Mathematics  III Mid  II, November  2014
1.The value of along the path y = x
Answer: C
2.The value of Where C is the circle x^{2} + y^{2} = 4

0

i

 i

2i

Answer: A
3.The value of along the line z = 0 to z = 1+i is

0

i

2i

2i

Answer: B
4.Cauchy’s integral theorem is applicable only for a  region R enclosed a simple curve C.

Simply connected

multiply connecte

Both A and B

None

Answer: A
5.If f(z) is analytic within and on a closed curve C, and if a is any point within C, then =

f(a)

2i f(a)

f(a) / 2

2f

Answer: B
6.power series within its circle of convergence

Convergence absolutely

Convergence uniformly

Divergence

both A and B

Answer: D
7.For , z = 0 is

Simple pole

Essential singularity

Removable singularity

None

Answer: C
8.Residue of z = /2 of tan z is

0

1

1

2

Answer: B
9.What kind of singularity of the function at z = 0

Essential singularity

Removable singularity

Isolated essential singularity

Non isolated essential singularity

Answer: B
10.The image of the circle I z1 I = 1 under the mapping w = 1/z is

Iw+1I = 1

u = 1/2

u = 1/2

v = 1/2

Answer: B
11.Taylor’s series expansion of in the region I z I < 1 …………………………
Answer:
12.The value of along the line y = x …………………………
Answer: 5/6
13.If f(z) is an analytic function of z and if f I (z) is continuous at each point within and on a closed Contour then ……………………….
Answer: 0
14.Write the principal part of the function at its singular point …..………………..
Answer:
15.If f(z) has a pole of order n at z = a the Res f(a) = …………………………
Answer:
16.The limit point of the poles of a function f(z) is ……………..
Answer: Non isolated essential singularity
17.The fixed points of the transformation are ………………………
Answer:
18.Bilinear transformation preserves ………………………of four points.
Answer: Cross – ratio.
19.Image of I z I = 2 under w = z + (3 + 2i) is ………………………
Answer: A circle with centre (3,2) and radius 2 in w – plane.
20.The point where f^{I} (z) = 0 is called …………………..of the transformation w = f(z).
Answer: Critical point