The number of solutions of the equation $2{e^{\left| x \right|}}{\tan ^{ - 1}}\left| x \right| = 1$ is

Function $f(x) = \sin x + \tan x + \operatorname{sgn}(x^2 - 6x + 10)$ is (where $\operatorname{sgn}$ is the signum function):

Let $f : \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow \mathbb{R}$ be defined by $f(x) = (\log(\sec x + \tan x))^3$. Then:

Let $[x]$ represent the greatest integer less than or equal to $x$,${x} = x - [x]$,$\sqrt{2} = 1.414$ and $\sqrt{3} = 1.732$. If $f(x) = \{x + [\frac{x}{1+x^2}]\}$ is a real-valued function,then $f(\sqrt{2}) + f(-\sqrt{3}) = $

Match the functions given in List-$I$ with their relevant characteristics from List-$II$.

List-$I$	List-$II$
$(A)$ $\sinh x$	$(I)$ Domain is $(-1, 1)$, even function
$(B)$ $\text{sech } x$	$(II)$ Domain is $[1, \infty)$, neither even nor odd function
$(C)$ $\tanh x$	$(III)$ Even function
$(D)$ $\text{cosech}^{-1} x$	$(IV)$ Range is $\mathbb{R}$, odd function
	$(V)$ Range is $(-1, 1)$, odd function

The correct answer is

For $\theta \in [0, \pi]$,let $f(\theta) = \sin(\cos \theta)$ and $g(\theta) = \cos(\sin \theta)$. Let $a = \max_{0 \leq \theta \leq \pi} f(\theta)$,$b = \min_{0 \leq \theta \leq \pi} f(\theta)$,$c = \max_{0 \leq \theta \leq \pi} g(\theta)$,and $d = \min_{0 \leq \theta \leq \pi} g(\theta)$. The correct inequalities satisfied by $a, b, c, d$ are: