MCQOPTIONS
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MCQOPTIONS
This section includes 7 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. |
What is the induction hypothesis assumption for the inequality m ! > 2m where m>=4? |
| A. | for m=k, k+1!>2<sup>k</sup> holds |
| B. | for m=k, k!>2<sup>k</sup> holds |
| C. | for m=k, k!>3<sup>k</sup> holds |
| D. | for m=k, k!>2<sup>k+1</sup> holds |
| Answer» C. for m=k, k!>3<sup>k</sup> holds | |
| 2. |
Which of the following is the base case for 4n+1 > (n+1)2 where n = 2? |
| A. | 64 > 9 |
| B. | 16 > 2 |
| C. | 27 < 91 |
| D. | 54 > 8 |
| Answer» B. 16 > 2 | |
| 3. |
According to principle of mathematical induction, if P(k+1) = m(k+1) + 5 is true then _____ must be true. |
| A. | P(k) = 3m<sup>(k)</sup> |
| B. | P(k) = m<sup>(k)</sup> + 5 |
| C. | P(k) = m<sup>(k+2)</sup> + 5 |
| D. | P(k) = m<sup>(k)</sup> |
| Answer» C. P(k) = m<sup>(k+2)</sup> + 5 | |
| 4. |
By induction hypothesis, the series 12 + 22 + 32 + + p2 can be proved equivalent to ____________ |
| A. | ( frac{p^2+2}{7} ) |
| B. | ( frac{p*(p + 1)*(2p + 1)}{6} ) |
| C. | ( frac{p*(p+1)}{4} ) |
| D. | p+p<sup>2</sup> |
| Answer» C. ( frac{p*(p+1)}{4} ) | |
| 5. |
For any integer m>=3, the series 2+4+6+ +(4m) can be equivalent to ________ |
| A. | m<sup>2</sup>+3 |
| B. | m+1 |
| C. | m<sup>m</sup> |
| D. | 3m<sup>2</sup>+4 |
| Answer» B. m+1 | |
| 6. |
For m = 1, 2, , 4m+2 is a multiple of ________ |
| A. | 3 |
| B. | 5 |
| C. | 6 |
| D. | 2 |
| Answer» E. | |
| 7. |
What is the base case for the inequality 7n > n3, where n = 3? |
| A. | 652 > 189 |
| B. | 42 < 132 |
| C. | 343 > 27 |
| D. | 42 <= 431 |
| Answer» D. 42 <= 431 | |