If 111.....1 (n digits) is divisible by 9, then the least value of n is:

Correct option is A

Given:

111...1 (n digits) is divisible by 9.

Formula Used :

Divisibility rule of 9: A number is divisible by 9 if the sum of its digits is divisible by 9.

Solution:

For the number 111...1 (n digits) to be divisible by 9, the sum of its digits must be divisible by 9.

The sum of the digits is simply n (since there are n ones).

Therefore, n must be a multiple of 9.

The smallest positive multiple of 9 is 9 itself.

So, the least value of n is 9.

Alternate Method:

We can test the divisibility of numbers formed by repeated ones:

n = 1: 1 (not divisible by 9)

n = 2: 11 (not divisible by 9)

n = 3: 111 (not divisible by 9)

...

n = 9: 111111111 (divisible by 9, as 1+1+1+1+1+1+1+1+1 = 9, which is divisible by 9