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

$$\int\limits_C {{{{z^3} - 6} \over {3z - i}}} dz$$ is where C is |z| = 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

$$I\, = \,\oint\limits_C {\sec z\,dz} $$, z being a complex variable. The value of I will be

Questions Asked from Complex Variable (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE CE Subjects

Engineering Mechanics

Strength of Materials Or Solid Mechanics

Structural Analysis

Construction Material and Management

Reinforced Cement Concrete

Steel Structures

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

Geomatics Engineering Or Surveying

Environmental Engineering

Transportation Engineering

Engineering Mathematics

General Aptitude