A hypothetical equation is given as $\rho = a \sqrt{P} + bT^2$, where $\rho$ is density, $P$ is pressure, and $T$ is temperature. The dimensions of $\frac{a}{b}$ are:

The time taken by an electron to go from ground state to excited state is one shake (one shake = ${10^{ - 8}}$ s) this time in nanosecond will be

There are atomic clocks capable of measuring time with an accuracy of 1 part in ${10^{11}}$. If two such clocks are operated with precision, then after running for 5000 years, these will record