MCQOPTIONS
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MCQOPTIONS
This section includes 9 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/x3 |
| C. | (1−x)G+6/x |
| D. | (1−x)G−x2 |
| Answer» B. (1−x)G−4/x3 | |
| 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 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,… | |
| 5. |
What is the recurrence relation for the sequence 1, 3, 7, 15, 31, 63,…? |
| A. | an = 3an-1−2an+2 |
| B. | an = 3an-1−2an-2 |
| C. | an = 3an-1−2an-1 |
| D. | an = 3an-1−2an-3 |
| Answer» C. an = 3an-1−2an-1 | |
| 6. |
What is the generating function for the generating sequence A = 1, 9, 25, 49,…?a) 1+(A-x2)b) (1-A)-1/xc) (1- |
| A. | 1+(A-x2) |
| B. | (1-A)-1/x |
| C. | (1-A)+1/x2 |
| D. | (A-x)/x3 |
| Answer» C. (1-A)+1/x2 | |
| 7. |
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. \(\frac{1}{(1-x2)}\) | |
| 8. |
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. | 1-6x2 |
| Answer» C. \(\frac{1}{(1-4x)}\) | |
| 9. |
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,… | |