The expression given below shows the variation of velocity $(v)$ with time $(t)$,$v=At^2+\frac{Bt}{C+t}$. The dimension of $ABC$ is

$A$ 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 the time period $T \propto P^a d^b E^c$,where $P$ is pressure,$d$ is density,and $E$ is energy,then the value of $c$ is:

Velocities $(V)$ and accelerations $(a)$ in two systems of units $1$ and $2$ are related as $V_2 = \frac{n}{m^2} V_1$ and $a_2 = \frac{a_1}{mn}$ respectively. Here $m$ and $n$ are constants. Dimensionally, the relations between distances ($S_1$ and $S_2$) and times ($t_1$ and $t_2$) in the two systems are respectively:

Assertion $(A)$: Energy per unit volume and angular momentum can be added dimensionally.
Reason $(R)$: Physical quantities having same dimensions can be added or subtracted.

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)