What is the value of $999 \frac{1}{2} + 999 \frac{1}{6} + 999 \frac{1}{12} + 999 \frac{1}{20} + 999 \frac{1}{30}$?

If $2p + \frac{1}{p} = 4$,then the value of $p^{3} + \frac{1}{8p^{3}}$ is:

If the numerator of a fraction is increased by $2$ and the denominator is increased by $3,$ the fraction becomes $\frac{7}{9},$ and if both the numerator and the denominator are decreased by $1,$ the fraction becomes $\frac{4}{5}.$ What is the original fraction?

$\frac{1}{\left(2 \frac{1}{3}\right)}+\frac{1}{\left(1 \frac{3}{4}\right)}$ is equal to

The value of $\frac{(243)^{\frac{n}{5}} \times 3^{2n+1}}{9^{n} \times 3^{n-1}}$ is

Choose the incorrect relation$(s)$ from the following:
$(i)$ $\sqrt{6}+\sqrt{2}=\sqrt{5}+\sqrt{3}$
$(ii)$ $\sqrt{6}+\sqrt{2}<\sqrt{5}+\sqrt{3}$
$(iii)$ $\sqrt{6}+\sqrt{2}>\sqrt{5}+\sqrt{3}$