With 87.88 percentile in JEE Main, your expected rank would be around 1.5-1.7 lakh. You may get branches in lower NITs under home state quota, some IIITs, and GFTIs. State government colleges in Maharashtra, MP, UP, and Rajasthan could also be options. Private universities like Amity, SRM, UPES, and LPU may offer good programs. Check past year JoSAA cutoffs and state counseling for better clarity. Exploring state engineering colleges through their respective counseling processes can further improve your chances.