Let $$f:R \to R$$ be a function defined by

$$f(x) = \min \left\{ {x + 1,\left| x \right| + 1} \right\}$$, then which of the following is true?

The largest interval lying in $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$ for which the function

$$f\left( x \right) = {4^{ - {x^2}}} + {\cos ^{ - 1}}\left( {{x \over 2} - 1} \right)$$$$ + \log \left( {\cos x} \right)$$,

is defined, is

If sin^-1$$\left( {{x \over 5}} \right)$$ + cosec^-1$$\left( {{5 \over 4}} \right)$$ = $${\pi \over 2}$$, then the value of x is :

If a line makes an angle of $$\pi /4$$ with the positive directions of each of $$x$$-axis and $$y$$-axis, then the angle that the line makes with the positive direction of the $$z$$-axis is :