Indian Institute of Technology Mumbai (IIT-M) 2009 Other Bachelor

8. The magnitude plot of a rational transfer function G(s) with real coefficients is
shown beneath. When of the subsequent compensators has such a magnitude plot?
(A) Lead compensator (B) Lag compensator
(C) PID compensator (D) Lead-lag compensator
9. A white noise process X(t) with two-sided power spectral density 1×10-10 W/Hz is
input to a filter whose magnitude squared response is shown beneath
The power of the output process Y(t) is provided by
(A) seven five ×10- W (B) six 1×10- W (C) six two ×10- W (D) five 1×10- W
10. Which of the subsequent statements is actual regarding the fundamental mode of the
metallic waveguides shown?
(A) Only P has no cutoff-frequency (B) Only Q has no cutoff-frequency
(C) Only R has no cutoff-frequency (D) all 3 have cutoff-frequency
P. Coaxial Q. Cylindrical
R:Rectangular
-40dB
20dB
G(jw)
logw
-10kHz 10kHz
1
( )2
H f
X(t) Y (t)
f
EC½ GATE Paper 2009 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. explain this ques. paper at www.gateforum.com. Page three of 15
11. A fair coin is tossed 10times. What is the probability that ONLY the 1st two
tosses will yield heads?
(A)
2
1
2


 
 
(B)
2
10
2
1
C
2


 
 
(C)
10
1
2


 
 
(D)
10
10
2
1
C
2


 
 
12. If the power spectral density of stationary random process is a sine-squared
function of frequency, the shape of its autocorrelation is
(A) (B) (C) (D)
13. ( ) ( ) 1
0 1
unit
circle
1 f z
If f z c c z , then dz is provided by
z
- +
= + 

(A) 2pc1 (B) ( ) 0 2p one + c (C) one 2pjc (D) ( ) 0 2pj one + c
14. In the interconnection of ideal sources shown in the figure, it is known that the
60V source is absorbing power
Which of the subsequent can be the value of the current source
?
(A) 10A (B) 13A (C) 15A (D) 18A
15. The ratio of the mobility to the diffusion coefficient in a semiconductor has the

Earning:   Approval pending.