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Cauchy's Integral Formula Mock Tests

5 questions available

Cauchy's Integral Formula Mock Test 1

Questions: 5

Sample Questions

GATE Mathematics
The value of the integral ∮_C cos(z)/z² dz where C is the circle |z| = 2 traversed counterclockwise is
A 0
B 2πi
C −2πi
D πi
GATE Mathematics
The value of the contour integral ∮_C dz/(z − 1) where C is the square with vertices at ±1 ± i traversed counterclockwise is
A 0
B 2πi
C πi
D 4πi
GATE Mathematics
The integral ∮_C (z² + 1)/(z − 1) dz where C is the circle |z| = 3 traversed counterclockwise equals
A 2πi
B 4πi
C 6πi
D 10πi
GATE Mathematics
The value of ∮_C e^z/z dz where C is the unit circle |z| = 1 traversed counterclockwise is
A 0
B 2πi
C πi
D e
GATE Mathematics
The function f(z) = e^(z²) is entire. The value of the contour integral ∮_|z|=1 f(z)/z⁵ dz is
A pi/6
B pi/3
C pi
D 4pi/3

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