If velocity $v$,acceleration $A$,and force $F$ are chosen as fundamental quantities,then the dimensional formula of angular momentum in terms of $v, A$,and $F$ would be

If the velocity of light $C$, the gravitational constant $G$, and Planck's constant $h$ are chosen as the fundamental units, the dimension of density in the new system is

Density of a liquid in $CGS$ system is $0.625 \ g/cm^3$. What is its magnitude in $SI$ system?

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity $X$ as follows: $[position] = [X^\alpha]$; $[speed] = [X^\beta]$; $[acceleration] = [X^p]$; $[linear momentum] = [X^q]$; $[force] = [X^r]$. Then -
$(A)$ $\alpha + p = 2\beta$
$(B)$ $p + q - r = \beta$
$(C)$ $p - q + r = \alpha$
$(D)$ $p + q + r = \beta$

The foundations of dimensional analysis were laid down by

Force is given by the expression, $F = A \cos(Bx) + C \cos(Dt)$, where $x$ is displacement and $t$ is time. The dimension of $\left(\frac{D}{B}\right)$ is the same as that of