If $\alpha$ and $\beta$ are the greatest common divisors of $n(n^2-1)$ and $2n(n^2+2)$ respectively for all $n \in N$, then $\alpha \beta=$

The total number of $4$-digit numbers whose greatest common divisor with $18$ is $3$ is .... .

The number of positive integers $n$ such that $n+3$ divides $n^3-3$ is

Let $N$ be the least positive integer such that whenever a non-zero digit $c \in \{1, 2, \dots, 9\}$ is written after the last digit of $N$,the resulting number is divisible by $c$. The sum of the digits of $N$ is:

If the number of terms in the expansion of ${\left( {1 - \frac{2}{x} + \frac{4}{{{x^2}}}} \right)^n}, x \ne 0$ is $28$,then the sum of the coefficients of all the terms in this expansion is:

The number of positive odd divisors of $216$ is