B.E.

Because you are not specific about the colleges, Hence the eligibility criteria of M.Des of NIFT and NID are given below for an idea. Eligibility criteria of NIFT : Undergraduate Degree in any discipline from any Institute / University recognised by law in India. Age criteria : No age limit
Selection criteria : The selection process comprises a written examination comprising of a Creative Ability Test CAT and General Ability Test (GAT) followed by Group Discussion and Personal Interview (GD/PI) for shortlisted candidates of the written examination. Website : https://www.nift.ac.in/
Eligibility criteria of NID : Bachelor degree of minimum 4-year duration in any specialisation, after 12th standard or equivalent to 12th standard from any university or institute recognised by law in India. Condition: Applicant must have passed the Bachelor degree examinations at the time of document verification. Or
Bachelor degree of minimum 3-year duration in any specialisation, after 12th standard or equivalent to 12th standard. Condition: Applicants must have passed the Bachelor degree examinations before June. Age criteria : For Indian Nationals in General Category & General EWS category: Only those candidates born on or after 1 July 1990 are eligible to apply for admission. Admission criteria : NID Entrance Exam comprises that Prelims and that Mains. Website : http://www.nid.edu/
So from above you can be eligible for M.Des. Courses of NIFT and NID if meeting the above eligibility criteria.