Download Graduate Aptitude Test in Engineering (GATE) 2015 Electronics and Communication Engg. Set 2 Question Paper
EC 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
For
1tan
tan 1
x
A
x
??
=
??
?
??
, the determinant of
1 T
A A
?
is
(A)
2
sec x
(B) cos 4x (C) 1 (D) 0
Q.2 The contour on the x-y plane, where the partial derivative of +
with respect to is equal to
the partial derivative of 6 + 4 with respect to , is
(A) = 2 (B) = 2 (C) + = 4
(D) ? = 0
Q.3 If is a circle of radius with centre , in the complex z-plane and if is a non-zero integer, then
?
(
)
equals
(A) 2 (B) 0
(C)
(D) 2
Q.4
Consider the function () sin(2 ) ()
t
gt e t u t ?
?
= where () ut is the unit step function. The area under
() gt is _______.
Q.5
The value of
0
1
2
n
n
n
?
=
??
??
??
?
is ______.
Q.6 For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b
is ________.
Q.7 In the circuit shown, the voltage V
X
(in Volts) is _______.
8 ? 20 ?
10 ?
5 A
V
X
+
-
+
-
0.25 V
X
0.5 V
X
12 V
3?
6?
1A
a
b
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EC 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
For
1tan
tan 1
x
A
x
??
=
??
?
??
, the determinant of
1 T
A A
?
is
(A)
2
sec x
(B) cos 4x (C) 1 (D) 0
Q.2 The contour on the x-y plane, where the partial derivative of +
with respect to is equal to
the partial derivative of 6 + 4 with respect to , is
(A) = 2 (B) = 2 (C) + = 4
(D) ? = 0
Q.3 If is a circle of radius with centre , in the complex z-plane and if is a non-zero integer, then
?
(
)
equals
(A) 2 (B) 0
(C)
(D) 2
Q.4
Consider the function () sin(2 ) ()
t
gt e t u t ?
?
= where () ut is the unit step function. The area under
() gt is _______.
Q.5
The value of
0
1
2
n
n
n
?
=
??
??
??
?
is ______.
Q.6 For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b
is ________.
Q.7 In the circuit shown, the voltage V
X
(in Volts) is _______.
8 ? 20 ?
10 ?
5 A
V
X
+
-
+
-
0.25 V
X
0.5 V
X
12 V
3?
6?
1A
a
b
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/14
Q.8 At very high frequencies, the peak output voltage V
0
(in Volts) is ________.
Q.9 Which one of the following processes is preferred to form the gate dielectric (SiO
2
) of MOSFETs ?
(A) Sputtering (B) Molecular beam epitaxy
(C) Wet oxidation (D) Dry oxidation
Q.10 If the base width in a bipolar junction transistor is doubled, which one of the following statements
will be TRUE?
(A) Current gain will increase.
(B) Unity gain frequency will increase.
(C) Emitter-base junction capacitance will increase.
(D) Early Voltage will increase.
Q.11 In the circuit shown in the figure, the BJT has a current gain ( ) of 50. For an emitter-base
voltage
= 600 mV, the emitter-collector voltage
(in Volts) is _______.
60 k ?
500 ?
3 V
100 ?F
100 ?F
100 ?F
1 k?
1 k?
1 k? 1 k?
1.0sin( ?t) V
V
0
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EC 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
For
1tan
tan 1
x
A
x
??
=
??
?
??
, the determinant of
1 T
A A
?
is
(A)
2
sec x
(B) cos 4x (C) 1 (D) 0
Q.2 The contour on the x-y plane, where the partial derivative of +
with respect to is equal to
the partial derivative of 6 + 4 with respect to , is
(A) = 2 (B) = 2 (C) + = 4
(D) ? = 0
Q.3 If is a circle of radius with centre , in the complex z-plane and if is a non-zero integer, then
?
(
)
equals
(A) 2 (B) 0
(C)
(D) 2
Q.4
Consider the function () sin(2 ) ()
t
gt e t u t ?
?
= where () ut is the unit step function. The area under
() gt is _______.
Q.5
The value of
0
1
2
n
n
n
?
=
??
??
??
?
is ______.
Q.6 For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b
is ________.
Q.7 In the circuit shown, the voltage V
X
(in Volts) is _______.
8 ? 20 ?
10 ?
5 A
V
X
+
-
+
-
0.25 V
X
0.5 V
X
12 V
3?
6?
1A
a
b
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/14
Q.8 At very high frequencies, the peak output voltage V
0
(in Volts) is ________.
Q.9 Which one of the following processes is preferred to form the gate dielectric (SiO
2
) of MOSFETs ?
(A) Sputtering (B) Molecular beam epitaxy
(C) Wet oxidation (D) Dry oxidation
Q.10 If the base width in a bipolar junction transistor is doubled, which one of the following statements
will be TRUE?
(A) Current gain will increase.
(B) Unity gain frequency will increase.
(C) Emitter-base junction capacitance will increase.
(D) Early Voltage will increase.
Q.11 In the circuit shown in the figure, the BJT has a current gain ( ) of 50. For an emitter-base
voltage
= 600 mV, the emitter-collector voltage
(in Volts) is _______.
60 k ?
500 ?
3 V
100 ?F
100 ?F
100 ?F
1 k?
1 k?
1 k? 1 k?
1.0sin( ?t) V
V
0
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/14
Q.12 In the circuit shown using an ideal opamp, the 3-dB cut-off frequency (in Hz) is _______.
v
i
10 k? 10 k?
10 k? 10 k?
0.1 ?F
v
o
+
?
Q.13 In the circuit shown, assume that diodes D
1
and D
2
are ideal. In the steady state condition, the
average voltage V
ab
(in Volts) across the 0.5 ?F capacitor is _____.
Q.14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset ( R
input).
The counter corresponding to this circuit is
(A) a modulo-5 binary up counter (B) a modulo-6 binary down counter
(C) a modulo-5 binary down counter (D) a modulo-6 binary up counter
50 sin (?t)
1 ?F
a
V
ab
0.5 ?F
D
1
D
2
b
+
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EC 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
For
1tan
tan 1
x
A
x
??
=
??
?
??
, the determinant of
1 T
A A
?
is
(A)
2
sec x
(B) cos 4x (C) 1 (D) 0
Q.2 The contour on the x-y plane, where the partial derivative of +
with respect to is equal to
the partial derivative of 6 + 4 with respect to , is
(A) = 2 (B) = 2 (C) + = 4
(D) ? = 0
Q.3 If is a circle of radius with centre , in the complex z-plane and if is a non-zero integer, then
?
(
)
equals
(A) 2 (B) 0
(C)
(D) 2
Q.4
Consider the function () sin(2 ) ()
t
gt e t u t ?
?
= where () ut is the unit step function. The area under
() gt is _______.
Q.5
The value of
0
1
2
n
n
n
?
=
??
??
??
?
is ______.
Q.6 For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b
is ________.
Q.7 In the circuit shown, the voltage V
X
(in Volts) is _______.
8 ? 20 ?
10 ?
5 A
V
X
+
-
+
-
0.25 V
X
0.5 V
X
12 V
3?
6?
1A
a
b
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/14
Q.8 At very high frequencies, the peak output voltage V
0
(in Volts) is ________.
Q.9 Which one of the following processes is preferred to form the gate dielectric (SiO
2
) of MOSFETs ?
(A) Sputtering (B) Molecular beam epitaxy
(C) Wet oxidation (D) Dry oxidation
Q.10 If the base width in a bipolar junction transistor is doubled, which one of the following statements
will be TRUE?
(A) Current gain will increase.
(B) Unity gain frequency will increase.
(C) Emitter-base junction capacitance will increase.
(D) Early Voltage will increase.
Q.11 In the circuit shown in the figure, the BJT has a current gain ( ) of 50. For an emitter-base
voltage
= 600 mV, the emitter-collector voltage
(in Volts) is _______.
60 k ?
500 ?
3 V
100 ?F
100 ?F
100 ?F
1 k?
1 k?
1 k? 1 k?
1.0sin( ?t) V
V
0
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/14
Q.12 In the circuit shown using an ideal opamp, the 3-dB cut-off frequency (in Hz) is _______.
v
i
10 k? 10 k?
10 k? 10 k?
0.1 ?F
v
o
+
?
Q.13 In the circuit shown, assume that diodes D
1
and D
2
are ideal. In the steady state condition, the
average voltage V
ab
(in Volts) across the 0.5 ?F capacitor is _____.
Q.14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset ( R
input).
The counter corresponding to this circuit is
(A) a modulo-5 binary up counter (B) a modulo-6 binary down counter
(C) a modulo-5 binary down counter (D) a modulo-6 binary up counter
50 sin (?t)
1 ?F
a
V
ab
0.5 ?F
D
1
D
2
b
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/14
Q.15 In the circuit shown, diodes D
1
, D
2
and D
3
are ideal, and the inputs E
1
, E
2
and E
3
are ?0 V? for
logic ?0? and ?10 V? for logic ?1?. What logic gate does the circuit represent?
(A) 3-input OR gate
(B) 3-input NOR gate
(C) 3-input AND gate
(D) 3-input XOR gate
Q.16 Which one of the following 8085 microprocessor programs correctly calculates the product of two
8-bit numbers stored in registers B and C?
(A) MVI A, 00H
JNZ LOOP
CMP C
LOOP DCR B
HLT
(B)
MVI A, 00H
CMP C
LOOP DCR B
JNZ LOOP
HLT
(C) MVI A, 00H
LOOP ADD C
DCR B
JNZ LOOP
HLT
(D) MVI A, 00H
ADD C
JNZ LOOP
LOOP INR B
HLT
Q.17 The impulse response of an LTI system can be obtained by
(A) differentiating the unit ramp response
(B) differentiating the unit step response
(C) integrating the unit ramp response
(D) integrating the unit step response
Q.18
Consider a four-point moving average filter defined by the equation
3
0
[] [ ]
i
i
yn x n i ?
=
=?
?
.
The condition on the filter coefficients that results in a null at zero frequency is
(A)
12 0 3
0; ?? ? ? == =? (B)
12 0 3
1; ?? ? ? == =?
(C)
03 1 2
0; ?? ? ? == = (D)
12 0 3
0; ?? ? ? == =
1 k?
V
0
10V
E
1
E
2
E
3
D
1
D
2
D
3
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EC 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
For
1tan
tan 1
x
A
x
??
=
??
?
??
, the determinant of
1 T
A A
?
is
(A)
2
sec x
(B) cos 4x (C) 1 (D) 0
Q.2 The contour on the x-y plane, where the partial derivative of +
with respect to is equal to
the partial derivative of 6 + 4 with respect to , is
(A) = 2 (B) = 2 (C) + = 4
(D) ? = 0
Q.3 If is a circle of radius with centre , in the complex z-plane and if is a non-zero integer, then
?
(
)
equals
(A) 2 (B) 0
(C)
(D) 2
Q.4
Consider the function () sin(2 ) ()
t
gt e t u t ?
?
= where () ut is the unit step function. The area under
() gt is _______.
Q.5
The value of
0
1
2
n
n
n
?
=
??
??
??
?
is ______.
Q.6 For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b
is ________.
Q.7 In the circuit shown, the voltage V
X
(in Volts) is _______.
8 ? 20 ?
10 ?
5 A
V
X
+
-
+
-
0.25 V
X
0.5 V
X
12 V
3?
6?
1A
a
b
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/14
Q.8 At very high frequencies, the peak output voltage V
0
(in Volts) is ________.
Q.9 Which one of the following processes is preferred to form the gate dielectric (SiO
2
) of MOSFETs ?
(A) Sputtering (B) Molecular beam epitaxy
(C) Wet oxidation (D) Dry oxidation
Q.10 If the base width in a bipolar junction transistor is doubled, which one of the following statements
will be TRUE?
(A) Current gain will increase.
(B) Unity gain frequency will increase.
(C) Emitter-base junction capacitance will increase.
(D) Early Voltage will increase.
Q.11 In the circuit shown in the figure, the BJT has a current gain ( ) of 50. For an emitter-base
voltage
= 600 mV, the emitter-collector voltage
(in Volts) is _______.
60 k ?
500 ?
3 V
100 ?F
100 ?F
100 ?F
1 k?
1 k?
1 k? 1 k?
1.0sin( ?t) V
V
0
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/14
Q.12 In the circuit shown using an ideal opamp, the 3-dB cut-off frequency (in Hz) is _______.
v
i
10 k? 10 k?
10 k? 10 k?
0.1 ?F
v
o
+
?
Q.13 In the circuit shown, assume that diodes D
1
and D
2
are ideal. In the steady state condition, the
average voltage V
ab
(in Volts) across the 0.5 ?F capacitor is _____.
Q.14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset ( R
input).
The counter corresponding to this circuit is
(A) a modulo-5 binary up counter (B) a modulo-6 binary down counter
(C) a modulo-5 binary down counter (D) a modulo-6 binary up counter
50 sin (?t)
1 ?F
a
V
ab
0.5 ?F
D
1
D
2
b
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/14
Q.15 In the circuit shown, diodes D
1
, D
2
and D
3
are ideal, and the inputs E
1
, E
2
and E
3
are ?0 V? for
logic ?0? and ?10 V? for logic ?1?. What logic gate does the circuit represent?
(A) 3-input OR gate
(B) 3-input NOR gate
(C) 3-input AND gate
(D) 3-input XOR gate
Q.16 Which one of the following 8085 microprocessor programs correctly calculates the product of two
8-bit numbers stored in registers B and C?
(A) MVI A, 00H
JNZ LOOP
CMP C
LOOP DCR B
HLT
(B)
MVI A, 00H
CMP C
LOOP DCR B
JNZ LOOP
HLT
(C) MVI A, 00H
LOOP ADD C
DCR B
JNZ LOOP
HLT
(D) MVI A, 00H
ADD C
JNZ LOOP
LOOP INR B
HLT
Q.17 The impulse response of an LTI system can be obtained by
(A) differentiating the unit ramp response
(B) differentiating the unit step response
(C) integrating the unit ramp response
(D) integrating the unit step response
Q.18
Consider a four-point moving average filter defined by the equation
3
0
[] [ ]
i
i
yn x n i ?
=
=?
?
.
The condition on the filter coefficients that results in a null at zero frequency is
(A)
12 0 3
0; ?? ? ? == =? (B)
12 0 3
1; ?? ? ? == =?
(C)
03 1 2
0; ?? ? ? == = (D)
12 0 3
0; ?? ? ? == =
1 k?
V
0
10V
E
1
E
2
E
3
D
1
D
2
D
3
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/14
Q.19 Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued.
The value of ?
(in Hz) is ___________.
Q.20
The phase margin (in degrees) of the system
10
()
( 10)
Gs
ss
=
+
is _______.
Q.21 The transfer function of a first-order controller is given as
( ) =
( + )
+
where , and are positive real numbers. The condition for this controller to act as a phase lead
compensator is
(A) < (B) > (C) < (D) >
Q.22 The modulation scheme commonly used for transmission from GSM mobile terminals is
(A) 4-QAM
(B) 16-PSK
(C) Walsh-Hadamard orthogonal codes
(D) Gaussian Minimum Shift Keying (GMSK)
Q.23 A message signal m(t) = A
m
sin(2 ?f
m
t) is used to modulate the phase of a carrier A
c
cos(2 ?f
c
t) to get
the modulated signal y(t) = A
c
cos(2 ?f
c
t + m(t)). The bandwidth of y(t)
(A) depends on A
m
but not on f
m
(B) depends on f
m
but not on A
m
(C) depends on both A
m
and f
m
(D) does not depend on A
m
or f
m
Q.24 The directivity of an antenna array can be increased by adding more antenna elements, as a larger
number of elements
(A) improves the radiation efficiency
(B) increases the effective area of the antenna
(C) results in a better impedance matching
(D) allows more power to be transmitted by the antenna
Freq. (Hz)
40 dB
300 900 f
L
f
H
0 dB
40 dB/dec
? 40 dB/dec
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GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
For
1tan
tan 1
x
A
x
??
=
??
?
??
, the determinant of
1 T
A A
?
is
(A)
2
sec x
(B) cos 4x (C) 1 (D) 0
Q.2 The contour on the x-y plane, where the partial derivative of +
with respect to is equal to
the partial derivative of 6 + 4 with respect to , is
(A) = 2 (B) = 2 (C) + = 4
(D) ? = 0
Q.3 If is a circle of radius with centre , in the complex z-plane and if is a non-zero integer, then
?
(
)
equals
(A) 2 (B) 0
(C)
(D) 2
Q.4
Consider the function () sin(2 ) ()
t
gt e t u t ?
?
= where () ut is the unit step function. The area under
() gt is _______.
Q.5
The value of
0
1
2
n
n
n
?
=
??
??
??
?
is ______.
Q.6 For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b
is ________.
Q.7 In the circuit shown, the voltage V
X
(in Volts) is _______.
8 ? 20 ?
10 ?
5 A
V
X
+
-
+
-
0.25 V
X
0.5 V
X
12 V
3?
6?
1A
a
b
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/14
Q.8 At very high frequencies, the peak output voltage V
0
(in Volts) is ________.
Q.9 Which one of the following processes is preferred to form the gate dielectric (SiO
2
) of MOSFETs ?
(A) Sputtering (B) Molecular beam epitaxy
(C) Wet oxidation (D) Dry oxidation
Q.10 If the base width in a bipolar junction transistor is doubled, which one of the following statements
will be TRUE?
(A) Current gain will increase.
(B) Unity gain frequency will increase.
(C) Emitter-base junction capacitance will increase.
(D) Early Voltage will increase.
Q.11 In the circuit shown in the figure, the BJT has a current gain ( ) of 50. For an emitter-base
voltage
= 600 mV, the emitter-collector voltage
(in Volts) is _______.
60 k ?
500 ?
3 V
100 ?F
100 ?F
100 ?F
1 k?
1 k?
1 k? 1 k?
1.0sin( ?t) V
V
0
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/14
Q.12 In the circuit shown using an ideal opamp, the 3-dB cut-off frequency (in Hz) is _______.
v
i
10 k? 10 k?
10 k? 10 k?
0.1 ?F
v
o
+
?
Q.13 In the circuit shown, assume that diodes D
1
and D
2
are ideal. In the steady state condition, the
average voltage V
ab
(in Volts) across the 0.5 ?F capacitor is _____.
Q.14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset ( R
input).
The counter corresponding to this circuit is
(A) a modulo-5 binary up counter (B) a modulo-6 binary down counter
(C) a modulo-5 binary down counter (D) a modulo-6 binary up counter
50 sin (?t)
1 ?F
a
V
ab
0.5 ?F
D
1
D
2
b
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/14
Q.15 In the circuit shown, diodes D
1
, D
2
and D
3
are ideal, and the inputs E
1
, E
2
and E
3
are ?0 V? for
logic ?0? and ?10 V? for logic ?1?. What logic gate does the circuit represent?
(A) 3-input OR gate
(B) 3-input NOR gate
(C) 3-input AND gate
(D) 3-input XOR gate
Q.16 Which one of the following 8085 microprocessor programs correctly calculates the product of two
8-bit numbers stored in registers B and C?
(A) MVI A, 00H
JNZ LOOP
CMP C
LOOP DCR B
HLT
(B)
MVI A, 00H
CMP C
LOOP DCR B
JNZ LOOP
HLT
(C) MVI A, 00H
LOOP ADD C
DCR B
JNZ LOOP
HLT
(D) MVI A, 00H
ADD C
JNZ LOOP
LOOP INR B
HLT
Q.17 The impulse response of an LTI system can be obtained by
(A) differentiating the unit ramp response
(B) differentiating the unit step response
(C) integrating the unit ramp response
(D) integrating the unit step response
Q.18
Consider a four-point moving average filter defined by the equation
3
0
[] [ ]
i
i
yn x n i ?
=
=?
?
.
The condition on the filter coefficients that results in a null at zero frequency is
(A)
12 0 3
0; ?? ? ? == =? (B)
12 0 3
1; ?? ? ? == =?
(C)
03 1 2
0; ?? ? ? == = (D)
12 0 3
0; ?? ? ? == =
1 k?
V
0
10V
E
1
E
2
E
3
D
1
D
2
D
3
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/14
Q.19 Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued.
The value of ?
(in Hz) is ___________.
Q.20
The phase margin (in degrees) of the system
10
()
( 10)
Gs
ss
=
+
is _______.
Q.21 The transfer function of a first-order controller is given as
( ) =
( + )
+
where , and are positive real numbers. The condition for this controller to act as a phase lead
compensator is
(A) < (B) > (C) < (D) >
Q.22 The modulation scheme commonly used for transmission from GSM mobile terminals is
(A) 4-QAM
(B) 16-PSK
(C) Walsh-Hadamard orthogonal codes
(D) Gaussian Minimum Shift Keying (GMSK)
Q.23 A message signal m(t) = A
m
sin(2 ?f
m
t) is used to modulate the phase of a carrier A
c
cos(2 ?f
c
t) to get
the modulated signal y(t) = A
c
cos(2 ?f
c
t + m(t)). The bandwidth of y(t)
(A) depends on A
m
but not on f
m
(B) depends on f
m
but not on A
m
(C) depends on both A
m
and f
m
(D) does not depend on A
m
or f
m
Q.24 The directivity of an antenna array can be increased by adding more antenna elements, as a larger
number of elements
(A) improves the radiation efficiency
(B) increases the effective area of the antenna
(C) results in a better impedance matching
(D) allows more power to be transmitted by the antenna
Freq. (Hz)
40 dB
300 900 f
L
f
H
0 dB
40 dB/dec
? 40 dB/dec
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/14
Q.25 A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with
Teflon
'
( 2.1, tan 0)
r
?? == . Which one of the following circuits can represent the lumped
element model of a small piece of this cable having length ? ?
(A)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
G?zC?z
?z
(B)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
C?z
?z
(C)
L?z / 2 L?z / 2
G?zC?z
?z
(D)
R?z
L?z
G?z
C?z
?z
Q. 26 ? Q. 55 carry two marks each.
Q.26 The Newton-Raphson method is used to solve the equation f (x) = x
3
? 5x
2
+ 6x ? 8 = 0. Taking the
initial guess as x = 5, the solution obtained at the end of the first iteration is __________.
Q.27 A fair die with faces {1, 2, 3, 4, 5, 6} is thrown repeatedly till ?3? is observed for the first time. Let
X denote the number of times the die is thrown. The expected value of X is ____.
Q.28 Consider the differential equation
()
+3
( )
+2() = 0.
Given x(0) = 20 and x(1) = 10/e, where e = 2.718, the value of x(2) is _________.
Q.29 A vector field =2
+
exists inside a cylindrical region enclosed by the surfaces
= 1, = 0 and = 5 . Let S be the surface bounding this cylindrical region. The surface integral
of this field on S ? .
is _______.
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GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
For
1tan
tan 1
x
A
x
??
=
??
?
??
, the determinant of
1 T
A A
?
is
(A)
2
sec x
(B) cos 4x (C) 1 (D) 0
Q.2 The contour on the x-y plane, where the partial derivative of +
with respect to is equal to
the partial derivative of 6 + 4 with respect to , is
(A) = 2 (B) = 2 (C) + = 4
(D) ? = 0
Q.3 If is a circle of radius with centre , in the complex z-plane and if is a non-zero integer, then
?
(
)
equals
(A) 2 (B) 0
(C)
(D) 2
Q.4
Consider the function () sin(2 ) ()
t
gt e t u t ?
?
= where () ut is the unit step function. The area under
() gt is _______.
Q.5
The value of
0
1
2
n
n
n
?
=
??
??
??
?
is ______.
Q.6 For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b
is ________.
Q.7 In the circuit shown, the voltage V
X
(in Volts) is _______.
8 ? 20 ?
10 ?
5 A
V
X
+
-
+
-
0.25 V
X
0.5 V
X
12 V
3?
6?
1A
a
b
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/14
Q.8 At very high frequencies, the peak output voltage V
0
(in Volts) is ________.
Q.9 Which one of the following processes is preferred to form the gate dielectric (SiO
2
) of MOSFETs ?
(A) Sputtering (B) Molecular beam epitaxy
(C) Wet oxidation (D) Dry oxidation
Q.10 If the base width in a bipolar junction transistor is doubled, which one of the following statements
will be TRUE?
(A) Current gain will increase.
(B) Unity gain frequency will increase.
(C) Emitter-base junction capacitance will increase.
(D) Early Voltage will increase.
Q.11 In the circuit shown in the figure, the BJT has a current gain ( ) of 50. For an emitter-base
voltage
= 600 mV, the emitter-collector voltage
(in Volts) is _______.
60 k ?
500 ?
3 V
100 ?F
100 ?F
100 ?F
1 k?
1 k?
1 k? 1 k?
1.0sin( ?t) V
V
0
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/14
Q.12 In the circuit shown using an ideal opamp, the 3-dB cut-off frequency (in Hz) is _______.
v
i
10 k? 10 k?
10 k? 10 k?
0.1 ?F
v
o
+
?
Q.13 In the circuit shown, assume that diodes D
1
and D
2
are ideal. In the steady state condition, the
average voltage V
ab
(in Volts) across the 0.5 ?F capacitor is _____.
Q.14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset ( R
input).
The counter corresponding to this circuit is
(A) a modulo-5 binary up counter (B) a modulo-6 binary down counter
(C) a modulo-5 binary down counter (D) a modulo-6 binary up counter
50 sin (?t)
1 ?F
a
V
ab
0.5 ?F
D
1
D
2
b
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/14
Q.15 In the circuit shown, diodes D
1
, D
2
and D
3
are ideal, and the inputs E
1
, E
2
and E
3
are ?0 V? for
logic ?0? and ?10 V? for logic ?1?. What logic gate does the circuit represent?
(A) 3-input OR gate
(B) 3-input NOR gate
(C) 3-input AND gate
(D) 3-input XOR gate
Q.16 Which one of the following 8085 microprocessor programs correctly calculates the product of two
8-bit numbers stored in registers B and C?
(A) MVI A, 00H
JNZ LOOP
CMP C
LOOP DCR B
HLT
(B)
MVI A, 00H
CMP C
LOOP DCR B
JNZ LOOP
HLT
(C) MVI A, 00H
LOOP ADD C
DCR B
JNZ LOOP
HLT
(D) MVI A, 00H
ADD C
JNZ LOOP
LOOP INR B
HLT
Q.17 The impulse response of an LTI system can be obtained by
(A) differentiating the unit ramp response
(B) differentiating the unit step response
(C) integrating the unit ramp response
(D) integrating the unit step response
Q.18
Consider a four-point moving average filter defined by the equation
3
0
[] [ ]
i
i
yn x n i ?
=
=?
?
.
The condition on the filter coefficients that results in a null at zero frequency is
(A)
12 0 3
0; ?? ? ? == =? (B)
12 0 3
1; ?? ? ? == =?
(C)
03 1 2
0; ?? ? ? == = (D)
12 0 3
0; ?? ? ? == =
1 k?
V
0
10V
E
1
E
2
E
3
D
1
D
2
D
3
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/14
Q.19 Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued.
The value of ?
(in Hz) is ___________.
Q.20
The phase margin (in degrees) of the system
10
()
( 10)
Gs
ss
=
+
is _______.
Q.21 The transfer function of a first-order controller is given as
( ) =
( + )
+
where , and are positive real numbers. The condition for this controller to act as a phase lead
compensator is
(A) < (B) > (C) < (D) >
Q.22 The modulation scheme commonly used for transmission from GSM mobile terminals is
(A) 4-QAM
(B) 16-PSK
(C) Walsh-Hadamard orthogonal codes
(D) Gaussian Minimum Shift Keying (GMSK)
Q.23 A message signal m(t) = A
m
sin(2 ?f
m
t) is used to modulate the phase of a carrier A
c
cos(2 ?f
c
t) to get
the modulated signal y(t) = A
c
cos(2 ?f
c
t + m(t)). The bandwidth of y(t)
(A) depends on A
m
but not on f
m
(B) depends on f
m
but not on A
m
(C) depends on both A
m
and f
m
(D) does not depend on A
m
or f
m
Q.24 The directivity of an antenna array can be increased by adding more antenna elements, as a larger
number of elements
(A) improves the radiation efficiency
(B) increases the effective area of the antenna
(C) results in a better impedance matching
(D) allows more power to be transmitted by the antenna
Freq. (Hz)
40 dB
300 900 f
L
f
H
0 dB
40 dB/dec
? 40 dB/dec
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/14
Q.25 A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with
Teflon
'
( 2.1, tan 0)
r
?? == . Which one of the following circuits can represent the lumped
element model of a small piece of this cable having length ? ?
(A)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
G?zC?z
?z
(B)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
C?z
?z
(C)
L?z / 2 L?z / 2
G?zC?z
?z
(D)
R?z
L?z
G?z
C?z
?z
Q. 26 ? Q. 55 carry two marks each.
Q.26 The Newton-Raphson method is used to solve the equation f (x) = x
3
? 5x
2
+ 6x ? 8 = 0. Taking the
initial guess as x = 5, the solution obtained at the end of the first iteration is __________.
Q.27 A fair die with faces {1, 2, 3, 4, 5, 6} is thrown repeatedly till ?3? is observed for the first time. Let
X denote the number of times the die is thrown. The expected value of X is ____.
Q.28 Consider the differential equation
()
+3
( )
+2() = 0.
Given x(0) = 20 and x(1) = 10/e, where e = 2.718, the value of x(2) is _________.
Q.29 A vector field =2
+
exists inside a cylindrical region enclosed by the surfaces
= 1, = 0 and = 5 . Let S be the surface bounding this cylindrical region. The surface integral
of this field on S ? .
is _______.
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/14
Q.30 In the circuit shown, the current I flowing through the 50 ? resistor will be zero if the value of
capacitor C (in ?F) is ______.
Q.31 The ABCD parameters of the following 2-port network are
(A) 3.5 +220.5
20 .5 3.5 ? 2
(B) 3.5 +230.5
0.5 3 .5 ? 2
(C) 10 2 + 0
2+010
(D) 7+40.5
30 .5 7 ? 4
Q.32 A network is described by the state model as
=2 ?
+3 =?4 ?
= 3 ?2
The transfer function ( ) =
()
( )
is
(A)
( ) ()
(B)
( ) ( )
(C)
( ) ( )
(D)
( ) ()
C
1 mH 1 mH
1 mH
50 ?
5? sin(5000t)
I
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GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
For
1tan
tan 1
x
A
x
??
=
??
?
??
, the determinant of
1 T
A A
?
is
(A)
2
sec x
(B) cos 4x (C) 1 (D) 0
Q.2 The contour on the x-y plane, where the partial derivative of +
with respect to is equal to
the partial derivative of 6 + 4 with respect to , is
(A) = 2 (B) = 2 (C) + = 4
(D) ? = 0
Q.3 If is a circle of radius with centre , in the complex z-plane and if is a non-zero integer, then
?
(
)
equals
(A) 2 (B) 0
(C)
(D) 2
Q.4
Consider the function () sin(2 ) ()
t
gt e t u t ?
?
= where () ut is the unit step function. The area under
() gt is _______.
Q.5
The value of
0
1
2
n
n
n
?
=
??
??
??
?
is ______.
Q.6 For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b
is ________.
Q.7 In the circuit shown, the voltage V
X
(in Volts) is _______.
8 ? 20 ?
10 ?
5 A
V
X
+
-
+
-
0.25 V
X
0.5 V
X
12 V
3?
6?
1A
a
b
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/14
Q.8 At very high frequencies, the peak output voltage V
0
(in Volts) is ________.
Q.9 Which one of the following processes is preferred to form the gate dielectric (SiO
2
) of MOSFETs ?
(A) Sputtering (B) Molecular beam epitaxy
(C) Wet oxidation (D) Dry oxidation
Q.10 If the base width in a bipolar junction transistor is doubled, which one of the following statements
will be TRUE?
(A) Current gain will increase.
(B) Unity gain frequency will increase.
(C) Emitter-base junction capacitance will increase.
(D) Early Voltage will increase.
Q.11 In the circuit shown in the figure, the BJT has a current gain ( ) of 50. For an emitter-base
voltage
= 600 mV, the emitter-collector voltage
(in Volts) is _______.
60 k ?
500 ?
3 V
100 ?F
100 ?F
100 ?F
1 k?
1 k?
1 k? 1 k?
1.0sin( ?t) V
V
0
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/14
Q.12 In the circuit shown using an ideal opamp, the 3-dB cut-off frequency (in Hz) is _______.
v
i
10 k? 10 k?
10 k? 10 k?
0.1 ?F
v
o
+
?
Q.13 In the circuit shown, assume that diodes D
1
and D
2
are ideal. In the steady state condition, the
average voltage V
ab
(in Volts) across the 0.5 ?F capacitor is _____.
Q.14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset ( R
input).
The counter corresponding to this circuit is
(A) a modulo-5 binary up counter (B) a modulo-6 binary down counter
(C) a modulo-5 binary down counter (D) a modulo-6 binary up counter
50 sin (?t)
1 ?F
a
V
ab
0.5 ?F
D
1
D
2
b
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/14
Q.15 In the circuit shown, diodes D
1
, D
2
and D
3
are ideal, and the inputs E
1
, E
2
and E
3
are ?0 V? for
logic ?0? and ?10 V? for logic ?1?. What logic gate does the circuit represent?
(A) 3-input OR gate
(B) 3-input NOR gate
(C) 3-input AND gate
(D) 3-input XOR gate
Q.16 Which one of the following 8085 microprocessor programs correctly calculates the product of two
8-bit numbers stored in registers B and C?
(A) MVI A, 00H
JNZ LOOP
CMP C
LOOP DCR B
HLT
(B)
MVI A, 00H
CMP C
LOOP DCR B
JNZ LOOP
HLT
(C) MVI A, 00H
LOOP ADD C
DCR B
JNZ LOOP
HLT
(D) MVI A, 00H
ADD C
JNZ LOOP
LOOP INR B
HLT
Q.17 The impulse response of an LTI system can be obtained by
(A) differentiating the unit ramp response
(B) differentiating the unit step response
(C) integrating the unit ramp response
(D) integrating the unit step response
Q.18
Consider a four-point moving average filter defined by the equation
3
0
[] [ ]
i
i
yn x n i ?
=
=?
?
.
The condition on the filter coefficients that results in a null at zero frequency is
(A)
12 0 3
0; ?? ? ? == =? (B)
12 0 3
1; ?? ? ? == =?
(C)
03 1 2
0; ?? ? ? == = (D)
12 0 3
0; ?? ? ? == =
1 k?
V
0
10V
E
1
E
2
E
3
D
1
D
2
D
3
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/14
Q.19 Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued.
The value of ?
(in Hz) is ___________.
Q.20
The phase margin (in degrees) of the system
10
()
( 10)
Gs
ss
=
+
is _______.
Q.21 The transfer function of a first-order controller is given as
( ) =
( + )
+
where , and are positive real numbers. The condition for this controller to act as a phase lead
compensator is
(A) < (B) > (C) < (D) >
Q.22 The modulation scheme commonly used for transmission from GSM mobile terminals is
(A) 4-QAM
(B) 16-PSK
(C) Walsh-Hadamard orthogonal codes
(D) Gaussian Minimum Shift Keying (GMSK)
Q.23 A message signal m(t) = A
m
sin(2 ?f
m
t) is used to modulate the phase of a carrier A
c
cos(2 ?f
c
t) to get
the modulated signal y(t) = A
c
cos(2 ?f
c
t + m(t)). The bandwidth of y(t)
(A) depends on A
m
but not on f
m
(B) depends on f
m
but not on A
m
(C) depends on both A
m
and f
m
(D) does not depend on A
m
or f
m
Q.24 The directivity of an antenna array can be increased by adding more antenna elements, as a larger
number of elements
(A) improves the radiation efficiency
(B) increases the effective area of the antenna
(C) results in a better impedance matching
(D) allows more power to be transmitted by the antenna
Freq. (Hz)
40 dB
300 900 f
L
f
H
0 dB
40 dB/dec
? 40 dB/dec
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/14
Q.25 A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with
Teflon
'
( 2.1, tan 0)
r
?? == . Which one of the following circuits can represent the lumped
element model of a small piece of this cable having length ? ?
(A)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
G?zC?z
?z
(B)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
C?z
?z
(C)
L?z / 2 L?z / 2
G?zC?z
?z
(D)
R?z
L?z
G?z
C?z
?z
Q. 26 ? Q. 55 carry two marks each.
Q.26 The Newton-Raphson method is used to solve the equation f (x) = x
3
? 5x
2
+ 6x ? 8 = 0. Taking the
initial guess as x = 5, the solution obtained at the end of the first iteration is __________.
Q.27 A fair die with faces {1, 2, 3, 4, 5, 6} is thrown repeatedly till ?3? is observed for the first time. Let
X denote the number of times the die is thrown. The expected value of X is ____.
Q.28 Consider the differential equation
()
+3
( )
+2() = 0.
Given x(0) = 20 and x(1) = 10/e, where e = 2.718, the value of x(2) is _________.
Q.29 A vector field =2
+
exists inside a cylindrical region enclosed by the surfaces
= 1, = 0 and = 5 . Let S be the surface bounding this cylindrical region. The surface integral
of this field on S ? .
is _______.
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/14
Q.30 In the circuit shown, the current I flowing through the 50 ? resistor will be zero if the value of
capacitor C (in ?F) is ______.
Q.31 The ABCD parameters of the following 2-port network are
(A) 3.5 +220.5
20 .5 3.5 ? 2
(B) 3.5 +230.5
0.5 3 .5 ? 2
(C) 10 2 + 0
2+010
(D) 7+40.5
30 .5 7 ? 4
Q.32 A network is described by the state model as
=2 ?
+3 =?4 ?
= 3 ?2
The transfer function ( ) =
()
( )
is
(A)
( ) ()
(B)
( ) ( )
(C)
( ) ( )
(D)
( ) ()
C
1 mH 1 mH
1 mH
50 ?
5? sin(5000t)
I
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/14
Q.33 The electric field profile in the depletion region of a p-n junction in equilibrium is shown in the
figure. Which one of the following statements is NOT TRUE?
(A) The left side of the junction is n-type and the right side is p-type
(B) Both the n-type and p-type depletion regions are uniformly doped
(C) The potential difference across the depletion region is 700 mV
(D) If the p-type region has a doping concentration of 10
15
cm
-3
, then the doping concentration in
the n-type region will be 10
16
cm
-3
Q.34 The current in an enhancement mode NMOS transistor biased in saturation mode was measured to
be 1 mA at a drain-source voltage of 5 V. When the drain-source voltage was increased to 6 V
while keeping gate-source voltage same, the drain current increased to 1.02 mA. Assume that drain
to source saturation voltage is much smaller than the applied drain-source voltage. The channel
length modulation parameter (in
) is _______.
Q.35
An npn BJT having reverse saturation current
S
I = 10
-15
A is biased in the forward active region
with
BE
V
= 700 mV. The thermal voltage (
T
V ) is 25 mV and the current gain ( ? ) may vary from
50 to 150 due to manufacturing variations. The maximum emitter current (in ?A) is ________.
Q.36 A three bit pseudo random number generator is shown. Initially the value of output
Y ? Y
2
Y
1
Y
0
is set to 111. The value of output Y after three clock cycles is
(A) 000 (B) 001 (C) 010 (D) 100
X (?m)
1.0 0.5 ? 0.1 0
10
4
E
(V/cm)
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GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
For
1tan
tan 1
x
A
x
??
=
??
?
??
, the determinant of
1 T
A A
?
is
(A)
2
sec x
(B) cos 4x (C) 1 (D) 0
Q.2 The contour on the x-y plane, where the partial derivative of +
with respect to is equal to
the partial derivative of 6 + 4 with respect to , is
(A) = 2 (B) = 2 (C) + = 4
(D) ? = 0
Q.3 If is a circle of radius with centre , in the complex z-plane and if is a non-zero integer, then
?
(
)
equals
(A) 2 (B) 0
(C)
(D) 2
Q.4
Consider the function () sin(2 ) ()
t
gt e t u t ?
?
= where () ut is the unit step function. The area under
() gt is _______.
Q.5
The value of
0
1
2
n
n
n
?
=
??
??
??
?
is ______.
Q.6 For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b
is ________.
Q.7 In the circuit shown, the voltage V
X
(in Volts) is _______.
8 ? 20 ?
10 ?
5 A
V
X
+
-
+
-
0.25 V
X
0.5 V
X
12 V
3?
6?
1A
a
b
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/14
Q.8 At very high frequencies, the peak output voltage V
0
(in Volts) is ________.
Q.9 Which one of the following processes is preferred to form the gate dielectric (SiO
2
) of MOSFETs ?
(A) Sputtering (B) Molecular beam epitaxy
(C) Wet oxidation (D) Dry oxidation
Q.10 If the base width in a bipolar junction transistor is doubled, which one of the following statements
will be TRUE?
(A) Current gain will increase.
(B) Unity gain frequency will increase.
(C) Emitter-base junction capacitance will increase.
(D) Early Voltage will increase.
Q.11 In the circuit shown in the figure, the BJT has a current gain ( ) of 50. For an emitter-base
voltage
= 600 mV, the emitter-collector voltage
(in Volts) is _______.
60 k ?
500 ?
3 V
100 ?F
100 ?F
100 ?F
1 k?
1 k?
1 k? 1 k?
1.0sin( ?t) V
V
0
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/14
Q.12 In the circuit shown using an ideal opamp, the 3-dB cut-off frequency (in Hz) is _______.
v
i
10 k? 10 k?
10 k? 10 k?
0.1 ?F
v
o
+
?
Q.13 In the circuit shown, assume that diodes D
1
and D
2
are ideal. In the steady state condition, the
average voltage V
ab
(in Volts) across the 0.5 ?F capacitor is _____.
Q.14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset ( R
input).
The counter corresponding to this circuit is
(A) a modulo-5 binary up counter (B) a modulo-6 binary down counter
(C) a modulo-5 binary down counter (D) a modulo-6 binary up counter
50 sin (?t)
1 ?F
a
V
ab
0.5 ?F
D
1
D
2
b
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/14
Q.15 In the circuit shown, diodes D
1
, D
2
and D
3
are ideal, and the inputs E
1
, E
2
and E
3
are ?0 V? for
logic ?0? and ?10 V? for logic ?1?. What logic gate does the circuit represent?
(A) 3-input OR gate
(B) 3-input NOR gate
(C) 3-input AND gate
(D) 3-input XOR gate
Q.16 Which one of the following 8085 microprocessor programs correctly calculates the product of two
8-bit numbers stored in registers B and C?
(A) MVI A, 00H
JNZ LOOP
CMP C
LOOP DCR B
HLT
(B)
MVI A, 00H
CMP C
LOOP DCR B
JNZ LOOP
HLT
(C) MVI A, 00H
LOOP ADD C
DCR B
JNZ LOOP
HLT
(D) MVI A, 00H
ADD C
JNZ LOOP
LOOP INR B
HLT
Q.17 The impulse response of an LTI system can be obtained by
(A) differentiating the unit ramp response
(B) differentiating the unit step response
(C) integrating the unit ramp response
(D) integrating the unit step response
Q.18
Consider a four-point moving average filter defined by the equation
3
0
[] [ ]
i
i
yn x n i ?
=
=?
?
.
The condition on the filter coefficients that results in a null at zero frequency is
(A)
12 0 3
0; ?? ? ? == =? (B)
12 0 3
1; ?? ? ? == =?
(C)
03 1 2
0; ?? ? ? == = (D)
12 0 3
0; ?? ? ? == =
1 k?
V
0
10V
E
1
E
2
E
3
D
1
D
2
D
3
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/14
Q.19 Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued.
The value of ?
(in Hz) is ___________.
Q.20
The phase margin (in degrees) of the system
10
()
( 10)
Gs
ss
=
+
is _______.
Q.21 The transfer function of a first-order controller is given as
( ) =
( + )
+
where , and are positive real numbers. The condition for this controller to act as a phase lead
compensator is
(A) < (B) > (C) < (D) >
Q.22 The modulation scheme commonly used for transmission from GSM mobile terminals is
(A) 4-QAM
(B) 16-PSK
(C) Walsh-Hadamard orthogonal codes
(D) Gaussian Minimum Shift Keying (GMSK)
Q.23 A message signal m(t) = A
m
sin(2 ?f
m
t) is used to modulate the phase of a carrier A
c
cos(2 ?f
c
t) to get
the modulated signal y(t) = A
c
cos(2 ?f
c
t + m(t)). The bandwidth of y(t)
(A) depends on A
m
but not on f
m
(B) depends on f
m
but not on A
m
(C) depends on both A
m
and f
m
(D) does not depend on A
m
or f
m
Q.24 The directivity of an antenna array can be increased by adding more antenna elements, as a larger
number of elements
(A) improves the radiation efficiency
(B) increases the effective area of the antenna
(C) results in a better impedance matching
(D) allows more power to be transmitted by the antenna
Freq. (Hz)
40 dB
300 900 f
L
f
H
0 dB
40 dB/dec
? 40 dB/dec
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/14
Q.25 A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with
Teflon
'
( 2.1, tan 0)
r
?? == . Which one of the following circuits can represent the lumped
element model of a small piece of this cable having length ? ?
(A)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
G?zC?z
?z
(B)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
C?z
?z
(C)
L?z / 2 L?z / 2
G?zC?z
?z
(D)
R?z
L?z
G?z
C?z
?z
Q. 26 ? Q. 55 carry two marks each.
Q.26 The Newton-Raphson method is used to solve the equation f (x) = x
3
? 5x
2
+ 6x ? 8 = 0. Taking the
initial guess as x = 5, the solution obtained at the end of the first iteration is __________.
Q.27 A fair die with faces {1, 2, 3, 4, 5, 6} is thrown repeatedly till ?3? is observed for the first time. Let
X denote the number of times the die is thrown. The expected value of X is ____.
Q.28 Consider the differential equation
()
+3
( )
+2() = 0.
Given x(0) = 20 and x(1) = 10/e, where e = 2.718, the value of x(2) is _________.
Q.29 A vector field =2
+
exists inside a cylindrical region enclosed by the surfaces
= 1, = 0 and = 5 . Let S be the surface bounding this cylindrical region. The surface integral
of this field on S ? .
is _______.
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/14
Q.30 In the circuit shown, the current I flowing through the 50 ? resistor will be zero if the value of
capacitor C (in ?F) is ______.
Q.31 The ABCD parameters of the following 2-port network are
(A) 3.5 +220.5
20 .5 3.5 ? 2
(B) 3.5 +230.5
0.5 3 .5 ? 2
(C) 10 2 + 0
2+010
(D) 7+40.5
30 .5 7 ? 4
Q.32 A network is described by the state model as
=2 ?
+3 =?4 ?
= 3 ?2
The transfer function ( ) =
()
( )
is
(A)
( ) ()
(B)
( ) ( )
(C)
( ) ( )
(D)
( ) ()
C
1 mH 1 mH
1 mH
50 ?
5? sin(5000t)
I
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/14
Q.33 The electric field profile in the depletion region of a p-n junction in equilibrium is shown in the
figure. Which one of the following statements is NOT TRUE?
(A) The left side of the junction is n-type and the right side is p-type
(B) Both the n-type and p-type depletion regions are uniformly doped
(C) The potential difference across the depletion region is 700 mV
(D) If the p-type region has a doping concentration of 10
15
cm
-3
, then the doping concentration in
the n-type region will be 10
16
cm
-3
Q.34 The current in an enhancement mode NMOS transistor biased in saturation mode was measured to
be 1 mA at a drain-source voltage of 5 V. When the drain-source voltage was increased to 6 V
while keeping gate-source voltage same, the drain current increased to 1.02 mA. Assume that drain
to source saturation voltage is much smaller than the applied drain-source voltage. The channel
length modulation parameter (in
) is _______.
Q.35
An npn BJT having reverse saturation current
S
I = 10
-15
A is biased in the forward active region
with
BE
V
= 700 mV. The thermal voltage (
T
V ) is 25 mV and the current gain ( ? ) may vary from
50 to 150 due to manufacturing variations. The maximum emitter current (in ?A) is ________.
Q.36 A three bit pseudo random number generator is shown. Initially the value of output
Y ? Y
2
Y
1
Y
0
is set to 111. The value of output Y after three clock cycles is
(A) 000 (B) 001 (C) 010 (D) 100
X (?m)
1.0 0.5 ? 0.1 0
10
4
E
(V/cm)
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/14
Q.37 A universal logic gate can implement any Boolean function by connecting sufficient number of
them appropriately. Three gates are shown.
Gate 1 Gate 2 Gate 3
Which one of the following statements is TRUE?
(A) Gate 1 is a universal gate.
(B) Gate 2 is a universal gate.
(C) Gate 3 is a universal gate.
(D) None of the gates shown is a universal gate.
Q.38 An SR latch is implemented using TTL gates as shown in the figure. The set and reset pulse inputs
are provided using the push-button switches. It is observed that the circuit fails to work as desired.
The SR latch can be made functional by changing
(A) NOR gates to NAND gates
(B) inverters to buffers
(C) NOR gates to NAND gates and inverters to buffers
(D) 5 V to ground
Q.39 In the circuit shown, assume that the opamp is ideal. If the gain (v
o
/ v
in
) is ?12, the value of
R (in k?) is _____.
v
in
v
0
R
10 k?
10 k? 10 k?
5 V
Q
Q
Set
Reset
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GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
For
1tan
tan 1
x
A
x
??
=
??
?
??
, the determinant of
1 T
A A
?
is
(A)
2
sec x
(B) cos 4x (C) 1 (D) 0
Q.2 The contour on the x-y plane, where the partial derivative of +
with respect to is equal to
the partial derivative of 6 + 4 with respect to , is
(A) = 2 (B) = 2 (C) + = 4
(D) ? = 0
Q.3 If is a circle of radius with centre , in the complex z-plane and if is a non-zero integer, then
?
(
)
equals
(A) 2 (B) 0
(C)
(D) 2
Q.4
Consider the function () sin(2 ) ()
t
gt e t u t ?
?
= where () ut is the unit step function. The area under
() gt is _______.
Q.5
The value of
0
1
2
n
n
n
?
=
??
??
??
?
is ______.
Q.6 For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b
is ________.
Q.7 In the circuit shown, the voltage V
X
(in Volts) is _______.
8 ? 20 ?
10 ?
5 A
V
X
+
-
+
-
0.25 V
X
0.5 V
X
12 V
3?
6?
1A
a
b
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/14
Q.8 At very high frequencies, the peak output voltage V
0
(in Volts) is ________.
Q.9 Which one of the following processes is preferred to form the gate dielectric (SiO
2
) of MOSFETs ?
(A) Sputtering (B) Molecular beam epitaxy
(C) Wet oxidation (D) Dry oxidation
Q.10 If the base width in a bipolar junction transistor is doubled, which one of the following statements
will be TRUE?
(A) Current gain will increase.
(B) Unity gain frequency will increase.
(C) Emitter-base junction capacitance will increase.
(D) Early Voltage will increase.
Q.11 In the circuit shown in the figure, the BJT has a current gain ( ) of 50. For an emitter-base
voltage
= 600 mV, the emitter-collector voltage
(in Volts) is _______.
60 k ?
500 ?
3 V
100 ?F
100 ?F
100 ?F
1 k?
1 k?
1 k? 1 k?
1.0sin( ?t) V
V
0
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/14
Q.12 In the circuit shown using an ideal opamp, the 3-dB cut-off frequency (in Hz) is _______.
v
i
10 k? 10 k?
10 k? 10 k?
0.1 ?F
v
o
+
?
Q.13 In the circuit shown, assume that diodes D
1
and D
2
are ideal. In the steady state condition, the
average voltage V
ab
(in Volts) across the 0.5 ?F capacitor is _____.
Q.14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset ( R
input).
The counter corresponding to this circuit is
(A) a modulo-5 binary up counter (B) a modulo-6 binary down counter
(C) a modulo-5 binary down counter (D) a modulo-6 binary up counter
50 sin (?t)
1 ?F
a
V
ab
0.5 ?F
D
1
D
2
b
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/14
Q.15 In the circuit shown, diodes D
1
, D
2
and D
3
are ideal, and the inputs E
1
, E
2
and E
3
are ?0 V? for
logic ?0? and ?10 V? for logic ?1?. What logic gate does the circuit represent?
(A) 3-input OR gate
(B) 3-input NOR gate
(C) 3-input AND gate
(D) 3-input XOR gate
Q.16 Which one of the following 8085 microprocessor programs correctly calculates the product of two
8-bit numbers stored in registers B and C?
(A) MVI A, 00H
JNZ LOOP
CMP C
LOOP DCR B
HLT
(B)
MVI A, 00H
CMP C
LOOP DCR B
JNZ LOOP
HLT
(C) MVI A, 00H
LOOP ADD C
DCR B
JNZ LOOP
HLT
(D) MVI A, 00H
ADD C
JNZ LOOP
LOOP INR B
HLT
Q.17 The impulse response of an LTI system can be obtained by
(A) differentiating the unit ramp response
(B) differentiating the unit step response
(C) integrating the unit ramp response
(D) integrating the unit step response
Q.18
Consider a four-point moving average filter defined by the equation
3
0
[] [ ]
i
i
yn x n i ?
=
=?
?
.
The condition on the filter coefficients that results in a null at zero frequency is
(A)
12 0 3
0; ?? ? ? == =? (B)
12 0 3
1; ?? ? ? == =?
(C)
03 1 2
0; ?? ? ? == = (D)
12 0 3
0; ?? ? ? == =
1 k?
V
0
10V
E
1
E
2
E
3
D
1
D
2
D
3
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/14
Q.19 Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued.
The value of ?
(in Hz) is ___________.
Q.20
The phase margin (in degrees) of the system
10
()
( 10)
Gs
ss
=
+
is _______.
Q.21 The transfer function of a first-order controller is given as
( ) =
( + )
+
where , and are positive real numbers. The condition for this controller to act as a phase lead
compensator is
(A) < (B) > (C) < (D) >
Q.22 The modulation scheme commonly used for transmission from GSM mobile terminals is
(A) 4-QAM
(B) 16-PSK
(C) Walsh-Hadamard orthogonal codes
(D) Gaussian Minimum Shift Keying (GMSK)
Q.23 A message signal m(t) = A
m
sin(2 ?f
m
t) is used to modulate the phase of a carrier A
c
cos(2 ?f
c
t) to get
the modulated signal y(t) = A
c
cos(2 ?f
c
t + m(t)). The bandwidth of y(t)
(A) depends on A
m
but not on f
m
(B) depends on f
m
but not on A
m
(C) depends on both A
m
and f
m
(D) does not depend on A
m
or f
m
Q.24 The directivity of an antenna array can be increased by adding more antenna elements, as a larger
number of elements
(A) improves the radiation efficiency
(B) increases the effective area of the antenna
(C) results in a better impedance matching
(D) allows more power to be transmitted by the antenna
Freq. (Hz)
40 dB
300 900 f
L
f
H
0 dB
40 dB/dec
? 40 dB/dec
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/14
Q.25 A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with
Teflon
'
( 2.1, tan 0)
r
?? == . Which one of the following circuits can represent the lumped
element model of a small piece of this cable having length ? ?
(A)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
G?zC?z
?z
(B)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
C?z
?z
(C)
L?z / 2 L?z / 2
G?zC?z
?z
(D)
R?z
L?z
G?z
C?z
?z
Q. 26 ? Q. 55 carry two marks each.
Q.26 The Newton-Raphson method is used to solve the equation f (x) = x
3
? 5x
2
+ 6x ? 8 = 0. Taking the
initial guess as x = 5, the solution obtained at the end of the first iteration is __________.
Q.27 A fair die with faces {1, 2, 3, 4, 5, 6} is thrown repeatedly till ?3? is observed for the first time. Let
X denote the number of times the die is thrown. The expected value of X is ____.
Q.28 Consider the differential equation
()
+3
( )
+2() = 0.
Given x(0) = 20 and x(1) = 10/e, where e = 2.718, the value of x(2) is _________.
Q.29 A vector field =2
+
exists inside a cylindrical region enclosed by the surfaces
= 1, = 0 and = 5 . Let S be the surface bounding this cylindrical region. The surface integral
of this field on S ? .
is _______.
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/14
Q.30 In the circuit shown, the current I flowing through the 50 ? resistor will be zero if the value of
capacitor C (in ?F) is ______.
Q.31 The ABCD parameters of the following 2-port network are
(A) 3.5 +220.5
20 .5 3.5 ? 2
(B) 3.5 +230.5
0.5 3 .5 ? 2
(C) 10 2 + 0
2+010
(D) 7+40.5
30 .5 7 ? 4
Q.32 A network is described by the state model as
=2 ?
+3 =?4 ?
= 3 ?2
The transfer function ( ) =
()
( )
is
(A)
( ) ()
(B)
( ) ( )
(C)
( ) ( )
(D)
( ) ()
C
1 mH 1 mH
1 mH
50 ?
5? sin(5000t)
I
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/14
Q.33 The electric field profile in the depletion region of a p-n junction in equilibrium is shown in the
figure. Which one of the following statements is NOT TRUE?
(A) The left side of the junction is n-type and the right side is p-type
(B) Both the n-type and p-type depletion regions are uniformly doped
(C) The potential difference across the depletion region is 700 mV
(D) If the p-type region has a doping concentration of 10
15
cm
-3
, then the doping concentration in
the n-type region will be 10
16
cm
-3
Q.34 The current in an enhancement mode NMOS transistor biased in saturation mode was measured to
be 1 mA at a drain-source voltage of 5 V. When the drain-source voltage was increased to 6 V
while keeping gate-source voltage same, the drain current increased to 1.02 mA. Assume that drain
to source saturation voltage is much smaller than the applied drain-source voltage. The channel
length modulation parameter (in
) is _______.
Q.35
An npn BJT having reverse saturation current
S
I = 10
-15
A is biased in the forward active region
with
BE
V
= 700 mV. The thermal voltage (
T
V ) is 25 mV and the current gain ( ? ) may vary from
50 to 150 due to manufacturing variations. The maximum emitter current (in ?A) is ________.
Q.36 A three bit pseudo random number generator is shown. Initially the value of output
Y ? Y
2
Y
1
Y
0
is set to 111. The value of output Y after three clock cycles is
(A) 000 (B) 001 (C) 010 (D) 100
X (?m)
1.0 0.5 ? 0.1 0
10
4
E
(V/cm)
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/14
Q.37 A universal logic gate can implement any Boolean function by connecting sufficient number of
them appropriately. Three gates are shown.
Gate 1 Gate 2 Gate 3
Which one of the following statements is TRUE?
(A) Gate 1 is a universal gate.
(B) Gate 2 is a universal gate.
(C) Gate 3 is a universal gate.
(D) None of the gates shown is a universal gate.
Q.38 An SR latch is implemented using TTL gates as shown in the figure. The set and reset pulse inputs
are provided using the push-button switches. It is observed that the circuit fails to work as desired.
The SR latch can be made functional by changing
(A) NOR gates to NAND gates
(B) inverters to buffers
(C) NOR gates to NAND gates and inverters to buffers
(D) 5 V to ground
Q.39 In the circuit shown, assume that the opamp is ideal. If the gain (v
o
/ v
in
) is ?12, the value of
R (in k?) is _____.
v
in
v
0
R
10 k?
10 k? 10 k?
5 V
Q
Q
Set
Reset
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 10/14
Q.40 In the circuit shown, both the enhancement mode NMOS transistors have the following
characteristics: =
( ?) =1 ? ;
=1 . Assume that the channel length
modulation parameter is zero and body is shorted to source. The minimum supply voltage
(in
volts) needed to ensure that transistor M
1
operates in saturation mode of operation is _______.
Q.41 In the circuit shown, assume that the diodes D
1
and D
2
are ideal. The average value of voltage V
ab
(in Volts), across terminals ?a? and ?b? is _________.
Q.42 Suppose [ ] is an absolutely summable discrete-time signal. Its z-transform is a rational function
with two poles and two zeroes. The poles are at = ?2 . Which one of the following statements is
TRUE for the signal [ ] ?
(A) It is a finite duration signal.
(B) It is a causal signal.
(C) It is a non-causal signal.
(D) It is a periodic signal.
M
1
M
2
V
DD
2V
20 k? 10 k?
10 k?
6? sin(?t)ab
D
1
D
2
V
ab
+
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
For
1tan
tan 1
x
A
x
??
=
??
?
??
, the determinant of
1 T
A A
?
is
(A)
2
sec x
(B) cos 4x (C) 1 (D) 0
Q.2 The contour on the x-y plane, where the partial derivative of +
with respect to is equal to
the partial derivative of 6 + 4 with respect to , is
(A) = 2 (B) = 2 (C) + = 4
(D) ? = 0
Q.3 If is a circle of radius with centre , in the complex z-plane and if is a non-zero integer, then
?
(
)
equals
(A) 2 (B) 0
(C)
(D) 2
Q.4
Consider the function () sin(2 ) ()
t
gt e t u t ?
?
= where () ut is the unit step function. The area under
() gt is _______.
Q.5
The value of
0
1
2
n
n
n
?
=
??
??
??
?
is ______.
Q.6 For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b
is ________.
Q.7 In the circuit shown, the voltage V
X
(in Volts) is _______.
8 ? 20 ?
10 ?
5 A
V
X
+
-
+
-
0.25 V
X
0.5 V
X
12 V
3?
6?
1A
a
b
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/14
Q.8 At very high frequencies, the peak output voltage V
0
(in Volts) is ________.
Q.9 Which one of the following processes is preferred to form the gate dielectric (SiO
2
) of MOSFETs ?
(A) Sputtering (B) Molecular beam epitaxy
(C) Wet oxidation (D) Dry oxidation
Q.10 If the base width in a bipolar junction transistor is doubled, which one of the following statements
will be TRUE?
(A) Current gain will increase.
(B) Unity gain frequency will increase.
(C) Emitter-base junction capacitance will increase.
(D) Early Voltage will increase.
Q.11 In the circuit shown in the figure, the BJT has a current gain ( ) of 50. For an emitter-base
voltage
= 600 mV, the emitter-collector voltage
(in Volts) is _______.
60 k ?
500 ?
3 V
100 ?F
100 ?F
100 ?F
1 k?
1 k?
1 k? 1 k?
1.0sin( ?t) V
V
0
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/14
Q.12 In the circuit shown using an ideal opamp, the 3-dB cut-off frequency (in Hz) is _______.
v
i
10 k? 10 k?
10 k? 10 k?
0.1 ?F
v
o
+
?
Q.13 In the circuit shown, assume that diodes D
1
and D
2
are ideal. In the steady state condition, the
average voltage V
ab
(in Volts) across the 0.5 ?F capacitor is _____.
Q.14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset ( R
input).
The counter corresponding to this circuit is
(A) a modulo-5 binary up counter (B) a modulo-6 binary down counter
(C) a modulo-5 binary down counter (D) a modulo-6 binary up counter
50 sin (?t)
1 ?F
a
V
ab
0.5 ?F
D
1
D
2
b
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/14
Q.15 In the circuit shown, diodes D
1
, D
2
and D
3
are ideal, and the inputs E
1
, E
2
and E
3
are ?0 V? for
logic ?0? and ?10 V? for logic ?1?. What logic gate does the circuit represent?
(A) 3-input OR gate
(B) 3-input NOR gate
(C) 3-input AND gate
(D) 3-input XOR gate
Q.16 Which one of the following 8085 microprocessor programs correctly calculates the product of two
8-bit numbers stored in registers B and C?
(A) MVI A, 00H
JNZ LOOP
CMP C
LOOP DCR B
HLT
(B)
MVI A, 00H
CMP C
LOOP DCR B
JNZ LOOP
HLT
(C) MVI A, 00H
LOOP ADD C
DCR B
JNZ LOOP
HLT
(D) MVI A, 00H
ADD C
JNZ LOOP
LOOP INR B
HLT
Q.17 The impulse response of an LTI system can be obtained by
(A) differentiating the unit ramp response
(B) differentiating the unit step response
(C) integrating the unit ramp response
(D) integrating the unit step response
Q.18
Consider a four-point moving average filter defined by the equation
3
0
[] [ ]
i
i
yn x n i ?
=
=?
?
.
The condition on the filter coefficients that results in a null at zero frequency is
(A)
12 0 3
0; ?? ? ? == =? (B)
12 0 3
1; ?? ? ? == =?
(C)
03 1 2
0; ?? ? ? == = (D)
12 0 3
0; ?? ? ? == =
1 k?
V
0
10V
E
1
E
2
E
3
D
1
D
2
D
3
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/14
Q.19 Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued.
The value of ?
(in Hz) is ___________.
Q.20
The phase margin (in degrees) of the system
10
()
( 10)
Gs
ss
=
+
is _______.
Q.21 The transfer function of a first-order controller is given as
( ) =
( + )
+
where , and are positive real numbers. The condition for this controller to act as a phase lead
compensator is
(A) < (B) > (C) < (D) >
Q.22 The modulation scheme commonly used for transmission from GSM mobile terminals is
(A) 4-QAM
(B) 16-PSK
(C) Walsh-Hadamard orthogonal codes
(D) Gaussian Minimum Shift Keying (GMSK)
Q.23 A message signal m(t) = A
m
sin(2 ?f
m
t) is used to modulate the phase of a carrier A
c
cos(2 ?f
c
t) to get
the modulated signal y(t) = A
c
cos(2 ?f
c
t + m(t)). The bandwidth of y(t)
(A) depends on A
m
but not on f
m
(B) depends on f
m
but not on A
m
(C) depends on both A
m
and f
m
(D) does not depend on A
m
or f
m
Q.24 The directivity of an antenna array can be increased by adding more antenna elements, as a larger
number of elements
(A) improves the radiation efficiency
(B) increases the effective area of the antenna
(C) results in a better impedance matching
(D) allows more power to be transmitted by the antenna
Freq. (Hz)
40 dB
300 900 f
L
f
H
0 dB
40 dB/dec
? 40 dB/dec
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/14
Q.25 A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with
Teflon
'
( 2.1, tan 0)
r
?? == . Which one of the following circuits can represent the lumped
element model of a small piece of this cable having length ? ?
(A)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
G?zC?z
?z
(B)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
C?z
?z
(C)
L?z / 2 L?z / 2
G?zC?z
?z
(D)
R?z
L?z
G?z
C?z
?z
Q. 26 ? Q. 55 carry two marks each.
Q.26 The Newton-Raphson method is used to solve the equation f (x) = x
3
? 5x
2
+ 6x ? 8 = 0. Taking the
initial guess as x = 5, the solution obtained at the end of the first iteration is __________.
Q.27 A fair die with faces {1, 2, 3, 4, 5, 6} is thrown repeatedly till ?3? is observed for the first time. Let
X denote the number of times the die is thrown. The expected value of X is ____.
Q.28 Consider the differential equation
()
+3
( )
+2() = 0.
Given x(0) = 20 and x(1) = 10/e, where e = 2.718, the value of x(2) is _________.
Q.29 A vector field =2
+
exists inside a cylindrical region enclosed by the surfaces
= 1, = 0 and = 5 . Let S be the surface bounding this cylindrical region. The surface integral
of this field on S ? .
is _______.
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/14
Q.30 In the circuit shown, the current I flowing through the 50 ? resistor will be zero if the value of
capacitor C (in ?F) is ______.
Q.31 The ABCD parameters of the following 2-port network are
(A) 3.5 +220.5
20 .5 3.5 ? 2
(B) 3.5 +230.5
0.5 3 .5 ? 2
(C) 10 2 + 0
2+010
(D) 7+40.5
30 .5 7 ? 4
Q.32 A network is described by the state model as
=2 ?
+3 =?4 ?
= 3 ?2
The transfer function ( ) =
()
( )
is
(A)
( ) ()
(B)
( ) ( )
(C)
( ) ( )
(D)
( ) ()
C
1 mH 1 mH
1 mH
50 ?
5? sin(5000t)
I
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/14
Q.33 The electric field profile in the depletion region of a p-n junction in equilibrium is shown in the
figure. Which one of the following statements is NOT TRUE?
(A) The left side of the junction is n-type and the right side is p-type
(B) Both the n-type and p-type depletion regions are uniformly doped
(C) The potential difference across the depletion region is 700 mV
(D) If the p-type region has a doping concentration of 10
15
cm
-3
, then the doping concentration in
the n-type region will be 10
16
cm
-3
Q.34 The current in an enhancement mode NMOS transistor biased in saturation mode was measured to
be 1 mA at a drain-source voltage of 5 V. When the drain-source voltage was increased to 6 V
while keeping gate-source voltage same, the drain current increased to 1.02 mA. Assume that drain
to source saturation voltage is much smaller than the applied drain-source voltage. The channel
length modulation parameter (in
) is _______.
Q.35
An npn BJT having reverse saturation current
S
I = 10
-15
A is biased in the forward active region
with
BE
V
= 700 mV. The thermal voltage (
T
V ) is 25 mV and the current gain ( ? ) may vary from
50 to 150 due to manufacturing variations. The maximum emitter current (in ?A) is ________.
Q.36 A three bit pseudo random number generator is shown. Initially the value of output
Y ? Y
2
Y
1
Y
0
is set to 111. The value of output Y after three clock cycles is
(A) 000 (B) 001 (C) 010 (D) 100
X (?m)
1.0 0.5 ? 0.1 0
10
4
E
(V/cm)
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/14
Q.37 A universal logic gate can implement any Boolean function by connecting sufficient number of
them appropriately. Three gates are shown.
Gate 1 Gate 2 Gate 3
Which one of the following statements is TRUE?
(A) Gate 1 is a universal gate.
(B) Gate 2 is a universal gate.
(C) Gate 3 is a universal gate.
(D) None of the gates shown is a universal gate.
Q.38 An SR latch is implemented using TTL gates as shown in the figure. The set and reset pulse inputs
are provided using the push-button switches. It is observed that the circuit fails to work as desired.
The SR latch can be made functional by changing
(A) NOR gates to NAND gates
(B) inverters to buffers
(C) NOR gates to NAND gates and inverters to buffers
(D) 5 V to ground
Q.39 In the circuit shown, assume that the opamp is ideal. If the gain (v
o
/ v
in
) is ?12, the value of
R (in k?) is _____.
v
in
v
0
R
10 k?
10 k? 10 k?
5 V
Q
Q
Set
Reset
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 10/14
Q.40 In the circuit shown, both the enhancement mode NMOS transistors have the following
characteristics: =
( ?) =1 ? ;
=1 . Assume that the channel length
modulation parameter is zero and body is shorted to source. The minimum supply voltage
(in
volts) needed to ensure that transistor M
1
operates in saturation mode of operation is _______.
Q.41 In the circuit shown, assume that the diodes D
1
and D
2
are ideal. The average value of voltage V
ab
(in Volts), across terminals ?a? and ?b? is _________.
Q.42 Suppose [ ] is an absolutely summable discrete-time signal. Its z-transform is a rational function
with two poles and two zeroes. The poles are at = ?2 . Which one of the following statements is
TRUE for the signal [ ] ?
(A) It is a finite duration signal.
(B) It is a causal signal.
(C) It is a non-causal signal.
(D) It is a periodic signal.
M
1
M
2
V
DD
2V
20 k? 10 k?
10 k?
6? sin(?t)ab
D
1
D
2
V
ab
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 11/14
Q.43 A realization of a stable discrete time system is shown in the figure. If the system is excited by a
unit step sequence input [] x n , the response [] y n is
(A)
12
4[]5 []
33
nn
un un
?? ? ?
???
?? ? ?
?? ? ?
(B)
21
5[]3 []
33
nn
un un
?? ? ?
???
?? ? ?
?? ? ?
(C)
12
5[]5 []
33
nn
un un
?? ? ?
?
?? ? ?
?? ? ?
(D)
21
5[]5 []
33
nn
un un
?? ? ?
?
?? ? ?
?? ? ?
Q.44
Let [ ] =1 + cos
be a periodic signal with period 16. Its DFS coefficients are defined by
[]
0
15
1
exp( )
16 8
n
k
axn jkn
?
=
=?
?
% for all k . The value of the coefficient
is _______.
Q.45 Consider a continuous-time signal defined as
( ) =
sin ( 2 ? )
( 2 ? )
? ? ( ? 10 )
?
?
where ? ?? denotes the convolution operation and t is in seconds. The Nyquist sampling rate (in
samples/sec) for ( ) is _____.
Q.46 The position control of a DC servo-motor is given in the figure. The values of the parameters are
2
1 N-m/A, 1 , 0.1H, 5kg-m , 1 N-m/(rad/sec) and 1V/(rad/sec)
Ta a b
KR L J B K ==?= = = = .
The steady-state position response (in radians) due to unit impulse disturbance torque is
_______.
K
b
1
s
V
a
(s)
+
+
-
-
T
d
(s)
1
J s+B
K
T
R
a
+L
a
s
?(s)
[ ]
+
+
+
[]
1
?2/9 5/3
?5/3
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
For
1tan
tan 1
x
A
x
??
=
??
?
??
, the determinant of
1 T
A A
?
is
(A)
2
sec x
(B) cos 4x (C) 1 (D) 0
Q.2 The contour on the x-y plane, where the partial derivative of +
with respect to is equal to
the partial derivative of 6 + 4 with respect to , is
(A) = 2 (B) = 2 (C) + = 4
(D) ? = 0
Q.3 If is a circle of radius with centre , in the complex z-plane and if is a non-zero integer, then
?
(
)
equals
(A) 2 (B) 0
(C)
(D) 2
Q.4
Consider the function () sin(2 ) ()
t
gt e t u t ?
?
= where () ut is the unit step function. The area under
() gt is _______.
Q.5
The value of
0
1
2
n
n
n
?
=
??
??
??
?
is ______.
Q.6 For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b
is ________.
Q.7 In the circuit shown, the voltage V
X
(in Volts) is _______.
8 ? 20 ?
10 ?
5 A
V
X
+
-
+
-
0.25 V
X
0.5 V
X
12 V
3?
6?
1A
a
b
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/14
Q.8 At very high frequencies, the peak output voltage V
0
(in Volts) is ________.
Q.9 Which one of the following processes is preferred to form the gate dielectric (SiO
2
) of MOSFETs ?
(A) Sputtering (B) Molecular beam epitaxy
(C) Wet oxidation (D) Dry oxidation
Q.10 If the base width in a bipolar junction transistor is doubled, which one of the following statements
will be TRUE?
(A) Current gain will increase.
(B) Unity gain frequency will increase.
(C) Emitter-base junction capacitance will increase.
(D) Early Voltage will increase.
Q.11 In the circuit shown in the figure, the BJT has a current gain ( ) of 50. For an emitter-base
voltage
= 600 mV, the emitter-collector voltage
(in Volts) is _______.
60 k ?
500 ?
3 V
100 ?F
100 ?F
100 ?F
1 k?
1 k?
1 k? 1 k?
1.0sin( ?t) V
V
0
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/14
Q.12 In the circuit shown using an ideal opamp, the 3-dB cut-off frequency (in Hz) is _______.
v
i
10 k? 10 k?
10 k? 10 k?
0.1 ?F
v
o
+
?
Q.13 In the circuit shown, assume that diodes D
1
and D
2
are ideal. In the steady state condition, the
average voltage V
ab
(in Volts) across the 0.5 ?F capacitor is _____.
Q.14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset ( R
input).
The counter corresponding to this circuit is
(A) a modulo-5 binary up counter (B) a modulo-6 binary down counter
(C) a modulo-5 binary down counter (D) a modulo-6 binary up counter
50 sin (?t)
1 ?F
a
V
ab
0.5 ?F
D
1
D
2
b
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/14
Q.15 In the circuit shown, diodes D
1
, D
2
and D
3
are ideal, and the inputs E
1
, E
2
and E
3
are ?0 V? for
logic ?0? and ?10 V? for logic ?1?. What logic gate does the circuit represent?
(A) 3-input OR gate
(B) 3-input NOR gate
(C) 3-input AND gate
(D) 3-input XOR gate
Q.16 Which one of the following 8085 microprocessor programs correctly calculates the product of two
8-bit numbers stored in registers B and C?
(A) MVI A, 00H
JNZ LOOP
CMP C
LOOP DCR B
HLT
(B)
MVI A, 00H
CMP C
LOOP DCR B
JNZ LOOP
HLT
(C) MVI A, 00H
LOOP ADD C
DCR B
JNZ LOOP
HLT
(D) MVI A, 00H
ADD C
JNZ LOOP
LOOP INR B
HLT
Q.17 The impulse response of an LTI system can be obtained by
(A) differentiating the unit ramp response
(B) differentiating the unit step response
(C) integrating the unit ramp response
(D) integrating the unit step response
Q.18
Consider a four-point moving average filter defined by the equation
3
0
[] [ ]
i
i
yn x n i ?
=
=?
?
.
The condition on the filter coefficients that results in a null at zero frequency is
(A)
12 0 3
0; ?? ? ? == =? (B)
12 0 3
1; ?? ? ? == =?
(C)
03 1 2
0; ?? ? ? == = (D)
12 0 3
0; ?? ? ? == =
1 k?
V
0
10V
E
1
E
2
E
3
D
1
D
2
D
3
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/14
Q.19 Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued.
The value of ?
(in Hz) is ___________.
Q.20
The phase margin (in degrees) of the system
10
()
( 10)
Gs
ss
=
+
is _______.
Q.21 The transfer function of a first-order controller is given as
( ) =
( + )
+
where , and are positive real numbers. The condition for this controller to act as a phase lead
compensator is
(A) < (B) > (C) < (D) >
Q.22 The modulation scheme commonly used for transmission from GSM mobile terminals is
(A) 4-QAM
(B) 16-PSK
(C) Walsh-Hadamard orthogonal codes
(D) Gaussian Minimum Shift Keying (GMSK)
Q.23 A message signal m(t) = A
m
sin(2 ?f
m
t) is used to modulate the phase of a carrier A
c
cos(2 ?f
c
t) to get
the modulated signal y(t) = A
c
cos(2 ?f
c
t + m(t)). The bandwidth of y(t)
(A) depends on A
m
but not on f
m
(B) depends on f
m
but not on A
m
(C) depends on both A
m
and f
m
(D) does not depend on A
m
or f
m
Q.24 The directivity of an antenna array can be increased by adding more antenna elements, as a larger
number of elements
(A) improves the radiation efficiency
(B) increases the effective area of the antenna
(C) results in a better impedance matching
(D) allows more power to be transmitted by the antenna
Freq. (Hz)
40 dB
300 900 f
L
f
H
0 dB
40 dB/dec
? 40 dB/dec
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/14
Q.25 A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with
Teflon
'
( 2.1, tan 0)
r
?? == . Which one of the following circuits can represent the lumped
element model of a small piece of this cable having length ? ?
(A)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
G?zC?z
?z
(B)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
C?z
?z
(C)
L?z / 2 L?z / 2
G?zC?z
?z
(D)
R?z
L?z
G?z
C?z
?z
Q. 26 ? Q. 55 carry two marks each.
Q.26 The Newton-Raphson method is used to solve the equation f (x) = x
3
? 5x
2
+ 6x ? 8 = 0. Taking the
initial guess as x = 5, the solution obtained at the end of the first iteration is __________.
Q.27 A fair die with faces {1, 2, 3, 4, 5, 6} is thrown repeatedly till ?3? is observed for the first time. Let
X denote the number of times the die is thrown. The expected value of X is ____.
Q.28 Consider the differential equation
()
+3
( )
+2() = 0.
Given x(0) = 20 and x(1) = 10/e, where e = 2.718, the value of x(2) is _________.
Q.29 A vector field =2
+
exists inside a cylindrical region enclosed by the surfaces
= 1, = 0 and = 5 . Let S be the surface bounding this cylindrical region. The surface integral
of this field on S ? .
is _______.
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/14
Q.30 In the circuit shown, the current I flowing through the 50 ? resistor will be zero if the value of
capacitor C (in ?F) is ______.
Q.31 The ABCD parameters of the following 2-port network are
(A) 3.5 +220.5
20 .5 3.5 ? 2
(B) 3.5 +230.5
0.5 3 .5 ? 2
(C) 10 2 + 0
2+010
(D) 7+40.5
30 .5 7 ? 4
Q.32 A network is described by the state model as
=2 ?
+3 =?4 ?
= 3 ?2
The transfer function ( ) =
()
( )
is
(A)
( ) ()
(B)
( ) ( )
(C)
( ) ( )
(D)
( ) ()
C
1 mH 1 mH
1 mH
50 ?
5? sin(5000t)
I
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/14
Q.33 The electric field profile in the depletion region of a p-n junction in equilibrium is shown in the
figure. Which one of the following statements is NOT TRUE?
(A) The left side of the junction is n-type and the right side is p-type
(B) Both the n-type and p-type depletion regions are uniformly doped
(C) The potential difference across the depletion region is 700 mV
(D) If the p-type region has a doping concentration of 10
15
cm
-3
, then the doping concentration in
the n-type region will be 10
16
cm
-3
Q.34 The current in an enhancement mode NMOS transistor biased in saturation mode was measured to
be 1 mA at a drain-source voltage of 5 V. When the drain-source voltage was increased to 6 V
while keeping gate-source voltage same, the drain current increased to 1.02 mA. Assume that drain
to source saturation voltage is much smaller than the applied drain-source voltage. The channel
length modulation parameter (in
) is _______.
Q.35
An npn BJT having reverse saturation current
S
I = 10
-15
A is biased in the forward active region
with
BE
V
= 700 mV. The thermal voltage (
T
V ) is 25 mV and the current gain ( ? ) may vary from
50 to 150 due to manufacturing variations. The maximum emitter current (in ?A) is ________.
Q.36 A three bit pseudo random number generator is shown. Initially the value of output
Y ? Y
2
Y
1
Y
0
is set to 111. The value of output Y after three clock cycles is
(A) 000 (B) 001 (C) 010 (D) 100
X (?m)
1.0 0.5 ? 0.1 0
10
4
E
(V/cm)
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/14
Q.37 A universal logic gate can implement any Boolean function by connecting sufficient number of
them appropriately. Three gates are shown.
Gate 1 Gate 2 Gate 3
Which one of the following statements is TRUE?
(A) Gate 1 is a universal gate.
(B) Gate 2 is a universal gate.
(C) Gate 3 is a universal gate.
(D) None of the gates shown is a universal gate.
Q.38 An SR latch is implemented using TTL gates as shown in the figure. The set and reset pulse inputs
are provided using the push-button switches. It is observed that the circuit fails to work as desired.
The SR latch can be made functional by changing
(A) NOR gates to NAND gates
(B) inverters to buffers
(C) NOR gates to NAND gates and inverters to buffers
(D) 5 V to ground
Q.39 In the circuit shown, assume that the opamp is ideal. If the gain (v
o
/ v
in
) is ?12, the value of
R (in k?) is _____.
v
in
v
0
R
10 k?
10 k? 10 k?
5 V
Q
Q
Set
Reset
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 10/14
Q.40 In the circuit shown, both the enhancement mode NMOS transistors have the following
characteristics: =
( ?) =1 ? ;
=1 . Assume that the channel length
modulation parameter is zero and body is shorted to source. The minimum supply voltage
(in
volts) needed to ensure that transistor M
1
operates in saturation mode of operation is _______.
Q.41 In the circuit shown, assume that the diodes D
1
and D
2
are ideal. The average value of voltage V
ab
(in Volts), across terminals ?a? and ?b? is _________.
Q.42 Suppose [ ] is an absolutely summable discrete-time signal. Its z-transform is a rational function
with two poles and two zeroes. The poles are at = ?2 . Which one of the following statements is
TRUE for the signal [ ] ?
(A) It is a finite duration signal.
(B) It is a causal signal.
(C) It is a non-causal signal.
(D) It is a periodic signal.
M
1
M
2
V
DD
2V
20 k? 10 k?
10 k?
6? sin(?t)ab
D
1
D
2
V
ab
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 11/14
Q.43 A realization of a stable discrete time system is shown in the figure. If the system is excited by a
unit step sequence input [] x n , the response [] y n is
(A)
12
4[]5 []
33
nn
un un
?? ? ?
???
?? ? ?
?? ? ?
(B)
21
5[]3 []
33
nn
un un
?? ? ?
???
?? ? ?
?? ? ?
(C)
12
5[]5 []
33
nn
un un
?? ? ?
?
?? ? ?
?? ? ?
(D)
21
5[]5 []
33
nn
un un
?? ? ?
?
?? ? ?
?? ? ?
Q.44
Let [ ] =1 + cos
be a periodic signal with period 16. Its DFS coefficients are defined by
[]
0
15
1
exp( )
16 8
n
k
axn jkn
?
=
=?
?
% for all k . The value of the coefficient
is _______.
Q.45 Consider a continuous-time signal defined as
( ) =
sin ( 2 ? )
( 2 ? )
? ? ( ? 10 )
?
?
where ? ?? denotes the convolution operation and t is in seconds. The Nyquist sampling rate (in
samples/sec) for ( ) is _____.
Q.46 The position control of a DC servo-motor is given in the figure. The values of the parameters are
2
1 N-m/A, 1 , 0.1H, 5kg-m , 1 N-m/(rad/sec) and 1V/(rad/sec)
Ta a b
KR L J B K ==?= = = = .
The steady-state position response (in radians) due to unit impulse disturbance torque is
_______.
K
b
1
s
V
a
(s)
+
+
-
-
T
d
(s)
1
J s+B
K
T
R
a
+L
a
s
?(s)
[ ]
+
+
+
[]
1
?2/9 5/3
?5/3
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 12/14
Q.47 For the system shown in the figure, = ?2.75 lies on the root locus if is _______.
Q.48 The characteristic equation of an LTI system is given by F(s) = s
5
+ 2s
4
+ 3s
3
+ 6s
2
? 4s ? 8 = 0.
The number of roots that lie strictly in the left half s-plane is _________.
Q.49 Two sequences [ ] and [ ] have the same energy. Suppose [ ] = 0.5
[ ], where is a
positive real number and [ ] is the unit step sequence. Assume
[ ] =
? 1.5 for = 0, 1
0otherwise.
Then the value of is _________.
Q.50
The variance of the random variable X with probability density function
1
()
2
x
fxxe
?
= is
_______.
Q.51
The complex envelope of the bandpass signal
sin( / 5)
() 2 sin( )
/5 4
t
xt t
t
??
?
?
??
=? ?
??
??
, centered
about
1
2
f = Hz, is
(A)
4
sin( / 5)
/5
j
t
e
t
?
?
?
??
??
??
(B)
4
sin( / 5)
/5
j
t
e
t
?
?
?
?
??
??
??
(C)
4
sin( / 5)
2
/5
j
t
e
t
?
?
?
??
??
??
(D)
4
sin( / 5)
2
/5
j
t
e
t
?
?
?
?
??
??
??
Y(s)
s+3
s+2
K
-
+
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
For
1tan
tan 1
x
A
x
??
=
??
?
??
, the determinant of
1 T
A A
?
is
(A)
2
sec x
(B) cos 4x (C) 1 (D) 0
Q.2 The contour on the x-y plane, where the partial derivative of +
with respect to is equal to
the partial derivative of 6 + 4 with respect to , is
(A) = 2 (B) = 2 (C) + = 4
(D) ? = 0
Q.3 If is a circle of radius with centre , in the complex z-plane and if is a non-zero integer, then
?
(
)
equals
(A) 2 (B) 0
(C)
(D) 2
Q.4
Consider the function () sin(2 ) ()
t
gt e t u t ?
?
= where () ut is the unit step function. The area under
() gt is _______.
Q.5
The value of
0
1
2
n
n
n
?
=
??
??
??
?
is ______.
Q.6 For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b
is ________.
Q.7 In the circuit shown, the voltage V
X
(in Volts) is _______.
8 ? 20 ?
10 ?
5 A
V
X
+
-
+
-
0.25 V
X
0.5 V
X
12 V
3?
6?
1A
a
b
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/14
Q.8 At very high frequencies, the peak output voltage V
0
(in Volts) is ________.
Q.9 Which one of the following processes is preferred to form the gate dielectric (SiO
2
) of MOSFETs ?
(A) Sputtering (B) Molecular beam epitaxy
(C) Wet oxidation (D) Dry oxidation
Q.10 If the base width in a bipolar junction transistor is doubled, which one of the following statements
will be TRUE?
(A) Current gain will increase.
(B) Unity gain frequency will increase.
(C) Emitter-base junction capacitance will increase.
(D) Early Voltage will increase.
Q.11 In the circuit shown in the figure, the BJT has a current gain ( ) of 50. For an emitter-base
voltage
= 600 mV, the emitter-collector voltage
(in Volts) is _______.
60 k ?
500 ?
3 V
100 ?F
100 ?F
100 ?F
1 k?
1 k?
1 k? 1 k?
1.0sin( ?t) V
V
0
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/14
Q.12 In the circuit shown using an ideal opamp, the 3-dB cut-off frequency (in Hz) is _______.
v
i
10 k? 10 k?
10 k? 10 k?
0.1 ?F
v
o
+
?
Q.13 In the circuit shown, assume that diodes D
1
and D
2
are ideal. In the steady state condition, the
average voltage V
ab
(in Volts) across the 0.5 ?F capacitor is _____.
Q.14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset ( R
input).
The counter corresponding to this circuit is
(A) a modulo-5 binary up counter (B) a modulo-6 binary down counter
(C) a modulo-5 binary down counter (D) a modulo-6 binary up counter
50 sin (?t)
1 ?F
a
V
ab
0.5 ?F
D
1
D
2
b
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/14
Q.15 In the circuit shown, diodes D
1
, D
2
and D
3
are ideal, and the inputs E
1
, E
2
and E
3
are ?0 V? for
logic ?0? and ?10 V? for logic ?1?. What logic gate does the circuit represent?
(A) 3-input OR gate
(B) 3-input NOR gate
(C) 3-input AND gate
(D) 3-input XOR gate
Q.16 Which one of the following 8085 microprocessor programs correctly calculates the product of two
8-bit numbers stored in registers B and C?
(A) MVI A, 00H
JNZ LOOP
CMP C
LOOP DCR B
HLT
(B)
MVI A, 00H
CMP C
LOOP DCR B
JNZ LOOP
HLT
(C) MVI A, 00H
LOOP ADD C
DCR B
JNZ LOOP
HLT
(D) MVI A, 00H
ADD C
JNZ LOOP
LOOP INR B
HLT
Q.17 The impulse response of an LTI system can be obtained by
(A) differentiating the unit ramp response
(B) differentiating the unit step response
(C) integrating the unit ramp response
(D) integrating the unit step response
Q.18
Consider a four-point moving average filter defined by the equation
3
0
[] [ ]
i
i
yn x n i ?
=
=?
?
.
The condition on the filter coefficients that results in a null at zero frequency is
(A)
12 0 3
0; ?? ? ? == =? (B)
12 0 3
1; ?? ? ? == =?
(C)
03 1 2
0; ?? ? ? == = (D)
12 0 3
0; ?? ? ? == =
1 k?
V
0
10V
E
1
E
2
E
3
D
1
D
2
D
3
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/14
Q.19 Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued.
The value of ?
(in Hz) is ___________.
Q.20
The phase margin (in degrees) of the system
10
()
( 10)
Gs
ss
=
+
is _______.
Q.21 The transfer function of a first-order controller is given as
( ) =
( + )
+
where , and are positive real numbers. The condition for this controller to act as a phase lead
compensator is
(A) < (B) > (C) < (D) >
Q.22 The modulation scheme commonly used for transmission from GSM mobile terminals is
(A) 4-QAM
(B) 16-PSK
(C) Walsh-Hadamard orthogonal codes
(D) Gaussian Minimum Shift Keying (GMSK)
Q.23 A message signal m(t) = A
m
sin(2 ?f
m
t) is used to modulate the phase of a carrier A
c
cos(2 ?f
c
t) to get
the modulated signal y(t) = A
c
cos(2 ?f
c
t + m(t)). The bandwidth of y(t)
(A) depends on A
m
but not on f
m
(B) depends on f
m
but not on A
m
(C) depends on both A
m
and f
m
(D) does not depend on A
m
or f
m
Q.24 The directivity of an antenna array can be increased by adding more antenna elements, as a larger
number of elements
(A) improves the radiation efficiency
(B) increases the effective area of the antenna
(C) results in a better impedance matching
(D) allows more power to be transmitted by the antenna
Freq. (Hz)
40 dB
300 900 f
L
f
H
0 dB
40 dB/dec
? 40 dB/dec
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/14
Q.25 A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with
Teflon
'
( 2.1, tan 0)
r
?? == . Which one of the following circuits can represent the lumped
element model of a small piece of this cable having length ? ?
(A)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
G?zC?z
?z
(B)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
C?z
?z
(C)
L?z / 2 L?z / 2
G?zC?z
?z
(D)
R?z
L?z
G?z
C?z
?z
Q. 26 ? Q. 55 carry two marks each.
Q.26 The Newton-Raphson method is used to solve the equation f (x) = x
3
? 5x
2
+ 6x ? 8 = 0. Taking the
initial guess as x = 5, the solution obtained at the end of the first iteration is __________.
Q.27 A fair die with faces {1, 2, 3, 4, 5, 6} is thrown repeatedly till ?3? is observed for the first time. Let
X denote the number of times the die is thrown. The expected value of X is ____.
Q.28 Consider the differential equation
()
+3
( )
+2() = 0.
Given x(0) = 20 and x(1) = 10/e, where e = 2.718, the value of x(2) is _________.
Q.29 A vector field =2
+
exists inside a cylindrical region enclosed by the surfaces
= 1, = 0 and = 5 . Let S be the surface bounding this cylindrical region. The surface integral
of this field on S ? .
is _______.
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/14
Q.30 In the circuit shown, the current I flowing through the 50 ? resistor will be zero if the value of
capacitor C (in ?F) is ______.
Q.31 The ABCD parameters of the following 2-port network are
(A) 3.5 +220.5
20 .5 3.5 ? 2
(B) 3.5 +230.5
0.5 3 .5 ? 2
(C) 10 2 + 0
2+010
(D) 7+40.5
30 .5 7 ? 4
Q.32 A network is described by the state model as
=2 ?
+3 =?4 ?
= 3 ?2
The transfer function ( ) =
()
( )
is
(A)
( ) ()
(B)
( ) ( )
(C)
( ) ( )
(D)
( ) ()
C
1 mH 1 mH
1 mH
50 ?
5? sin(5000t)
I
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/14
Q.33 The electric field profile in the depletion region of a p-n junction in equilibrium is shown in the
figure. Which one of the following statements is NOT TRUE?
(A) The left side of the junction is n-type and the right side is p-type
(B) Both the n-type and p-type depletion regions are uniformly doped
(C) The potential difference across the depletion region is 700 mV
(D) If the p-type region has a doping concentration of 10
15
cm
-3
, then the doping concentration in
the n-type region will be 10
16
cm
-3
Q.34 The current in an enhancement mode NMOS transistor biased in saturation mode was measured to
be 1 mA at a drain-source voltage of 5 V. When the drain-source voltage was increased to 6 V
while keeping gate-source voltage same, the drain current increased to 1.02 mA. Assume that drain
to source saturation voltage is much smaller than the applied drain-source voltage. The channel
length modulation parameter (in
) is _______.
Q.35
An npn BJT having reverse saturation current
S
I = 10
-15
A is biased in the forward active region
with
BE
V
= 700 mV. The thermal voltage (
T
V ) is 25 mV and the current gain ( ? ) may vary from
50 to 150 due to manufacturing variations. The maximum emitter current (in ?A) is ________.
Q.36 A three bit pseudo random number generator is shown. Initially the value of output
Y ? Y
2
Y
1
Y
0
is set to 111. The value of output Y after three clock cycles is
(A) 000 (B) 001 (C) 010 (D) 100
X (?m)
1.0 0.5 ? 0.1 0
10
4
E
(V/cm)
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/14
Q.37 A universal logic gate can implement any Boolean function by connecting sufficient number of
them appropriately. Three gates are shown.
Gate 1 Gate 2 Gate 3
Which one of the following statements is TRUE?
(A) Gate 1 is a universal gate.
(B) Gate 2 is a universal gate.
(C) Gate 3 is a universal gate.
(D) None of the gates shown is a universal gate.
Q.38 An SR latch is implemented using TTL gates as shown in the figure. The set and reset pulse inputs
are provided using the push-button switches. It is observed that the circuit fails to work as desired.
The SR latch can be made functional by changing
(A) NOR gates to NAND gates
(B) inverters to buffers
(C) NOR gates to NAND gates and inverters to buffers
(D) 5 V to ground
Q.39 In the circuit shown, assume that the opamp is ideal. If the gain (v
o
/ v
in
) is ?12, the value of
R (in k?) is _____.
v
in
v
0
R
10 k?
10 k? 10 k?
5 V
Q
Q
Set
Reset
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 10/14
Q.40 In the circuit shown, both the enhancement mode NMOS transistors have the following
characteristics: =
( ?) =1 ? ;
=1 . Assume that the channel length
modulation parameter is zero and body is shorted to source. The minimum supply voltage
(in
volts) needed to ensure that transistor M
1
operates in saturation mode of operation is _______.
Q.41 In the circuit shown, assume that the diodes D
1
and D
2
are ideal. The average value of voltage V
ab
(in Volts), across terminals ?a? and ?b? is _________.
Q.42 Suppose [ ] is an absolutely summable discrete-time signal. Its z-transform is a rational function
with two poles and two zeroes. The poles are at = ?2 . Which one of the following statements is
TRUE for the signal [ ] ?
(A) It is a finite duration signal.
(B) It is a causal signal.
(C) It is a non-causal signal.
(D) It is a periodic signal.
M
1
M
2
V
DD
2V
20 k? 10 k?
10 k?
6? sin(?t)ab
D
1
D
2
V
ab
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 11/14
Q.43 A realization of a stable discrete time system is shown in the figure. If the system is excited by a
unit step sequence input [] x n , the response [] y n is
(A)
12
4[]5 []
33
nn
un un
?? ? ?
???
?? ? ?
?? ? ?
(B)
21
5[]3 []
33
nn
un un
?? ? ?
???
?? ? ?
?? ? ?
(C)
12
5[]5 []
33
nn
un un
?? ? ?
?
?? ? ?
?? ? ?
(D)
21
5[]5 []
33
nn
un un
?? ? ?
?
?? ? ?
?? ? ?
Q.44
Let [ ] =1 + cos
be a periodic signal with period 16. Its DFS coefficients are defined by
[]
0
15
1
exp( )
16 8
n
k
axn jkn
?
=
=?
?
% for all k . The value of the coefficient
is _______.
Q.45 Consider a continuous-time signal defined as
( ) =
sin ( 2 ? )
( 2 ? )
? ? ( ? 10 )
?
?
where ? ?? denotes the convolution operation and t is in seconds. The Nyquist sampling rate (in
samples/sec) for ( ) is _____.
Q.46 The position control of a DC servo-motor is given in the figure. The values of the parameters are
2
1 N-m/A, 1 , 0.1H, 5kg-m , 1 N-m/(rad/sec) and 1V/(rad/sec)
Ta a b
KR L J B K ==?= = = = .
The steady-state position response (in radians) due to unit impulse disturbance torque is
_______.
K
b
1
s
V
a
(s)
+
+
-
-
T
d
(s)
1
J s+B
K
T
R
a
+L
a
s
?(s)
[ ]
+
+
+
[]
1
?2/9 5/3
?5/3
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 12/14
Q.47 For the system shown in the figure, = ?2.75 lies on the root locus if is _______.
Q.48 The characteristic equation of an LTI system is given by F(s) = s
5
+ 2s
4
+ 3s
3
+ 6s
2
? 4s ? 8 = 0.
The number of roots that lie strictly in the left half s-plane is _________.
Q.49 Two sequences [ ] and [ ] have the same energy. Suppose [ ] = 0.5
[ ], where is a
positive real number and [ ] is the unit step sequence. Assume
[ ] =
? 1.5 for = 0, 1
0otherwise.
Then the value of is _________.
Q.50
The variance of the random variable X with probability density function
1
()
2
x
fxxe
?
= is
_______.
Q.51
The complex envelope of the bandpass signal
sin( / 5)
() 2 sin( )
/5 4
t
xt t
t
??
?
?
??
=? ?
??
??
, centered
about
1
2
f = Hz, is
(A)
4
sin( / 5)
/5
j
t
e
t
?
?
?
??
??
??
(B)
4
sin( / 5)
/5
j
t
e
t
?
?
?
?
??
??
??
(C)
4
sin( / 5)
2
/5
j
t
e
t
?
?
?
??
??
??
(D)
4
sin( / 5)
2
/5
j
t
e
t
?
?
?
?
??
??
??
Y(s)
s+3
s+2
K
-
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 13/14
Q.52 A random binary wave ( ) is given by
( ) = ( ? ? )
where ( ) = ( ) ?( ?) , u(t) is the unit step function and is an independent random
variable with uniform distribution in [0,T]. The sequence {
} consists of independent and
identically distributed binary valued random variables with { = +1 } = { = ?1 } =0.5 for
each n.
The value of the autocorrelation
? ( ) ?
equals ________.
Q.53 Consider the 3 m long lossless air-filled transmission line shown in the figure. It has a characteristic
impedance of 120? ?, is terminated by a short circuit, and is excited with a frequency of 37.5 MHz.
What is the nature of the input impedance (Z
in
)?
(A) Open (B) Short (C) Inductive (D) Capacitive
Q.54 A 200 m long transmission line having parameters shown in the figure is terminated into a load .
The line is connected to a 400 V source having source resistance through a switch, which is
closed at t = 0. The transient response of the circuit at the input of the line (z = 0) is also drawn in
the figure. The value of (in ? ) is ________.
Q.55 A coaxial capacitor of inner radius 1 mm and outer radius 5 mm has a capacitance per unit length of
172 pF/m. If the ratio of outer radius to inner radius is doubled, the capacitance per unit length
(in pF/m) is ________.
Z
L
=0
Z
in 3 m
R
L
V
S
= 400 V
R
S
=
150 ?
z = 0 z = L
200 m
R
0
= 50?
?
r,eff
= 2.25
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/14
Q. 1 ? Q. 25 carry one mark each.
Q.1
For
1tan
tan 1
x
A
x
??
=
??
?
??
, the determinant of
1 T
A A
?
is
(A)
2
sec x
(B) cos 4x (C) 1 (D) 0
Q.2 The contour on the x-y plane, where the partial derivative of +
with respect to is equal to
the partial derivative of 6 + 4 with respect to , is
(A) = 2 (B) = 2 (C) + = 4
(D) ? = 0
Q.3 If is a circle of radius with centre , in the complex z-plane and if is a non-zero integer, then
?
(
)
equals
(A) 2 (B) 0
(C)
(D) 2
Q.4
Consider the function () sin(2 ) ()
t
gt e t u t ?
?
= where () ut is the unit step function. The area under
() gt is _______.
Q.5
The value of
0
1
2
n
n
n
?
=
??
??
??
?
is ______.
Q.6 For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b
is ________.
Q.7 In the circuit shown, the voltage V
X
(in Volts) is _______.
8 ? 20 ?
10 ?
5 A
V
X
+
-
+
-
0.25 V
X
0.5 V
X
12 V
3?
6?
1A
a
b
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/14
Q.8 At very high frequencies, the peak output voltage V
0
(in Volts) is ________.
Q.9 Which one of the following processes is preferred to form the gate dielectric (SiO
2
) of MOSFETs ?
(A) Sputtering (B) Molecular beam epitaxy
(C) Wet oxidation (D) Dry oxidation
Q.10 If the base width in a bipolar junction transistor is doubled, which one of the following statements
will be TRUE?
(A) Current gain will increase.
(B) Unity gain frequency will increase.
(C) Emitter-base junction capacitance will increase.
(D) Early Voltage will increase.
Q.11 In the circuit shown in the figure, the BJT has a current gain ( ) of 50. For an emitter-base
voltage
= 600 mV, the emitter-collector voltage
(in Volts) is _______.
60 k ?
500 ?
3 V
100 ?F
100 ?F
100 ?F
1 k?
1 k?
1 k? 1 k?
1.0sin( ?t) V
V
0
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/14
Q.12 In the circuit shown using an ideal opamp, the 3-dB cut-off frequency (in Hz) is _______.
v
i
10 k? 10 k?
10 k? 10 k?
0.1 ?F
v
o
+
?
Q.13 In the circuit shown, assume that diodes D
1
and D
2
are ideal. In the steady state condition, the
average voltage V
ab
(in Volts) across the 0.5 ?F capacitor is _____.
Q.14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset ( R
input).
The counter corresponding to this circuit is
(A) a modulo-5 binary up counter (B) a modulo-6 binary down counter
(C) a modulo-5 binary down counter (D) a modulo-6 binary up counter
50 sin (?t)
1 ?F
a
V
ab
0.5 ?F
D
1
D
2
b
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/14
Q.15 In the circuit shown, diodes D
1
, D
2
and D
3
are ideal, and the inputs E
1
, E
2
and E
3
are ?0 V? for
logic ?0? and ?10 V? for logic ?1?. What logic gate does the circuit represent?
(A) 3-input OR gate
(B) 3-input NOR gate
(C) 3-input AND gate
(D) 3-input XOR gate
Q.16 Which one of the following 8085 microprocessor programs correctly calculates the product of two
8-bit numbers stored in registers B and C?
(A) MVI A, 00H
JNZ LOOP
CMP C
LOOP DCR B
HLT
(B)
MVI A, 00H
CMP C
LOOP DCR B
JNZ LOOP
HLT
(C) MVI A, 00H
LOOP ADD C
DCR B
JNZ LOOP
HLT
(D) MVI A, 00H
ADD C
JNZ LOOP
LOOP INR B
HLT
Q.17 The impulse response of an LTI system can be obtained by
(A) differentiating the unit ramp response
(B) differentiating the unit step response
(C) integrating the unit ramp response
(D) integrating the unit step response
Q.18
Consider a four-point moving average filter defined by the equation
3
0
[] [ ]
i
i
yn x n i ?
=
=?
?
.
The condition on the filter coefficients that results in a null at zero frequency is
(A)
12 0 3
0; ?? ? ? == =? (B)
12 0 3
1; ?? ? ? == =?
(C)
03 1 2
0; ?? ? ? == = (D)
12 0 3
0; ?? ? ? == =
1 k?
V
0
10V
E
1
E
2
E
3
D
1
D
2
D
3
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/14
Q.19 Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued.
The value of ?
(in Hz) is ___________.
Q.20
The phase margin (in degrees) of the system
10
()
( 10)
Gs
ss
=
+
is _______.
Q.21 The transfer function of a first-order controller is given as
( ) =
( + )
+
where , and are positive real numbers. The condition for this controller to act as a phase lead
compensator is
(A) < (B) > (C) < (D) >
Q.22 The modulation scheme commonly used for transmission from GSM mobile terminals is
(A) 4-QAM
(B) 16-PSK
(C) Walsh-Hadamard orthogonal codes
(D) Gaussian Minimum Shift Keying (GMSK)
Q.23 A message signal m(t) = A
m
sin(2 ?f
m
t) is used to modulate the phase of a carrier A
c
cos(2 ?f
c
t) to get
the modulated signal y(t) = A
c
cos(2 ?f
c
t + m(t)). The bandwidth of y(t)
(A) depends on A
m
but not on f
m
(B) depends on f
m
but not on A
m
(C) depends on both A
m
and f
m
(D) does not depend on A
m
or f
m
Q.24 The directivity of an antenna array can be increased by adding more antenna elements, as a larger
number of elements
(A) improves the radiation efficiency
(B) increases the effective area of the antenna
(C) results in a better impedance matching
(D) allows more power to be transmitted by the antenna
Freq. (Hz)
40 dB
300 900 f
L
f
H
0 dB
40 dB/dec
? 40 dB/dec
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/14
Q.25 A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with
Teflon
'
( 2.1, tan 0)
r
?? == . Which one of the following circuits can represent the lumped
element model of a small piece of this cable having length ? ?
(A)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
G?zC?z
?z
(B)
R?z / 2 L?z / 2 R?z / 2 L?z / 2
C?z
?z
(C)
L?z / 2 L?z / 2
G?zC?z
?z
(D)
R?z
L?z
G?z
C?z
?z
Q. 26 ? Q. 55 carry two marks each.
Q.26 The Newton-Raphson method is used to solve the equation f (x) = x
3
? 5x
2
+ 6x ? 8 = 0. Taking the
initial guess as x = 5, the solution obtained at the end of the first iteration is __________.
Q.27 A fair die with faces {1, 2, 3, 4, 5, 6} is thrown repeatedly till ?3? is observed for the first time. Let
X denote the number of times the die is thrown. The expected value of X is ____.
Q.28 Consider the differential equation
()
+3
( )
+2() = 0.
Given x(0) = 20 and x(1) = 10/e, where e = 2.718, the value of x(2) is _________.
Q.29 A vector field =2
+
exists inside a cylindrical region enclosed by the surfaces
= 1, = 0 and = 5 . Let S be the surface bounding this cylindrical region. The surface integral
of this field on S ? .
is _______.
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/14
Q.30 In the circuit shown, the current I flowing through the 50 ? resistor will be zero if the value of
capacitor C (in ?F) is ______.
Q.31 The ABCD parameters of the following 2-port network are
(A) 3.5 +220.5
20 .5 3.5 ? 2
(B) 3.5 +230.5
0.5 3 .5 ? 2
(C) 10 2 + 0
2+010
(D) 7+40.5
30 .5 7 ? 4
Q.32 A network is described by the state model as
=2 ?
+3 =?4 ?
= 3 ?2
The transfer function ( ) =
()
( )
is
(A)
( ) ()
(B)
( ) ( )
(C)
( ) ( )
(D)
( ) ()
C
1 mH 1 mH
1 mH
50 ?
5? sin(5000t)
I
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/14
Q.33 The electric field profile in the depletion region of a p-n junction in equilibrium is shown in the
figure. Which one of the following statements is NOT TRUE?
(A) The left side of the junction is n-type and the right side is p-type
(B) Both the n-type and p-type depletion regions are uniformly doped
(C) The potential difference across the depletion region is 700 mV
(D) If the p-type region has a doping concentration of 10
15
cm
-3
, then the doping concentration in
the n-type region will be 10
16
cm
-3
Q.34 The current in an enhancement mode NMOS transistor biased in saturation mode was measured to
be 1 mA at a drain-source voltage of 5 V. When the drain-source voltage was increased to 6 V
while keeping gate-source voltage same, the drain current increased to 1.02 mA. Assume that drain
to source saturation voltage is much smaller than the applied drain-source voltage. The channel
length modulation parameter (in
) is _______.
Q.35
An npn BJT having reverse saturation current
S
I = 10
-15
A is biased in the forward active region
with
BE
V
= 700 mV. The thermal voltage (
T
V ) is 25 mV and the current gain ( ? ) may vary from
50 to 150 due to manufacturing variations. The maximum emitter current (in ?A) is ________.
Q.36 A three bit pseudo random number generator is shown. Initially the value of output
Y ? Y
2
Y
1
Y
0
is set to 111. The value of output Y after three clock cycles is
(A) 000 (B) 001 (C) 010 (D) 100
X (?m)
1.0 0.5 ? 0.1 0
10
4
E
(V/cm)
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/14
Q.37 A universal logic gate can implement any Boolean function by connecting sufficient number of
them appropriately. Three gates are shown.
Gate 1 Gate 2 Gate 3
Which one of the following statements is TRUE?
(A) Gate 1 is a universal gate.
(B) Gate 2 is a universal gate.
(C) Gate 3 is a universal gate.
(D) None of the gates shown is a universal gate.
Q.38 An SR latch is implemented using TTL gates as shown in the figure. The set and reset pulse inputs
are provided using the push-button switches. It is observed that the circuit fails to work as desired.
The SR latch can be made functional by changing
(A) NOR gates to NAND gates
(B) inverters to buffers
(C) NOR gates to NAND gates and inverters to buffers
(D) 5 V to ground
Q.39 In the circuit shown, assume that the opamp is ideal. If the gain (v
o
/ v
in
) is ?12, the value of
R (in k?) is _____.
v
in
v
0
R
10 k?
10 k? 10 k?
5 V
Q
Q
Set
Reset
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 10/14
Q.40 In the circuit shown, both the enhancement mode NMOS transistors have the following
characteristics: =
( ?) =1 ? ;
=1 . Assume that the channel length
modulation parameter is zero and body is shorted to source. The minimum supply voltage
(in
volts) needed to ensure that transistor M
1
operates in saturation mode of operation is _______.
Q.41 In the circuit shown, assume that the diodes D
1
and D
2
are ideal. The average value of voltage V
ab
(in Volts), across terminals ?a? and ?b? is _________.
Q.42 Suppose [ ] is an absolutely summable discrete-time signal. Its z-transform is a rational function
with two poles and two zeroes. The poles are at = ?2 . Which one of the following statements is
TRUE for the signal [ ] ?
(A) It is a finite duration signal.
(B) It is a causal signal.
(C) It is a non-causal signal.
(D) It is a periodic signal.
M
1
M
2
V
DD
2V
20 k? 10 k?
10 k?
6? sin(?t)ab
D
1
D
2
V
ab
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 11/14
Q.43 A realization of a stable discrete time system is shown in the figure. If the system is excited by a
unit step sequence input [] x n , the response [] y n is
(A)
12
4[]5 []
33
nn
un un
?? ? ?
???
?? ? ?
?? ? ?
(B)
21
5[]3 []
33
nn
un un
?? ? ?
???
?? ? ?
?? ? ?
(C)
12
5[]5 []
33
nn
un un
?? ? ?
?
?? ? ?
?? ? ?
(D)
21
5[]5 []
33
nn
un un
?? ? ?
?
?? ? ?
?? ? ?
Q.44
Let [ ] =1 + cos
be a periodic signal with period 16. Its DFS coefficients are defined by
[]
0
15
1
exp( )
16 8
n
k
axn jkn
?
=
=?
?
% for all k . The value of the coefficient
is _______.
Q.45 Consider a continuous-time signal defined as
( ) =
sin ( 2 ? )
( 2 ? )
? ? ( ? 10 )
?
?
where ? ?? denotes the convolution operation and t is in seconds. The Nyquist sampling rate (in
samples/sec) for ( ) is _____.
Q.46 The position control of a DC servo-motor is given in the figure. The values of the parameters are
2
1 N-m/A, 1 , 0.1H, 5kg-m , 1 N-m/(rad/sec) and 1V/(rad/sec)
Ta a b
KR L J B K ==?= = = = .
The steady-state position response (in radians) due to unit impulse disturbance torque is
_______.
K
b
1
s
V
a
(s)
+
+
-
-
T
d
(s)
1
J s+B
K
T
R
a
+L
a
s
?(s)
[ ]
+
+
+
[]
1
?2/9 5/3
?5/3
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 12/14
Q.47 For the system shown in the figure, = ?2.75 lies on the root locus if is _______.
Q.48 The characteristic equation of an LTI system is given by F(s) = s
5
+ 2s
4
+ 3s
3
+ 6s
2
? 4s ? 8 = 0.
The number of roots that lie strictly in the left half s-plane is _________.
Q.49 Two sequences [ ] and [ ] have the same energy. Suppose [ ] = 0.5
[ ], where is a
positive real number and [ ] is the unit step sequence. Assume
[ ] =
? 1.5 for = 0, 1
0otherwise.
Then the value of is _________.
Q.50
The variance of the random variable X with probability density function
1
()
2
x
fxxe
?
= is
_______.
Q.51
The complex envelope of the bandpass signal
sin( / 5)
() 2 sin( )
/5 4
t
xt t
t
??
?
?
??
=? ?
??
??
, centered
about
1
2
f = Hz, is
(A)
4
sin( / 5)
/5
j
t
e
t
?
?
?
??
??
??
(B)
4
sin( / 5)
/5
j
t
e
t
?
?
?
?
??
??
??
(C)
4
sin( / 5)
2
/5
j
t
e
t
?
?
?
??
??
??
(D)
4
sin( / 5)
2
/5
j
t
e
t
?
?
?
?
??
??
??
Y(s)
s+3
s+2
K
-
+
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 13/14
Q.52 A random binary wave ( ) is given by
( ) = ( ? ? )
where ( ) = ( ) ?( ?) , u(t) is the unit step function and is an independent random
variable with uniform distribution in [0,T]. The sequence {
} consists of independent and
identically distributed binary valued random variables with { = +1 } = { = ?1 } =0.5 for
each n.
The value of the autocorrelation
? ( ) ?
equals ________.
Q.53 Consider the 3 m long lossless air-filled transmission line shown in the figure. It has a characteristic
impedance of 120? ?, is terminated by a short circuit, and is excited with a frequency of 37.5 MHz.
What is the nature of the input impedance (Z
in
)?
(A) Open (B) Short (C) Inductive (D) Capacitive
Q.54 A 200 m long transmission line having parameters shown in the figure is terminated into a load .
The line is connected to a 400 V source having source resistance through a switch, which is
closed at t = 0. The transient response of the circuit at the input of the line (z = 0) is also drawn in
the figure. The value of (in ? ) is ________.
Q.55 A coaxial capacitor of inner radius 1 mm and outer radius 5 mm has a capacitance per unit length of
172 pF/m. If the ratio of outer radius to inner radius is doubled, the capacitance per unit length
(in pF/m) is ________.
Z
L
=0
Z
in 3 m
R
L
V
S
= 400 V
R
S
=
150 ?
z = 0 z = L
200 m
R
0
= 50?
?
r,eff
= 2.25
GATE 2015 SET-3 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 14/14
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This post was last modified on 19 December 2019