Explore topic-wise MCQs in Partial Differential Equations.

This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Partial Differential Equations knowledge and support exam preparation. Choose a topic below to get started.

1.

Singular solution of a differential equation is one that cannot be obtained from the general solution gotten by the usual method of solving the differential equation.

A. True
B. False
Answer» B. False
Discussion
2.

Elliptic equations have no characteristic curves.

A. True
B. False
Answer» B. False
Discussion
3.

The condition that a second order partial differential equation should satisfy to be parabolic is b2-ac=0.

A. True
B. False
Answer» B. False
Discussion
4.

Which of the following represents the family of the characteristic curves for parabolic equations?

A. a <sub>x</sub>+b <sub>y</sub>=0
B. a <sub>x</sub>+b=0
C. a+ <sub>y</sub>=0
D. a( <sub>x</sub>+ <sub>y</sub>)=0
Answer» B. a <sub>x</sub>+b=0
Discussion
5.

The condition which a second order partial differential equation must satisfy to be elliptical isb2-ac=0.

A. True
B. False
Answer» C.
Discussion
6.

What is the reason behind the non-existence of any real function which satisfies the differential equation, (y )2 + 1 = 0?

A. Because for any real function, the left-hand side of the equation will be less than, or equal to one and thus cannot be zero
B. Because for any real function, the left-hand side of the equation becomes zero
C. Because for any real function, the left-hand side of the equation will be greater than, or equal to one and thus cannot be zero
D. Because for any real function, the left-hand side of the equation becomes infinity
Answer» D. Because for any real function, the left-hand side of the equation becomes infinity
Discussion
7.

The solution of the general form of second order non-linear partial differential equation is obtained by Monge s method.

A. False
B. True
Answer» C.
Discussion
8.

What is the general form of second order non-linear partial differential equations (x and y being independent variables and z being a dependent variable)?

A. (F(x,y,z, frac{ z}{ x}, frac{ z}{ y}, frac{ ^2 z}{ x^2}, frac{ ^2 z}{ y^2}, frac{ ^2 z}{ x y})=0 )
B. (F(x,z, frac{ z}{ x}, frac{ z}{ y}, frac{ ^2 z}{ x^2}, frac{ ^2 z}{ y^2})=0 )
C. (F(y,z, frac{ z}{ x}, frac{ z}{ y})=0 )
D. F(x,y)=0
Answer» B. (F(x,z, frac{ z}{ x}, frac{ z}{ y}, frac{ ^2 z}{ x^2}, frac{ ^2 z}{ y^2})=0 )
Discussion