e.
 If the state variable description of a discrete-time system is given as then, the roots of the characteristic equation of the system can be obtained as _______.
(A) 4 and 1       (B) 3 and 2
(C) 4 and 2       (D) 3 and 1
 
f.
 If the z - transform of x(k) is X(z), then z - transform of will be ___________.
(A)    (B)   
(C)    (D)   
 
g.
 The system described by the state-space equations
and is____________.
(A) controllable and unobservable          (B) controllable and observable
(C) uncontrollable and unobservable      (D) uncontrollable and observable
 
h.

Considering the mapping between the s - plane and the z - plane of Fig.2, the points a, b and c in the s-plane will map to the _________ of the z-plane whereas the points d and e will map to the _________ of the z-plane.
(A) Interior of the unit circle,      periphery of the unit circle.
(B) Periphery of the unit circle,  origin of the unit circle.
(C) Periphery of the unit circle,  interior of the unit circle.
(D) Interior of the unit circle,     origin of the unit circle.
PART I
Answer any THREE Questions. Each question carries 14 marks.
Q.2
 For the system shown in Fig.3, determine the final value of c(t) with the input r(t) as a unit impulse function and with T = 0.2 sec. (14)
2
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