Colleges in Pune

You should score above 85% in class 12th but sometimes it goes higher than this too.

No, Maths subject is not necessary for hotel management courses. The eligibility criteria of D.Y. Patil IHMCT college for BHMCT program is as under.
Eligibility: Candidate should have passed the H.S.C. (Std XII) examination of Maharashtra State Board of Secondary & Higher Secondary Education or its equivalent examination in Science/Home Science Commerce/Arts/MCVC with English as one of the subject and secured minimum 45% marks in aggregate (40% marks in aggregate for reserved class category candidates belonging to Maharashtra State only).
And Candidate should have appeared for MAH/HM/CET securing a non-zero score.

Yes, you can definitely get admission in this college at this rank and under this course, in the second or in the last round of the counselling.

Hi,
Please use this college predictor tool for better approximation
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwi16pvN7MDiAhUIbn0KHXEMDQEQFjAAegQIBRAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H
Best wishes!

Hi Aatish Lahane
Kindly predict your college in this college predictor. JEE Main rank predictor is an online tool which predicts the candidates rank range and probable colleges based on the difficulty level of the examination, average marks scored in JEE Main and seats available in IITs, NITs, GFTIs, and other SFTIs. The rank predicted might not be accurate but it certainly does give an idea to the aspirant. Know your college admission chances based on your JEE Main Rank, Home State, Caste, Gender, etc. Here https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

No chance in IIIT bangalore or in any NIT at this percentile. You may try for good private colleges in Karnataka.