1
GATE CE 2009
+2
-0.6
The value of the integral $$\int\limits_C {{{\cos \left( {2\pi z} \right)} \over {\left( {2z - 1} \right)\left( {z - 3} \right)}}} dz$$ where C is a closed curve given by |z| = 1 is
A
$$- \pi i$$
B
$${{\pi i} \over 5}$$
C
$${{2\pi i} \over 5}$$
D
$$\pi i$$
2
GATE CE 2006
+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
3
GATE CE 2005
+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
GATE CE Subjects
Engineering Mechanics
Construction Material and Management
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
General Aptitude
EXAM MAP
Medical
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