If $a+b+c=0,$ then find the value of $a^{3}+b^{3}+c^{3}$.

The number of solutions of the equation $\ln(\ln x) = \log_x e$ is:

Solve the given two equations and select the correct answer from the given options.
$I.$ $63x - 194\sqrt{x} + 143 = 0$
$II.$ $99y - 255\sqrt{y} + 150 = 0$

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2 + bx - c = 0$,then the equation whose roots are $b$ and $c$ is

The roots of $\frac{x+4}{x-4}+\frac{x-4}{x+4}=\frac{10}{3}$ are:

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