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Dear Yash,
The relationship between marks in JEE and the All India Rank in JEE is not exactly explicable. It varies to a very high extent every year.The cutoff marks depends on the level of toughness of the exam and so the availability of options cant be stated in terms of marks in the entrance exam. If you are projecting Mechanical Engineering at IIT Bombay you should score All India Rank better than 500. Even if you dont get good enough AIR so that you may get Mechanical but you get good enough AIR so that you may get some other branch then you should take admission in some other branch too. You can get your branch changed after 1st year if you perform well in the 1st year and your 1st year Grades are in Top 1%
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