Will a 2,000 rank in the AP EAMCET give a seat in JNTUK?

This totally depends mainly upon your caste. If you are OBC/General, then you can get a seat in petrochemical engineering/petroleum engineering, which are quite good courses.

If you are from other castes and if you have reservation, then you will definitely get the branch you desired about.

You may also get your seat like this. In every exam, top students are of good ranks. So if all of them opt for NITs and IITs, seats in EAMCET-related colleges will be free, and you will certainly get your seat in JNTUK

The factual information to let you know better about ranks. Cutoffs of 2019 are -

Note: There may be differences in cutoffs as they depend upon the courses chosen by you.

With 2000 rank, it is possible to get seated in JNTUK through the AP EAMCET exam.

But the only thing is, it all depends on the opening and closing ranks of the corresponding branches over the past two years. So when choosing a certain branch option check briefly. You can review the opening and closing ranks of the branch if you are interested in joining (from the previous 2 years).