The value of $k$ for which the roots $\alpha, \beta$ of the equation $x^{2}-6x+k=0$ satisfy the relation $3\alpha+2\beta=20$ is:

The number which exceeds its positive square root by $12$ is

If the product of the roots of the equation ${x^2} - 3kx + 2{e^{2\log k}} - 1 = 0$ is $7$,then for what value of $k$ will its roots be real?

If one of the roots of the equation ${x^2} + ax + 3 = 0$ is $3$ and one of the roots of the equation ${x^2} + ax + b = 0$ is three times the other root,then the value of $b$ is equal to

$I. \quad p^{2}-18 p+77=0$
$II. \quad 3 q^{2}-25 q+28=0$
$Quantity \, 1$: Value of $p$
$Quantity \, 2$: Value of $q$

Solve the given two equations and select the correct option.
$I.$ $x^{2}-8 \sqrt{3} x+45=0$
$II.$ $y^{2}-\sqrt{2} y-24=0$