Electronics and Communication Engineering (EC) 2005 GATE Paper without solution

# Electronics and Communication Engineering (EC) 2005 GATE Paper without solution PDF Download

``` Page 1

GATE EC - 2005

1
x(t)
-1
0
t
Q.1 – Q.30 carry one mark each
1. The following differential equation has
3
2
2
2
3 4 2
d y dy
y x
dt
dt
? ?
+ + + =
? ?
? ?
(a) degree=2, order=1 (b) degree=3, order=2
(c) degree=4, order=3 (d) degree=2, order=3
2. Choose the function ( ); 1 , f t -8 < < +8 for which a Fourier series cannot be
defined.
(a) 3sin(25t) (b) 4cos(20t+3)+2sin(10t)
(c) exp
( )
t - sin(25t) (d) 1
3. A fair dice is rolled twice. The probability that an odd number will follow an even
number is
(a)
1
2
(b)
1
6
(c)
1
3
(d)
1
4
4. A solution of the following differential equation is given by
2
2
5 6 0
d y dy
y
dx
dx
- + =
(a)
2 3 x x
y e e
-
= + (b)
2 3 x x
y e e = +
(c)
2 3 x x
y e e
-
= + (d)
2 3 x x
y e e
- -
= +
5. The function x(t) is shown in figure. Even and odd parts of a unit-step function
u(t) are respectively.
(a) ( )
1 1
,
2 2
x t (b) ( )
1 1
,
2 2
x t - (c) ( )
1 1
,
2 2
x t - (d) ( )
1 1
,
2 2
x t - -
Page 2

GATE EC - 2005

1
x(t)
-1
0
t
Q.1 – Q.30 carry one mark each
1. The following differential equation has
3
2
2
2
3 4 2
d y dy
y x
dt
dt
? ?
+ + + =
? ?
? ?
(a) degree=2, order=1 (b) degree=3, order=2
(c) degree=4, order=3 (d) degree=2, order=3
2. Choose the function ( ); 1 , f t -8 < < +8 for which a Fourier series cannot be
defined.
(a) 3sin(25t) (b) 4cos(20t+3)+2sin(10t)
(c) exp
( )
t - sin(25t) (d) 1
3. A fair dice is rolled twice. The probability that an odd number will follow an even
number is
(a)
1
2
(b)
1
6
(c)
1
3
(d)
1
4
4. A solution of the following differential equation is given by
2
2
5 6 0
d y dy
y
dx
dx
- + =
(a)
2 3 x x
y e e
-
= + (b)
2 3 x x
y e e = +
(c)
2 3 x x
y e e
-
= + (d)
2 3 x x
y e e
- -
= +
5. The function x(t) is shown in figure. Even and odd parts of a unit-step function
u(t) are respectively.
(a) ( )
1 1
,
2 2
x t (b) ( )
1 1
,
2 2
x t - (c) ( )
1 1
,
2 2
x t - (d) ( )
1 1
,
2 2
x t - -
GATE EC - 2005

L
R
+
-
u(t)
C y(t)
6. The region of convergence of Z-transform of the sequence
( ) ( )
5 6
1
6 5
n n
u n u n
? ? ? ?
- - -
? ? ? ?
? ? ? ?
must be
(a)
5
6
z < (b)
6
5
z > (c)
5 6
6 5
z < < (d)
6
5
z < < 8
7. The condition on R, L and C such that the step response y(t) in figure has no
oscillations, is
(a)
1
2
L
R
C
= (b)
L
R
C
= (c) 2
L
R
C
= (d)
1
R
LC
=
8. The ABCD parameters of an ideal n:1 transformer shown in figure are
0
.
0
n
X
? ?
? ?
? ?
The value of X will be
(a) n (b)
1
n
(c) n
2
(d)
2
1
n
9. In a series RLC circuit R = 2kO, L=1H, and C =
1
.
400
F µ The resonant frequency
is
(a)
4
2 10 Hz × (b)
4
1
10 Hz
p
× (c)
4
10 Hz (d)
4
2 10 Hz p ×
I 1 I 2
V 2 V 1
n:1
Page 3

GATE EC - 2005

1
x(t)
-1
0
t
Q.1 – Q.30 carry one mark each
1. The following differential equation has
3
2
2
2
3 4 2
d y dy
y x
dt
dt
? ?
+ + + =
? ?
? ?
(a) degree=2, order=1 (b) degree=3, order=2
(c) degree=4, order=3 (d) degree=2, order=3
2. Choose the function ( ); 1 , f t -8 < < +8 for which a Fourier series cannot be
defined.
(a) 3sin(25t) (b) 4cos(20t+3)+2sin(10t)
(c) exp
( )
t - sin(25t) (d) 1
3. A fair dice is rolled twice. The probability that an odd number will follow an even
number is
(a)
1
2
(b)
1
6
(c)
1
3
(d)
1
4
4. A solution of the following differential equation is given by
2
2
5 6 0
d y dy
y
dx
dx
- + =
(a)
2 3 x x
y e e
-
= + (b)
2 3 x x
y e e = +
(c)
2 3 x x
y e e
-
= + (d)
2 3 x x
y e e
- -
= +
5. The function x(t) is shown in figure. Even and odd parts of a unit-step function
u(t) are respectively.
(a) ( )
1 1
,
2 2
x t (b) ( )
1 1
,
2 2
x t - (c) ( )
1 1
,
2 2
x t - (d) ( )
1 1
,
2 2
x t - -
GATE EC - 2005

L
R
+
-
u(t)
C y(t)
6. The region of convergence of Z-transform of the sequence
( ) ( )
5 6
1
6 5
n n
u n u n
? ? ? ?
- - -
? ? ? ?
? ? ? ?
must be
(a)
5
6
z < (b)
6
5
z > (c)
5 6
6 5
z < < (d)
6
5
z < < 8
7. The condition on R, L and C such that the step response y(t) in figure has no
oscillations, is
(a)
1
2
L
R
C
= (b)
L
R
C
= (c) 2
L
R
C
= (d)
1
R
LC
=
8. The ABCD parameters of an ideal n:1 transformer shown in figure are
0
.
0
n
X
? ?
? ?
? ?
The value of X will be
(a) n (b)
1
n
(c) n
2
(d)
2
1
n
9. In a series RLC circuit R = 2kO, L=1H, and C =
1
.
400
F µ The resonant frequency
is
(a)
4
2 10 Hz × (b)
4
1
10 Hz
p
× (c)
4
10 Hz (d)
4
2 10 Hz p ×
I 1 I 2
V 2 V 1
n:1
GATE EC - 2005

10. The maximum power that can be transferred to the load resistor
L
R from the
voltage source in figure is
(a) 1 W (b) 10 W (c) 0.25 W (d) 0.5 W
11. The band gap of Silicon at room temperature is:
(a) 1.3 eV (b) 0.7 eV (c) 1.1 eV (d) 1.4 eV
12. A Silicon PN junction at a temperature of 20°C has a reverse saturation current of
10 pico-Amperes (pA). The reverse saturation current at 40°C for the same bias
is approximately
(a) 30 pA (b) 40 pA (c) 50 pA (d) 60 pA
13. The primary reason for the widespread use of Silicon in semiconductor device
technology is
(a) abundance of Silicon on the surface of the Earth.
(b) larger bandgap of Silicon in comparison to Germanium.
(c) favorable properties of Silicon-dioxide (SiO
2
)
(d) lower melting point
14. The effect of current shunt feedback in an amplifier is to
(a) increase the input resistance and decrease the output resistance.
(b) increase both input and output resistances.
(c) decreases both input and output resistances.
(d) decrease the input resistance and increase the output resistance.
+
-
100O
R L
10V
Page 4

GATE EC - 2005

1
x(t)
-1
0
t
Q.1 – Q.30 carry one mark each
1. The following differential equation has
3
2
2
2
3 4 2
d y dy
y x
dt
dt
? ?
+ + + =
? ?
? ?
(a) degree=2, order=1 (b) degree=3, order=2
(c) degree=4, order=3 (d) degree=2, order=3
2. Choose the function ( ); 1 , f t -8 < < +8 for which a Fourier series cannot be
defined.
(a) 3sin(25t) (b) 4cos(20t+3)+2sin(10t)
(c) exp
( )
t - sin(25t) (d) 1
3. A fair dice is rolled twice. The probability that an odd number will follow an even
number is
(a)
1
2
(b)
1
6
(c)
1
3
(d)
1
4
4. A solution of the following differential equation is given by
2
2
5 6 0
d y dy
y
dx
dx
- + =
(a)
2 3 x x
y e e
-
= + (b)
2 3 x x
y e e = +
(c)
2 3 x x
y e e
-
= + (d)
2 3 x x
y e e
- -
= +
5. The function x(t) is shown in figure. Even and odd parts of a unit-step function
u(t) are respectively.
(a) ( )
1 1
,
2 2
x t (b) ( )
1 1
,
2 2
x t - (c) ( )
1 1
,
2 2
x t - (d) ( )
1 1
,
2 2
x t - -
GATE EC - 2005

L
R
+
-
u(t)
C y(t)
6. The region of convergence of Z-transform of the sequence
( ) ( )
5 6
1
6 5
n n
u n u n
? ? ? ?
- - -
? ? ? ?
? ? ? ?
must be
(a)
5
6
z < (b)
6
5
z > (c)
5 6
6 5
z < < (d)
6
5
z < < 8
7. The condition on R, L and C such that the step response y(t) in figure has no
oscillations, is
(a)
1
2
L
R
C
= (b)
L
R
C
= (c) 2
L
R
C
= (d)
1
R
LC
=
8. The ABCD parameters of an ideal n:1 transformer shown in figure are
0
.
0
n
X
? ?
? ?
? ?
The value of X will be
(a) n (b)
1
n
(c) n
2
(d)
2
1
n
9. In a series RLC circuit R = 2kO, L=1H, and C =
1
.
400
F µ The resonant frequency
is
(a)
4
2 10 Hz × (b)
4
1
10 Hz
p
× (c)
4
10 Hz (d)
4
2 10 Hz p ×
I 1 I 2
V 2 V 1
n:1
GATE EC - 2005

10. The maximum power that can be transferred to the load resistor
L
R from the
voltage source in figure is
(a) 1 W (b) 10 W (c) 0.25 W (d) 0.5 W
11. The band gap of Silicon at room temperature is:
(a) 1.3 eV (b) 0.7 eV (c) 1.1 eV (d) 1.4 eV
12. A Silicon PN junction at a temperature of 20°C has a reverse saturation current of
10 pico-Amperes (pA). The reverse saturation current at 40°C for the same bias
is approximately
(a) 30 pA (b) 40 pA (c) 50 pA (d) 60 pA
13. The primary reason for the widespread use of Silicon in semiconductor device
technology is
(a) abundance of Silicon on the surface of the Earth.
(b) larger bandgap of Silicon in comparison to Germanium.
(c) favorable properties of Silicon-dioxide (SiO
2
)
(d) lower melting point
14. The effect of current shunt feedback in an amplifier is to
(a) increase the input resistance and decrease the output resistance.
(b) increase both input and output resistances.
(c) decreases both input and output resistances.
(d) decrease the input resistance and increase the output resistance.
+
-
100O
R L
10V
GATE EC - 2005

0 0
1 1
f
C
B
A
E
C
15. The input resistance
i
R of the amplifier shown in figure is
(a)
30
4
kO (b) 10kO (c) 40 kO (d) infinite
16. The first and the last critical frequency of an RC-driving point impedance function
must respectively be
(a) a zero and a pole   (b) a zero and a zero
(c) a pole and a pole   (d) a pole and a zero
17. The cascode amplifier is a multistage configuration of
(a) CC-CB (b) CE-CB (c) CB-CC (d) CE-CC
18. Decimal 43 in Hexadecimal and BCD number system is respectively
(a) B2, 0100 0011   (b) 2B, 0100 0011
(c) 2B, 0011 0100   (d) B2, 0100 0100
19. The Boolean function f implemented in figure using two input multiplexers is
(a) ABC ABC + (b)  C ABC AB + (c)   C ABC A B + (d)  A BC ABC +
~
R i
10K
30K
+
-
ideal operational amplifier
Page 5

GATE EC - 2005

1
x(t)
-1
0
t
Q.1 – Q.30 carry one mark each
1. The following differential equation has
3
2
2
2
3 4 2
d y dy
y x
dt
dt
? ?
+ + + =
? ?
? ?
(a) degree=2, order=1 (b) degree=3, order=2
(c) degree=4, order=3 (d) degree=2, order=3
2. Choose the function ( ); 1 , f t -8 < < +8 for which a Fourier series cannot be
defined.
(a) 3sin(25t) (b) 4cos(20t+3)+2sin(10t)
(c) exp
( )
t - sin(25t) (d) 1
3. A fair dice is rolled twice. The probability that an odd number will follow an even
number is
(a)
1
2
(b)
1
6
(c)
1
3
(d)
1
4
4. A solution of the following differential equation is given by
2
2
5 6 0
d y dy
y
dx
dx
- + =
(a)
2 3 x x
y e e
-
= + (b)
2 3 x x
y e e = +
(c)
2 3 x x
y e e
-
= + (d)
2 3 x x
y e e
- -
= +
5. The function x(t) is shown in figure. Even and odd parts of a unit-step function
u(t) are respectively.
(a) ( )
1 1
,
2 2
x t (b) ( )
1 1
,
2 2
x t - (c) ( )
1 1
,
2 2
x t - (d) ( )
1 1
,
2 2
x t - -
GATE EC - 2005

L
R
+
-
u(t)
C y(t)
6. The region of convergence of Z-transform of the sequence
( ) ( )
5 6
1
6 5
n n
u n u n
? ? ? ?
- - -
? ? ? ?
? ? ? ?
must be
(a)
5
6
z < (b)
6
5
z > (c)
5 6
6 5
z < < (d)
6
5
z < < 8
7. The condition on R, L and C such that the step response y(t) in figure has no
oscillations, is
(a)
1
2
L
R
C
= (b)
L
R
C
= (c) 2
L
R
C
= (d)
1
R
LC
=
8. The ABCD parameters of an ideal n:1 transformer shown in figure are
0
.
0
n
X
? ?
? ?
? ?
The value of X will be
(a) n (b)
1
n
(c) n
2
(d)
2
1
n
9. In a series RLC circuit R = 2kO, L=1H, and C =
1
.
400
F µ The resonant frequency
is
(a)
4
2 10 Hz × (b)
4
1
10 Hz
p
× (c)
4
10 Hz (d)
4
2 10 Hz p ×
I 1 I 2
V 2 V 1
n:1
GATE EC - 2005

10. The maximum power that can be transferred to the load resistor
L
R from the
voltage source in figure is
(a) 1 W (b) 10 W (c) 0.25 W (d) 0.5 W
11. The band gap of Silicon at room temperature is:
(a) 1.3 eV (b) 0.7 eV (c) 1.1 eV (d) 1.4 eV
12. A Silicon PN junction at a temperature of 20°C has a reverse saturation current of
10 pico-Amperes (pA). The reverse saturation current at 40°C for the same bias
is approximately
(a) 30 pA (b) 40 pA (c) 50 pA (d) 60 pA
13. The primary reason for the widespread use of Silicon in semiconductor device
technology is
(a) abundance of Silicon on the surface of the Earth.
(b) larger bandgap of Silicon in comparison to Germanium.
(c) favorable properties of Silicon-dioxide (SiO
2
)
(d) lower melting point
14. The effect of current shunt feedback in an amplifier is to
(a) increase the input resistance and decrease the output resistance.
(b) increase both input and output resistances.
(c) decreases both input and output resistances.
(d) decrease the input resistance and increase the output resistance.
+
-
100O
R L
10V
GATE EC - 2005

0 0
1 1
f
C
B
A
E
C
15. The input resistance
i
R of the amplifier shown in figure is
(a)
30
4
kO (b) 10kO (c) 40 kO (d) infinite
16. The first and the last critical frequency of an RC-driving point impedance function
must respectively be
(a) a zero and a pole   (b) a zero and a zero
(c) a pole and a pole   (d) a pole and a zero
17. The cascode amplifier is a multistage configuration of
(a) CC-CB (b) CE-CB (c) CB-CC (d) CE-CC
18. Decimal 43 in Hexadecimal and BCD number system is respectively
(a) B2, 0100 0011   (b) 2B, 0100 0011
(c) 2B, 0011 0100   (d) B2, 0100 0100
19. The Boolean function f implemented in figure using two input multiplexers is
(a) ABC ABC + (b)  C ABC AB + (c)   C ABC A B + (d)  A BC ABC +
~
R i
10K
30K
+
-
ideal operational amplifier
GATE EC - 2005

20. Which of the following can be impulse response of a causal system?
(a) (b)
(c) (d)
21. Let
( ) ( ) ( ) ( )
( )
( )
( )
2
0
1
, ,
2
and  be the Fourier transform of . Then  is
n
j j
x n u n y n x n
Y e y n Y e
?
? ?
= =
? ?
? ?
(a)
1
4
(b) 2 (c) 4 (d)
4
3
22. Find the correct match between group 1 and group 2.
Group 1 Group 2
P - ( ) { } ( ) 1 sin
c
km t A t ? +
W – Phase modulation
Q - ( ) ( ) sin
c
km t A t ? X – Frequency modulation
R - ( ) { }
sin
c
A t km t ? +
Y – Amplitude modulation
S - ( ) sin
t
c
A t k m d ? t t
-8
? ?
? ?
+
? ?
? ?
?

Z – DSB-SC modulation
(a) P -  Z  Q  - Y   R – X   S - W (b) P – W  Q – X   R – Y   S - Z
(c) P - X   Q – W  R – Z   S - Y (d) P – Y   Q – Z   R – W  S - X
t
h(t)
t
h(t)
t
h(t)
t
h(t)
```

## FAQs on Electronics and Communication Engineering (EC) 2005 GATE Paper without solution

 1. What is Electronics and Communication Engineering (EC)?
Ans. Electronics and Communication Engineering (EC) is a field of engineering that focuses on the design, development, testing, and maintenance of electronic devices, systems, and communication networks. It deals with the study of electronic circuits, microprocessors, communication systems, signal processing, and electromagnetic fields.
 2. What are the career prospects for Electronics and Communication Engineering graduates?
Ans. Electronics and Communication Engineering graduates have a wide range of career opportunities in various industries such as telecommunications, electronics manufacturing, IT, research and development, aerospace, defense, and government organizations. They can work as design engineers, communication specialists, network administrators, system analysts, research scientists, and consultants.
 3. What topics are covered in the GATE exam for Electronics and Communication Engineering?
Ans. The GATE exam for Electronics and Communication Engineering covers a wide range of topics including electronic devices and circuits, analog and digital electronics, signals and systems, control systems, communication systems, electromagnetic fields, network theory, digital signal processing, and microprocessors. It also includes general aptitude and engineering mathematics.
 4. How can I prepare for the GATE exam in Electronics and Communication Engineering?
Ans. To prepare for the GATE exam in Electronics and Communication Engineering, it is important to have a thorough understanding of the core subjects and practice solving previous year question papers and mock tests. It is also beneficial to refer to standard textbooks, join coaching classes or online courses, and revise important concepts regularly. Time management, regular practice, and staying updated with the latest syllabus are key to success.
 5. What is the eligibility criteria for appearing in the GATE exam for Electronics and Communication Engineering?
Ans. The eligibility criteria for appearing in the GATE exam for Electronics and Communication Engineering require the candidate to have completed a bachelor's degree in Engineering/Technology or a master's degree in any relevant science subject. There is no age limit, and candidates from both Indian and international backgrounds can apply.
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