Am I eligible for EAMCET, born in Arunachal Pradesh (AP), but not studied there???

Yes you can apply for EAMCET entrance examination. there is 15% quota for non local students but no other caste based reservations entertain prior to the 15% reservation.

Engineering, Agriculture and Medical Common Entrance Test is an aptitude test which is carried out by Andhra Pradesh State Council of Higher Education (APSCHE).

Eligibility Criteria of EAMCET 2014
You should be of India Nationality and should belong to the state of Andhra Pradesh.
For admissions to medical, engineering and agriculture courses, the candidate must pass in the 12th (HSC) class examination in the science stream.

EAMCET syllabus :
Physics
Atoms, Molecules and Nuclei
Description of Motion
Measurement
Rotational Motion
Electrons and Photons
Laws of Motion
Gravitation
Current Electricity
Work, Energy and Power
Electromagnetic Induction and Alternating Currents
Ray Optics and Optical Instruments
Thermal and Chemical Effects of Currents
Electromagnetic Waves
Oscillations
Magnetic Effect of Currents
Heat and Thermodynamics
Electrostatics
Surface Tension
Magnetism
Solids and Semiconductor Devices
Waves
Kinematics - Dynamics

Mathematics
Theory of Equations, Sequence and Series
Complex Numbers & Trigonometry
Differential Calculus
Analytical Geometry
Discrete Mathematics
Integral Calculus
Matrices and Determinants
Vector Algebra
Differential Equations
Probability Distributions
Trigonometry
Algebra

Chemistry
States of matter
Noble Gases
Classification of elements
Basic concepts in Chemistry
Solutions
Gaseous State
Chemical bonding
Environmental Chemistry
Equilibrium
Chemical thermodynamics
Solid state Chemistry
Electrochemistry
Chemical kinetics
Hydrogen
Atomic structure
Surface chemistry
Nuclear Chemistry
Stoichiometry
Acids and Bases
VI Group Elements

Biology
Plant Physiology
Functional Anatomy of Rabbit
Cell-The Unit of Life- Structure and Function
Vegetative Morphology
Diversity in Living World
Biotechnology and its Applications
World of Plant Life
Animal Organisation
Biology and Human Welfare
Genetics and Evolution
Reproduction, Growth and Movement in Plants/Animals
Biotechnology
Ecology and Environment
Structure and Function – Animals and Plants
Man and Biosphere
Applied Zoology
Reproductive Morphology
Classification of Flowering Plants
Phylum
Plant Pathology
Organic Evolution
Locomotion and Reproduction in Protozoa