In the equation $x = a + bt + ct^2$,where $x$ is in meters and $t$ is in seconds,find the units of $a, b,$ and $c$.

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

The entropy of any system is given by
$S = \alpha^{2} \beta \ln \left[\frac{\mu k R}{J \beta^{2}} + 3\right]$
Where $\alpha$ and $\beta$ are constants. $\mu, J, k$ and $R$ are the number of moles,mechanical equivalent of heat,Boltzmann constant,and gas constant respectively. [Take $S = \frac{dQ}{T}$].
Choose the incorrect option from the following:

$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. We know that the equation $AD = C \ln(BD)$ holds true. Which of the following combinations is not a meaningful quantity?

In an experiment,four quantities $a, b, c,$ and $d$ are measured with percentage errors of $1\%, 2\%, 3\%,$ and $4\%$ respectively. The quantity $P$ is calculated as $P = \frac{a^3 b^2}{cd}$. The percentage error in $P$ is ........ $\%$

Obtain the relation between the units of some physical quantity in two different systems of units. Obtain the relation between the $MKS$ and $CGS$ unit of work.