If domain of the function $$\log _{e}\left(\frac{6 x^{2}+5 x+1}{2 x-1}\right)+\cos ^{-1}\left(\frac{2 x^{2}-3 x+4}{3 x-5}\right)$$ is $$(\alpha, \beta) \cup(\gamma, \delta]$$, then $$18\left(\alpha^{2}+\beta^{2}+\gamma^{2}+\delta^{2}\right)$$ is equal to ______________.

Let $$S=\{1,2,3,4,5,6\}$$. Then the number of one-one functions $$f: \mathrm{S} \rightarrow \mathrm{P}(\mathrm{S})$$, where $$\mathrm{P}(\mathrm{S})$$ denote the power set of $$\mathrm{S}$$, such that $$f(n) \subset f(\mathrm{~m})$$ where $$n < m$$ is ____________.

Suppose $$f$$ is a function satisfying $$f(x + y) = f(x) + f(y)$$ for all $$x,y \in N$$ and $$f(1) = {1 \over 5}$$. If $$\sum\limits_{n = 1}^m {{{f(n)} \over {n(n + 1)(n + 2)}} = {1 \over {12}}} $$, then $$m$$ is equal to __________.