Yes. Page 1 of the IRS US Tax Guide for Aliens states:
Resident aliens are generally taxed on their worldwide income, the same as U.S. citizens. Nonresident aliens are taxed only on their income from sources within the United States and on certain income connected with the conduct of a trade or business in the United States.
You may be eligible for the foreign tax credit. See here.
The India - US tax treaty may also provide relief. See here.
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