Let $$\mathrm{R}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}\}$$ and $$\mathrm{S}=\{1,2,3,4\}$$. Total number of onto functions $$f: \mathrm{R} \rightarrow \mathrm{S}$$ such that $$f(\mathrm{a}) \neq 1$$, is equal to ______________.

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 ____________.