If the sum of all the solutions of $${\tan ^{ - 1}}\left( {{{2x} \over {1 - {x^2}}}} \right) + {\cot ^{ - 1}}\left( {{{1 - {x^2}} \over {2x}}} \right) = {\pi \over 3}, - 1 < x < 1,x \ne 0$$, is $$\alpha - {4 \over {\sqrt 3 }}$$, then $$\alpha$$ is equal to _____________.

A parallel plate capacitor has plate area 40 cm$$^2$$ and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system is :

Match List I with List II

Choose the correct answer from the options given below :

The root mean square velocity of molecules of gas is