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(D) The dimensions are calculated as follows:$1$. For $Pa \cdot s$ (Coefficient of viscosity):$[Pa \cdot s] = [ML^{-1} T^{-2}] \cdot [T] = [ML^{-1} T^

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(iii), (iv), $(i)$, (ii)

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(D) The dimensions are calculated as follows:$1$. For $Pa \cdot s$ (Coefficient of viscosity):$[Pa \cdot s] = [ML^{-1} T^{-2}] \cdot [T] = [ML^{-1} T^{-1}]$. This matches $(iii)$.$2$. For $N \cdot m \cdot K^{-1}$ (Torque/Energy per Kelvin):$[N \cdot m \cdot K^{-1}] = [MLT^{-2}] \cdot [L] \cdot [K]^{-1} = [ML^2 T^{-2} K^{-1}]$. This matches $(iv)$.$3$. For $J \cdot kg^{-1} \cdot K^{-1}$ (Specific heat capacity):$[J \cdot kg^{-1} \cdot K^{-1}] = [ML^2 T^{-2}] \cdot [M]^{-1} \cdot [K]^{-1} = [L^2 T^{-2} K^{-1}]$. This matches $(i)$.$4$. For $W \cdot m^{-1} \cdot K^{-1}$ (Thermal conductivity):$[W \cdot m^{-1} \cdot K^{-1}] = [ML^2 T^{-3}] \cdot [L]^{-1} \cdot [K]^{-1} = [MLT^{-3} K^{-1}]$. This matches $(ii)$.Therefore, the correct matching is $A-(iii), B-(iv), C-(i), D-(ii)$, which corresponds to option $(d)$.

$A$. $Pa \cdot s$	$(i)$. $[L^2 T^{-2} K^{-1}]$
$B$. $N \cdot m \cdot K^{-1}$	$(ii)$. $[MLT^{-3} K^{-1}]$
$C$. $J \cdot kg^{-1} \cdot K^{-1}$	$(iii)$. $[ML^{-1} T^{-1}]$
$D$. $W \cdot m^{-1} \cdot K^{-1}$	$(iv)$. $[ML^2 T^{-2} K^{-1}]$

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