Electronics and Communication Engineering (EC) 2006 GATE Paper without solution

# Electronics and Communication Engineering (EC) 2006 GATE Paper without solution PDF Download

``` Page 1

GATE EC - 2006

Q.1 – Q.20 Carry One Mark Each.
1. The rank of the matrix
1 1 1
1 1 0
1 1 1
? ?
? ?
-
? ?
? ?
? ?
is:
(A) 0
(B) 1
(C) 2
(D) 3
2. , where P P ?×?× is a vector, is equal to
(A)
2
P P P ×?× -?
(B) ( )
2
P P ? +? ?•
(C)
2
P P ? +?×
(D) ( )
2
P P ? ?• -?
3. ( ) , P ds ?× •
??
where P is a vector, is equal to
(A) P dl •
? 
(B) P dl ?×?× •
? 
(C) P dl ?× •
? 
(D) Pd? ?•
???
4. A probability density function is of the form
( ) ( ) , , .
x
p x Ke x
a -
= ? -8 8
The value of K is
(A) 0.5
(B) 1
(C) 0.5a
(D) a
5. A solution for the differential equation
( ) ( ) ( ) 2 x t x t t d + =
&
with initial condition ( ) 0 0 x - = is:
Page 2

GATE EC - 2006

Q.1 – Q.20 Carry One Mark Each.
1. The rank of the matrix
1 1 1
1 1 0
1 1 1
? ?
? ?
-
? ?
? ?
? ?
is:
(A) 0
(B) 1
(C) 2
(D) 3
2. , where P P ?×?× is a vector, is equal to
(A)
2
P P P ×?× -?
(B) ( )
2
P P ? +? ?•
(C)
2
P P ? +?×
(D) ( )
2
P P ? ?• -?
3. ( ) , P ds ?× •
??
where P is a vector, is equal to
(A) P dl •
? 
(B) P dl ?×?× •
? 
(C) P dl ?× •
? 
(D) Pd? ?•
???
4. A probability density function is of the form
( ) ( ) , , .
x
p x Ke x
a -
= ? -8 8
The value of K is
(A) 0.5
(B) 1
(C) 0.5a
(D) a
5. A solution for the differential equation
( ) ( ) ( ) 2 x t x t t d + =
&
with initial condition ( ) 0 0 x - = is:
GATE EC - 2006

(A) ( )
2t
e u t
-
(B) ( )
2t
e u t
(C) ( )
t
e u t
-
(D) ( )
t
e u t
6. A low-pass filter having a frequency response ( ) ( )
( ) j
H j A e
f ?
? ? = does not
produce any phase distortion if
(A) ( ) ( )
2 3
, A C k ? ? f ? ? = =
(B) ( ) ( )
2
, A C k ? ? f ? ? = =
(C) ( ) ( )
2
, A C k ? ? f ? ? = =
(D) ( ) ( )
1
, A C k ? f ? ?
-
= =
7. The values of voltage ( )
D
V across a tunnel-diode corresponding to peak and valley
currents are  and
P V
V V respectively. The range of tunnel-diode voltage
D
V for
which the slope of its
D
I V - characteristics is negative would be
(A) 0
D
V <
(B) 0
D P
V V = <
(C)
P D V
V V V = <
(D)
D V
V V =
8. The concentration of minority carriers in an extrinsic semiconductor under
equilibrium is:
(A) directly proportional to the doping concentration
(B) inversely proportional to the doping concentration
(C) directly proportional to the intrinsic concentration
(D) inversely proportional to the intrinsic concentration
9. Under low level injection assumption, the injected minority carrier current for an
extrinsic semiconductor is essentially the
(A) diffusion current
(B) drift current
(C) recombination current
(D) induced current
Page 3

GATE EC - 2006

Q.1 – Q.20 Carry One Mark Each.
1. The rank of the matrix
1 1 1
1 1 0
1 1 1
? ?
? ?
-
? ?
? ?
? ?
is:
(A) 0
(B) 1
(C) 2
(D) 3
2. , where P P ?×?× is a vector, is equal to
(A)
2
P P P ×?× -?
(B) ( )
2
P P ? +? ?•
(C)
2
P P ? +?×
(D) ( )
2
P P ? ?• -?
3. ( ) , P ds ?× •
??
where P is a vector, is equal to
(A) P dl •
? 
(B) P dl ?×?× •
? 
(C) P dl ?× •
? 
(D) Pd? ?•
???
4. A probability density function is of the form
( ) ( ) , , .
x
p x Ke x
a -
= ? -8 8
The value of K is
(A) 0.5
(B) 1
(C) 0.5a
(D) a
5. A solution for the differential equation
( ) ( ) ( ) 2 x t x t t d + =
&
with initial condition ( ) 0 0 x - = is:
GATE EC - 2006

(A) ( )
2t
e u t
-
(B) ( )
2t
e u t
(C) ( )
t
e u t
-
(D) ( )
t
e u t
6. A low-pass filter having a frequency response ( ) ( )
( ) j
H j A e
f ?
? ? = does not
produce any phase distortion if
(A) ( ) ( )
2 3
, A C k ? ? f ? ? = =
(B) ( ) ( )
2
, A C k ? ? f ? ? = =
(C) ( ) ( )
2
, A C k ? ? f ? ? = =
(D) ( ) ( )
1
, A C k ? f ? ?
-
= =
7. The values of voltage ( )
D
V across a tunnel-diode corresponding to peak and valley
currents are  and
P V
V V respectively. The range of tunnel-diode voltage
D
V for
which the slope of its
D
I V - characteristics is negative would be
(A) 0
D
V <
(B) 0
D P
V V = <
(C)
P D V
V V V = <
(D)
D V
V V =
8. The concentration of minority carriers in an extrinsic semiconductor under
equilibrium is:
(A) directly proportional to the doping concentration
(B) inversely proportional to the doping concentration
(C) directly proportional to the intrinsic concentration
(D) inversely proportional to the intrinsic concentration
9. Under low level injection assumption, the injected minority carrier current for an
extrinsic semiconductor is essentially the
(A) diffusion current
(B) drift current
(C) recombination current
(D) induced current
GATE EC - 2006

10. The phenomenon known as “Early Effect” in a bipolar transistor refers to a
reduction of the effective base-width caused by
(A) electron-hole recombination at the base
(B) the reverse biasing of the base-collector junction
(C) the forward biasing of emitter-base junction
(D) the early removal of stored base charge during saturation-to-cutoff
switching.
11. The input impedance ( )
i
Z and the output impedance ( )
0
Z of an ideal trans-
conductance (voltage controlled current source) amplifier are
(A)
0
0, 0
i
Z Z = =
(B)
0
0,
i
Z Z = = 8
(C)
0
, 0
i
Z Z = 8 =
(D)
0
,
i
Z Z = 8 = 8
12. An n-channel depletion MOSFET has following two points on its
D GS
I V - curve:
(i) 0 at 12
GS D
V I mA = = and
(ii) 6 Volts at 0
GS D
V I = - =
Which of the following Q-points will give the highest trans-conductance gain for
small signals?
(A) 6 Volts
GS
V = -
(B) 3 Volts
GS
V = -
(C) 0 Volts
GS
V =
(D) 3 Volts
GS
V =
13. The number of product terms in the minimized sum-of-product expression
obtained through the following K-map is (where “d” denotes don’t care states)
1 0 0 1
0 d 0 0
0 0 d 1
1 0 0 1
(A) 2
(B) 3
(C) 4
(D) 5
Page 4

GATE EC - 2006

Q.1 – Q.20 Carry One Mark Each.
1. The rank of the matrix
1 1 1
1 1 0
1 1 1
? ?
? ?
-
? ?
? ?
? ?
is:
(A) 0
(B) 1
(C) 2
(D) 3
2. , where P P ?×?× is a vector, is equal to
(A)
2
P P P ×?× -?
(B) ( )
2
P P ? +? ?•
(C)
2
P P ? +?×
(D) ( )
2
P P ? ?• -?
3. ( ) , P ds ?× •
??
where P is a vector, is equal to
(A) P dl •
? 
(B) P dl ?×?× •
? 
(C) P dl ?× •
? 
(D) Pd? ?•
???
4. A probability density function is of the form
( ) ( ) , , .
x
p x Ke x
a -
= ? -8 8
The value of K is
(A) 0.5
(B) 1
(C) 0.5a
(D) a
5. A solution for the differential equation
( ) ( ) ( ) 2 x t x t t d + =
&
with initial condition ( ) 0 0 x - = is:
GATE EC - 2006

(A) ( )
2t
e u t
-
(B) ( )
2t
e u t
(C) ( )
t
e u t
-
(D) ( )
t
e u t
6. A low-pass filter having a frequency response ( ) ( )
( ) j
H j A e
f ?
? ? = does not
produce any phase distortion if
(A) ( ) ( )
2 3
, A C k ? ? f ? ? = =
(B) ( ) ( )
2
, A C k ? ? f ? ? = =
(C) ( ) ( )
2
, A C k ? ? f ? ? = =
(D) ( ) ( )
1
, A C k ? f ? ?
-
= =
7. The values of voltage ( )
D
V across a tunnel-diode corresponding to peak and valley
currents are  and
P V
V V respectively. The range of tunnel-diode voltage
D
V for
which the slope of its
D
I V - characteristics is negative would be
(A) 0
D
V <
(B) 0
D P
V V = <
(C)
P D V
V V V = <
(D)
D V
V V =
8. The concentration of minority carriers in an extrinsic semiconductor under
equilibrium is:
(A) directly proportional to the doping concentration
(B) inversely proportional to the doping concentration
(C) directly proportional to the intrinsic concentration
(D) inversely proportional to the intrinsic concentration
9. Under low level injection assumption, the injected minority carrier current for an
extrinsic semiconductor is essentially the
(A) diffusion current
(B) drift current
(C) recombination current
(D) induced current
GATE EC - 2006

10. The phenomenon known as “Early Effect” in a bipolar transistor refers to a
reduction of the effective base-width caused by
(A) electron-hole recombination at the base
(B) the reverse biasing of the base-collector junction
(C) the forward biasing of emitter-base junction
(D) the early removal of stored base charge during saturation-to-cutoff
switching.
11. The input impedance ( )
i
Z and the output impedance ( )
0
Z of an ideal trans-
conductance (voltage controlled current source) amplifier are
(A)
0
0, 0
i
Z Z = =
(B)
0
0,
i
Z Z = = 8
(C)
0
, 0
i
Z Z = 8 =
(D)
0
,
i
Z Z = 8 = 8
12. An n-channel depletion MOSFET has following two points on its
D GS
I V - curve:
(i) 0 at 12
GS D
V I mA = = and
(ii) 6 Volts at 0
GS D
V I = - =
Which of the following Q-points will give the highest trans-conductance gain for
small signals?
(A) 6 Volts
GS
V = -
(B) 3 Volts
GS
V = -
(C) 0 Volts
GS
V =
(D) 3 Volts
GS
V =
13. The number of product terms in the minimized sum-of-product expression
obtained through the following K-map is (where “d” denotes don’t care states)
1 0 0 1
0 d 0 0
0 0 d 1
1 0 0 1
(A) 2
(B) 3
(C) 4
(D) 5
GATE EC - 2006

14. Let ( ) ( ) x t X j? ? be Fourier Transform pair. The Fourier Transform of the signal
( ) 5 3 x t - in terms of ( ) X j? is given as
(A)
3
5
1
5 5
j
j
e X
?
?
-
? ?
? ?
? ?
(B)
3
5
1
5 5
j
j
e X
?
? ? ?
? ?
? ?
(C)
3
1
5 5
j
j
e X
?
?
-
? ?
? ?
? ?
(D)
3
1
5 5
j
j
e X
?
? ? ?
? ?
? ?

15. The Dirac delta function ( ) t d is defined as
(A) ( )
1 0
0 otherwise
t
t d
= ?
=
?
?
(B) ( )
0
0 otherwise
t
t d
8 = ?
=
?
?
(C) ( ) ( )
1 0
and 1
0 otherwise
t
t t dt d d
8
-8
= ?
= =
?
?
?

(D) ( ) ( )
0
and 1
0 otherwise
t
t t dt d d
8
-8
8 = ?
= =
?
?
?

16. If the region of convergence of
1 2
x n x n + ? ? ? ?
? ? ? ?
is
1 2
,
3 3
z < < then the region of
convergence of
2 n
x n x n - ? ? ? ?
? ? ? ?
includes
(A)
1
3
3
z < <
(B)
2
3
3
z < <
(C)
3
3
2
z < <
(D)
1 2
3 3
z < <
17. The open-loop transfer function of a unity-gain feedback control system is given
by
Page 5

GATE EC - 2006

Q.1 – Q.20 Carry One Mark Each.
1. The rank of the matrix
1 1 1
1 1 0
1 1 1
? ?
? ?
-
? ?
? ?
? ?
is:
(A) 0
(B) 1
(C) 2
(D) 3
2. , where P P ?×?× is a vector, is equal to
(A)
2
P P P ×?× -?
(B) ( )
2
P P ? +? ?•
(C)
2
P P ? +?×
(D) ( )
2
P P ? ?• -?
3. ( ) , P ds ?× •
??
where P is a vector, is equal to
(A) P dl •
? 
(B) P dl ?×?× •
? 
(C) P dl ?× •
? 
(D) Pd? ?•
???
4. A probability density function is of the form
( ) ( ) , , .
x
p x Ke x
a -
= ? -8 8
The value of K is
(A) 0.5
(B) 1
(C) 0.5a
(D) a
5. A solution for the differential equation
( ) ( ) ( ) 2 x t x t t d + =
&
with initial condition ( ) 0 0 x - = is:
GATE EC - 2006

(A) ( )
2t
e u t
-
(B) ( )
2t
e u t
(C) ( )
t
e u t
-
(D) ( )
t
e u t
6. A low-pass filter having a frequency response ( ) ( )
( ) j
H j A e
f ?
? ? = does not
produce any phase distortion if
(A) ( ) ( )
2 3
, A C k ? ? f ? ? = =
(B) ( ) ( )
2
, A C k ? ? f ? ? = =
(C) ( ) ( )
2
, A C k ? ? f ? ? = =
(D) ( ) ( )
1
, A C k ? f ? ?
-
= =
7. The values of voltage ( )
D
V across a tunnel-diode corresponding to peak and valley
currents are  and
P V
V V respectively. The range of tunnel-diode voltage
D
V for
which the slope of its
D
I V - characteristics is negative would be
(A) 0
D
V <
(B) 0
D P
V V = <
(C)
P D V
V V V = <
(D)
D V
V V =
8. The concentration of minority carriers in an extrinsic semiconductor under
equilibrium is:
(A) directly proportional to the doping concentration
(B) inversely proportional to the doping concentration
(C) directly proportional to the intrinsic concentration
(D) inversely proportional to the intrinsic concentration
9. Under low level injection assumption, the injected minority carrier current for an
extrinsic semiconductor is essentially the
(A) diffusion current
(B) drift current
(C) recombination current
(D) induced current
GATE EC - 2006

10. The phenomenon known as “Early Effect” in a bipolar transistor refers to a
reduction of the effective base-width caused by
(A) electron-hole recombination at the base
(B) the reverse biasing of the base-collector junction
(C) the forward biasing of emitter-base junction
(D) the early removal of stored base charge during saturation-to-cutoff
switching.
11. The input impedance ( )
i
Z and the output impedance ( )
0
Z of an ideal trans-
conductance (voltage controlled current source) amplifier are
(A)
0
0, 0
i
Z Z = =
(B)
0
0,
i
Z Z = = 8
(C)
0
, 0
i
Z Z = 8 =
(D)
0
,
i
Z Z = 8 = 8
12. An n-channel depletion MOSFET has following two points on its
D GS
I V - curve:
(i) 0 at 12
GS D
V I mA = = and
(ii) 6 Volts at 0
GS D
V I = - =
Which of the following Q-points will give the highest trans-conductance gain for
small signals?
(A) 6 Volts
GS
V = -
(B) 3 Volts
GS
V = -
(C) 0 Volts
GS
V =
(D) 3 Volts
GS
V =
13. The number of product terms in the minimized sum-of-product expression
obtained through the following K-map is (where “d” denotes don’t care states)
1 0 0 1
0 d 0 0
0 0 d 1
1 0 0 1
(A) 2
(B) 3
(C) 4
(D) 5
GATE EC - 2006

14. Let ( ) ( ) x t X j? ? be Fourier Transform pair. The Fourier Transform of the signal
( ) 5 3 x t - in terms of ( ) X j? is given as
(A)
3
5
1
5 5
j
j
e X
?
?
-
? ?
? ?
? ?
(B)
3
5
1
5 5
j
j
e X
?
? ? ?
? ?
? ?
(C)
3
1
5 5
j
j
e X
?
?
-
? ?
? ?
? ?
(D)
3
1
5 5
j
j
e X
?
? ? ?
? ?
? ?

15. The Dirac delta function ( ) t d is defined as
(A) ( )
1 0
0 otherwise
t
t d
= ?
=
?
?
(B) ( )
0
0 otherwise
t
t d
8 = ?
=
?
?
(C) ( ) ( )
1 0
and 1
0 otherwise
t
t t dt d d
8
-8
= ?
= =
?
?
?

(D) ( ) ( )
0
and 1
0 otherwise
t
t t dt d d
8
-8
8 = ?
= =
?
?
?

16. If the region of convergence of
1 2
x n x n + ? ? ? ?
? ? ? ?
is
1 2
,
3 3
z < < then the region of
convergence of
2 n
x n x n - ? ? ? ?
? ? ? ?
includes
(A)
1
3
3
z < <
(B)
2
3
3
z < <
(C)
3
3
2
z < <
(D)
1 2
3 3
z < <
17. The open-loop transfer function of a unity-gain feedback control system is given
by
GATE EC - 2006

( )
( )( )
.
1 2
K
G s
s s
=
+ +
The gain margin of the system in dB is given by
(A) 0
(B) 1
(C) 20
(D) 8
18. In the system shown below, ( ) ( ) ( ) sin . x t t u t = In steady-sate, the response
( ) y t will be:
(A)
1
sin
4
2
t
p ? ?
-
? ?
? ?

(B)
1
sin
4
2
t
p ? ?
+
? ?
? ?

(C)
1
sin
2
t
e t
-
(D) sin cos t t -
19. The electric field of an electromagnetic wave propagating in the positive z-
direction is given by
\$
( )
\$
sin sin .
2
x y E a t z a t z
p
? ß ? ß
? ?
= - + - +
? ?
? ?

The wave is
(A) linearly polarized in the z-direction
(B) elliptically polarized
(C) left-hand circularly polarized
(D) right-hand circularly polarized
20. A transmission line is feeding 1 Watt of power to a horn antenna having a gain of
10 dB. The antenna is matched to the transmission line. The total power radiated
by the horn antenna into the free-space is:
(A) 10 Watts
( ) x t ( ) y t
1
1 s+
```

## FAQs on Electronics and Communication Engineering (EC) 2006 GATE Paper without solution

 1. What is Electronics and Communication Engineering (EC)?
Ans. Electronics and Communication Engineering (EC) is a branch of engineering that focuses on the design and development of electronic devices, circuits, communication systems, and their integration. It involves studying subjects like analog and digital electronics, signal processing, electromagnetic theory, communication theory, and networking.
 2. What are the career prospects for Electronics and Communication Engineering (EC) graduates?
Ans. Electronics and Communication Engineering (EC) graduates have a wide range of career opportunities. They can work in industries like telecommunications, consumer electronics, aerospace, defense, healthcare, and automation. They can also pursue careers in research and development, design and testing, project management, and software development in various sectors.
 3. How can I prepare for the GATE exam in Electronics and Communication Engineering (EC)?
Ans. To prepare for the GATE exam in Electronics and Communication Engineering (EC), start by understanding the exam pattern and syllabus. Then, create a study plan and allocate time for each subject. Practice solving previous years' question papers and take mock tests to improve your time management and problem-solving skills. It is also beneficial to join coaching classes or online courses for guidance and expert advice.
 4. What are the important topics to focus on in the GATE exam for Electronics and Communication Engineering (EC)?
Ans. Some important topics to focus on in the GATE exam for Electronics and Communication Engineering (EC) include electronic devices and circuits, digital electronics, signals and systems, network theory, control systems, electromagnetic theory, communications, and analog and digital communication systems. It is essential to have a strong understanding of these topics and solve numerical problems related to them.
 5. Are there any recommended books or study materials for the GATE exam in Electronics and Communication Engineering (EC)?
Ans. Yes, there are several recommended books and study materials for the GATE exam in Electronics and Communication Engineering (EC). Some popular ones include "GATE Electronics and Communication Engineering" by RK Kanodia, "GATE Guide Electronics & Communication Engg." by GKP, "Electronic Devices and Circuit Theory" by Robert L. Boylestad and Louis Nashelsky, and "Communication Systems" by Simon Haykin. It is also important to refer to the GATE syllabus and study materials provided by reputed coaching institutes or online platforms.
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