If $E$,$L$,$m$ and $G$ denote the quantities as energy,angular momentum,mass and constant of gravitation respectively,then the dimensions of $P$ in the formula $P = EL^2 m^{-5} G^{-2}$ are

If the present units of length,time,and mass $(m, s, kg)$ are changed to $100 \; m, 100 \; s, 0.1 \; kg$,then:

$A$ 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:

The efficiency of an engine is given by $\eta = \frac{\alpha \beta}{\sin \theta} \cdot \log_{e} \frac{\beta x}{kT}$, where $\alpha$ and $\beta$ are constants. If $T$ is the absolute temperature, $k$ is the Boltzmann constant, $\theta$ is angular displacement, and $x$ is distance, then the incorrect statement is:

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

From the equation $\tan \theta = \frac{rg}{v^2}$,one can obtain the angle of banking $\theta$ for a cyclist taking a curve (the symbols have their usual meanings). Then say,it is