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(A) The dimensional formulas are calculated as follows:$(a)$ Wave vector $(k = 2\pi / \lambda)$: The dimension is $[L^{-1}]$, which corresponds to $M^

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$a-iii, b-iv, c-i, d-ii$

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(A) The dimensional formulas are calculated as follows:$(a)$ Wave vector $(k = 2\pi / \lambda)$: The dimension is $[L^{-1}]$, which corresponds to $M^0L^{-1}T^0$ $(iii)$.$(b)$ Linear mass density $(\mu = 	ext{mass} / 	ext{length})$: The dimension is $[ML^{-1}]$, which corresponds to $M^1L^{-1}T^0$ $(iv)$.$(c)$ Intensity of a wave $(I = 	ext{Power} / 	ext{Area})$: Power is $ML^2T^{-3}$, so $I = (ML^2T^{-3}) / L^2 = MT^{-3}$, which corresponds to $M^1L^0T^{-3}$ $(i)$.$(d)$ Volume elasticity coefficient $(B = 	ext{Stress} / 	ext{Strain})$: Stress is $ML^{-1}T^{-2}$ and strain is dimensionless, so $B$ is $M^1L^{-1}T^{-2}$ $(ii)$.Therefore, the correct matching is $(a-iii, b-iv, c-i, d-ii)$.

Column-$1$	Column-$2$
$(a)$ Wave vector	$(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density	$(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave	$(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient	$(iv)$ $M^1L^{-1}T^0$

Match Column-$1$ with Column-$2$.
Column-$1$ Column-$2$
$(a)$ Wave vector $(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density $(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave $(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient $(iv)$ $M^1L^{-1}T^0$

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Match Column-$1$ with Column-$2$.Column-$1$Column-$2$$(a)$ Wave vector$(i)$ $M^1L^0T^{-3}$$(b)$ Linear mass density$(ii)$ $M^1L^{-1}T^{-2}$$(c)$ Intensity of a wave$(iii)$ $M^0L^{-1}T^0$$(d)$ Volume elasticity coefficient$(iv)$ $M^1L^{-1}T^0$