Complex Variables and Partial Differential Equations (3130005) MCQ

MCQs of Complex Integral, Sequence & Series

MCQ No - 1

The value of integral #$$\int_0^{1+\mathrm i}\mathrm z\;\operatorname d\mathrm z$$# along the line #$$\mathrm y=\mathrm x$$# is _____ .

(A)

1

(B)

2

(C)

#$$i$$#

(D)

0


C
MCQ No - 2

The value of integral #$$\int_{\mathrm C}\;\overline{\mathrm z}\;\operatorname d\mathrm z$$# , where C is shortest path joining A(0, 0) to B(1, 1) , is _____ .

(A)

1

(B)

2

(C)

#$$i$$#

(D)

0


A
MCQ No - 3

The value of integral #$$\int_{\mathrm C}\;\frac{3\mathrm z}{\mathrm z+2}\;\operatorname d\mathrm z$$# , where #$$\mathrm C\;:\;\left|\mathrm z\right|=1$$# , is _____ .

(A)

1

(B)

2

(C)

3

(D)

0


D
MCQ No - 4

The value of integral #$$\int_{\mathrm C}\;\frac{\mathrm{dz}}{\mathrm z(\mathrm z-2)}$$#, where #$$\mathrm C\;:\;\left|\mathrm z\right|=1$$# , is _____ .

(A)

#$$2\mathrm{πi}$$#

(B)

#$$\mathrm{πi}$$#

(C)

#$$-2\mathrm{πi}$$#

(D)

#$$-\mathrm{πi}$$#


D
MCQ No - 5

Let C be a circle #$$\left|\mathrm z-1\right|=3$$# in the complex plane, then #$$\int_{\mathrm C}\;\frac{\cos\;\mathrm z}{\mathrm z-\mathrm\pi}\;\operatorname d\mathrm z$$# , is _____ .

(A)

#$$2\mathrm{πi}$$#

(B)

#$$4\mathrm{πi}$$#

(C)

#$$-2\mathrm{πi}$$#

(D)

none of these


C