The physical quantity which has the same dimensional formula as that of $\frac{\mathrm{Energy}}{\mathrm{Mass}\times \mathrm{Length}}$ is

Choose the correct statement(s).

$\left(\mathrm{i}\right)$ A dimensionally correct equation may be correct.

$\left(\mathrm{ii}\right)$ A dimensionally correct equation may be incorrect.

$\left(\mathrm{iii}\right)$ A dimensionally incorrect equation may be correct.

$\left(\mathrm{iv}\right)$ A dimensionally incorrect equation may be incorrect.

For ${10}^{(\mathrm{at}+3)}$, the dimensions of $a$ is (here, $t=$time),