With a TS EAMCET rank of 61,000 and being in the EWS category, you might have chances for admission in various engineering colleges and universities, particularly in branches with lower cutoffs. Some potential options include:

1. State universities like Osmania University and JNTU Hyderabad (for branches like Civil or Mechanical).

2. Private colleges like Vignan's University, MGIT, or CVR College of Engineering.

For more details you can visit the link given below

https://engineering.careers360.com/articles/ts-eamcet-eapcet-rank-wise-colleges-list