Consider the following molecules/species:
The correct order of carbon-oxygen double bond length is:

Solution

Chemistry ma’am · 4 steps

Ask how much single-bond character resonance gives each C=O. More of it means a longer bond.

1. The rule. A C=O bond gets longer when resonance shifts electrons onto oxygen and gives the bond partial single-bond character. So rank the three species by how much single-bond character their C=O has.

   Species	Key resonance form	C–O character	Bond length
   x (tropone)	C⁺-O⁻, and the ring becomes an aromatic tropylium ring (6π electrons)	most single-bond character	longest
   z (acetate)	negative charge shared equally by the two oxygens	partial double bond	intermediate
   y (acetone)	no strong resonance partner	almost a pure double bond	shortest

2. Why tropone wins. In tropone, the charge-separated form turns the seven-membered ring into an aromatic tropylium cation. Aromaticity makes this form the major contributor, so the C–O bond in x has the most single-bond character.
3. Acetate versus acetone. In acetate, the two C–O bonds share one double bond, so each one is part double and part single. Acetone has no such delocalisation, so its C=O keeps full double-bond character and stays shortest.
4. So. The C–O bond length order is x > z > y, which is option (d).

The idea to keep. A C=O bond lengthens when its charge-separated form is stabilised. If that form is aromatic, as in tropone, it dominates the resonance and the C–O bond gets the most single-bond character.

Answer from the NTA final answer key. Solution by PrepWiser.