Suppose $m, n$ are positive integers such that $6^m+2^{m+n} \cdot 3^w+2^n=332$. The value of the expression $m^2+m n+n^2$ is

If $\sqrt {3{x^2} – 7x – 30} + \sqrt {2{x^2} – 7x – 5} = x + 5$,then $x$ is equal to

The set of values of $x$ which satisfy $5x + 2 < 3x + 8$ and $\frac{{x + 2}}{{x – 1}} < 4,$ is

If $\alpha ,\beta $ and $\gamma $ are the roots of ${x^3} + px + q = 0$, then the value of ${\alpha ^3} + {\beta ^3} + {\gamma ^3}$ is equal to

Sum of the solutions of the equation $\left[ {{x^2}} \right] – 2x + 1 = 0$ is (where $[.]$ denotes greatest integer function)