GATE CE 2005 | Complex Variable Question 10 | Engineering Mathematics

GATE CE 2005

MCQ (Single Correct Answer)

-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 = 0 ; Singularities set = $$\phi $$

I = 0 ; Singularities set = $$\left\{ { \pm {{\left( {2n + 1} \right)} \over 2}\pi \,\,;\,n = 0,1,2,.....} \right\}$$

I = 0 ; Singularities set = $$\left\{ { \pm \,n\pi \,\,;\,n = 0,1,2,.....} \right\}$$

None of the above

GATE CE Subjects

Construction Material and Management

Critical Path Method Construction Materials Program Evolution Review Technique

Geomatics Engineering Or Surveying

Levelling Traversing Theodolites and Plane Table Surveying Measurement of Area, Volume and Theory of Errors and Survey Adjustment Curves Field Astronomy and Photogrammetric Surveying Basics of GIS, GPS and Remote Sensing Angular Measurements and Compass Survey Basic Concepts Linear Measurements and Chain Survey

Engineering Mechanics

Equilibrium of Force Systems Work Energy Principle and Impulse Momentum Equation

Hydrology

Precipitation and Frequency of Rainfall Data Evaporation and Transpiration Infiltration Hydrograph Flood Estimation and Flood Routing Well Hydraulics and River Gauging

Transportation Engineering

Highway Devolopment and Planning Highway Geometric Design Traffic Engineering Highway Materials Pavement Design Railway, Runway and Taxiway Design

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Reinforced Cement Concrete

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Steel Structures

Materials and Specifications Tension Members Riveted Joints and Bolted Joints Welded Connections Eccentric Connections Compression Members Beams Plate Girder

Irrigation

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Environmental Engineering

Sources and Coveyances Water Quality Control of Water Treatment of Water Water Demand Waste Water Characteristics Sewage System and Sewer Appurtenances Treatment of Sewage Disposal of Sewage Effluent Solid Waste Management Air Pollution Noise Pollution

Engineering Mathematics

Probability and Statistics Differential Equations Transform Theory Calculus Complex Variable Linear Algebra Vector Calculus Numerical Methods

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