Let $$\overrightarrow a $$ and $$\overrightarrow b $$ be two non-zero vectors perpendicular to each other and $$|\overrightarrow a | = |\overrightarrow b |$$. If $$|\overrightarrow a \times \overrightarrow b | = |\overrightarrow a |$$, then the angle between the vectors $$\left( {\overrightarrow a + \overrightarrow b + \left( {\overrightarrow a \times \overrightarrow b } \right)} \right)$$ and $${\overrightarrow a }$$ is equal to :

A pole stands vertically inside a triangular park ABC. Let the angle of elevation of the top of the pole from each corner of the park be $${\pi \over 3}$$. If the radius of the circumcircle of $$\Delta$$ABC is 2, then the height of the pole is equal to :

Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to :

Let a complex number be w = 1 $$-$$ $${\sqrt 3 }$$i. Let another complex number z be such that |zw| = 1 and arg(z) $$-$$ arg(w) = $${\pi \over 2}$$. Then the area of the triangle with vertices origin, z and w is equal to :