The random variable $$X$$ takes on the values $$1,$$ $$2$$ (or) $$3$$ with probabilities $$\,{{2 + 5P} \over 5},{{1 + 3P} \over 5}\,\,$$ and $$\,\,{{1.5 + 2P} \over 5}\,\,$$ respectively the values of $$P$$ and $$E(X)$$ are respectively

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

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