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
-0.67
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
-0.67
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 Complex Variable (Marks 2)
Number in Brackets after Paper Indicates No. of Questions
GATE ECE Subjects
Signals and Systems
Representation of Continuous Time Signal Fourier Series Discrete Time Signal Fourier Series Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Transmission of Signal Through Continuous Time LTI Systems Discrete Time Linear Time Invariant Systems Sampling Continuous Time Signal Laplace Transform Discrete Fourier Transform and Fast Fourier Transform Transmission of Signal Through Discrete Time Lti Systems Miscellaneous Fourier Transform
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics