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# Electronics and Communication Engineering (EC) 2007 GATE Paper without solution Electronics and Communication Engineering (ECE) Notes | EduRev

## Electronics and Communication Engineering (ECE) : Electronics and Communication Engineering (EC) 2007 GATE Paper without solution Electronics and Communication Engineering (ECE) Notes | EduRev

``` Page 1

EC? GATE Paper 2007
Q.1 – Q.20 Carry One Mark Each
1. If E denotes expectation, the variance of a random variable X is given by
(A)
2 2
E X E X
? ?
- ? ?
? ?
? ?
(B)
2 2
E X E X
? ?
+ ? ?
? ?
? ?
(C)
2
E X
? ?
? ?
(D)
2
E X ? ?
? ?
2. The following plot shows a function y which varies linearly with x . The value of
the integral
2
1
I y dx =
?
is
(A) 1.0 (B) 2.5 (C) 4.0 (D) 5.0
3. For 1, x << ( ) coth x can be approximated as
(A) x (B)
2
x (C)
1
x
(D)
2
1
x
4.
( )
0
sin 2
lim
?
?
? ?
is:
(A) 0.5 (B) 1 (C) 2 (D) not defined
5. Which one of the following functions is strictly bounded?
(A)
2
1
x
(B)
x
e (C)
2
x (D)
2
x
e
-
6. For the function ,
x
e
-
the linear approximation around 2 x = is:
(A) ( )
2
3 x e
-
- (B) 1 x -
(C)
( )
2
3 2 2 1 2 x e
-
? ?
+ - +
? ?
(D)
2
e
-
7. An independent voltage source in series with an impedance
s s s
Z R jX = + delivers
a maximum average power to a load impedance
L
Z when
(A)
L s s
Z R jX = + (B)
L s
Z R =
(C)
L s
Z jX = (D)
L s s
Z R jX = -
1 2 3
x
1
2
3
y
-1
Page 2

EC? GATE Paper 2007
Q.1 – Q.20 Carry One Mark Each
1. If E denotes expectation, the variance of a random variable X is given by
(A)
2 2
E X E X
? ?
- ? ?
? ?
? ?
(B)
2 2
E X E X
? ?
+ ? ?
? ?
? ?
(C)
2
E X
? ?
? ?
(D)
2
E X ? ?
? ?
2. The following plot shows a function y which varies linearly with x . The value of
the integral
2
1
I y dx =
?
is
(A) 1.0 (B) 2.5 (C) 4.0 (D) 5.0
3. For 1, x << ( ) coth x can be approximated as
(A) x (B)
2
x (C)
1
x
(D)
2
1
x
4.
( )
0
sin 2
lim
?
?
? ?
is:
(A) 0.5 (B) 1 (C) 2 (D) not defined
5. Which one of the following functions is strictly bounded?
(A)
2
1
x
(B)
x
e (C)
2
x (D)
2
x
e
-
6. For the function ,
x
e
-
the linear approximation around 2 x = is:
(A) ( )
2
3 x e
-
- (B) 1 x -
(C)
( )
2
3 2 2 1 2 x e
-
? ?
+ - +
? ?
(D)
2
e
-
7. An independent voltage source in series with an impedance
s s s
Z R jX = + delivers
a maximum average power to a load impedance
L
Z when
(A)
L s s
Z R jX = + (B)
L s
Z R =
(C)
L s
Z jX = (D)
L s s
Z R jX = -
1 2 3
x
1
2
3
y
-1
EC? GATE Paper 2007
8. The RC circuit shown in the figure is
(A) a low-pass filter   (B) a high-pass filter
(C) a band-pass filter (D) a band-reject filter
9. The electron and hole concentrations in an intrinsic semiconductor are
i
n per
3
cm at 300 K. Now, if acceptor impurities are introduced with a concentration of
A
N per
3
cm ( ) where
A i
N n >> , the electron concentration per
3
cm at 300 K will
be:
(A)
i
n (B)
i A
n N + (C)
A i
N n - (D)
2
i
A
n
N
10. In a p n
+
junction diode under reverse bias, the magnitude of electric field is
maximum at
(A) the edge of the depletion region on the p-side
(B) the edge of the depletion region on the n-side
(C) the p n
+
junction
(D) the centre of the depletion region on the n-side
11. The correct full wave rectifier circuit is:
(A) (B)
R
C
R
C
i
V
o
V
+
-
+
-
Input
Output
Input
Output
Page 3

EC? GATE Paper 2007
Q.1 – Q.20 Carry One Mark Each
1. If E denotes expectation, the variance of a random variable X is given by
(A)
2 2
E X E X
? ?
- ? ?
? ?
? ?
(B)
2 2
E X E X
? ?
+ ? ?
? ?
? ?
(C)
2
E X
? ?
? ?
(D)
2
E X ? ?
? ?
2. The following plot shows a function y which varies linearly with x . The value of
the integral
2
1
I y dx =
?
is
(A) 1.0 (B) 2.5 (C) 4.0 (D) 5.0
3. For 1, x << ( ) coth x can be approximated as
(A) x (B)
2
x (C)
1
x
(D)
2
1
x
4.
( )
0
sin 2
lim
?
?
? ?
is:
(A) 0.5 (B) 1 (C) 2 (D) not defined
5. Which one of the following functions is strictly bounded?
(A)
2
1
x
(B)
x
e (C)
2
x (D)
2
x
e
-
6. For the function ,
x
e
-
the linear approximation around 2 x = is:
(A) ( )
2
3 x e
-
- (B) 1 x -
(C)
( )
2
3 2 2 1 2 x e
-
? ?
+ - +
? ?
(D)
2
e
-
7. An independent voltage source in series with an impedance
s s s
Z R jX = + delivers
a maximum average power to a load impedance
L
Z when
(A)
L s s
Z R jX = + (B)
L s
Z R =
(C)
L s
Z jX = (D)
L s s
Z R jX = -
1 2 3
x
1
2
3
y
-1
EC? GATE Paper 2007
8. The RC circuit shown in the figure is
(A) a low-pass filter   (B) a high-pass filter
(C) a band-pass filter (D) a band-reject filter
9. The electron and hole concentrations in an intrinsic semiconductor are
i
n per
3
cm at 300 K. Now, if acceptor impurities are introduced with a concentration of
A
N per
3
cm ( ) where
A i
N n >> , the electron concentration per
3
cm at 300 K will
be:
(A)
i
n (B)
i A
n N + (C)
A i
N n - (D)
2
i
A
n
N
10. In a p n
+
junction diode under reverse bias, the magnitude of electric field is
maximum at
(A) the edge of the depletion region on the p-side
(B) the edge of the depletion region on the n-side
(C) the p n
+
junction
(D) the centre of the depletion region on the n-side
11. The correct full wave rectifier circuit is:
(A) (B)
R
C
R
C
i
V
o
V
+
-
+
-
Input
Output
Input
Output
EC? GATE Paper 2007
(C) (D)
12. In a transconductance amplifier, it is desirable to have
(A) a large input resistance and a large output resistance
(B) a large input resistance and a small output resistance
(C) a small input resistance and a large output resistance
(D) a small input resistance and a small output resistance
13. X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two’s
complement format. The sum of X and Y represented in two’s complement format
using 6 bits is:
(A) 100111 (B) 001000 (C) 000111 (D) 101001
14. The Boolean function Y AB CD = + is to be realized using only 2-input NAND
gates. The minimum number of gates required is:
(A) 2 (B) 3 (C) 4 (D) 5
15. If the closed-loop transfer function of a control system is given as
( )
( )( )
5
,
2 3
s
T s
s s
-
=
+ +
then it is
(A) an unstable system  (B) an uncontrollable system
(C) a minimum phase system (D) a non-minimum phase system
16. If the Laplace transform of a signal ( ) y t is ( )
( )
1
,
1
Y s
s s
=
-
then its final value is:
(A) -1 (B) 0 (C) 1 (D) unbounded
17. If ( ) R t is the autocorrelation function of a real, wide-sense stationary random
process, then which of the following is NOT true?
(A) ( ) ( ) R R t t = - (B) ( ) ( ) 0 R R t = (C) ( ) ( ) R R t t = - -
(D) The mean square value of the process is ( ) 0 R
Input
Output
Input
Output
Page 4

EC? GATE Paper 2007
Q.1 – Q.20 Carry One Mark Each
1. If E denotes expectation, the variance of a random variable X is given by
(A)
2 2
E X E X
? ?
- ? ?
? ?
? ?
(B)
2 2
E X E X
? ?
+ ? ?
? ?
? ?
(C)
2
E X
? ?
? ?
(D)
2
E X ? ?
? ?
2. The following plot shows a function y which varies linearly with x . The value of
the integral
2
1
I y dx =
?
is
(A) 1.0 (B) 2.5 (C) 4.0 (D) 5.0
3. For 1, x << ( ) coth x can be approximated as
(A) x (B)
2
x (C)
1
x
(D)
2
1
x
4.
( )
0
sin 2
lim
?
?
? ?
is:
(A) 0.5 (B) 1 (C) 2 (D) not defined
5. Which one of the following functions is strictly bounded?
(A)
2
1
x
(B)
x
e (C)
2
x (D)
2
x
e
-
6. For the function ,
x
e
-
the linear approximation around 2 x = is:
(A) ( )
2
3 x e
-
- (B) 1 x -
(C)
( )
2
3 2 2 1 2 x e
-
? ?
+ - +
? ?
(D)
2
e
-
7. An independent voltage source in series with an impedance
s s s
Z R jX = + delivers
a maximum average power to a load impedance
L
Z when
(A)
L s s
Z R jX = + (B)
L s
Z R =
(C)
L s
Z jX = (D)
L s s
Z R jX = -
1 2 3
x
1
2
3
y
-1
EC? GATE Paper 2007
8. The RC circuit shown in the figure is
(A) a low-pass filter   (B) a high-pass filter
(C) a band-pass filter (D) a band-reject filter
9. The electron and hole concentrations in an intrinsic semiconductor are
i
n per
3
cm at 300 K. Now, if acceptor impurities are introduced with a concentration of
A
N per
3
cm ( ) where
A i
N n >> , the electron concentration per
3
cm at 300 K will
be:
(A)
i
n (B)
i A
n N + (C)
A i
N n - (D)
2
i
A
n
N
10. In a p n
+
junction diode under reverse bias, the magnitude of electric field is
maximum at
(A) the edge of the depletion region on the p-side
(B) the edge of the depletion region on the n-side
(C) the p n
+
junction
(D) the centre of the depletion region on the n-side
11. The correct full wave rectifier circuit is:
(A) (B)
R
C
R
C
i
V
o
V
+
-
+
-
Input
Output
Input
Output
EC? GATE Paper 2007
(C) (D)
12. In a transconductance amplifier, it is desirable to have
(A) a large input resistance and a large output resistance
(B) a large input resistance and a small output resistance
(C) a small input resistance and a large output resistance
(D) a small input resistance and a small output resistance
13. X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two’s
complement format. The sum of X and Y represented in two’s complement format
using 6 bits is:
(A) 100111 (B) 001000 (C) 000111 (D) 101001
14. The Boolean function Y AB CD = + is to be realized using only 2-input NAND
gates. The minimum number of gates required is:
(A) 2 (B) 3 (C) 4 (D) 5
15. If the closed-loop transfer function of a control system is given as
( )
( )( )
5
,
2 3
s
T s
s s
-
=
+ +
then it is
(A) an unstable system  (B) an uncontrollable system
(C) a minimum phase system (D) a non-minimum phase system
16. If the Laplace transform of a signal ( ) y t is ( )
( )
1
,
1
Y s
s s
=
-
then its final value is:
(A) -1 (B) 0 (C) 1 (D) unbounded
17. If ( ) R t is the autocorrelation function of a real, wide-sense stationary random
process, then which of the following is NOT true?
(A) ( ) ( ) R R t t = - (B) ( ) ( ) 0 R R t = (C) ( ) ( ) R R t t = - -
(D) The mean square value of the process is ( ) 0 R
Input
Output
Input
Output
EC? GATE Paper 2007
18. If ( ) S f is the power spectral density of a real, wide-sense stationary random
process, then which of the following is ALWAYS true?
(A) ( ) ( ) 0 S S f = (B) ( ) 0 S f = (C) ( ) ( ) S f S f - = - (D) ( ) 0 S f df
8
-8
=
?
19. A plane wave of wavelength ? is traveling in a direction making an angle 30° with
positive x-axis and 90° with positive y-axis. The E
u r
field of the plane wave can be
represented as ( ) is constant
o
E
(A)
µ
3
0
j t x z
E yE e
p p
?
? ?
? ?
- - ? ?
? ?
? ?
=
u r
(B)
µ
3
0
j t x z
E yE e
p p
?
? ?
? ?
- - ? ?
? ?
? ?
=
u r
(C)
µ
3
0
j t x z
E yE e
p p
?
? ?
? ?
+ + ? ?
? ?
? ?
=
u r
(D)
µ
3
0
j t x z
E yE e
p p
?
? ?
? ?
- + ? ?
? ?
? ?
=
u r
20. If C is a closed curve enclosing a surface S, then the magnetic field intensity , H
u r
the current density J
r
and the electric flux density D
u r
are related by
(A) . .
s c
D
H ds J dl
t
? ?
?
= + ? ?
? ?
?
? ?
?? ?
u r
u r r r r
Ñ
(B) . .
c s
D
H dl J d ds
t
? ?
?
= + ? ?
? ?
?
? ?
? ??
u r
r u r r r
Ò
(C) . .
s c
D
H ds J dl
t
? ?
?
= + ? ?
? ?
?
? ?
?? ?
u r
u r r r r
Ò
(D) . .
c s
D
H dl J ds
t
? ?
?
= + ? ?
? ?
?
? ?
? ??
u r
u r r r r
Ñ
Q.21 – Q.75 Carry Two Marks Each
21. It is given that
1 2
, ,....
M
X x X are M non-zero, orthogonal vectors. The dimension of
the vector space spanned by the 2M vectors
1 2 1 2
, ,... , , ,...
M M
X X X X X X - - - is:
(A) 2M (B) M + 1 (C) M
(D) dependent on the choice of
1 2
, ,...
M
X X X
22. Consider the function ( )
2
2. f x x x = - - The maximum value of ( ) f x in the closed
interval 4,4 - ? ?
? ?
is:
(A) 18 (B) 10
(C) -2.25 (D) indeterminate
23. An examination consists of two papers, Paper 1 and Paper 2. The probability of
failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed
in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student
failing in both the papers is:
(A) 0.5 (B) 0.18 (C) 0.12 (D) 0.06
Page 5

EC? GATE Paper 2007
Q.1 – Q.20 Carry One Mark Each
1. If E denotes expectation, the variance of a random variable X is given by
(A)
2 2
E X E X
? ?
- ? ?
? ?
? ?
(B)
2 2
E X E X
? ?
+ ? ?
? ?
? ?
(C)
2
E X
? ?
? ?
(D)
2
E X ? ?
? ?
2. The following plot shows a function y which varies linearly with x . The value of
the integral
2
1
I y dx =
?
is
(A) 1.0 (B) 2.5 (C) 4.0 (D) 5.0
3. For 1, x << ( ) coth x can be approximated as
(A) x (B)
2
x (C)
1
x
(D)
2
1
x
4.
( )
0
sin 2
lim
?
?
? ?
is:
(A) 0.5 (B) 1 (C) 2 (D) not defined
5. Which one of the following functions is strictly bounded?
(A)
2
1
x
(B)
x
e (C)
2
x (D)
2
x
e
-
6. For the function ,
x
e
-
the linear approximation around 2 x = is:
(A) ( )
2
3 x e
-
- (B) 1 x -
(C)
( )
2
3 2 2 1 2 x e
-
? ?
+ - +
? ?
(D)
2
e
-
7. An independent voltage source in series with an impedance
s s s
Z R jX = + delivers
a maximum average power to a load impedance
L
Z when
(A)
L s s
Z R jX = + (B)
L s
Z R =
(C)
L s
Z jX = (D)
L s s
Z R jX = -
1 2 3
x
1
2
3
y
-1
EC? GATE Paper 2007
8. The RC circuit shown in the figure is
(A) a low-pass filter   (B) a high-pass filter
(C) a band-pass filter (D) a band-reject filter
9. The electron and hole concentrations in an intrinsic semiconductor are
i
n per
3
cm at 300 K. Now, if acceptor impurities are introduced with a concentration of
A
N per
3
cm ( ) where
A i
N n >> , the electron concentration per
3
cm at 300 K will
be:
(A)
i
n (B)
i A
n N + (C)
A i
N n - (D)
2
i
A
n
N
10. In a p n
+
junction diode under reverse bias, the magnitude of electric field is
maximum at
(A) the edge of the depletion region on the p-side
(B) the edge of the depletion region on the n-side
(C) the p n
+
junction
(D) the centre of the depletion region on the n-side
11. The correct full wave rectifier circuit is:
(A) (B)
R
C
R
C
i
V
o
V
+
-
+
-
Input
Output
Input
Output
EC? GATE Paper 2007
(C) (D)
12. In a transconductance amplifier, it is desirable to have
(A) a large input resistance and a large output resistance
(B) a large input resistance and a small output resistance
(C) a small input resistance and a large output resistance
(D) a small input resistance and a small output resistance
13. X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two’s
complement format. The sum of X and Y represented in two’s complement format
using 6 bits is:
(A) 100111 (B) 001000 (C) 000111 (D) 101001
14. The Boolean function Y AB CD = + is to be realized using only 2-input NAND
gates. The minimum number of gates required is:
(A) 2 (B) 3 (C) 4 (D) 5
15. If the closed-loop transfer function of a control system is given as
( )
( )( )
5
,
2 3
s
T s
s s
-
=
+ +
then it is
(A) an unstable system  (B) an uncontrollable system
(C) a minimum phase system (D) a non-minimum phase system
16. If the Laplace transform of a signal ( ) y t is ( )
( )
1
,
1
Y s
s s
=
-
then its final value is:
(A) -1 (B) 0 (C) 1 (D) unbounded
17. If ( ) R t is the autocorrelation function of a real, wide-sense stationary random
process, then which of the following is NOT true?
(A) ( ) ( ) R R t t = - (B) ( ) ( ) 0 R R t = (C) ( ) ( ) R R t t = - -
(D) The mean square value of the process is ( ) 0 R
Input
Output
Input
Output
EC? GATE Paper 2007
18. If ( ) S f is the power spectral density of a real, wide-sense stationary random
process, then which of the following is ALWAYS true?
(A) ( ) ( ) 0 S S f = (B) ( ) 0 S f = (C) ( ) ( ) S f S f - = - (D) ( ) 0 S f df
8
-8
=
?
19. A plane wave of wavelength ? is traveling in a direction making an angle 30° with
positive x-axis and 90° with positive y-axis. The E
u r
field of the plane wave can be
represented as ( ) is constant
o
E
(A)
µ
3
0
j t x z
E yE e
p p
?
? ?
? ?
- - ? ?
? ?
? ?
=
u r
(B)
µ
3
0
j t x z
E yE e
p p
?
? ?
? ?
- - ? ?
? ?
? ?
=
u r
(C)
µ
3
0
j t x z
E yE e
p p
?
? ?
? ?
+ + ? ?
? ?
? ?
=
u r
(D)
µ
3
0
j t x z
E yE e
p p
?
? ?
? ?
- + ? ?
? ?
? ?
=
u r
20. If C is a closed curve enclosing a surface S, then the magnetic field intensity , H
u r
the current density J
r
and the electric flux density D
u r
are related by
(A) . .
s c
D
H ds J dl
t
? ?
?
= + ? ?
? ?
?
? ?
?? ?
u r
u r r r r
Ñ
(B) . .
c s
D
H dl J d ds
t
? ?
?
= + ? ?
? ?
?
? ?
? ??
u r
r u r r r
Ò
(C) . .
s c
D
H ds J dl
t
? ?
?
= + ? ?
? ?
?
? ?
?? ?
u r
u r r r r
Ò
(D) . .
c s
D
H dl J ds
t
? ?
?
= + ? ?
? ?
?
? ?
? ??
u r
u r r r r
Ñ
Q.21 – Q.75 Carry Two Marks Each
21. It is given that
1 2
, ,....
M
X x X are M non-zero, orthogonal vectors. The dimension of
the vector space spanned by the 2M vectors
1 2 1 2
, ,... , , ,...
M M
X X X X X X - - - is:
(A) 2M (B) M + 1 (C) M
(D) dependent on the choice of
1 2
, ,...
M
X X X
22. Consider the function ( )
2
2. f x x x = - - The maximum value of ( ) f x in the closed
interval 4,4 - ? ?
? ?
is:
(A) 18 (B) 10
(C) -2.25 (D) indeterminate
23. An examination consists of two papers, Paper 1 and Paper 2. The probability of
failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed
in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student
failing in both the papers is:
(A) 0.5 (B) 0.18 (C) 0.12 (D) 0.06
EC? GATE Paper 2007
24. The solution of the differential equation
2
2
2
2
d y
k y y
dx
= - under the boundary
conditions (i)
1
y y = at 0 x = and (ii)
2
y y = at x = 8 , where , k
1
y and
2
y are
constants, is
(A) ( )
( )
2
1 2 2
exp y y y x k y = - - + (B) ( ) ( )
2 1 1
exp y y y x k y = - - +
(C) ( ) ( )
1 2 1
sinh y y y x k y = - + (D) ( ) ( )
1 2 2
exp y y y x k y = - - +
25. The equation
3 2
4 4 0 x x x - + - = is to be solved using the Newton-Raphson
method. If 2 x = is taken as the initial approximation of the solution, then the
next approximation using this method will be:
(A)
2
3
(B)
4
3
(C) 1 (D)
3
2
26. Three functions ( ) ( ) ( )
1 2 3
, and , f t f t f t
which are zero outside the interval [0,T],
are shown in the figure. Which of the
following statements is correct?
(A) ( ) ( )
1 2
and  f t f t are orthogonal
(B) ( ) ( )
1 3
and  f t f t are orthogonal
(C) ( ) ( )
2 3
and  f t f t are orthogonal
(D) ( ) ( )
1 2
and  f t f t are orthonormal
27. If the semi-circular contour D of radius 2 is as shown in the figure, then the value
of the integral
( )
2
1
1
D
ds
s -
? Ñ
is:
(A) jp (B) -jp (C) -p (D) p
t
t
t
2
-2
1
2
-1
1
-3
( )
1
f t
( )
2
f t
( )
3
f t
0
3
T
2
3
T
T
j?
j2
D
2 0
0
s
-j2
```
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## GATE Past Year Papers for Practice (All Branches)

380 docs|127 tests

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