If pressure $P$,velocity $V$ and time $T$ are taken as fundamental physical quantities,the dimensional formula of force is

In the equation,pressure $P = \frac{c - t^{2}}{DS}$,where $S$ and $t$ represent the distance and time respectively. The dimensions of $\left(\frac{D}{c}\right)$ are

Consider a spongy block of mass $m$ floating on a flowing river. The maximum mass of the block is related to the speed of the river flow $v$, acceleration due to gravity $g$, and the density of the block $\rho$ such that $m_{\max} = k v^x g^y \rho^z$ ($k$ is a constant). The values of $x, y$, and $z$ should then respectively be:
(Mass of the spongy block is assumed to vary due to absorption of water by it)

If $P, Q$ and $R$ are physical quantities having different dimensions,which of the following combinations can never be a meaningful quantity?

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.

If the force is given by $F = at + bt^2$ where $t$ is time, the dimensions of $a$ and $b$ are: