MCQOPTIONS
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MCQOPTIONS
This section includes 10 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. |
While solving any partial differentiation equation using a variable separable method which is of order 1 or 2, we use the formula of fourier series to find the coefficients at last. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 2. |
When solving a 1-Dimensional heat equation using a variable separable method, we get the solution if ______________ |
| A. | k is positive |
| B. | k is negative |
| C. | k is 0 |
| D. | k can be anything |
| Answer» C. k is 0 | |
| 3. |
When solving a 1-Dimensional wave equation using variable separable method, we get the solution if _____________ |
| A. | k is positive |
| B. | k is negative |
| C. | k is 0 |
| D. | k can be anything |
| Answer» C. k is 0 | |
| 4. |
While solving a partial differential equation using a variable separable method, we equate the ratio to a constant which? |
| A. | can be positive or negative integer or zero |
| B. | can be positive or negative rational number or zero |
| C. | must be a positive integer |
| D. | must be a negative integer |
| Answer» C. must be a positive integer | |
| 5. |
While solving a partial differential equation using a variable separable method, we assume that the function can be written as the product of two functions which depend on one variable only. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 6. |
Solve the differential equation (x^2 frac{ u}{ x}+y^2 frac{ u}{ y}=u ) using the method of separation of variables if (u(0,y) = e^{ frac{2}{y}} ). |
| A. | (e^{ frac{-3}{y}} e^{ frac{2}{x}} ) |
| B. | (e^{ frac{3}{y}} e^{ frac{2}{x}} ) |
| C. | (e^{ frac{-3}{x}} e^{ frac{2}{y}} ) |
| D. | (e^{ frac{3}{x}} e^{ frac{2}{y}} ) |
| Answer» D. (e^{ frac{3}{x}} e^{ frac{2}{y}} ) | |
| 7. |
Solve the differential equation (5 frac{ u}{ x}+3 frac{ u}{ y}=2u ) using the method of separation of variables if (u(0,y) = 9e^{-5y}. ) |
| A. | (9e^{ frac{17}{5} x} e^{-5y} ) |
| B. | (9e^{ frac{13}{5} x} e^{-5y} ) |
| C. | (9e^{ frac{-17}{5} x} e^{-5y} ) |
| D. | (9e^{ frac{-13}{5} x} e^{-5y} ) |
| Answer» B. (9e^{ frac{13}{5} x} e^{-5y} ) | |
| 8. |
Solve the partial differential equation (x^3 frac{ u}{ x} +y^2 frac{ u}{ y} = 0 ) using method of separation of variables if (u(0,y) = 10 , e^{ frac{5}{y}}. ) |
| A. | (10e^{ frac{5}{2x^2}} e^{ frac{5}{y}} ) |
| B. | (10e^{ frac{-5}{2y^2}} e^{ frac{5}{x}} ) |
| C. | (10e^{ frac{-5}{2y^2}} e^{ frac{-5}{x}} ) |
| D. | (10e^{ frac{-5}{2x^2}} e^{ frac{5}{y}} ) |
| Answer» E. | |
| 9. |
Find the solution of ( frac{ u}{ x}=36 frac{ u}{ t}+10u ) if ( frac{ u}{ x} (t=0)=3e^{-2x} ) using the method of separation of variables. |
| A. | ( frac{-3}{2} e^{-2x} e^{-t/3} ) |
| B. | (3e^x e^{-t/3} ) |
| C. | ( frac{3}{2} e^{2x} e^{-t/3} ) |
| D. | (3e^{-x} e^{-t/3} ) |
| Answer» B. (3e^x e^{-t/3} ) | |
| 10. |
Solve ( frac{ u}{ x}=6 frac{ u}{ t}+u ) using the method of separation of variables if u(x,0) = 10 e-x. |
| A. | 10 e<sup>-x</sup> e<sup>-t/3</sup> |
| B. | 10 e<sup>x</sup> e<sup>-t/3</sup> |
| C. | 10 e<sup>x/3</sup> e<sup>-t</sup> |
| D. | 10 e<sup>-x/3</sup> e<sup>-t</sup> |
| Answer» B. 10 e<sup>x</sup> e<sup>-t/3</sup> | |