I found the answer that I was looking for.
Quoting a paragraph from Article 21 of US-India Tax Treaty Technical Explanation document:
If a student who is resident in a Contracting State remains in the other State for a period of time exceeding the period during which he is present principally for the purpose of his education or training, the Contracting State which he is visiting may tax the individual under its national law, but only for the period after the purpose of the student's visit has changed.
My understanding is that you can claim standard deduction if the income you earned on F-1 was greater than the deduction amount.
Source: https://www.irs.gov/pub/irs-trty/inditech.pdf
Source for the actual treaty: https://www.irs.gov/pub/irs-trty/india.pdf
