316. Consider a unity-gain feedback control system whose open-loop transfer function is as +1 G(s) = s2 The value of 'a' so that the system has a phase-margin equal to ? is approximately equal to

A.2.4

B.1.4

C.0.84

D.0.74

317. Consider a unity-gain feedback control system whose open-loop transfer function is as +1 G(s) = s2 With the value of 'a' set for a phase-margin of ?, the value of unit-4 K(s + 1)(s3 + as2 + 2s + 1) impulse response of the open-loop system at t = 1 second is equal to

A.3.4

B.2.4

C.1.84

D.1.74

318. Which one of the following function is strictly bounded?

A. fi(t) and f2(t) are orthogonal

B.fi(t) and f3(t) are orthogonal

C.f2(t) and f3(t) are orthogonal

D.fi(t) and f2(t) are orthonomal

319. Four the function approximation around

A. (3 - x)e-2

B. 1 ? x

C. [3 +21i -(1+x]e-2

D. e-2

320. If the closed-loop transfer function of a control system is given as s- 5 T(s) = , then it is (s + 2)(s + 3)

A. an unstable system

B. an uncontrollable system

C. a minimum phase system

D. a non-minimum phase system

321. Consider the function f(x) = x2 - x -2. The maximum value off(x) in the closed interval 1-4, 41 is

A.18

B.(c) -2.25

C.B

D. e2

322. The solution of the differential equation 2 d2Yk --2- = y - y2 under the boundary dx conditions (i) y = yi at x = 0 and (ii) y = y2 at x = 00, where k, y1 and y2 are constants, is

A. y = (y1 - y2) exp(-x/k2) + y2

B. y = (y2 - y1) exp(-x/k) + yi

C. y = (y1 - y2) sin h(x/k) + y1

D. y = (y1 - y2) exp(-x/k) + y2

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