# CSIR-NET Mathematical Science - ODE & PDE MCQ - Attempt Here!

By Astha Singh|Updated : May 29th, 2022

Hi Aspirants,

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We at BYJU'S Exam Prep always provide convenient and easy to use study materials for the candidates preparing for CSIR NET 2022 exam. We already received excellent feedback from many aspirants for all the study materials, and we hope these MCQ questions will also help you to make your weaker areas stronger and help you to clear your CSIR NET 2022 exam with flying colours.

### ODE & PDE MCQ

Question 1-

1.  2x2y2 = –1
2. 4x4y = – 1
3. 2xy4 = –1
4. 4x4y4 = –1

Question 2- Using the method of variation of parameters, the particular integral  of the differential equation  can be expressed as , where A(x) and B(x) are given by

A. (x) =
B.
C.
D.

Question 3-
The general solution of the differential equation  is of the form F(u, v) = 0 where u(x, y, z) = C1 and v(x, y, z) = C2 are given by
A.
B.
C.
D.

Question 4-

For x = r cos q, y = r sin q, which of the following is/are correct

A.
B.
C.
D.

Question 5-

Let u (x, t) be the solution of utt = uxx: 0 < x < 1, t > 0, u(x, 0) = x(1 + x), ut(x­, 0) = 0 then

A. u (1, 0) = 4

B.

C. u (1, 0) = 2

D.

Question 6-

For the differential equation

A. x = 1 is an ordinary point

B. x = 1 is a regular singular point

C. x = 0 is an irregular singular point

D. x = 0 is an ordinary point

Question 7-
##### The general solution of the system of differential equations

is given

A.  :
B.  :
C.  :
D.  :

Question 8-

Let  be solutions of y” – 2xy + (sin x2) y = 0 such that  & . Then the value of the Wronskian  at x = 0 is-

A. 0
B. 1
C. E
D. None

Question 9-

The general solution  of the system x’ = -x + 2y & y’ = 4x + y is given by

A.
B.
C.
D.

Question 10-

Which of the following is/are false for the partial differential equation

A. Elliptic in the region x < 0, y < 0, xy > 1
B. Elliptic in the region x > 0, y > 0, xy > 1
C. Parabolic in the region x < 0, 4 < 0, xy > 1
D. Hyperbolic in the region x < 0, y < 0, xy > 1

 Answer Key For ODE & PDE MCQ Question Number Answer Key 1 B 2 B 3 B 4 D 5 B and C 6 B 7 C 8 D 9 A 10 A, B and C

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