Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is :

Let C be a curve given by y(x) = 1 + $$\sqrt {4x - 3} ,x > {3 \over 4}.$$ If P is a point on C, such that the tangent at P has slope $${2 \over 3}$$, then a point through which the normal at P passes, is :

Let f(x) = sin⁴x + cos⁴ x. Then f is an increasing function in the interval :

The minimum distance of a point on the curve y = x²−4 from the origin is :