MCQOPTIONS
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MCQOPTIONS
This section includes 11 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 | |
| 2. |
Elliptic equations have no characteristic curves. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 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 | |
| 4. |
Which of the following represents the family of the characteristic curves for parabolic equations? |
| A. | aζx+bζy=0 |
| B. | aζx+b=0 |
| C. | a+ζy=0 |
| D. | a(ζx+ζy)=0 |
| Answer» B. aζx+b=0 | |
| 5. |
The condition which a second order partial differential equation must satisfy to be elliptical isb2-ac=0. |
| A. | True |
| B. | False |
| Answer» C. | |
| 6. |
Which of the following represents the canonical form of a second order parabolic PDE? |
| A. | \(\frac{∂^2 z}{∂η^2}+⋯=0 \) |
| B. | \(\frac{∂^2 z}{∂ζ∂η}+⋯=0\) |
| C. | \(\frac{∂^2 z}{∂α^2}+\frac{∂^2 z}{∂β^2}…=0\) |
| D. | \(\frac{∂^2 z}{∂ζ^2}+⋯=0\) |
| Answer» B. \(\frac{∂^2 z}{∂ζ∂η}+⋯=0\) | |
| 7. |
Which of the following is the condition for a second order partial differential equation to be hyperbolic? |
| A. | b2-ac<0 |
| B. | b2-ac=0 |
| C. | b2-ac>0 |
| D. | b2-ac=<0 |
| Answer» D. b2-ac=<0 | |
| 8. |
What is the order of the partial differential equation, \(\frac{∂^2 z}{∂x^2}-(\frac{∂z}{∂y})^5+\frac{∂^2 z}{∂x∂y}=0\)? |
| A. | Order-5 |
| B. | Order-1 |
| C. | Order-4 |
| D. | Order-2 |
| Answer» E. | |
| 9. |
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 | |
| 10. |
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. | |
| 11. |
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 |
| E. | ?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. \(F(x,z,\frac{∂z}{∂x},\frac{∂z}{∂y},\frac{∂^2 z}{∂x^2},\frac{∂^2 z}{∂y^2})=0\) | |