1
GATE ECE 2022
Numerical
+1
-0.33
A simple closed path C in the complex plane is shown in the figure. If
$$\oint\limits_c {{{{2^z}} \over {{z^2} - 1}}dz = - i\pi A} $$,
where $$i = \sqrt { - 1} $$, then the value of A is ___________ (rounded off to two decimal places).
Your input ____
2
GATE ECE 2022
MCQ (More than One Correct Answer)
+1
-0.33
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 2017 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The residues of a function $$f\left( z \right) = {1 \over {\left( {z - 4} \right){{\left( {z + 1} \right)}^3}}}$$ are
4
GATE ECE 2016 Set 3
Numerical
+1
-0
For $$f\left( z \right) = {{\sin \left( z \right)} \over {{z^2}}},$$ the residue of the pole at $$z=0$$ ________.
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Questions Asked from Complex Variable (Marks 1)
Number in Brackets after Paper Indicates No. of Questions
GATE ECE Subjects
Signals and Systems
Representation of Continuous Time Signal Fourier Series
Fourier Transform
Continuous Time Signal Laplace Transform
Discrete Time Signal Fourier Series Fourier Transform
Discrete Fourier Transform and Fast Fourier Transform
Discrete Time Signal Z Transform
Continuous Time Linear Invariant System
Discrete Time Linear Time Invariant Systems
Transmission of Signal Through Continuous Time LTI Systems
Sampling
Transmission of Signal Through Discrete Time Lti Systems
Miscellaneous
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics