Q.The $\text{C=O}$ bond length in formaldehyde ($1.21\ \text{\AA}$) is shorter than a typical $\text{C-O}$ single bond. Explain this using the bonding picture of the carbonyl group (one $\sigma$ and one $\pi$ bond) and state the shape around the carbonyl carbon.

A $\text{C-O}$ single bond involves only one shared electron pair (a $\sigma$ bond); the carbonyl $\text{C=O}$ bond additionally has a $\pi$ bond formed by sideways overlap of unhybridised $p$ orbitals on carbon and oxygen. This second bond pulls the two nuclei measurably closer together, which is why $\text{C=O}$ ($\approx 1.21\ \text{\AA}$) is shorter than $\text{C-O}$ ($\approx 1.43\ \text{\AA}$) -- exactly analogous to why $\text{C=C}$ is shorter than $\text{C-C}$. The carbonyl carbon itself is $sp^2$ hybridised, so it and its three attached atoms all lie in one plane with bond angles close to $120^\circ$.

Compare bond order: a double bond (one $\sigma$ + one $\pi$) is always shorter and stronger than a single bond ($\sigma$ only) between the same two elements.

Attributing the short bond length only to 'electronegativity' -- electronegativity explains the bond's POLARITY, but the shortness is a bond-ORDER effect (an extra $\pi$ bond), a separate idea.