NCERT Exemplar Solutions
Class 11 - Mathematics - Chapter 4 : PRINCIPLE OF MATHEMATICAL INDUCTION
Multiple Choice Questions

Choose the correct answers

Question. 26

If \(10^n + 3\cdot 4^{\,n+2} + k\) is divisible by 9 for all \(n \in \mathbb{N}\), then the least positive integral value of \(k\) is

(a)

5

(b)

3

(c)

7

(d)

1

Question. 27

For all \(n \in \mathbb{N}\), \(3\cdot 5^{2n+1} + 2^{3n+1}\) is divisible by

(a)

19

(b)

17

(c)

23

(d)

25

Question. 28

If \(x^n - 1\) is divisible by \(x - k\), then the least positive integral value of \(k\) is

(a)

1

(b)

2

(c)

3

(d)

4