With a 63 percentile in JEE Main and a rank of 13,000 as an ST candidate, you have a good chance of securing admission to some government engineering colleges, particularly those with lower admission cutoffs. However, getting into the very top-tier institutions like NITs or IIITs with a 63 percentile might be challenging.

Here's a breakdown of how to approach college selection:

1. Consider your options:

Lower-tier NITs or IIITs:

While top NITs might be difficult, you could explore options with lower cutoffs and more flexible admission criteria.

Government-funded technical institutes (GFTIs):

These are also an option and may offer lower cutoffs for certain branches.

Private engineering colleges:

Many private colleges accept candidates with a 63 percentile, and some offer good placement opportunities.

CSAB Counseling:

You can also participate in the Centralized Single-Window Counseling for Allottee Colleges (CSAB) for potentially better options.

2. Factors to consider when choosing a college:

Placement rates:

Research the placement records of different colleges to see their record in placing students in good companies.

Placement packages:

Investigate the average and highest package offered to graduates of different colleges.

Course offerings:

Make sure the college offers the specific engineering branch you're interested in (e.g., Mechanical, Electrical, Computer Science).

Location:

Consider the proximity of the college to your home or other important locations for you and your family.

Infrastructure and facilities:

Look into the quality of campus facilities, including labs, libraries, and other resources.

3. Specific Colleges to Consider:

Netaji Subhas University of Technology (NSUT):

This is a public university that might be a good option for a 63 percentile.

Other GFTIs:

Explore other government-funded technical institutes in your region or of interest.

Private colleges with good placement records:

Several private colleges have good placement rates and might be suitable for your percentile.

4. Important Notes:

Research thoroughly:

Don't just rely on rankings; delve into specific placement data, course offerings, and campus facilities.

Be flexible:

You might need to consider different branches or even different locations to find the best fit.

Don't give up:

A 63 percentile is still a decent score, and with careful research and a flexible mindset, you can find a good engineering college.

You can also use JEE predictor tool to know colleges according to your percentile .