# Operational Transforms MCQ’s

This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Operational Transforms”.

1. The Laplace transform of f_{1} (t) + f_{2} (t) is?

a) F_{1}(s) + F_{2}(s)

b) F_{1}(s) – F_{2}(s)

c) F_{1}(s) – 2F_{2}(s)

d) F_{1}(s) + 2F_{2}(s)

2. Find the Laplace transform of the function f (t) = 4t^{3} + t^{2} – 6t + 7.

a) 24/s^{4} + 2/s^{3} + 6/s^{2} + 7/s

b) 24/s^{4} – 2/s^{3} – 6/s^{2} + 7/s

c) 24/s^{4} + 2/s^{3} – 6/s^{2} + 7/s

d) 24/s^{4} – 2/s^{3} + 6/s^{2} + 7/s

3. The Laplace transform of kf(t) is?

a) F(s)

b) kF(s)

c) F(s)/k

d) k^{2} F(s)

4. Find the Laplace transform of the function f(t) = cos2t.

a) (2s^{2}+4)/2s(s^{2}-4)

b) (2s^{2}-4)/2s(s^{2}-4)

c) (2s^{2}-4)/2s(s^{2}+4)

d) (2s^{2}+4)/2s(s^{2}+4)

5. Find the Laplace transform of e^{at}sinbt.

a) b/((s-a)^{2}+b^{2})

b) b/((s+a)^{2}+b^{2})

c) b/((s+a)^{2}-b^{2})

d) b/((s-a)^{2}-b^{2})

6. Find the Laplace transform of ramp function r (t) = t.

a) 1/s

b) 1/s^{2}

c) 1/s^{3}

d) 1/s^{4}

7. Find the Laplace transform of the function f (t) = 3t^{4} – 2t^{3} + 4e^{-3t} – 2sin5t + 3cos2t.

a) 72/s^{5} – 12/s^{4} + 4/(s+3)+10/(s^{2}+25)+3s/(s^{2}+4)

b) 72/s^{5} – 12/s^{4} + 4/(s+3)-10/(s^{2}+25)+3s/(s^{2}+4)

c) 72/s^{5} – 12/s^{4} – 4/(s+3)+10/(s^{2}+25)+3s/(s^{2}+4)

d) 72/s^{5} – 12/s^{4} – 4/(s+3)-10/(s^{2}+25)+3s/(s^{2}+4)

8. Find the Laplace transform of (t + 2)^{2} e^{t}.

a) 2/(s-1)^{3} – 2/(s-1)^{2} + 4/(s-1)

b) 2/(s-1)^{3} – 2/(s-1)^{2} – 4/(s-1)

c) 2/(s-1)^{3} + 2/(s-1)^{2} + 4/(s-1)

d) 2/(s-1)^{3} + 2/(s-1)^{2} – 4/(s-1)

9.Find the Laplace transform of the function f (t) = tsin2t.

a) 4s/(s^{2}+4)^{2}

b) -4s/(s^{2}+4)^{2}

c) -4s/(s^{2}-4)^{2}

d) 4s/(s^{2}-4)^{2}

10.If u (t) = 1 for t >= 0 and u (t) = 0 for t < 0, determine the Laplace transform of [u (t) – u (t – a)].

a) 1/s(1+e^{(-as)})

b) 1/s(1-e^{(-as)})

c) 1/s(1+e^{as})

d) 1/s(1-e^{as})

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