If $$\int\limits_0^{{\pi \over 2}} {{{\cot x} \over {\cot x + \cos ecx}}} dx$$ = m($$\pi $$ + n), then m.n is equal to

For x $$ \in $$ (0, 3/2), let f(x) = $$\sqrt x $$ , g(x) = tan x and h(x) = $${{1 - {x^2}} \over {1 + {x^2}}}$$. If $$\phi $$ (x) = ((hof)og)(x), then $$\phi \left( {{\pi \over 3}} \right)$$ is equal to :

The integral $$\int {{{2{x^3} - 1} \over {{x^4} + x}}} dx$$ is equal to :
(Here C is a constant of integration)

The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is :