Download Graduate Aptitude Test in Engineering (GATE) 2015 ECE Electronics and Communication Engg. Set 1 Question Paper
EC 1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a system of linear equations:
23 1 xy z ?+ =? ,
34 1 xy z ?+ = , and
24 6 . xy zk ?+ ? =
The value of k
for which the system has infinitely many solutions is ______.
Q.2
A function
23
() 1 fxxx =? + is defined in the closed interval [ ]
1, 1 ? . The value of x , in the
open interval () 1, 1 ?
for which the mean value theorem is satisfied, is
(A) ?1 2 ? (B) ?1 3 ? (C) 13 ? (D) 1/2
Q.3
Suppose and B are two independent events with probabilities ( )?0 and ( ) ? 0 . Let
and be their complements. Which one of the following statements is FALSE?
(A) ( ? ) = ( ) () (B) ( | ) =( )
(C) ( ? ) = ( ) +()
(D) ? = ( )
Q.4 Let zx iy =+ be a complex variable. Consider that contour integration is performed along the unit
circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
(A) The residue of
2
1
z
z ?
at 1 z = is 1/2
(B) ? = 0
(C)
?
= 1
(D) z (complex conjugate of z ) is an analytical function
Q.5
The value of p such that the vector 1
2
3
is an eigenvector of the matrix 412
2 1
14 ?4 10
is
_______.
Q.6 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the
capacitor is ________.
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GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a system of linear equations:
23 1 xy z ?+ =? ,
34 1 xy z ?+ = , and
24 6 . xy zk ?+ ? =
The value of k
for which the system has infinitely many solutions is ______.
Q.2
A function
23
() 1 fxxx =? + is defined in the closed interval [ ]
1, 1 ? . The value of x , in the
open interval () 1, 1 ?
for which the mean value theorem is satisfied, is
(A) ?1 2 ? (B) ?1 3 ? (C) 13 ? (D) 1/2
Q.3
Suppose and B are two independent events with probabilities ( )?0 and ( ) ? 0 . Let
and be their complements. Which one of the following statements is FALSE?
(A) ( ? ) = ( ) () (B) ( | ) =( )
(C) ( ? ) = ( ) +()
(D) ? = ( )
Q.4 Let zx iy =+ be a complex variable. Consider that contour integration is performed along the unit
circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
(A) The residue of
2
1
z
z ?
at 1 z = is 1/2
(B) ? = 0
(C)
?
= 1
(D) z (complex conjugate of z ) is an analytical function
Q.5
The value of p such that the vector 1
2
3
is an eigenvector of the matrix 412
2 1
14 ?4 10
is
_______.
Q.6 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the
capacitor is ________.
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/13
Q.7 In the network shown in the figure, all resistors are identical with R = 300 ?. The resistance
R
ab
(in ?) of the network is ______.
Q.8
In the given circuit, the values of
12
and VV respectively are
4?
4?
4? 5A
+
V
2
-
+
V
1
-
2 ?
?
(A) 5 V, 25 V (B) 10 V, 30 V (C) 15 V, 35 V (D) 0 V, 20 V
Q.9 A region of negative differential resistance is observed in the current voltage characteristics of a
silicon PN junction if
(A) both the P-region and the N-region are heavily doped
(B) the N-region is heavily doped compared to the P-region
(C) the P-region is heavily doped compared to the N-region
(D) an intrinsic silicon region is inserted between the P-region and the N-region
Q.10 A silicon sample is uniformly doped with donor type impurities with a concentration of 10
16
/cm
3
.
The electron and hole mobilities in the sample are 1200 cm
2
/V-s and 400 cm
2
/V-s respectively.
Assume complete ionization of impurities. The charge of an electron is 1.6 ?10
-19
C. The resistivity
of the sample (in ?-cm) is ____________.
a
b
R
R
R
RR R R
R RR
R
R
R R R
R = 300 ?
R
ab
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GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a system of linear equations:
23 1 xy z ?+ =? ,
34 1 xy z ?+ = , and
24 6 . xy zk ?+ ? =
The value of k
for which the system has infinitely many solutions is ______.
Q.2
A function
23
() 1 fxxx =? + is defined in the closed interval [ ]
1, 1 ? . The value of x , in the
open interval () 1, 1 ?
for which the mean value theorem is satisfied, is
(A) ?1 2 ? (B) ?1 3 ? (C) 13 ? (D) 1/2
Q.3
Suppose and B are two independent events with probabilities ( )?0 and ( ) ? 0 . Let
and be their complements. Which one of the following statements is FALSE?
(A) ( ? ) = ( ) () (B) ( | ) =( )
(C) ( ? ) = ( ) +()
(D) ? = ( )
Q.4 Let zx iy =+ be a complex variable. Consider that contour integration is performed along the unit
circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
(A) The residue of
2
1
z
z ?
at 1 z = is 1/2
(B) ? = 0
(C)
?
= 1
(D) z (complex conjugate of z ) is an analytical function
Q.5
The value of p such that the vector 1
2
3
is an eigenvector of the matrix 412
2 1
14 ?4 10
is
_______.
Q.6 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the
capacitor is ________.
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/13
Q.7 In the network shown in the figure, all resistors are identical with R = 300 ?. The resistance
R
ab
(in ?) of the network is ______.
Q.8
In the given circuit, the values of
12
and VV respectively are
4?
4?
4? 5A
+
V
2
-
+
V
1
-
2 ?
?
(A) 5 V, 25 V (B) 10 V, 30 V (C) 15 V, 35 V (D) 0 V, 20 V
Q.9 A region of negative differential resistance is observed in the current voltage characteristics of a
silicon PN junction if
(A) both the P-region and the N-region are heavily doped
(B) the N-region is heavily doped compared to the P-region
(C) the P-region is heavily doped compared to the N-region
(D) an intrinsic silicon region is inserted between the P-region and the N-region
Q.10 A silicon sample is uniformly doped with donor type impurities with a concentration of 10
16
/cm
3
.
The electron and hole mobilities in the sample are 1200 cm
2
/V-s and 400 cm
2
/V-s respectively.
Assume complete ionization of impurities. The charge of an electron is 1.6 ?10
-19
C. The resistivity
of the sample (in ?-cm) is ____________.
a
b
R
R
R
RR R R
R RR
R
R
R R R
R = 300 ?
R
ab
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/13
Q.11 For the circuit with ideal diodes shown in the figure, the shape of the output (
) for the given
sine wave input (
) will be
(A)
(B)
(C)
(D)
Q.12 In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6 V. The output
voltage (in volts) is_______.
Q.13 In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The
energy (in ?J) taken from the 3 V source to charge the 0.1 ?F capacitor from 0 V to 3 V is
(A) 0.3 (B) 0.45 (C) 0.9 (D) 3
1k?
10V 1k?
+
V
O
-
SW
3 V
0.1 ?F
120 ?
t = 0
B A
+
?
+
?
0 T 0.5T
v
in
v
out
0 T 0.5T
0 T 0.5T
T
0.5T
0
0 T 0.5T
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GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a system of linear equations:
23 1 xy z ?+ =? ,
34 1 xy z ?+ = , and
24 6 . xy zk ?+ ? =
The value of k
for which the system has infinitely many solutions is ______.
Q.2
A function
23
() 1 fxxx =? + is defined in the closed interval [ ]
1, 1 ? . The value of x , in the
open interval () 1, 1 ?
for which the mean value theorem is satisfied, is
(A) ?1 2 ? (B) ?1 3 ? (C) 13 ? (D) 1/2
Q.3
Suppose and B are two independent events with probabilities ( )?0 and ( ) ? 0 . Let
and be their complements. Which one of the following statements is FALSE?
(A) ( ? ) = ( ) () (B) ( | ) =( )
(C) ( ? ) = ( ) +()
(D) ? = ( )
Q.4 Let zx iy =+ be a complex variable. Consider that contour integration is performed along the unit
circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
(A) The residue of
2
1
z
z ?
at 1 z = is 1/2
(B) ? = 0
(C)
?
= 1
(D) z (complex conjugate of z ) is an analytical function
Q.5
The value of p such that the vector 1
2
3
is an eigenvector of the matrix 412
2 1
14 ?4 10
is
_______.
Q.6 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the
capacitor is ________.
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/13
Q.7 In the network shown in the figure, all resistors are identical with R = 300 ?. The resistance
R
ab
(in ?) of the network is ______.
Q.8
In the given circuit, the values of
12
and VV respectively are
4?
4?
4? 5A
+
V
2
-
+
V
1
-
2 ?
?
(A) 5 V, 25 V (B) 10 V, 30 V (C) 15 V, 35 V (D) 0 V, 20 V
Q.9 A region of negative differential resistance is observed in the current voltage characteristics of a
silicon PN junction if
(A) both the P-region and the N-region are heavily doped
(B) the N-region is heavily doped compared to the P-region
(C) the P-region is heavily doped compared to the N-region
(D) an intrinsic silicon region is inserted between the P-region and the N-region
Q.10 A silicon sample is uniformly doped with donor type impurities with a concentration of 10
16
/cm
3
.
The electron and hole mobilities in the sample are 1200 cm
2
/V-s and 400 cm
2
/V-s respectively.
Assume complete ionization of impurities. The charge of an electron is 1.6 ?10
-19
C. The resistivity
of the sample (in ?-cm) is ____________.
a
b
R
R
R
RR R R
R RR
R
R
R R R
R = 300 ?
R
ab
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/13
Q.11 For the circuit with ideal diodes shown in the figure, the shape of the output (
) for the given
sine wave input (
) will be
(A)
(B)
(C)
(D)
Q.12 In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6 V. The output
voltage (in volts) is_______.
Q.13 In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The
energy (in ?J) taken from the 3 V source to charge the 0.1 ?F capacitor from 0 V to 3 V is
(A) 0.3 (B) 0.45 (C) 0.9 (D) 3
1k?
10V 1k?
+
V
O
-
SW
3 V
0.1 ?F
120 ?
t = 0
B A
+
?
+
?
0 T 0.5T
v
in
v
out
0 T 0.5T
0 T 0.5T
T
0.5T
0
0 T 0.5T
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/13
Q.14 In an 8085 microprocessor, the shift registers which store the result of an addition and the overflow
bit are, respectively
(A) B and F
(B) A and F
(C) H and F
(D) A and C
Q.15 A 16 Kb (=16,384 bit) memory array is designed as a square with an aspect ratio of one (number of
rows is equal to the number of columns). The minimum number of address lines needed for the
row decoder is _______.
Q.16 Consider a four bit D to A converter. The analog value corresponding to digital signals of values
0000 and 0001 are 0 V and 0.0625 V respectively. The analog value (in Volts) corresponding to
the digital signal 1111 is ________.
Q.17 The result of the convolution ( ? ) ?(? ? ) is
(A) ( + ) (B) ( ? ) (C) (? + ) (D) (? ? )
Q.18 The waveform of a periodic signal () x t
is shown in the figure.
A signal () gt is defined by
1
()
2
t
gt x
? ??
=
??
??
. The average power of () gt is _______.
Q.19 Negative feedback in a closed-loop control system DOES NOT
(A) reduce the overall gain (B) reduce bandwidth
(C) improve disturbance rejection (D) reduce sensitivity to parameter variation
Q.20
A unity negative feedback system has the open-loop transfer function ( ) =
( +1 ) (+3)
. The
value of the gain K (>0) at which the root locus crosses the imaginary axis is ________.
Q.21
The polar plot of the transfer function ( ) =
10 (+1)
+1 0
for 0 ? ? < ? will be in the
(A) first quadrant
(B) second quadrant
(C) third quadrant
(D) fourth quadrant
1
2 3
4
t
x(t)
-1
-2
-3 -4
3
-3
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GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a system of linear equations:
23 1 xy z ?+ =? ,
34 1 xy z ?+ = , and
24 6 . xy zk ?+ ? =
The value of k
for which the system has infinitely many solutions is ______.
Q.2
A function
23
() 1 fxxx =? + is defined in the closed interval [ ]
1, 1 ? . The value of x , in the
open interval () 1, 1 ?
for which the mean value theorem is satisfied, is
(A) ?1 2 ? (B) ?1 3 ? (C) 13 ? (D) 1/2
Q.3
Suppose and B are two independent events with probabilities ( )?0 and ( ) ? 0 . Let
and be their complements. Which one of the following statements is FALSE?
(A) ( ? ) = ( ) () (B) ( | ) =( )
(C) ( ? ) = ( ) +()
(D) ? = ( )
Q.4 Let zx iy =+ be a complex variable. Consider that contour integration is performed along the unit
circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
(A) The residue of
2
1
z
z ?
at 1 z = is 1/2
(B) ? = 0
(C)
?
= 1
(D) z (complex conjugate of z ) is an analytical function
Q.5
The value of p such that the vector 1
2
3
is an eigenvector of the matrix 412
2 1
14 ?4 10
is
_______.
Q.6 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the
capacitor is ________.
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/13
Q.7 In the network shown in the figure, all resistors are identical with R = 300 ?. The resistance
R
ab
(in ?) of the network is ______.
Q.8
In the given circuit, the values of
12
and VV respectively are
4?
4?
4? 5A
+
V
2
-
+
V
1
-
2 ?
?
(A) 5 V, 25 V (B) 10 V, 30 V (C) 15 V, 35 V (D) 0 V, 20 V
Q.9 A region of negative differential resistance is observed in the current voltage characteristics of a
silicon PN junction if
(A) both the P-region and the N-region are heavily doped
(B) the N-region is heavily doped compared to the P-region
(C) the P-region is heavily doped compared to the N-region
(D) an intrinsic silicon region is inserted between the P-region and the N-region
Q.10 A silicon sample is uniformly doped with donor type impurities with a concentration of 10
16
/cm
3
.
The electron and hole mobilities in the sample are 1200 cm
2
/V-s and 400 cm
2
/V-s respectively.
Assume complete ionization of impurities. The charge of an electron is 1.6 ?10
-19
C. The resistivity
of the sample (in ?-cm) is ____________.
a
b
R
R
R
RR R R
R RR
R
R
R R R
R = 300 ?
R
ab
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/13
Q.11 For the circuit with ideal diodes shown in the figure, the shape of the output (
) for the given
sine wave input (
) will be
(A)
(B)
(C)
(D)
Q.12 In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6 V. The output
voltage (in volts) is_______.
Q.13 In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The
energy (in ?J) taken from the 3 V source to charge the 0.1 ?F capacitor from 0 V to 3 V is
(A) 0.3 (B) 0.45 (C) 0.9 (D) 3
1k?
10V 1k?
+
V
O
-
SW
3 V
0.1 ?F
120 ?
t = 0
B A
+
?
+
?
0 T 0.5T
v
in
v
out
0 T 0.5T
0 T 0.5T
T
0.5T
0
0 T 0.5T
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/13
Q.14 In an 8085 microprocessor, the shift registers which store the result of an addition and the overflow
bit are, respectively
(A) B and F
(B) A and F
(C) H and F
(D) A and C
Q.15 A 16 Kb (=16,384 bit) memory array is designed as a square with an aspect ratio of one (number of
rows is equal to the number of columns). The minimum number of address lines needed for the
row decoder is _______.
Q.16 Consider a four bit D to A converter. The analog value corresponding to digital signals of values
0000 and 0001 are 0 V and 0.0625 V respectively. The analog value (in Volts) corresponding to
the digital signal 1111 is ________.
Q.17 The result of the convolution ( ? ) ?(? ? ) is
(A) ( + ) (B) ( ? ) (C) (? + ) (D) (? ? )
Q.18 The waveform of a periodic signal () x t
is shown in the figure.
A signal () gt is defined by
1
()
2
t
gt x
? ??
=
??
??
. The average power of () gt is _______.
Q.19 Negative feedback in a closed-loop control system DOES NOT
(A) reduce the overall gain (B) reduce bandwidth
(C) improve disturbance rejection (D) reduce sensitivity to parameter variation
Q.20
A unity negative feedback system has the open-loop transfer function ( ) =
( +1 ) (+3)
. The
value of the gain K (>0) at which the root locus crosses the imaginary axis is ________.
Q.21
The polar plot of the transfer function ( ) =
10 (+1)
+1 0
for 0 ? ? < ? will be in the
(A) first quadrant
(B) second quadrant
(C) third quadrant
(D) fourth quadrant
1
2 3
4
t
x(t)
-1
-2
-3 -4
3
-3
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/13
Q.22 A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and
step-size ?
of the delta modulator are 20,000 samples per second and 0.1 V, respectively.
To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is
(A)
1
2?
(B)
1
?
(C)
2
?
(D) ?
Q.23
Consider the signal ? () ()cos(2 ) ()sin(2 )
cc
s t mt ft mt ft ?? =+ where ?() mt denotes the Hilbert
transform of () mt and the bandwidth of () mt is very small compared to
c
f . The signal () st is a
(A) high-pass signal
(B) low-pass signal
(C) band-pass signal
(D) double sideband suppressed carrier signal
Q.24 Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the
following plots (in linear scale) qualitatively represents the dependence of H
?
on r, where H
?
is the
magnitude of the azimuthal component of magnetic field outside the conductor and r is the radial
distance from the conductor?
(A) (B)
(C) (D)
Q.25 The electric field component of a plane wave traveling in a lossless dielectric medium is given by
8
? (, ) 2cos 10
2
y
z
Ez t a t
??
=?
??
??
r
V/m. The wavelength (in m) for the wave is ___________.
H
?
r
H
?
r
H
?
r
H
?
r
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GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a system of linear equations:
23 1 xy z ?+ =? ,
34 1 xy z ?+ = , and
24 6 . xy zk ?+ ? =
The value of k
for which the system has infinitely many solutions is ______.
Q.2
A function
23
() 1 fxxx =? + is defined in the closed interval [ ]
1, 1 ? . The value of x , in the
open interval () 1, 1 ?
for which the mean value theorem is satisfied, is
(A) ?1 2 ? (B) ?1 3 ? (C) 13 ? (D) 1/2
Q.3
Suppose and B are two independent events with probabilities ( )?0 and ( ) ? 0 . Let
and be their complements. Which one of the following statements is FALSE?
(A) ( ? ) = ( ) () (B) ( | ) =( )
(C) ( ? ) = ( ) +()
(D) ? = ( )
Q.4 Let zx iy =+ be a complex variable. Consider that contour integration is performed along the unit
circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
(A) The residue of
2
1
z
z ?
at 1 z = is 1/2
(B) ? = 0
(C)
?
= 1
(D) z (complex conjugate of z ) is an analytical function
Q.5
The value of p such that the vector 1
2
3
is an eigenvector of the matrix 412
2 1
14 ?4 10
is
_______.
Q.6 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the
capacitor is ________.
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/13
Q.7 In the network shown in the figure, all resistors are identical with R = 300 ?. The resistance
R
ab
(in ?) of the network is ______.
Q.8
In the given circuit, the values of
12
and VV respectively are
4?
4?
4? 5A
+
V
2
-
+
V
1
-
2 ?
?
(A) 5 V, 25 V (B) 10 V, 30 V (C) 15 V, 35 V (D) 0 V, 20 V
Q.9 A region of negative differential resistance is observed in the current voltage characteristics of a
silicon PN junction if
(A) both the P-region and the N-region are heavily doped
(B) the N-region is heavily doped compared to the P-region
(C) the P-region is heavily doped compared to the N-region
(D) an intrinsic silicon region is inserted between the P-region and the N-region
Q.10 A silicon sample is uniformly doped with donor type impurities with a concentration of 10
16
/cm
3
.
The electron and hole mobilities in the sample are 1200 cm
2
/V-s and 400 cm
2
/V-s respectively.
Assume complete ionization of impurities. The charge of an electron is 1.6 ?10
-19
C. The resistivity
of the sample (in ?-cm) is ____________.
a
b
R
R
R
RR R R
R RR
R
R
R R R
R = 300 ?
R
ab
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/13
Q.11 For the circuit with ideal diodes shown in the figure, the shape of the output (
) for the given
sine wave input (
) will be
(A)
(B)
(C)
(D)
Q.12 In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6 V. The output
voltage (in volts) is_______.
Q.13 In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The
energy (in ?J) taken from the 3 V source to charge the 0.1 ?F capacitor from 0 V to 3 V is
(A) 0.3 (B) 0.45 (C) 0.9 (D) 3
1k?
10V 1k?
+
V
O
-
SW
3 V
0.1 ?F
120 ?
t = 0
B A
+
?
+
?
0 T 0.5T
v
in
v
out
0 T 0.5T
0 T 0.5T
T
0.5T
0
0 T 0.5T
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/13
Q.14 In an 8085 microprocessor, the shift registers which store the result of an addition and the overflow
bit are, respectively
(A) B and F
(B) A and F
(C) H and F
(D) A and C
Q.15 A 16 Kb (=16,384 bit) memory array is designed as a square with an aspect ratio of one (number of
rows is equal to the number of columns). The minimum number of address lines needed for the
row decoder is _______.
Q.16 Consider a four bit D to A converter. The analog value corresponding to digital signals of values
0000 and 0001 are 0 V and 0.0625 V respectively. The analog value (in Volts) corresponding to
the digital signal 1111 is ________.
Q.17 The result of the convolution ( ? ) ?(? ? ) is
(A) ( + ) (B) ( ? ) (C) (? + ) (D) (? ? )
Q.18 The waveform of a periodic signal () x t
is shown in the figure.
A signal () gt is defined by
1
()
2
t
gt x
? ??
=
??
??
. The average power of () gt is _______.
Q.19 Negative feedback in a closed-loop control system DOES NOT
(A) reduce the overall gain (B) reduce bandwidth
(C) improve disturbance rejection (D) reduce sensitivity to parameter variation
Q.20
A unity negative feedback system has the open-loop transfer function ( ) =
( +1 ) (+3)
. The
value of the gain K (>0) at which the root locus crosses the imaginary axis is ________.
Q.21
The polar plot of the transfer function ( ) =
10 (+1)
+1 0
for 0 ? ? < ? will be in the
(A) first quadrant
(B) second quadrant
(C) third quadrant
(D) fourth quadrant
1
2 3
4
t
x(t)
-1
-2
-3 -4
3
-3
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/13
Q.22 A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and
step-size ?
of the delta modulator are 20,000 samples per second and 0.1 V, respectively.
To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is
(A)
1
2?
(B)
1
?
(C)
2
?
(D) ?
Q.23
Consider the signal ? () ()cos(2 ) ()sin(2 )
cc
s t mt ft mt ft ?? =+ where ?() mt denotes the Hilbert
transform of () mt and the bandwidth of () mt is very small compared to
c
f . The signal () st is a
(A) high-pass signal
(B) low-pass signal
(C) band-pass signal
(D) double sideband suppressed carrier signal
Q.24 Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the
following plots (in linear scale) qualitatively represents the dependence of H
?
on r, where H
?
is the
magnitude of the azimuthal component of magnetic field outside the conductor and r is the radial
distance from the conductor?
(A) (B)
(C) (D)
Q.25 The electric field component of a plane wave traveling in a lossless dielectric medium is given by
8
? (, ) 2cos 10
2
y
z
Ez t a t
??
=?
??
??
r
V/m. The wavelength (in m) for the wave is ___________.
H
?
r
H
?
r
H
?
r
H
?
r
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/13
Q. 26 ? Q. 55 carry two marks each.
Q.26
The solution of the differential equation
2
2
20
dy dy
y
dt dt
++= with (0) (0) 1 yy? == is
(A) (2 )
t
te ? (B) (1 2 )
t
te
?
+
(C) (2 )
t
te
?
+ (D) (1 2 )
t
te ?
Q.27
A vector is given by =
?
?
. Which one of the following statements
is TRUE?
(A) is solenoidal, but not irrotational
(B) is irrotational, but not solenoidal
(C) is neither solenoidal nor irrotational
(D) is both solenoidal and irrotational
Q.28 Which one of the following graphs describes the function f ( x ) =
( x
+ x+ 1 ) ?
(A)
(B)
(C)
(D)
Q.29
The maximum area (in square units) of a rectangle whose vertices lie on the ellipse
22
41 xy += is
_______.
Q.30 The damping ratio of a series RLC circuit can be expressed as
(A)
2
2
R C
L
(B)
2
2L
R C
(C)
2
R C
L
(D)
2 L
R C
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a system of linear equations:
23 1 xy z ?+ =? ,
34 1 xy z ?+ = , and
24 6 . xy zk ?+ ? =
The value of k
for which the system has infinitely many solutions is ______.
Q.2
A function
23
() 1 fxxx =? + is defined in the closed interval [ ]
1, 1 ? . The value of x , in the
open interval () 1, 1 ?
for which the mean value theorem is satisfied, is
(A) ?1 2 ? (B) ?1 3 ? (C) 13 ? (D) 1/2
Q.3
Suppose and B are two independent events with probabilities ( )?0 and ( ) ? 0 . Let
and be their complements. Which one of the following statements is FALSE?
(A) ( ? ) = ( ) () (B) ( | ) =( )
(C) ( ? ) = ( ) +()
(D) ? = ( )
Q.4 Let zx iy =+ be a complex variable. Consider that contour integration is performed along the unit
circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
(A) The residue of
2
1
z
z ?
at 1 z = is 1/2
(B) ? = 0
(C)
?
= 1
(D) z (complex conjugate of z ) is an analytical function
Q.5
The value of p such that the vector 1
2
3
is an eigenvector of the matrix 412
2 1
14 ?4 10
is
_______.
Q.6 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the
capacitor is ________.
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/13
Q.7 In the network shown in the figure, all resistors are identical with R = 300 ?. The resistance
R
ab
(in ?) of the network is ______.
Q.8
In the given circuit, the values of
12
and VV respectively are
4?
4?
4? 5A
+
V
2
-
+
V
1
-
2 ?
?
(A) 5 V, 25 V (B) 10 V, 30 V (C) 15 V, 35 V (D) 0 V, 20 V
Q.9 A region of negative differential resistance is observed in the current voltage characteristics of a
silicon PN junction if
(A) both the P-region and the N-region are heavily doped
(B) the N-region is heavily doped compared to the P-region
(C) the P-region is heavily doped compared to the N-region
(D) an intrinsic silicon region is inserted between the P-region and the N-region
Q.10 A silicon sample is uniformly doped with donor type impurities with a concentration of 10
16
/cm
3
.
The electron and hole mobilities in the sample are 1200 cm
2
/V-s and 400 cm
2
/V-s respectively.
Assume complete ionization of impurities. The charge of an electron is 1.6 ?10
-19
C. The resistivity
of the sample (in ?-cm) is ____________.
a
b
R
R
R
RR R R
R RR
R
R
R R R
R = 300 ?
R
ab
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/13
Q.11 For the circuit with ideal diodes shown in the figure, the shape of the output (
) for the given
sine wave input (
) will be
(A)
(B)
(C)
(D)
Q.12 In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6 V. The output
voltage (in volts) is_______.
Q.13 In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The
energy (in ?J) taken from the 3 V source to charge the 0.1 ?F capacitor from 0 V to 3 V is
(A) 0.3 (B) 0.45 (C) 0.9 (D) 3
1k?
10V 1k?
+
V
O
-
SW
3 V
0.1 ?F
120 ?
t = 0
B A
+
?
+
?
0 T 0.5T
v
in
v
out
0 T 0.5T
0 T 0.5T
T
0.5T
0
0 T 0.5T
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/13
Q.14 In an 8085 microprocessor, the shift registers which store the result of an addition and the overflow
bit are, respectively
(A) B and F
(B) A and F
(C) H and F
(D) A and C
Q.15 A 16 Kb (=16,384 bit) memory array is designed as a square with an aspect ratio of one (number of
rows is equal to the number of columns). The minimum number of address lines needed for the
row decoder is _______.
Q.16 Consider a four bit D to A converter. The analog value corresponding to digital signals of values
0000 and 0001 are 0 V and 0.0625 V respectively. The analog value (in Volts) corresponding to
the digital signal 1111 is ________.
Q.17 The result of the convolution ( ? ) ?(? ? ) is
(A) ( + ) (B) ( ? ) (C) (? + ) (D) (? ? )
Q.18 The waveform of a periodic signal () x t
is shown in the figure.
A signal () gt is defined by
1
()
2
t
gt x
? ??
=
??
??
. The average power of () gt is _______.
Q.19 Negative feedback in a closed-loop control system DOES NOT
(A) reduce the overall gain (B) reduce bandwidth
(C) improve disturbance rejection (D) reduce sensitivity to parameter variation
Q.20
A unity negative feedback system has the open-loop transfer function ( ) =
( +1 ) (+3)
. The
value of the gain K (>0) at which the root locus crosses the imaginary axis is ________.
Q.21
The polar plot of the transfer function ( ) =
10 (+1)
+1 0
for 0 ? ? < ? will be in the
(A) first quadrant
(B) second quadrant
(C) third quadrant
(D) fourth quadrant
1
2 3
4
t
x(t)
-1
-2
-3 -4
3
-3
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/13
Q.22 A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and
step-size ?
of the delta modulator are 20,000 samples per second and 0.1 V, respectively.
To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is
(A)
1
2?
(B)
1
?
(C)
2
?
(D) ?
Q.23
Consider the signal ? () ()cos(2 ) ()sin(2 )
cc
s t mt ft mt ft ?? =+ where ?() mt denotes the Hilbert
transform of () mt and the bandwidth of () mt is very small compared to
c
f . The signal () st is a
(A) high-pass signal
(B) low-pass signal
(C) band-pass signal
(D) double sideband suppressed carrier signal
Q.24 Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the
following plots (in linear scale) qualitatively represents the dependence of H
?
on r, where H
?
is the
magnitude of the azimuthal component of magnetic field outside the conductor and r is the radial
distance from the conductor?
(A) (B)
(C) (D)
Q.25 The electric field component of a plane wave traveling in a lossless dielectric medium is given by
8
? (, ) 2cos 10
2
y
z
Ez t a t
??
=?
??
??
r
V/m. The wavelength (in m) for the wave is ___________.
H
?
r
H
?
r
H
?
r
H
?
r
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/13
Q. 26 ? Q. 55 carry two marks each.
Q.26
The solution of the differential equation
2
2
20
dy dy
y
dt dt
++= with (0) (0) 1 yy? == is
(A) (2 )
t
te ? (B) (1 2 )
t
te
?
+
(C) (2 )
t
te
?
+ (D) (1 2 )
t
te ?
Q.27
A vector is given by =
?
?
. Which one of the following statements
is TRUE?
(A) is solenoidal, but not irrotational
(B) is irrotational, but not solenoidal
(C) is neither solenoidal nor irrotational
(D) is both solenoidal and irrotational
Q.28 Which one of the following graphs describes the function f ( x ) =
( x
+ x+ 1 ) ?
(A)
(B)
(C)
(D)
Q.29
The maximum area (in square units) of a rectangle whose vertices lie on the ellipse
22
41 xy += is
_______.
Q.30 The damping ratio of a series RLC circuit can be expressed as
(A)
2
2
R C
L
(B)
2
2L
R C
(C)
2
R C
L
(D)
2 L
R C
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/13
Q.31 In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value of
v
c
(t) (in Volts) at t = 1 sec is ________.
Q.32 In the given circuit, the maximum power (in Watts) that can be transferred to the load R
L
is
_______.
2?
R
L
4 0 V
rms
j2?
Q.33 The built-in potential of an abrupt p-n junction is 0.75 V. If its junction capacitance (C
J
) at a reverse
bias (V
R
) of 1.25 V is 5 pF, the value of C
J
(in pF) when V
R
= 7.25 V is ________.
Q.34 A MOSFET in saturation has a drain current of 1 mA for V
DS
= 0.5 V. If the channel length
modulation coefficient is 0.05 V
-1
, the output resistance (in k?) of the MOSFET is _________.
Q.35 For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are
1 ? 10
17
cm
-3
and 1 ? 10
15
cm
-3
, respectively. The lifetimes of electrons in P region and holes in N
region are both 100 ?s. The electron and hole diffusion coefficients are 49 cm
2
/s and 36 cm
2
/s,
respectively. Assume kT/q = 26 mV, the intrinsic carrier concentration is 1 ? 10
10
cm
-3
, and
q = 1.6 ? 10
-19
C. When a forward voltage of 208 mV is applied across the diode, the hole current
density (in nA/cm
2
) injected from P region to N region is _____________.
Q.36 The Boolean expression F(X,Y,Z) = X
Y Z
+X Y
Z
+X Y Z
+ X Y Z converted into the canonical
product of sum (POS) form is
(A) (X+ Y +Z)(X+ Y +Z
)(X+ Y
+Z
)(X
+ Y+Z
) (B) (X+ Y
+Z)(X
+ Y +Z
)(X
+ Y
+Z)(X
+ Y
+Z
)
(C) (X+ Y +Z)(X
+ Y +Z
)(X+ Y
+Z)(X
+ Y
+Z
) (D) (X+ Y
+Z
)(X
+ Y +Z)(X
+ Y
+Z)(X+ Y +Z)
v
c
(t)
3 ?
10 V
2 ?
SW
t = 0
+
5
F
6
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a system of linear equations:
23 1 xy z ?+ =? ,
34 1 xy z ?+ = , and
24 6 . xy zk ?+ ? =
The value of k
for which the system has infinitely many solutions is ______.
Q.2
A function
23
() 1 fxxx =? + is defined in the closed interval [ ]
1, 1 ? . The value of x , in the
open interval () 1, 1 ?
for which the mean value theorem is satisfied, is
(A) ?1 2 ? (B) ?1 3 ? (C) 13 ? (D) 1/2
Q.3
Suppose and B are two independent events with probabilities ( )?0 and ( ) ? 0 . Let
and be their complements. Which one of the following statements is FALSE?
(A) ( ? ) = ( ) () (B) ( | ) =( )
(C) ( ? ) = ( ) +()
(D) ? = ( )
Q.4 Let zx iy =+ be a complex variable. Consider that contour integration is performed along the unit
circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
(A) The residue of
2
1
z
z ?
at 1 z = is 1/2
(B) ? = 0
(C)
?
= 1
(D) z (complex conjugate of z ) is an analytical function
Q.5
The value of p such that the vector 1
2
3
is an eigenvector of the matrix 412
2 1
14 ?4 10
is
_______.
Q.6 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the
capacitor is ________.
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/13
Q.7 In the network shown in the figure, all resistors are identical with R = 300 ?. The resistance
R
ab
(in ?) of the network is ______.
Q.8
In the given circuit, the values of
12
and VV respectively are
4?
4?
4? 5A
+
V
2
-
+
V
1
-
2 ?
?
(A) 5 V, 25 V (B) 10 V, 30 V (C) 15 V, 35 V (D) 0 V, 20 V
Q.9 A region of negative differential resistance is observed in the current voltage characteristics of a
silicon PN junction if
(A) both the P-region and the N-region are heavily doped
(B) the N-region is heavily doped compared to the P-region
(C) the P-region is heavily doped compared to the N-region
(D) an intrinsic silicon region is inserted between the P-region and the N-region
Q.10 A silicon sample is uniformly doped with donor type impurities with a concentration of 10
16
/cm
3
.
The electron and hole mobilities in the sample are 1200 cm
2
/V-s and 400 cm
2
/V-s respectively.
Assume complete ionization of impurities. The charge of an electron is 1.6 ?10
-19
C. The resistivity
of the sample (in ?-cm) is ____________.
a
b
R
R
R
RR R R
R RR
R
R
R R R
R = 300 ?
R
ab
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/13
Q.11 For the circuit with ideal diodes shown in the figure, the shape of the output (
) for the given
sine wave input (
) will be
(A)
(B)
(C)
(D)
Q.12 In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6 V. The output
voltage (in volts) is_______.
Q.13 In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The
energy (in ?J) taken from the 3 V source to charge the 0.1 ?F capacitor from 0 V to 3 V is
(A) 0.3 (B) 0.45 (C) 0.9 (D) 3
1k?
10V 1k?
+
V
O
-
SW
3 V
0.1 ?F
120 ?
t = 0
B A
+
?
+
?
0 T 0.5T
v
in
v
out
0 T 0.5T
0 T 0.5T
T
0.5T
0
0 T 0.5T
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/13
Q.14 In an 8085 microprocessor, the shift registers which store the result of an addition and the overflow
bit are, respectively
(A) B and F
(B) A and F
(C) H and F
(D) A and C
Q.15 A 16 Kb (=16,384 bit) memory array is designed as a square with an aspect ratio of one (number of
rows is equal to the number of columns). The minimum number of address lines needed for the
row decoder is _______.
Q.16 Consider a four bit D to A converter. The analog value corresponding to digital signals of values
0000 and 0001 are 0 V and 0.0625 V respectively. The analog value (in Volts) corresponding to
the digital signal 1111 is ________.
Q.17 The result of the convolution ( ? ) ?(? ? ) is
(A) ( + ) (B) ( ? ) (C) (? + ) (D) (? ? )
Q.18 The waveform of a periodic signal () x t
is shown in the figure.
A signal () gt is defined by
1
()
2
t
gt x
? ??
=
??
??
. The average power of () gt is _______.
Q.19 Negative feedback in a closed-loop control system DOES NOT
(A) reduce the overall gain (B) reduce bandwidth
(C) improve disturbance rejection (D) reduce sensitivity to parameter variation
Q.20
A unity negative feedback system has the open-loop transfer function ( ) =
( +1 ) (+3)
. The
value of the gain K (>0) at which the root locus crosses the imaginary axis is ________.
Q.21
The polar plot of the transfer function ( ) =
10 (+1)
+1 0
for 0 ? ? < ? will be in the
(A) first quadrant
(B) second quadrant
(C) third quadrant
(D) fourth quadrant
1
2 3
4
t
x(t)
-1
-2
-3 -4
3
-3
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/13
Q.22 A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and
step-size ?
of the delta modulator are 20,000 samples per second and 0.1 V, respectively.
To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is
(A)
1
2?
(B)
1
?
(C)
2
?
(D) ?
Q.23
Consider the signal ? () ()cos(2 ) ()sin(2 )
cc
s t mt ft mt ft ?? =+ where ?() mt denotes the Hilbert
transform of () mt and the bandwidth of () mt is very small compared to
c
f . The signal () st is a
(A) high-pass signal
(B) low-pass signal
(C) band-pass signal
(D) double sideband suppressed carrier signal
Q.24 Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the
following plots (in linear scale) qualitatively represents the dependence of H
?
on r, where H
?
is the
magnitude of the azimuthal component of magnetic field outside the conductor and r is the radial
distance from the conductor?
(A) (B)
(C) (D)
Q.25 The electric field component of a plane wave traveling in a lossless dielectric medium is given by
8
? (, ) 2cos 10
2
y
z
Ez t a t
??
=?
??
??
r
V/m. The wavelength (in m) for the wave is ___________.
H
?
r
H
?
r
H
?
r
H
?
r
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/13
Q. 26 ? Q. 55 carry two marks each.
Q.26
The solution of the differential equation
2
2
20
dy dy
y
dt dt
++= with (0) (0) 1 yy? == is
(A) (2 )
t
te ? (B) (1 2 )
t
te
?
+
(C) (2 )
t
te
?
+ (D) (1 2 )
t
te ?
Q.27
A vector is given by =
?
?
. Which one of the following statements
is TRUE?
(A) is solenoidal, but not irrotational
(B) is irrotational, but not solenoidal
(C) is neither solenoidal nor irrotational
(D) is both solenoidal and irrotational
Q.28 Which one of the following graphs describes the function f ( x ) =
( x
+ x+ 1 ) ?
(A)
(B)
(C)
(D)
Q.29
The maximum area (in square units) of a rectangle whose vertices lie on the ellipse
22
41 xy += is
_______.
Q.30 The damping ratio of a series RLC circuit can be expressed as
(A)
2
2
R C
L
(B)
2
2L
R C
(C)
2
R C
L
(D)
2 L
R C
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/13
Q.31 In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value of
v
c
(t) (in Volts) at t = 1 sec is ________.
Q.32 In the given circuit, the maximum power (in Watts) that can be transferred to the load R
L
is
_______.
2?
R
L
4 0 V
rms
j2?
Q.33 The built-in potential of an abrupt p-n junction is 0.75 V. If its junction capacitance (C
J
) at a reverse
bias (V
R
) of 1.25 V is 5 pF, the value of C
J
(in pF) when V
R
= 7.25 V is ________.
Q.34 A MOSFET in saturation has a drain current of 1 mA for V
DS
= 0.5 V. If the channel length
modulation coefficient is 0.05 V
-1
, the output resistance (in k?) of the MOSFET is _________.
Q.35 For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are
1 ? 10
17
cm
-3
and 1 ? 10
15
cm
-3
, respectively. The lifetimes of electrons in P region and holes in N
region are both 100 ?s. The electron and hole diffusion coefficients are 49 cm
2
/s and 36 cm
2
/s,
respectively. Assume kT/q = 26 mV, the intrinsic carrier concentration is 1 ? 10
10
cm
-3
, and
q = 1.6 ? 10
-19
C. When a forward voltage of 208 mV is applied across the diode, the hole current
density (in nA/cm
2
) injected from P region to N region is _____________.
Q.36 The Boolean expression F(X,Y,Z) = X
Y Z
+X Y
Z
+X Y Z
+ X Y Z converted into the canonical
product of sum (POS) form is
(A) (X+ Y +Z)(X+ Y +Z
)(X+ Y
+Z
)(X
+ Y+Z
) (B) (X+ Y
+Z)(X
+ Y +Z
)(X
+ Y
+Z)(X
+ Y
+Z
)
(C) (X+ Y +Z)(X
+ Y +Z
)(X+ Y
+Z)(X
+ Y
+Z
) (D) (X+ Y
+Z
)(X
+ Y +Z)(X
+ Y
+Z)(X+ Y +Z)
v
c
(t)
3 ?
10 V
2 ?
SW
t = 0
+
5
F
6
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/13
Q.37 All the logic gates shown in the figure have a propagation delay of 20 ns. Let A = C = 0 and B = 1
until time t = 0. At t = 0, all the inputs flip (i.e., A = C = 1 and B = 0) and remain in that state. For
t > 0, output Z = 1 for a duration (in ns) of ______________.
Q.38 A 3-input majority gate is defined by the logic function (, , ) M abc ab bc ca =+ + . Which one of
the following gates is represented by the function ((,,), (,, ),) M Mabc Mabc c ?
(A) 3-input NAND gate (B) 3-input XOR gate
(C) 3-input NOR gate (D) 3-input XNOR gate
Q.39 For the NMOSFET in the circuit shown, the threshold voltage is
, where
> 0. The source
voltage
is varied from 0 to
. Neglecting the channel length modulation, the drain current
as a function of
is represented by
(A)
(B)
(C)
(D)
V
SS
I
D
V
DD
? V
th
V
SS
I
D
V
DD
- V
th
V
SS
V
th
I
D
I
D
V
SS
V
DD
? V
th
V
SS
V
DD
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a system of linear equations:
23 1 xy z ?+ =? ,
34 1 xy z ?+ = , and
24 6 . xy zk ?+ ? =
The value of k
for which the system has infinitely many solutions is ______.
Q.2
A function
23
() 1 fxxx =? + is defined in the closed interval [ ]
1, 1 ? . The value of x , in the
open interval () 1, 1 ?
for which the mean value theorem is satisfied, is
(A) ?1 2 ? (B) ?1 3 ? (C) 13 ? (D) 1/2
Q.3
Suppose and B are two independent events with probabilities ( )?0 and ( ) ? 0 . Let
and be their complements. Which one of the following statements is FALSE?
(A) ( ? ) = ( ) () (B) ( | ) =( )
(C) ( ? ) = ( ) +()
(D) ? = ( )
Q.4 Let zx iy =+ be a complex variable. Consider that contour integration is performed along the unit
circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
(A) The residue of
2
1
z
z ?
at 1 z = is 1/2
(B) ? = 0
(C)
?
= 1
(D) z (complex conjugate of z ) is an analytical function
Q.5
The value of p such that the vector 1
2
3
is an eigenvector of the matrix 412
2 1
14 ?4 10
is
_______.
Q.6 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the
capacitor is ________.
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/13
Q.7 In the network shown in the figure, all resistors are identical with R = 300 ?. The resistance
R
ab
(in ?) of the network is ______.
Q.8
In the given circuit, the values of
12
and VV respectively are
4?
4?
4? 5A
+
V
2
-
+
V
1
-
2 ?
?
(A) 5 V, 25 V (B) 10 V, 30 V (C) 15 V, 35 V (D) 0 V, 20 V
Q.9 A region of negative differential resistance is observed in the current voltage characteristics of a
silicon PN junction if
(A) both the P-region and the N-region are heavily doped
(B) the N-region is heavily doped compared to the P-region
(C) the P-region is heavily doped compared to the N-region
(D) an intrinsic silicon region is inserted between the P-region and the N-region
Q.10 A silicon sample is uniformly doped with donor type impurities with a concentration of 10
16
/cm
3
.
The electron and hole mobilities in the sample are 1200 cm
2
/V-s and 400 cm
2
/V-s respectively.
Assume complete ionization of impurities. The charge of an electron is 1.6 ?10
-19
C. The resistivity
of the sample (in ?-cm) is ____________.
a
b
R
R
R
RR R R
R RR
R
R
R R R
R = 300 ?
R
ab
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/13
Q.11 For the circuit with ideal diodes shown in the figure, the shape of the output (
) for the given
sine wave input (
) will be
(A)
(B)
(C)
(D)
Q.12 In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6 V. The output
voltage (in volts) is_______.
Q.13 In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The
energy (in ?J) taken from the 3 V source to charge the 0.1 ?F capacitor from 0 V to 3 V is
(A) 0.3 (B) 0.45 (C) 0.9 (D) 3
1k?
10V 1k?
+
V
O
-
SW
3 V
0.1 ?F
120 ?
t = 0
B A
+
?
+
?
0 T 0.5T
v
in
v
out
0 T 0.5T
0 T 0.5T
T
0.5T
0
0 T 0.5T
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/13
Q.14 In an 8085 microprocessor, the shift registers which store the result of an addition and the overflow
bit are, respectively
(A) B and F
(B) A and F
(C) H and F
(D) A and C
Q.15 A 16 Kb (=16,384 bit) memory array is designed as a square with an aspect ratio of one (number of
rows is equal to the number of columns). The minimum number of address lines needed for the
row decoder is _______.
Q.16 Consider a four bit D to A converter. The analog value corresponding to digital signals of values
0000 and 0001 are 0 V and 0.0625 V respectively. The analog value (in Volts) corresponding to
the digital signal 1111 is ________.
Q.17 The result of the convolution ( ? ) ?(? ? ) is
(A) ( + ) (B) ( ? ) (C) (? + ) (D) (? ? )
Q.18 The waveform of a periodic signal () x t
is shown in the figure.
A signal () gt is defined by
1
()
2
t
gt x
? ??
=
??
??
. The average power of () gt is _______.
Q.19 Negative feedback in a closed-loop control system DOES NOT
(A) reduce the overall gain (B) reduce bandwidth
(C) improve disturbance rejection (D) reduce sensitivity to parameter variation
Q.20
A unity negative feedback system has the open-loop transfer function ( ) =
( +1 ) (+3)
. The
value of the gain K (>0) at which the root locus crosses the imaginary axis is ________.
Q.21
The polar plot of the transfer function ( ) =
10 (+1)
+1 0
for 0 ? ? < ? will be in the
(A) first quadrant
(B) second quadrant
(C) third quadrant
(D) fourth quadrant
1
2 3
4
t
x(t)
-1
-2
-3 -4
3
-3
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/13
Q.22 A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and
step-size ?
of the delta modulator are 20,000 samples per second and 0.1 V, respectively.
To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is
(A)
1
2?
(B)
1
?
(C)
2
?
(D) ?
Q.23
Consider the signal ? () ()cos(2 ) ()sin(2 )
cc
s t mt ft mt ft ?? =+ where ?() mt denotes the Hilbert
transform of () mt and the bandwidth of () mt is very small compared to
c
f . The signal () st is a
(A) high-pass signal
(B) low-pass signal
(C) band-pass signal
(D) double sideband suppressed carrier signal
Q.24 Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the
following plots (in linear scale) qualitatively represents the dependence of H
?
on r, where H
?
is the
magnitude of the azimuthal component of magnetic field outside the conductor and r is the radial
distance from the conductor?
(A) (B)
(C) (D)
Q.25 The electric field component of a plane wave traveling in a lossless dielectric medium is given by
8
? (, ) 2cos 10
2
y
z
Ez t a t
??
=?
??
??
r
V/m. The wavelength (in m) for the wave is ___________.
H
?
r
H
?
r
H
?
r
H
?
r
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/13
Q. 26 ? Q. 55 carry two marks each.
Q.26
The solution of the differential equation
2
2
20
dy dy
y
dt dt
++= with (0) (0) 1 yy? == is
(A) (2 )
t
te ? (B) (1 2 )
t
te
?
+
(C) (2 )
t
te
?
+ (D) (1 2 )
t
te ?
Q.27
A vector is given by =
?
?
. Which one of the following statements
is TRUE?
(A) is solenoidal, but not irrotational
(B) is irrotational, but not solenoidal
(C) is neither solenoidal nor irrotational
(D) is both solenoidal and irrotational
Q.28 Which one of the following graphs describes the function f ( x ) =
( x
+ x+ 1 ) ?
(A)
(B)
(C)
(D)
Q.29
The maximum area (in square units) of a rectangle whose vertices lie on the ellipse
22
41 xy += is
_______.
Q.30 The damping ratio of a series RLC circuit can be expressed as
(A)
2
2
R C
L
(B)
2
2L
R C
(C)
2
R C
L
(D)
2 L
R C
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/13
Q.31 In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value of
v
c
(t) (in Volts) at t = 1 sec is ________.
Q.32 In the given circuit, the maximum power (in Watts) that can be transferred to the load R
L
is
_______.
2?
R
L
4 0 V
rms
j2?
Q.33 The built-in potential of an abrupt p-n junction is 0.75 V. If its junction capacitance (C
J
) at a reverse
bias (V
R
) of 1.25 V is 5 pF, the value of C
J
(in pF) when V
R
= 7.25 V is ________.
Q.34 A MOSFET in saturation has a drain current of 1 mA for V
DS
= 0.5 V. If the channel length
modulation coefficient is 0.05 V
-1
, the output resistance (in k?) of the MOSFET is _________.
Q.35 For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are
1 ? 10
17
cm
-3
and 1 ? 10
15
cm
-3
, respectively. The lifetimes of electrons in P region and holes in N
region are both 100 ?s. The electron and hole diffusion coefficients are 49 cm
2
/s and 36 cm
2
/s,
respectively. Assume kT/q = 26 mV, the intrinsic carrier concentration is 1 ? 10
10
cm
-3
, and
q = 1.6 ? 10
-19
C. When a forward voltage of 208 mV is applied across the diode, the hole current
density (in nA/cm
2
) injected from P region to N region is _____________.
Q.36 The Boolean expression F(X,Y,Z) = X
Y Z
+X Y
Z
+X Y Z
+ X Y Z converted into the canonical
product of sum (POS) form is
(A) (X+ Y +Z)(X+ Y +Z
)(X+ Y
+Z
)(X
+ Y+Z
) (B) (X+ Y
+Z)(X
+ Y +Z
)(X
+ Y
+Z)(X
+ Y
+Z
)
(C) (X+ Y +Z)(X
+ Y +Z
)(X+ Y
+Z)(X
+ Y
+Z
) (D) (X+ Y
+Z
)(X
+ Y +Z)(X
+ Y
+Z)(X+ Y +Z)
v
c
(t)
3 ?
10 V
2 ?
SW
t = 0
+
5
F
6
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/13
Q.37 All the logic gates shown in the figure have a propagation delay of 20 ns. Let A = C = 0 and B = 1
until time t = 0. At t = 0, all the inputs flip (i.e., A = C = 1 and B = 0) and remain in that state. For
t > 0, output Z = 1 for a duration (in ns) of ______________.
Q.38 A 3-input majority gate is defined by the logic function (, , ) M abc ab bc ca =+ + . Which one of
the following gates is represented by the function ((,,), (,, ),) M Mabc Mabc c ?
(A) 3-input NAND gate (B) 3-input XOR gate
(C) 3-input NOR gate (D) 3-input XNOR gate
Q.39 For the NMOSFET in the circuit shown, the threshold voltage is
, where
> 0. The source
voltage
is varied from 0 to
. Neglecting the channel length modulation, the drain current
as a function of
is represented by
(A)
(B)
(C)
(D)
V
SS
I
D
V
DD
? V
th
V
SS
I
D
V
DD
- V
th
V
SS
V
th
I
D
I
D
V
SS
V
DD
? V
th
V
SS
V
DD
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/13
Q.40 In the circuit shown, assume that the opamp is ideal. The bridge output voltage V
0
(in mV) for
? = 0.05 is _______.
Q.41 The circuit shown in the figure has an ideal opamp. The oscillation frequency and the condition to
sustain the oscillations, respectively, are
(A)
C R
and R
1
= R
2
(B)
C R
and R
1
= 4R
2
(C)
C R
and R
1
= R
2
(D)
C R
and R
1
= 4R
2
Q.42 In the circuit shown, I
1
= 80 mA and I
2
= 4 mA. Transistors T
1
and T
2
are identical. Assume that the
thermal voltage V
T
is 26 mV at 27
o
C. At 50
o
C, the value of the voltage
12 1 2
VV V =? (in mV) is
_______.
250 (1-?) ?
250 (1-?) ?
250 (1+?) ?
250 (1+?) ?
100 ?
100 ?
V
0
50 ?
1V
+
V
S
I
1
I
2
T
1
T
2
V
1
V
2
V
12
+
v
out
2R
+
?
R
2
C
2C
R
R
1
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a system of linear equations:
23 1 xy z ?+ =? ,
34 1 xy z ?+ = , and
24 6 . xy zk ?+ ? =
The value of k
for which the system has infinitely many solutions is ______.
Q.2
A function
23
() 1 fxxx =? + is defined in the closed interval [ ]
1, 1 ? . The value of x , in the
open interval () 1, 1 ?
for which the mean value theorem is satisfied, is
(A) ?1 2 ? (B) ?1 3 ? (C) 13 ? (D) 1/2
Q.3
Suppose and B are two independent events with probabilities ( )?0 and ( ) ? 0 . Let
and be their complements. Which one of the following statements is FALSE?
(A) ( ? ) = ( ) () (B) ( | ) =( )
(C) ( ? ) = ( ) +()
(D) ? = ( )
Q.4 Let zx iy =+ be a complex variable. Consider that contour integration is performed along the unit
circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
(A) The residue of
2
1
z
z ?
at 1 z = is 1/2
(B) ? = 0
(C)
?
= 1
(D) z (complex conjugate of z ) is an analytical function
Q.5
The value of p such that the vector 1
2
3
is an eigenvector of the matrix 412
2 1
14 ?4 10
is
_______.
Q.6 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the
capacitor is ________.
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/13
Q.7 In the network shown in the figure, all resistors are identical with R = 300 ?. The resistance
R
ab
(in ?) of the network is ______.
Q.8
In the given circuit, the values of
12
and VV respectively are
4?
4?
4? 5A
+
V
2
-
+
V
1
-
2 ?
?
(A) 5 V, 25 V (B) 10 V, 30 V (C) 15 V, 35 V (D) 0 V, 20 V
Q.9 A region of negative differential resistance is observed in the current voltage characteristics of a
silicon PN junction if
(A) both the P-region and the N-region are heavily doped
(B) the N-region is heavily doped compared to the P-region
(C) the P-region is heavily doped compared to the N-region
(D) an intrinsic silicon region is inserted between the P-region and the N-region
Q.10 A silicon sample is uniformly doped with donor type impurities with a concentration of 10
16
/cm
3
.
The electron and hole mobilities in the sample are 1200 cm
2
/V-s and 400 cm
2
/V-s respectively.
Assume complete ionization of impurities. The charge of an electron is 1.6 ?10
-19
C. The resistivity
of the sample (in ?-cm) is ____________.
a
b
R
R
R
RR R R
R RR
R
R
R R R
R = 300 ?
R
ab
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/13
Q.11 For the circuit with ideal diodes shown in the figure, the shape of the output (
) for the given
sine wave input (
) will be
(A)
(B)
(C)
(D)
Q.12 In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6 V. The output
voltage (in volts) is_______.
Q.13 In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The
energy (in ?J) taken from the 3 V source to charge the 0.1 ?F capacitor from 0 V to 3 V is
(A) 0.3 (B) 0.45 (C) 0.9 (D) 3
1k?
10V 1k?
+
V
O
-
SW
3 V
0.1 ?F
120 ?
t = 0
B A
+
?
+
?
0 T 0.5T
v
in
v
out
0 T 0.5T
0 T 0.5T
T
0.5T
0
0 T 0.5T
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/13
Q.14 In an 8085 microprocessor, the shift registers which store the result of an addition and the overflow
bit are, respectively
(A) B and F
(B) A and F
(C) H and F
(D) A and C
Q.15 A 16 Kb (=16,384 bit) memory array is designed as a square with an aspect ratio of one (number of
rows is equal to the number of columns). The minimum number of address lines needed for the
row decoder is _______.
Q.16 Consider a four bit D to A converter. The analog value corresponding to digital signals of values
0000 and 0001 are 0 V and 0.0625 V respectively. The analog value (in Volts) corresponding to
the digital signal 1111 is ________.
Q.17 The result of the convolution ( ? ) ?(? ? ) is
(A) ( + ) (B) ( ? ) (C) (? + ) (D) (? ? )
Q.18 The waveform of a periodic signal () x t
is shown in the figure.
A signal () gt is defined by
1
()
2
t
gt x
? ??
=
??
??
. The average power of () gt is _______.
Q.19 Negative feedback in a closed-loop control system DOES NOT
(A) reduce the overall gain (B) reduce bandwidth
(C) improve disturbance rejection (D) reduce sensitivity to parameter variation
Q.20
A unity negative feedback system has the open-loop transfer function ( ) =
( +1 ) (+3)
. The
value of the gain K (>0) at which the root locus crosses the imaginary axis is ________.
Q.21
The polar plot of the transfer function ( ) =
10 (+1)
+1 0
for 0 ? ? < ? will be in the
(A) first quadrant
(B) second quadrant
(C) third quadrant
(D) fourth quadrant
1
2 3
4
t
x(t)
-1
-2
-3 -4
3
-3
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/13
Q.22 A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and
step-size ?
of the delta modulator are 20,000 samples per second and 0.1 V, respectively.
To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is
(A)
1
2?
(B)
1
?
(C)
2
?
(D) ?
Q.23
Consider the signal ? () ()cos(2 ) ()sin(2 )
cc
s t mt ft mt ft ?? =+ where ?() mt denotes the Hilbert
transform of () mt and the bandwidth of () mt is very small compared to
c
f . The signal () st is a
(A) high-pass signal
(B) low-pass signal
(C) band-pass signal
(D) double sideband suppressed carrier signal
Q.24 Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the
following plots (in linear scale) qualitatively represents the dependence of H
?
on r, where H
?
is the
magnitude of the azimuthal component of magnetic field outside the conductor and r is the radial
distance from the conductor?
(A) (B)
(C) (D)
Q.25 The electric field component of a plane wave traveling in a lossless dielectric medium is given by
8
? (, ) 2cos 10
2
y
z
Ez t a t
??
=?
??
??
r
V/m. The wavelength (in m) for the wave is ___________.
H
?
r
H
?
r
H
?
r
H
?
r
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/13
Q. 26 ? Q. 55 carry two marks each.
Q.26
The solution of the differential equation
2
2
20
dy dy
y
dt dt
++= with (0) (0) 1 yy? == is
(A) (2 )
t
te ? (B) (1 2 )
t
te
?
+
(C) (2 )
t
te
?
+ (D) (1 2 )
t
te ?
Q.27
A vector is given by =
?
?
. Which one of the following statements
is TRUE?
(A) is solenoidal, but not irrotational
(B) is irrotational, but not solenoidal
(C) is neither solenoidal nor irrotational
(D) is both solenoidal and irrotational
Q.28 Which one of the following graphs describes the function f ( x ) =
( x
+ x+ 1 ) ?
(A)
(B)
(C)
(D)
Q.29
The maximum area (in square units) of a rectangle whose vertices lie on the ellipse
22
41 xy += is
_______.
Q.30 The damping ratio of a series RLC circuit can be expressed as
(A)
2
2
R C
L
(B)
2
2L
R C
(C)
2
R C
L
(D)
2 L
R C
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/13
Q.31 In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value of
v
c
(t) (in Volts) at t = 1 sec is ________.
Q.32 In the given circuit, the maximum power (in Watts) that can be transferred to the load R
L
is
_______.
2?
R
L
4 0 V
rms
j2?
Q.33 The built-in potential of an abrupt p-n junction is 0.75 V. If its junction capacitance (C
J
) at a reverse
bias (V
R
) of 1.25 V is 5 pF, the value of C
J
(in pF) when V
R
= 7.25 V is ________.
Q.34 A MOSFET in saturation has a drain current of 1 mA for V
DS
= 0.5 V. If the channel length
modulation coefficient is 0.05 V
-1
, the output resistance (in k?) of the MOSFET is _________.
Q.35 For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are
1 ? 10
17
cm
-3
and 1 ? 10
15
cm
-3
, respectively. The lifetimes of electrons in P region and holes in N
region are both 100 ?s. The electron and hole diffusion coefficients are 49 cm
2
/s and 36 cm
2
/s,
respectively. Assume kT/q = 26 mV, the intrinsic carrier concentration is 1 ? 10
10
cm
-3
, and
q = 1.6 ? 10
-19
C. When a forward voltage of 208 mV is applied across the diode, the hole current
density (in nA/cm
2
) injected from P region to N region is _____________.
Q.36 The Boolean expression F(X,Y,Z) = X
Y Z
+X Y
Z
+X Y Z
+ X Y Z converted into the canonical
product of sum (POS) form is
(A) (X+ Y +Z)(X+ Y +Z
)(X+ Y
+Z
)(X
+ Y+Z
) (B) (X+ Y
+Z)(X
+ Y +Z
)(X
+ Y
+Z)(X
+ Y
+Z
)
(C) (X+ Y +Z)(X
+ Y +Z
)(X+ Y
+Z)(X
+ Y
+Z
) (D) (X+ Y
+Z
)(X
+ Y +Z)(X
+ Y
+Z)(X+ Y +Z)
v
c
(t)
3 ?
10 V
2 ?
SW
t = 0
+
5
F
6
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/13
Q.37 All the logic gates shown in the figure have a propagation delay of 20 ns. Let A = C = 0 and B = 1
until time t = 0. At t = 0, all the inputs flip (i.e., A = C = 1 and B = 0) and remain in that state. For
t > 0, output Z = 1 for a duration (in ns) of ______________.
Q.38 A 3-input majority gate is defined by the logic function (, , ) M abc ab bc ca =+ + . Which one of
the following gates is represented by the function ((,,), (,, ),) M Mabc Mabc c ?
(A) 3-input NAND gate (B) 3-input XOR gate
(C) 3-input NOR gate (D) 3-input XNOR gate
Q.39 For the NMOSFET in the circuit shown, the threshold voltage is
, where
> 0. The source
voltage
is varied from 0 to
. Neglecting the channel length modulation, the drain current
as a function of
is represented by
(A)
(B)
(C)
(D)
V
SS
I
D
V
DD
? V
th
V
SS
I
D
V
DD
- V
th
V
SS
V
th
I
D
I
D
V
SS
V
DD
? V
th
V
SS
V
DD
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/13
Q.40 In the circuit shown, assume that the opamp is ideal. The bridge output voltage V
0
(in mV) for
? = 0.05 is _______.
Q.41 The circuit shown in the figure has an ideal opamp. The oscillation frequency and the condition to
sustain the oscillations, respectively, are
(A)
C R
and R
1
= R
2
(B)
C R
and R
1
= 4R
2
(C)
C R
and R
1
= R
2
(D)
C R
and R
1
= 4R
2
Q.42 In the circuit shown, I
1
= 80 mA and I
2
= 4 mA. Transistors T
1
and T
2
are identical. Assume that the
thermal voltage V
T
is 26 mV at 27
o
C. At 50
o
C, the value of the voltage
12 1 2
VV V =? (in mV) is
_______.
250 (1-?) ?
250 (1-?) ?
250 (1+?) ?
250 (1+?) ?
100 ?
100 ?
V
0
50 ?
1V
+
V
S
I
1
I
2
T
1
T
2
V
1
V
2
V
12
+
v
out
2R
+
?
R
2
C
2C
R
R
1
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 10/13
Q.43
Two sequences [ ]
,, abc and [ ]
,, AB C are related as,
2
12
3
33 3
24
33
11 1
1where .
1
j
Aa
B WW b W e
CW W c
?
??
??
?? ? ?? ?
?? ? ?? ?
==
?? ? ?? ?
?? ? ?? ?
?? ? ?? ?
If another sequence [ ]
,, p qr is derived as,
12 2
33 3
24 4
33 3
11 1 1 0 0 /3
10 0/3
100 /3
pA
qWW W B
rWW WC
? ? ? ?? ?? ?
? ? ? ?? ?? ?
=
? ? ? ?? ?? ?
? ? ? ?? ?? ?
? ? ? ?? ?? ?
,
then the relationship between the sequences [ ]
,, p qr and [ ]
,, abc is
(A) [ ] [ ]
,, ,, p qr b a c = (B) [ ] [ ]
,, , , p qr b c a =
(C) [ ] [ ]
,, ,, p qr c a b = (D) [ ] [ ]
,, , , p qr c b a =
Q.44 For the discrete-time system shown in the figure, the poles of the system transfer function are
located at
(A) 2, 3
(B)
,3 (C)
,
(D) 2,
Q.45 The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero
at the origin has multiplicity 4. The impulse response of the system is ?[] . If ? [ 0 ] = 1, we can
conclude
(A) ?[] is real for all
(B) ?[] is purely imaginary for all
(C) ?[] is real for only even
(D) ?[] is purely imaginary for only odd
0.5
0.5
-0.5
-0.5
4
Im(z)
Re(z)
X[n] Y[n]
?1
6
5
6
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GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a system of linear equations:
23 1 xy z ?+ =? ,
34 1 xy z ?+ = , and
24 6 . xy zk ?+ ? =
The value of k
for which the system has infinitely many solutions is ______.
Q.2
A function
23
() 1 fxxx =? + is defined in the closed interval [ ]
1, 1 ? . The value of x , in the
open interval () 1, 1 ?
for which the mean value theorem is satisfied, is
(A) ?1 2 ? (B) ?1 3 ? (C) 13 ? (D) 1/2
Q.3
Suppose and B are two independent events with probabilities ( )?0 and ( ) ? 0 . Let
and be their complements. Which one of the following statements is FALSE?
(A) ( ? ) = ( ) () (B) ( | ) =( )
(C) ( ? ) = ( ) +()
(D) ? = ( )
Q.4 Let zx iy =+ be a complex variable. Consider that contour integration is performed along the unit
circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
(A) The residue of
2
1
z
z ?
at 1 z = is 1/2
(B) ? = 0
(C)
?
= 1
(D) z (complex conjugate of z ) is an analytical function
Q.5
The value of p such that the vector 1
2
3
is an eigenvector of the matrix 412
2 1
14 ?4 10
is
_______.
Q.6 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the
capacitor is ________.
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/13
Q.7 In the network shown in the figure, all resistors are identical with R = 300 ?. The resistance
R
ab
(in ?) of the network is ______.
Q.8
In the given circuit, the values of
12
and VV respectively are
4?
4?
4? 5A
+
V
2
-
+
V
1
-
2 ?
?
(A) 5 V, 25 V (B) 10 V, 30 V (C) 15 V, 35 V (D) 0 V, 20 V
Q.9 A region of negative differential resistance is observed in the current voltage characteristics of a
silicon PN junction if
(A) both the P-region and the N-region are heavily doped
(B) the N-region is heavily doped compared to the P-region
(C) the P-region is heavily doped compared to the N-region
(D) an intrinsic silicon region is inserted between the P-region and the N-region
Q.10 A silicon sample is uniformly doped with donor type impurities with a concentration of 10
16
/cm
3
.
The electron and hole mobilities in the sample are 1200 cm
2
/V-s and 400 cm
2
/V-s respectively.
Assume complete ionization of impurities. The charge of an electron is 1.6 ?10
-19
C. The resistivity
of the sample (in ?-cm) is ____________.
a
b
R
R
R
RR R R
R RR
R
R
R R R
R = 300 ?
R
ab
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/13
Q.11 For the circuit with ideal diodes shown in the figure, the shape of the output (
) for the given
sine wave input (
) will be
(A)
(B)
(C)
(D)
Q.12 In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6 V. The output
voltage (in volts) is_______.
Q.13 In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The
energy (in ?J) taken from the 3 V source to charge the 0.1 ?F capacitor from 0 V to 3 V is
(A) 0.3 (B) 0.45 (C) 0.9 (D) 3
1k?
10V 1k?
+
V
O
-
SW
3 V
0.1 ?F
120 ?
t = 0
B A
+
?
+
?
0 T 0.5T
v
in
v
out
0 T 0.5T
0 T 0.5T
T
0.5T
0
0 T 0.5T
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/13
Q.14 In an 8085 microprocessor, the shift registers which store the result of an addition and the overflow
bit are, respectively
(A) B and F
(B) A and F
(C) H and F
(D) A and C
Q.15 A 16 Kb (=16,384 bit) memory array is designed as a square with an aspect ratio of one (number of
rows is equal to the number of columns). The minimum number of address lines needed for the
row decoder is _______.
Q.16 Consider a four bit D to A converter. The analog value corresponding to digital signals of values
0000 and 0001 are 0 V and 0.0625 V respectively. The analog value (in Volts) corresponding to
the digital signal 1111 is ________.
Q.17 The result of the convolution ( ? ) ?(? ? ) is
(A) ( + ) (B) ( ? ) (C) (? + ) (D) (? ? )
Q.18 The waveform of a periodic signal () x t
is shown in the figure.
A signal () gt is defined by
1
()
2
t
gt x
? ??
=
??
??
. The average power of () gt is _______.
Q.19 Negative feedback in a closed-loop control system DOES NOT
(A) reduce the overall gain (B) reduce bandwidth
(C) improve disturbance rejection (D) reduce sensitivity to parameter variation
Q.20
A unity negative feedback system has the open-loop transfer function ( ) =
( +1 ) (+3)
. The
value of the gain K (>0) at which the root locus crosses the imaginary axis is ________.
Q.21
The polar plot of the transfer function ( ) =
10 (+1)
+1 0
for 0 ? ? < ? will be in the
(A) first quadrant
(B) second quadrant
(C) third quadrant
(D) fourth quadrant
1
2 3
4
t
x(t)
-1
-2
-3 -4
3
-3
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/13
Q.22 A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and
step-size ?
of the delta modulator are 20,000 samples per second and 0.1 V, respectively.
To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is
(A)
1
2?
(B)
1
?
(C)
2
?
(D) ?
Q.23
Consider the signal ? () ()cos(2 ) ()sin(2 )
cc
s t mt ft mt ft ?? =+ where ?() mt denotes the Hilbert
transform of () mt and the bandwidth of () mt is very small compared to
c
f . The signal () st is a
(A) high-pass signal
(B) low-pass signal
(C) band-pass signal
(D) double sideband suppressed carrier signal
Q.24 Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the
following plots (in linear scale) qualitatively represents the dependence of H
?
on r, where H
?
is the
magnitude of the azimuthal component of magnetic field outside the conductor and r is the radial
distance from the conductor?
(A) (B)
(C) (D)
Q.25 The electric field component of a plane wave traveling in a lossless dielectric medium is given by
8
? (, ) 2cos 10
2
y
z
Ez t a t
??
=?
??
??
r
V/m. The wavelength (in m) for the wave is ___________.
H
?
r
H
?
r
H
?
r
H
?
r
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/13
Q. 26 ? Q. 55 carry two marks each.
Q.26
The solution of the differential equation
2
2
20
dy dy
y
dt dt
++= with (0) (0) 1 yy? == is
(A) (2 )
t
te ? (B) (1 2 )
t
te
?
+
(C) (2 )
t
te
?
+ (D) (1 2 )
t
te ?
Q.27
A vector is given by =
?
?
. Which one of the following statements
is TRUE?
(A) is solenoidal, but not irrotational
(B) is irrotational, but not solenoidal
(C) is neither solenoidal nor irrotational
(D) is both solenoidal and irrotational
Q.28 Which one of the following graphs describes the function f ( x ) =
( x
+ x+ 1 ) ?
(A)
(B)
(C)
(D)
Q.29
The maximum area (in square units) of a rectangle whose vertices lie on the ellipse
22
41 xy += is
_______.
Q.30 The damping ratio of a series RLC circuit can be expressed as
(A)
2
2
R C
L
(B)
2
2L
R C
(C)
2
R C
L
(D)
2 L
R C
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/13
Q.31 In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value of
v
c
(t) (in Volts) at t = 1 sec is ________.
Q.32 In the given circuit, the maximum power (in Watts) that can be transferred to the load R
L
is
_______.
2?
R
L
4 0 V
rms
j2?
Q.33 The built-in potential of an abrupt p-n junction is 0.75 V. If its junction capacitance (C
J
) at a reverse
bias (V
R
) of 1.25 V is 5 pF, the value of C
J
(in pF) when V
R
= 7.25 V is ________.
Q.34 A MOSFET in saturation has a drain current of 1 mA for V
DS
= 0.5 V. If the channel length
modulation coefficient is 0.05 V
-1
, the output resistance (in k?) of the MOSFET is _________.
Q.35 For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are
1 ? 10
17
cm
-3
and 1 ? 10
15
cm
-3
, respectively. The lifetimes of electrons in P region and holes in N
region are both 100 ?s. The electron and hole diffusion coefficients are 49 cm
2
/s and 36 cm
2
/s,
respectively. Assume kT/q = 26 mV, the intrinsic carrier concentration is 1 ? 10
10
cm
-3
, and
q = 1.6 ? 10
-19
C. When a forward voltage of 208 mV is applied across the diode, the hole current
density (in nA/cm
2
) injected from P region to N region is _____________.
Q.36 The Boolean expression F(X,Y,Z) = X
Y Z
+X Y
Z
+X Y Z
+ X Y Z converted into the canonical
product of sum (POS) form is
(A) (X+ Y +Z)(X+ Y +Z
)(X+ Y
+Z
)(X
+ Y+Z
) (B) (X+ Y
+Z)(X
+ Y +Z
)(X
+ Y
+Z)(X
+ Y
+Z
)
(C) (X+ Y +Z)(X
+ Y +Z
)(X+ Y
+Z)(X
+ Y
+Z
) (D) (X+ Y
+Z
)(X
+ Y +Z)(X
+ Y
+Z)(X+ Y +Z)
v
c
(t)
3 ?
10 V
2 ?
SW
t = 0
+
5
F
6
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/13
Q.37 All the logic gates shown in the figure have a propagation delay of 20 ns. Let A = C = 0 and B = 1
until time t = 0. At t = 0, all the inputs flip (i.e., A = C = 1 and B = 0) and remain in that state. For
t > 0, output Z = 1 for a duration (in ns) of ______________.
Q.38 A 3-input majority gate is defined by the logic function (, , ) M abc ab bc ca =+ + . Which one of
the following gates is represented by the function ((,,), (,, ),) M Mabc Mabc c ?
(A) 3-input NAND gate (B) 3-input XOR gate
(C) 3-input NOR gate (D) 3-input XNOR gate
Q.39 For the NMOSFET in the circuit shown, the threshold voltage is
, where
> 0. The source
voltage
is varied from 0 to
. Neglecting the channel length modulation, the drain current
as a function of
is represented by
(A)
(B)
(C)
(D)
V
SS
I
D
V
DD
? V
th
V
SS
I
D
V
DD
- V
th
V
SS
V
th
I
D
I
D
V
SS
V
DD
? V
th
V
SS
V
DD
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/13
Q.40 In the circuit shown, assume that the opamp is ideal. The bridge output voltage V
0
(in mV) for
? = 0.05 is _______.
Q.41 The circuit shown in the figure has an ideal opamp. The oscillation frequency and the condition to
sustain the oscillations, respectively, are
(A)
C R
and R
1
= R
2
(B)
C R
and R
1
= 4R
2
(C)
C R
and R
1
= R
2
(D)
C R
and R
1
= 4R
2
Q.42 In the circuit shown, I
1
= 80 mA and I
2
= 4 mA. Transistors T
1
and T
2
are identical. Assume that the
thermal voltage V
T
is 26 mV at 27
o
C. At 50
o
C, the value of the voltage
12 1 2
VV V =? (in mV) is
_______.
250 (1-?) ?
250 (1-?) ?
250 (1+?) ?
250 (1+?) ?
100 ?
100 ?
V
0
50 ?
1V
+
V
S
I
1
I
2
T
1
T
2
V
1
V
2
V
12
+
v
out
2R
+
?
R
2
C
2C
R
R
1
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 10/13
Q.43
Two sequences [ ]
,, abc and [ ]
,, AB C are related as,
2
12
3
33 3
24
33
11 1
1where .
1
j
Aa
B WW b W e
CW W c
?
??
??
?? ? ?? ?
?? ? ?? ?
==
?? ? ?? ?
?? ? ?? ?
?? ? ?? ?
If another sequence [ ]
,, p qr is derived as,
12 2
33 3
24 4
33 3
11 1 1 0 0 /3
10 0/3
100 /3
pA
qWW W B
rWW WC
? ? ? ?? ?? ?
? ? ? ?? ?? ?
=
? ? ? ?? ?? ?
? ? ? ?? ?? ?
? ? ? ?? ?? ?
,
then the relationship between the sequences [ ]
,, p qr and [ ]
,, abc is
(A) [ ] [ ]
,, ,, p qr b a c = (B) [ ] [ ]
,, , , p qr b c a =
(C) [ ] [ ]
,, ,, p qr c a b = (D) [ ] [ ]
,, , , p qr c b a =
Q.44 For the discrete-time system shown in the figure, the poles of the system transfer function are
located at
(A) 2, 3
(B)
,3 (C)
,
(D) 2,
Q.45 The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero
at the origin has multiplicity 4. The impulse response of the system is ?[] . If ? [ 0 ] = 1, we can
conclude
(A) ?[] is real for all
(B) ?[] is purely imaginary for all
(C) ?[] is real for only even
(D) ?[] is purely imaginary for only odd
0.5
0.5
-0.5
-0.5
4
Im(z)
Re(z)
X[n] Y[n]
?1
6
5
6
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 11/13
Q.46 The open-loop transfer function of a plant in a unity feedback configuration is given as
2
(4)
()
(8)( 9)
Ks
Gs
ss
+
=
+?
. The value of the gain (0) K > for which 12 j ?+ lies on the root locus is
_______.
Q.47 A lead compensator network includes a parallel combination of R and C in the feed-forward path. If
the transfer function of the compensator is
2
()
4
c
s
Gs
s
+
=
+
, the value of RC is ________.
Q.48
A plant transfer function is given as
1
()
(2)
I
P
K
Gs K
sss
??
=+
??
+
??
. When the plant operates in a
unity feedback configuration, the condition for the stability of the closed loop system is
(A) 0
2
I
P
K
K>>
(B) 20
IP
KK >> (C) 2
IP
KK < (D) 2
IP
KK >
Q.49 The input X to the Binary Symmetric Channel (BSC) shown in the figure is ?1? with probability 0.8.
The cross-over probability is 1/7. If the received bit Y = 0, the conditional probability that ?1? was
transmitted is _______.
Q.50 The transmitted signal in a GSM system is of 200 kHz bandwidth and 8 users share a common
bandwidth using TDMA. If at a given time 12 users are talking in a cell, the total bandwidth of the
signal received by the base station of the cell will be at least (in kHz) ________.
0 0
1 1
6/7
6/7
XY
P[X = 0] = 0.2
P[X = 1] = 0.8
1/71/7
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a system of linear equations:
23 1 xy z ?+ =? ,
34 1 xy z ?+ = , and
24 6 . xy zk ?+ ? =
The value of k
for which the system has infinitely many solutions is ______.
Q.2
A function
23
() 1 fxxx =? + is defined in the closed interval [ ]
1, 1 ? . The value of x , in the
open interval () 1, 1 ?
for which the mean value theorem is satisfied, is
(A) ?1 2 ? (B) ?1 3 ? (C) 13 ? (D) 1/2
Q.3
Suppose and B are two independent events with probabilities ( )?0 and ( ) ? 0 . Let
and be their complements. Which one of the following statements is FALSE?
(A) ( ? ) = ( ) () (B) ( | ) =( )
(C) ( ? ) = ( ) +()
(D) ? = ( )
Q.4 Let zx iy =+ be a complex variable. Consider that contour integration is performed along the unit
circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
(A) The residue of
2
1
z
z ?
at 1 z = is 1/2
(B) ? = 0
(C)
?
= 1
(D) z (complex conjugate of z ) is an analytical function
Q.5
The value of p such that the vector 1
2
3
is an eigenvector of the matrix 412
2 1
14 ?4 10
is
_______.
Q.6 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the
capacitor is ________.
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/13
Q.7 In the network shown in the figure, all resistors are identical with R = 300 ?. The resistance
R
ab
(in ?) of the network is ______.
Q.8
In the given circuit, the values of
12
and VV respectively are
4?
4?
4? 5A
+
V
2
-
+
V
1
-
2 ?
?
(A) 5 V, 25 V (B) 10 V, 30 V (C) 15 V, 35 V (D) 0 V, 20 V
Q.9 A region of negative differential resistance is observed in the current voltage characteristics of a
silicon PN junction if
(A) both the P-region and the N-region are heavily doped
(B) the N-region is heavily doped compared to the P-region
(C) the P-region is heavily doped compared to the N-region
(D) an intrinsic silicon region is inserted between the P-region and the N-region
Q.10 A silicon sample is uniformly doped with donor type impurities with a concentration of 10
16
/cm
3
.
The electron and hole mobilities in the sample are 1200 cm
2
/V-s and 400 cm
2
/V-s respectively.
Assume complete ionization of impurities. The charge of an electron is 1.6 ?10
-19
C. The resistivity
of the sample (in ?-cm) is ____________.
a
b
R
R
R
RR R R
R RR
R
R
R R R
R = 300 ?
R
ab
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/13
Q.11 For the circuit with ideal diodes shown in the figure, the shape of the output (
) for the given
sine wave input (
) will be
(A)
(B)
(C)
(D)
Q.12 In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6 V. The output
voltage (in volts) is_______.
Q.13 In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The
energy (in ?J) taken from the 3 V source to charge the 0.1 ?F capacitor from 0 V to 3 V is
(A) 0.3 (B) 0.45 (C) 0.9 (D) 3
1k?
10V 1k?
+
V
O
-
SW
3 V
0.1 ?F
120 ?
t = 0
B A
+
?
+
?
0 T 0.5T
v
in
v
out
0 T 0.5T
0 T 0.5T
T
0.5T
0
0 T 0.5T
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/13
Q.14 In an 8085 microprocessor, the shift registers which store the result of an addition and the overflow
bit are, respectively
(A) B and F
(B) A and F
(C) H and F
(D) A and C
Q.15 A 16 Kb (=16,384 bit) memory array is designed as a square with an aspect ratio of one (number of
rows is equal to the number of columns). The minimum number of address lines needed for the
row decoder is _______.
Q.16 Consider a four bit D to A converter. The analog value corresponding to digital signals of values
0000 and 0001 are 0 V and 0.0625 V respectively. The analog value (in Volts) corresponding to
the digital signal 1111 is ________.
Q.17 The result of the convolution ( ? ) ?(? ? ) is
(A) ( + ) (B) ( ? ) (C) (? + ) (D) (? ? )
Q.18 The waveform of a periodic signal () x t
is shown in the figure.
A signal () gt is defined by
1
()
2
t
gt x
? ??
=
??
??
. The average power of () gt is _______.
Q.19 Negative feedback in a closed-loop control system DOES NOT
(A) reduce the overall gain (B) reduce bandwidth
(C) improve disturbance rejection (D) reduce sensitivity to parameter variation
Q.20
A unity negative feedback system has the open-loop transfer function ( ) =
( +1 ) (+3)
. The
value of the gain K (>0) at which the root locus crosses the imaginary axis is ________.
Q.21
The polar plot of the transfer function ( ) =
10 (+1)
+1 0
for 0 ? ? < ? will be in the
(A) first quadrant
(B) second quadrant
(C) third quadrant
(D) fourth quadrant
1
2 3
4
t
x(t)
-1
-2
-3 -4
3
-3
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/13
Q.22 A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and
step-size ?
of the delta modulator are 20,000 samples per second and 0.1 V, respectively.
To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is
(A)
1
2?
(B)
1
?
(C)
2
?
(D) ?
Q.23
Consider the signal ? () ()cos(2 ) ()sin(2 )
cc
s t mt ft mt ft ?? =+ where ?() mt denotes the Hilbert
transform of () mt and the bandwidth of () mt is very small compared to
c
f . The signal () st is a
(A) high-pass signal
(B) low-pass signal
(C) band-pass signal
(D) double sideband suppressed carrier signal
Q.24 Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the
following plots (in linear scale) qualitatively represents the dependence of H
?
on r, where H
?
is the
magnitude of the azimuthal component of magnetic field outside the conductor and r is the radial
distance from the conductor?
(A) (B)
(C) (D)
Q.25 The electric field component of a plane wave traveling in a lossless dielectric medium is given by
8
? (, ) 2cos 10
2
y
z
Ez t a t
??
=?
??
??
r
V/m. The wavelength (in m) for the wave is ___________.
H
?
r
H
?
r
H
?
r
H
?
r
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/13
Q. 26 ? Q. 55 carry two marks each.
Q.26
The solution of the differential equation
2
2
20
dy dy
y
dt dt
++= with (0) (0) 1 yy? == is
(A) (2 )
t
te ? (B) (1 2 )
t
te
?
+
(C) (2 )
t
te
?
+ (D) (1 2 )
t
te ?
Q.27
A vector is given by =
?
?
. Which one of the following statements
is TRUE?
(A) is solenoidal, but not irrotational
(B) is irrotational, but not solenoidal
(C) is neither solenoidal nor irrotational
(D) is both solenoidal and irrotational
Q.28 Which one of the following graphs describes the function f ( x ) =
( x
+ x+ 1 ) ?
(A)
(B)
(C)
(D)
Q.29
The maximum area (in square units) of a rectangle whose vertices lie on the ellipse
22
41 xy += is
_______.
Q.30 The damping ratio of a series RLC circuit can be expressed as
(A)
2
2
R C
L
(B)
2
2L
R C
(C)
2
R C
L
(D)
2 L
R C
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/13
Q.31 In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value of
v
c
(t) (in Volts) at t = 1 sec is ________.
Q.32 In the given circuit, the maximum power (in Watts) that can be transferred to the load R
L
is
_______.
2?
R
L
4 0 V
rms
j2?
Q.33 The built-in potential of an abrupt p-n junction is 0.75 V. If its junction capacitance (C
J
) at a reverse
bias (V
R
) of 1.25 V is 5 pF, the value of C
J
(in pF) when V
R
= 7.25 V is ________.
Q.34 A MOSFET in saturation has a drain current of 1 mA for V
DS
= 0.5 V. If the channel length
modulation coefficient is 0.05 V
-1
, the output resistance (in k?) of the MOSFET is _________.
Q.35 For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are
1 ? 10
17
cm
-3
and 1 ? 10
15
cm
-3
, respectively. The lifetimes of electrons in P region and holes in N
region are both 100 ?s. The electron and hole diffusion coefficients are 49 cm
2
/s and 36 cm
2
/s,
respectively. Assume kT/q = 26 mV, the intrinsic carrier concentration is 1 ? 10
10
cm
-3
, and
q = 1.6 ? 10
-19
C. When a forward voltage of 208 mV is applied across the diode, the hole current
density (in nA/cm
2
) injected from P region to N region is _____________.
Q.36 The Boolean expression F(X,Y,Z) = X
Y Z
+X Y
Z
+X Y Z
+ X Y Z converted into the canonical
product of sum (POS) form is
(A) (X+ Y +Z)(X+ Y +Z
)(X+ Y
+Z
)(X
+ Y+Z
) (B) (X+ Y
+Z)(X
+ Y +Z
)(X
+ Y
+Z)(X
+ Y
+Z
)
(C) (X+ Y +Z)(X
+ Y +Z
)(X+ Y
+Z)(X
+ Y
+Z
) (D) (X+ Y
+Z
)(X
+ Y +Z)(X
+ Y
+Z)(X+ Y +Z)
v
c
(t)
3 ?
10 V
2 ?
SW
t = 0
+
5
F
6
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/13
Q.37 All the logic gates shown in the figure have a propagation delay of 20 ns. Let A = C = 0 and B = 1
until time t = 0. At t = 0, all the inputs flip (i.e., A = C = 1 and B = 0) and remain in that state. For
t > 0, output Z = 1 for a duration (in ns) of ______________.
Q.38 A 3-input majority gate is defined by the logic function (, , ) M abc ab bc ca =+ + . Which one of
the following gates is represented by the function ((,,), (,, ),) M Mabc Mabc c ?
(A) 3-input NAND gate (B) 3-input XOR gate
(C) 3-input NOR gate (D) 3-input XNOR gate
Q.39 For the NMOSFET in the circuit shown, the threshold voltage is
, where
> 0. The source
voltage
is varied from 0 to
. Neglecting the channel length modulation, the drain current
as a function of
is represented by
(A)
(B)
(C)
(D)
V
SS
I
D
V
DD
? V
th
V
SS
I
D
V
DD
- V
th
V
SS
V
th
I
D
I
D
V
SS
V
DD
? V
th
V
SS
V
DD
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/13
Q.40 In the circuit shown, assume that the opamp is ideal. The bridge output voltage V
0
(in mV) for
? = 0.05 is _______.
Q.41 The circuit shown in the figure has an ideal opamp. The oscillation frequency and the condition to
sustain the oscillations, respectively, are
(A)
C R
and R
1
= R
2
(B)
C R
and R
1
= 4R
2
(C)
C R
and R
1
= R
2
(D)
C R
and R
1
= 4R
2
Q.42 In the circuit shown, I
1
= 80 mA and I
2
= 4 mA. Transistors T
1
and T
2
are identical. Assume that the
thermal voltage V
T
is 26 mV at 27
o
C. At 50
o
C, the value of the voltage
12 1 2
VV V =? (in mV) is
_______.
250 (1-?) ?
250 (1-?) ?
250 (1+?) ?
250 (1+?) ?
100 ?
100 ?
V
0
50 ?
1V
+
V
S
I
1
I
2
T
1
T
2
V
1
V
2
V
12
+
v
out
2R
+
?
R
2
C
2C
R
R
1
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 10/13
Q.43
Two sequences [ ]
,, abc and [ ]
,, AB C are related as,
2
12
3
33 3
24
33
11 1
1where .
1
j
Aa
B WW b W e
CW W c
?
??
??
?? ? ?? ?
?? ? ?? ?
==
?? ? ?? ?
?? ? ?? ?
?? ? ?? ?
If another sequence [ ]
,, p qr is derived as,
12 2
33 3
24 4
33 3
11 1 1 0 0 /3
10 0/3
100 /3
pA
qWW W B
rWW WC
? ? ? ?? ?? ?
? ? ? ?? ?? ?
=
? ? ? ?? ?? ?
? ? ? ?? ?? ?
? ? ? ?? ?? ?
,
then the relationship between the sequences [ ]
,, p qr and [ ]
,, abc is
(A) [ ] [ ]
,, ,, p qr b a c = (B) [ ] [ ]
,, , , p qr b c a =
(C) [ ] [ ]
,, ,, p qr c a b = (D) [ ] [ ]
,, , , p qr c b a =
Q.44 For the discrete-time system shown in the figure, the poles of the system transfer function are
located at
(A) 2, 3
(B)
,3 (C)
,
(D) 2,
Q.45 The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero
at the origin has multiplicity 4. The impulse response of the system is ?[] . If ? [ 0 ] = 1, we can
conclude
(A) ?[] is real for all
(B) ?[] is purely imaginary for all
(C) ?[] is real for only even
(D) ?[] is purely imaginary for only odd
0.5
0.5
-0.5
-0.5
4
Im(z)
Re(z)
X[n] Y[n]
?1
6
5
6
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 11/13
Q.46 The open-loop transfer function of a plant in a unity feedback configuration is given as
2
(4)
()
(8)( 9)
Ks
Gs
ss
+
=
+?
. The value of the gain (0) K > for which 12 j ?+ lies on the root locus is
_______.
Q.47 A lead compensator network includes a parallel combination of R and C in the feed-forward path. If
the transfer function of the compensator is
2
()
4
c
s
Gs
s
+
=
+
, the value of RC is ________.
Q.48
A plant transfer function is given as
1
()
(2)
I
P
K
Gs K
sss
??
=+
??
+
??
. When the plant operates in a
unity feedback configuration, the condition for the stability of the closed loop system is
(A) 0
2
I
P
K
K>>
(B) 20
IP
KK >> (C) 2
IP
KK < (D) 2
IP
KK >
Q.49 The input X to the Binary Symmetric Channel (BSC) shown in the figure is ?1? with probability 0.8.
The cross-over probability is 1/7. If the received bit Y = 0, the conditional probability that ?1? was
transmitted is _______.
Q.50 The transmitted signal in a GSM system is of 200 kHz bandwidth and 8 users share a common
bandwidth using TDMA. If at a given time 12 users are talking in a cell, the total bandwidth of the
signal received by the base station of the cell will be at least (in kHz) ________.
0 0
1 1
6/7
6/7
XY
P[X = 0] = 0.2
P[X = 1] = 0.8
1/71/7
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 12/13
Q.51 In the system shown in Figure (a), m(t) is a low-pass signal with bandwidth W Hz. The frequency
response of the band-pass filter H( f ) is shown in Figure (b). If it is desired that the output signal
( ) = 10 ( ) , the maximum value of (in Hz) should be strictly less than ________.
Q.52
A source emits bit 0with probability
1
3
and bit 1 with probability
2
3
. The emitted bits are
communicated to the receiver. The receiver decides for either 0 or 1
based on the received value
R . It is given that the conditional density functions of R are as
0
1
,3 1,
()
4
0, otherwise,
R
x
r f
?
?? ?
?
=
?
?
?
and
1
1
,1 5,
() 6
0, otherwise.
R
x
r f
?
?? ?
?
=
?
?
?
The minimum decision error probability is
(A) 0 (B) 1/12 (C) 1/9 (D) 1/6
Q.53 The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made
of a perfect electric conductor is given by the following expression
( ,,, ) =0.1 cos ( 25 ) cos ( 30 .3 ) cos ( 12 ? 10
? ) ( / )
The cross-sectional dimensions of the waveguide are given as = 0 . 08 and = 0.033 . The
mode of propagation inside the waveguide is
(A)
12
TM (B)
21
TM
(C)
21
TE (D)
12
TE
Q.54 The electric field intensity of a plane wave traveling in free space is given by the following
expression
( , ) =
24 c os ( ? ) ( V/m )
In this field, consider a square area 10 cm x 10 cm on a plane + = 1 . The total time-averaged
power (in mW) passing through the square area is _______.
x(t) = m(t) cos(2400 ?t)
Amplifier
y(t) = 10x (t) + x
2
(t) z(t)
Band-pass
filter
H( f )
H( f )
1700 f (Hz)
0
1
700 -700 -1700
(a)
(b)
FirstRanker.com - FirstRanker's Choice
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 1/13
Q. 1 ? Q. 25 carry one mark each.
Q.1 Consider a system of linear equations:
23 1 xy z ?+ =? ,
34 1 xy z ?+ = , and
24 6 . xy zk ?+ ? =
The value of k
for which the system has infinitely many solutions is ______.
Q.2
A function
23
() 1 fxxx =? + is defined in the closed interval [ ]
1, 1 ? . The value of x , in the
open interval () 1, 1 ?
for which the mean value theorem is satisfied, is
(A) ?1 2 ? (B) ?1 3 ? (C) 13 ? (D) 1/2
Q.3
Suppose and B are two independent events with probabilities ( )?0 and ( ) ? 0 . Let
and be their complements. Which one of the following statements is FALSE?
(A) ( ? ) = ( ) () (B) ( | ) =( )
(C) ( ? ) = ( ) +()
(D) ? = ( )
Q.4 Let zx iy =+ be a complex variable. Consider that contour integration is performed along the unit
circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
(A) The residue of
2
1
z
z ?
at 1 z = is 1/2
(B) ? = 0
(C)
?
= 1
(D) z (complex conjugate of z ) is an analytical function
Q.5
The value of p such that the vector 1
2
3
is an eigenvector of the matrix 412
2 1
14 ?4 10
is
_______.
Q.6 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the
capacitor is ________.
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 2/13
Q.7 In the network shown in the figure, all resistors are identical with R = 300 ?. The resistance
R
ab
(in ?) of the network is ______.
Q.8
In the given circuit, the values of
12
and VV respectively are
4?
4?
4? 5A
+
V
2
-
+
V
1
-
2 ?
?
(A) 5 V, 25 V (B) 10 V, 30 V (C) 15 V, 35 V (D) 0 V, 20 V
Q.9 A region of negative differential resistance is observed in the current voltage characteristics of a
silicon PN junction if
(A) both the P-region and the N-region are heavily doped
(B) the N-region is heavily doped compared to the P-region
(C) the P-region is heavily doped compared to the N-region
(D) an intrinsic silicon region is inserted between the P-region and the N-region
Q.10 A silicon sample is uniformly doped with donor type impurities with a concentration of 10
16
/cm
3
.
The electron and hole mobilities in the sample are 1200 cm
2
/V-s and 400 cm
2
/V-s respectively.
Assume complete ionization of impurities. The charge of an electron is 1.6 ?10
-19
C. The resistivity
of the sample (in ?-cm) is ____________.
a
b
R
R
R
RR R R
R RR
R
R
R R R
R = 300 ?
R
ab
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 3/13
Q.11 For the circuit with ideal diodes shown in the figure, the shape of the output (
) for the given
sine wave input (
) will be
(A)
(B)
(C)
(D)
Q.12 In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6 V. The output
voltage (in volts) is_______.
Q.13 In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The
energy (in ?J) taken from the 3 V source to charge the 0.1 ?F capacitor from 0 V to 3 V is
(A) 0.3 (B) 0.45 (C) 0.9 (D) 3
1k?
10V 1k?
+
V
O
-
SW
3 V
0.1 ?F
120 ?
t = 0
B A
+
?
+
?
0 T 0.5T
v
in
v
out
0 T 0.5T
0 T 0.5T
T
0.5T
0
0 T 0.5T
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 4/13
Q.14 In an 8085 microprocessor, the shift registers which store the result of an addition and the overflow
bit are, respectively
(A) B and F
(B) A and F
(C) H and F
(D) A and C
Q.15 A 16 Kb (=16,384 bit) memory array is designed as a square with an aspect ratio of one (number of
rows is equal to the number of columns). The minimum number of address lines needed for the
row decoder is _______.
Q.16 Consider a four bit D to A converter. The analog value corresponding to digital signals of values
0000 and 0001 are 0 V and 0.0625 V respectively. The analog value (in Volts) corresponding to
the digital signal 1111 is ________.
Q.17 The result of the convolution ( ? ) ?(? ? ) is
(A) ( + ) (B) ( ? ) (C) (? + ) (D) (? ? )
Q.18 The waveform of a periodic signal () x t
is shown in the figure.
A signal () gt is defined by
1
()
2
t
gt x
? ??
=
??
??
. The average power of () gt is _______.
Q.19 Negative feedback in a closed-loop control system DOES NOT
(A) reduce the overall gain (B) reduce bandwidth
(C) improve disturbance rejection (D) reduce sensitivity to parameter variation
Q.20
A unity negative feedback system has the open-loop transfer function ( ) =
( +1 ) (+3)
. The
value of the gain K (>0) at which the root locus crosses the imaginary axis is ________.
Q.21
The polar plot of the transfer function ( ) =
10 (+1)
+1 0
for 0 ? ? < ? will be in the
(A) first quadrant
(B) second quadrant
(C) third quadrant
(D) fourth quadrant
1
2 3
4
t
x(t)
-1
-2
-3 -4
3
-3
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 5/13
Q.22 A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and
step-size ?
of the delta modulator are 20,000 samples per second and 0.1 V, respectively.
To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is
(A)
1
2?
(B)
1
?
(C)
2
?
(D) ?
Q.23
Consider the signal ? () ()cos(2 ) ()sin(2 )
cc
s t mt ft mt ft ?? =+ where ?() mt denotes the Hilbert
transform of () mt and the bandwidth of () mt is very small compared to
c
f . The signal () st is a
(A) high-pass signal
(B) low-pass signal
(C) band-pass signal
(D) double sideband suppressed carrier signal
Q.24 Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the
following plots (in linear scale) qualitatively represents the dependence of H
?
on r, where H
?
is the
magnitude of the azimuthal component of magnetic field outside the conductor and r is the radial
distance from the conductor?
(A) (B)
(C) (D)
Q.25 The electric field component of a plane wave traveling in a lossless dielectric medium is given by
8
? (, ) 2cos 10
2
y
z
Ez t a t
??
=?
??
??
r
V/m. The wavelength (in m) for the wave is ___________.
H
?
r
H
?
r
H
?
r
H
?
r
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 6/13
Q. 26 ? Q. 55 carry two marks each.
Q.26
The solution of the differential equation
2
2
20
dy dy
y
dt dt
++= with (0) (0) 1 yy? == is
(A) (2 )
t
te ? (B) (1 2 )
t
te
?
+
(C) (2 )
t
te
?
+ (D) (1 2 )
t
te ?
Q.27
A vector is given by =
?
?
. Which one of the following statements
is TRUE?
(A) is solenoidal, but not irrotational
(B) is irrotational, but not solenoidal
(C) is neither solenoidal nor irrotational
(D) is both solenoidal and irrotational
Q.28 Which one of the following graphs describes the function f ( x ) =
( x
+ x+ 1 ) ?
(A)
(B)
(C)
(D)
Q.29
The maximum area (in square units) of a rectangle whose vertices lie on the ellipse
22
41 xy += is
_______.
Q.30 The damping ratio of a series RLC circuit can be expressed as
(A)
2
2
R C
L
(B)
2
2L
R C
(C)
2
R C
L
(D)
2 L
R C
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 7/13
Q.31 In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value of
v
c
(t) (in Volts) at t = 1 sec is ________.
Q.32 In the given circuit, the maximum power (in Watts) that can be transferred to the load R
L
is
_______.
2?
R
L
4 0 V
rms
j2?
Q.33 The built-in potential of an abrupt p-n junction is 0.75 V. If its junction capacitance (C
J
) at a reverse
bias (V
R
) of 1.25 V is 5 pF, the value of C
J
(in pF) when V
R
= 7.25 V is ________.
Q.34 A MOSFET in saturation has a drain current of 1 mA for V
DS
= 0.5 V. If the channel length
modulation coefficient is 0.05 V
-1
, the output resistance (in k?) of the MOSFET is _________.
Q.35 For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are
1 ? 10
17
cm
-3
and 1 ? 10
15
cm
-3
, respectively. The lifetimes of electrons in P region and holes in N
region are both 100 ?s. The electron and hole diffusion coefficients are 49 cm
2
/s and 36 cm
2
/s,
respectively. Assume kT/q = 26 mV, the intrinsic carrier concentration is 1 ? 10
10
cm
-3
, and
q = 1.6 ? 10
-19
C. When a forward voltage of 208 mV is applied across the diode, the hole current
density (in nA/cm
2
) injected from P region to N region is _____________.
Q.36 The Boolean expression F(X,Y,Z) = X
Y Z
+X Y
Z
+X Y Z
+ X Y Z converted into the canonical
product of sum (POS) form is
(A) (X+ Y +Z)(X+ Y +Z
)(X+ Y
+Z
)(X
+ Y+Z
) (B) (X+ Y
+Z)(X
+ Y +Z
)(X
+ Y
+Z)(X
+ Y
+Z
)
(C) (X+ Y +Z)(X
+ Y +Z
)(X+ Y
+Z)(X
+ Y
+Z
) (D) (X+ Y
+Z
)(X
+ Y +Z)(X
+ Y
+Z)(X+ Y +Z)
v
c
(t)
3 ?
10 V
2 ?
SW
t = 0
+
5
F
6
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 8/13
Q.37 All the logic gates shown in the figure have a propagation delay of 20 ns. Let A = C = 0 and B = 1
until time t = 0. At t = 0, all the inputs flip (i.e., A = C = 1 and B = 0) and remain in that state. For
t > 0, output Z = 1 for a duration (in ns) of ______________.
Q.38 A 3-input majority gate is defined by the logic function (, , ) M abc ab bc ca =+ + . Which one of
the following gates is represented by the function ((,,), (,, ),) M Mabc Mabc c ?
(A) 3-input NAND gate (B) 3-input XOR gate
(C) 3-input NOR gate (D) 3-input XNOR gate
Q.39 For the NMOSFET in the circuit shown, the threshold voltage is
, where
> 0. The source
voltage
is varied from 0 to
. Neglecting the channel length modulation, the drain current
as a function of
is represented by
(A)
(B)
(C)
(D)
V
SS
I
D
V
DD
? V
th
V
SS
I
D
V
DD
- V
th
V
SS
V
th
I
D
I
D
V
SS
V
DD
? V
th
V
SS
V
DD
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 9/13
Q.40 In the circuit shown, assume that the opamp is ideal. The bridge output voltage V
0
(in mV) for
? = 0.05 is _______.
Q.41 The circuit shown in the figure has an ideal opamp. The oscillation frequency and the condition to
sustain the oscillations, respectively, are
(A)
C R
and R
1
= R
2
(B)
C R
and R
1
= 4R
2
(C)
C R
and R
1
= R
2
(D)
C R
and R
1
= 4R
2
Q.42 In the circuit shown, I
1
= 80 mA and I
2
= 4 mA. Transistors T
1
and T
2
are identical. Assume that the
thermal voltage V
T
is 26 mV at 27
o
C. At 50
o
C, the value of the voltage
12 1 2
VV V =? (in mV) is
_______.
250 (1-?) ?
250 (1-?) ?
250 (1+?) ?
250 (1+?) ?
100 ?
100 ?
V
0
50 ?
1V
+
V
S
I
1
I
2
T
1
T
2
V
1
V
2
V
12
+
v
out
2R
+
?
R
2
C
2C
R
R
1
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 10/13
Q.43
Two sequences [ ]
,, abc and [ ]
,, AB C are related as,
2
12
3
33 3
24
33
11 1
1where .
1
j
Aa
B WW b W e
CW W c
?
??
??
?? ? ?? ?
?? ? ?? ?
==
?? ? ?? ?
?? ? ?? ?
?? ? ?? ?
If another sequence [ ]
,, p qr is derived as,
12 2
33 3
24 4
33 3
11 1 1 0 0 /3
10 0/3
100 /3
pA
qWW W B
rWW WC
? ? ? ?? ?? ?
? ? ? ?? ?? ?
=
? ? ? ?? ?? ?
? ? ? ?? ?? ?
? ? ? ?? ?? ?
,
then the relationship between the sequences [ ]
,, p qr and [ ]
,, abc is
(A) [ ] [ ]
,, ,, p qr b a c = (B) [ ] [ ]
,, , , p qr b c a =
(C) [ ] [ ]
,, ,, p qr c a b = (D) [ ] [ ]
,, , , p qr c b a =
Q.44 For the discrete-time system shown in the figure, the poles of the system transfer function are
located at
(A) 2, 3
(B)
,3 (C)
,
(D) 2,
Q.45 The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero
at the origin has multiplicity 4. The impulse response of the system is ?[] . If ? [ 0 ] = 1, we can
conclude
(A) ?[] is real for all
(B) ?[] is purely imaginary for all
(C) ?[] is real for only even
(D) ?[] is purely imaginary for only odd
0.5
0.5
-0.5
-0.5
4
Im(z)
Re(z)
X[n] Y[n]
?1
6
5
6
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 11/13
Q.46 The open-loop transfer function of a plant in a unity feedback configuration is given as
2
(4)
()
(8)( 9)
Ks
Gs
ss
+
=
+?
. The value of the gain (0) K > for which 12 j ?+ lies on the root locus is
_______.
Q.47 A lead compensator network includes a parallel combination of R and C in the feed-forward path. If
the transfer function of the compensator is
2
()
4
c
s
Gs
s
+
=
+
, the value of RC is ________.
Q.48
A plant transfer function is given as
1
()
(2)
I
P
K
Gs K
sss
??
=+
??
+
??
. When the plant operates in a
unity feedback configuration, the condition for the stability of the closed loop system is
(A) 0
2
I
P
K
K>>
(B) 20
IP
KK >> (C) 2
IP
KK < (D) 2
IP
KK >
Q.49 The input X to the Binary Symmetric Channel (BSC) shown in the figure is ?1? with probability 0.8.
The cross-over probability is 1/7. If the received bit Y = 0, the conditional probability that ?1? was
transmitted is _______.
Q.50 The transmitted signal in a GSM system is of 200 kHz bandwidth and 8 users share a common
bandwidth using TDMA. If at a given time 12 users are talking in a cell, the total bandwidth of the
signal received by the base station of the cell will be at least (in kHz) ________.
0 0
1 1
6/7
6/7
XY
P[X = 0] = 0.2
P[X = 1] = 0.8
1/71/7
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 12/13
Q.51 In the system shown in Figure (a), m(t) is a low-pass signal with bandwidth W Hz. The frequency
response of the band-pass filter H( f ) is shown in Figure (b). If it is desired that the output signal
( ) = 10 ( ) , the maximum value of (in Hz) should be strictly less than ________.
Q.52
A source emits bit 0with probability
1
3
and bit 1 with probability
2
3
. The emitted bits are
communicated to the receiver. The receiver decides for either 0 or 1
based on the received value
R . It is given that the conditional density functions of R are as
0
1
,3 1,
()
4
0, otherwise,
R
x
r f
?
?? ?
?
=
?
?
?
and
1
1
,1 5,
() 6
0, otherwise.
R
x
r f
?
?? ?
?
=
?
?
?
The minimum decision error probability is
(A) 0 (B) 1/12 (C) 1/9 (D) 1/6
Q.53 The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made
of a perfect electric conductor is given by the following expression
( ,,, ) =0.1 cos ( 25 ) cos ( 30 .3 ) cos ( 12 ? 10
? ) ( / )
The cross-sectional dimensions of the waveguide are given as = 0 . 08 and = 0.033 . The
mode of propagation inside the waveguide is
(A)
12
TM (B)
21
TM
(C)
21
TE (D)
12
TE
Q.54 The electric field intensity of a plane wave traveling in free space is given by the following
expression
( , ) =
24 c os ( ? ) ( V/m )
In this field, consider a square area 10 cm x 10 cm on a plane + = 1 . The total time-averaged
power (in mW) passing through the square area is _______.
x(t) = m(t) cos(2400 ?t)
Amplifier
y(t) = 10x (t) + x
2
(t) z(t)
Band-pass
filter
H( f )
H( f )
1700 f (Hz)
0
1
700 -700 -1700
(a)
(b)
GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC
EC 13/13
Q.55 Consider a uniform plane wave with amplitude (E
0
) of 10 V/m and 1.1 GHz frequency travelling in
air, and incident normally on a dielectric medium with complex relative permittivity (?
r
) and
permeability (?
r
) as shown in the figure.
The magnitude of the transmitted electric field component (in V/m) after it has travelled a distance
of 10 cm inside the dielectric region is _________.
END OF THE QUESTION PAPER
Dielectric
?
r
= 1 ? j2
?
r
= 1 ? j2
Air
? = 120??
|E
0
| = 10 V/m
Freq = 1.1 GHz
10 cm
|E| = ?
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This post was last modified on 19 December 2019