The velocity of water waves $v$ may depend upon their wavelength $\lambda $, the density of water $\rho $ and the acceleration due to gravity $g$. The method of dimensions gives the relation between these quantities as

From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is

The speed of light $(c)$, gravitational constant $(G)$ and planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be

If energy $(E)$, velocity $(v)$and force $(F)$ be taken as fundamental quantity, then what are the dimensions of mass

In the relation $P = \frac{\alpha }{\beta }{e^{ – \frac{{\alpha Z}}{{k\theta }}}}$ $P$ is pressure, $Z$ is the distance, $k$ is Boltzmann constant and $\theta$ is the temperature. The dimensional formula of $\beta$ will be