If the tangent to the curve y² = x³ at (m², m³) is also a normal to the curve at (m², m³), then the value of mM is

If the function $$f(x) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1$$ [a > 0] attains its maximum and minimum at p and q respectively such that p² = q, then a is equal to

Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 12$$.

Then

In open interval $$\left( {0,\,{\pi \over 2}} \right)$$