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

Let $f(x) = ax^2 + bx + c$,where $a, b, c$ are integers. Suppose $f(1) = 0$,$40 < f(6) < 50$,$60 < f(7) < 70$,and $1000t < f(50) < 1000(t+1)$ for some integer $t$. Then,the value of $t$ is

If $x = \sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}$,then $x^2(x-4)^2$ is equal to :

If $l, m, n$ are real and $l \neq m$,then the roots of the equation $(l - m)x^2 - 5(l + m)x - 2(l - m) = 0$ are

The roots of $ax^2 + b = 0$ are real and distinct if:

If $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \dots \text{to } \infty}}}$,then