# Problems on Initial and Final Value Theorem MCQ’s

This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Problems on Initial and Final Value Theorem”.

1. What is the steady state value of F (t), if it is known that F(s) = 1(s−1)(s+2)?
a) 1
b) –12
c) 12
d) Cannot be determined

2. What is the steady state value of F (t), if it is known that F(s) = 1(s+2)2(s+4)?
a) 116
b) Cannot be determined
c) 0
d) 18

3. What is the steady state value of F (t), if it is known that F(s) = 2s(S+1)(s+2)(s+3)?
a) 12
b) 13
c) 14
d) Cannot be determined

4. What is the steady state value of F (t), if it is known that F(s) = 10(s+1)(s2+1)?
a) -5
b) 5
c) 10
d) Cannot be determined

5. The inverse Laplace transform of F(s) = 2s2+3s+2 is ______________
a) -2e-2t + 2e-t
b) 2e-2t + 2e-t
c) -2e-2t – 2e-t
d) 2e-t + e-2t

6. The inverse Laplace transform of F(s) = 3s+5s2+7 is _____________
a) 3 sin (7–√t) – 57√ cos (7–√ t)
b) 3 sin (7–√t) + 57√ cos (7–√ t)
c) 3 cos (7–√t) + 57√ sin (7–√ t)
d) 3 cos (7–√t) – 57√ sin (7–√ t)

7. What is the steady state value of F (t), if it is known that F(s) = b/(s(s+1)(s+a)), where a>0?
a) ba
b) ab
c) 1
d) Cannot be determined

8. The inverse Laplace transform of F(s) = 2s+ce−bs is _____________
a) 2e-k (t+b) u (t+b)
b) 2e-k (t-b) u (t-b)
c) 2ek (t-b) u (t-b)
d) 2ek (t-b) u (t+b)

9. The inverse Laplace transform of F(s) = 5s2−9 is ______________
a) 16e3t+56e−3t
b) 16e3t–56e−3t
c) 56e3t+56e−3t
d) 56e3t–56e−3t

10. Given a sinusoidal voltage that has a peak to peak value of 100 V. The RMS value of the sinusoidal voltage is ___________
a) 50 V
b) 70.7 V
c) 35.35 V
d) 141.41 V

11. Convolution of step signal 100 times that is 100 convolution operations. The Laplace transform is ______________
a) 1s100
b) 1s50
c) 1
d) s100

12. The inverse Laplace transform of F(s) = e−3ss(s2+3s+2) is ______________
a) {0.5 + 0.5e-2(t+3) – e-(t+3)} u (t+3)
b) {0.5 + 0.5e-2(t+3) – e-(t-3)} u (t-3)
c) {0.5 – 0.5e-2(t-3) – e-(t-3)} u (t-3)
d) 0.5 + 0.5e-2t – e-t)

13. The Laplace transform of F(t) = sin(2t)cos(2t) is ______________
a) 42(s2+16)
b) 1s+4–2s+2+1s
c) 2s3
d) 12s+s2(s2+36)

14. For the circuit given below, the Time-constant is __________

a) 1.5
b) 1.25
c) 2.5
d) 2.25

15. In a dual slop integrating type digital voltmeter, the first integrating is carried out for 50 periods of the supply frequency of 50 Hz. If the reference voltage used is 10 V, the total conversion time for an input of 40 V is?
a) 3 s
b) 2 s
c) 4 s
d) 1 s