If $h(x) = [\ln(x/e)] + [\ln(e/x)]$,where $[.]$ denotes the greatest integer function,then which of the following is false?

The number of solutions of the equation $2^x = x^2$ is

Let $f:(-1,1) \rightarrow \mathbb{R}$ be such that $f(\cos 4 \theta) = \frac{2}{2-\sec^2 \theta}$ for $\theta \in \left(0, \frac{\pi}{4}\right) \cup \left(\frac{\pi}{4}, \frac{\pi}{2}\right)$. Then the value$(s)$ of $f\left(\frac{1}{3}\right)$ is (are):

Given $f'(x) > 0$ and $g'(x) < 0$ for all $x \in R$,then which of the following is true?

If $f : R \rightarrow R$ is defined by $f(x) = \begin{cases} x + 4, & x < -4 \\ 3x + 2, & -4 \leq x < 4 \\ x - 4, & x \geq 4 \end{cases}$ then the correct matching of List-$I$ from List-$II$ is :
List-$I$
$(A) f(-5) + f(-4)$
$(B) f(|f(-8)|)$
$(C) f(f(-7) + f(3))$
$(D) f(f(f(f(0)))) + 1$
List-$II$
$(i) 14$
$(ii) 4$
$(iii) -11$
$(iv) -1$
$(v) 1$
$(vi) 0$

Let $f_1: R \rightarrow R$,$f_2:[0, \infty) \rightarrow R$,$f_3: R \rightarrow R$ and $f_4: R \rightarrow [0, \infty)$ be defined by:
$f_1(x) = \begin{cases} |x| & \text{if } x < 0 \\ e^x & \text{if } x \geq 0 \end{cases}$
$f_2(x) = x^2$
$f_3(x) = \begin{cases} \sin x & \text{if } x < 0 \\ x & \text{if } x \geq 0 \end{cases}$ and
$f_4(x) = \begin{cases} f_2(f_1(x)) & \text{if } x < 0 \\ f_2(f_1(x)) - 1 & \text{if } x \geq 0 \end{cases}$

List $I$	List $II$
$P. f_4$ is	$1. \text{onto but not one-one}$
$Q. f_3$ is	$2. \text{neither continuous nor one-one}$
$R. f_2 \circ f_1$ is	$3. \text{differentiable but not one-one}$
$S. f_2$ is	$4. \text{continuous and one-one}$

Codes: $P \quad Q \quad R \quad S$