Exam

The reserved category perks may still allow you to enrol in B.Tech programs in Mumbai if your MAH CET score is 59 and you fall into the NT-B category. The following are a few universities that might accept low MAH CET percentiles

New Panvel's Pillai College of Engineering is well known for its industrial partnerships and respectable placement rates.
Atharva College of Engineering has robust student support system and strong campus facilities.
A reasonably priced choice with helpful instructors is Vidyavardhinis College of Engineering and Technology in Vasai.
Universal College of Engineering is renowned for its reduced cut offs and student-friendly practices.
Shah & Anchor Kutchhi Engineering College offers affordable high quality academic programs.
For fee waivers and the lenient deadlines concentrate on applying through the CAP rounds and make use of the NT-B reserve

Your chances of being admitted to NITs, IIITs, or GFTIs with an 87.20% JEE 67% in your 12th grade exams and 56% in PCM may vary depending on the cutoff and qualifying requirements of the particular institute Your 56% in PCM may raise questions because NITs and IIITs often to require a minimum of 75% in your 12th grade (or the top 20%ile on your board test) for eligibility.Although there is still fierce competition you may have some leeway in the cutoff because you fall under EWS category. Your eligibility will be determined by the particular needs of the institute for the current academic year but you can still apply through the counselling procedure

With an 82 percentile in JEE Mains, direct admission to the B.Tech in Computer Science at Shiv Nadar University (SNU) is unlikely. SNU does not offer direct admissions; candidates must qualify through either JEE Main scores or the Shiv Nadar University Scholastic Aptitude Test (SNUSAT) and Academic Proficiency Test (APT).
In most popular specializations, including Computer Science, the cutoff goes above 90 percentile. Your score would suffice the minimum eligibility criteria, but might not be good enough to get into competitive programs such as Computer Science in SNU. Apply via SNUSAT or improve your chances through strong academic credentials.

It all depends upon which IIM you get shortlisted, but considering your percentile in CAT 2023 that is 70, a very good chance stands by your side if the cutoff will be met by you in terms of that IIM.
For example, IIM Ahmedabad will set the minimum overall cutoff at 60 percentile for ST candidates while others may be different. Normally, top IIMs such as IIM Ahmedabad, Bangalore, and Calcutta are higher with cut-off values generally more than 90 percentile in most of the cases but relax it for the reserved categories.
Although your score may suffice for admission into some IIMs, admission is not guaranteed and will depend on your overall profile, including academic performance and performance in subsequent rounds like interviews.