Electronics and Communication Engineering (EC) 2003 GATE Paper without solution PDF Download

 Page 1


GATE EC - 2003
R 
R 
R 
R ~ 
C C 
C 
2O
+
-
i(t) 
sin t 
2H 
1F 
Q.1 – Q.30 Carry One Mark Each 
1. The minimum number of equations required to analyze the circuit shown in
Fig.Q.1 is
(a) 3 (b) 4 (c) 6 (d) 7 
2. A source of angular frequency 1 rad/sec has a source impedance consisting of 1O
resistance in series with 1 H inductance. The load that will obtain the maximum
power transfer is
(a) 1 O resistance
(b) 1 O resistance in parallel with 1 H inductance
(c) 1 O resistance in series with 1 F capacitor
(d) 1 O resistance in parallel with 1 F capacitor
3. A series RLC circuit has a resonance frequency of 1 kHz and a quality factor Q =
100. If each R, L and C is doubled from its original value, the new Q of the circuit
is
(a) 25 (b) 50 (c) 100 (d) 200 
4. The Laplace transform of i(t) is given by ( )
( )
=
+
2
1
I s
s s
As t 
 8 , the value of i(t) tends to 
(a) 0 (b) 1 (c) 2 (d) 8
5. The differential equation for the current i(t) in the circuit of Figure Q.5 is
(a) ( )
2
2
2 2 sin
d i di
i t t
dt
dt
+ + =
(b) ( )
2
2
2 2 cos
d i di
i t t
dt
dt
+ + =
(c) ( )
2
2
2 2 cos
d i di
i t t
dt
dt
+ + =
(d) ( )
2
2
2 2 sin
d i di
i t t
dt
dt
+ + =
Page 2


GATE EC - 2003
R 
R 
R 
R ~ 
C C 
C 
2O
+
-
i(t) 
sin t 
2H 
1F 
Q.1 – Q.30 Carry One Mark Each 
1. The minimum number of equations required to analyze the circuit shown in
Fig.Q.1 is
(a) 3 (b) 4 (c) 6 (d) 7 
2. A source of angular frequency 1 rad/sec has a source impedance consisting of 1O
resistance in series with 1 H inductance. The load that will obtain the maximum
power transfer is
(a) 1 O resistance
(b) 1 O resistance in parallel with 1 H inductance
(c) 1 O resistance in series with 1 F capacitor
(d) 1 O resistance in parallel with 1 F capacitor
3. A series RLC circuit has a resonance frequency of 1 kHz and a quality factor Q =
100. If each R, L and C is doubled from its original value, the new Q of the circuit
is
(a) 25 (b) 50 (c) 100 (d) 200 
4. The Laplace transform of i(t) is given by ( )
( )
=
+
2
1
I s
s s
As t 
 8 , the value of i(t) tends to 
(a) 0 (b) 1 (c) 2 (d) 8
5. The differential equation for the current i(t) in the circuit of Figure Q.5 is
(a) ( )
2
2
2 2 sin
d i di
i t t
dt
dt
+ + =
(b) ( )
2
2
2 2 cos
d i di
i t t
dt
dt
+ + =
(c) ( )
2
2
2 2 cos
d i di
i t t
dt
dt
+ + =
(d) ( )
2
2
2 2 sin
d i di
i t t
dt
dt
+ + =
GATE EC - 2003
6. n-type silicon is obtained by doping silicon with
(a) Germanium (b) Aluminum (c) Boron (d) Phosphorus 
7. The bandgap of silicon at 300 K is
(a) 1.36 eV (b) 1.10 eV (c) 0.80 eV (d) 0.67 eV 
8. The intrinsic carrier concentration of silicon sample of 300 K is 1.5 ×10
16
/m
3
. If
after doping, the number of majority carriers is 5 × 10
20
/m
3
, the minority carrier
density is
(a) 4.50 × 10
11
/m
3
(b) 3.33 × 10
4
/m
3
 
(c) 5.00 × 10
20
/m
3
(d) 3.00 × 10
-5
/m
3
 
9. Choose proper substitutes for X and Y to make the following statement correct
Tunnel diode and Avalanche photodiode are operated in X bias and Y bias
respectively.
(a) X: reverse, Y: reverse (b) X: reverse, Y: forward 
(c) X: forward, Y: reverse (d) X: forward, Y: forward 
10. For an n-channel enhancement type MOSFET, if the source is connected at a 
higher potential than that of the bulk (i.e. V
SB
 > 0), the threshold voltage V
T
 of 
the MOSFET will 
(a) remain unchanged (b) decrease 
(c) change polarity (d) increase 
11. Choose the correct match for input resistance of various amplifier configurations
shown below.
Configuration Input resistance 
CB: Common Base LO: Low 
CC: Common Collector MO: Moderate 
CE: Common Emitter HI: High 
(a) CB-LO, CC-MO, CE-HI  (b) CB-LO, CC-HI, CE-MO 
(c) CB-MO, CC-HI, CE-LO  (d) CB-HI, CC-LO, CE-MO 
12. The circuit shown in figure is best described as a
(a) bridge rectifier
(b) ring modulator
(c) frequency discriminatory
(d) voltage doubler
output 
~ 
Page 3


GATE EC - 2003
R 
R 
R 
R ~ 
C C 
C 
2O
+
-
i(t) 
sin t 
2H 
1F 
Q.1 – Q.30 Carry One Mark Each 
1. The minimum number of equations required to analyze the circuit shown in
Fig.Q.1 is
(a) 3 (b) 4 (c) 6 (d) 7 
2. A source of angular frequency 1 rad/sec has a source impedance consisting of 1O
resistance in series with 1 H inductance. The load that will obtain the maximum
power transfer is
(a) 1 O resistance
(b) 1 O resistance in parallel with 1 H inductance
(c) 1 O resistance in series with 1 F capacitor
(d) 1 O resistance in parallel with 1 F capacitor
3. A series RLC circuit has a resonance frequency of 1 kHz and a quality factor Q =
100. If each R, L and C is doubled from its original value, the new Q of the circuit
is
(a) 25 (b) 50 (c) 100 (d) 200 
4. The Laplace transform of i(t) is given by ( )
( )
=
+
2
1
I s
s s
As t 
 8 , the value of i(t) tends to 
(a) 0 (b) 1 (c) 2 (d) 8
5. The differential equation for the current i(t) in the circuit of Figure Q.5 is
(a) ( )
2
2
2 2 sin
d i di
i t t
dt
dt
+ + =
(b) ( )
2
2
2 2 cos
d i di
i t t
dt
dt
+ + =
(c) ( )
2
2
2 2 cos
d i di
i t t
dt
dt
+ + =
(d) ( )
2
2
2 2 sin
d i di
i t t
dt
dt
+ + =
GATE EC - 2003
6. n-type silicon is obtained by doping silicon with
(a) Germanium (b) Aluminum (c) Boron (d) Phosphorus 
7. The bandgap of silicon at 300 K is
(a) 1.36 eV (b) 1.10 eV (c) 0.80 eV (d) 0.67 eV 
8. The intrinsic carrier concentration of silicon sample of 300 K is 1.5 ×10
16
/m
3
. If
after doping, the number of majority carriers is 5 × 10
20
/m
3
, the minority carrier
density is
(a) 4.50 × 10
11
/m
3
(b) 3.33 × 10
4
/m
3
 
(c) 5.00 × 10
20
/m
3
(d) 3.00 × 10
-5
/m
3
 
9. Choose proper substitutes for X and Y to make the following statement correct
Tunnel diode and Avalanche photodiode are operated in X bias and Y bias
respectively.
(a) X: reverse, Y: reverse (b) X: reverse, Y: forward 
(c) X: forward, Y: reverse (d) X: forward, Y: forward 
10. For an n-channel enhancement type MOSFET, if the source is connected at a 
higher potential than that of the bulk (i.e. V
SB
 > 0), the threshold voltage V
T
 of 
the MOSFET will 
(a) remain unchanged (b) decrease 
(c) change polarity (d) increase 
11. Choose the correct match for input resistance of various amplifier configurations
shown below.
Configuration Input resistance 
CB: Common Base LO: Low 
CC: Common Collector MO: Moderate 
CE: Common Emitter HI: High 
(a) CB-LO, CC-MO, CE-HI  (b) CB-LO, CC-HI, CE-MO 
(c) CB-MO, CC-HI, CE-LO  (d) CB-HI, CC-LO, CE-MO 
12. The circuit shown in figure is best described as a
(a) bridge rectifier
(b) ring modulator
(c) frequency discriminatory
(d) voltage doubler
output 
~ 
GATE EC - 2003
13. If the input to the ideal comparator shown in figure is a sinusoidal signal of 8V
(peak to peak) without any DC component, then the output of the comparator
has a duty cycle of
(a) 
1
2
(b) 
1
3
(c) 
1
6
(d) 
12
q
14. If the differential voltage gain and the common mode voltage gain of a
differential amplifier are 48 dB and 2 dB respectively, then its common mode
rejection ratio is
(a) 23 dB (b) 25 dB (c) 46 dB (d) 50 dB 
15. Generally, the gain of a transistor amplifier falls at high frequencies due to the
(a) internal capacitances of the device
(b) coupling capacitor at the input
(c) skin effect
(d) coupling capacitor at the output
16. The number of distinct Boolean expression of 4 variables is
(a) 16 (b) 256 (c) 1024 (d) 65536 
17. The minimum number of comparators required to build an 8 it flash ADC is
(a) 8 (b) 63 (c) 255 (d) 256
18. The output of the 74 series of TTL gates is taken from a BJT in
(a) totem pole and common collector configuration
(b) either totem pole or open collector configuration
(c) common base configuration
(d) common collector configuration
19. Without any additional circuitry, an 8:1 MUX can be used to obtain
(a) some but not all Boolean functions of 3 variables
(b) all function of 3 variables but none of 4 variables
(c) all functions of 3 variables and some but not all of 4 variables
(d) all functions of 4 variables
Input 
Output 
V ref =2V 
+ 
- 
Page 4


GATE EC - 2003
R 
R 
R 
R ~ 
C C 
C 
2O
+
-
i(t) 
sin t 
2H 
1F 
Q.1 – Q.30 Carry One Mark Each 
1. The minimum number of equations required to analyze the circuit shown in
Fig.Q.1 is
(a) 3 (b) 4 (c) 6 (d) 7 
2. A source of angular frequency 1 rad/sec has a source impedance consisting of 1O
resistance in series with 1 H inductance. The load that will obtain the maximum
power transfer is
(a) 1 O resistance
(b) 1 O resistance in parallel with 1 H inductance
(c) 1 O resistance in series with 1 F capacitor
(d) 1 O resistance in parallel with 1 F capacitor
3. A series RLC circuit has a resonance frequency of 1 kHz and a quality factor Q =
100. If each R, L and C is doubled from its original value, the new Q of the circuit
is
(a) 25 (b) 50 (c) 100 (d) 200 
4. The Laplace transform of i(t) is given by ( )
( )
=
+
2
1
I s
s s
As t 
 8 , the value of i(t) tends to 
(a) 0 (b) 1 (c) 2 (d) 8
5. The differential equation for the current i(t) in the circuit of Figure Q.5 is
(a) ( )
2
2
2 2 sin
d i di
i t t
dt
dt
+ + =
(b) ( )
2
2
2 2 cos
d i di
i t t
dt
dt
+ + =
(c) ( )
2
2
2 2 cos
d i di
i t t
dt
dt
+ + =
(d) ( )
2
2
2 2 sin
d i di
i t t
dt
dt
+ + =
GATE EC - 2003
6. n-type silicon is obtained by doping silicon with
(a) Germanium (b) Aluminum (c) Boron (d) Phosphorus 
7. The bandgap of silicon at 300 K is
(a) 1.36 eV (b) 1.10 eV (c) 0.80 eV (d) 0.67 eV 
8. The intrinsic carrier concentration of silicon sample of 300 K is 1.5 ×10
16
/m
3
. If
after doping, the number of majority carriers is 5 × 10
20
/m
3
, the minority carrier
density is
(a) 4.50 × 10
11
/m
3
(b) 3.33 × 10
4
/m
3
 
(c) 5.00 × 10
20
/m
3
(d) 3.00 × 10
-5
/m
3
 
9. Choose proper substitutes for X and Y to make the following statement correct
Tunnel diode and Avalanche photodiode are operated in X bias and Y bias
respectively.
(a) X: reverse, Y: reverse (b) X: reverse, Y: forward 
(c) X: forward, Y: reverse (d) X: forward, Y: forward 
10. For an n-channel enhancement type MOSFET, if the source is connected at a 
higher potential than that of the bulk (i.e. V
SB
 > 0), the threshold voltage V
T
 of 
the MOSFET will 
(a) remain unchanged (b) decrease 
(c) change polarity (d) increase 
11. Choose the correct match for input resistance of various amplifier configurations
shown below.
Configuration Input resistance 
CB: Common Base LO: Low 
CC: Common Collector MO: Moderate 
CE: Common Emitter HI: High 
(a) CB-LO, CC-MO, CE-HI  (b) CB-LO, CC-HI, CE-MO 
(c) CB-MO, CC-HI, CE-LO  (d) CB-HI, CC-LO, CE-MO 
12. The circuit shown in figure is best described as a
(a) bridge rectifier
(b) ring modulator
(c) frequency discriminatory
(d) voltage doubler
output 
~ 
GATE EC - 2003
13. If the input to the ideal comparator shown in figure is a sinusoidal signal of 8V
(peak to peak) without any DC component, then the output of the comparator
has a duty cycle of
(a) 
1
2
(b) 
1
3
(c) 
1
6
(d) 
12
q
14. If the differential voltage gain and the common mode voltage gain of a
differential amplifier are 48 dB and 2 dB respectively, then its common mode
rejection ratio is
(a) 23 dB (b) 25 dB (c) 46 dB (d) 50 dB 
15. Generally, the gain of a transistor amplifier falls at high frequencies due to the
(a) internal capacitances of the device
(b) coupling capacitor at the input
(c) skin effect
(d) coupling capacitor at the output
16. The number of distinct Boolean expression of 4 variables is
(a) 16 (b) 256 (c) 1024 (d) 65536 
17. The minimum number of comparators required to build an 8 it flash ADC is
(a) 8 (b) 63 (c) 255 (d) 256
18. The output of the 74 series of TTL gates is taken from a BJT in
(a) totem pole and common collector configuration
(b) either totem pole or open collector configuration
(c) common base configuration
(d) common collector configuration
19. Without any additional circuitry, an 8:1 MUX can be used to obtain
(a) some but not all Boolean functions of 3 variables
(b) all function of 3 variables but none of 4 variables
(c) all functions of 3 variables and some but not all of 4 variables
(d) all functions of 4 variables
Input 
Output 
V ref =2V 
+ 
- 
GATE EC - 2003
20. A 0 to 6 counter consists of 3 flip flops and a combination circuit of 2 input 
gate(s). The combination circuit consists of 
(a) one AND gate   (b) one OR gate 
(c) one AND gate and one OR gate (d) two AND gates 
21. The Fourier series expansion of a real periodic signal with fundamental frequency
f
0 
is given by ( )
2
o
j nf t
p n
n
g t c e
p
8
=-8
=
?
it is given that C
3
 = 3 + j5. Then C
-3 
is 
(a) 5+j3 (b) -3-j5 (c) -5+j3 (d) 3-j5 
22. Let x(t) be the input to a linear, time-invariant system. The required output is
4x(t-2). The transfer function of the system should be
(a) 4
4 j f
e
p
 (b) 2
8 j f
e
p -
 (c) 4
4 j f
e
p -
 (d) 2
8 j f
e
p
23. A sequence x(n) with the z-transform X(z) =
4 2 4
2 2 3 z z z z
-
+ - + - is applied as 
an input to a linear, time-invariant system with the impulse response h(n) = 
2d(n-3) where 
( )
1, 0
0, otherwise
n
n d
= ?
=
?
?
The output at n  = 4 is 
(a) -6 (b) zero (c) 2 (d) -4 
24. Figure shows the Nyquist plot of the open-loop transfer function G(s)H(s) of a
system. If G(s)H(s) has one right hand pole, the closed loop system is
(a) always stable 
(b) unstable with one closed loop right hand pole 
(c) unstable with two closed loop right hand poles 
(d) unstable with three closed loop right hand poles 
Im 
GH-plane 
?=0 
? positive 
(-1,0) 
Re 
Page 5


GATE EC - 2003
R 
R 
R 
R ~ 
C C 
C 
2O
+
-
i(t) 
sin t 
2H 
1F 
Q.1 – Q.30 Carry One Mark Each 
1. The minimum number of equations required to analyze the circuit shown in
Fig.Q.1 is
(a) 3 (b) 4 (c) 6 (d) 7 
2. A source of angular frequency 1 rad/sec has a source impedance consisting of 1O
resistance in series with 1 H inductance. The load that will obtain the maximum
power transfer is
(a) 1 O resistance
(b) 1 O resistance in parallel with 1 H inductance
(c) 1 O resistance in series with 1 F capacitor
(d) 1 O resistance in parallel with 1 F capacitor
3. A series RLC circuit has a resonance frequency of 1 kHz and a quality factor Q =
100. If each R, L and C is doubled from its original value, the new Q of the circuit
is
(a) 25 (b) 50 (c) 100 (d) 200 
4. The Laplace transform of i(t) is given by ( )
( )
=
+
2
1
I s
s s
As t 
 8 , the value of i(t) tends to 
(a) 0 (b) 1 (c) 2 (d) 8
5. The differential equation for the current i(t) in the circuit of Figure Q.5 is
(a) ( )
2
2
2 2 sin
d i di
i t t
dt
dt
+ + =
(b) ( )
2
2
2 2 cos
d i di
i t t
dt
dt
+ + =
(c) ( )
2
2
2 2 cos
d i di
i t t
dt
dt
+ + =
(d) ( )
2
2
2 2 sin
d i di
i t t
dt
dt
+ + =
GATE EC - 2003
6. n-type silicon is obtained by doping silicon with
(a) Germanium (b) Aluminum (c) Boron (d) Phosphorus 
7. The bandgap of silicon at 300 K is
(a) 1.36 eV (b) 1.10 eV (c) 0.80 eV (d) 0.67 eV 
8. The intrinsic carrier concentration of silicon sample of 300 K is 1.5 ×10
16
/m
3
. If
after doping, the number of majority carriers is 5 × 10
20
/m
3
, the minority carrier
density is
(a) 4.50 × 10
11
/m
3
(b) 3.33 × 10
4
/m
3
 
(c) 5.00 × 10
20
/m
3
(d) 3.00 × 10
-5
/m
3
 
9. Choose proper substitutes for X and Y to make the following statement correct
Tunnel diode and Avalanche photodiode are operated in X bias and Y bias
respectively.
(a) X: reverse, Y: reverse (b) X: reverse, Y: forward 
(c) X: forward, Y: reverse (d) X: forward, Y: forward 
10. For an n-channel enhancement type MOSFET, if the source is connected at a 
higher potential than that of the bulk (i.e. V
SB
 > 0), the threshold voltage V
T
 of 
the MOSFET will 
(a) remain unchanged (b) decrease 
(c) change polarity (d) increase 
11. Choose the correct match for input resistance of various amplifier configurations
shown below.
Configuration Input resistance 
CB: Common Base LO: Low 
CC: Common Collector MO: Moderate 
CE: Common Emitter HI: High 
(a) CB-LO, CC-MO, CE-HI  (b) CB-LO, CC-HI, CE-MO 
(c) CB-MO, CC-HI, CE-LO  (d) CB-HI, CC-LO, CE-MO 
12. The circuit shown in figure is best described as a
(a) bridge rectifier
(b) ring modulator
(c) frequency discriminatory
(d) voltage doubler
output 
~ 
GATE EC - 2003
13. If the input to the ideal comparator shown in figure is a sinusoidal signal of 8V
(peak to peak) without any DC component, then the output of the comparator
has a duty cycle of
(a) 
1
2
(b) 
1
3
(c) 
1
6
(d) 
12
q
14. If the differential voltage gain and the common mode voltage gain of a
differential amplifier are 48 dB and 2 dB respectively, then its common mode
rejection ratio is
(a) 23 dB (b) 25 dB (c) 46 dB (d) 50 dB 
15. Generally, the gain of a transistor amplifier falls at high frequencies due to the
(a) internal capacitances of the device
(b) coupling capacitor at the input
(c) skin effect
(d) coupling capacitor at the output
16. The number of distinct Boolean expression of 4 variables is
(a) 16 (b) 256 (c) 1024 (d) 65536 
17. The minimum number of comparators required to build an 8 it flash ADC is
(a) 8 (b) 63 (c) 255 (d) 256
18. The output of the 74 series of TTL gates is taken from a BJT in
(a) totem pole and common collector configuration
(b) either totem pole or open collector configuration
(c) common base configuration
(d) common collector configuration
19. Without any additional circuitry, an 8:1 MUX can be used to obtain
(a) some but not all Boolean functions of 3 variables
(b) all function of 3 variables but none of 4 variables
(c) all functions of 3 variables and some but not all of 4 variables
(d) all functions of 4 variables
Input 
Output 
V ref =2V 
+ 
- 
GATE EC - 2003
20. A 0 to 6 counter consists of 3 flip flops and a combination circuit of 2 input 
gate(s). The combination circuit consists of 
(a) one AND gate   (b) one OR gate 
(c) one AND gate and one OR gate (d) two AND gates 
21. The Fourier series expansion of a real periodic signal with fundamental frequency
f
0 
is given by ( )
2
o
j nf t
p n
n
g t c e
p
8
=-8
=
?
it is given that C
3
 = 3 + j5. Then C
-3 
is 
(a) 5+j3 (b) -3-j5 (c) -5+j3 (d) 3-j5 
22. Let x(t) be the input to a linear, time-invariant system. The required output is
4x(t-2). The transfer function of the system should be
(a) 4
4 j f
e
p
 (b) 2
8 j f
e
p -
 (c) 4
4 j f
e
p -
 (d) 2
8 j f
e
p
23. A sequence x(n) with the z-transform X(z) =
4 2 4
2 2 3 z z z z
-
+ - + - is applied as 
an input to a linear, time-invariant system with the impulse response h(n) = 
2d(n-3) where 
( )
1, 0
0, otherwise
n
n d
= ?
=
?
?
The output at n  = 4 is 
(a) -6 (b) zero (c) 2 (d) -4 
24. Figure shows the Nyquist plot of the open-loop transfer function G(s)H(s) of a
system. If G(s)H(s) has one right hand pole, the closed loop system is
(a) always stable 
(b) unstable with one closed loop right hand pole 
(c) unstable with two closed loop right hand poles 
(d) unstable with three closed loop right hand poles 
Im 
GH-plane 
?=0 
? positive 
(-1,0) 
Re 
GATE EC - 2003
25. A PD controller is used to compensate a system. Compared to the
uncompensated system, the compensated system has
(a) a higher type number  (b) reduced damping
(c) higher noise amplification (d) larger transient overshoot
26. The input to a coherent detector is DSB-SC signal plus noise. The noise at the
detector output is
(a) the in-phase component (b) the quadrature-component
(c) zero   (d) the envelope
27. The noise at the input to an ideal frequency detector is white. The detector is
operating above threshold. The power spectral density of the noise at the output
is
(a) raised cosine (b) flat (c) parabolic (d) Gaussian 
28. At a given probability of error, binary coherent FSK is inferior to binary coherent
PSK by
(a) 6 dB (b) 3 dB (c) 2 dB (d) 0 dB
29. The unit of ? × H is
(a) Ampere (b) Ampere/meter 
(c) Ampere/meter
2
(d) Ampere-meter 
30. The depth of penetration of electromagnetic wave in a medium having 
conductivity s at a frequency of 1 MHz is 25 cm. The depth of penetration at a 
frequency of 4 MHz will be 
(a) 6.25 cm (b) 12.50 cm (c) 50.00 cm (d) 100.00 cm 
Q.31 – Q.90 Carry Two Marks Each 
31. Twelve 1O resistances are used as edges to form a cube. The resistance between
two diagonally opposite corners of the cube is
(a) 
5
6
O (b) 
1
6
O (c) 
6
5
O (d) 
3
2
O
32. The current flowing through the resistance R in the circuit in figure has the form
P cos 4t, where P is 
(a) (0.18+j0.72) 
(b) (0.46+j1.90) 
(c) -(0.18+j1.90) 
(d) -(0.192+j0.144)
R=3.92O
V=2cos4t 
M=0.75H 
1/10.24F 
3O 
~