Hi

hope you doing well

It will be challenging to secure a seat in the top or more popular NITs or IIITs with an ST category rank of 13,000 in JEE Mains , especially for branches like CSE or ECE, as they typically have higher cutoffs. However, you might have a chance in the following:

For NIT's:

• Newer NITs or those in less competitive locations may offer seats in branches like Civil, Mechanical, or Metallurgy.
• NITs with Home State Quota: If you apply under the home state quota, some NITs may have lower cutoffs for the ST category.

For IIIT's:

• Newer IIITs or IIITs with less demand may offer you a chance, although it may not be for the most sought-after branches.

For better analysis you can refer to this link:

JEE College Predictor

https://engineering.careers360.com/jee-main-college-predictor?utm_source=qna&utm_medium=jee_cp

Best wishes.