Explore topic-wise MCQs in Partial Differential Equations.

This section includes 12 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.

A particular solution for an equation is derived by eliminating arbitrary constants.

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

Separation of variables was first used by L Hospital in 1750.

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

The symbol used for partial derivatives, , was first used in mathematics by Marquis de Condorcet.

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

u (x, t) = e 2 *2t*sin x is the solution of the two-dimensional Laplace equation.

A. True
B. False
Answer» C.
Discussion
5.

In the formation of differential equation by elimination of arbitrary constants, after differentiating the equation with respect to independent variable, the arbitrary constant gets eliminated.

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

Which of the following is true with respect to formation of differential equation by elimination of arbitrary constants?

A. The given equation should be differentiated with respect to independent variable
B. Elimination of the arbitrary constant by replacing it using derivative
C. If n arbitrary constant is present, the given equation should be differentiated n number of times
D. To eliminate the arbitrary constants, the given equation must be integrated with respect to the dependent variable
Answer» E.
Discussion
7.

What is the solution of, ( frac{ ^2 u}{ x^2}=2xe^t, ) after applying method of separation of variables ((u(0,t)=t, frac{ u}{ x} (0,t)= e^t) )?

A. (u= frac{x^3}{3} e^t+xe^t )
B. (u= frac{x^3}{3} e^t+xe^t+t )
C. (u= frac{x^3}{3} e^t+e^t+t )
D. (u= frac{x^2}{2} e^t+xe^t+t )
Answer» C. (u= frac{x^3}{3} e^t+e^t+t )
Discussion
8.

For a partial differential equation, in a function (x, y) and two variables x, y, what is the form obtained after separation of variables is applied?

A. (x, y) = X(x)+Y(y)
B. (x, y) = X(x)-Y(y)
C. (x, y) = X(x)Y(y)
D. (x, y) = X(x)/Y(y)
Answer» D. (x, y) = X(x)/Y(y)
Discussion
9.

The matrix form of the separation of variables is the Kronecker sum.

A. True
B. False
Answer» B. False
Discussion
10.

Which of the following equations cannot be solved by using the method of separation of variables?

A. Laplace Equation
B. Helmholtz Equation
C. Alpha Equation
D. Biharmonic Equation
Answer» D. Biharmonic Equation
Discussion
11.

Separation of variables, in mathematics, is also known as Fourier method.

A. False
B. True
Answer» C.
Discussion
12.

By using the method of separation of variables, the determination of solution to P.D.E. reduces to determination of solution to O.D.E.

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