MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Computational Fluid Dynamics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
A system of equations with which of these coefficient matrices can be solved using the Thomas algorithm? |
| A. | \(\begin{bmatrix}1 & 2 & 0 \\3 & 4 & 5 \\0 & 6 &7\end{bmatrix} \) |
| B. | \(\begin{bmatrix}1 & 2 & 3 \\0 & 4 & 5 \\0 & 0 & 7\end{bmatrix}\) |
| C. | \(\begin{bmatrix}1 & 0 & 0 \\3 & 4 & 0 \\5 & 6 & 7\end{bmatrix}\) |
| D. | \(\begin{bmatrix}1 & 2 & 3 \\3 & 4 & 5 \\5 & 6 & 7\end{bmatrix}\) |
| Answer» B. \(\begin{bmatrix}1 & 2 & 3 \\0 & 4 & 5 \\0 & 0 & 7\end{bmatrix}\) | |
| 2. |
Consider a system of equations where the ith equation is aiΦi=bi Φi+1+ciΦi-1+di. While solving this system using Thomas algorithm, we get Φi=PiΦi+1+Qi. What are P1 and Q1? |
| A. | \(P_1=\frac{d_1}{a_1-c_1};Q_1=\frac{b_1}{a_1-c_1}\) |
| B. | \(P_1=\frac{b_1}{a_1-c_1};Q_1=\frac{d_1}{a_1-c_1}\) |
| C. | \(P_1=\frac{d_1}{a_1};Q_1=\frac{b_1}{a_1}\) |
| D. | \(P_1=\frac{b_1}{a_1};Q_1=\frac{d_1}{a_1}\) |
| Answer» E. | |
| 3. |
After finding all the values of Pi and Qi, in which order are the values of Φi found? |
| A. | Forward |
| B. | Simultaneously |
| C. | Backwards |
| D. | Depends on the problem |
| Answer» D. Depends on the problem | |
| 4. |
While solving a system of equations with the Thomas algorithm, in which order are the values of Pi and Qi found? |
| A. | Backwards |
| B. | Forward |
| C. | Simultaneously |
| D. | Depends on the problem |
| Answer» C. Simultaneously | |
| 5. |
Using the Thomas algorithm, if the ith unknown is Φi=Pi Φi+1+Qi. what is the last unknown value ΦN equal to? |
| A. | 0 |
| B. | PN |
| C. | QN |
| D. | 1 |
| Answer» D. 1 | |
| 6. |
Let the ith equation of a system of n equations be aiΦi=bi Φi+1+ciΦi-1+di. Which of these is correct? |
| A. | cN=0; bN=0 |
| B. | cN=0; b1=0 |
| C. | c1=0; bN=0 |
| D. | c1=0; b1=0 |
| Answer» D. c1=0; b1=0 | |
| 7. |
Consider a system of equations where the ith equation is ai Φi=bi Φ(i+1)+ci Φ(i+1)+di. While solving this system using Thomas algorithm, we get Φi=Pi Φ(i+1)+Qi. What are Pi and Qi? |
| A. | \(P_i=\frac{c_i Q_{i-1}+d_i}{a_i-c_i P_{i-1}};Q_i=\frac{b_i}{a_i-c_i P_{i-1}}\) |
| B. | \(P_i=\frac{b_i}{a_i-c_i P_{i-1}};Q_i=\frac{c_i Q_{i-1}+d_i}{a_i-c_i P_{i-1}}\) |
| C. | \(P_i=\frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}};Q_i=\frac{d_i}{a_i-c_i P_{i-1}}\) |
| D. | \(P_i=\frac{d_i}{a_i-c_i P_{i-1}};Q_i=\frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}}\) |
| Answer» C. \(P_i=\frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}};Q_i=\frac{d_i}{a_i-c_i P_{i-1}}\) | |
| 8. |
Thomas algorithm is _________ |
| A. | an analytical method |
| B. | a direct method |
| C. | an iterative method |
| D. | a least squares method |
| Answer» D. a least squares method | |
| 9. |
Thomas algorithm can be used to solve __________ |
| A. | any matrix |
| B. | all square matrices |
| C. | only penta-diagonal matrices |
| D. | only tri-diagonal matrices |
| Answer» E. | |
| 10. |
Thomas algorithm is a ___________ |
| A. | Linear equations solver |
| B. | Quadratic equations solver |
| C. | Discretization method |
| D. | Linear least square system |
| Answer» B. Quadratic equations solver | |