English GDPI

After clearing the CAT entrance test, candidates will have to appear for a further selection round. Admission criteria of IIMs and other B-schools include Writing Ability Test (WAT), Group Discussion (GD), Personal Interview (PI).
And interviews are done in english languages

Truthfully, communication and English is important to get through. But, I would say, do give it a try.

Yes, it is necessary to speak fluent English for Personal interview. The medium of instruction in all IIMs is English and all the classes are designed to interactive. Also there are a lot of foreign faculty who expect you to communicate effectively in English. To account for these factors, there was a dedicated section in CAT to test your verbal skills. However you should not worry about it too much, as you have already qualified CAT and hence possess certain level of knowledge of English language.