# Network Theory Questions and Answers – Inverse Transforms

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

1. For the function F (s) = (s2+s+1)/s(s+5)(s+3), after splitting this function into partial fractions, the co-efficient of the term 1/s is?
a) 1/5
b) 1/10
c) 1/15
d) 1/20

Explanation: To obtain the constant A, multiply the given equation with (s) and putting s = 0. The co-efficient of the term 1/s is A = sF (s)|s=0 = (s2+s+1)/(s+5)(s+3)|s=0 =1/15.

2. For the function F (s) = (s2+s+1)/s(s+5)(s+3), after splitting this function into partial fractions, the co-efficient of 1/(s+5) is?
a) 1.1
b) 2.1
c) 3.1
d) 4.1

Explanation: To obtain the constant B, multiply the given equation with (s+5) and putting s = -5. B = (s + 5)F (s) |s=-5 = (s2+s+1)/s(s+3)|s=-5 = 2.1.

3. For the function F (s) = (s2+s+1)/s(s+5)(s+3), after splitting this function into partial fractions, co-efficient of 1/(s+3) is?
a) -1.17
b) 1.17
c) -2.27
d) 2.27

Explanation: To obtain the constant C, multiply the given equation with (s+3) and putting s = -3. C = (s + 3)F (s)|s = -3 = (s2+s+1)/s(s+5)|s=-3 = -1.17.

4. For the function F (s) = (s2+s+1)/s(s+5)(s+3), after splitting this function into partial fractions. Find the partial fraction expansion of the function.
a) 1/15s-2.1/(s+5)+1.17/(s+3)
b) 1/15s-2.1/(s+5)-1.17/(s+3)
c) 1/15s+2.1/(s+5)+1.17/(s+3)
d) 1/15s+2.1/(s+5)-1.17/(s+3)

Explanation: The values of A, B,C are A = 1/15, B = 2.1, C = -1.17. Partial fraction expansion of the function is (s2+s+1)/s(s+5)(s+3) =1/15s+2.1/(s+5)-1.17/(s+3).

5. For the function F (s) = (s+5)/s(s2+2s+5), after splitting this function into the partial fractions, 1/s co-efficient is?
a) 1
b) 2
c) 3
d) 4

Explanation: To obtain the constant A, multiply the given equation with (s) and putting s = 0. A= sF(s)|s=0 = (s+5)/((s2+2s+5))=1.

6. For the function F (s) = (s+5)/s(s2+2s+5), after splitting this function into the partial fractions, the co-efficient of 1/(s+1-j2) is?
a) 1/2
b) -1/2
c) 1/4
d) -1/4

Explanation: To obtain the constant B, multiply the given equation with (s+1-j2) and putting s = -1+j2. B = (s + 1 – j2)F (s)|s = (-1+j2) = (s+5)/s(s+1+j2)|s=-1+j2 = -1/2.

7. For the function F (s) = (s+5)/s(s2+2s+5), after splitting this function into the partial fractions, determine the co-efficient of 1/(s+1-j2)?
a) -1/4
b) 1/4
c) -1/2
d) 1/2

Explanation: To obtain the constant B*, multiply the given equation with (s+1+j2) and putting s = -1-j2. B* = (s + 1 + j2)F (s)|s = -1 – j2 = (s+5)/s(s+1-j2)|s=-1-j2 = -1/2.

8. For the function F (s) = (s+5)/s(s2+2s+5), after splitting this function into the partial fractions. What is the expression of F (s) after splitting into partial fractions is?
a) 1/s-1/2(s+1-j2) -1/2(s+1+j2)
b) 1/s+1/2(s+1-j2) -1/2(s+1+j2)
c) 1/s+1/2(s+1-j2) +1/2(s+1+j2)
d) 1/s-1/2(s+1-j2) +1/2(s+1+j2)

Explanation: The expression of F (s) after splitting into partial fractions is (s+5)/s(s2+2s+5) = 1/s-1/2(s+1-j2) -1/2(s+1+j2).

9. For the function F (s) = (s+5)/s(s2+2s+5), after splitting this function into the partial fractions. What is the inverse transform of F (s) is?
a) 1+ 1/2 e(-1+j2)t-1/2 e(-1-j2)t
b) 1+ 1/2 e(-1+j2)t+1/2 e(-1-j2)t
c) 1- 1/2 e(-1+j2)t-1/2 e(-1-j2)t
d) 1- 1/2 e(-1+j2)t+1/2 e(-1-j2)t

Explanation: The inverse transform F(s) is f(t), f (t) = L-1(F (s)) = L-1(1/s-1/2(s+1-j2) – 1/2(s+1+j2)) = 1-1/2 e(-1+j2)t-1/2 e(-1-j2)t.

10. The inverse transform of the function k/(s+a) is?
a) ke-at u(t)
b) keat u(t)
c) ke-at u(t-a)
d) keat u(t-a)

Explanation: The inverse transform of the function k/(s) is k. The inverse transform of the function k/(s+a) is keat u(t). k/(s+a) <—–> keat u(t).

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