Show that ${97}^3+{24}^3$ is divisible by $11$.

If $x+\frac{1}{x}=4$, find the values of $\left(x^2-\frac{1}{x^2}\right)$.

In the given figure, area of $△\mathrm{PQR}=44.8 {\mathrm{cm}}^2, \mathrm{PL}=\mathrm{LR}$ and $\mathrm{QM}=\mathrm{MR}$. Find the area of $△\mathrm{LMR}$ in ${\mathrm{cm}}^2$

If $x-\frac{2}{x}=4$, find the value of $x^3-\frac{8}{x^3}$.

Factorize: $6a^3+10a^2-24a$

Find the value of $\theta$ if $2\tan 3\theta \cos 3\theta -\tan 3\theta +1=2\cos 3\theta$