GATE Exam  >  GATE Notes  >  Electronics and Communication Engineering (EC) 2009 GATE Paper without solution (unsolved)

Electronics and Communication Engineering (EC) 2009 GATE Paper without solution (unsolved) PDF Download

Download, print and study this document offline
Please wait while the PDF view is loading
 Page 1


        EC? GATE Paper 2007         www.gateforum.com  
 
© All rights reserved by GATE Forum Educational Services Pvt. Ltd.  No part of this booklet may be reproduced or utilized in any form without the 
written permission. Discuss this questions paper at www.gateforum.com.                                                                  Page 1 of 19 
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         www.gateforum.com  
 
© All rights reserved by GATE Forum Educational Services Pvt. Ltd.  No part of this booklet may be reproduced or utilized in any form without the 
written permission. Discuss this questions paper at www.gateforum.com.                                                                  Page 1 of 19 
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         www.gateforum.com  
 
© All rights reserved by GATE Forum Educational Services Pvt. Ltd.  No part of this booklet may be reproduced or utilized in any form without the 
written permission. Discuss this questions paper at www.gateforum.com.                                                                  Page 2 of 19 
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         www.gateforum.com  
 
© All rights reserved by GATE Forum Educational Services Pvt. Ltd.  No part of this booklet may be reproduced or utilized in any form without the 
written permission. Discuss this questions paper at www.gateforum.com.                                                                  Page 1 of 19 
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         www.gateforum.com  
 
© All rights reserved by GATE Forum Educational Services Pvt. Ltd.  No part of this booklet may be reproduced or utilized in any form without the 
written permission. Discuss this questions paper at www.gateforum.com.                                                                  Page 2 of 19 
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         www.gateforum.com  
 
© All rights reserved by GATE Forum Educational Services Pvt. Ltd.  No part of this booklet may be reproduced or utilized in any form without the 
written permission. Discuss this questions paper at www.gateforum.com.                                                                  Page 3 of 19 
 (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         www.gateforum.com  
 
© All rights reserved by GATE Forum Educational Services Pvt. Ltd.  No part of this booklet may be reproduced or utilized in any form without the 
written permission. Discuss this questions paper at www.gateforum.com.                                                                  Page 1 of 19 
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         www.gateforum.com  
 
© All rights reserved by GATE Forum Educational Services Pvt. Ltd.  No part of this booklet may be reproduced or utilized in any form without the 
written permission. Discuss this questions paper at www.gateforum.com.                                                                  Page 2 of 19 
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         www.gateforum.com  
 
© All rights reserved by GATE Forum Educational Services Pvt. Ltd.  No part of this booklet may be reproduced or utilized in any form without the 
written permission. Discuss this questions paper at www.gateforum.com.                                                                  Page 3 of 19 
 (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         www.gateforum.com  
 
© All rights reserved by GATE Forum Educational Services Pvt. Ltd.  No part of this booklet may be reproduced or utilized in any form without the 
written permission. Discuss this questions paper at www.gateforum.com.                                                                  Page 4 of 19 
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         www.gateforum.com  
 
© All rights reserved by GATE Forum Educational Services Pvt. Ltd.  No part of this booklet may be reproduced or utilized in any form without the 
written permission. Discuss this questions paper at www.gateforum.com.                                                                  Page 1 of 19 
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         www.gateforum.com  
 
© All rights reserved by GATE Forum Educational Services Pvt. Ltd.  No part of this booklet may be reproduced or utilized in any form without the 
written permission. Discuss this questions paper at www.gateforum.com.                                                                  Page 2 of 19 
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         www.gateforum.com  
 
© All rights reserved by GATE Forum Educational Services Pvt. Ltd.  No part of this booklet may be reproduced or utilized in any form without the 
written permission. Discuss this questions paper at www.gateforum.com.                                                                  Page 3 of 19 
 (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         www.gateforum.com  
 
© All rights reserved by GATE Forum Educational Services Pvt. Ltd.  No part of this booklet may be reproduced or utilized in any form without the 
written permission. Discuss this questions paper at www.gateforum.com.                                                                  Page 4 of 19 
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         www.gateforum.com  
 
© All rights reserved by GATE Forum Educational Services Pvt. Ltd.  No part of this booklet may be reproduced or utilized in any form without the 
written permission. Discuss this questions paper at www.gateforum.com.                                                                  Page 5 of 19 
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 
Read More

FAQs on Electronics and Communication Engineering (EC) 2009 GATE Paper without solution (unsolved)

1. What is Electronics and Communication Engineering (EC)?
Ans. Electronics and Communication Engineering (EC) is a branch of engineering that deals with the design, development, and application of electronic devices, circuits, and communication systems. It involves the study of subjects such as electronics, digital systems, microprocessors, communication theory, and signal processing.
2. What is the significance of Electronics and Communication Engineering in today's world?
Ans. Electronics and Communication Engineering plays a crucial role in today's world as it is responsible for the design and development of various electronic devices and communication systems. It is the backbone of the modern telecommunications industry and is essential for the functioning of various sectors such as telecommunications, information technology, defense, healthcare, and entertainment.
3. How can one pursue a career in Electronics and Communication Engineering?
Ans. To pursue a career in Electronics and Communication Engineering, one must have a strong foundation in mathematics and physics. After completing the 10+2 education with science stream, one can appear for engineering entrance exams such as JEE Main or state-level engineering entrance exams. Upon qualifying, they can enroll in a Bachelor's degree program in Electronics and Communication Engineering. After completing the undergraduate program, one can further specialize by pursuing a Master's or Ph.D. in the field.
4. What are the job prospects for Electronics and Communication Engineering graduates?
Ans. Electronics and Communication Engineering graduates have a wide range of job opportunities. They can work in industries involved in the design and manufacturing of electronic devices, telecommunications companies, IT companies, research organizations, defense organizations, and government agencies. Some common job roles for EC graduates include Electronics Engineer, Communication Engineer, Network Engineer, Embedded Systems Engineer, and Research Scientist.
5. Is it necessary to pursue higher studies after completing a Bachelor's degree in Electronics and Communication Engineering?
Ans. Pursuing higher studies after completing a Bachelor's degree in Electronics and Communication Engineering is not mandatory but can be beneficial for career growth. Higher studies provide opportunities for specialization in specific areas, research experience, and enhanced knowledge. It can open up avenues for higher-level job roles, teaching positions, and research opportunities. However, it ultimately depends on an individual's career goals and aspirations.
Download as PDF

Top Courses for GATE

Related Searches

practice quizzes

,

mock tests for examination

,

Free

,

Electronics and Communication Engineering (EC) 2009 GATE Paper without solution (unsolved)

,

Summary

,

shortcuts and tricks

,

Electronics and Communication Engineering (EC) 2009 GATE Paper without solution (unsolved)

,

Previous Year Questions with Solutions

,

pdf

,

past year papers

,

Semester Notes

,

video lectures

,

Electronics and Communication Engineering (EC) 2009 GATE Paper without solution (unsolved)

,

ppt

,

Extra Questions

,

Viva Questions

,

study material

,

Sample Paper

,

Objective type Questions

,

Important questions

,

MCQs

,

Exam

;