If $A, B, C$ and $D$ represent velocity,acceleration,inductance and capacitance respectively,then $A^{-1} BCD$ has the dimensions of

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:

In a relation $F = a \sin(k_1x) + b \sin(k_2t)$,where $F$,$x$,and $t$ denote force,distance,and time respectively. The units of $k_1$ and $k_2$ are respectively:

Which of the following operations can be performed on two physical quantities $A$ and $B$ if they possess different dimensions?

When a wave traverses a medium, the displacement of a particle located at $x$ at a time $t$ is given by $y = a \sin (bt - cx)$, where $a, b,$ and $c$ are constants of the wave. Which of the following is a quantity with dimensions?

The potential energy of a point particle is given by the expression $V(x) = -\alpha x + \beta \sin(x / \gamma)$. $A$ dimensionless combination of the constants $\alpha, \beta$ and $\gamma$ is