Complex Variables and Partial Differential Equations (3140610) MCQs

MCQs of Complex Variable-Integration, Sequence and Series

Showing 1 to 10 out of 19 Questions
1.

The value of integral 01+iz dz along the line y=x is _____ .

(a)

1

(b)

2

(c)

i

(d)

0

Answer:

Option (c)

2.

The value of integral C z¯ dz , where C is shortest path joining A(0, 0) to B(1, 1) , is _____ .

(a)

1

(b)

2

(c)

i

(d)

0

Answer:

Option (a)

3.

The value of integral C 3zz+2 dz , where C : z=1 , is _____ .

(a)

1

(b)

2

(c)

3

(d)

0

Answer:

Option (d)

4.

The value of integral C dzz(z-2) , where C : z=1 , is _____ .

(a)

2πi

(b)

πi

(c)

-2πi

(d)

-πi

Answer:

Option (d)

5.

Let C be a circle z-1=3 in the complex plane, then C cos zz-π dz , is _____ .

(a)

2πi

(b)

4πi

(c)

-2πi

(d)

none of these

Answer:

Option (c)

6.

As per cauchy's integral formula C f(z)z-z0 dz= _____ .

(a)

2πi f(z0)

(b)

2πi

(c)

π

(d)

2π f(z0)

Answer:

Option (a)

7.

As per cauchy's integral formula C f(z)(z-z0)n+1 dz= _____ .

(a)

2πi

(b)

2πin! fn(z0)

(c)

2πi fn(z0)

(d)

none of these

Answer:

Option (b)

8.

The value of C ez(z-1)2 dz , C : z=2 , is _____ .

(a)

4πie2

(b)

2πie2

(c)

4πie

(d)

none of these

Answer:

Option (d)

9.

Let C be a circle |z|=3 in the complex plane & Cez(z-2)3dz = 2πik then k=_____ .

(a)

e2

(b)

e22

(c)

e23

(d)

none of these

Answer:

Option (b)

10.

Let C be a circle |z|=3 in the complex plane & Csin z(z + π2)3dz = 2πik then k=_____ .

(a)

0.5

(b)

0.75

(c)

1

(d)

0

Answer:

Option (a)

Showing 1 to 10 out of 19 Questions