The mass of a liquid flowing per second per unit area of cross section of a tube is proportional to $P^x$ and $v^y$,where $P$ is the pressure difference and $v$ is the velocity. Then,the relation between $x$ and $y$ is

In the expression $P = El^2m^{-5}G^{-2}$,$E$,$l$,$m$ and $G$ denote energy,angular momentum,mass and gravitational constant respectively. Show that $P$ is a dimensionless quantity.

The characteristic distance at which quantum gravitational effects are significant,the Planck length,can be determined from a suitable combination of the fundamental physical constants $G, h$ and $c$. Which of the following correctly gives the Planck length?

In a system of units,if force $(F)$,acceleration $(A)$,and time $(T)$ are taken as fundamental units,then the dimensional formula of energy is:

The frequency of vibration $f$ of a mass $m$ suspended from a spring of spring constant $K$ is given by a relation of the type $f = C\,{m^x}{K^y}$,where $C$ is a dimensionless quantity. The values of $x$ and $y$ are:

$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. We know that the equation $AD = C \ln(BD)$ holds true. Which of the following combinations is not a meaningful quantity?