Match List$-I$ with List$-II.$

List$-I$	List$-II$
$(a)$ Torque	$(i)$ ${MLT}^{-1}$
$(b)$ Impulse	$(ii)$ ${MT}^{-2}$
$(c)$ Tension	$(iii)$ ${ML}^{2} {T}^{-2}$
$(d)$ Surface Tension	$(iv)$ ${ML} {T}^{-2}$

Choose the most appropriate answer from the option given below :

An expression of energy density is given by $u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)$, where $\alpha, \beta$ are constants, $x$ is displacement, $k$ is Boltzmann constant and $t$ is the temperature. The dimensions of $\beta$ 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 $p$ and radius of the drop is $r$, then $T = k \sqrt{ pr ^{3} / s ^{3 / 2}}$ is dimensionally correct, where $K$ is dimensionless.

Reason $(R)$: Using dimensional analysis we get $R.H.S.$ having different dimension than that of time period.

In the light of above statements, choose the correct answer from the options given below.

The entropy of any system is given by

${S}=\alpha^{2} \beta \ln \left[\frac{\mu {kR}}{J \beta^{2}}+3\right]$

Where $\alpha$ and $\beta$ are the constants. $\mu, J, K$ and $R$ are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant repectively. [Take ${S}=\frac{{dQ}}{{T}}$ ]

Choose the incorrect option from the following:

Force $(F)$ and density $(d)$ are related as $F\, = \,\frac{\alpha }{{\beta \, + \,\sqrt d }}$ then dimension of $\alpha $ are

Which of the following is dimensionally incorrect?