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 x2 + y2 = 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 z-1 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 fI (z) = 0 is called …………………..of the transformation w = f(z).
Answer: Critical point