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 unitstep 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 unitstep 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 Ztransform 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 unitstep 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 Ztransform 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 picoAmperes (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 Silicondioxide (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 unitstep 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 Ztransform 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 picoAmperes (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 Silicondioxide (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 RCdriving 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) CCCB (b) CECB (c) CBCC (d) CECC
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 unitstep 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 Ztransform 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 picoAmperes (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 Silicondioxide (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 RCdriving 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) CCCB (b) CECB (c) CBCC (d) CECC
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 – DSBSC 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)
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