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 $${\cos ^{ - 1}}(2x - 3)$$ ?

A matrix $$A = {[{a_{ij}}]_{3 \times 3}}$$ is defined by $${a_{ij}} = \left\{ {\matrix{ {2i + 3j} & , & {i < j} \cr 5 & , & {i = j} \cr {3i - 2j} & , & {i > j} \cr } } \right.$$

The number of elements in A which are more than 5, is

If a function f defined by $$f(x) = \left\{ {\matrix{ {{{k\cos x} \over {\pi - 2x}}} & , & {if\,x \ne {\pi \over 2}} \cr 3 & , & {if\,x = {\pi \over 2}} \cr } } \right.$$ is continuous at $$x = {\pi \over 2}$$, then the value of k is