The function $$f:R \to \left[ { - {1 \over 2},{1 \over 2}} \right]$$ defined as

$$f\left( x \right) = {x \over {1 + {x^2}}}$$, is

If $$5\left( {{{\tan }^2}x - {{\cos }^2}x} \right) = 2\cos 2x + 9$$,

then the value of $$\cos 4x$$ is :

If two different numbers are taken from the set {0, 1, 2, 3, ........, 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is :

For three events A, B and C,

P(Exactly one of A or B occurs)
= P(Exactly one of B or C occurs)
= P (Exactly one of C or A occurs) = $${1 \over 4}$$
and P(All the three events occur simultaneously) = $${1 \over {16}}$$.

Then the probability that at least one of the events occurs, is :