The basic eligibility criteria to apply for BCECE is candidate should be class 12th pass with 45% marks in Science stream(with Physics, Chemistry and Biology). As BCECE is a state level exam therefore only Bihar state candidates can apply for the exam. As you have said that your father has been transferred to Bihar so if u are a proper resident of Bihar that means you have a domicile certificate in Bihar so your are eligible. If you have any other queries feel free to ask. All The Best!!!