[1] The system represented by the input-output relationship y(t)=

^{5t}∫_{-∞ }x(τ)dτ, t>0 is
(a) Linear and casual

(b) Linear but not casual

(c) Casual but not linear

(d) Neither linear nor casual

[2] For the system 2/(s+1), the approximate time taken for a step response to reach 98% of its final value is

(a) 1s

(b) 2s

(c) 4s

(d) 8s

[3] Given the finite length input x[n] and the corresponding finite length output y[n] of an LTI system as shown below, the impulse response h[n] of the system is

(a) h[n]={1,0,0,1}

(b) h[n]={1,0,1}

(c) h[n]={1,1,1,1}

(d) h[n]={1,1,1}

[4] The frequency response of G(s)=1/[s(s+1)(s+2)] plotted in the complex G(jω) plane (for 0< ω<∞) is....Options A, B, C, D are given below

A.

[5] The system x=Ax+Bu with

A=

B=

(a) Stable and controllable

(b) Stable but uncontrollable

(c) Unstable but controllable

(d) Unstable and uncontrollable

[6] The characteristic equation of a closed-loop system is a(s+1)(s+3)+k(s+2)=0,k>0. Which of the following statements is true?

(a) Its roots are always real

(b) It cannot have a breakaway point in the range -1<Re[s]<0

(c) Two of its roots tend to infinity along the asymptotes Re[s]=-1

(d) It may have complex roots in the right half plane

[7] The frequency response of a linear system G(jω) is provided in the tabular form below

|G(jω)| | 1.3 | 1.2 | 1.0 | 0.8 | 0.5 | 0.3 |

∠G(jω) | -130° | -140° | -150° | -160° | -180° | -200° |

(a) 6dB and 30°

(b) 6dB and -30°

(c) -6dB and 30°

(d) -6dB and -30°

[8] An openloop system represented by the transfer function G(s) = [(s+1)/(s+2)(s+3)] is

a) Stable and of the minimum phase type

b) Stable and of the non-minimum phase type

c) Unstable and of the minimum phase type

d) Stable and of the non-minimum phase type

[9] The open loop transfer function G(s) of a unity feedback control system is given as, G(s)=[ k(s+2/3) / s

^{2}(s+2) ] From the root locus, it can be inferred that when k tends to positive infinity.
(a) Three roots with nearly equal real parts exist on the left half of the s-plane

(b) One real root is found on the right half of the s-plane

(c) The root loci cross the jω axis for a finite value of k; k not equal to 0

(d) Three real roots are found on the right half of the s-plane

[10] The response h(t) of a linear time invariant system to an impulse δ(t), under initially relaxed condition is h(t) = e

^{-t}+e^{-2t}. The response of this system for a unit step input u(t) is
(a) u(t)+e

^{-t}+e^{-2t}
(b) (e

^{-t}+e^{-2t}) u(t)
(c) (1.5-e

^{-t}-0.5e^{-2t}) u(t)
(d) e

^{-t}δ(t)+e^{-2t}u(t)
Question no. 8 the system is minimum phase system because all the poles and zero lie in the left half s-plane

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