If mass is written as $\mathrm{m}=\mathrm{kc}^{\mathrm{p}} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}$ then the value of $P$ will be : (Constants have their usual meaning with $\mathrm{k}$ a dimensionless constant)

Time $(T)$, velocity $(C)$ and angular momentum $(h)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be

A beaker contains a fluid of density $\rho \, kg / m^3$, specific heat $S\, J / kg\,^oC$ and viscosity $\eta $. The beaker is filled upto height $h$. To estimate the rate of heat transfer per unit area $(Q / A)$ by convection when beaker is put on a hot plate, a student proposes that it should depend on $\eta \,,\,\left( {\frac{{S\Delta \theta }}{h}} \right)$ and $\left( {\frac{1}{{\rho g}}} \right)$ when $\Delta \theta $ (in $^oC$) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for $(Q / A)$ is

The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right)\,(V - b) = RT$. Here $P$ is the pressure, $V$ is the volume, $T$ is the absolute temperature and $a,\,b,\,R$ are constants. The dimensions of $'a'$ are

Dimension of electric current is

Which of the following quantities is dimensionless