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You can only hget branches like metallurgy and engineering chemistry where closing rank is near to 4000.
The below link gives you details about cutoffs at IIT bombay for all branches:
https://engineering.careers360.com/articles/jee-advanced-cutoff-for-iit-bombay
You can alternatively try out other IIts where you have great chances for securing admissions.
The cutoffs for alll top IITs and NITs is given below:-
https://engineering.careers360.com/articles/jee-advanced-cutoff
No ciurse shall come free for meritorius students at IITs, although scholarship is made avaialable through, central government schemes mentioned below.
https://www.ndtv.com/education/iit-iisc-phd-researchers-to-get-rs-70-000-monthly-central-fellowship-1739484
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