Let slope of the tangent line to a curve at any point P(x, y) be given by $${{x{y^2} + y} \over x}$$. If the curve intersects the line x + 2y = 4 at x = $$-$$2, then the value of y, for which the point (3, y) lies on the curve, is :

The maximum slope of the curve $$y = {1 \over 2}{x^4} - 5{x^3} + 18{x^2} - 19x$$ occurs at the point :

Let f be any function defined on R and let it satisfy the condition : $$|f(x) - f(y)|\, \le \,|{(x - y)^2}|,\forall (x,y) \in R$$

If f(0) = 1, then :

If the curves, $${{{x^2}} \over a} + {{{y^2}} \over b} = 1$$ and $${{{x^2}} \over c} + {{{y^2}} \over d} = 1$$ intersect each other at an angle of 90$$^\circ$$, then which of the following relations is TRUE?