MCQOPTIONS
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MCQOPTIONS
This section includes 11 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
What will be P(k + 1) for P(n) = n3 (n + 1)? |
| A. | (k + 1)<sup>4</sup> |
| B. | k<sup>4</sup> + 5k<sup>3</sup> + 9k<sup>2</sup> + 7k + 2 |
| C. | k<sup>4</sup> + 6k<sup>3</sup> + 9k<sup>2</sup> + 7k + 2 |
| D. | k<sup>4</sup> + 3k<sup>3</sup> + 9k<sup>2</sup> + 6k + 2 |
| Answer» C. k<sup>4</sup> + 6k<sup>3</sup> + 9k<sup>2</sup> + 7k + 2 | |
| 2. |
State whether the following series is true or not.1 + 2 + 3 + ..+ n = ( frac{n(n + 1)}{2} ) |
| A. | True |
| B. | False |
| Answer» B. False | |
| 3. |
n3 + 5n is divisible by which of the following? |
| A. | 3 |
| B. | 5 |
| C. | 7 |
| D. | 11 |
| Answer» B. 5 | |
| 4. |
n2 + 3n is always divisible by which number, provided n is an integer? |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 5 |
| Answer» B. 3 | |
| 5. |
If P(k) = k2 (k + 3) (k2 1) is true, then what is P(k + 1)? |
| A. | (k + 1)<sup>2</sup> (k + 3) (k<sup>2</sup> 1) |
| B. | (k + 1)<sup>2</sup> (k + 4) (k<sup>2</sup> 1) |
| C. | (k + 1)<sup>2</sup> (k + 4) k (k + 2) |
| D. | (k + 1) (k + 4) k (k +2) |
| Answer» D. (k + 1) (k + 4) k (k +2) | |
| 6. |
What would be the hypothesis of mathematical induction for n(n + 1) < n! (where n 4) ? |
| A. | It is assumed that at n = k, k(k + 1)! > k! |
| B. | It is assumed that at n = k, k(k + 1)! < k! |
| C. | It is assumed that at n = k, k(k + 1)! > (k + 1)! |
| D. | It is assumed that at n = k, (k + 1)(k + 2)! < k! |
| Answer» C. It is assumed that at n = k, k(k + 1)! > (k + 1)! | |
| 7. |
P(n) = n(n2 1). Which of the following does not divide P(k+1)? |
| A. | k |
| B. | k + 2 |
| C. | k + 3 |
| D. | k + 1 |
| Answer» D. k + 1 | |
| 8. |
If 103n + 24k + 1. 9 + k, is divisible by 11, then what is the least positive value of k? |
| A. | 7 |
| B. | 6 |
| C. | 8 |
| D. | 10 |
| Answer» E. | |
| 9. |
By principle of mathematical induction, 24n-1 is divisible by which of the following? |
| A. | 8 |
| B. | 3 |
| C. | 5 |
| D. | 7 |
| Answer» B. 3 | |
| 10. |
72n + 22n 2 . 3n 1 is divisible by 50 by principle of mathematical induction. |
| A. | True |
| B. | False |
| Answer» C. | |
| 11. |
For principle of mathematical induction to be true, what type of number should n be? |
| A. | Whole number |
| B. | Natural number |
| C. | Rational number |
| D. | Any form of number |
| Answer» B. Natural number | |