A firm is compulsorily dissolved :

The correct answer is Option (3) → When the business of the firm becomes illegal

A firm is dissolved compulsorily when all or all but one partner become insolvent, when the business becomes illegal, or when an event makes it unlawful to carry it on.

Option (1) When the business of the firm can not be carried on except at a loss — Incorrect. This is a ground for dissolution by the court on a partner's suit.

Option (2) When a partner persistently commits breach of partnership agreement — Incorrect. Also a ground for dissolution by the court.

Option (4) When a partner becomes insane — Incorrect. The court may dissolve the firm on this ground; it is not automatic.