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 lowpass 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 tunneldiode corresponding to peak and valley
currents are and
P V
V V respectively. The range of tunneldiode 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 lowpass 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 tunneldiode corresponding to peak and valley
currents are and
P V
V V respectively. The range of tunneldiode 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 basewidth caused by
(A) electronhole recombination at the base
(B) the reverse biasing of the basecollector junction
(C) the forward biasing of emitterbase junction
(D) the early removal of stored base charge during saturationtocutoff
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 nchannel 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 Qpoints will give the highest transconductance 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 sumofproduct expression
obtained through the following Kmap 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 lowpass 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 tunneldiode corresponding to peak and valley
currents are and
P V
V V respectively. The range of tunneldiode 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 basewidth caused by
(A) electronhole recombination at the base
(B) the reverse biasing of the basecollector junction
(C) the forward biasing of emitterbase junction
(D) the early removal of stored base charge during saturationtocutoff
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 nchannel 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 Qpoints will give the highest transconductance 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 sumofproduct expression
obtained through the following Kmap 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 openloop transfer function of a unitygain 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 lowpass 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 tunneldiode corresponding to peak and valley
currents are and
P V
V V respectively. The range of tunneldiode 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 basewidth caused by
(A) electronhole recombination at the base
(B) the reverse biasing of the basecollector junction
(C) the forward biasing of emitterbase junction
(D) the early removal of stored base charge during saturationtocutoff
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 nchannel 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 Qpoints will give the highest transconductance 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 sumofproduct expression
obtained through the following Kmap 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 openloop transfer function of a unitygain 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 steadysate, 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 zdirection
(B) elliptically polarized
(C) lefthand circularly polarized
(D) righthand 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 freespace is:
(A) 10 Watts
( ) x t ( ) y t
1
1 s+
Read More