No, you can’t apply for admission if my board exam results are not declared. Because, candidates need to meet the eligibility criteria in order to apply for admission into any course. 

Candidates must receive at least 50% or the equivalent in the Class 12th exams conducted by any Indian board in order to be eligible for Azim Premji University undergraduate admission whereas,  for PG admissions, requirements include a bachelor's degree in law (LL.B. 3 years / 5 years) from an accredited university for the LLM Law and Development course. Candidates with work experience are actively encouraged to apply for other PG courses if they have a bachelor's degree in any discipline (including sciences, social sciences, humanities, engineering, medicine, agriculture, commerce, and management, etc.).