As agreeing to the view of Dirajlal sir above, a Partnership cannot be formed for the non-economic purpose as the definition of Partnership itself says as it is for sharing of profits, etc. Please go through the definition below,
A Partnership is defined by the Indian Partnership Act, 1932, as 'the relation between persons who have agreed to share profits of the business carried on by all or any of them acting for all'. This definition gives three minimum requirements to constitute a partnership, viz.
(1) there must be an agreement entered into orally or in writing by the persons who desire to form a partnership,
(2) the object of the agreement must be to share the profits of business intended to be carried on by the partnership, and
(3) the business must be carried on by all the partners or by any of them acting for all of them.