Solve the given two equations and select the correct answer from the given options.
$I.$ $91x^2 + 298x + 187 = 0$
$II.$ $247y^2 + 216y - 391 = 0$

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.

If ${x_1}, {x_2}, {x_3}$ are distinct roots of the equation $ax^2 + bx + c = 0$,then:

If $\alpha, \beta, \gamma$ are roots of the equation $x^3 - x - 1 = 0$,then the equation whose roots are $\frac{1}{\beta + \gamma}, \frac{1}{\gamma + \alpha}, \frac{1}{\alpha + \beta}$ is:

If the ratio of the roots of $ax^2 + 2bx + c = 0$ is the same as the ratio of the roots of $px^2 + 2qx + r = 0$,then

The exact set of values of $a$ for which the equation ${x^3}(x + 1) = 2(x + a)(x + 2a)$ has four real solutions is: