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

(D) 6, -1 + 3j,0, -1 - 3j

43. The feedback configuration and the pole-zero locations of ( ) 2
2
s 2s 2
G s
s 2s 2
- +
=
+ +
are
shown beneath. The root locus for negative values of k, i.e. for -¥ < k < 0, has
breakaway/break in points and angle of departure at pole P (with respect to the
positive real axis) equal to
(A) ± two and 0ºError! Not a valid link.
(B) ± two and 45º
(C) ± three and 0º
(D) ± three and 45º
0 t
h(t)
+
+
-
K G(s)
Im (s)
o ×
o ×P
Re(s)
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44. An LTI system having transfer function
2
2
s 1
s 2s 1
+
+ +
and input x(t)=sin(t+1) is in
steady state. The output is sampled at a rate wS rad/s to find the final output
{y(k)}. Which of the subsequent is true?
(A) y(.) is zero for all sampling frequencies wS
(B) y(.) is nonzero for all sampling frequencies wS
(C) y(.) is nonzero for ws>2, but zero for ws>2
(D) y(.) is zero for ws>2 but nonzero for ws>2
45. The unit step response of an under-damped 2nd order system has steady
state value of -2. Which 1 of the subsequent transfer functions has these
properties?
(A) 2
2.24
s 2.59s 1.12
-
+ +
(B) 2
3.82
s 1.91s 1.91
-
+ +
(C) 2
2.24
s 2.59s 1.12
-
- +
(D) 2
3.82
s 1.91s 1.91
-
- +
46. A discrete random variable X takes values from one to five with probabilities as shown
in the table. A learner calculates the mean of X and 3.5 and her teacher
calculates the variance of X as 1.5. Which of the subsequent statements is true?
( )
k one two three four 5
P X = k 0.1 0.2 0.4 0.2 0.1
(A) Both the learner and the teacher are right
(B) Both the learner and the teacher are wrong
(C) Both the learner is wrong but the teacher is right
(D) The learner is right but the teacher is wrong
47. A message signal provided by
( ) one 2
1 1
m t cos t sin t
2 2

Earning:   Approval pending.