MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
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. |
What is the degree of the differential equation, x3-6x3 y3+2xy=0? |
| A. | 3 |
| B. | 5 |
| C. | 6 |
| D. | 8 |
| Answer» D. 8 | |
| 2. |
In recurrence relation, each further term of a sequence or array is defined as a function of its succeeding terms. |
| A. | True |
| B. | False |
| Answer» C. | |
| 3. |
What is the complete solution of the equation, (q= e^ frac{-p}{ } )? |
| A. | (z=ae^ frac{-a}{ } y ) |
| B. | (z=x+e^ frac{-a}{ } y ) |
| C. | (z=ax+e^ frac{-a}{ } y+c ) |
| D. | (z=e^ frac{-a}{ } y ) |
| Answer» D. (z=e^ frac{-a}{ } y ) | |
| 4. |
A particular solution for an equation is derived by substituting particular values to the arbitrary constants in the complete solution. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 5. |
The Integrating factor of a differential equation is also called the primitive. |
| A. | True |
| B. | False |
| Answer» C. | |
| 6. |
What is the degree of the non-homogeneous partial differential equation, (( frac{ ^2 u}{ x y})^5+ frac{ ^2 u}{ y^2}+ frac{ u}{ x}=x^2-y^3 )? |
| A. | Degree-2 |
| B. | Degree-1 |
| C. | Degree-0 |
| D. | Degree-5 |
| Answer» E. | |
| 7. |
What is the order of the non-homogeneous partial differential equation, ( frac{ ^2 u}{ x^2}+( frac{ ^2 u}{ x y})^2+ frac{ ^2 u}{ y^2}=x^2+y^2 )? |
| A. | Order-3 |
| B. | Order-2 |
| C. | Order-0 |
| D. | Order-1 |
| Answer» C. Order-0 | |
| 8. |
Which of the following methods is not used in solving non-homogeneous equations? |
| A. | Exponential Response Formula |
| B. | Method of Undetermined Coefficients |
| C. | Orthogonal Method |
| D. | Variation of Constants |
| Answer» D. Variation of Constants | |
| 9. |
While an ODE of order m has m linearly independent solutions, a PDE has infinitely many. |
| A. | False |
| B. | True |
| Answer» C. | |
| 10. |
What is the general form of the general solution of a non-homogeneous DE (uh(t)= general solution of the homogeneous equation, up(t)= any particular solution of the non-homogeneous equation)? |
| A. | u(t)=u<sub>h</sub> (t)/u<sub>p</sub> (t) |
| B. | u(t)=u<sub>h</sub> (t)*u<sub>p</sub> (t) |
| C. | u(t)=u<sub>h</sub> (t)+u<sub>p</sub> (t) |
| D. | u(t)=u<sub>h</sub> (t)-u<sub>p</sub> (t) |
| Answer» D. u(t)=u<sub>h</sub> (t)-u<sub>p</sub> (t) | |
| 11. |
Which of the following is a non-homogeneous equation? |
| A. | ( frac{ ^2 u}{ t^2}-c^2 frac{ ^2 u}{ x^2}=0 ) |
| B. | ( frac{ ^2 u}{ x^2}+ frac{ ^2 u}{ y^2}=0 ) |
| C. | ( frac{ ^2 u}{ x^2}+( frac{ ^2 u}{ x y})^2+ frac{ ^2 u}{ y^2}=x^2+y^2 ) |
| D. | ( frac{ u}{ t}-T frac{ ^2 u}{ x^2}=0 ) |
| Answer» D. ( frac{ u}{ t}-T frac{ ^2 u}{ x^2}=0 ) | |
| 12. |
Non-homogeneous which may contain terms which only depend on the independent variable. |
| A. | True |
| B. | False |
| Answer» B. False | |