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The admission in IITs in M.Sc. courses are based on ranks obtained in IIT Joint Admission Test for Masters (JAM) conducted by IISc Bangalore.
From the Academic Session 2004-05, IITs started conducting a Joint Admission test for M.Sc. (JAM). The objective of JAM is to provide admissions to M.Sc. (Two Years), Joint M.Sc.-Ph.D., M.Sc.-Ph.D. Dual Degree, and other Post-Bachelor Degree Programmes at the IITs and Integrated Ph.D. Degree Programmes at the IISc and to consolidate Science as a career option for bright students across the country. JAM has been established as a benchmark for the undergraduate level science education in the country.
Eligibility requirements of IIT JAM : The candidates who qualify in JAM 2021 shall have to fulfill the following Eligibility Requirements (ERs) for admissions to IITs.
All candidates admitted through JAM should have a Bachelors degree. In the qualifying degree, the aggregate marks or CGPA/CPI without rounding-off (taking into account all subjects, including languages and subsidiaries, all years combined) should be at least 55% or 5.5 out of 10 for General/OBC (NCL)/EWS category candidates, and 50% or 5.0 out of 10 for SC/ST and PwD category candidates.
So from above the 55% is the minimum requirement for General/OBC (NCL)/EWS category, while 50% for SC/ST candidates. Hence you are not eligible.

The admission in IIST Bangalore are based on the ranks secured in JEE Advanced. So you have to fist appear in JEE Main exam and qualify the JEE Main exam being among the top 2,50,000 rank holders are eligible to apply for JEE Advanced examination. As mentioned just before, the candidates who qualify the JEE Main examination below 2,50,000 ranks have to apply for Joint Entrance Examination JEE Advanced. The exam is conducted once a year by one of the Indian Institutes of Technology which changes every year. In the next step you have to qualify the JEE Advanced cutoff as set by the conducting authorities. Than you have to participate in JoSAA Counselling conducted in online mode, Thereafter, the authorities will release the rank list according to which allocation of seats will take place and admissions will be done in IIST Bangalore. So above is the procedure for getting admission in IIST Bangalore. The 3 years Engineering Diploma courses are considered as the qualifying exam for JEE Main. So you are eligible for JEE Main subjected to the meeting the percentage of marks criteria I. e 75% for IIST.

Hello Samruddhi, it's a very interesting question that you are asking. Frankly speaking it's quite tough to say what percentile will get you what rank. This is so since how many students will be e above a certain percentile is very difficult to say since it's only the percentage of students that can be stated. For example if 1 Lacs students appeared for an examination and a student gets a percentile of 90 it means 10% of 100000 students are above him and hence his ranking would be about 10,000. In this fashion you can calculate as to how much percentile should get for obtaining rank under 3000. You can safely assume a figure of about 10 Lacs students appearing for JEE Main. Best wishes to you.