If one the vertices of the square circumscribing the circle $$\left| {z - 1} \right| = \sqrt 2 \,is\,2 + \sqrt {3\,} \,i$$. Find the other vertices of the square.

Find the area bounded by the curves $${x^2} = y,{x^2} = - y$$ and $${y^2} = 4x - 3.$$

If $$p(x)$$ be a polynomial of degree $$3$$ satisfying $$p(-1)=10, p(1)=-6$$ and $$p(x)$$ has maxima at $$x=-1$$ and $$p'(x)$$ has minima at $$x=1$$. Find the distance between the local maxima and local minima of the curve.

In an equilateral triangle, $$3$$ coins of radii $$1$$ unit each are kept so that they touch each other and also the sides of the triangle. Area of the triangle is