Explore topic-wise MCQs in Engineering Mathematics.

This section includes 9 Mcqs, each offering curated multiple-choice questions to sharpen your Engineering Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.

Find the inverse laplace transform of \(Y(s)=\frac{2s}{1-s^2}e^{-s}\).

A. -e-t + 1 + et – 1
B. -e-t + 1 – et + 1
C. -e-t + 1 + et + 1
D. -e-t + 1 – et – 1
Answer» E.
Discussion
2.

Find the inverse lapace of \(\frac{(s+1)}{[(s+1)^2+4][(s+1)^2+1]}\).

A. 1⁄3 et [Cos(t) – Cos(2t)].
B. 1⁄3 e-t [Cos(t) + Cos(2t)].
C. 1⁄3 et [Cos(t) + Cos(2t)].
D. 1⁄3 e-t [Cos(t) – Cos(2t)].
Answer» E.
Discussion
3.

Find the value of x(0) if \(X(s)=\frac{2s^2+5s+12/s}{s^3+4s^2+14s+20}\).

A. 5
B. 4
C. 12
D. 2
Answer» E.
Discussion
4.

Find the value of x(∞) if \(X(s)=\frac{2s^2+5s+12/s}{s^3+4s^2+14s+20}\).

A. 5
B. 4
C. 12⁄20
D. 2
Answer» D. 2
Discussion
5.

Initial value theorem states that ___________

A. x(0)=\(\lim_{x\rightarrow ∞} sX(s)\)
B. x(∞)=\(\lim_{x\rightarrow ∞} sX(s)\)
C. x(0)=\(\lim_{x\rightarrow 0} sX(s)\)
D. x(∞)=\(\lim_{x\rightarrow 0} ⁡sX(s)\)
Answer» B. x(∞)=\(\lim_{x\rightarrow ∞} sX(s)\)
Discussion
6.

Final value theorem states that _________

A. x(0)=\(\lim_{x\rightarrow ∞} sX(s)\)
B. x(∞)=\(\lim_{x\rightarrow ∞} sX(s)\)
C. x(0)=\(\lim_{x\rightarrow 0} sX(s)\)
D. x(∞)=\(\lim_{x\rightarrow 0} ⁡sX(s)\)
Answer» E.
Discussion
7.

Find the inverse laplace transform of \(\frac{s}{(s^2+ 4)^2}\).

A. 1⁄4 sin(2t)
B. t2⁄4 sin(2t)
C. t⁄4 sin(2t)
D. t⁄4 sin(2t2)
Answer» D. t⁄4 sin(2t2)
Discussion
8.

Inverse Laplace transform of \(\frac{1}{(s+1)(s-1)(s+2)}\) is?

A. –1⁄2 et + 1⁄6 e-t + 1⁄3 e2t
B. –1⁄2 e-t + 1⁄6 et + 1⁄3 e-2t
C. 1⁄2 e-t – 1⁄6 et – 1⁄3 e-2
D. –1⁄2 e-t + 1⁄6 e-t + 1⁄3 e-2
Answer» C. 1⁄2 e-t – 1⁄6 et – 1⁄3 e-2
Discussion
9.

Time domain function of \(\frac{s}{a^2+s^2}\) is given by?

A. Cos(at)
B. Sin(at)
C. Cos(at)Sin(at)
D. Sin(t)
Answer» B. Sin(at)
Discussion