OTHER ENGINEERING EXAMS(STATE LEVEL):
Some of the states conduct their own entrance examination for the admission into the state-run and some of the private engineering colleges (in those states). Though some of the state entrance examinations are known beyond that state's borders, often admission into those institutes is restricted by the domicile clause.
Andhra Pradesh has AP EAMCET (Engineering,Agriculture and Medical Entrance Examination), Telangana has TS EAMCET,West Bengal has WBJEE(West Bengal Engineering Entrance Examination), to name a few.
Clicking on the following links will give a fair idea about the examinations.