If ƒ(x) is a non-zero polynomial of degree four, having local extreme points at x = –1, 0, 1; then the set
S = {x $$ \in $$ R : ƒ(x) = ƒ(0)}
Contains exactly :

The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is

Given that the slope of the tangent to a curve y = y(x) at any point (x, y) is $$2y \over x^2$$. If the curve passes through the centre of the circle x² + y² – 2x – 2y = 0, then its equation is :

Let ƒ : [0, 2] $$ \to $$ R be a twice differentiable function such that ƒ''(x) > 0, for all x $$ \in $$ (0, 2). If $$\phi $$(x) = ƒ(x) + ƒ(2 – x), then $$\phi $$ is :