The power of the Supreme Court of India to decide disputes between the Centre (federal government) and the States falls under its original jurisdiction. This means that the Supreme Court has the authority to be the first and final arbiter in these types of cases.

Option 1, advisory jurisdiction, refers to the Supreme Court`s power to provide advice and opinions on legal matters when asked by the President or the government, but it does not involve deciding disputes between the Centre and the States.

Option 3, appellate jurisdiction, refers to the Supreme Court`s power to hear appeals from lower courts and tribunals. While the Supreme Court does exercise appellate jurisdiction, this question specifically asks about disputes between the Centre and the States, which falls under its original jurisdiction.

Option 4, jurisprudence, refers to the philosophy, study, or system of law. It does not pertain directly to the Supreme Court`s power to decide disputes between the Centre and the States.

Overall, the correct answer is option 2, original jurisdiction.