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Practice the mathematical induction questions given below for the better understanding of the concept. Using mathematical induction to
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prove that 1⋅2⋅3 + 2⋅3⋅4 + … + n (n + 1) (n + 2) = [n (n + 1) (n + 2) (n + 3)]/4 for n ∈ N. Prove that 2n > n for all positive integers n.
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Table of Contents
MATHEMATICAL INDUCTION QUESTIONS
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3.Let P(n)
is a natural number, is a true statement
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(a).Only for n > 1
(b).Only for n is an odd positive integer
(c).Only for n is an even positive integer
(d).
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5. If a and b are natural numbers such that
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(a). a + b
(b). a – b
(c). ab
(d). 1
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6.If n is positive integer then
is divisible by
(a).574
(b).576
(c).675
(d).674
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7. Which among the following is true for all natural numbers n?
(a).
(b).
(c).
(d).None of these
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(a).9
(b). 121
(c). 11
(d). 13
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Find the value of k.
(a).1
(b).4
(c). 6
(d). None of these
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(d). None of these
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15.By using principle of mathematical induction for every natural number
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(a).3
(b).5
(c). 7
(d). 8
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(d) none of these
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(a).27
(b).19
(c). 18
(d).81
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(a).4
(b).3
(c).5
(d).7
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(a).-1
(b).-2
(c).-3
(d). -4
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(d). None of these
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(a).13
(b).11
(c).1
(d).5
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(a).6
(b).5
(c).8
(d).9
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(a).1
(b).3!
(c).3
(d).9!
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Choose the correct option.
(a).Both II and III are not true.
(b).Only II is not true
(c).Only IV is not true.
(d). Both I and IV are not true
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(d).None of these
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(b) 2
(c) 3
(d) 4
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(b) -2
(c) -3
(d) -4
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37. The sum of the cubes of three consecutive natural numbers is divisible by
(a). 9
(b). 18
(c). 27
(d). None of these
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38.For all positive integers n,
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(a).Integer
(b). Rational number
(c). Real number
(d).None of these
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(d).None of these
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(d). None of these
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(d) None of these
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(c).Only for odd integers
(d). None of these
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ANSWERS:
| 1. (c) | 11. (c) | 21. (a) | 31. (d) | 41. (b) |
| 2. (b) | 12. (b) | 22. (a) | 32. (d) | 42. (b) |
| 3. (d) | 13. (c) | 23. (a) | 33. (d) | 43. (a) |
| 4. (b) | 14. (c) | 24. (c) | 34. (a) | 44. (b) |
| 5. (a) | 15. (a) | 25. (c) | 35. (b) | 45. (c) |
| 6. (b) | 16. (d) | 26. (a) | 36. (a) | 46. (a) |
| 7. (c) | 17. (c) | 27. (b) | 37. (a) | 47. (b) |
| 8. (c) | 18. (a) | 28. (c) | 38. (a) | 48. (d) |
| 9. (b) | 19. (a) | 29. (a) | 39. (b) | 49. (b) |
| 10. (d) | 20. (b) | 30. (a) | 40. (a) | 50. (a) |
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ALSO VISIT: JEE
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DOWNLOAD MOBILE APPLICATION TO LEARN MORE: MATHEMATICAL INDUCTION QUESTIONS
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