If one real root of the quadratic equation 81x² + kx + 256 = 0 is cube of the other root, then a value of k is

The maximum value of the function f(x) = 3x³ – 18x² + 27x – 40 on the set S = $$\left\{ {x\, \in R:{x^2} + 30 \le 11x} \right\}$$ is :

Let A = $$\left( {\matrix{ 0 & {2q} & r \cr p & q & { - r} \cr p & { - q} & r \cr } } \right).$$   If  AA^T = I₃,   then   $$\left| p \right|$$ is :

Let f : R $$ \to $$ R be defined by f(x) = $${x \over {1 + {x^2}}},x \in R$$.   Then the range of f is :