The principal value of $$[{\tan ^{ - 1}}\sqrt 3 - {\cot ^{ - 1}}( - \sqrt 3 )]$$ is

The maximum value of $${\left( {{1 \over x}} \right)^{x}}$$ is

Let matrix $$X = [{x_{ij}}]$$ is given by $$X = \left[ {\matrix{ 1 & { - 1} & 2 \cr 3 & 4 & { - 5} \cr 2 & { - 1} & 3 \cr } } \right]$$. Then the matrix $$Y = [{m_{ij}}]$$, where m_ij = Minor of x_ij, is

A function f : R $$\to$$ R defined by f(x) = 2 + x² is