# CSIR-NET Mathematical Science - Complex Analysis MCQ - Attempt Here!

By Astha Singh|Updated : July 1st, 2022

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## Multiple Choice Questions On Complex Analysis

Question 1.
Let C denote the positively oriented boundary of the square whose sides lie along the line Let then

1. π/8
2. -4π
3. None Of These

Question 2.

find the residue of at its essential singularity
1. 21/22
2. 22/23
3. 23/24
4. 24/25

Question 3.

Let then
1. f has a pole of order 2 at z=0
2. f is analytic function at z=0
3. where the integral is taken anticlockwise
4. The residue of f at z=0 is

Question 4.

Let then
1. The number of zeros of f(z) in |z|<1 is 2022
2. The number of zeros of f(z) in |z|<1 is 1011
3. All the zeros of f(z) are simple.
4. All the zeros of f(z) are need not be simple.

Question 5.

##### If f(z) is analytic on Δ, open unit disc such that f(0) = 0, |f(z)| < 1 for all z ∈ Δ, f(z) is analytic at z = 1 and f(z) = 1 . Then
1.
2. |f’(1)| = 1
3. |f’(x)| < 1

Question 6.

For any complex valued function f let Df denote the set on which the function f satisfies Cauchy-Riemann equations. Identify the functions for which Df is equal to ℂ .
1. f(z) =
2. f(z) = {cos x – sin y) + i{sin x + cos y), where z = x + it
3. f(z) =
4. f(z) = x2 + iy2, where z = x + iy

Question 7.

Let u(x, y) = x3 + ax2y + bx y2 + 2y3 be a harmonic function v(x, y) its harmonic conjugate. If u(0, 0) = 1 then |a –b + v(1, 0)| equal to
1. 2
2. 4
3. 1
4. 6

Question 8.

Let  be the open unit disc. Consider the family F of all holomorphic maps f : D → D such that  for f ∈ F, then impossible value of |f’(0)| are

1.
2.
3. 1

Question 9.

Consider the function f(z) =  for 0 < |z| < 1 where m n are positive integers. Then z _ Q Is
1. A removable singularity if m  2n
2. A pole if m < 2n
3. A pole if m  2n
4. An essential singularity for some values of m, n

 Answer Key For Complex Analysis Question Number Answer Key 1 D 2 C 3 B and C 4 A and C 5 B 6 C 7 D 8 A, B And D 9 A And B

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