If $$f$$ is a function defined on $$(0,1)$$ by $$f(x)=\min \{x-[x],-x-[x]\}$$, then $$(f \circ f o f o f)(x)$$ is equal to $$\rightarrow([\cdot]$$ greatest integer function)

If $${({x^2} + 5x + 5)^{x + 5}} = 1$$, then the number of integers satisfying this equation is

If $$\frac{x^4}{(x-1)(x-2)}=f(x)+\frac{A}{x-1}+\frac{B}{x-2}$$, then

Which statement among the following is true?

(i) the function $$f(x)=x|x|$$ is strictly increasing on $$R-\{0\}$$.

(ii) the function $$f(x)=\log _{(1 / 4)} x$$ is strictly increasing on $$(0, \infty)$$.

(iii) a one-one function is always an increasing function.

(iv) $$f(x)=x^{1 / 3}$$ is strictly decreasing on $$R$$