Dissolution of a partnership firm can occur in various ways, including on the death of a partner, on the insolvency of a partner, or by mutual agreement of all the partners. Let's understand each of these scenarios in detail:

1. Death of a partner (Option B):
When a partner of a partnership firm dies, it results in the dissolution of the partnership. This is because a partnership is considered a relationship between individuals, and the death of a partner terminates their association with the firm. The remaining partners may choose to continue the business by forming a new partnership or by incorporating as a new entity.

2. Insolvency of a partner (Option C):
If a partner becomes insolvent, it can lead to the dissolution of the partnership firm. Insolvency refers to a situation where a partner is unable to pay off their debts or fulfill their financial obligations. In such cases, the insolvent partner's share in the partnership may be used to settle their debts, and the partnership may be dissolved if the remaining partners decide not to continue the business.

3. Mutual agreement of all the partners (Option D):
Partnership firms can be dissolved by mutual agreement of all the partners. This means that all partners must come to a consensus and decide to terminate the partnership. Dissolution by mutual agreement can occur for various reasons, such as a change in business objectives, disputes among partners, or retirement of one or more partners. In such cases, the partners may decide to wind up the affairs of the partnership and distribute the assets and liabilities among themselves.

4. Order of the court (Option A):
Contrary to the given options, dissolution of a partnership firm does not necessarily require an order of the court. While it is true that a court order may be sought in certain situations, such as when there are disputes among the partners or when the partnership agreement specifies the need for a court order, it is not a prerequisite for dissolution in all cases.

In conclusion, the dissolution of a partnership firm can occur on the death of a partner, on the insolvency of a partner, or by mutual agreement of all the partners. These scenarios represent the most common ways in which a partnership can be dissolved.