A positive integer $k$, is perfect if the sum of its positive divisors equals $2k$. If $n$, is a perfect number, then the sum of the reciprocal of its positive divisors

If $a$ is the number of all even divisors and $b$ is the number of all odd divisors of the number $10800$, then $2a+3b=$

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

If $m$ is the $A.M.$of two distinct real numbers $I$ and $n$ $\left(I, n>1\right)$  and $G_1, G_2 \text{and }{G}_3$ are three geometric means between $I \text{and} n$, then $G_1^4+2G_2^4+G_3^4$ equals

Consider the following statements
$\mathrm{i}$. Number of ways of placing $\text{'}n\text{'}$objects in $k$ bins $k\le n$ ) such that no bin is empty is ${}^{(n-1)}C_{k-1}$

$\mathrm{ii}$. Number of ways of writing a positive integer " $n$ ' into a sum of $k$ positive integers is ${}^{(n-1)}C_{k-1}$

$\mathrm{iii}$. Number of ways of placing ' $n$ ' objects in $k$ bins such that at least one bin is non-empty is ${}^{(n-1)}C_{k-1}$

$\mathrm{iv}$. ${}^{n}C_k-{}^{n-1}C_k={}^{(n-1)}C_{k-1}$