of period T ?
(A) RC << T (B) RC = 0.35 T (C) RC ? T (D) RC >> T
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/15
Q.12 In the circuit shown, V
0
= V
0A
for switch SW in position A and V
0
= V
0B
for SW in position B.
Assume that the opamp is ideal. The value of
0
0
B
A
V
V
is ___________.
Q.13 In the bistable circuit shown, the ideal opamp has saturation levels of ? 5 V. The value of R
1
(in
k ?) that gives a hysteresis width of 500 mV is ________.
Q.14 In the figure shown, the output is required to be = + ? . The gates G1
and G2 must be,
respectively,
(A) NOR, OR (B) OR, NAND
(C) NAND, OR (D) AND, NAND
Q.15 In an 8085 microprocessor, which one of the following instructions changes the content of the
accumulator?
(A) MOV B,M (B) PCHL (C) RNZ (D) SBI BEH
5 V
V
0
1 V
B A
1 k?
SW
1 k?
1 k?
1 k?
1 k?
+
?
+
?
R
2
= 20 k ?
R
1
v
out
v
in
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/15
Q.16 A mod-n counter using a synchronous binary up-counter with synchronous clear input is shown in
the figure. The value of n is _______.
Q.17 Let the signal ( ) = 0 outside the interval [
,
], where and are finite. Furthermore,
| ( )| < ? . The region of convergence (RoC) of the signal?s bilateral Laplace transform ( ) is
(A) a parallel strip containing the ? axis
(B) a parallel strip not containing the ? axis
(C) the entire -plane
(D) a half plane containing the ? axis
Q.18
Two causal discrete-time signals [] x n and [] y n are related as
0
[] [ ]
n
m
yn x m
=
=
?
.
If the z-transform of y[n] is
()
, the value of [2] x is _______.
Q.19 By performing cascading and/or summing/differencing operations using transfer function blocks
1
() Gs and
2
() Gs , one CANNOT realize a transfer function of the form
(A)
12
() () GsG s
(B)
1
2
()
()
Gs
Gs
(C)
12
1
1
() ()
()
Gs G s
Gs
??
+
??
??
(D)
12
1
1
() ()
()
Gs G s
Gs
??
?
??
??
Q
A
CLEAR
CLK
4-Bit Binary
Counter
Q
B
Q
C
Q
D
Q
A
Q
B
Q
C
Q
D
CLOCK
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GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/15
Q. 1 ? Q. 25 carry one mark each.
Q.1
The bilateral Laplace transform of a function
1 if
()
0 otherwise
at b
ft
?? ?
=
?
?
is
(A)
ab
s
?
(B)
()
s
ea b
s
?
(C)
as bs
ee
s
??
?
(D)
() s ab
e
s
?
Q.2 The value of for which all the eigen-values of the matrix given below are real is
10 5 + 4
20 2
42 ?10
(A) 5+ j (B) 5? (C) 1?5 (D) 1+5
Q.3
Let ( ) =
. If ( ) = ( ) for all ?
, = 2, = 4 a nd = 5, then should be
equal to _______.
Q.4
The general solution of the differential equation
1cos2
1cos2
dy y
dx x
+
=
?
is
(A) tan cot yxc ?= ( c is a constant) (B) tan cot x yc ?= ( c is a constant)
(C) tan cot yxc += ( c is a constant) (D) tan cot x yc += ( c is a constant)
Q.5 The magnitude and phase of the complex Fourier series coefficients of a periodic signal () are
shown in the figure. Choose the correct statement from the four choices given. Notation: is the
set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary
numbers.
(A) ( ) ?
(B) ( ) ?
(C) ( ) ?( ?)
(D) the information given is not sufficient to draw any conclusion about ( )
01
1
k
2 3 -3 -2 -1
|a
k
|
2
3
2
3
-5 4 -4
k
-4 -5 -3 -2 -1
0
1 23 4
? ?
a
k
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/15
Q.6 The voltage ( ) across the capacitor (in Volts) in the network shown is ______ .
Q.7 In the circuit shown, the average value of the voltage V
ab
(in Volts) in steady state condition is
________.
Q.8 The 2-port admittance matrix of the circuit shown is given by
(A) 0.3 0 .2
0.2 0 .3
(B) 15 5
515
(C) 3.3 3 5
53.33
(D) 0.3 0 .4
0.4 0 .3
Q.9 An n-type silicon sample is uniformly illuminated with light which generates 10
20
electron-hole
pairs per cm
3
per second. The minority carrier lifetime in the sample is 1 ?s. In the steady state, the
hole concentration in the sample is approximately 10
x
, where x is an integer. The value of x is ___.
5? sin(5000t)
1 k? 2 k? 1 ?F
1 mH
5 V
a b
+
V
ab
80 V 40 V
~
100 V,
50 Hz
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/15
Q.10 A piece of silicon is doped uniformly with phosphorous with a doping concentration of
10
16
/cm
3
. The expected value of mobility versus doping concentration for silicon assuming full
dopant ionization is shown below. The charge of an electron is 1.6 ?10
-19
C. The conductivity
(in
1
S cm
?
) of the silicon sample at 300
K is _______.
Q.11 If the circuit shown has to function as a clamping circuit, then which one of the following
conditions should be satisfied for the sinusoidal signal of period T ?
(A) RC << T (B) RC = 0.35 T (C) RC ? T (D) RC >> T
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/15
Q.12 In the circuit shown, V
0
= V
0A
for switch SW in position A and V
0
= V
0B
for SW in position B.
Assume that the opamp is ideal. The value of
0
0
B
A
V
V
is ___________.
Q.13 In the bistable circuit shown, the ideal opamp has saturation levels of ? 5 V. The value of R
1
(in
k ?) that gives a hysteresis width of 500 mV is ________.
Q.14 In the figure shown, the output is required to be = + ? . The gates G1
and G2 must be,
respectively,
(A) NOR, OR (B) OR, NAND
(C) NAND, OR (D) AND, NAND
Q.15 In an 8085 microprocessor, which one of the following instructions changes the content of the
accumulator?
(A) MOV B,M (B) PCHL (C) RNZ (D) SBI BEH
5 V
V
0
1 V
B A
1 k?
SW
1 k?
1 k?
1 k?
1 k?
+
?
+
?
R
2
= 20 k ?
R
1
v
out
v
in
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/15
Q.16 A mod-n counter using a synchronous binary up-counter with synchronous clear input is shown in
the figure. The value of n is _______.
Q.17 Let the signal ( ) = 0 outside the interval [
,
], where and are finite. Furthermore,
| ( )| < ? . The region of convergence (RoC) of the signal?s bilateral Laplace transform ( ) is
(A) a parallel strip containing the ? axis
(B) a parallel strip not containing the ? axis
(C) the entire -plane
(D) a half plane containing the ? axis
Q.18
Two causal discrete-time signals [] x n and [] y n are related as
0
[] [ ]
n
m
yn x m
=
=
?
.
If the z-transform of y[n] is
()
, the value of [2] x is _______.
Q.19 By performing cascading and/or summing/differencing operations using transfer function blocks
1
() Gs and
2
() Gs , one CANNOT realize a transfer function of the form
(A)
12
() () GsG s
(B)
1
2
()
()
Gs
Gs
(C)
12
1
1
() ()
()
Gs G s
Gs
??
+
??
??
(D)
12
1
1
() ()
()
Gs G s
Gs
??
?
??
??
Q
A
CLEAR
CLK
4-Bit Binary
Counter
Q
B
Q
C
Q
D
Q
A
Q
B
Q
C
Q
D
CLOCK
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/15
Q.20
For the signal flow graph shown in the figure, the value of
()
()
Cs
R s
is
(A)
12 3 4
12134 2 233123412
1
GG G G
GG H GG H GG H GGGG H H ?? ? +
(B)
12 3 4
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
GG G G
GG H GG H GG H GGGG H H ++ + +
(C)
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
1 GG H GG H GG H GGGG H H ++ + +
(D)
12134 2 233123412
1
1 GG H GG H GG H GGGG H H ?? ? +
Q.21
A unity negative feedback system has an open-loop transfer function ( ) =
( +10 )
. The gain
for the system to have a damping ratio of 0.25 is ________.
Q.22 A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal
utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8
dB, the number of levels in the quantizer is _______.
Q.23
The signal cos 10
4
t
?
?
??
+
??
??
is ideally sampled at a sampling frequency of 15 Hz. The sampled
signal is passed through a filter with impulse response
sin( )
cos 40 .
2
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
The filter
output is
(A)
15
cos 40
24
t
?
?
??
?
??
??
(B)
15 sin( )
cos 10
24
t
t
t
??
?
?
??? ?
+
??? ?
??? ?
(C)
15
cos 10
24
t
?
?
??
?
??
??
(D)
15 sin( )
cos 40
22
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
-H
3
R(s)
1
X
1
X
2
X
3
X
4
X
5
C(s)
-H
1
-H
2
G
1
G
2
G
3
G
4
1
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/15
Q. 1 ? Q. 25 carry one mark each.
Q.1
The bilateral Laplace transform of a function
1 if
()
0 otherwise
at b
ft
?? ?
=
?
?
is
(A)
ab
s
?
(B)
()
s
ea b
s
?
(C)
as bs
ee
s
??
?
(D)
() s ab
e
s
?
Q.2 The value of for which all the eigen-values of the matrix given below are real is
10 5 + 4
20 2
42 ?10
(A) 5+ j (B) 5? (C) 1?5 (D) 1+5
Q.3
Let ( ) =
. If ( ) = ( ) for all ?
, = 2, = 4 a nd = 5, then should be
equal to _______.
Q.4
The general solution of the differential equation
1cos2
1cos2
dy y
dx x
+
=
?
is
(A) tan cot yxc ?= ( c is a constant) (B) tan cot x yc ?= ( c is a constant)
(C) tan cot yxc += ( c is a constant) (D) tan cot x yc += ( c is a constant)
Q.5 The magnitude and phase of the complex Fourier series coefficients of a periodic signal () are
shown in the figure. Choose the correct statement from the four choices given. Notation: is the
set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary
numbers.
(A) ( ) ?
(B) ( ) ?
(C) ( ) ?( ?)
(D) the information given is not sufficient to draw any conclusion about ( )
01
1
k
2 3 -3 -2 -1
|a
k
|
2
3
2
3
-5 4 -4
k
-4 -5 -3 -2 -1
0
1 23 4
? ?
a
k
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/15
Q.6 The voltage ( ) across the capacitor (in Volts) in the network shown is ______ .
Q.7 In the circuit shown, the average value of the voltage V
ab
(in Volts) in steady state condition is
________.
Q.8 The 2-port admittance matrix of the circuit shown is given by
(A) 0.3 0 .2
0.2 0 .3
(B) 15 5
515
(C) 3.3 3 5
53.33
(D) 0.3 0 .4
0.4 0 .3
Q.9 An n-type silicon sample is uniformly illuminated with light which generates 10
20
electron-hole
pairs per cm
3
per second. The minority carrier lifetime in the sample is 1 ?s. In the steady state, the
hole concentration in the sample is approximately 10
x
, where x is an integer. The value of x is ___.
5? sin(5000t)
1 k? 2 k? 1 ?F
1 mH
5 V
a b
+
V
ab
80 V 40 V
~
100 V,
50 Hz
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/15
Q.10 A piece of silicon is doped uniformly with phosphorous with a doping concentration of
10
16
/cm
3
. The expected value of mobility versus doping concentration for silicon assuming full
dopant ionization is shown below. The charge of an electron is 1.6 ?10
-19
C. The conductivity
(in
1
S cm
?
) of the silicon sample at 300
K is _______.
Q.11 If the circuit shown has to function as a clamping circuit, then which one of the following
conditions should be satisfied for the sinusoidal signal of period T ?
(A) RC << T (B) RC = 0.35 T (C) RC ? T (D) RC >> T
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/15
Q.12 In the circuit shown, V
0
= V
0A
for switch SW in position A and V
0
= V
0B
for SW in position B.
Assume that the opamp is ideal. The value of
0
0
B
A
V
V
is ___________.
Q.13 In the bistable circuit shown, the ideal opamp has saturation levels of ? 5 V. The value of R
1
(in
k ?) that gives a hysteresis width of 500 mV is ________.
Q.14 In the figure shown, the output is required to be = + ? . The gates G1
and G2 must be,
respectively,
(A) NOR, OR (B) OR, NAND
(C) NAND, OR (D) AND, NAND
Q.15 In an 8085 microprocessor, which one of the following instructions changes the content of the
accumulator?
(A) MOV B,M (B) PCHL (C) RNZ (D) SBI BEH
5 V
V
0
1 V
B A
1 k?
SW
1 k?
1 k?
1 k?
1 k?
+
?
+
?
R
2
= 20 k ?
R
1
v
out
v
in
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/15
Q.16 A mod-n counter using a synchronous binary up-counter with synchronous clear input is shown in
the figure. The value of n is _______.
Q.17 Let the signal ( ) = 0 outside the interval [
,
], where and are finite. Furthermore,
| ( )| < ? . The region of convergence (RoC) of the signal?s bilateral Laplace transform ( ) is
(A) a parallel strip containing the ? axis
(B) a parallel strip not containing the ? axis
(C) the entire -plane
(D) a half plane containing the ? axis
Q.18
Two causal discrete-time signals [] x n and [] y n are related as
0
[] [ ]
n
m
yn x m
=
=
?
.
If the z-transform of y[n] is
()
, the value of [2] x is _______.
Q.19 By performing cascading and/or summing/differencing operations using transfer function blocks
1
() Gs and
2
() Gs , one CANNOT realize a transfer function of the form
(A)
12
() () GsG s
(B)
1
2
()
()
Gs
Gs
(C)
12
1
1
() ()
()
Gs G s
Gs
??
+
??
??
(D)
12
1
1
() ()
()
Gs G s
Gs
??
?
??
??
Q
A
CLEAR
CLK
4-Bit Binary
Counter
Q
B
Q
C
Q
D
Q
A
Q
B
Q
C
Q
D
CLOCK
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/15
Q.20
For the signal flow graph shown in the figure, the value of
()
()
Cs
R s
is
(A)
12 3 4
12134 2 233123412
1
GG G G
GG H GG H GG H GGGG H H ?? ? +
(B)
12 3 4
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
GG G G
GG H GG H GG H GGGG H H ++ + +
(C)
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
1 GG H GG H GG H GGGG H H ++ + +
(D)
12134 2 233123412
1
1 GG H GG H GG H GGGG H H ?? ? +
Q.21
A unity negative feedback system has an open-loop transfer function ( ) =
( +10 )
. The gain
for the system to have a damping ratio of 0.25 is ________.
Q.22 A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal
utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8
dB, the number of levels in the quantizer is _______.
Q.23
The signal cos 10
4
t
?
?
??
+
??
??
is ideally sampled at a sampling frequency of 15 Hz. The sampled
signal is passed through a filter with impulse response
sin( )
cos 40 .
2
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
The filter
output is
(A)
15
cos 40
24
t
?
?
??
?
??
??
(B)
15 sin( )
cos 10
24
t
t
t
??
?
?
??? ?
+
??? ?
??? ?
(C)
15
cos 10
24
t
?
?
??
?
??
??
(D)
15 sin( )
cos 40
22
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
-H
3
R(s)
1
X
1
X
2
X
3
X
4
X
5
C(s)
-H
1
-H
2
G
1
G
2
G
3
G
4
1
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/15
Q.24 In a source free region in vacuum, if the electrostatic potential = 2 + + , the value
of constant must be _______.
Q.25 The electric field of a uniform plane electromagnetic wave is
= + 4 e x p [ ( 2 ? 1 0
? 0.2 ) ] .
The polarization of the wave is
(A) right handed circular (B) right handed elliptical
(C) left handed circular (D) left handed elliptical
Q. 26 ? Q. 55 carry two marks each.
Q.26
Consider the differential equation 10 0.2
dx
x
dt
=? with initial condition (0) 1 x = . The response
() x t for 0 t > is
(A)
0.2
2
t
e
?
? (B)
0.2
2
t
e ? (C)
0.2
50 49
t
e
?
? (D)
0.2
50 49
t
e ?
Q.27
The value of the integral 12
sin(4 )
cos(2 )
4
?
?
?
t
tdt
t
is ___________.
Q.28 If denotes the counterclockwise unit circle, the value of the contour integral
1
2
{ }
is _______.
Q.29
Let the random variable X represent the number of times a fair coin needs to be tossed till two
consecutive heads appear for the first time. The expectation of X is _______.
Q.30 An LC
tank circuit consists of an ideal capacitor C
connected in parallel with a coil of inductance
L having an internal resistance R . The resonant frequency of the tank circuit is
(A)
1
2 LC ?
(B)
2
1
1
2
C
R
L LC ?
?
(C)
2
1
1
2
L
RC LC ?
?
(D)
2
1
1
2
C
R
L LC ?
??
?
??
??
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/15
Q. 1 ? Q. 25 carry one mark each.
Q.1
The bilateral Laplace transform of a function
1 if
()
0 otherwise
at b
ft
?? ?
=
?
?
is
(A)
ab
s
?
(B)
()
s
ea b
s
?
(C)
as bs
ee
s
??
?
(D)
() s ab
e
s
?
Q.2 The value of for which all the eigen-values of the matrix given below are real is
10 5 + 4
20 2
42 ?10
(A) 5+ j (B) 5? (C) 1?5 (D) 1+5
Q.3
Let ( ) =
. If ( ) = ( ) for all ?
, = 2, = 4 a nd = 5, then should be
equal to _______.
Q.4
The general solution of the differential equation
1cos2
1cos2
dy y
dx x
+
=
?
is
(A) tan cot yxc ?= ( c is a constant) (B) tan cot x yc ?= ( c is a constant)
(C) tan cot yxc += ( c is a constant) (D) tan cot x yc += ( c is a constant)
Q.5 The magnitude and phase of the complex Fourier series coefficients of a periodic signal () are
shown in the figure. Choose the correct statement from the four choices given. Notation: is the
set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary
numbers.
(A) ( ) ?
(B) ( ) ?
(C) ( ) ?( ?)
(D) the information given is not sufficient to draw any conclusion about ( )
01
1
k
2 3 -3 -2 -1
|a
k
|
2
3
2
3
-5 4 -4
k
-4 -5 -3 -2 -1
0
1 23 4
? ?
a
k
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/15
Q.6 The voltage ( ) across the capacitor (in Volts) in the network shown is ______ .
Q.7 In the circuit shown, the average value of the voltage V
ab
(in Volts) in steady state condition is
________.
Q.8 The 2-port admittance matrix of the circuit shown is given by
(A) 0.3 0 .2
0.2 0 .3
(B) 15 5
515
(C) 3.3 3 5
53.33
(D) 0.3 0 .4
0.4 0 .3
Q.9 An n-type silicon sample is uniformly illuminated with light which generates 10
20
electron-hole
pairs per cm
3
per second. The minority carrier lifetime in the sample is 1 ?s. In the steady state, the
hole concentration in the sample is approximately 10
x
, where x is an integer. The value of x is ___.
5? sin(5000t)
1 k? 2 k? 1 ?F
1 mH
5 V
a b
+
V
ab
80 V 40 V
~
100 V,
50 Hz
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/15
Q.10 A piece of silicon is doped uniformly with phosphorous with a doping concentration of
10
16
/cm
3
. The expected value of mobility versus doping concentration for silicon assuming full
dopant ionization is shown below. The charge of an electron is 1.6 ?10
-19
C. The conductivity
(in
1
S cm
?
) of the silicon sample at 300
K is _______.
Q.11 If the circuit shown has to function as a clamping circuit, then which one of the following
conditions should be satisfied for the sinusoidal signal of period T ?
(A) RC << T (B) RC = 0.35 T (C) RC ? T (D) RC >> T
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/15
Q.12 In the circuit shown, V
0
= V
0A
for switch SW in position A and V
0
= V
0B
for SW in position B.
Assume that the opamp is ideal. The value of
0
0
B
A
V
V
is ___________.
Q.13 In the bistable circuit shown, the ideal opamp has saturation levels of ? 5 V. The value of R
1
(in
k ?) that gives a hysteresis width of 500 mV is ________.
Q.14 In the figure shown, the output is required to be = + ? . The gates G1
and G2 must be,
respectively,
(A) NOR, OR (B) OR, NAND
(C) NAND, OR (D) AND, NAND
Q.15 In an 8085 microprocessor, which one of the following instructions changes the content of the
accumulator?
(A) MOV B,M (B) PCHL (C) RNZ (D) SBI BEH
5 V
V
0
1 V
B A
1 k?
SW
1 k?
1 k?
1 k?
1 k?
+
?
+
?
R
2
= 20 k ?
R
1
v
out
v
in
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/15
Q.16 A mod-n counter using a synchronous binary up-counter with synchronous clear input is shown in
the figure. The value of n is _______.
Q.17 Let the signal ( ) = 0 outside the interval [
,
], where and are finite. Furthermore,
| ( )| < ? . The region of convergence (RoC) of the signal?s bilateral Laplace transform ( ) is
(A) a parallel strip containing the ? axis
(B) a parallel strip not containing the ? axis
(C) the entire -plane
(D) a half plane containing the ? axis
Q.18
Two causal discrete-time signals [] x n and [] y n are related as
0
[] [ ]
n
m
yn x m
=
=
?
.
If the z-transform of y[n] is
()
, the value of [2] x is _______.
Q.19 By performing cascading and/or summing/differencing operations using transfer function blocks
1
() Gs and
2
() Gs , one CANNOT realize a transfer function of the form
(A)
12
() () GsG s
(B)
1
2
()
()
Gs
Gs
(C)
12
1
1
() ()
()
Gs G s
Gs
??
+
??
??
(D)
12
1
1
() ()
()
Gs G s
Gs
??
?
??
??
Q
A
CLEAR
CLK
4-Bit Binary
Counter
Q
B
Q
C
Q
D
Q
A
Q
B
Q
C
Q
D
CLOCK
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/15
Q.20
For the signal flow graph shown in the figure, the value of
()
()
Cs
R s
is
(A)
12 3 4
12134 2 233123412
1
GG G G
GG H GG H GG H GGGG H H ?? ? +
(B)
12 3 4
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
GG G G
GG H GG H GG H GGGG H H ++ + +
(C)
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
1 GG H GG H GG H GGGG H H ++ + +
(D)
12134 2 233123412
1
1 GG H GG H GG H GGGG H H ?? ? +
Q.21
A unity negative feedback system has an open-loop transfer function ( ) =
( +10 )
. The gain
for the system to have a damping ratio of 0.25 is ________.
Q.22 A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal
utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8
dB, the number of levels in the quantizer is _______.
Q.23
The signal cos 10
4
t
?
?
??
+
??
??
is ideally sampled at a sampling frequency of 15 Hz. The sampled
signal is passed through a filter with impulse response
sin( )
cos 40 .
2
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
The filter
output is
(A)
15
cos 40
24
t
?
?
??
?
??
??
(B)
15 sin( )
cos 10
24
t
t
t
??
?
?
??? ?
+
??? ?
??? ?
(C)
15
cos 10
24
t
?
?
??
?
??
??
(D)
15 sin( )
cos 40
22
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
-H
3
R(s)
1
X
1
X
2
X
3
X
4
X
5
C(s)
-H
1
-H
2
G
1
G
2
G
3
G
4
1
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/15
Q.24 In a source free region in vacuum, if the electrostatic potential = 2 + + , the value
of constant must be _______.
Q.25 The electric field of a uniform plane electromagnetic wave is
= + 4 e x p [ ( 2 ? 1 0
? 0.2 ) ] .
The polarization of the wave is
(A) right handed circular (B) right handed elliptical
(C) left handed circular (D) left handed elliptical
Q. 26 ? Q. 55 carry two marks each.
Q.26
Consider the differential equation 10 0.2
dx
x
dt
=? with initial condition (0) 1 x = . The response
() x t for 0 t > is
(A)
0.2
2
t
e
?
? (B)
0.2
2
t
e ? (C)
0.2
50 49
t
e
?
? (D)
0.2
50 49
t
e ?
Q.27
The value of the integral 12
sin(4 )
cos(2 )
4
?
?
?
t
tdt
t
is ___________.
Q.28 If denotes the counterclockwise unit circle, the value of the contour integral
1
2
{ }
is _______.
Q.29
Let the random variable X represent the number of times a fair coin needs to be tossed till two
consecutive heads appear for the first time. The expectation of X is _______.
Q.30 An LC
tank circuit consists of an ideal capacitor C
connected in parallel with a coil of inductance
L having an internal resistance R . The resonant frequency of the tank circuit is
(A)
1
2 LC ?
(B)
2
1
1
2
C
R
L LC ?
?
(C)
2
1
1
2
L
RC LC ?
?
(D)
2
1
1
2
C
R
L LC ?
??
?
??
??
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/15
Q.31 In the circuit shown, the Norton equivalent resistance (in ? ) across terminals a-b is _______.
+
-
4 ?
2?
2? 4?
?
a
b
Q.32 In the circuit shown, the initial voltages across the capacitors C
1
and C
2
are 1 V and 3 V,
respectively. The switch is closed at time = 0 . The total energy dissipated (in Joules) in the
resistor R until steady state is reached, is __________.
Q.33 A dc voltage of 10 V is applied across an n-type silicon bar having a rectangular cross-section and a
length of 1 cm as shown in figure. The donor doping concentration N
D
and the mobility of electrons
n
? are 10
16
cm
-3
and 1000 cm
2
V
-1
s
-1
, respectively. The average time (in ?s) taken by the electrons
to move from one end of the bar to other end is ________.
Q.34 In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer thickness
is 100 nm. The permittivities of the semiconductor and the oxide layer are ?
s
and ?
ox
respectively.
Assuming ?
s
/?
ox
= 3, the ratio of the maximum capacitance to the minimum capacitance of this
MOS capacitor is ________.
1 cm
10 V
n-Si
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/15
Q. 1 ? Q. 25 carry one mark each.
Q.1
The bilateral Laplace transform of a function
1 if
()
0 otherwise
at b
ft
?? ?
=
?
?
is
(A)
ab
s
?
(B)
()
s
ea b
s
?
(C)
as bs
ee
s
??
?
(D)
() s ab
e
s
?
Q.2 The value of for which all the eigen-values of the matrix given below are real is
10 5 + 4
20 2
42 ?10
(A) 5+ j (B) 5? (C) 1?5 (D) 1+5
Q.3
Let ( ) =
. If ( ) = ( ) for all ?
, = 2, = 4 a nd = 5, then should be
equal to _______.
Q.4
The general solution of the differential equation
1cos2
1cos2
dy y
dx x
+
=
?
is
(A) tan cot yxc ?= ( c is a constant) (B) tan cot x yc ?= ( c is a constant)
(C) tan cot yxc += ( c is a constant) (D) tan cot x yc += ( c is a constant)
Q.5 The magnitude and phase of the complex Fourier series coefficients of a periodic signal () are
shown in the figure. Choose the correct statement from the four choices given. Notation: is the
set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary
numbers.
(A) ( ) ?
(B) ( ) ?
(C) ( ) ?( ?)
(D) the information given is not sufficient to draw any conclusion about ( )
01
1
k
2 3 -3 -2 -1
|a
k
|
2
3
2
3
-5 4 -4
k
-4 -5 -3 -2 -1
0
1 23 4
? ?
a
k
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/15
Q.6 The voltage ( ) across the capacitor (in Volts) in the network shown is ______ .
Q.7 In the circuit shown, the average value of the voltage V
ab
(in Volts) in steady state condition is
________.
Q.8 The 2-port admittance matrix of the circuit shown is given by
(A) 0.3 0 .2
0.2 0 .3
(B) 15 5
515
(C) 3.3 3 5
53.33
(D) 0.3 0 .4
0.4 0 .3
Q.9 An n-type silicon sample is uniformly illuminated with light which generates 10
20
electron-hole
pairs per cm
3
per second. The minority carrier lifetime in the sample is 1 ?s. In the steady state, the
hole concentration in the sample is approximately 10
x
, where x is an integer. The value of x is ___.
5? sin(5000t)
1 k? 2 k? 1 ?F
1 mH
5 V
a b
+
V
ab
80 V 40 V
~
100 V,
50 Hz
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/15
Q.10 A piece of silicon is doped uniformly with phosphorous with a doping concentration of
10
16
/cm
3
. The expected value of mobility versus doping concentration for silicon assuming full
dopant ionization is shown below. The charge of an electron is 1.6 ?10
-19
C. The conductivity
(in
1
S cm
?
) of the silicon sample at 300
K is _______.
Q.11 If the circuit shown has to function as a clamping circuit, then which one of the following
conditions should be satisfied for the sinusoidal signal of period T ?
(A) RC << T (B) RC = 0.35 T (C) RC ? T (D) RC >> T
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/15
Q.12 In the circuit shown, V
0
= V
0A
for switch SW in position A and V
0
= V
0B
for SW in position B.
Assume that the opamp is ideal. The value of
0
0
B
A
V
V
is ___________.
Q.13 In the bistable circuit shown, the ideal opamp has saturation levels of ? 5 V. The value of R
1
(in
k ?) that gives a hysteresis width of 500 mV is ________.
Q.14 In the figure shown, the output is required to be = + ? . The gates G1
and G2 must be,
respectively,
(A) NOR, OR (B) OR, NAND
(C) NAND, OR (D) AND, NAND
Q.15 In an 8085 microprocessor, which one of the following instructions changes the content of the
accumulator?
(A) MOV B,M (B) PCHL (C) RNZ (D) SBI BEH
5 V
V
0
1 V
B A
1 k?
SW
1 k?
1 k?
1 k?
1 k?
+
?
+
?
R
2
= 20 k ?
R
1
v
out
v
in
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/15
Q.16 A mod-n counter using a synchronous binary up-counter with synchronous clear input is shown in
the figure. The value of n is _______.
Q.17 Let the signal ( ) = 0 outside the interval [
,
], where and are finite. Furthermore,
| ( )| < ? . The region of convergence (RoC) of the signal?s bilateral Laplace transform ( ) is
(A) a parallel strip containing the ? axis
(B) a parallel strip not containing the ? axis
(C) the entire -plane
(D) a half plane containing the ? axis
Q.18
Two causal discrete-time signals [] x n and [] y n are related as
0
[] [ ]
n
m
yn x m
=
=
?
.
If the z-transform of y[n] is
()
, the value of [2] x is _______.
Q.19 By performing cascading and/or summing/differencing operations using transfer function blocks
1
() Gs and
2
() Gs , one CANNOT realize a transfer function of the form
(A)
12
() () GsG s
(B)
1
2
()
()
Gs
Gs
(C)
12
1
1
() ()
()
Gs G s
Gs
??
+
??
??
(D)
12
1
1
() ()
()
Gs G s
Gs
??
?
??
??
Q
A
CLEAR
CLK
4-Bit Binary
Counter
Q
B
Q
C
Q
D
Q
A
Q
B
Q
C
Q
D
CLOCK
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/15
Q.20
For the signal flow graph shown in the figure, the value of
()
()
Cs
R s
is
(A)
12 3 4
12134 2 233123412
1
GG G G
GG H GG H GG H GGGG H H ?? ? +
(B)
12 3 4
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
GG G G
GG H GG H GG H GGGG H H ++ + +
(C)
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
1 GG H GG H GG H GGGG H H ++ + +
(D)
12134 2 233123412
1
1 GG H GG H GG H GGGG H H ?? ? +
Q.21
A unity negative feedback system has an open-loop transfer function ( ) =
( +10 )
. The gain
for the system to have a damping ratio of 0.25 is ________.
Q.22 A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal
utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8
dB, the number of levels in the quantizer is _______.
Q.23
The signal cos 10
4
t
?
?
??
+
??
??
is ideally sampled at a sampling frequency of 15 Hz. The sampled
signal is passed through a filter with impulse response
sin( )
cos 40 .
2
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
The filter
output is
(A)
15
cos 40
24
t
?
?
??
?
??
??
(B)
15 sin( )
cos 10
24
t
t
t
??
?
?
??? ?
+
??? ?
??? ?
(C)
15
cos 10
24
t
?
?
??
?
??
??
(D)
15 sin( )
cos 40
22
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
-H
3
R(s)
1
X
1
X
2
X
3
X
4
X
5
C(s)
-H
1
-H
2
G
1
G
2
G
3
G
4
1
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/15
Q.24 In a source free region in vacuum, if the electrostatic potential = 2 + + , the value
of constant must be _______.
Q.25 The electric field of a uniform plane electromagnetic wave is
= + 4 e x p [ ( 2 ? 1 0
? 0.2 ) ] .
The polarization of the wave is
(A) right handed circular (B) right handed elliptical
(C) left handed circular (D) left handed elliptical
Q. 26 ? Q. 55 carry two marks each.
Q.26
Consider the differential equation 10 0.2
dx
x
dt
=? with initial condition (0) 1 x = . The response
() x t for 0 t > is
(A)
0.2
2
t
e
?
? (B)
0.2
2
t
e ? (C)
0.2
50 49
t
e
?
? (D)
0.2
50 49
t
e ?
Q.27
The value of the integral 12
sin(4 )
cos(2 )
4
?
?
?
t
tdt
t
is ___________.
Q.28 If denotes the counterclockwise unit circle, the value of the contour integral
1
2
{ }
is _______.
Q.29
Let the random variable X represent the number of times a fair coin needs to be tossed till two
consecutive heads appear for the first time. The expectation of X is _______.
Q.30 An LC
tank circuit consists of an ideal capacitor C
connected in parallel with a coil of inductance
L having an internal resistance R . The resonant frequency of the tank circuit is
(A)
1
2 LC ?
(B)
2
1
1
2
C
R
L LC ?
?
(C)
2
1
1
2
L
RC LC ?
?
(D)
2
1
1
2
C
R
L LC ?
??
?
??
??
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/15
Q.31 In the circuit shown, the Norton equivalent resistance (in ? ) across terminals a-b is _______.
+
-
4 ?
2?
2? 4?
?
a
b
Q.32 In the circuit shown, the initial voltages across the capacitors C
1
and C
2
are 1 V and 3 V,
respectively. The switch is closed at time = 0 . The total energy dissipated (in Joules) in the
resistor R until steady state is reached, is __________.
Q.33 A dc voltage of 10 V is applied across an n-type silicon bar having a rectangular cross-section and a
length of 1 cm as shown in figure. The donor doping concentration N
D
and the mobility of electrons
n
? are 10
16
cm
-3
and 1000 cm
2
V
-1
s
-1
, respectively. The average time (in ?s) taken by the electrons
to move from one end of the bar to other end is ________.
Q.34 In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer thickness
is 100 nm. The permittivities of the semiconductor and the oxide layer are ?
s
and ?
ox
respectively.
Assuming ?
s
/?
ox
= 3, the ratio of the maximum capacitance to the minimum capacitance of this
MOS capacitor is ________.
1 cm
10 V
n-Si
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/15
Q.35
The energy band diagram and the electron density profile n ( x ) in a semiconductor are shown in
the figures. Assume that n ( x ) =10
cm
-3
, with = 0.1 V /cm and x expressed in cm.
Given
= 0 .026 V, =36 cm
s
, and
=
. The electron current density (in A/cm
) at
x= 0 is
(A) ?4.4 ? 1 0
(B) ?2.2 ? 1 0
(C) 0 (D) 2.2 ? 1 0
Q.36 A function of Boolean variables X, Y and Z is expressed in terms of the min-terms as
F(X, Y, Z) = ? (1, 2, 5, 6, 7)
Which one of the product of sums given below is equal to the function F(X, Y, Z)?
(A) ) ( ) ( ) ( Z Y X Z Y X Z Y X + + ? + + ? + +
(B) ) ( ) ( ) ( Z Y X Z Y X Z Y X + + ? + + ? + +
(C) ) ( ) ( ) ( ) ( ) ( Z Y X Z Y X Z Y X Z Y X Z Y X + + ? + + ? + + ? + + ? + +
(D) ) ( ) ( ) ( ) ( ) ( Z Y X Z Y X Z Y X Z Y X Z Y X + + ? + + ? + + ? + + ? + +
Q.37 The figure shows a binary counter with synchronous clear input. With the decoding logic shown,
the counter works as a
Binary
Counter
Q
0
CLR
CLK
Q
1
Q
2
Q
3
(A) mod-2 counter (B) mod-4 counter (C) mod-5 counter (D) mod-6 counter
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/15
Q. 1 ? Q. 25 carry one mark each.
Q.1
The bilateral Laplace transform of a function
1 if
()
0 otherwise
at b
ft
?? ?
=
?
?
is
(A)
ab
s
?
(B)
()
s
ea b
s
?
(C)
as bs
ee
s
??
?
(D)
() s ab
e
s
?
Q.2 The value of for which all the eigen-values of the matrix given below are real is
10 5 + 4
20 2
42 ?10
(A) 5+ j (B) 5? (C) 1?5 (D) 1+5
Q.3
Let ( ) =
. If ( ) = ( ) for all ?
, = 2, = 4 a nd = 5, then should be
equal to _______.
Q.4
The general solution of the differential equation
1cos2
1cos2
dy y
dx x
+
=
?
is
(A) tan cot yxc ?= ( c is a constant) (B) tan cot x yc ?= ( c is a constant)
(C) tan cot yxc += ( c is a constant) (D) tan cot x yc += ( c is a constant)
Q.5 The magnitude and phase of the complex Fourier series coefficients of a periodic signal () are
shown in the figure. Choose the correct statement from the four choices given. Notation: is the
set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary
numbers.
(A) ( ) ?
(B) ( ) ?
(C) ( ) ?( ?)
(D) the information given is not sufficient to draw any conclusion about ( )
01
1
k
2 3 -3 -2 -1
|a
k
|
2
3
2
3
-5 4 -4
k
-4 -5 -3 -2 -1
0
1 23 4
? ?
a
k
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/15
Q.6 The voltage ( ) across the capacitor (in Volts) in the network shown is ______ .
Q.7 In the circuit shown, the average value of the voltage V
ab
(in Volts) in steady state condition is
________.
Q.8 The 2-port admittance matrix of the circuit shown is given by
(A) 0.3 0 .2
0.2 0 .3
(B) 15 5
515
(C) 3.3 3 5
53.33
(D) 0.3 0 .4
0.4 0 .3
Q.9 An n-type silicon sample is uniformly illuminated with light which generates 10
20
electron-hole
pairs per cm
3
per second. The minority carrier lifetime in the sample is 1 ?s. In the steady state, the
hole concentration in the sample is approximately 10
x
, where x is an integer. The value of x is ___.
5? sin(5000t)
1 k? 2 k? 1 ?F
1 mH
5 V
a b
+
V
ab
80 V 40 V
~
100 V,
50 Hz
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/15
Q.10 A piece of silicon is doped uniformly with phosphorous with a doping concentration of
10
16
/cm
3
. The expected value of mobility versus doping concentration for silicon assuming full
dopant ionization is shown below. The charge of an electron is 1.6 ?10
-19
C. The conductivity
(in
1
S cm
?
) of the silicon sample at 300
K is _______.
Q.11 If the circuit shown has to function as a clamping circuit, then which one of the following
conditions should be satisfied for the sinusoidal signal of period T ?
(A) RC << T (B) RC = 0.35 T (C) RC ? T (D) RC >> T
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/15
Q.12 In the circuit shown, V
0
= V
0A
for switch SW in position A and V
0
= V
0B
for SW in position B.
Assume that the opamp is ideal. The value of
0
0
B
A
V
V
is ___________.
Q.13 In the bistable circuit shown, the ideal opamp has saturation levels of ? 5 V. The value of R
1
(in
k ?) that gives a hysteresis width of 500 mV is ________.
Q.14 In the figure shown, the output is required to be = + ? . The gates G1
and G2 must be,
respectively,
(A) NOR, OR (B) OR, NAND
(C) NAND, OR (D) AND, NAND
Q.15 In an 8085 microprocessor, which one of the following instructions changes the content of the
accumulator?
(A) MOV B,M (B) PCHL (C) RNZ (D) SBI BEH
5 V
V
0
1 V
B A
1 k?
SW
1 k?
1 k?
1 k?
1 k?
+
?
+
?
R
2
= 20 k ?
R
1
v
out
v
in
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/15
Q.16 A mod-n counter using a synchronous binary up-counter with synchronous clear input is shown in
the figure. The value of n is _______.
Q.17 Let the signal ( ) = 0 outside the interval [
,
], where and are finite. Furthermore,
| ( )| < ? . The region of convergence (RoC) of the signal?s bilateral Laplace transform ( ) is
(A) a parallel strip containing the ? axis
(B) a parallel strip not containing the ? axis
(C) the entire -plane
(D) a half plane containing the ? axis
Q.18
Two causal discrete-time signals [] x n and [] y n are related as
0
[] [ ]
n
m
yn x m
=
=
?
.
If the z-transform of y[n] is
()
, the value of [2] x is _______.
Q.19 By performing cascading and/or summing/differencing operations using transfer function blocks
1
() Gs and
2
() Gs , one CANNOT realize a transfer function of the form
(A)
12
() () GsG s
(B)
1
2
()
()
Gs
Gs
(C)
12
1
1
() ()
()
Gs G s
Gs
??
+
??
??
(D)
12
1
1
() ()
()
Gs G s
Gs
??
?
??
??
Q
A
CLEAR
CLK
4-Bit Binary
Counter
Q
B
Q
C
Q
D
Q
A
Q
B
Q
C
Q
D
CLOCK
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/15
Q.20
For the signal flow graph shown in the figure, the value of
()
()
Cs
R s
is
(A)
12 3 4
12134 2 233123412
1
GG G G
GG H GG H GG H GGGG H H ?? ? +
(B)
12 3 4
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
GG G G
GG H GG H GG H GGGG H H ++ + +
(C)
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
1 GG H GG H GG H GGGG H H ++ + +
(D)
12134 2 233123412
1
1 GG H GG H GG H GGGG H H ?? ? +
Q.21
A unity negative feedback system has an open-loop transfer function ( ) =
( +10 )
. The gain
for the system to have a damping ratio of 0.25 is ________.
Q.22 A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal
utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8
dB, the number of levels in the quantizer is _______.
Q.23
The signal cos 10
4
t
?
?
??
+
??
??
is ideally sampled at a sampling frequency of 15 Hz. The sampled
signal is passed through a filter with impulse response
sin( )
cos 40 .
2
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
The filter
output is
(A)
15
cos 40
24
t
?
?
??
?
??
??
(B)
15 sin( )
cos 10
24
t
t
t
??
?
?
??? ?
+
??? ?
??? ?
(C)
15
cos 10
24
t
?
?
??
?
??
??
(D)
15 sin( )
cos 40
22
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
-H
3
R(s)
1
X
1
X
2
X
3
X
4
X
5
C(s)
-H
1
-H
2
G
1
G
2
G
3
G
4
1
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/15
Q.24 In a source free region in vacuum, if the electrostatic potential = 2 + + , the value
of constant must be _______.
Q.25 The electric field of a uniform plane electromagnetic wave is
= + 4 e x p [ ( 2 ? 1 0
? 0.2 ) ] .
The polarization of the wave is
(A) right handed circular (B) right handed elliptical
(C) left handed circular (D) left handed elliptical
Q. 26 ? Q. 55 carry two marks each.
Q.26
Consider the differential equation 10 0.2
dx
x
dt
=? with initial condition (0) 1 x = . The response
() x t for 0 t > is
(A)
0.2
2
t
e
?
? (B)
0.2
2
t
e ? (C)
0.2
50 49
t
e
?
? (D)
0.2
50 49
t
e ?
Q.27
The value of the integral 12
sin(4 )
cos(2 )
4
?
?
?
t
tdt
t
is ___________.
Q.28 If denotes the counterclockwise unit circle, the value of the contour integral
1
2
{ }
is _______.
Q.29
Let the random variable X represent the number of times a fair coin needs to be tossed till two
consecutive heads appear for the first time. The expectation of X is _______.
Q.30 An LC
tank circuit consists of an ideal capacitor C
connected in parallel with a coil of inductance
L having an internal resistance R . The resonant frequency of the tank circuit is
(A)
1
2 LC ?
(B)
2
1
1
2
C
R
L LC ?
?
(C)
2
1
1
2
L
RC LC ?
?
(D)
2
1
1
2
C
R
L LC ?
??
?
??
??
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/15
Q.31 In the circuit shown, the Norton equivalent resistance (in ? ) across terminals a-b is _______.
+
-
4 ?
2?
2? 4?
?
a
b
Q.32 In the circuit shown, the initial voltages across the capacitors C
1
and C
2
are 1 V and 3 V,
respectively. The switch is closed at time = 0 . The total energy dissipated (in Joules) in the
resistor R until steady state is reached, is __________.
Q.33 A dc voltage of 10 V is applied across an n-type silicon bar having a rectangular cross-section and a
length of 1 cm as shown in figure. The donor doping concentration N
D
and the mobility of electrons
n
? are 10
16
cm
-3
and 1000 cm
2
V
-1
s
-1
, respectively. The average time (in ?s) taken by the electrons
to move from one end of the bar to other end is ________.
Q.34 In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer thickness
is 100 nm. The permittivities of the semiconductor and the oxide layer are ?
s
and ?
ox
respectively.
Assuming ?
s
/?
ox
= 3, the ratio of the maximum capacitance to the minimum capacitance of this
MOS capacitor is ________.
1 cm
10 V
n-Si
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/15
Q.35
The energy band diagram and the electron density profile n ( x ) in a semiconductor are shown in
the figures. Assume that n ( x ) =10
cm
-3
, with = 0.1 V /cm and x expressed in cm.
Given
= 0 .026 V, =36 cm
s
, and
=
. The electron current density (in A/cm
) at
x= 0 is
(A) ?4.4 ? 1 0
(B) ?2.2 ? 1 0
(C) 0 (D) 2.2 ? 1 0
Q.36 A function of Boolean variables X, Y and Z is expressed in terms of the min-terms as
F(X, Y, Z) = ? (1, 2, 5, 6, 7)
Which one of the product of sums given below is equal to the function F(X, Y, Z)?
(A) ) ( ) ( ) ( Z Y X Z Y X Z Y X + + ? + + ? + +
(B) ) ( ) ( ) ( Z Y X Z Y X Z Y X + + ? + + ? + +
(C) ) ( ) ( ) ( ) ( ) ( Z Y X Z Y X Z Y X Z Y X Z Y X + + ? + + ? + + ? + + ? + +
(D) ) ( ) ( ) ( ) ( ) ( Z Y X Z Y X Z Y X Z Y X Z Y X + + ? + + ? + + ? + + ? + +
Q.37 The figure shows a binary counter with synchronous clear input. With the decoding logic shown,
the counter works as a
Binary
Counter
Q
0
CLR
CLK
Q
1
Q
2
Q
3
(A) mod-2 counter (B) mod-4 counter (C) mod-5 counter (D) mod-6 counter
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 10/15
Q.38 A 1-to-8 demultiplexer with data input D
in
, address inputs S
0
, S
1
, S
2
(with S
0
as the LSB) and
Y
0
t o Y
7
as the eight demultiplexed outputs, is to be designed using two 2-to-4 decoders (with
enable input and address inputs A
0
and A
1
) as shown in the figure. D
in
, S
0
, S
1
and S
2
are to be
connected to P, Q, R and S, but not necessarily in this order. The respective input connections to P,
Q, R, and S terminals should be
(A) S
2
, D
in
, S
0
, S
1
(B) S
1
, D
in
, S
0
, S
2
(C) D
in
, S
0
, S
1
, S
2
(D) D
in
, S
2
, S
0
, S
1
Q.39 The diode in the circuit given below has
=0.7 but is ideal otherwise. The current (in mA) in
the 4 k ? resistor is _______.
Q.40 Assuming that the opamp in the circuit shown below is ideal, the output voltage (in volts)
is________.
1k?
3k?
4k? 6k?
2k?
1mA
D
2k?
12V
-12V
V
O
1V
1k?
1Y
0 1E
1A
0
1A
1
1Y
1
1Y
2
1Y
3
2-to-4
Decoder
2Y
0 2E
2A
0
2A
1
2Y
1
2Y
2
2Y
3
2-to-4
Decoder
P
Q
R
S
Y
0
Y
1
Y
2
Y
3
Y
4
Y
5
Y
6
Y
7
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/15
Q. 1 ? Q. 25 carry one mark each.
Q.1
The bilateral Laplace transform of a function
1 if
()
0 otherwise
at b
ft
?? ?
=
?
?
is
(A)
ab
s
?
(B)
()
s
ea b
s
?
(C)
as bs
ee
s
??
?
(D)
() s ab
e
s
?
Q.2 The value of for which all the eigen-values of the matrix given below are real is
10 5 + 4
20 2
42 ?10
(A) 5+ j (B) 5? (C) 1?5 (D) 1+5
Q.3
Let ( ) =
. If ( ) = ( ) for all ?
, = 2, = 4 a nd = 5, then should be
equal to _______.
Q.4
The general solution of the differential equation
1cos2
1cos2
dy y
dx x
+
=
?
is
(A) tan cot yxc ?= ( c is a constant) (B) tan cot x yc ?= ( c is a constant)
(C) tan cot yxc += ( c is a constant) (D) tan cot x yc += ( c is a constant)
Q.5 The magnitude and phase of the complex Fourier series coefficients of a periodic signal () are
shown in the figure. Choose the correct statement from the four choices given. Notation: is the
set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary
numbers.
(A) ( ) ?
(B) ( ) ?
(C) ( ) ?( ?)
(D) the information given is not sufficient to draw any conclusion about ( )
01
1
k
2 3 -3 -2 -1
|a
k
|
2
3
2
3
-5 4 -4
k
-4 -5 -3 -2 -1
0
1 23 4
? ?
a
k
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/15
Q.6 The voltage ( ) across the capacitor (in Volts) in the network shown is ______ .
Q.7 In the circuit shown, the average value of the voltage V
ab
(in Volts) in steady state condition is
________.
Q.8 The 2-port admittance matrix of the circuit shown is given by
(A) 0.3 0 .2
0.2 0 .3
(B) 15 5
515
(C) 3.3 3 5
53.33
(D) 0.3 0 .4
0.4 0 .3
Q.9 An n-type silicon sample is uniformly illuminated with light which generates 10
20
electron-hole
pairs per cm
3
per second. The minority carrier lifetime in the sample is 1 ?s. In the steady state, the
hole concentration in the sample is approximately 10
x
, where x is an integer. The value of x is ___.
5? sin(5000t)
1 k? 2 k? 1 ?F
1 mH
5 V
a b
+
V
ab
80 V 40 V
~
100 V,
50 Hz
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/15
Q.10 A piece of silicon is doped uniformly with phosphorous with a doping concentration of
10
16
/cm
3
. The expected value of mobility versus doping concentration for silicon assuming full
dopant ionization is shown below. The charge of an electron is 1.6 ?10
-19
C. The conductivity
(in
1
S cm
?
) of the silicon sample at 300
K is _______.
Q.11 If the circuit shown has to function as a clamping circuit, then which one of the following
conditions should be satisfied for the sinusoidal signal of period T ?
(A) RC << T (B) RC = 0.35 T (C) RC ? T (D) RC >> T
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/15
Q.12 In the circuit shown, V
0
= V
0A
for switch SW in position A and V
0
= V
0B
for SW in position B.
Assume that the opamp is ideal. The value of
0
0
B
A
V
V
is ___________.
Q.13 In the bistable circuit shown, the ideal opamp has saturation levels of ? 5 V. The value of R
1
(in
k ?) that gives a hysteresis width of 500 mV is ________.
Q.14 In the figure shown, the output is required to be = + ? . The gates G1
and G2 must be,
respectively,
(A) NOR, OR (B) OR, NAND
(C) NAND, OR (D) AND, NAND
Q.15 In an 8085 microprocessor, which one of the following instructions changes the content of the
accumulator?
(A) MOV B,M (B) PCHL (C) RNZ (D) SBI BEH
5 V
V
0
1 V
B A
1 k?
SW
1 k?
1 k?
1 k?
1 k?
+
?
+
?
R
2
= 20 k ?
R
1
v
out
v
in
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/15
Q.16 A mod-n counter using a synchronous binary up-counter with synchronous clear input is shown in
the figure. The value of n is _______.
Q.17 Let the signal ( ) = 0 outside the interval [
,
], where and are finite. Furthermore,
| ( )| < ? . The region of convergence (RoC) of the signal?s bilateral Laplace transform ( ) is
(A) a parallel strip containing the ? axis
(B) a parallel strip not containing the ? axis
(C) the entire -plane
(D) a half plane containing the ? axis
Q.18
Two causal discrete-time signals [] x n and [] y n are related as
0
[] [ ]
n
m
yn x m
=
=
?
.
If the z-transform of y[n] is
()
, the value of [2] x is _______.
Q.19 By performing cascading and/or summing/differencing operations using transfer function blocks
1
() Gs and
2
() Gs , one CANNOT realize a transfer function of the form
(A)
12
() () GsG s
(B)
1
2
()
()
Gs
Gs
(C)
12
1
1
() ()
()
Gs G s
Gs
??
+
??
??
(D)
12
1
1
() ()
()
Gs G s
Gs
??
?
??
??
Q
A
CLEAR
CLK
4-Bit Binary
Counter
Q
B
Q
C
Q
D
Q
A
Q
B
Q
C
Q
D
CLOCK
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/15
Q.20
For the signal flow graph shown in the figure, the value of
()
()
Cs
R s
is
(A)
12 3 4
12134 2 233123412
1
GG G G
GG H GG H GG H GGGG H H ?? ? +
(B)
12 3 4
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
GG G G
GG H GG H GG H GGGG H H ++ + +
(C)
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
1 GG H GG H GG H GGGG H H ++ + +
(D)
12134 2 233123412
1
1 GG H GG H GG H GGGG H H ?? ? +
Q.21
A unity negative feedback system has an open-loop transfer function ( ) =
( +10 )
. The gain
for the system to have a damping ratio of 0.25 is ________.
Q.22 A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal
utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8
dB, the number of levels in the quantizer is _______.
Q.23
The signal cos 10
4
t
?
?
??
+
??
??
is ideally sampled at a sampling frequency of 15 Hz. The sampled
signal is passed through a filter with impulse response
sin( )
cos 40 .
2
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
The filter
output is
(A)
15
cos 40
24
t
?
?
??
?
??
??
(B)
15 sin( )
cos 10
24
t
t
t
??
?
?
??? ?
+
??? ?
??? ?
(C)
15
cos 10
24
t
?
?
??
?
??
??
(D)
15 sin( )
cos 40
22
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
-H
3
R(s)
1
X
1
X
2
X
3
X
4
X
5
C(s)
-H
1
-H
2
G
1
G
2
G
3
G
4
1
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/15
Q.24 In a source free region in vacuum, if the electrostatic potential = 2 + + , the value
of constant must be _______.
Q.25 The electric field of a uniform plane electromagnetic wave is
= + 4 e x p [ ( 2 ? 1 0
? 0.2 ) ] .
The polarization of the wave is
(A) right handed circular (B) right handed elliptical
(C) left handed circular (D) left handed elliptical
Q. 26 ? Q. 55 carry two marks each.
Q.26
Consider the differential equation 10 0.2
dx
x
dt
=? with initial condition (0) 1 x = . The response
() x t for 0 t > is
(A)
0.2
2
t
e
?
? (B)
0.2
2
t
e ? (C)
0.2
50 49
t
e
?
? (D)
0.2
50 49
t
e ?
Q.27
The value of the integral 12
sin(4 )
cos(2 )
4
?
?
?
t
tdt
t
is ___________.
Q.28 If denotes the counterclockwise unit circle, the value of the contour integral
1
2
{ }
is _______.
Q.29
Let the random variable X represent the number of times a fair coin needs to be tossed till two
consecutive heads appear for the first time. The expectation of X is _______.
Q.30 An LC
tank circuit consists of an ideal capacitor C
connected in parallel with a coil of inductance
L having an internal resistance R . The resonant frequency of the tank circuit is
(A)
1
2 LC ?
(B)
2
1
1
2
C
R
L LC ?
?
(C)
2
1
1
2
L
RC LC ?
?
(D)
2
1
1
2
C
R
L LC ?
??
?
??
??
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/15
Q.31 In the circuit shown, the Norton equivalent resistance (in ? ) across terminals a-b is _______.
+
-
4 ?
2?
2? 4?
?
a
b
Q.32 In the circuit shown, the initial voltages across the capacitors C
1
and C
2
are 1 V and 3 V,
respectively. The switch is closed at time = 0 . The total energy dissipated (in Joules) in the
resistor R until steady state is reached, is __________.
Q.33 A dc voltage of 10 V is applied across an n-type silicon bar having a rectangular cross-section and a
length of 1 cm as shown in figure. The donor doping concentration N
D
and the mobility of electrons
n
? are 10
16
cm
-3
and 1000 cm
2
V
-1
s
-1
, respectively. The average time (in ?s) taken by the electrons
to move from one end of the bar to other end is ________.
Q.34 In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer thickness
is 100 nm. The permittivities of the semiconductor and the oxide layer are ?
s
and ?
ox
respectively.
Assuming ?
s
/?
ox
= 3, the ratio of the maximum capacitance to the minimum capacitance of this
MOS capacitor is ________.
1 cm
10 V
n-Si
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/15
Q.35
The energy band diagram and the electron density profile n ( x ) in a semiconductor are shown in
the figures. Assume that n ( x ) =10
cm
-3
, with = 0.1 V /cm and x expressed in cm.
Given
= 0 .026 V, =36 cm
s
, and
=
. The electron current density (in A/cm
) at
x= 0 is
(A) ?4.4 ? 1 0
(B) ?2.2 ? 1 0
(C) 0 (D) 2.2 ? 1 0
Q.36 A function of Boolean variables X, Y and Z is expressed in terms of the min-terms as
F(X, Y, Z) = ? (1, 2, 5, 6, 7)
Which one of the product of sums given below is equal to the function F(X, Y, Z)?
(A) ) ( ) ( ) ( Z Y X Z Y X Z Y X + + ? + + ? + +
(B) ) ( ) ( ) ( Z Y X Z Y X Z Y X + + ? + + ? + +
(C) ) ( ) ( ) ( ) ( ) ( Z Y X Z Y X Z Y X Z Y X Z Y X + + ? + + ? + + ? + + ? + +
(D) ) ( ) ( ) ( ) ( ) ( Z Y X Z Y X Z Y X Z Y X Z Y X + + ? + + ? + + ? + + ? + +
Q.37 The figure shows a binary counter with synchronous clear input. With the decoding logic shown,
the counter works as a
Binary
Counter
Q
0
CLR
CLK
Q
1
Q
2
Q
3
(A) mod-2 counter (B) mod-4 counter (C) mod-5 counter (D) mod-6 counter
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 10/15
Q.38 A 1-to-8 demultiplexer with data input D
in
, address inputs S
0
, S
1
, S
2
(with S
0
as the LSB) and
Y
0
t o Y
7
as the eight demultiplexed outputs, is to be designed using two 2-to-4 decoders (with
enable input and address inputs A
0
and A
1
) as shown in the figure. D
in
, S
0
, S
1
and S
2
are to be
connected to P, Q, R and S, but not necessarily in this order. The respective input connections to P,
Q, R, and S terminals should be
(A) S
2
, D
in
, S
0
, S
1
(B) S
1
, D
in
, S
0
, S
2
(C) D
in
, S
0
, S
1
, S
2
(D) D
in
, S
2
, S
0
, S
1
Q.39 The diode in the circuit given below has
=0.7 but is ideal otherwise. The current (in mA) in
the 4 k ? resistor is _______.
Q.40 Assuming that the opamp in the circuit shown below is ideal, the output voltage (in volts)
is________.
1k?
3k?
4k? 6k?
2k?
1mA
D
2k?
12V
-12V
V
O
1V
1k?
1Y
0 1E
1A
0
1A
1
1Y
1
1Y
2
1Y
3
2-to-4
Decoder
2Y
0 2E
2A
0
2A
1
2Y
1
2Y
2
2Y
3
2-to-4
Decoder
P
Q
R
S
Y
0
Y
1
Y
2
Y
3
Y
4
Y
5
Y
6
Y
7
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 11/15
Q.41 For the voltage regulator circuit shown, the input voltage (V
in
) is 20 V ? 20% and the regulated
output voltage (V
out
) is 10 V. Assume the opamp to be ideal. For a load R
L
drawing 200 mA, the
maximum power dissipation in Q
1
(in Watts) is ________.
Q.42 In the ac equivalent circuit shown, the two BJTs are biased in active region and have identical
parameters with ? >>1. The open circuit small signal voltage gain is approximately _______.
Q.43 Input () x t and output () y t of an LTI system are related by the differential equation
() ( ) 6 ( ) ( ) y t y t ytxt ?? ? ?? = . If the system is neither causal nor stable, the impulse response () ht of
the system is
(A)
32
11
() ()
55
tt
eu t e u t
?
?+ ? (B)
32
11
() ()
55
tt
eu t e u t
?
??+ ?
(C)
32
11
() ()
55
tt
eu t e ut
?
?? (D)
32
11
() ()
55
tt
eu t e ut
?
???
V
out
Q
1
V
ref
R
2
= 10 k ?
R
1
R
L
V
in
+
?
4 V
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/15
Q. 1 ? Q. 25 carry one mark each.
Q.1
The bilateral Laplace transform of a function
1 if
()
0 otherwise
at b
ft
?? ?
=
?
?
is
(A)
ab
s
?
(B)
()
s
ea b
s
?
(C)
as bs
ee
s
??
?
(D)
() s ab
e
s
?
Q.2 The value of for which all the eigen-values of the matrix given below are real is
10 5 + 4
20 2
42 ?10
(A) 5+ j (B) 5? (C) 1?5 (D) 1+5
Q.3
Let ( ) =
. If ( ) = ( ) for all ?
, = 2, = 4 a nd = 5, then should be
equal to _______.
Q.4
The general solution of the differential equation
1cos2
1cos2
dy y
dx x
+
=
?
is
(A) tan cot yxc ?= ( c is a constant) (B) tan cot x yc ?= ( c is a constant)
(C) tan cot yxc += ( c is a constant) (D) tan cot x yc += ( c is a constant)
Q.5 The magnitude and phase of the complex Fourier series coefficients of a periodic signal () are
shown in the figure. Choose the correct statement from the four choices given. Notation: is the
set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary
numbers.
(A) ( ) ?
(B) ( ) ?
(C) ( ) ?( ?)
(D) the information given is not sufficient to draw any conclusion about ( )
01
1
k
2 3 -3 -2 -1
|a
k
|
2
3
2
3
-5 4 -4
k
-4 -5 -3 -2 -1
0
1 23 4
? ?
a
k
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/15
Q.6 The voltage ( ) across the capacitor (in Volts) in the network shown is ______ .
Q.7 In the circuit shown, the average value of the voltage V
ab
(in Volts) in steady state condition is
________.
Q.8 The 2-port admittance matrix of the circuit shown is given by
(A) 0.3 0 .2
0.2 0 .3
(B) 15 5
515
(C) 3.3 3 5
53.33
(D) 0.3 0 .4
0.4 0 .3
Q.9 An n-type silicon sample is uniformly illuminated with light which generates 10
20
electron-hole
pairs per cm
3
per second. The minority carrier lifetime in the sample is 1 ?s. In the steady state, the
hole concentration in the sample is approximately 10
x
, where x is an integer. The value of x is ___.
5? sin(5000t)
1 k? 2 k? 1 ?F
1 mH
5 V
a b
+
V
ab
80 V 40 V
~
100 V,
50 Hz
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/15
Q.10 A piece of silicon is doped uniformly with phosphorous with a doping concentration of
10
16
/cm
3
. The expected value of mobility versus doping concentration for silicon assuming full
dopant ionization is shown below. The charge of an electron is 1.6 ?10
-19
C. The conductivity
(in
1
S cm
?
) of the silicon sample at 300
K is _______.
Q.11 If the circuit shown has to function as a clamping circuit, then which one of the following
conditions should be satisfied for the sinusoidal signal of period T ?
(A) RC << T (B) RC = 0.35 T (C) RC ? T (D) RC >> T
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/15
Q.12 In the circuit shown, V
0
= V
0A
for switch SW in position A and V
0
= V
0B
for SW in position B.
Assume that the opamp is ideal. The value of
0
0
B
A
V
V
is ___________.
Q.13 In the bistable circuit shown, the ideal opamp has saturation levels of ? 5 V. The value of R
1
(in
k ?) that gives a hysteresis width of 500 mV is ________.
Q.14 In the figure shown, the output is required to be = + ? . The gates G1
and G2 must be,
respectively,
(A) NOR, OR (B) OR, NAND
(C) NAND, OR (D) AND, NAND
Q.15 In an 8085 microprocessor, which one of the following instructions changes the content of the
accumulator?
(A) MOV B,M (B) PCHL (C) RNZ (D) SBI BEH
5 V
V
0
1 V
B A
1 k?
SW
1 k?
1 k?
1 k?
1 k?
+
?
+
?
R
2
= 20 k ?
R
1
v
out
v
in
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/15
Q.16 A mod-n counter using a synchronous binary up-counter with synchronous clear input is shown in
the figure. The value of n is _______.
Q.17 Let the signal ( ) = 0 outside the interval [
,
], where and are finite. Furthermore,
| ( )| < ? . The region of convergence (RoC) of the signal?s bilateral Laplace transform ( ) is
(A) a parallel strip containing the ? axis
(B) a parallel strip not containing the ? axis
(C) the entire -plane
(D) a half plane containing the ? axis
Q.18
Two causal discrete-time signals [] x n and [] y n are related as
0
[] [ ]
n
m
yn x m
=
=
?
.
If the z-transform of y[n] is
()
, the value of [2] x is _______.
Q.19 By performing cascading and/or summing/differencing operations using transfer function blocks
1
() Gs and
2
() Gs , one CANNOT realize a transfer function of the form
(A)
12
() () GsG s
(B)
1
2
()
()
Gs
Gs
(C)
12
1
1
() ()
()
Gs G s
Gs
??
+
??
??
(D)
12
1
1
() ()
()
Gs G s
Gs
??
?
??
??
Q
A
CLEAR
CLK
4-Bit Binary
Counter
Q
B
Q
C
Q
D
Q
A
Q
B
Q
C
Q
D
CLOCK
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/15
Q.20
For the signal flow graph shown in the figure, the value of
()
()
Cs
R s
is
(A)
12 3 4
12134 2 233123412
1
GG G G
GG H GG H GG H GGGG H H ?? ? +
(B)
12 3 4
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
GG G G
GG H GG H GG H GGGG H H ++ + +
(C)
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
1 GG H GG H GG H GGGG H H ++ + +
(D)
12134 2 233123412
1
1 GG H GG H GG H GGGG H H ?? ? +
Q.21
A unity negative feedback system has an open-loop transfer function ( ) =
( +10 )
. The gain
for the system to have a damping ratio of 0.25 is ________.
Q.22 A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal
utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8
dB, the number of levels in the quantizer is _______.
Q.23
The signal cos 10
4
t
?
?
??
+
??
??
is ideally sampled at a sampling frequency of 15 Hz. The sampled
signal is passed through a filter with impulse response
sin( )
cos 40 .
2
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
The filter
output is
(A)
15
cos 40
24
t
?
?
??
?
??
??
(B)
15 sin( )
cos 10
24
t
t
t
??
?
?
??? ?
+
??? ?
??? ?
(C)
15
cos 10
24
t
?
?
??
?
??
??
(D)
15 sin( )
cos 40
22
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
-H
3
R(s)
1
X
1
X
2
X
3
X
4
X
5
C(s)
-H
1
-H
2
G
1
G
2
G
3
G
4
1
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/15
Q.24 In a source free region in vacuum, if the electrostatic potential = 2 + + , the value
of constant must be _______.
Q.25 The electric field of a uniform plane electromagnetic wave is
= + 4 e x p [ ( 2 ? 1 0
? 0.2 ) ] .
The polarization of the wave is
(A) right handed circular (B) right handed elliptical
(C) left handed circular (D) left handed elliptical
Q. 26 ? Q. 55 carry two marks each.
Q.26
Consider the differential equation 10 0.2
dx
x
dt
=? with initial condition (0) 1 x = . The response
() x t for 0 t > is
(A)
0.2
2
t
e
?
? (B)
0.2
2
t
e ? (C)
0.2
50 49
t
e
?
? (D)
0.2
50 49
t
e ?
Q.27
The value of the integral 12
sin(4 )
cos(2 )
4
?
?
?
t
tdt
t
is ___________.
Q.28 If denotes the counterclockwise unit circle, the value of the contour integral
1
2
{ }
is _______.
Q.29
Let the random variable X represent the number of times a fair coin needs to be tossed till two
consecutive heads appear for the first time. The expectation of X is _______.
Q.30 An LC
tank circuit consists of an ideal capacitor C
connected in parallel with a coil of inductance
L having an internal resistance R . The resonant frequency of the tank circuit is
(A)
1
2 LC ?
(B)
2
1
1
2
C
R
L LC ?
?
(C)
2
1
1
2
L
RC LC ?
?
(D)
2
1
1
2
C
R
L LC ?
??
?
??
??
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/15
Q.31 In the circuit shown, the Norton equivalent resistance (in ? ) across terminals a-b is _______.
+
-
4 ?
2?
2? 4?
?
a
b
Q.32 In the circuit shown, the initial voltages across the capacitors C
1
and C
2
are 1 V and 3 V,
respectively. The switch is closed at time = 0 . The total energy dissipated (in Joules) in the
resistor R until steady state is reached, is __________.
Q.33 A dc voltage of 10 V is applied across an n-type silicon bar having a rectangular cross-section and a
length of 1 cm as shown in figure. The donor doping concentration N
D
and the mobility of electrons
n
? are 10
16
cm
-3
and 1000 cm
2
V
-1
s
-1
, respectively. The average time (in ?s) taken by the electrons
to move from one end of the bar to other end is ________.
Q.34 In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer thickness
is 100 nm. The permittivities of the semiconductor and the oxide layer are ?
s
and ?
ox
respectively.
Assuming ?
s
/?
ox
= 3, the ratio of the maximum capacitance to the minimum capacitance of this
MOS capacitor is ________.
1 cm
10 V
n-Si
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/15
Q.35
The energy band diagram and the electron density profile n ( x ) in a semiconductor are shown in
the figures. Assume that n ( x ) =10
cm
-3
, with = 0.1 V /cm and x expressed in cm.
Given
= 0 .026 V, =36 cm
s
, and
=
. The electron current density (in A/cm
) at
x= 0 is
(A) ?4.4 ? 1 0
(B) ?2.2 ? 1 0
(C) 0 (D) 2.2 ? 1 0
Q.36 A function of Boolean variables X, Y and Z is expressed in terms of the min-terms as
F(X, Y, Z) = ? (1, 2, 5, 6, 7)
Which one of the product of sums given below is equal to the function F(X, Y, Z)?
(A) ) ( ) ( ) ( Z Y X Z Y X Z Y X + + ? + + ? + +
(B) ) ( ) ( ) ( Z Y X Z Y X Z Y X + + ? + + ? + +
(C) ) ( ) ( ) ( ) ( ) ( Z Y X Z Y X Z Y X Z Y X Z Y X + + ? + + ? + + ? + + ? + +
(D) ) ( ) ( ) ( ) ( ) ( Z Y X Z Y X Z Y X Z Y X Z Y X + + ? + + ? + + ? + + ? + +
Q.37 The figure shows a binary counter with synchronous clear input. With the decoding logic shown,
the counter works as a
Binary
Counter
Q
0
CLR
CLK
Q
1
Q
2
Q
3
(A) mod-2 counter (B) mod-4 counter (C) mod-5 counter (D) mod-6 counter
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 10/15
Q.38 A 1-to-8 demultiplexer with data input D
in
, address inputs S
0
, S
1
, S
2
(with S
0
as the LSB) and
Y
0
t o Y
7
as the eight demultiplexed outputs, is to be designed using two 2-to-4 decoders (with
enable input and address inputs A
0
and A
1
) as shown in the figure. D
in
, S
0
, S
1
and S
2
are to be
connected to P, Q, R and S, but not necessarily in this order. The respective input connections to P,
Q, R, and S terminals should be
(A) S
2
, D
in
, S
0
, S
1
(B) S
1
, D
in
, S
0
, S
2
(C) D
in
, S
0
, S
1
, S
2
(D) D
in
, S
2
, S
0
, S
1
Q.39 The diode in the circuit given below has
=0.7 but is ideal otherwise. The current (in mA) in
the 4 k ? resistor is _______.
Q.40 Assuming that the opamp in the circuit shown below is ideal, the output voltage (in volts)
is________.
1k?
3k?
4k? 6k?
2k?
1mA
D
2k?
12V
-12V
V
O
1V
1k?
1Y
0 1E
1A
0
1A
1
1Y
1
1Y
2
1Y
3
2-to-4
Decoder
2Y
0 2E
2A
0
2A
1
2Y
1
2Y
2
2Y
3
2-to-4
Decoder
P
Q
R
S
Y
0
Y
1
Y
2
Y
3
Y
4
Y
5
Y
6
Y
7
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 11/15
Q.41 For the voltage regulator circuit shown, the input voltage (V
in
) is 20 V ? 20% and the regulated
output voltage (V
out
) is 10 V. Assume the opamp to be ideal. For a load R
L
drawing 200 mA, the
maximum power dissipation in Q
1
(in Watts) is ________.
Q.42 In the ac equivalent circuit shown, the two BJTs are biased in active region and have identical
parameters with ? >>1. The open circuit small signal voltage gain is approximately _______.
Q.43 Input () x t and output () y t of an LTI system are related by the differential equation
() ( ) 6 ( ) ( ) y t y t ytxt ?? ? ?? = . If the system is neither causal nor stable, the impulse response () ht of
the system is
(A)
32
11
() ()
55
tt
eu t e u t
?
?+ ? (B)
32
11
() ()
55
tt
eu t e u t
?
??+ ?
(C)
32
11
() ()
55
tt
eu t e ut
?
?? (D)
32
11
() ()
55
tt
eu t e ut
?
???
V
out
Q
1
V
ref
R
2
= 10 k ?
R
1
R
L
V
in
+
?
4 V
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 12/15
Q.44 Consider two real sequences with time-origin marked by the bold value,
[ ] = {, 2, 3 , 0} , [ ] = { , 3, 2, 1}
Let ( ) and ( ) be 4-point DFTs of [ ] and
[ ], respectively.
Another sequence [ ] is derived by taking 4-point inverse DFT of ( ) =
( ) ( ) .
The value of [2] is ______.
Q.45 Let ( ) = ( ) +(?) with ( ) =
( ) , where ( ) is unit step function. If the bilateral
Laplace transform of () x t is
()
2
16
16
Xs
s
=
?
{ } 4Re 4 s ?< < ;
then the value of ? is _______.
Q.46 The state variable representation of a system is given as
01
01
x x
??
=
??
?
??
& ; ( 0 ) = 1
0
[ ] 01 yx =
The response ( ) is
(A) sin( ) t
(B) 1
t
e ?
(C) 1cos() t ? (D) 0
Q.47 The output of a standard second-order system for a unit step input is given as
2
() 1 cos 3
6 3
t
yt e t
?
?
??
=? ?
??
??
. The transfer function of the system is
(A)
2
(2)( 3) ss ++
(B)
2
1
21 ss ++
(C)
2
3
23 ss ++
(D)
2
4
24 ss ++
Q.48 The transfer function of a mass-spring-damper system is given by
( ) =
1
+ +
The frequency response data for the system are given in the following table.
? in rad/s | ( )| in dB arg ( ( ) ) in deg
0.01 -18.5 -0.2
0.1 -18.5 -1.3
0.2 -18.4 -2.6
1 -16 -16.9
2 -11.4 -89.4
3 -21.5 -151
5 -32.8 -167
10 -45.3 -174.5
The unit step response of the system approaches a steady state value of ________ .
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/15
Q. 1 ? Q. 25 carry one mark each.
Q.1
The bilateral Laplace transform of a function
1 if
()
0 otherwise
at b
ft
?? ?
=
?
?
is
(A)
ab
s
?
(B)
()
s
ea b
s
?
(C)
as bs
ee
s
??
?
(D)
() s ab
e
s
?
Q.2 The value of for which all the eigen-values of the matrix given below are real is
10 5 + 4
20 2
42 ?10
(A) 5+ j (B) 5? (C) 1?5 (D) 1+5
Q.3
Let ( ) =
. If ( ) = ( ) for all ?
, = 2, = 4 a nd = 5, then should be
equal to _______.
Q.4
The general solution of the differential equation
1cos2
1cos2
dy y
dx x
+
=
?
is
(A) tan cot yxc ?= ( c is a constant) (B) tan cot x yc ?= ( c is a constant)
(C) tan cot yxc += ( c is a constant) (D) tan cot x yc += ( c is a constant)
Q.5 The magnitude and phase of the complex Fourier series coefficients of a periodic signal () are
shown in the figure. Choose the correct statement from the four choices given. Notation: is the
set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary
numbers.
(A) ( ) ?
(B) ( ) ?
(C) ( ) ?( ?)
(D) the information given is not sufficient to draw any conclusion about ( )
01
1
k
2 3 -3 -2 -1
|a
k
|
2
3
2
3
-5 4 -4
k
-4 -5 -3 -2 -1
0
1 23 4
? ?
a
k
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/15
Q.6 The voltage ( ) across the capacitor (in Volts) in the network shown is ______ .
Q.7 In the circuit shown, the average value of the voltage V
ab
(in Volts) in steady state condition is
________.
Q.8 The 2-port admittance matrix of the circuit shown is given by
(A) 0.3 0 .2
0.2 0 .3
(B) 15 5
515
(C) 3.3 3 5
53.33
(D) 0.3 0 .4
0.4 0 .3
Q.9 An n-type silicon sample is uniformly illuminated with light which generates 10
20
electron-hole
pairs per cm
3
per second. The minority carrier lifetime in the sample is 1 ?s. In the steady state, the
hole concentration in the sample is approximately 10
x
, where x is an integer. The value of x is ___.
5? sin(5000t)
1 k? 2 k? 1 ?F
1 mH
5 V
a b
+
V
ab
80 V 40 V
~
100 V,
50 Hz
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/15
Q.10 A piece of silicon is doped uniformly with phosphorous with a doping concentration of
10
16
/cm
3
. The expected value of mobility versus doping concentration for silicon assuming full
dopant ionization is shown below. The charge of an electron is 1.6 ?10
-19
C. The conductivity
(in
1
S cm
?
) of the silicon sample at 300
K is _______.
Q.11 If the circuit shown has to function as a clamping circuit, then which one of the following
conditions should be satisfied for the sinusoidal signal of period T ?
(A) RC << T (B) RC = 0.35 T (C) RC ? T (D) RC >> T
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/15
Q.12 In the circuit shown, V
0
= V
0A
for switch SW in position A and V
0
= V
0B
for SW in position B.
Assume that the opamp is ideal. The value of
0
0
B
A
V
V
is ___________.
Q.13 In the bistable circuit shown, the ideal opamp has saturation levels of ? 5 V. The value of R
1
(in
k ?) that gives a hysteresis width of 500 mV is ________.
Q.14 In the figure shown, the output is required to be = + ? . The gates G1
and G2 must be,
respectively,
(A) NOR, OR (B) OR, NAND
(C) NAND, OR (D) AND, NAND
Q.15 In an 8085 microprocessor, which one of the following instructions changes the content of the
accumulator?
(A) MOV B,M (B) PCHL (C) RNZ (D) SBI BEH
5 V
V
0
1 V
B A
1 k?
SW
1 k?
1 k?
1 k?
1 k?
+
?
+
?
R
2
= 20 k ?
R
1
v
out
v
in
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/15
Q.16 A mod-n counter using a synchronous binary up-counter with synchronous clear input is shown in
the figure. The value of n is _______.
Q.17 Let the signal ( ) = 0 outside the interval [
,
], where and are finite. Furthermore,
| ( )| < ? . The region of convergence (RoC) of the signal?s bilateral Laplace transform ( ) is
(A) a parallel strip containing the ? axis
(B) a parallel strip not containing the ? axis
(C) the entire -plane
(D) a half plane containing the ? axis
Q.18
Two causal discrete-time signals [] x n and [] y n are related as
0
[] [ ]
n
m
yn x m
=
=
?
.
If the z-transform of y[n] is
()
, the value of [2] x is _______.
Q.19 By performing cascading and/or summing/differencing operations using transfer function blocks
1
() Gs and
2
() Gs , one CANNOT realize a transfer function of the form
(A)
12
() () GsG s
(B)
1
2
()
()
Gs
Gs
(C)
12
1
1
() ()
()
Gs G s
Gs
??
+
??
??
(D)
12
1
1
() ()
()
Gs G s
Gs
??
?
??
??
Q
A
CLEAR
CLK
4-Bit Binary
Counter
Q
B
Q
C
Q
D
Q
A
Q
B
Q
C
Q
D
CLOCK
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/15
Q.20
For the signal flow graph shown in the figure, the value of
()
()
Cs
R s
is
(A)
12 3 4
12134 2 233123412
1
GG G G
GG H GG H GG H GGGG H H ?? ? +
(B)
12 3 4
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
GG G G
GG H GG H GG H GGGG H H ++ + +
(C)
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
1 GG H GG H GG H GGGG H H ++ + +
(D)
12134 2 233123412
1
1 GG H GG H GG H GGGG H H ?? ? +
Q.21
A unity negative feedback system has an open-loop transfer function ( ) =
( +10 )
. The gain
for the system to have a damping ratio of 0.25 is ________.
Q.22 A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal
utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8
dB, the number of levels in the quantizer is _______.
Q.23
The signal cos 10
4
t
?
?
??
+
??
??
is ideally sampled at a sampling frequency of 15 Hz. The sampled
signal is passed through a filter with impulse response
sin( )
cos 40 .
2
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
The filter
output is
(A)
15
cos 40
24
t
?
?
??
?
??
??
(B)
15 sin( )
cos 10
24
t
t
t
??
?
?
??? ?
+
??? ?
??? ?
(C)
15
cos 10
24
t
?
?
??
?
??
??
(D)
15 sin( )
cos 40
22
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
-H
3
R(s)
1
X
1
X
2
X
3
X
4
X
5
C(s)
-H
1
-H
2
G
1
G
2
G
3
G
4
1
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/15
Q.24 In a source free region in vacuum, if the electrostatic potential = 2 + + , the value
of constant must be _______.
Q.25 The electric field of a uniform plane electromagnetic wave is
= + 4 e x p [ ( 2 ? 1 0
? 0.2 ) ] .
The polarization of the wave is
(A) right handed circular (B) right handed elliptical
(C) left handed circular (D) left handed elliptical
Q. 26 ? Q. 55 carry two marks each.
Q.26
Consider the differential equation 10 0.2
dx
x
dt
=? with initial condition (0) 1 x = . The response
() x t for 0 t > is
(A)
0.2
2
t
e
?
? (B)
0.2
2
t
e ? (C)
0.2
50 49
t
e
?
? (D)
0.2
50 49
t
e ?
Q.27
The value of the integral 12
sin(4 )
cos(2 )
4
?
?
?
t
tdt
t
is ___________.
Q.28 If denotes the counterclockwise unit circle, the value of the contour integral
1
2
{ }
is _______.
Q.29
Let the random variable X represent the number of times a fair coin needs to be tossed till two
consecutive heads appear for the first time. The expectation of X is _______.
Q.30 An LC
tank circuit consists of an ideal capacitor C
connected in parallel with a coil of inductance
L having an internal resistance R . The resonant frequency of the tank circuit is
(A)
1
2 LC ?
(B)
2
1
1
2
C
R
L LC ?
?
(C)
2
1
1
2
L
RC LC ?
?
(D)
2
1
1
2
C
R
L LC ?
??
?
??
??
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/15
Q.31 In the circuit shown, the Norton equivalent resistance (in ? ) across terminals a-b is _______.
+
-
4 ?
2?
2? 4?
?
a
b
Q.32 In the circuit shown, the initial voltages across the capacitors C
1
and C
2
are 1 V and 3 V,
respectively. The switch is closed at time = 0 . The total energy dissipated (in Joules) in the
resistor R until steady state is reached, is __________.
Q.33 A dc voltage of 10 V is applied across an n-type silicon bar having a rectangular cross-section and a
length of 1 cm as shown in figure. The donor doping concentration N
D
and the mobility of electrons
n
? are 10
16
cm
-3
and 1000 cm
2
V
-1
s
-1
, respectively. The average time (in ?s) taken by the electrons
to move from one end of the bar to other end is ________.
Q.34 In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer thickness
is 100 nm. The permittivities of the semiconductor and the oxide layer are ?
s
and ?
ox
respectively.
Assuming ?
s
/?
ox
= 3, the ratio of the maximum capacitance to the minimum capacitance of this
MOS capacitor is ________.
1 cm
10 V
n-Si
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/15
Q.35
The energy band diagram and the electron density profile n ( x ) in a semiconductor are shown in
the figures. Assume that n ( x ) =10
cm
-3
, with = 0.1 V /cm and x expressed in cm.
Given
= 0 .026 V, =36 cm
s
, and
=
. The electron current density (in A/cm
) at
x= 0 is
(A) ?4.4 ? 1 0
(B) ?2.2 ? 1 0
(C) 0 (D) 2.2 ? 1 0
Q.36 A function of Boolean variables X, Y and Z is expressed in terms of the min-terms as
F(X, Y, Z) = ? (1, 2, 5, 6, 7)
Which one of the product of sums given below is equal to the function F(X, Y, Z)?
(A) ) ( ) ( ) ( Z Y X Z Y X Z Y X + + ? + + ? + +
(B) ) ( ) ( ) ( Z Y X Z Y X Z Y X + + ? + + ? + +
(C) ) ( ) ( ) ( ) ( ) ( Z Y X Z Y X Z Y X Z Y X Z Y X + + ? + + ? + + ? + + ? + +
(D) ) ( ) ( ) ( ) ( ) ( Z Y X Z Y X Z Y X Z Y X Z Y X + + ? + + ? + + ? + + ? + +
Q.37 The figure shows a binary counter with synchronous clear input. With the decoding logic shown,
the counter works as a
Binary
Counter
Q
0
CLR
CLK
Q
1
Q
2
Q
3
(A) mod-2 counter (B) mod-4 counter (C) mod-5 counter (D) mod-6 counter
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 10/15
Q.38 A 1-to-8 demultiplexer with data input D
in
, address inputs S
0
, S
1
, S
2
(with S
0
as the LSB) and
Y
0
t o Y
7
as the eight demultiplexed outputs, is to be designed using two 2-to-4 decoders (with
enable input and address inputs A
0
and A
1
) as shown in the figure. D
in
, S
0
, S
1
and S
2
are to be
connected to P, Q, R and S, but not necessarily in this order. The respective input connections to P,
Q, R, and S terminals should be
(A) S
2
, D
in
, S
0
, S
1
(B) S
1
, D
in
, S
0
, S
2
(C) D
in
, S
0
, S
1
, S
2
(D) D
in
, S
2
, S
0
, S
1
Q.39 The diode in the circuit given below has
=0.7 but is ideal otherwise. The current (in mA) in
the 4 k ? resistor is _______.
Q.40 Assuming that the opamp in the circuit shown below is ideal, the output voltage (in volts)
is________.
1k?
3k?
4k? 6k?
2k?
1mA
D
2k?
12V
-12V
V
O
1V
1k?
1Y
0 1E
1A
0
1A
1
1Y
1
1Y
2
1Y
3
2-to-4
Decoder
2Y
0 2E
2A
0
2A
1
2Y
1
2Y
2
2Y
3
2-to-4
Decoder
P
Q
R
S
Y
0
Y
1
Y
2
Y
3
Y
4
Y
5
Y
6
Y
7
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 11/15
Q.41 For the voltage regulator circuit shown, the input voltage (V
in
) is 20 V ? 20% and the regulated
output voltage (V
out
) is 10 V. Assume the opamp to be ideal. For a load R
L
drawing 200 mA, the
maximum power dissipation in Q
1
(in Watts) is ________.
Q.42 In the ac equivalent circuit shown, the two BJTs are biased in active region and have identical
parameters with ? >>1. The open circuit small signal voltage gain is approximately _______.
Q.43 Input () x t and output () y t of an LTI system are related by the differential equation
() ( ) 6 ( ) ( ) y t y t ytxt ?? ? ?? = . If the system is neither causal nor stable, the impulse response () ht of
the system is
(A)
32
11
() ()
55
tt
eu t e u t
?
?+ ? (B)
32
11
() ()
55
tt
eu t e u t
?
??+ ?
(C)
32
11
() ()
55
tt
eu t e ut
?
?? (D)
32
11
() ()
55
tt
eu t e ut
?
???
V
out
Q
1
V
ref
R
2
= 10 k ?
R
1
R
L
V
in
+
?
4 V
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 12/15
Q.44 Consider two real sequences with time-origin marked by the bold value,
[ ] = {, 2, 3 , 0} , [ ] = { , 3, 2, 1}
Let ( ) and ( ) be 4-point DFTs of [ ] and
[ ], respectively.
Another sequence [ ] is derived by taking 4-point inverse DFT of ( ) =
( ) ( ) .
The value of [2] is ______.
Q.45 Let ( ) = ( ) +(?) with ( ) =
( ) , where ( ) is unit step function. If the bilateral
Laplace transform of () x t is
()
2
16
16
Xs
s
=
?
{ } 4Re 4 s ?< < ;
then the value of ? is _______.
Q.46 The state variable representation of a system is given as
01
01
x x
??
=
??
?
??
& ; ( 0 ) = 1
0
[ ] 01 yx =
The response ( ) is
(A) sin( ) t
(B) 1
t
e ?
(C) 1cos() t ? (D) 0
Q.47 The output of a standard second-order system for a unit step input is given as
2
() 1 cos 3
6 3
t
yt e t
?
?
??
=? ?
??
??
. The transfer function of the system is
(A)
2
(2)( 3) ss ++
(B)
2
1
21 ss ++
(C)
2
3
23 ss ++
(D)
2
4
24 ss ++
Q.48 The transfer function of a mass-spring-damper system is given by
( ) =
1
+ +
The frequency response data for the system are given in the following table.
? in rad/s | ( )| in dB arg ( ( ) ) in deg
0.01 -18.5 -0.2
0.1 -18.5 -1.3
0.2 -18.4 -2.6
1 -16 -16.9
2 -11.4 -89.4
3 -21.5 -151
5 -32.8 -167
10 -45.3 -174.5
The unit step response of the system approaches a steady state value of ________ .
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 13/15
Q.49
A zero mean white Gaussian noise having power spectral density
0
2
N
is passed through an LTI
filter whose impulse response () ht is shown in the figure. The variance of the filtered noise at
4 t =
is
(A)
2
0
3
2
AN (B)
2
0
3
4
AN
(C)
2
0
A N (D)
2
0
1
2
AN
Q.50
{}
n
n
n
X
=?
=??
is an independent and identically distributed (i.i.d.) random process with equally
likely to be 1 + or 1 ? .
{}
n
n
n
Y
=?
=??
is another random process obtained as
= + 0.5 . The
autocorrelation function of
{}
n
n
n
Y
=?
=??
, denoted by R
Y
[k], is
(A) (B)
(C)
(D)
01
1
R
Y
[k]
k
2 3 -3 -2 -1
0 1
1.25 R
Y
[k]
k
2 3 -3 -2 -1
0.5 0.5
0 1
1.25
R
Y
[k]
k
2 -2 -1
0.5 0.5
0.25 0.25
0 1
1.25
R
Y
[k]
k
2 3 -3 -2 -1
0.25 0.25
?()
0 1 2 3
?
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/15
Q. 1 ? Q. 25 carry one mark each.
Q.1
The bilateral Laplace transform of a function
1 if
()
0 otherwise
at b
ft
?? ?
=
?
?
is
(A)
ab
s
?
(B)
()
s
ea b
s
?
(C)
as bs
ee
s
??
?
(D)
() s ab
e
s
?
Q.2 The value of for which all the eigen-values of the matrix given below are real is
10 5 + 4
20 2
42 ?10
(A) 5+ j (B) 5? (C) 1?5 (D) 1+5
Q.3
Let ( ) =
. If ( ) = ( ) for all ?
, = 2, = 4 a nd = 5, then should be
equal to _______.
Q.4
The general solution of the differential equation
1cos2
1cos2
dy y
dx x
+
=
?
is
(A) tan cot yxc ?= ( c is a constant) (B) tan cot x yc ?= ( c is a constant)
(C) tan cot yxc += ( c is a constant) (D) tan cot x yc += ( c is a constant)
Q.5 The magnitude and phase of the complex Fourier series coefficients of a periodic signal () are
shown in the figure. Choose the correct statement from the four choices given. Notation: is the
set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary
numbers.
(A) ( ) ?
(B) ( ) ?
(C) ( ) ?( ?)
(D) the information given is not sufficient to draw any conclusion about ( )
01
1
k
2 3 -3 -2 -1
|a
k
|
2
3
2
3
-5 4 -4
k
-4 -5 -3 -2 -1
0
1 23 4
? ?
a
k
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/15
Q.6 The voltage ( ) across the capacitor (in Volts) in the network shown is ______ .
Q.7 In the circuit shown, the average value of the voltage V
ab
(in Volts) in steady state condition is
________.
Q.8 The 2-port admittance matrix of the circuit shown is given by
(A) 0.3 0 .2
0.2 0 .3
(B) 15 5
515
(C) 3.3 3 5
53.33
(D) 0.3 0 .4
0.4 0 .3
Q.9 An n-type silicon sample is uniformly illuminated with light which generates 10
20
electron-hole
pairs per cm
3
per second. The minority carrier lifetime in the sample is 1 ?s. In the steady state, the
hole concentration in the sample is approximately 10
x
, where x is an integer. The value of x is ___.
5? sin(5000t)
1 k? 2 k? 1 ?F
1 mH
5 V
a b
+
V
ab
80 V 40 V
~
100 V,
50 Hz
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/15
Q.10 A piece of silicon is doped uniformly with phosphorous with a doping concentration of
10
16
/cm
3
. The expected value of mobility versus doping concentration for silicon assuming full
dopant ionization is shown below. The charge of an electron is 1.6 ?10
-19
C. The conductivity
(in
1
S cm
?
) of the silicon sample at 300
K is _______.
Q.11 If the circuit shown has to function as a clamping circuit, then which one of the following
conditions should be satisfied for the sinusoidal signal of period T ?
(A) RC << T (B) RC = 0.35 T (C) RC ? T (D) RC >> T
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/15
Q.12 In the circuit shown, V
0
= V
0A
for switch SW in position A and V
0
= V
0B
for SW in position B.
Assume that the opamp is ideal. The value of
0
0
B
A
V
V
is ___________.
Q.13 In the bistable circuit shown, the ideal opamp has saturation levels of ? 5 V. The value of R
1
(in
k ?) that gives a hysteresis width of 500 mV is ________.
Q.14 In the figure shown, the output is required to be = + ? . The gates G1
and G2 must be,
respectively,
(A) NOR, OR (B) OR, NAND
(C) NAND, OR (D) AND, NAND
Q.15 In an 8085 microprocessor, which one of the following instructions changes the content of the
accumulator?
(A) MOV B,M (B) PCHL (C) RNZ (D) SBI BEH
5 V
V
0
1 V
B A
1 k?
SW
1 k?
1 k?
1 k?
1 k?
+
?
+
?
R
2
= 20 k ?
R
1
v
out
v
in
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/15
Q.16 A mod-n counter using a synchronous binary up-counter with synchronous clear input is shown in
the figure. The value of n is _______.
Q.17 Let the signal ( ) = 0 outside the interval [
,
], where and are finite. Furthermore,
| ( )| < ? . The region of convergence (RoC) of the signal?s bilateral Laplace transform ( ) is
(A) a parallel strip containing the ? axis
(B) a parallel strip not containing the ? axis
(C) the entire -plane
(D) a half plane containing the ? axis
Q.18
Two causal discrete-time signals [] x n and [] y n are related as
0
[] [ ]
n
m
yn x m
=
=
?
.
If the z-transform of y[n] is
()
, the value of [2] x is _______.
Q.19 By performing cascading and/or summing/differencing operations using transfer function blocks
1
() Gs and
2
() Gs , one CANNOT realize a transfer function of the form
(A)
12
() () GsG s
(B)
1
2
()
()
Gs
Gs
(C)
12
1
1
() ()
()
Gs G s
Gs
??
+
??
??
(D)
12
1
1
() ()
()
Gs G s
Gs
??
?
??
??
Q
A
CLEAR
CLK
4-Bit Binary
Counter
Q
B
Q
C
Q
D
Q
A
Q
B
Q
C
Q
D
CLOCK
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/15
Q.20
For the signal flow graph shown in the figure, the value of
()
()
Cs
R s
is
(A)
12 3 4
12134 2 233123412
1
GG G G
GG H GG H GG H GGGG H H ?? ? +
(B)
12 3 4
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
GG G G
GG H GG H GG H GGGG H H ++ + +
(C)
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
1 GG H GG H GG H GGGG H H ++ + +
(D)
12134 2 233123412
1
1 GG H GG H GG H GGGG H H ?? ? +
Q.21
A unity negative feedback system has an open-loop transfer function ( ) =
( +10 )
. The gain
for the system to have a damping ratio of 0.25 is ________.
Q.22 A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal
utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8
dB, the number of levels in the quantizer is _______.
Q.23
The signal cos 10
4
t
?
?
??
+
??
??
is ideally sampled at a sampling frequency of 15 Hz. The sampled
signal is passed through a filter with impulse response
sin( )
cos 40 .
2
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
The filter
output is
(A)
15
cos 40
24
t
?
?
??
?
??
??
(B)
15 sin( )
cos 10
24
t
t
t
??
?
?
??? ?
+
??? ?
??? ?
(C)
15
cos 10
24
t
?
?
??
?
??
??
(D)
15 sin( )
cos 40
22
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
-H
3
R(s)
1
X
1
X
2
X
3
X
4
X
5
C(s)
-H
1
-H
2
G
1
G
2
G
3
G
4
1
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/15
Q.24 In a source free region in vacuum, if the electrostatic potential = 2 + + , the value
of constant must be _______.
Q.25 The electric field of a uniform plane electromagnetic wave is
= + 4 e x p [ ( 2 ? 1 0
? 0.2 ) ] .
The polarization of the wave is
(A) right handed circular (B) right handed elliptical
(C) left handed circular (D) left handed elliptical
Q. 26 ? Q. 55 carry two marks each.
Q.26
Consider the differential equation 10 0.2
dx
x
dt
=? with initial condition (0) 1 x = . The response
() x t for 0 t > is
(A)
0.2
2
t
e
?
? (B)
0.2
2
t
e ? (C)
0.2
50 49
t
e
?
? (D)
0.2
50 49
t
e ?
Q.27
The value of the integral 12
sin(4 )
cos(2 )
4
?
?
?
t
tdt
t
is ___________.
Q.28 If denotes the counterclockwise unit circle, the value of the contour integral
1
2
{ }
is _______.
Q.29
Let the random variable X represent the number of times a fair coin needs to be tossed till two
consecutive heads appear for the first time. The expectation of X is _______.
Q.30 An LC
tank circuit consists of an ideal capacitor C
connected in parallel with a coil of inductance
L having an internal resistance R . The resonant frequency of the tank circuit is
(A)
1
2 LC ?
(B)
2
1
1
2
C
R
L LC ?
?
(C)
2
1
1
2
L
RC LC ?
?
(D)
2
1
1
2
C
R
L LC ?
??
?
??
??
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/15
Q.31 In the circuit shown, the Norton equivalent resistance (in ? ) across terminals a-b is _______.
+
-
4 ?
2?
2? 4?
?
a
b
Q.32 In the circuit shown, the initial voltages across the capacitors C
1
and C
2
are 1 V and 3 V,
respectively. The switch is closed at time = 0 . The total energy dissipated (in Joules) in the
resistor R until steady state is reached, is __________.
Q.33 A dc voltage of 10 V is applied across an n-type silicon bar having a rectangular cross-section and a
length of 1 cm as shown in figure. The donor doping concentration N
D
and the mobility of electrons
n
? are 10
16
cm
-3
and 1000 cm
2
V
-1
s
-1
, respectively. The average time (in ?s) taken by the electrons
to move from one end of the bar to other end is ________.
Q.34 In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer thickness
is 100 nm. The permittivities of the semiconductor and the oxide layer are ?
s
and ?
ox
respectively.
Assuming ?
s
/?
ox
= 3, the ratio of the maximum capacitance to the minimum capacitance of this
MOS capacitor is ________.
1 cm
10 V
n-Si
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/15
Q.35
The energy band diagram and the electron density profile n ( x ) in a semiconductor are shown in
the figures. Assume that n ( x ) =10
cm
-3
, with = 0.1 V /cm and x expressed in cm.
Given
= 0 .026 V, =36 cm
s
, and
=
. The electron current density (in A/cm
) at
x= 0 is
(A) ?4.4 ? 1 0
(B) ?2.2 ? 1 0
(C) 0 (D) 2.2 ? 1 0
Q.36 A function of Boolean variables X, Y and Z is expressed in terms of the min-terms as
F(X, Y, Z) = ? (1, 2, 5, 6, 7)
Which one of the product of sums given below is equal to the function F(X, Y, Z)?
(A) ) ( ) ( ) ( Z Y X Z Y X Z Y X + + ? + + ? + +
(B) ) ( ) ( ) ( Z Y X Z Y X Z Y X + + ? + + ? + +
(C) ) ( ) ( ) ( ) ( ) ( Z Y X Z Y X Z Y X Z Y X Z Y X + + ? + + ? + + ? + + ? + +
(D) ) ( ) ( ) ( ) ( ) ( Z Y X Z Y X Z Y X Z Y X Z Y X + + ? + + ? + + ? + + ? + +
Q.37 The figure shows a binary counter with synchronous clear input. With the decoding logic shown,
the counter works as a
Binary
Counter
Q
0
CLR
CLK
Q
1
Q
2
Q
3
(A) mod-2 counter (B) mod-4 counter (C) mod-5 counter (D) mod-6 counter
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 10/15
Q.38 A 1-to-8 demultiplexer with data input D
in
, address inputs S
0
, S
1
, S
2
(with S
0
as the LSB) and
Y
0
t o Y
7
as the eight demultiplexed outputs, is to be designed using two 2-to-4 decoders (with
enable input and address inputs A
0
and A
1
) as shown in the figure. D
in
, S
0
, S
1
and S
2
are to be
connected to P, Q, R and S, but not necessarily in this order. The respective input connections to P,
Q, R, and S terminals should be
(A) S
2
, D
in
, S
0
, S
1
(B) S
1
, D
in
, S
0
, S
2
(C) D
in
, S
0
, S
1
, S
2
(D) D
in
, S
2
, S
0
, S
1
Q.39 The diode in the circuit given below has
=0.7 but is ideal otherwise. The current (in mA) in
the 4 k ? resistor is _______.
Q.40 Assuming that the opamp in the circuit shown below is ideal, the output voltage (in volts)
is________.
1k?
3k?
4k? 6k?
2k?
1mA
D
2k?
12V
-12V
V
O
1V
1k?
1Y
0 1E
1A
0
1A
1
1Y
1
1Y
2
1Y
3
2-to-4
Decoder
2Y
0 2E
2A
0
2A
1
2Y
1
2Y
2
2Y
3
2-to-4
Decoder
P
Q
R
S
Y
0
Y
1
Y
2
Y
3
Y
4
Y
5
Y
6
Y
7
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 11/15
Q.41 For the voltage regulator circuit shown, the input voltage (V
in
) is 20 V ? 20% and the regulated
output voltage (V
out
) is 10 V. Assume the opamp to be ideal. For a load R
L
drawing 200 mA, the
maximum power dissipation in Q
1
(in Watts) is ________.
Q.42 In the ac equivalent circuit shown, the two BJTs are biased in active region and have identical
parameters with ? >>1. The open circuit small signal voltage gain is approximately _______.
Q.43 Input () x t and output () y t of an LTI system are related by the differential equation
() ( ) 6 ( ) ( ) y t y t ytxt ?? ? ?? = . If the system is neither causal nor stable, the impulse response () ht of
the system is
(A)
32
11
() ()
55
tt
eu t e u t
?
?+ ? (B)
32
11
() ()
55
tt
eu t e u t
?
??+ ?
(C)
32
11
() ()
55
tt
eu t e ut
?
?? (D)
32
11
() ()
55
tt
eu t e ut
?
???
V
out
Q
1
V
ref
R
2
= 10 k ?
R
1
R
L
V
in
+
?
4 V
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 12/15
Q.44 Consider two real sequences with time-origin marked by the bold value,
[ ] = {, 2, 3 , 0} , [ ] = { , 3, 2, 1}
Let ( ) and ( ) be 4-point DFTs of [ ] and
[ ], respectively.
Another sequence [ ] is derived by taking 4-point inverse DFT of ( ) =
( ) ( ) .
The value of [2] is ______.
Q.45 Let ( ) = ( ) +(?) with ( ) =
( ) , where ( ) is unit step function. If the bilateral
Laplace transform of () x t is
()
2
16
16
Xs
s
=
?
{ } 4Re 4 s ?< < ;
then the value of ? is _______.
Q.46 The state variable representation of a system is given as
01
01
x x
??
=
??
?
??
& ; ( 0 ) = 1
0
[ ] 01 yx =
The response ( ) is
(A) sin( ) t
(B) 1
t
e ?
(C) 1cos() t ? (D) 0
Q.47 The output of a standard second-order system for a unit step input is given as
2
() 1 cos 3
6 3
t
yt e t
?
?
??
=? ?
??
??
. The transfer function of the system is
(A)
2
(2)( 3) ss ++
(B)
2
1
21 ss ++
(C)
2
3
23 ss ++
(D)
2
4
24 ss ++
Q.48 The transfer function of a mass-spring-damper system is given by
( ) =
1
+ +
The frequency response data for the system are given in the following table.
? in rad/s | ( )| in dB arg ( ( ) ) in deg
0.01 -18.5 -0.2
0.1 -18.5 -1.3
0.2 -18.4 -2.6
1 -16 -16.9
2 -11.4 -89.4
3 -21.5 -151
5 -32.8 -167
10 -45.3 -174.5
The unit step response of the system approaches a steady state value of ________ .
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 13/15
Q.49
A zero mean white Gaussian noise having power spectral density
0
2
N
is passed through an LTI
filter whose impulse response () ht is shown in the figure. The variance of the filtered noise at
4 t =
is
(A)
2
0
3
2
AN (B)
2
0
3
4
AN
(C)
2
0
A N (D)
2
0
1
2
AN
Q.50
{}
n
n
n
X
=?
=??
is an independent and identically distributed (i.i.d.) random process with equally
likely to be 1 + or 1 ? .
{}
n
n
n
Y
=?
=??
is another random process obtained as
= + 0.5 . The
autocorrelation function of
{}
n
n
n
Y
=?
=??
, denoted by R
Y
[k], is
(A) (B)
(C)
(D)
01
1
R
Y
[k]
k
2 3 -3 -2 -1
0 1
1.25 R
Y
[k]
k
2 3 -3 -2 -1
0.5 0.5
0 1
1.25
R
Y
[k]
k
2 -2 -1
0.5 0.5
0.25 0.25
0 1
1.25
R
Y
[k]
k
2 3 -3 -2 -1
0.25 0.25
?()
0 1 2 3
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 14/15
Q.51 Consider a binary, digital communication system which uses pulses () gt and () gt ? for transmitting
bits over an AWGN channel. If the receiver uses a matched filter, which one of the following
pulses will give the minimum probability of bit error?
(A)
t
1
1 0
g(t)
(B)
t
1
1 0
g(t)
(C)
t
1
1 0
g(t)
(D)
t
1
1 0
g(t)
Q.52 Let ? {0,1} and ? {0,1} be two independent binary random variables. If (= 0 ) =
and (= 0 ) = , then (+ ? 1 ) is equal to
(A) + (1 ? )(1 ? ) (B)
(C) (1 ? )
(D) 1?
Q.53
An air-filled rectangular waveguide of internal dimensions a
cm ?
b cm () ab > has a cutoff
frequency of 6 GHz for the dominant
10
TE mode. For the same waveguide, if the cutoff frequency
of the
11
TM mode is 15 GHz, the cutoff frequency of the
01
TE mode in GHz is __________.
Q.54 Two half-wave dipole antennas placed as shown in the figure are excited with sinusoidally varying
currents of frequency 3 MHz and phase shift of ?/2 between them (the element at the origin leads in
phase). If the maximum radiated E-field at the point P in the x-y plane occurs at an azimuthal angle
of 60?, the distance d (in meters) between the antennas is _________.
O
P x
y
z
d
OP >> d
60?
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GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/15
Q. 1 ? Q. 25 carry one mark each.
Q.1
The bilateral Laplace transform of a function
1 if
()
0 otherwise
at b
ft
?? ?
=
?
?
is
(A)
ab
s
?
(B)
()
s
ea b
s
?
(C)
as bs
ee
s
??
?
(D)
() s ab
e
s
?
Q.2 The value of for which all the eigen-values of the matrix given below are real is
10 5 + 4
20 2
42 ?10
(A) 5+ j (B) 5? (C) 1?5 (D) 1+5
Q.3
Let ( ) =
. If ( ) = ( ) for all ?
, = 2, = 4 a nd = 5, then should be
equal to _______.
Q.4
The general solution of the differential equation
1cos2
1cos2
dy y
dx x
+
=
?
is
(A) tan cot yxc ?= ( c is a constant) (B) tan cot x yc ?= ( c is a constant)
(C) tan cot yxc += ( c is a constant) (D) tan cot x yc += ( c is a constant)
Q.5 The magnitude and phase of the complex Fourier series coefficients of a periodic signal () are
shown in the figure. Choose the correct statement from the four choices given. Notation: is the
set of complex numbers, is the set of purely real numbers, and is the set of purely imaginary
numbers.
(A) ( ) ?
(B) ( ) ?
(C) ( ) ?( ?)
(D) the information given is not sufficient to draw any conclusion about ( )
01
1
k
2 3 -3 -2 -1
|a
k
|
2
3
2
3
-5 4 -4
k
-4 -5 -3 -2 -1
0
1 23 4
? ?
a
k
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/15
Q.6 The voltage ( ) across the capacitor (in Volts) in the network shown is ______ .
Q.7 In the circuit shown, the average value of the voltage V
ab
(in Volts) in steady state condition is
________.
Q.8 The 2-port admittance matrix of the circuit shown is given by
(A) 0.3 0 .2
0.2 0 .3
(B) 15 5
515
(C) 3.3 3 5
53.33
(D) 0.3 0 .4
0.4 0 .3
Q.9 An n-type silicon sample is uniformly illuminated with light which generates 10
20
electron-hole
pairs per cm
3
per second. The minority carrier lifetime in the sample is 1 ?s. In the steady state, the
hole concentration in the sample is approximately 10
x
, where x is an integer. The value of x is ___.
5? sin(5000t)
1 k? 2 k? 1 ?F
1 mH
5 V
a b
+
V
ab
80 V 40 V
~
100 V,
50 Hz
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/15
Q.10 A piece of silicon is doped uniformly with phosphorous with a doping concentration of
10
16
/cm
3
. The expected value of mobility versus doping concentration for silicon assuming full
dopant ionization is shown below. The charge of an electron is 1.6 ?10
-19
C. The conductivity
(in
1
S cm
?
) of the silicon sample at 300
K is _______.
Q.11 If the circuit shown has to function as a clamping circuit, then which one of the following
conditions should be satisfied for the sinusoidal signal of period T ?
(A) RC << T (B) RC = 0.35 T (C) RC ? T (D) RC >> T
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/15
Q.12 In the circuit shown, V
0
= V
0A
for switch SW in position A and V
0
= V
0B
for SW in position B.
Assume that the opamp is ideal. The value of
0
0
B
A
V
V
is ___________.
Q.13 In the bistable circuit shown, the ideal opamp has saturation levels of ? 5 V. The value of R
1
(in
k ?) that gives a hysteresis width of 500 mV is ________.
Q.14 In the figure shown, the output is required to be = + ? . The gates G1
and G2 must be,
respectively,
(A) NOR, OR (B) OR, NAND
(C) NAND, OR (D) AND, NAND
Q.15 In an 8085 microprocessor, which one of the following instructions changes the content of the
accumulator?
(A) MOV B,M (B) PCHL (C) RNZ (D) SBI BEH
5 V
V
0
1 V
B A
1 k?
SW
1 k?
1 k?
1 k?
1 k?
+
?
+
?
R
2
= 20 k ?
R
1
v
out
v
in
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/15
Q.16 A mod-n counter using a synchronous binary up-counter with synchronous clear input is shown in
the figure. The value of n is _______.
Q.17 Let the signal ( ) = 0 outside the interval [
,
], where and are finite. Furthermore,
| ( )| < ? . The region of convergence (RoC) of the signal?s bilateral Laplace transform ( ) is
(A) a parallel strip containing the ? axis
(B) a parallel strip not containing the ? axis
(C) the entire -plane
(D) a half plane containing the ? axis
Q.18
Two causal discrete-time signals [] x n and [] y n are related as
0
[] [ ]
n
m
yn x m
=
=
?
.
If the z-transform of y[n] is
()
, the value of [2] x is _______.
Q.19 By performing cascading and/or summing/differencing operations using transfer function blocks
1
() Gs and
2
() Gs , one CANNOT realize a transfer function of the form
(A)
12
() () GsG s
(B)
1
2
()
()
Gs
Gs
(C)
12
1
1
() ()
()
Gs G s
Gs
??
+
??
??
(D)
12
1
1
() ()
()
Gs G s
Gs
??
?
??
??
Q
A
CLEAR
CLK
4-Bit Binary
Counter
Q
B
Q
C
Q
D
Q
A
Q
B
Q
C
Q
D
CLOCK
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/15
Q.20
For the signal flow graph shown in the figure, the value of
()
()
Cs
R s
is
(A)
12 3 4
12134 2 233123412
1
GG G G
GG H GG H GG H GGGG H H ?? ? +
(B)
12 3 4
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
GG G G
GG H GG H GG H GGGG H H ++ + +
(C)
12 1 3 4 2 2 3 3 1 2 3 4 1 2
1
1 GG H GG H GG H GGGG H H ++ + +
(D)
12134 2 233123412
1
1 GG H GG H GG H GGGG H H ?? ? +
Q.21
A unity negative feedback system has an open-loop transfer function ( ) =
( +10 )
. The gain
for the system to have a damping ratio of 0.25 is ________.
Q.22 A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal
utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8
dB, the number of levels in the quantizer is _______.
Q.23
The signal cos 10
4
t
?
?
??
+
??
??
is ideally sampled at a sampling frequency of 15 Hz. The sampled
signal is passed through a filter with impulse response
sin( )
cos 40 .
2
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
The filter
output is
(A)
15
cos 40
24
t
?
?
??
?
??
??
(B)
15 sin( )
cos 10
24
t
t
t
??
?
?
??? ?
+
??? ?
??? ?
(C)
15
cos 10
24
t
?
?
??
?
??
??
(D)
15 sin( )
cos 40
22
t
t
t
??
?
?
??? ?
?
??? ?
??? ?
-H
3
R(s)
1
X
1
X
2
X
3
X
4
X
5
C(s)
-H
1
-H
2
G
1
G
2
G
3
G
4
1
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/15
Q.24 In a source free region in vacuum, if the electrostatic potential = 2 + + , the value
of constant must be _______.
Q.25 The electric field of a uniform plane electromagnetic wave is
= + 4 e x p [ ( 2 ? 1 0
? 0.2 ) ] .
The polarization of the wave is
(A) right handed circular (B) right handed elliptical
(C) left handed circular (D) left handed elliptical
Q. 26 ? Q. 55 carry two marks each.
Q.26
Consider the differential equation 10 0.2
dx
x
dt
=? with initial condition (0) 1 x = . The response
() x t for 0 t > is
(A)
0.2
2
t
e
?
? (B)
0.2
2
t
e ? (C)
0.2
50 49
t
e
?
? (D)
0.2
50 49
t
e ?
Q.27
The value of the integral 12
sin(4 )
cos(2 )
4
?
?
?
t
tdt
t
is ___________.
Q.28 If denotes the counterclockwise unit circle, the value of the contour integral
1
2
{ }
is _______.
Q.29
Let the random variable X represent the number of times a fair coin needs to be tossed till two
consecutive heads appear for the first time. The expectation of X is _______.
Q.30 An LC
tank circuit consists of an ideal capacitor C
connected in parallel with a coil of inductance
L having an internal resistance R . The resonant frequency of the tank circuit is
(A)
1
2 LC ?
(B)
2
1
1
2
C
R
L LC ?
?
(C)
2
1
1
2
L
RC LC ?
?
(D)
2
1
1
2
C
R
L LC ?
??
?
??
??
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/15
Q.31 In the circuit shown, the Norton equivalent resistance (in ? ) across terminals a-b is _______.
+
-
4 ?
2?
2? 4?
?
a
b
Q.32 In the circuit shown, the initial voltages across the capacitors C
1
and C
2
are 1 V and 3 V,
respectively. The switch is closed at time = 0 . The total energy dissipated (in Joules) in the
resistor R until steady state is reached, is __________.
Q.33 A dc voltage of 10 V is applied across an n-type silicon bar having a rectangular cross-section and a
length of 1 cm as shown in figure. The donor doping concentration N
D
and the mobility of electrons
n
? are 10
16
cm
-3
and 1000 cm
2
V
-1
s
-1
, respectively. The average time (in ?s) taken by the electrons
to move from one end of the bar to other end is ________.
Q.34 In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer thickness
is 100 nm. The permittivities of the semiconductor and the oxide layer are ?
s
and ?
ox
respectively.
Assuming ?
s
/?
ox
= 3, the ratio of the maximum capacitance to the minimum capacitance of this
MOS capacitor is ________.
1 cm
10 V
n-Si
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/15
Q.35
The energy band diagram and the electron density profile n ( x ) in a semiconductor are shown in
the figures. Assume that n ( x ) =10
cm
-3
, with = 0.1 V /cm and x expressed in cm.
Given
= 0 .026 V, =36 cm
s
, and
=
. The electron current density (in A/cm
) at
x= 0 is
(A) ?4.4 ? 1 0
(B) ?2.2 ? 1 0
(C) 0 (D) 2.2 ? 1 0
Q.36 A function of Boolean variables X, Y and Z is expressed in terms of the min-terms as
F(X, Y, Z) = ? (1, 2, 5, 6, 7)
Which one of the product of sums given below is equal to the function F(X, Y, Z)?
(A) ) ( ) ( ) ( Z Y X Z Y X Z Y X + + ? + + ? + +
(B) ) ( ) ( ) ( Z Y X Z Y X Z Y X + + ? + + ? + +
(C) ) ( ) ( ) ( ) ( ) ( Z Y X Z Y X Z Y X Z Y X Z Y X + + ? + + ? + + ? + + ? + +
(D) ) ( ) ( ) ( ) ( ) ( Z Y X Z Y X Z Y X Z Y X Z Y X + + ? + + ? + + ? + + ? + +
Q.37 The figure shows a binary counter with synchronous clear input. With the decoding logic shown,
the counter works as a
Binary
Counter
Q
0
CLR
CLK
Q
1
Q
2
Q
3
(A) mod-2 counter (B) mod-4 counter (C) mod-5 counter (D) mod-6 counter
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 10/15
Q.38 A 1-to-8 demultiplexer with data input D
in
, address inputs S
0
, S
1
, S
2
(with S
0
as the LSB) and
Y
0
t o Y
7
as the eight demultiplexed outputs, is to be designed using two 2-to-4 decoders (with
enable input and address inputs A
0
and A
1
) as shown in the figure. D
in
, S
0
, S
1
and S
2
are to be
connected to P, Q, R and S, but not necessarily in this order. The respective input connections to P,
Q, R, and S terminals should be
(A) S
2
, D
in
, S
0
, S
1
(B) S
1
, D
in
, S
0
, S
2
(C) D
in
, S
0
, S
1
, S
2
(D) D
in
, S
2
, S
0
, S
1
Q.39 The diode in the circuit given below has
=0.7 but is ideal otherwise. The current (in mA) in
the 4 k ? resistor is _______.
Q.40 Assuming that the opamp in the circuit shown below is ideal, the output voltage (in volts)
is________.
1k?
3k?
4k? 6k?
2k?
1mA
D
2k?
12V
-12V
V
O
1V
1k?
1Y
0 1E
1A
0
1A
1
1Y
1
1Y
2
1Y
3
2-to-4
Decoder
2Y
0 2E
2A
0
2A
1
2Y
1
2Y
2
2Y
3
2-to-4
Decoder
P
Q
R
S
Y
0
Y
1
Y
2
Y
3
Y
4
Y
5
Y
6
Y
7
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 11/15
Q.41 For the voltage regulator circuit shown, the input voltage (V
in
) is 20 V ? 20% and the regulated
output voltage (V
out
) is 10 V. Assume the opamp to be ideal. For a load R
L
drawing 200 mA, the
maximum power dissipation in Q
1
(in Watts) is ________.
Q.42 In the ac equivalent circuit shown, the two BJTs are biased in active region and have identical
parameters with ? >>1. The open circuit small signal voltage gain is approximately _______.
Q.43 Input () x t and output () y t of an LTI system are related by the differential equation
() ( ) 6 ( ) ( ) y t y t ytxt ?? ? ?? = . If the system is neither causal nor stable, the impulse response () ht of
the system is
(A)
32
11
() ()
55
tt
eu t e u t
?
?+ ? (B)
32
11
() ()
55
tt
eu t e u t
?
??+ ?
(C)
32
11
() ()
55
tt
eu t e ut
?
?? (D)
32
11
() ()
55
tt
eu t e ut
?
???
V
out
Q
1
V
ref
R
2
= 10 k ?
R
1
R
L
V
in
+
?
4 V
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 12/15
Q.44 Consider two real sequences with time-origin marked by the bold value,
[ ] = {, 2, 3 , 0} , [ ] = { , 3, 2, 1}
Let ( ) and ( ) be 4-point DFTs of [ ] and
[ ], respectively.
Another sequence [ ] is derived by taking 4-point inverse DFT of ( ) =
( ) ( ) .
The value of [2] is ______.
Q.45 Let ( ) = ( ) +(?) with ( ) =
( ) , where ( ) is unit step function. If the bilateral
Laplace transform of () x t is
()
2
16
16
Xs
s
=
?
{ } 4Re 4 s ?< < ;
then the value of ? is _______.
Q.46 The state variable representation of a system is given as
01
01
x x
??
=
??
?
??
& ; ( 0 ) = 1
0
[ ] 01 yx =
The response ( ) is
(A) sin( ) t
(B) 1
t
e ?
(C) 1cos() t ? (D) 0
Q.47 The output of a standard second-order system for a unit step input is given as
2
() 1 cos 3
6 3
t
yt e t
?
?
??
=? ?
??
??
. The transfer function of the system is
(A)
2
(2)( 3) ss ++
(B)
2
1
21 ss ++
(C)
2
3
23 ss ++
(D)
2
4
24 ss ++
Q.48 The transfer function of a mass-spring-damper system is given by
( ) =
1
+ +
The frequency response data for the system are given in the following table.
? in rad/s | ( )| in dB arg ( ( ) ) in deg
0.01 -18.5 -0.2
0.1 -18.5 -1.3
0.2 -18.4 -2.6
1 -16 -16.9
2 -11.4 -89.4
3 -21.5 -151
5 -32.8 -167
10 -45.3 -174.5
The unit step response of the system approaches a steady state value of ________ .
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 13/15
Q.49
A zero mean white Gaussian noise having power spectral density
0
2
N
is passed through an LTI
filter whose impulse response () ht is shown in the figure. The variance of the filtered noise at
4 t =
is
(A)
2
0
3
2
AN (B)
2
0
3
4
AN
(C)
2
0
A N (D)
2
0
1
2
AN
Q.50
{}
n
n
n
X
=?
=??
is an independent and identically distributed (i.i.d.) random process with equally
likely to be 1 + or 1 ? .
{}
n
n
n
Y
=?
=??
is another random process obtained as
= + 0.5 . The
autocorrelation function of
{}
n
n
n
Y
=?
=??
, denoted by R
Y
[k], is
(A) (B)
(C)
(D)
01
1
R
Y
[k]
k
2 3 -3 -2 -1
0 1
1.25 R
Y
[k]
k
2 3 -3 -2 -1
0.5 0.5
0 1
1.25
R
Y
[k]
k
2 -2 -1
0.5 0.5
0.25 0.25
0 1
1.25
R
Y
[k]
k
2 3 -3 -2 -1
0.25 0.25
?()
0 1 2 3
?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 14/15
Q.51 Consider a binary, digital communication system which uses pulses () gt and () gt ? for transmitting
bits over an AWGN channel. If the receiver uses a matched filter, which one of the following
pulses will give the minimum probability of bit error?
(A)
t
1
1 0
g(t)
(B)
t
1
1 0
g(t)
(C)
t
1
1 0
g(t)
(D)
t
1
1 0
g(t)
Q.52 Let ? {0,1} and ? {0,1} be two independent binary random variables. If (= 0 ) =
and (= 0 ) = , then (+ ? 1 ) is equal to
(A) + (1 ? )(1 ? ) (B)
(C) (1 ? )
(D) 1?
Q.53
An air-filled rectangular waveguide of internal dimensions a
cm ?
b cm () ab > has a cutoff
frequency of 6 GHz for the dominant
10
TE mode. For the same waveguide, if the cutoff frequency
of the
11
TM mode is 15 GHz, the cutoff frequency of the
01
TE mode in GHz is __________.
Q.54 Two half-wave dipole antennas placed as shown in the figure are excited with sinusoidally varying
currents of frequency 3 MHz and phase shift of ?/2 between them (the element at the origin leads in
phase). If the maximum radiated E-field at the point P in the x-y plane occurs at an azimuthal angle
of 60?, the distance d (in meters) between the antennas is _________.
O
P x
y
z
d
OP >> d
60?
GATE 2015 SET-2 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 15/15
Q.55 The electric field of a plane wave propagating in a lossless non-magnetic medium is given by the
following expression
( , ) = 5 c os ( 2 ? 1 0
+ ) +
3cos 2 ? 1 0
+ ?
2
The type of the polarization is
(A) Right Hand Circular. (B) Left Hand Elliptical.
(C) Right Hand Elliptical. (D) Linear.
END OF THE QUESTION PAPER
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This post was last modified on 19 December 2019