1
GATE CE 2006
MCQ (Single Correct Answer)
+2
-0.6
Using Cauchy's Integral Theorem, the value of the integral (integration being taken in counter clockwise direction)

$$\int\limits_C {{{{z^3} - 6} \over {3z - i}}} dz$$ is where C is |z| = 1
A
$${{2\pi } \over {81}} - 4\pi i$$
B
$${\pi \over 8} - 6\pi i$$
C
$${{4\pi } \over {81}} - 6\pi i$$
D
1
2
GATE CE 2005
MCQ (Single Correct Answer)
+2
-0.6
Consider likely applicability of Cauchy's Integral theorem to evaluate the following integral counterclockwise around the unit circle C.

$$I\, = \,\oint\limits_C {\sec z\,dz} $$, z being a complex variable. The value of I will be
A
I = 0 ; Singularities set = $$\phi $$
B
I = 0 ; Singularities set = $$\left\{ { \pm {{\left( {2n + 1} \right)} \over 2}\pi \,\,;\,n = 0,1,2,.....} \right\}$$
C
I = 0 ; Singularities set = $$\left\{ { \pm \,n\pi \,\,;\,n = 0,1,2,.....} \right\}$$
D
None of the above
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