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 byjusexamprepLet byjusexamprepthen byjusexamprep

  1. π/8
  2. -4π
  3. None Of These

Question 2.

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

Question 3.

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

Question 4.

Let byjusexamprepthen
  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. byjusexamprep 
  2. byjusexamprep
  3. |f’(1)| = 1
  4. |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) = byjusexamprep
  2. f(z) = {cos byjusexamprepx – sin byjusexamprepy) + i{sin byjusexamprepx + cos byjusexamprepy), where z = x + it
  3. f(z) = byjusexamprep
  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 byjusexamprep be the open unit disc. Consider the family F of all holomorphic maps f : D → D such that byjusexamprep for f ∈ F, then impossible value of |f’(0)| are

  1. byjusexamprep 
  2. byjusexamprep
  3. byjusexamprep 
  4. 1

Question 9.

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


Answer Key For Complex Analysis
Question NumberAnswer Key
3B and C
4A and C
8A, B And D
9A And B

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