sir , i got 871 mechanical branch rank and 2005 integrated rank in AP ECET , cast BC-D , can i get a seat in JNTUK or JNTUA college . please reply sir.

Hello,
As per the cutoff trends for last few years, with this rank in AP-CET, expecting a seat in JNTUA and JNTUK is quite difficult.
However you can expect a seat in many colleges. Here is the list of some of the colleges for you.

Chaitanya Engineering College
Chaitanya Bharathi Institute of Technology
Adarsh College of Engineering
Chaitanya Institute of Science & Technology
Avanthi Institute of Engineering and Technology
Sri Chundi Ranganayakulu Engineering College
Priyadarshini Institute of Technology & Science
Sai Tirumala nvr Engineering College,narsaraopet
DJR College of Engineering & Technology
Anantha Lakshmi Institute of Technology & Sciences
Sri Venkateswara College of Engineering & Technology

These predictions are based on previous years data. The cutoff varies every year depending on number of factors such as:
Total number of applicants
Total participants who sat for the exam
Difficulty of the exam that varies every year and many more. So, these are not the actual results, these are just predictions based on previous year data.

For more details about all the colleges accepting the AP-ECET score you can refer the link.
https://engineering.careers360.com/colleges/ranking/top-engineering-colleges-in-India-accepting-ap-ecet-score