Five numbers $${x_1},{x_2},{x_3},{x_4},{x_5}$$ are randomly selected from the numbers 1, 2, 3, ......., 18 and are arranged in the increasing order $$({x_1} < {x_2} < {x_3} < {x_4} < {x_5})$$. The probability that $${x_2} = 7$$ and $${x_4} = 11$$ is :

The value of $$\cos \left( {{{2\pi } \over 7}} \right) + \cos \left( {{{4\pi } \over 7}} \right) + \cos \left( {{{6\pi } \over 7}} \right)$$ is equal to :

$${\sin ^1}\left( {\sin {{2\pi } \over 3}} \right) + {\cos ^{ - 1}}\left( {\cos {{7\pi } \over 6}} \right) + {\tan ^{ - 1}}\left( {\tan {{3\pi } \over 4}} \right)$$ 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 ______________.