Analysis of complex variables - Engineering Mathematics - Biomedical Engineering Previous Year Questions

1

2020 · Biomedical Engineering · Engineering Mathematics · Analysis of complex variables

Biomedical Engineering (BM) 2020

The value of the integral evaluated over the contour C: |z| = 3/2 is ________
\[ \frac{1}{2\pi j} \oint \frac{z}{(z-1)(z-2)} dz \]

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2

2022 · Biomedical Engineering · Engineering Mathematics · Analysis of complex variables

Biomedical Engineering (BM) 2022

In the complex z-domain, the value of the integral \(\oint_{C} \frac{z^3 - 9}{3z - i} dz\) is

A

\(\frac{2\pi}{81} - 6i\pi\)

B

\(\frac{2\pi}{81} + 6i\pi\)

C

\(-\frac{2\pi}{81} + 6i\pi\)

D

\(-\frac{2\pi}{81} - 6i\pi\)

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3

2023 · Biomedical Engineering · Engineering Mathematics · Analysis of complex variables

Biomedical Engineering (BM) 2023

The function \(f(Z) = \frac{1}{Z-1}\) of a complex variable Z is integrated on a closed contour in an anti-clockwise direction. For which of the following contours, does this integral have a non-zero value?

A

\(|Z - 2| = 0.01\)

B

\(|Z - 1| = 0.1\)

C

\(|Z - 3| = 5\)

D

\(|Z| = 2\)

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4

2024 · Biomedical Engineering · Engineering Mathematics · Analysis of complex variables

Biomedical Engineering (BM) 2024

What is the value of the following complex line integral counter-clockwise? \(\oint_{|z|=3} \frac{8}{z(z-2)(z-4)} dz\)

A

\(+j2\pi\)

B

\(-j2\pi\)

C

\(-j10\pi\)

D

\(+j10\pi\)

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5

2024 · Biomedical Engineering · Engineering Mathematics · Analysis of complex variables

Biomedical Engineering (BM) 2024

What is the value of the following complex line integral counter-clockwise? \[ \oint_{|z|=3} \frac{8}{z(z-2)(z-4)} \, dz \]

A

\(+j2\pi\)

B

\(-j2\pi\)

C

\(-j10\pi\)

D

\(+j10\pi\)

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6

2024 · Biomedical Engineering · Engineering Mathematics · Analysis of complex variables

Biomedical Engineering (BM) 2024

What is the value of the following integral using the residue integration method? \[ \int_{-\infty}^{\infty} \frac{dx}{1+x^4} \]

A

\(\frac{\pi}{\sqrt{2}} \)

B

\(\frac{\pi}{2\sqrt{2}} \)

C

\(\frac{\pi}{4} \)

D

\(\frac{\pi}{2} \)

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7

2025 · Biomedical Engineering · Engineering Mathematics · Analysis of complex variables

Biomedical Engineering (BM) 2025

Which of the following is/are CORRECT about the value of \( y = \log_e(-e^x) \), where x is a real number.

A

y is real valued

B

y is complex valued

C

\(y = x \pm in\pi \), where n is an odd integer and \(i = \sqrt{-1} \)

D

\(y = x \pm in\pi \), where n is an even integer and \(i = \sqrt{-1} \)

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