Hello, Shiva. You mentioned your percentile in JEE Mains 2021 is 77.70. Based on your percentile, your AIR should lie within the range of 228129 - 256450. With this rank, the chances are very less to get a seat in NIT Warangal through JoSAA Counselling or CSAB Counselling even if you opt for Home State Quota.

As per records, NIT Warangal 2020 cutoffs for SC (Home State/Male) as per CSAB Counselling are given below:

1. B.Tech Biotechnology - Closing rank - 130996
2. B.Tech Chemical Engineering - Closing rank - 94605
3. B.Tech Civil Engineering - Closing rank - 69015
4. B.Tech Computer Science and Engineering - Closing rank - 27987
5. B.Tech Electrical and Electronics Engineering - Closing rank - 49300
6. B.Tech Mechanical Engineering  - Closing rank - 60479

To know more about cut-offs of NIT Warangal, follow this link: https://www.careers360.com/university/national-institute-of-technology-warangal/cut-off

To now your eligibility at various departments in various colleges, feel free to use J EE Main 2021 College Predictor .

I hope this information helps you.

All the best for your career and future.

Thank you.