Consider the matrix $$A = \left( {\matrix{ 2 & 1 & 1 \cr 2 & 3 & 4 \cr { - 1} & { - 1} & { - 2} \cr } } \right)$$ whose eigen values are $$1, -1$$ and $$3$$. Then trace of $$\left( {{A^3} - 3{A^2}} \right)$$ is ________.

$$\mathop {\lim }\limits_{n \to \infty } \left( {\sqrt {{n^2} + n} - \sqrt {{n^2} + 1} } \right)\,\,$$ is ________.

A straight line of the form $$y=mx+c$$ passes through the origin and the point $$(x, y)=(2,6).$$ The value of $$m$$ is

Let $$\,\,f:\left[ { - 1, - } \right] \to R,\,\,$$ where $$\,f\left( x \right) = 2{x^3} - {x^4} - 10.$$ The minimum value of $$f(x)$$ is _______.