Solve the given two equations and select the correct option.
$I.$ $x = \frac{\sqrt{256}}{\sqrt{576}}$
$II.$ $3y^2 + y - 2 = 0$

Let $[t]$ denote the greatest integer $\leq t$. Then the equation in $x$,$[x]^{2} + 2[x + 2] - 7 = 0$,has

Solve the given two equations and select the correct answer from the given options.
$I.$ $\sqrt{25} x + \sqrt{16} y = 41$
$II.$ $\sqrt{16} x + \sqrt{25} y = 40$

If $\alpha$ and $\beta$ are roots of $ax^2 + 2bx + c = 0$,then $\sqrt{\frac{\alpha}{\beta}} + \sqrt{\frac{\beta}{\alpha}}$ is equal to

If the roots of the equation $x^2 + px + q = 0$ are $\alpha$ and $\beta$,and the roots of the equation $x^2 - xr + s = 0$ are $\alpha^4$ and $\beta^4$,then the roots of the equation $x^2 - 4qx + 2q^2 - r = 0$ will be:

If a root of the equation $x^2 + px + 12 = 0$ is $4$,while the roots of the equation $x^2 + px + q = 0$ are equal,then the value of $q$ will be