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 :

If the tangent at a point P, with parameter t, on the curve x = 4t² + 3, y = 8t³−1, t $$ \in $$ R, meets the curve again at a point Q, then the coordinates of Q are :

A wire of length $$2$$ units is cut into two parts which are bent respectively to form a square of side $$=x$$ units and a circle of radius $$=r$$ units. If the sum of the areas of the square and the circle so formed is minimum, then: