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(A) Boltzmann constant $(k)$: $k = \frac{PV}{NT}$. Dimensional formula $[k] = \frac{[ML^2 T^{-2}]}{[K]} = ML^2 T^{-2} K^{-1}$. (Matches $III$)$(B)$ Co

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$A-III, B-IV, C-I, D-II$

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(A) Boltzmann constant $(k)$: $k = \frac{PV}{NT}$. Dimensional formula $[k] = \frac{[ML^2 T^{-2}]}{[K]} = ML^2 T^{-2} K^{-1}$. (Matches $III$)$(B)$ Coefficient of viscosity $(\eta)$: $F = 6\pi \eta rv$. Dimensional formula $[\eta] = \frac{[F]}{[r][v]} = \frac{[MLT^{-2}]}{[L][LT^{-1}]} = ML^{-1} T^{-1}$. (Matches $IV$)$(C)$ Planck's constant $(h)$: $E = hf$. Dimensional formula $[h] = \frac{[E]}{[f]} = \frac{[ML^2 T^{-2}]}{[T^{-1}]} = ML^2 T^{-1}$. (Matches $I$)$(D)$ Thermal conductivity $(k)$: $\frac{dQ}{dt} = k A \frac{dT}{dx}$. Dimensional formula $[k] = \frac{[ML^2 T^{-3}][L]}{[L^2][K]} = MLT^{-3} K^{-1}$. (Matches $II$)Therefore,the correct matching is $A-III, B-IV, C-I, D-II$.

$\text{LIST-I}$	$\text{LIST-II}$
$A$. Boltzmann constant	$I$. $ML^2 T^{-1}$
$B$. Coefficient of viscosity	$II$. $MLT^{-3} K^{-1}$
$C$. Planck's constant	$III$. $ML^2 T^{-2} K^{-1}$
$D$. Thermal conductivity	$IV$. $ML^{-1} T^{-1}$

List-$I$	List-$II$
$A$. Boltzmann constant	$I$. $[M^{-1}L^3T^{-2}]$
$B$. Stefan's constant	$II$. $[ML^2T^{-1}]$
$C$. Planck's constant	$III$. $[ML^2T^{-2}K^{-1}]$
$D$. Gravitational constant	$IV$. $[ML^0T^{-3}K^{-4}]$

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