In an experiment,the percentage errors in the measurement of physical quantities $A, B, C,$ and $D$ are $1\%, 2\%, 3\%,$ and $4\%$ respectively. The maximum percentage error in the measurement of $X,$ where $X = \frac{A^2 B^{1/2}}{C^{1/3} D^3},$ will be:

Given below are two statements: One is labelled as Assertion $(A)$ and other is labelled as Reason $(R)$.
Assertion $(A)$: Time period of oscillation of a liquid drop depends on surface tension $(S)$,if density of the liquid is $\rho$ and radius of the drop is $r$,then $T = k \sqrt{\rho r^{3} / S}$ is dimensionally correct,where $k$ is dimensionless.
Reason $(R)$: Using dimensional analysis,we find that the $R.H.S.$ has different dimensions than that of the time period.

Given that $v$ is speed,$r$ is the radius,and $g$ is the acceleration due to gravity. Which of the following is dimensionless?

$A$ and $B$ possess unequal dimensional formulas. Then,which of the following operations is not possible in any case?

Which of the following relations can be derived using dimensional analysis?

The speed of light $(c)$,gravitational constant $(G)$,and Planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be