Using mathematical induction, the numbers&nbs

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsShort Answer Type

11.

If A = 1201, then by the principle of Mathematical induction, prove that An12n01


 Multiple Choice QuestionsMultiple Choice Questions

12.

The value of 2, 6, 10 ... (4n - 6)(4n - 2) is equal to

  • C(2n, n)

  • (n + 1)(n + 2)(n + 3) ... (2n)

  • n! P (2n, n)

  • None of above


Advertisement

13.

Using mathematical induction, the numbers an 's are defined by,a0 = 1, an + 1 = 3n2 + n + an, n  0Then an = ?

  • n3 + n2 + 1

  • n3 - n2 + 1

  • n3 - n2

  • n3 + n2


B.

n3 - n2 + 1

Given, a0 = 1, an + 1 = 3n2 + n + an       a1 = 30 +0 + a0 = 1and     a2 = 312 + 1 +a1 = 3 +1 +1 = 5From option (b),Let  P(n) = n3 - n2 +1   P(0) = 0 - 0 + 1 = 1 = a0       P(1) = 12 - 12 + 1 = 1 = a1       P(2) = 22 - 22 + 1 = 1 = a2Hence option b is correct


Advertisement
Advertisement