[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) / s2(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-tδ(t)+e-2tu(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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