In a new system of units,energy $(E)$,density $(d)$,and power $(P)$ are taken as fundamental units. Then the dimensional formula of the universal gravitational constant $G$ will be .......

The density of a material in $SI$ units is $128 \ kg \ m^{-3}$. In a system of units where the unit of length is $25 \ cm$ and the unit of mass is $50 \ g$,the numerical value of the density of the material is:

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

$E, m, l$ and $G$ denote energy,mass,angular momentum,and gravitational constant respectively. Then the dimensions of $\frac{El^2}{m^5G^2}$ are:

$A$ dimensionally consistent relation for the volume $V$ of a liquid of coefficient of viscosity $\eta$ flowing per second through a tube of radius $r$ and length $l$,having a pressure difference $P$ across its ends,is:

If speed of light in vacuum $\left(3 \times 10^8 \,m/s\right)$, acceleration due to gravity $\left(10 \,m/s^2\right)$ and mass of electron $\left(9.1 \times 10^{-31} \,kg\right)$ are taken as fundamental physical quantities, then the unit of time in this system is