For two matrices $$P = \left[ {\matrix{ 3 & 4 \cr { - 1} & 2 \cr 0 & 1 \cr } } \right]$$ and $${Q^T} = \left[ {\matrix{ { - 1} & 2 & 1 \cr 1 & 2 & 3 \cr } } \right]$$ P $$-$$ Q is

The function $$f(x) = 2{x^3} - 15{x^2} + 36x + 6$$ is increasing in the interval

If $$x = 2\cos \theta - \cos 2\theta $$ and $$y = 2\sin \theta - \sin 2\theta $$, then $${{dy} \over {dx}}$$ is

What is the domain of the function $${\cos ^{ - 1}}(2x - 3)$$ ?