Hi Vinay, 

As of now it is only IIM Indore among the olf IIMs which offers a five-year integrated course BBA+MBA through IPMAT exam.  As per the IPMAT eligibility criteria set by the conducting body, candidates must have passed their standard X/ SSC and Standard XII/ HSC or equivalent examinations with a minimum of 60 per cent aggregate marks. IPMAT 2019 will be conducted in computer-based mode across various test centres in India. Thereafter, candidates who clear the IPMAT 2019 cutoff will further be called for the selection rounds followed by the final admission process. You can go for it if you are willing to take up this course. Goodluck!

Hello Vinay,
IIM – A only provides with MBA courses. You will have to give CAT if you want to get into IIMA. However, BBA+MBA is provided by IIM Indore, for which you will have to clear IPMAT.
Hope this was helpful and all the best.