If the area of an equilateral triangle inscribed in the circle x² + y² + 10x + 12y + c = 0 is $$27\sqrt 3 $$ sq units then c is equal to :

Let f : ($$-$$1, 1) $$ \to $$ R be a function defined by f(x) = max $$\left\{ { - \left| x \right|, - \sqrt {1 - {x^2}} } \right\}.$$ If K be the set of all points at which f is not differentiable, then K has exactly -

A helicopter is flying along the curve given by y – x^3/2 = 7, (x $$ \ge $$ 0). A soldier positioned at the point $$\left( {{1 \over 2},7} \right)$$ wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is -

If  $$\int\limits_0^x \, $$f(t) dt = x² + $$\int\limits_x^1 \, $$ t²f(t) dt then f '$$\left( {{1 \over 2}} \right)$$ is -