MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find the sequence generated by 1/1 x2 x4.,assume that 1, 1, 2, 3, 5, 8, has generating function 1/1 x x2. |
| A. | 0, 0, 1, 1, 2, 3, 5, 8, |
| B. | 0, 1, 2, 3, 5, 8, |
| C. | 1, 1, 2, 2, 4, 6, 8, |
| D. | 1, 4, 3, 5, 7, |
| Answer» B. 0, 1, 2, 3, 5, 8, | |
| 2. |
Suppose G is the generating function for the sequence 4, 7, 10, 13, 16, 19, , the find a generating function (in terms of G) for the sequence of differences between terms. |
| A. | (1 x)G 4/x |
| B. | (1 x)G 4/x<sup>3</sup> |
| C. | (1 x)G+6/x |
| D. | (1 x)G x<sup>2</sup> |
| Answer» B. (1 x)G 4/x<sup>3</sup> | |
| 3. |
What is the generating function for the sequence with closed formula an=4(7n)+6( 2)n? |
| A. | (4/1 7x)+6! |
| B. | (3/1 8x) |
| C. | (4/1 7x)+(6/1+2x) |
| D. | (6/1-2x)+8 |
| Answer» D. (6/1-2x)+8 | |
| 4. |
What will be the sequence generated by the generating function 4x/(1-x)2? |
| A. | 12, 16, 20, 24, |
| B. | 1, 3, 5, 7, 9, |
| C. | 0, 4, 8, 12, 16, 20, |
| D. | 0, 1, 1, 3, 5, 8, 13, |
| Answer» D. 0, 1, 1, 3, 5, 8, 13, | |
| 5. |
What is multiplication of the sequence 1, 2, 3, 4, by the sequence 1, 3, 5, 7, 11, .? |
| A. | 1, 5, 14, 30, |
| B. | 2, 8, 16, 35, |
| C. | 1, 4, 7, 9, 13, |
| D. | 4, 8, 9, 14, 28, |
| Answer» B. 2, 8, 16, 35, | |
| 6. |
What is the recurrence relation for the sequence 1, 3, 7, 15, 31, 63, ? |
| A. | a<sub>n</sub> = 3a<sub>n-1</sub> 2a<sub>n+2</sub> |
| B. | a<sub>n</sub> = 3a<sub>n-1</sub> 2a<sub>n-2</sub> |
| C. | a<sub>n</sub> = 3a<sub>n-1</sub> 2a<sub>n-1</sub> |
| D. | a<sub>n</sub> = 3a<sub>n-1</sub> 2a<sub>n-3</sub> |
| Answer» C. a<sub>n</sub> = 3a<sub>n-1</sub> 2a<sub>n-1</sub> | |
| 7. |
What is the generating function for the generating sequence A = 1, 9, 25, 49, ? |
| A. | 1+(A-x<sup>2</sup>) |
| B. | (1-A)-1/x |
| C. | (1-A)+1/x<sup>2</sup> |
| D. | (A-x)/x<sup>3</sup> |
| Answer» C. (1-A)+1/x<sup>2</sup> | |
| 8. |
What is the generating function for generating series 1, 2, 3, 4, 5, ? |
| A. | ( frac{2}{(1-3x)} ) |
| B. | ( frac{1}{(1+x)} ) |
| C. | ( frac{1}{(1 x)^2} ) |
| D. | ( frac{1}{(1-x2)} ) |
| Answer» D. ( frac{1}{(1-x2)} ) | |
| 9. |
What is the generating function for the sequence 1, 6, 16, 216, .? |
| A. | ( frac{(1+6x)}{x^3} ) |
| B. | ( frac{1}{(1-6x)} ) |
| C. | ( frac{1}{(1-4x)} ) |
| D. | 1-6x<sup>2</sup> |
| Answer» C. ( frac{1}{(1-4x)} ) | |
| 10. |
What is the sequence depicted by the generating series 4 + 15x2 + 10x3 + 25x5 + 16x6+ ? |
| A. | 10, 4, 0, 16, 25, |
| B. | 0, 4, 15, 10, 16, 25, |
| C. | 4, 0, 15, 10, 25, 16, |
| D. | 4, 10, 15, 25, |
| Answer» D. 4, 10, 15, 25, | |