Solve the given two equations and select the correct answer from the given options.
$I.$ $17 x^{2}+48 x=9$
$II.$ $13 y^{2}=32 y-12$

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:

If the inequality $kx^2 - 2x + k \geq 0$ holds good for at least one real $x$,then the complete set of values of $k$ is

The value of $p$ for which one root of the equation ${x^2} - 30x + p = 0$ is the square of the other,are

Solve the given two equations and select the correct option.
$I.$ $x^{2}+5x+6=0$
$II.$ $y^{2}+3y+2=0$

The largest possible right circular cylinder is cut out from a wooden cube of edge $7 \, cm$.
$Quantity \, I$: Volume of the cube left over after cutting out the cylinder.
$Quantity \, II$: Surface area of the cube remaining after cutting out the cylinder.
$Note$: Compare the magnitudes of both quantities.