1
GATE ECE 2010
+1
-0.3
The residues of a complex function $$X\left( z \right) = {{1 - 2z} \over {z\left( {z - 1} \right)\left( {z - 2} \right)}}$$ at it poles
A
$${1 \over 2},\,\, - {1 \over 2},\,1$$
B
$${1 \over 2},\,\, - {1 \over 2},\, - 1$$
C
$${1 \over 2},\,\,1,\,\, - {3 \over 2}$$
D
$${1 \over 2},\,\, - 1,\,\,{3 \over 2}$$
2
GATE ECE 2009
+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
$$2\,\pi \,j\,(1 + {C_0})$$
3
GATE ECE 2008
+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
4
GATE ECE 2008
+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
$${1 \over {32}}$$
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