1
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 _______.
2
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?
3
GATE ECE 2018
Numerical
+2
-0
The contour
C
given below is on the complex plane $$z = x + jy$$, where $$j = \sqrt { - 1} $$.
The value of the integral $${1 \over {\pi j}}\oint\limits_C {{{dz} \over {{z^2} - 1}}} $$ is ________________.
The value of the integral $${1 \over {\pi j}}\oint\limits_C {{{dz} \over {{z^2} - 1}}} $$ is ________________.Your input ____
4
GATE ECE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
An integral $${\rm I}$$ over a counter clock wise circle $$C$$ is given by $${\rm I} = \oint\limits_c {{{{z^2} - 1} \over {{z^2} + 1}}} \,\,{e^z}\,dz$$
If $$C$$ is defined as $$\left| z \right| = 3,$$ then the value of $${\rm I}$$ is
If $$C$$ is defined as $$\left| z \right| = 3,$$ then the value of $${\rm I}$$ is
Questions Asked from Marks 2
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