If $\theta$ is small $\&$ positive number then which of the following is/are correct ?

The domain of the function $f(x) = \frac{{{{\sin }^{ - 1}}(3 - x)}}{{\ln (|x|\; - 2)}}$ is

The function $f(x) =$ ${x^{\frac{1}{{\ln \,x}}}}$

Let $x$ denote the total number of one-one functions from a set $A$ with $3$ elements to a set $B$ with $5$ elements and $y$ denote the total number of one-one functions from the set $A$ to the set $A \times B$. Then ...... .

Let $2{\sin ^2}x + 3\sin x - 2 > 0$ and ${x^2} - x - 2 < 0$ ($x$ is measured in radians). Then $x$  lies in the interval

Let $R$ be the set of all real numbers and let $f$ be a function from $R$ to $R$ such that $f(x)+\left(x+\frac{1}{2}\right) f(1-x)=1$, for all $x \in R$. Then $2 f(0)+3 f(1)$ is equal to