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

1. For the function F (s) = (s^{2}+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

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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 =(s

^{2}+s+1)/(s+5)(s+3) |s=0 =1/15.

2. For the question 1, the co-efficient of 1/(s+5) is?

a) 1.1

b) 2.1

c) 3.1

d) 4.1

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

^{2}+s+1)/s(s+3) |s=-5 =2.1.

3. For the question 1, co-efficient of 1/(s+3) is?

a) -1.17

b) 1.17

c) -2.27

d) 2.27

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

^{2}+s+1)/s(s+5) |s=-3 = -1.17.

4. The partial fraction expansion of the function in question 1 is?

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)

View Answer

Explanation: The values of A, B,C are A = 1/15, B = 2.1, C = -1.17. Partial fraction expansion of the function in question 1 is (s

^{2}+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(s^{2}+2s+5) , after splitting this function into the partial fractions, 1/s co-efficient is?

a) 1

b) 2

c) 3

d) 4

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

^{2}+2s+5) )=1.

6. For the question 5, the co-efficient of 1/(s+1-j2) is?

a) 1/2

b) -1/2

c) 1/4

d) -1/4

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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 question 5, determine the co-efficient of 1/(s+1-j2)?

a) -1/4

b) 1/4

c) -1/2

d) 1/2

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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. The expression of F (s) after splitting into partial fractions in the question 5 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)

View Answer

Explanation: The expression of F (s) after splitting into partial fractions in the question 5 is

(s+5)/s(s

^{2}+2s+5) =1/s-1/2(s+1-j2) -1/2(s+1+j2).

9. The inverse transform of F (s) in the question 5 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}

View Answer

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) ke^{at} u(t)

c) ke^{-at} u(t-a)

d) ke^{at} u(t-a)

View Answer

Explanation: The inverse transform of the function k/(s) is k. The inverse transform of the function k/(s+a) is ke

^{at}u(t). k/(s+a) <—–> ke

^{at}u(t).

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