The jurisdiction that allows the Supreme Court of India to settle disputes between the Centre and States, or among different States, is the Original Jurisdiction.

Detailed Explanation

Under Article 131 of the Indian Constitution, the Supreme Court has exclusive Original Jurisdiction over federal disputes. "Original" means that the case can be brought directly to the Supreme Court in the first instance, without having to go through lower courts or an appeals process.

-The Supreme Court can hear disputes under this jurisdiction involving:

-The Government of India (Centre) vs. One or more States.

-The Government of India and any State(s) on one side vs. One or more other States on the other side.

-Two or more States against each other.

Limitations of Original Jurisdiction

It is important to note that not all disputes between the Centre and States can be brought under Article 131. The jurisdiction does not extend to:

-A dispute arising out of any pre-Constitution treaty, agreement, covenant, or engagement.

-Inter-State water disputes (which are specifically handled by separate tribunals under Article 262).

-Matters referred to the Finance Commission (Article 280).

-Ordinary commercial grievances between the Centre and States.

Other Jurisdictions of the Supreme Court (For Context)

Writ Jurisdiction (Article 32): Allows the court to enforce Fundamental Rights. Anyone can approach the court if their basic rights are violated.

Appellate Jurisdiction (Articles 132-136): Allows the court to hear appeals against judgments passed by High Courts or lower tribunals.

Advisory Jurisdiction (Article 143): Allows the President of India to seek the legal opinion of the Supreme Court on matters of public importance or law.