If $x=a(b-c), y=b(c-a)$ and $z=c(a-b),$ then $\left(\frac{x}{a}\right)^{3}+\left(\frac{y}{b}\right)^{3}+\left(\frac{z}{c}\right)^{3}=?$

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

If $\left(\frac{p^{-1} q^{2}}{p^{3} q^{-2}}\right)^{\frac{1}{3}}+\left(\frac{p^{5} q^{-3}}{p^{-2} q^{3}}\right)^{\frac{1}{3}}=p^{a} q^{b},$ then the value of $a+b,$ where $p$ and $q$ are different positive positive primes,is

If the roots of the equation ${x^2} - 8x + ({a^2} - 6a) = 0$ are real,then

Number of equations of the form $ax^2 + bx + 1 = 0$ having real roots,where $a, b \in \{1, 2, 3, 4\}$ is-

If the sum of the roots of the equation ${x^2} + px + q = 0$ is equal to the sum of their squares,then