1
GATE ECE 2009
MCQ (Single Correct Answer)
+1
-0.3
If $$f\left( z \right) = {C_0} + {C_1}{z^{ - 1}}\,\,$$ then $$\oint\limits_{|z| = 1} {{{1 + f\left( z \right)} \over z}} \,\,dz$$ is given
A
$$2\,\pi \,{C_1}$$
B
$$2\,\pi \,(1 + {C_0})$$
C
$$2\,\pi \,j\,{C_1}$$
D
$$2\,\pi \,j\,(1 + {C_0})$$
2
GATE ECE 2008
MCQ (Single Correct Answer)
+1
-0.3
The equation sin(z) = 10 has
A
no real (or) complex solution
B
exactly two distinct complex solutions
C
a unique solution
D
an infinite no of complex solutions
3
GATE ECE 2008
MCQ (Single Correct Answer)
+1
-0.3
The residue of the function
$$f(z) = {1 \over {{{\left( {z + 2} \right)}^2}{{\left( {z - 2} \right)}^2}}}$$ at z = 2 is
A
$$- {1 \over {32}}$$
B
$$- {1 \over {16}}$$
C
$${1 \over {16}}$$
D
$${1 \over {32}}$$
4
GATE ECE 2007
MCQ (Single Correct Answer)
+1
-0.3
The value of $$\oint\limits_C {{1 \over {\left( {1 + {z^2}} \right)}}} dz$$ where C is the contour $$\,\left| {z - {i \over 2}} \right| = 1$$ is
A
$$2\pi i$$
B
$$\pi$$
C
$${\tan ^{ - 1}}(z)$$
D
$$\pi i{\tan ^{ - 1}}(z)$$
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
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