Engineering Mathematics
Linear Algebra
Marks 1Marks 2
Vector Calculus
Marks 1Marks 2
Complex Variable
Marks 1Marks 2
Probability and Statistics
Marks 1Marks 2
Differential Equations
Marks 1Marks 2
Numerical Methods
Marks 1Marks 2
Transform Theory
Marks 1Marks 2
1
GATE ECE 2023
MCQ (Single Correct Answer)
+1
-0.33

The value of the contour integral, $$\oint\limits_C {\left( {{{z + 2} \over {{z^2} + 2z + 2}}} \right)dz} $$, where the contour C is $$\left\{ {z:\left| {z + 1 - {3 \over 2}j} \right| = 1} \right\}$$, taken in the counter clockwise direction, is

A
$$ - \pi (1 + j)$$
B
$$\pi (1 + j)$$
C
$$\pi (1 - j)$$
D
$$ - \pi (1 - j)$$
2
GATE ECE 2022
Numerical
+1
-0

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).

GATE ECE 2022 Engineering Mathematics - Complex Variable Question 4 English

Your input ____
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
A
$${{ - 1} \over {27}}$$ and $${{ - 1} \over {125}}$$
B
$${1 \over {125}}$$ and $${{ - 1} \over {125}}$$
C
$${{ - 1} \over {27}}$$ and $${1 \over 5}$$
D
$${1 \over {125}}$$ and $${{ - 1} \over 5}$$
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 $$z=0$$ ________.
Your input ____
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