IIT

A 96 percentile in JEE Mains will put you in the general percentage of score between 33000 and 48000. The score is not enough to get an admission in best IITs or most popular faculty members (such as CSE ) in best NITs. But you can easily get into mid-tier NITs (e.g. NIT Agartala, NIT Raipur, NIT SIlchar, NIT Srinagar) in core subjects such as Civil, Mechanical, Chemical, or even Metallurgy. You may even secure a place in newer (e.g. IIIT Manipur, IIIT Bhagalpur, IIIT Dharwad) institutes to other branches such as ECE. This is also dependent on your category and quota of home state.

The expected package for a BTech Computer Science and Engineering graduate from an IIT varies but generally ranges from INR 15 Lacs per anum to INR 50 Lacs per annum with potential for much higher service especially for top performers and those in specialise role some sources suggest that the median salary is around INR 25 Lacs per annum while the average can be higher depending on the IIT and the specific placement Seasons the highest package can exceed INR 1 Crore for international offer or quantitative trading roles

To pursue astrophysics at an IIT, you typically need to first gain admission to a B.Tech programme in Physics or Engineering Physics at an IIT, and then specialize in astrophysics at the postgraduate (M.Tech or PhD) level. There isn't a dedicated undergraduate programme in astrophysics at IITs. 

IIT Bhilai round 6 cutoff has been released for admission to various BTech specialisations. The cutoff was released for different categories belonging to the All India quota. The cutoff ranks among the General AI category closed between 7382 and 17478. Therefore, 350 is an excellent score to get admission to IIT Bhilai for candidates belonging to the General AI category. 

For your rank it is not possible to get in NITS but you have a chance to get into IIIT's 

Unfortunately, with a JEE Main AIR of 60,000, you cannot get into an IIT, as IIT admissions are through JEE Advanced, not JEE Main.However, with AIR 60,000 in JEE Main, you can target top NITs, IIITs, and GFTIs for ECE. Some good options include:-

1)IIIT Lucknow / IIIT Nagpur

2)NIT Raipur / NIT Goa / NIT Sikkim

3)IIIT Bhubaneswar (State quota)

4)GFTIs like Assam University

With an All India OBC rank of 84 and a Science stream (Math) background, your chances of getting into a top IIT are excellent.You can expect Top IITs like Bombay, Delhi, Madras, Kanpur, Kharagpur.Be sure to participate in JoSAA counseling and keep backups from IIT Hyderabad, Gandhinagar, BHU, ISM Dhanbad, etc.

Yes, Mechatronics is good in VIT Vellore as it involves a modern curriculum, strong labs and research, good faculty, and industry exposure. Mechatromics is equally good, I'm IIT, NIT with slight differences.