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1
GATE ECE 2025
MCQ (More than One Correct Answer)
+2
-0

Which of the following statements involving contour integrals (evaluated counter-clockwise) on the unit circle $C$ in the complex plane is/are TRUE?

A
$\oint_C e^z d z=0$
B
$\oint_C z^n d z=0$, where $n$ is an even integer
C
$\oint_C \cos z d z \neq 0$
D
$\oint_C \sec z d z \neq 0$
2
GATE ECE 2024
MCQ (Single Correct Answer)
+2
-1.33

Let $z$ be a complex variable. If $f(z)=\frac{\sin(\pi z)}{z^{7}(z-2)}$ and $C$ is the circle in the complex plane with $|z|=3$ then $\oint\limits_{C} f(z)dz$ is _______.

A

$ \pi^2 j $

B

$ j\pi\left(\frac{1}{2}-\pi\right) $

C

$ j\pi\left(\frac{1}{2}+\pi\right) $

D

$-\pi^2 j$

3
GATE ECE 2022
MCQ (More than One Correct Answer)
+2
-0

Consider the following series :

$$\sum\limits_{n = 1}^\infty {{{{n^d}} \over {{c^n}}}} $$

For which of the following combinations of c, d values does this series converge?

A
c = 1, d = $$-$$1
B
c = 2, d = 1
C
c = 0.5, d = $$-$$10
D
c = 1, d = $$-$$2
4
GATE ECE 2018
Numerical
+2
-0
The contour C given below is on the complex plane $$z = x + jy$$, where $$j = \sqrt { - 1} $$. GATE ECE 2018 Engineering Mathematics - Complex Variable Question 6 English The value of the integral $${1 \over {\pi j}}\oint\limits_C {{{dz} \over {{z^2} - 1}}} $$ is ________________.
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GATE ECE Subjects
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics