Page 1
EC? GATE Paper 2008
Q. 1 to 20 Carry One Mark Each
1. All the four entries of the 2×2 matrix
11 12
21 22
p p
P
p p
? ?
=
? ?
? ?
are nonzero, and one of its
eigenvalues is zero. Which of the following statements is true?
(A)
11 22 12 21
p p p p 1  = (B)
11 22 12 21
p p p p 1  = 
(C)
11 22 12 21
p p p p 0  = (D)
11 22 12 21
p p p p 0 + =
2. The system of linear equations
4x 2y 7
2x y 6
+ =
+ =
has
(A) a unique solution (B) no solution
(C) an infinite number of solutions (D) exactly two distinct solutions
3. The equation ( ) sin z 10has =
(A) no real or complex solution
(B) exactly two distinct complex solutions
(C) a unique solution
(D) an infinite number of complex solutions
4. For real values of x, the minimum value of the function ( ) ( ) ( ) f x exp x exp x is = + 
(A) 2 (B) 1 (C) 0.5 (D) 0
5. Which of the following functions would have only odd powers of x in its Taylor
series expansion about the point x=0?
(A)
( )
3
sin x (B)
( )
2
sin x (C)
( )
3
cos x (D)
( )
2
cos x
6. Which of the following is a solution to the differential equation
( )
( )
dx t
3x t 0?
dt
+ =
(A) ( )
t
x t 3e

= (B) ( )
3t
x t 2e

= (C) ( )
2
3
x t t
2
=  (D) ( )
2
x t 3t =
7. In the following graph, the number of trees (P) and the number of cutsets (Q)
are
(A) P=2, Q=2
(B) P=2, Q=6
(C) P=4, Q=6
(D) P=4, Q=10
( ) 4
( ) 1
( ) 2
( ) 3
Page 2
EC? GATE Paper 2008
Q. 1 to 20 Carry One Mark Each
1. All the four entries of the 2×2 matrix
11 12
21 22
p p
P
p p
? ?
=
? ?
? ?
are nonzero, and one of its
eigenvalues is zero. Which of the following statements is true?
(A)
11 22 12 21
p p p p 1  = (B)
11 22 12 21
p p p p 1  = 
(C)
11 22 12 21
p p p p 0  = (D)
11 22 12 21
p p p p 0 + =
2. The system of linear equations
4x 2y 7
2x y 6
+ =
+ =
has
(A) a unique solution (B) no solution
(C) an infinite number of solutions (D) exactly two distinct solutions
3. The equation ( ) sin z 10has =
(A) no real or complex solution
(B) exactly two distinct complex solutions
(C) a unique solution
(D) an infinite number of complex solutions
4. For real values of x, the minimum value of the function ( ) ( ) ( ) f x exp x exp x is = + 
(A) 2 (B) 1 (C) 0.5 (D) 0
5. Which of the following functions would have only odd powers of x in its Taylor
series expansion about the point x=0?
(A)
( )
3
sin x (B)
( )
2
sin x (C)
( )
3
cos x (D)
( )
2
cos x
6. Which of the following is a solution to the differential equation
( )
( )
dx t
3x t 0?
dt
+ =
(A) ( )
t
x t 3e

= (B) ( )
3t
x t 2e

= (C) ( )
2
3
x t t
2
=  (D) ( )
2
x t 3t =
7. In the following graph, the number of trees (P) and the number of cutsets (Q)
are
(A) P=2, Q=2
(B) P=2, Q=6
(C) P=4, Q=6
(D) P=4, Q=10
( ) 4
( ) 1
( ) 2
( ) 3
EC? GATE Paper 2008
8. In the following circuit, the switch S is closed at t=0. The rate of change of
current ( )
di
0
dt
+ is given by
(A) 0 (B)
S S
R I
L
(C)
( )
S S
R R I
L
+
(D) 8
9. The input and output of a continuous time system are respectively denoted by
x(t) and y(t). Which of the following descriptions corresponds to a causal system?
(A) ( ) ( ) ( ) y t x t 2 x t 4 =  + + (B) ( ) ( ) ( ) y t t 4 x t 1 =  +
(C) ( ) ( ) ( ) y t t 4 x t 1 = +  (D) ( ) ( ) ( ) y t t 5 x t 5 = + +
10. The impulse response h(t) of a linear timeinvariant continuous time system is
described by ( ) ( ) ( ) ( ) ( ) h t exp t u t exp t u t , = a + ß  where u(t) denotes the unit step
function, and a and ß are real constants. This system is stable if
(A) a is positive and ß is positive (B) a is negative and ß is negative
(C) a is positive and ß is negative (D) a is negative and ß is positive
11. The polezero plot given below corresponds to a
(A) Low pass filter (B) High pass filter (C) Band pass filter (D) Notch filter
12. Step responses of a set of three secondorder underdamped systems all have the
same percentage overshoot. Which of the following diagrams represents the
poles of the three systems?
S
R
( ) i t
L
S
R
S
I
s
j?
O
O
X X
Page 3
EC? GATE Paper 2008
Q. 1 to 20 Carry One Mark Each
1. All the four entries of the 2×2 matrix
11 12
21 22
p p
P
p p
? ?
=
? ?
? ?
are nonzero, and one of its
eigenvalues is zero. Which of the following statements is true?
(A)
11 22 12 21
p p p p 1  = (B)
11 22 12 21
p p p p 1  = 
(C)
11 22 12 21
p p p p 0  = (D)
11 22 12 21
p p p p 0 + =
2. The system of linear equations
4x 2y 7
2x y 6
+ =
+ =
has
(A) a unique solution (B) no solution
(C) an infinite number of solutions (D) exactly two distinct solutions
3. The equation ( ) sin z 10has =
(A) no real or complex solution
(B) exactly two distinct complex solutions
(C) a unique solution
(D) an infinite number of complex solutions
4. For real values of x, the minimum value of the function ( ) ( ) ( ) f x exp x exp x is = + 
(A) 2 (B) 1 (C) 0.5 (D) 0
5. Which of the following functions would have only odd powers of x in its Taylor
series expansion about the point x=0?
(A)
( )
3
sin x (B)
( )
2
sin x (C)
( )
3
cos x (D)
( )
2
cos x
6. Which of the following is a solution to the differential equation
( )
( )
dx t
3x t 0?
dt
+ =
(A) ( )
t
x t 3e

= (B) ( )
3t
x t 2e

= (C) ( )
2
3
x t t
2
=  (D) ( )
2
x t 3t =
7. In the following graph, the number of trees (P) and the number of cutsets (Q)
are
(A) P=2, Q=2
(B) P=2, Q=6
(C) P=4, Q=6
(D) P=4, Q=10
( ) 4
( ) 1
( ) 2
( ) 3
EC? GATE Paper 2008
8. In the following circuit, the switch S is closed at t=0. The rate of change of
current ( )
di
0
dt
+ is given by
(A) 0 (B)
S S
R I
L
(C)
( )
S S
R R I
L
+
(D) 8
9. The input and output of a continuous time system are respectively denoted by
x(t) and y(t). Which of the following descriptions corresponds to a causal system?
(A) ( ) ( ) ( ) y t x t 2 x t 4 =  + + (B) ( ) ( ) ( ) y t t 4 x t 1 =  +
(C) ( ) ( ) ( ) y t t 4 x t 1 = +  (D) ( ) ( ) ( ) y t t 5 x t 5 = + +
10. The impulse response h(t) of a linear timeinvariant continuous time system is
described by ( ) ( ) ( ) ( ) ( ) h t exp t u t exp t u t , = a + ß  where u(t) denotes the unit step
function, and a and ß are real constants. This system is stable if
(A) a is positive and ß is positive (B) a is negative and ß is negative
(C) a is positive and ß is negative (D) a is negative and ß is positive
11. The polezero plot given below corresponds to a
(A) Low pass filter (B) High pass filter (C) Band pass filter (D) Notch filter
12. Step responses of a set of three secondorder underdamped systems all have the
same percentage overshoot. Which of the following diagrams represents the
poles of the three systems?
S
R
( ) i t
L
S
R
S
I
s
j?
O
O
X X
EC? GATE Paper 2008
(A) (B)
(C) (D)
13. Which of the following is NOT associated with a pn junction?
(A) Junction capacitance (B) Charge Storage Capacitance
(C) Depletion Capacitance (D) Channel Length Modulation
14. Which of the following is true?
(A) A silicon wafer heavily doped with boron is a p
+
substrate
(B) A silicon wafer lightly doped with boron is a p
+
substrate
(C) A silicon wafer heavily doped with arsenic is a p
+
substrate
(D) A silicon wafer lightly doped with arsenic is a p
+
substrate
15. For a Hertz dipole antenna, the half power beam width (HPBW) in the Eplane is
(A) 360º (B) 180º (C) 90º (D) 45º
16. For static electric and magnetic fields in an inhomogeneous sourcefree medium,
which of the following represents the correct form of two of Maxwell’s equations?
(A)
.E 0
B 0
? =
? × =
(B)
.E 0
.B 0
? =
? =
(C)
E 0
B 0
? × =
? × =
(D)
E 0
.B 0
? × =
? =
s
j?
.
.
.
.
.
.
.
.
X
X
X
X
X
X
s
j?
· · · X X X · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·
· · · X X X · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·
s
j?
·
·
·
·
·
·
X
X
X
.
.
.
.
X
X
X
.
.
s
j?
X
.
X
X
X
X
X
.
.
.
.
.
.
.
.
.
.
.
Page 4
EC? GATE Paper 2008
Q. 1 to 20 Carry One Mark Each
1. All the four entries of the 2×2 matrix
11 12
21 22
p p
P
p p
? ?
=
? ?
? ?
are nonzero, and one of its
eigenvalues is zero. Which of the following statements is true?
(A)
11 22 12 21
p p p p 1  = (B)
11 22 12 21
p p p p 1  = 
(C)
11 22 12 21
p p p p 0  = (D)
11 22 12 21
p p p p 0 + =
2. The system of linear equations
4x 2y 7
2x y 6
+ =
+ =
has
(A) a unique solution (B) no solution
(C) an infinite number of solutions (D) exactly two distinct solutions
3. The equation ( ) sin z 10has =
(A) no real or complex solution
(B) exactly two distinct complex solutions
(C) a unique solution
(D) an infinite number of complex solutions
4. For real values of x, the minimum value of the function ( ) ( ) ( ) f x exp x exp x is = + 
(A) 2 (B) 1 (C) 0.5 (D) 0
5. Which of the following functions would have only odd powers of x in its Taylor
series expansion about the point x=0?
(A)
( )
3
sin x (B)
( )
2
sin x (C)
( )
3
cos x (D)
( )
2
cos x
6. Which of the following is a solution to the differential equation
( )
( )
dx t
3x t 0?
dt
+ =
(A) ( )
t
x t 3e

= (B) ( )
3t
x t 2e

= (C) ( )
2
3
x t t
2
=  (D) ( )
2
x t 3t =
7. In the following graph, the number of trees (P) and the number of cutsets (Q)
are
(A) P=2, Q=2
(B) P=2, Q=6
(C) P=4, Q=6
(D) P=4, Q=10
( ) 4
( ) 1
( ) 2
( ) 3
EC? GATE Paper 2008
8. In the following circuit, the switch S is closed at t=0. The rate of change of
current ( )
di
0
dt
+ is given by
(A) 0 (B)
S S
R I
L
(C)
( )
S S
R R I
L
+
(D) 8
9. The input and output of a continuous time system are respectively denoted by
x(t) and y(t). Which of the following descriptions corresponds to a causal system?
(A) ( ) ( ) ( ) y t x t 2 x t 4 =  + + (B) ( ) ( ) ( ) y t t 4 x t 1 =  +
(C) ( ) ( ) ( ) y t t 4 x t 1 = +  (D) ( ) ( ) ( ) y t t 5 x t 5 = + +
10. The impulse response h(t) of a linear timeinvariant continuous time system is
described by ( ) ( ) ( ) ( ) ( ) h t exp t u t exp t u t , = a + ß  where u(t) denotes the unit step
function, and a and ß are real constants. This system is stable if
(A) a is positive and ß is positive (B) a is negative and ß is negative
(C) a is positive and ß is negative (D) a is negative and ß is positive
11. The polezero plot given below corresponds to a
(A) Low pass filter (B) High pass filter (C) Band pass filter (D) Notch filter
12. Step responses of a set of three secondorder underdamped systems all have the
same percentage overshoot. Which of the following diagrams represents the
poles of the three systems?
S
R
( ) i t
L
S
R
S
I
s
j?
O
O
X X
EC? GATE Paper 2008
(A) (B)
(C) (D)
13. Which of the following is NOT associated with a pn junction?
(A) Junction capacitance (B) Charge Storage Capacitance
(C) Depletion Capacitance (D) Channel Length Modulation
14. Which of the following is true?
(A) A silicon wafer heavily doped with boron is a p
+
substrate
(B) A silicon wafer lightly doped with boron is a p
+
substrate
(C) A silicon wafer heavily doped with arsenic is a p
+
substrate
(D) A silicon wafer lightly doped with arsenic is a p
+
substrate
15. For a Hertz dipole antenna, the half power beam width (HPBW) in the Eplane is
(A) 360º (B) 180º (C) 90º (D) 45º
16. For static electric and magnetic fields in an inhomogeneous sourcefree medium,
which of the following represents the correct form of two of Maxwell’s equations?
(A)
.E 0
B 0
? =
? × =
(B)
.E 0
.B 0
? =
? =
(C)
E 0
B 0
? × =
? × =
(D)
E 0
.B 0
? × =
? =
s
j?
.
.
.
.
.
.
.
.
X
X
X
X
X
X
s
j?
· · · X X X · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·
· · · X X X · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·
s
j?
·
·
·
·
·
·
X
X
X
.
.
.
.
X
X
X
.
.
s
j?
X
.
X
X
X
X
X
.
.
.
.
.
.
.
.
.
.
.
EC? GATE Paper 2008
17. In the following limiter circuit, an input voltage
i
V 10sin100 t = p applied. Assume
that the diode drop is 0.7V when it is forward biased. The Zener breakdown
voltage is 6.8V.
The maximum and minimum values of the output voltage respectively are
(A) 6.1V, 0.7V  (B) 0.7V, 7.5V  (C) 7.5V, 0.7V  (D) 7.5V, 7.5V 
18. A silicon wafer has 100nm of oxide on it and is inserted in a furnace at a
temperature above 1000ºC for further oxidation in dry oxygen. The oxidation
rate
(A) is independent of current oxide thickness and temperature
(B) is independent of current oxide thickness but depends on temperature
(C) slows down as the oxide grows
(D) is zero as the existing oxide prevents further oxidation
19. The drain current of a MOSFET in saturation is given by ( )
2
p GS r
K V V =  l where K
is a constant. The magnitude of the transconductance g
m
is
(A)
( )
2
GS T
DS
K V V
V

(B) ( )
GS T
2K V V  (C)
d
GS DS
I
V V 
(D)
( )
2
GS T
GS
K V V
V

20. Consider the amplitude modulated (AM) signal
C c m c
A cos t 2cos t cos t. ? + ? ? For
demodulating the signal using envelope detector, the minimum value of A
c
should
be
(A) 2 (B) 1 (C) 0.5 (D) 0
Q. 21 to 75 carry two Marks Each
21. The Thevenin equivalent impedance Z
th
between the nodes P and Q in the
following circuit is
(A) 1 (B)
1
1 s
s
+ + (C)
1
2 s
s
+ + (D)
2
2
s s 1
s 2s 1
+ +
+ +
1K D1
0
D2 V
6.8V
Z
i
V
+

1O
10V
1H
1 F
1O
1 A
Q
P
Page 5
EC? GATE Paper 2008
Q. 1 to 20 Carry One Mark Each
1. All the four entries of the 2×2 matrix
11 12
21 22
p p
P
p p
? ?
=
? ?
? ?
are nonzero, and one of its
eigenvalues is zero. Which of the following statements is true?
(A)
11 22 12 21
p p p p 1  = (B)
11 22 12 21
p p p p 1  = 
(C)
11 22 12 21
p p p p 0  = (D)
11 22 12 21
p p p p 0 + =
2. The system of linear equations
4x 2y 7
2x y 6
+ =
+ =
has
(A) a unique solution (B) no solution
(C) an infinite number of solutions (D) exactly two distinct solutions
3. The equation ( ) sin z 10has =
(A) no real or complex solution
(B) exactly two distinct complex solutions
(C) a unique solution
(D) an infinite number of complex solutions
4. For real values of x, the minimum value of the function ( ) ( ) ( ) f x exp x exp x is = + 
(A) 2 (B) 1 (C) 0.5 (D) 0
5. Which of the following functions would have only odd powers of x in its Taylor
series expansion about the point x=0?
(A)
( )
3
sin x (B)
( )
2
sin x (C)
( )
3
cos x (D)
( )
2
cos x
6. Which of the following is a solution to the differential equation
( )
( )
dx t
3x t 0?
dt
+ =
(A) ( )
t
x t 3e

= (B) ( )
3t
x t 2e

= (C) ( )
2
3
x t t
2
=  (D) ( )
2
x t 3t =
7. In the following graph, the number of trees (P) and the number of cutsets (Q)
are
(A) P=2, Q=2
(B) P=2, Q=6
(C) P=4, Q=6
(D) P=4, Q=10
( ) 4
( ) 1
( ) 2
( ) 3
EC? GATE Paper 2008
8. In the following circuit, the switch S is closed at t=0. The rate of change of
current ( )
di
0
dt
+ is given by
(A) 0 (B)
S S
R I
L
(C)
( )
S S
R R I
L
+
(D) 8
9. The input and output of a continuous time system are respectively denoted by
x(t) and y(t). Which of the following descriptions corresponds to a causal system?
(A) ( ) ( ) ( ) y t x t 2 x t 4 =  + + (B) ( ) ( ) ( ) y t t 4 x t 1 =  +
(C) ( ) ( ) ( ) y t t 4 x t 1 = +  (D) ( ) ( ) ( ) y t t 5 x t 5 = + +
10. The impulse response h(t) of a linear timeinvariant continuous time system is
described by ( ) ( ) ( ) ( ) ( ) h t exp t u t exp t u t , = a + ß  where u(t) denotes the unit step
function, and a and ß are real constants. This system is stable if
(A) a is positive and ß is positive (B) a is negative and ß is negative
(C) a is positive and ß is negative (D) a is negative and ß is positive
11. The polezero plot given below corresponds to a
(A) Low pass filter (B) High pass filter (C) Band pass filter (D) Notch filter
12. Step responses of a set of three secondorder underdamped systems all have the
same percentage overshoot. Which of the following diagrams represents the
poles of the three systems?
S
R
( ) i t
L
S
R
S
I
s
j?
O
O
X X
EC? GATE Paper 2008
(A) (B)
(C) (D)
13. Which of the following is NOT associated with a pn junction?
(A) Junction capacitance (B) Charge Storage Capacitance
(C) Depletion Capacitance (D) Channel Length Modulation
14. Which of the following is true?
(A) A silicon wafer heavily doped with boron is a p
+
substrate
(B) A silicon wafer lightly doped with boron is a p
+
substrate
(C) A silicon wafer heavily doped with arsenic is a p
+
substrate
(D) A silicon wafer lightly doped with arsenic is a p
+
substrate
15. For a Hertz dipole antenna, the half power beam width (HPBW) in the Eplane is
(A) 360º (B) 180º (C) 90º (D) 45º
16. For static electric and magnetic fields in an inhomogeneous sourcefree medium,
which of the following represents the correct form of two of Maxwell’s equations?
(A)
.E 0
B 0
? =
? × =
(B)
.E 0
.B 0
? =
? =
(C)
E 0
B 0
? × =
? × =
(D)
E 0
.B 0
? × =
? =
s
j?
.
.
.
.
.
.
.
.
X
X
X
X
X
X
s
j?
· · · X X X · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·
· · · X X X · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·
s
j?
·
·
·
·
·
·
X
X
X
.
.
.
.
X
X
X
.
.
s
j?
X
.
X
X
X
X
X
.
.
.
.
.
.
.
.
.
.
.
EC? GATE Paper 2008
17. In the following limiter circuit, an input voltage
i
V 10sin100 t = p applied. Assume
that the diode drop is 0.7V when it is forward biased. The Zener breakdown
voltage is 6.8V.
The maximum and minimum values of the output voltage respectively are
(A) 6.1V, 0.7V  (B) 0.7V, 7.5V  (C) 7.5V, 0.7V  (D) 7.5V, 7.5V 
18. A silicon wafer has 100nm of oxide on it and is inserted in a furnace at a
temperature above 1000ºC for further oxidation in dry oxygen. The oxidation
rate
(A) is independent of current oxide thickness and temperature
(B) is independent of current oxide thickness but depends on temperature
(C) slows down as the oxide grows
(D) is zero as the existing oxide prevents further oxidation
19. The drain current of a MOSFET in saturation is given by ( )
2
p GS r
K V V =  l where K
is a constant. The magnitude of the transconductance g
m
is
(A)
( )
2
GS T
DS
K V V
V

(B) ( )
GS T
2K V V  (C)
d
GS DS
I
V V 
(D)
( )
2
GS T
GS
K V V
V

20. Consider the amplitude modulated (AM) signal
C c m c
A cos t 2cos t cos t. ? + ? ? For
demodulating the signal using envelope detector, the minimum value of A
c
should
be
(A) 2 (B) 1 (C) 0.5 (D) 0
Q. 21 to 75 carry two Marks Each
21. The Thevenin equivalent impedance Z
th
between the nodes P and Q in the
following circuit is
(A) 1 (B)
1
1 s
s
+ + (C)
1
2 s
s
+ + (D)
2
2
s s 1
s 2s 1
+ +
+ +
1K D1
0
D2 V
6.8V
Z
i
V
+

1O
10V
1H
1 F
1O
1 A
Q
P
EC? GATE Paper 2008
22. The driving point impedance of the following network
is given by ( )
2
0.2s
Z s .
s 0.1s 2
=
+ +
The component values are
(A) L 5H, R 0.5 , C 0.1F = = O = (B) L 0.1H, R 0.5 , C 5F = = O =
(C) L 5H, R 2 , C 0.1F = = O = (D) L 0.1H, R 2 , C 5F = = O =
23. The circuit shown in the figure is used to charge the capacitor C alternately from
two current sources as indicated. The switches S1 and S2 are mechanically
coupled and connected as follows
( ) ( )
( ) ( ) ( )
For 2nT t 2n 1 T, n 0,1,2,... S1 to P1 and S2 to P2
For 2n 1 T t 2n 2 T, n 0,1,2,... S1 to Q1 and S2 to Q2
= < + =
+ = < + =
Assume that the capacitor has zero initial charge. Given that u(t) is a unit step
function, the voltage V
c
(t) across the capacitor is given be
(A) ( ) ( )
n
n 0
1 tu t nT
8
=
 
?
(B) ( ) ( ) ( )
n
n 0
u t 2 1 u t nT
8
=
+  
?
(C) ( ) ( ) ( ) ( )
n
n 0
tu t 2 1 t nT u t nT
8
=
+   
?
(D)
( ) ( ) t 2nT t 2nT T
n 0
0.5 e 0.5e
8
    
=
? ?
 +
? ?
?
24. The probability density function (PDF) of a random variable X is as shown below
R
( ) Z s
L O
( )
C
V t
+
 1A 1A
1F
C
1O
S2 S1
0.5O
1O
Q1 P1 Q2 P2
1O
1
1  0 1 x
PDF
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