The equation of state of a real gas is given by $(P+\frac{a}{V^2})(V-b)=RT$,where $P, V$ and $T$ are pressure,volume and temperature respectively and $R$ is the universal gas constant. The dimensions of $\frac{a}{b^2}$ are similar to that of:

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:

Assertion $(A) :$ Physical relations involving addition and subtraction cannot be derived by dimensional analysis.
Reason $(R) :$ Numerical constants cannot be deduced by the method of dimensions.

Which one of the following combinations of constants has the dimensions of time? $[G=$ gravitational constant,$h=$ Planck's constant,$c=$ velocity of light$]$

Which of the following expressions can be deduced on the basis of dimensional analysis? (All symbols have their usual meanings)