Is Mechatronics good in VIT Vellore? Is Mechatronics good in any other colleges like IIT, NIT?

No — VIT-AP does not admit or offer free seat under EAPCET counselling and you cannot admit to VIT-AP without VITEEE (or management quota).
The clear explanation is described below:

 1. Is VIT-AP EAMCET/ EAPCET rankable?
No.
VIT-AP does not engage in Andhra Pradesh EAPCET counselling.
They do not believe in EAMCET ranks to B.Tech admissions.

The admissions of VIT-AP are largely by way of:

VITEEE (compulsory in merit seats of B.Tech)

Direct/Management quota (increased fee)

Scholarships depend on the VITEEE ranking / board marks (unlimited)

Your EAPCET rank is therefore not accepted to be admitted to VIT-AP.

 2. Is it possible to secure a free/no fee seat in VIT-AP via EAPCET?

No. There are no free seats / scholarship seats on EAPCET rank.

Scholarships are usually provided on the basis of:

Top VITEEE ranks (up to 50k–70k)

State/CBSE toppers (under GV School Scholarship)

VIT-AP does not offer you the slightest advantage based on your EAPCET rank (50006000).

 3. Do you qualify to be enrolled in VIT-AP without writing VITEEE?

Without VITEEE only management quota seats can be done but:

The charges are significantly more expensive ( 2.5 3.5 lakh/year or so, depending on branch).

No scholarship in most cases.

Then, to get a merit seat, VITEEE is mandatory.