Solve the given two equations and choose the correct option.
$I.$ $99 x^{2} + 149 x + 56 = 0$
$II.$ $156 y^{2} + 287 y + 132 = 0$

The least integer $k$ which makes the roots of the equation ${x^2} + 5x + k = 0$ imaginary is

If $\alpha$ and $\beta$ are the roots of the equation ${x^2} - (1 + {n^2})x + \frac{1}{2}(1 + {n^2} + {n^4}) = 0$,then the value of ${\alpha ^2} + {\beta ^2}$ is:

If $\alpha$ and $\beta$ are the roots of the equation $x^2 + 2x + 4 = 0$,then $\frac{1}{\alpha^3} + \frac{1}{\beta^3}$ is equal to

If $5x + 9y = 5$ and $125x^3 + 729y^3 = 120$,then the value of the product of $x$ and $y$ is:

The surface area of a pipe,open at both ends,is equal to $628 \, m^2$. The difference between its length and its radius is $15 \, m$. If the pipe were closed at one end,what amount of water could it hold (in $, m^3$)?