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+