Consider the following two statements

$I$. Any pair of consistent liner equations in two variables must have a unique solution.

$II$. There do not exist two consecutive integers, the sum of whose squares is $365$.Then,

The set of all real numbers $x$ for which ${x^2} - |x + 2| + x > 0,$ is

If the quadratic equation ${x^2} + \left( {2 - \tan \theta } \right)x - \left( {1 + \tan \theta } \right) = 0$ has $2$ integral roots, then sum of all possible values of $\theta $ in interval $(0, 2\pi )$ is $k\pi $, then $k$ equals 

If $x$ is real, the expression $\frac{{x + 2}}{{2{x^2} + 3x + 6}}$ takes all value in the interval

Let $\mathrm{a}=\max _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}$ and $\beta=\min _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}$

If $8 x^{2}+b x+c=0$ is a quadratic equation whose roots are $\alpha^{1 / 5}$ and $\beta^{1 / 5}$, then the value of $c-b$ is equal to:

If $x, y$ are real numbers such that $3^{(x / y)+1}-3^{(x / y)-1}=24$ then the value of $(x+y) /(x-y)$ is