Signal & System UNIT III & IV MCQ PDF

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UNIT:III Laplace Transform 1. Laplace of function f(t) is given by? F(s)=∫f(t)e−stdt F(t)=∫f(t)e−tdt f(s)=∫f(t)e−stdt f(t)=∫f(t)e−tdt Answer: A 2. Laplace transform if sin(at)u(t) is? s ⁄ a2+s2 a ⁄ a2+s2 s2 ⁄ a2+s2 a2 ⁄ a2+s2 Answer: B 3. Laplace transform if cos(at)u(t) is? s ⁄ a2+s2 a ⁄ a2+s2 s2 ⁄ a2+s2 a2 ⁄ a2+s2 Answer: A

4. Find the laplace transform of et Sin(t). aa2+(s+1)2 aa2+(s−1)2 s+1a2+(s+1)2 s+1a2+(s+1)2

Answer: B

5. . Laplace transform of t2 sin(2t). [12s2−16(s2+4)4] [3s2−4(s2+4)3] [12s2−16(s2+4)6] [12s2−16(s2+4)3] Answer: D

6. Find the laplace transform of y(t)=et.t.Sin(t)Cos(t). 4(s−1)[(s−1)2+4]2 2(s+1)[(s+1)2+4]2 4(s+1)[(s+1)2+4]2 2(s−1)[(s−1)2+4]2 Answer: D 7. Find the laplace transform of y(t)=e|t-1| u(t). 2s1−s2es 2s1+s2e−s 2s1+s2es 2s1−s2e−s Answer: D 8. Find the laplace transform of input x(t) if the system given by d3

⁄dt3 y(t) – 2 d2⁄dt2 y(t) –d⁄dt y(t) + 2y(t) = x(t), is stable.

s+1 s–1 s+2 s–2

Answer: B 9. Final value theorem states that _________ x(0)=limx→∞sX(s) x(∞)=limx→∞sX(s) x(0)=limx→0sX(s) x(∞)=limx→0sX(s)

Answer: D 10.Initial value theorem states that ___________ x(0)=limx→∞sX(s) x(∞)=limx→∞sX(s) x(0)=limx→0sX(s) x(∞)=limx→0sX(s) Answer: A 11.Find the value of x(∞) if X(s)=2s2+5s+12/ss3+4s2+14s+20. 5 4 12 ⁄20 2 Answer: c 12.Find the value of x(0) if X(s)=2s2+5s+12/ss3+4s2+14s+20. 5 4 12 2 Answer: D 13.Find the L(sin3 t). 34(s2+1)−14(s2+9) 34(s2+1)−34(s2+9)

34(s2+1)−94(s2+9) 34(s2−1)−34(s2+9) Answer: b 14.Find the L(e2t(1+t)2). 1s−2+2(s−2)3+2(s−2)2 3s−2+2(s−2)3+2(s−2)2 1s−2+2(s+2)3+2(s−2)2 1s−2+2(s−2)3 Answer: a 15.

Find the Laplace Transform of g(t) which has value (t-1)3 for t>1 and 0 for t - a ω / (s + a) 2 + ω2 with ROC σ > - a s + a / (s + a)2 + ω2 with ROC σ > - a Aω / s2 + ω2 with ROC σ > 0

Answer: C

s + a / (s + a)2 + ω2 with ROC σ > - a

18.According to the time-shifting property of Laplace Transform, shifting the signal in time domain corresponds to the ______ Multiplication by e-st in the time domain Multiplication by e-st in the frequency domain Multiplication by est in the time domain Multiplication by est in the frequency domain

Answer:

b. Multiplication by e-st in the frequency domain

19.Unilateral Laplace Transform is applicable for the determination of linear constant coefficient differential equations with ________ Zero initial condition Non-zero initial condition

Zero final condition Non-zero final condition Answer:

b. Non-zero initial condition

20.What should be location of poles corresponding to ROC for bilateral Inverse Laplace Transform especially for determining the nature of time domain signal? On L.H.S of ROC On R.H.S of ROC On both sides of ROC None of the above

Answer:

c. On both sides of ROC

21. Generally, the convolution process associated with the Laplace Transform in time domain results into________ Simple multiplication in complex frequency domain Simple division in complex frequency domain Simple multiplication in complex time domain Simple division in complex time domain ANSWER: a. Simple multiplication in complex frequency domain

22.When is the system said to be causal as well as stable in accordance to pole/zero of ROC specified by system transfer function? Only if all the poles of system transfer function lie in left-half of S-plane Only if all the poles of system transfer function lie in right-half of S-plane Only if all the poles of system transfer function lie at the centre of S-plane None of the above

ANSWER: a. Only if all the poles of system transfer function lie in lefthalf of

S-plane

23.Find the value of L(3^2t). 1s−2log(3) 1s+2log(3) 1s−3log(2) 1s+3log(2) Answer: a 24.Find Laplace transform of L{t^n } n!/Sn+1 2(n+1) !/Sn n!/Sn 4(n+1) !/Sn+1 Answer: a

25.Laplace Transform of Unit Step function is 1/s2 1/s3 1/s 1/1+s Answer: C 26.Laplace Transform of sinhωot is ω0 /s2 -w02

ω0 /s2+-w02

s /s2 -w02

s /s2+-w02 Answer: a 27. The Laplace transform of Periodic rectangular function shown in figure is

0

T

2T

A/S Tanh (ST/2) A/S Cot(ST/2) S/A Tanh (sT/2) A/S Sinh(ST/2)

Answer: a

28.If f(t) = eat, its Laplace Transform is given by? a ⁄ s2+a2 √π ⁄ 2√s 1 ⁄ s-a Does not exist

Answer: c 29.If f(t) = e^at sin(bt), then its Laplace transform is given by? s2-a2 ⁄ (s – a)2 b ⁄ (s + a)2 + b2 b ⁄ (s – a)2 + b2 Indeterminate Answer: c

UNIT:IV Z Transform 30.The Z-Transform X(z) of a discrete time signal x(n) is defined as ____________ ∑∞ 𝑛=0 𝑥(𝑛)𝑧 − 𝑛 ∑∞ 𝑛−∞ 𝑥(𝑛)𝑧 − 𝑛 ∑0𝑛−∞ 𝑥(𝑛)𝑧 − 𝑛 None of the mentioned Answer: b 31.What is the set of all values of z for which X(z) attains a finite value? Radius of convergence Radius of divergence Feasible solution None of the mentioned

Answer: a

32.What is the z-transform of the following finite duration signal? 2 + 4z + 5z2 + 7z3 + z4 2 + 4z + 5z2 + 7z3 + z5 2 + 4z-1 + 5z-2 + 7z-3 + z-5 2z2 + 4z + 5 +7z-1 + z-3

Answer: d 33.What is the ROC of the signal x(n)=δ(n-k), k>0? z=0 z=∞ Entire z-plane, except at z=0 Entire z-plane, except at z=∞ Answer: c

34.What is the z-transform of the signal x(n)=(0.5)nu(n)?

11−0.5z−1;ROC|z|>0.5 11−0.5z−1;ROC|z|0.5 11+0.5z−1;ROC|z|...