Engineering Entrance Exam

FIITJEE is the best institute.

You need these book:
Loney's Coordinate Geometry and Trigonometry
Hall and Steven's Geometry
Hall and Knight's Elementary Algebra and Higher Algebra
Calculus by GP Thomas
University Physics by Resnick and Halliday
University Physics by Sear Zemansky
Problem in Physics, Irodov
Organic Chemistry by Morrison B

University Physics by Resnick and Halliday
University Physics by Sears Zemansky
Irodov's Problem in Physics and Solution
Calculus by GP Thomas
Loney's Trigonometry and Coordinate Geometry
Hall and Knight's Elementary Algebra and Higher Algebra
Organic Chemistry by Morrison Boyd.

Hall and Knight's Elementary and Higher Algebra
Loney's Trigonometry Coordinate Geometry
Calculus by GP Thomas.

The counselling will begin on 25th July, 5 rounds will be held at all 42 TNEA institutions.

It will be from 2019 onwards.

Actually, the third counselling of EAMCET has also been completed. And the allocation of seats also has been done. So, wait for any further notifications or try in management quota.

Without any preparation means it's hard to qualify in JEE Mains but there are less chances for qualifying in EAMCET. But just qualifying doesn't gives you anything, so you have to work hard for reaching your goals. Without working, you can't get anything.
All the best.

It depends on the performance and difficulty level of the paper. So it's purely based on the ranks and ranks cutoff also differs somewhat every year.