Question

In $n$ is a whole number greater than $1$, then $n^2(n^2-1)$ is always divisible by

• A. $12$
• B. $12$ and $24$
• C. $24$
• D. $36$

Answer 1

Answer: (A)

$12$

If $n$ is a whole number, then least value of
$n=2,3,4,....$
$n^2(n^2-1)=n^2(n+1)(n-1)$
$\therefore {\left[4(2+1)(2-1)\right]}_{n=2}=12$
Hence, the given expression is always divisible by $12$.