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

By Astha Singh|Updated : May 29th, 2022

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Are you looking for Online Mock Quiz for CSIR NET Preparation? Do you want to practice the most important questions for CSIR-NET preparation for the Life Sciences subject, then you have come to the right place.

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### 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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