If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2; then p(0) is equal to :

The value of

$${\left( {{{1 + \sin {{2\pi } \over 9} + i\cos {{2\pi } \over 9}} \over {1 + \sin {{2\pi } \over 9} - i\cos {{2\pi } \over 9}}}} \right)^3}$$ is :

The domain of the function
f(x) = $${\sin ^{ - 1}}\left( {{{\left| x \right| + 5} \over {{x^2} + 1}}} \right)$$ is (– $$\infty $$, -a]$$ \cup $$[a, $$\infty $$). Then a is equal to :

Let $$\alpha $$ and $$\beta $$ be the roots of the equation
5x² + 6x – 2 = 0. If S_n = $$\alpha $$ⁿ + $$\beta $$ⁿ, n = 1, 2, 3...., then :