The maximum value of $$f\left( x \right) = 2{x^3} - 9{x^2} + 12x - 3$$
in the interval $$\,0 \le x \le 3$$ is __________.

For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the angle between the hypotenuse and the side is

The Taylor series expansion of $$\,\,{{\sin x} \over {x - \pi }}\,\,$$ at $$x = \pi $$ is given by

In the Taylor series expansion of $${e^x} + \sin x$$ about the point $$x = \pi ,$$ the coefficient of $${\left( {x = \pi } \right)^2}$$ is