Which of the following functions are odd?
$I. f(x)=x\left(\frac{e^x-1}{e^x+1}\right)$
$II. f(x)=k^x+k^{-x}+\cos x$
$III. f(x)=\log \left(x+\sqrt{x^2+1}\right)$

The equation $6^{x}+8^{x}=10^{x}$ has

If $f(x) = \frac{1}{\sqrt{x+2 \sqrt{2x-4}}} + \frac{1}{\sqrt{x-2 \sqrt{2x-4}}}$ for $x > 2$, then $f(11)$ is equal to

The number of positive integral values of $K$ for which the equation $K = |x + |2x - 1|| - |x - |2x - 1||$ has exactly three real solutions is

For a real number $r$,we denote by $[r]$ the largest integer less than or equal to $r$. If $x, y$ are real numbers with $x, y \geq 1$,then which of the following statements is always true?

The real valued function $f(x) = \frac{|x-a|}{x-a}$ is