The force $F$ is given in terms of time $t$ and displacement $x$ by the equation $F = A\,cos\,Bx + C\,sin\,Dt.$ The dimensional formulae of $D/B$ is

If energy $(E),$ velocity $(V)$ and time $(T)$ are chosen as the fundamental quantities, the dimensional formula of surface tension will be

The force of interaction between two atoms is given by $F\, = \,\alpha \beta \,\exp \,\left( { – \frac{{{x^2}}}{{\alpha kt}}} \right);$ where $x$ is the distance, $k$ is the Boltzmann constant and $T$ is temperature and $\alpha $ and $\beta $ are two constants. The dimension of $\beta $ is

A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let $R$ be the radius of its largest horizontal section. A small disturbance causes the drop to vibrate with frequency $v$ about its equilibrium shape. By dimensional analysis, the ratio $\frac{v}{\sqrt{\sigma / \rho R^3}}$ can be (Here, $\sigma$ is surface tension, $\rho$ is density, $g$ is acceleration due to gravity and $k$ is an arbitrary dimensionless constant)

In terms of potential difference $V$, electric current $I$, permittivity $\varepsilon_0$, permeability $\mu_0$ and speed of light $c$, the dimensionally correct equation$(s)$ is(are)

$(A)$ $\mu_0 I ^2=\varepsilon_0 V ^2$ $(B)$ $\varepsilon_0 I =\mu_0 V$ $(C)$ $I =\varepsilon_0 cV$ $(D)$ $\mu_0 cI =\varepsilon_0 V$