Solve the given two equations and select the correct answer from the given options.
$I.$ $\quad x = \sqrt[3]{2197}$
$II.$ $\quad y^2 = 169$

Solve the given two equations and select the correct option.
$I.$ $2x^2 + 3x + 1 = 0$
$II.$ $12y^2 + 7y + 1 = 0$

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2} = 14641$
$II.$ $y = \sqrt{14641}$

If $(x^{3}-y^{3}):(x^{2}+xy+y^{2})=5:1$ and $(x^{2}-y^{2}):(x-y)=7:1$,then the ratio $2x:3y$ equals

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 $, m^3$)?

Consider the equation $x^2 + \alpha x + \beta = 0$ having roots $\alpha, \beta$ such that $\alpha \neq \beta$. Also consider the inequality $| |y - \beta| - \alpha | < \alpha$,then: