The number of bijective functions $f :\{1,3,5, 7, \ldots \ldots . .99\} \rightarrow\{2,4,6,8, \ldots \ldots, 100\}$, such that $f(3) \geq f(9) \geq f(15) \geq f(21) \geq \ldots \ldots f(99), \quad$ is

The function $f(x) = \;|px – q|\; + r|x|,\;x \in ( – \infty ,\;\infty )$, where $p > 0,\;q > 0,\;r > 0$ assumes its minimum value only at one point, if

The graph of $y = f(x)$ is shown then number of solutions of the equation $f(f(x)) =2$ is

If $x = {\log _2}\left( {\sqrt {56 + \sqrt {56 + \sqrt {56 +  …. + \infty } } } } \right)$ then 

Let $f : R \rightarrow R$ be a function such that $f(x)=\frac{x^2+2 x+1}{x^2+1}$. Then