When $a = -5, b = -6$ and $c = 10$,find the value of $\frac{a^{3} + b^{3} + c^{3} - 3abc}{ab + bc + ca - a^{2} - b^{2} - c^{2}}$.

If $ax^2 + bx + c = 0$ has real and distinct roots,$\alpha$ and $\beta$ $(\beta > \alpha)$. Further $a > 0, b < 0$ and $c < 0$ then :-

Solve the given two equations and select the correct answer from the given options.
$I.$ $3216 x^{2} + 3859 x + 481 = 0$
$II.$ $8132 y^{2} - 4839 y + 978 = 0$

The value of $p$ so that both the roots of the equation $(p - 5)x^2 - 2px + (p - 4) = 0$ are positive,one is less than $2$ and other is lying between $2$ and $3$,lies in the interval:

Solve the given two equations and select the correct option.
$I.$ $x^{2}-5x+6=0$
$II.$ $2y^{2}-15y+27=0$

Solve the given two equations and select the correct answer from the given options:
$I.$ $\sqrt{1225} x + \sqrt{4900} = 0$
$II.$ $(81)^{1/4} y + (343)^{1/3} = 0$