If $$X$$ is a continuous random variable whose probability density function is given by $$$\,\,\,f\left( x \right) = \left\{ {\matrix{ {k\left( {5x - 2{x^2}} \right),} & {0 \le x \le 2} \cr {0,} & {Otherwise} \cr } } \right.\,\,\,\,$$$
Then $$P\left( {x > 1} \right)$$ is

The angle (in degrees) between two planar vectors $$\vec a = {{\sqrt 3 } \over 2}\widehat i + {1 \over 2}\widehat j$$ and $$\vec b = {{ - \sqrt 3 } \over 2}\widehat i + {1 \over 2}\widehat j$$ is

For the function $$\,\,f\left( {x,y} \right) = {x^2} - {y^2}\,\,$$ defined on $${R^2},$$ the point $$(0,0)$$ is

What is the value of $$\mathop {Lim}\limits_{x \to \pi /4} {{\cos x - \sin x} \over {x - \pi /4}}\,\,$$