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 :

Let S be the set of all values of x for which the tangent to the curve
y = ƒ(x) = x³ – x² – 2x at (x, y) is parallel to the line segment joining the points (1, ƒ(1)) and (–1, ƒ(–1)), then S is equal to :

If the tangent to the curve, y = x³ + ax – b at the point (1, –5) is perpendicular to the line, –x + y + 4 = 0, then which one of the following points lies on the curve ?

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