Is there a specific SAT India exam?

Yes, but only non-CAS (computer algebra system) calculators are allowed in SAT India.

• A valid photo ID
• Admission ticket
• Fully charged testing device with the Bluebook application installed 
• Pencils or pens for rough work
• College Board username and password
• Acceptable calculator

If you arrive late after the SAT India centre doors have closed, you will not be allowed to take the test.

You can locate a test city near you by using the "SAT Test Centre Search" on the College Board website.

For Ivy League schools, a SAT score of 1500+ is generally expected.