You can apply for IIT Bombay through JOSAA, but first of all you will have to clear JEE Advance with a decent rank

For Btech.. You have to clear jee advanced examination and attend jossa counselling
For M.Tech or M. Sc or phd.. You have to clear gate examination and apply for admission in their respective websites..for suppose you want to opt for M. Tech in IIT Bombay.. You should apply In respective website and attend written test / person interview.
And for top rankers in gate examination they will give direct admissions..
Thanks for reading...

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