I have completed my B.A. LL.B. In 2014 but not done the enrollment so can I now get enrolled and give the AIBE exam?

To identify the best reference material, candidates should check: 

AIBE Reference material is free of grammatical errors 
Legal concepts are explained clearly 
All illustrations, examples, and other such representations are accurate 
The reference book for AIBE is reviewed by law exp

For the AIBE exam, the best books are bare acts (without comments) for core subjects like the new BNS, BNSS, BSA, CPC, and others, alongside comprehensive guides like Universal's or Taxmann's publications, and subject-specific texts like Durga Das Basu for the Constitution or C.K. Takwani for CPC, f

No candidates can actually prepare for AIBE Exam along with their class 12th exam. They just need to take out time to prepare for the entrance exam. 

If you have topped while pursuing law there is still some chance. But if you were an average student who have not prepared even once for the exam, it is next to impossible to prepare for the exam in one month. 

The AIBE 21 Exam will be held in pen-and-paper mode. No notification mentioning that it will be held in online mode has been released by the council yet.