1
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
2
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
$$ {1 \over {32}}$$
3
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
$$\pi i{\tan ^{ - 1}}(z)$$
4
GATE ECE 2006
MCQ (Single Correct Answer)
+1
-0.3
The value of the counter integral $$$\int\limits_{\left| {z - j} \right| = 2} {{1 \over {{z^2} + 4}}\,} dz\,\,in\,the\,positive\,sense\,is$$$
A
$${{j\pi } \over 2}$$
B
$${{ - \pi } \over 2}$$
C
$${{ - j\pi } \over 2}$$
D
$${\pi \over 2}$$
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