CSIR-NET Mathematical Science - COV And LIE MCQ - Attempt Here!

By Astha Singh|Updated : June 7th, 2022

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Question 1.

The solution of the integral equation byjusexamprep is given by

Question 2.

Consider byjusexamprep subject to y (0) = 0 and y (2) = 4 then int J(y) is
A. byjusexamprep 
B. byjusexamprep
C. byjusexamprep 
D. does not exist.
Question 3.
Given the functional byjusexamprep
  1. The extremal is byjusexamprep 
  2. The extremal is y = x2 + h
  3. The extremal is u = sin x + cos x
  4. The extremal is y = cos 2x

Question 4. 

Consider the problem of extremizing the functional byjusexamprep with boundary condition y(1) = 1 and y(3) = 2 Which of the following is/are true?
A. There is a unique extremal
B. byjusexamprep is an extremal
C. byjusexamprep is an extremal
D. There are no extremal.
Question 5.
Consider the integral equation

byjusexamprep. Then

  1. there exists a continuous function f: [–1, 1] byjusexamprep for which solution exists
  2. there exists a continuous function f: [–1,1] byjusexamprep for which solution exists
  3. for f(x) = e–x(1 – 3x2), a solution exists
  4. for f(x) = e–x(x + x3 + x5), a solution exists

Question 6. 

Extremals y = y(x) for the variational problem byjusexamprep satisfy the differential equation
  1. y’’ + y = 0
  2. y’’ – y= 0
  3. y’’ + y’ = 0
  4. y’ + y = 0
Question 7.
Let y = f(x) be the extremizing function for the functional byjusexamprep subject to y(0) = 0, y(2) = 1 . Then f(1/8) is
  1. 1/2
  2. 1/8
  3. 1/4
  4. 1/12

Question 8.

If y is a solution of byjusexamprep, then which of the following is true?
  1. y is bounded in byjusexamprep
  2. y is periodic in byjusexamprep
  3. y(1) = 5(e + e-1)
  4. y(0) = 0

Question 9.

In Legendre’s test the integral byjusexamprep, is maximum if value of byjusexamprep is
  1. positive
  2. Not positive
  3. Negative
  4. Neither positive nor negative

Question 10. 

The eigen value l of the following Fredholm integral equation byjusexamprep is
  1. -2
  2. 2
  3. 4
  4. not – 4
Answer Key For COV And LIE
Question NumberAnswer Key
5C And D
9B And C
10B And C

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