MCQOPTIONS
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MCQOPTIONS
This section includes 9 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 partial differential equation is one in which a dependent variable (say y ) depends on one or more independent variables (say x , t etc.) |
| A. | False |
| B. | True |
| Answer» C. | |
| 2. |
The equation 2 ( frac{dy}{dx} xy = y^{-2}, ) is an example for Bernoulli s equation. |
| A. | False |
| B. | True |
| Answer» C. | |
| 3. |
Find the general solution of the linear partial differential equation, yzp+zxq=xy. |
| A. | (x<sup>2</sup>-y<sup>2</sup> z<sup>2</sup> )=0 |
| B. | (x<sup>2</sup>-y<sup>2</sup>, y<sup>2</sup>-z<sup>2</sup> )=0 |
| C. | (x<sup>2</sup>-y<sup>2</sup>, y<sup>2</sup>-x<sup>2</sup> )=0 |
| D. | (x<sup>2</sup>-z<sup>2</sup>, z<sup>2</sup>-x<sup>2</sup> )=0 |
| Answer» C. (x<sup>2</sup>-y<sup>2</sup>, y<sup>2</sup>-x<sup>2</sup> )=0 | |
| 4. |
What is the nature of Lagrange s linear partial differential equation? |
| A. | First-order, Third-degree |
| B. | Second-order, First-degree |
| C. | First-order, Second-degree |
| D. | First-order, First-degree |
| Answer» E. | |
| 5. |
Which of the following is an example for first order linear partial differential equation? |
| A. | Lagrange s Partial Differential Equation |
| B. | Clairaut s Partial Differential Equation |
| C. | One-dimensional Wave Equation |
| D. | One-dimensional Heat Equation |
| Answer» B. Clairaut s Partial Differential Equation | |
| 6. |
Which of the following is one of the criterions for linearity of an equation? |
| A. | The dependent variable and its derivatives should be of second order |
| B. | The dependent variable and its derivatives should not be of same order |
| C. | Each coefficient does not depend on the independent variable |
| D. | Each coefficient depends only on the independent variable |
| Answer» E. | |
| 7. |
In the equation, y= x2+c,c is known as the parameter and x and y are known as the main variables. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 8. |
What is the order of the equation, (xy^3( frac{ y}{ x})^2+yx^2+ frac{ y}{ x}=0 )? |
| A. | Third Order |
| B. | Second Order |
| C. | First Order |
| D. | Zero Order |
| Answer» D. Zero Order | |
| 9. |
First order partial differential equations arise in the calculus of variations. |
| A. | True |
| B. | False |
| Answer» B. False | |