Question

If $n$ is any natural number then $n^2(n^2-1)$ is always divisible by

• A. $12$
• B. $24$
• C. $12-n$
• D. $8$

Answer 1

The correct option is A $12$

For n = 2 Given exp. = $2^2(2^2-1)=4\times 3=12$
n = 3 Given exp. = $3^2(3^2-1)=9\times 8=72$
n = 4 Given exp. = $4^2(4^2-1)=16\times 15=240$ etc
Thus we can see that $n^2(n^2-1)$ is always
divisible by 12 for any natural number