Let a function f : R $$\to$$ R be defined as $$f(x) = \left\{ {\matrix{ {\sin x - {e^x}} & {if} & {x \le 0} \cr {a + [ - x]} & {if} & {0 < x < 1} \cr {2x - b} & {if} & {x \ge 1} \cr } } \right.$$

where [ x ] is the greatest integer less than or equal to x. If f is continuous on R, then (a + b) is equal to:

Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is :

The probability of selecting integers a$$\in$$[$$-$$ 5, 30] such that x² + 2(a + 4)x $$-$$ 5a + 64 > 0, for all x$$\in$$R, is :

Let $$\overrightarrow a $$, $$\overrightarrow b $$, $$\overrightarrow c $$ be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle $$\theta$$, with the vector $$\overrightarrow a $$ + $$\overrightarrow b $$ + $$\overrightarrow c $$. Then 36cos²2$$\theta$$ is equal to ___________.