It is you who is terribly misinformed, before partition it was Urdu for Muslim of subcontinent & Hindi for Hindus & Sikhs of subcontinent.
Also today India has 2 official languages English & Hindi, not tamil or bengali. Just difference in Pakistan was English made an official language & Urdu national language. People who doesn't knew Urdu or have allergy with it could talk in English, same as today people who don't know Urdu can talk in English anywhere in Pakistan. Pakistan had later after 52 made Bengali as a national language too.
The official language of the Indian Union is Hindi with English as an additional language for official work; states in India can legislate their own official languages.[1] Neither the Constitution of India, nor any Indian law defines any national language.
All the states have their own official language.