MCQOPTIONS
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MCQOPTIONS
This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Fourier Analysis knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The ends A and B of a rod of 20cm length are kept at 30 C and 80 C until steady state prevails. What is the condition u(x,0)? |
| A. | 20 + <sup>5</sup> <sub>2</sub> x |
| B. | 30 + <sup>5</sup> <sub>2</sub> x |
| C. | 30 + 2x |
| D. | 20 + 2x |
| Answer» C. 30 + 2x | |
| 2. |
If two ends of a bar of length l is insulated then what are the conditions to solve the heat flow equation? |
| A. | u<sub>x</sub>(0,t) = 0 = u<sub>x</sub>(l,t) |
| B. | u<sub>t</sub>(0,t) = 0 = u<sub>t</sub>(l,t) |
| C. | u(0,t) = 0 = u(l,t) |
| D. | u<sub>xx</sub>(0,t) = 0 = u<sub>xx</sub>(l,t) |
| Answer» B. u<sub>t</sub>(0,t) = 0 = u<sub>t</sub>(l,t) | |
| 3. |
Solve the equation ut = uxx with the boundary conditions u(x,0) = 3 sin (n x) and u(0,t)=0=u(1,t) where 0<x<1 and t>0. |
| A. | (3 _{n=1}^ ) e<sup>-n<sup>2</sup> <sup>2</sup> t</sup> cos u2061(n x) |
| B. | ( _{n=1}^ ) e<sup>-n<sup>2</sup> <sup>2</sup> t</sup> sin u2061(n x) |
| C. | (3 _{n=1}^ ) e<sup>-n<sup>2</sup> <sup>2</sup> t</sup> sin u2061(n x) |
| D. | ( _{n=1}^ ) e<sup>-n<sup>2</sup> <sup>2</sup> t</sup> cos(n x) |
| Answer» D. ( _{n=1}^ ) e<sup>-n<sup>2</sup> <sup>2</sup> t</sup> cos(n x) | |
| 4. |
Is it possible to have a solution for 1-Dimensional heat equation which does not converge as time approaches infinity? |
| A. | Yes |
| B. | No |
| Answer» C. | |
| 5. |
A rod of 30cm length has its ends P and Q kept 20 C and 80 C respectively until steady state condition prevail. The temperature at each point end is suddenly reduced to 0 C and kept so. Find the conditions for solving the equation. |
| A. | u(0,t) = 0 = u(30,t) and u(x,0) = 20 + 60/10 x |
| B. | u<sub>x</sub>(0,t) = 0 = u<sub>x</sub>(30,t) and u(x,0) = 20 + 60/30 x |
| C. | u<sub>t</sub>(0,t) = 0 = u<sub>t</sub>(30,t) and u(x,0) = 20 + 60/10 x |
| D. | u(0,t) = 0 = u(30,t) and u(x,0) = 20 + 60/30 x |
| Answer» E. | |
| 6. |
The one dimensional heat equation can be solved using a variable separable method. The constant which appears in the solution should be __________ |
| A. | Positive |
| B. | Negative |
| C. | Zero |
| D. | Can be anything |
| Answer» C. Zero | |
| 7. |
When using the variable separable method to solve a partial differential equation, then the function can be written as the product of functions depending only on one variable. For example, U(x,t) = X(x)T(t). |
| A. | True |
| B. | False |
| Answer» B. False | |
| 8. |
The partial differential equation of 1-Dimensional heat equation is ___________ |
| A. | u<sub>t</sub> = c<sup>2</sup>u<sub>xx</sub> |
| B. | u<sub>t</sub> = pu<sub>xx</sub> |
| C. | u<sub>tt</sub> = c<sup>2</sup>u<sub>xx</sub> |
| D. | u<sub>t</sub> = c<sup>2</sup>u<sub>xx</sub> |
| Answer» B. u<sub>t</sub> = pu<sub>xx</sub> | |