Solve the given two equations and select the correct option.
$I.$ $\sqrt{500} x + \sqrt{402} = 0$
$II.$ $\sqrt{360} y + \sqrt{200} = 0$

If $\alpha_1 < \alpha_2 < \alpha_3 < \alpha_4 < \alpha_5 < \alpha_6$,then the equation $(x - \alpha_1)(x - \alpha_3)(x - \alpha_5) + 3(x - \alpha_2)(x - \alpha_4)(x - \alpha_6) = 0$ has :-

The solution set of the equation $x^{\log_x(1 - x)^2} = 9$ is

Let $\alpha$ and $\beta$ be the roots of the equation $x^2 - 6x - 2 = 0$. If $a_n = \alpha^n - \beta^n$ for $n \ge 1$,then the value of $\frac{a_{10} - 2a_8}{2a_9}$ is equal to:

Solve the given two equations and choose the correct answer from the given options.
$I.$ $x^{2} = 729$
$II.$ $y = \sqrt{729}$

Solve the given two equations and select the correct answer from the given options.
$I.$ $5x^2 + 3x - 14 = 0$
$II.$ $10y^2 - 3y - 27 = 0$