A new partner can be admitted:

According to Section 31(1) of the Indian Partnership Act, 1932, a new partner can be admitted into the firm only with the consent of all the existing partners, unless otherwise agreed upon in the partnership deed.

This requirement exists because partnership is based on mutual trust and confidence among partners. Since all partners have unlimited liability and share profits/losses together, no partner can be forced to accept a new partner without their agreement.

Why other options are incorrect:

Option 1 (Majority consent) - Partnership admission is not a democratic process where majority rules. Even if one partner objects, a new partner cannot be admitted.

Option 2 (Draw of lot) - Partnership decisions cannot be made by chance or lottery. It requires conscious agreement of all partners.

Option 4 (Desire of one partner) - No single partner has the unilateral right to admit a new partner. This would violate the rights of other partners who may not want to associate with the new person.

Exception: If the partnership deed specifically contains a clause allowing admission by majority or any other method, then that clause would be valid as partners can mutually agree to modify this rule at the time of forming the partnership.