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

By Astha Singh|Updated : June 7th, 2022

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## COV And LIE MCQ

Question 1.

The solution of the integral equation  is given by

Question 2.

Consider  subject to y (0) = 0 and y (2) = 4 then int J(y) is

A.
B.
C.
D. does not exist.

Question 3.
Given the functional
1. The extremal is
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  with boundary condition y(1) = 1 and y(3) = 2 Which of the following is/are true?

A. There is a unique extremal

B.  is an extremal
C.  is an extremal
D. There are no extremal.

Question 5.

Consider the integral equation

. Then

1. there exists a continuous function f: [–1, 1]  for which solution exists
2. there exists a continuous function f: [–1,1]  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  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  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 , then which of the following is true?

1. y is bounded in
2. y is periodic in
3. y(1) = 5(e + e-1)
4. y(0) = 0

Question 9.

In Legendre’s test the integral , is maximum if value of  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  is

1. -2
2. 2
3. 4
4. not – 4
 Answer Key For COV And LIE Question Number Answer Key 1 B 2 A 3 A 4 D 5 C And D 6 B 7 C 8 C 9 B And C 10 B And C

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