$${\sin ^1}\left( {\sin {{2\pi } \over 3}} \right) + {\cos ^{ - 1}}\left( {\cos {{7\pi } \over 6}} \right) + {\tan ^{ - 1}}\left( {\tan {{3\pi } \over 4}} \right)$$ is equal to :

Let f : R $$\to$$ R be a function defined by $$f(x) = {{2{e^{2x}}} \over {{e^{2x}} + e}}$$. Then $$f\left( {{1 \over {100}}} \right) + f\left( {{2 \over {100}}} \right) + f\left( {{3 \over {100}}} \right) + \,\,\,.....\,\,\, + \,\,\,f\left( {{{99} \over {100}}} \right)$$ is equal to ______________.

If the sum of all the roots of the equation

$${e^{2x}} - 11{e^x} - 45{e^{ - x}} + {{81} \over 2} = 0$$ is $${\log _e}p$$, then p is equal to ____________.

The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is _____________.