COV And LIE MCQ
Question 1.
The solution of the integral equation 
is given by
is given by
Question 2.
Consider subject to y (0) = 0 and y (2) = 4 then int J(y) is
subject to y (0) = 0 and y (2) = 4 then int J(y) isA.
B.
C.
D. does not exist.
Question 3.
Given the functional
- The extremal is
- The extremal is y = x2 + h
- The extremal is u = sin x + cos x
- 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?
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
is an extremalC. is an extremal
is an extremalD. There are no extremal.
Question 5.
Consider the integral equation
. Then
- there exists a continuous function f: [–1, 1] for which solution exists
- there exists a continuous function f: [–1,1] for which solution exists
- for f(x) = e–x(1 – 3x2), a solution exists
- for f(x) = e–x(x + x3 + x5), a solution exists
for which solution exists
for which solution existsQuestion 6.
Extremals y = y(x) for the variational problem satisfy the differential equation
satisfy the differential equation- y’’ + y = 0
- y’’ – y= 0
- y’’ + y’ = 0
- y’ + y = 0
Let y = f(x) be the extremizing function for the functional subject to y(0) = 0, y(2) = 1 . Then f(1/8) is
subject to y(0) = 0, y(2) = 1 . Then f(1/8) is- 1/2
- 1/8
- 1/4
- 1/12
Question 8.
If y is a solution of , then which of the following is true?
, then which of the following is true?- y is bounded in
- y is periodic in
- y(1) = 5(e + e-1)
- y(0) = 0
Question 9.
In Legendre’s test the integral , is maximum if value of is
, is maximum if value of 
is- positive
- Not positive
- Negative
- Neither positive nor negative
Question 10.
The eigen value l of the following Fredholm integral equation is
is- -2
- 2
- 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 |
Check Out:
- Previous Year's Papers for CSIR-NET Exam: Attempt Here
- Study Notes for Part A: General Aptitude - Download PDF Here
- Study Notes for CSIR-NET Chemical Science - Download PDF Here
- Study Notes for CSIR-NET Life Science - Download PDF Here
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