Yes. Although India has some very reputable institution when it comes to pursuing PhD but even though I would suggest to study from abroad . The universities abroad provide better grants to student and also landing into a reputable job would be easier.
Also I made this video on how you can go abroad for Phd. Programs. Please have a look and let me know in the comment section about further queries.
Kriti Kumari, works at Studying
Source: Quora Digest