Observe the following statements regarding \(\mathrm{C}_{60}\).
i. All carbons are \(s p^2\)-hybridised.
ii. It contains 12 rings of five carbons each and 20 rings of six carbons each.
iii. It is a non-aromatic compound.
iv. It is pure form of carbon.
v. \(\mathrm{C}-\mathrm{C}\) bond lengths in it are 143.5 and \(138.3 \mathrm{pm}\).
vi. It is prepared by heating graphite in an electric arc in the presence of oxygen.
The correct statements are

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.