(A) The correct matching is as follows:
$(A)$ Resonance structures of the carbonyl group represent the polarity of the bond,where carbon acts as an electrophilic centre and oxygen as a nucleophilic centre. Thus,$A \rightarrow iv$.
$(B)$ The geometry shows the $sp^2$ hybridized carbon with a planar triangular structure and bond angles of approximately $120^{\circ}$. Thus,$B \rightarrow iii$.
$(C)$ The $\sigma$-bonding involves the overlap of orbitals forming the skeleton of the carbonyl group. Thus,$C \rightarrow ii$ (referring to the non-bonding $2p$ orbitals perpendicular to the plane).
$(D)$ The $\pi$-bonding involves the overlap of $p$-orbitals above and below the plane. Thus,$D \rightarrow i$.
Therefore,the correct match is $A$ $\rightarrow iv, B$ $\rightarrow iii, C$ $\rightarrow ii, D$ $\rightarrow i$.