KVPY

The following the ways for getting admission in IISER in BS/BS-MS admission 2020.
Candidates who have passed 10+2 or equivalent level exam with science stream in 2019 or 2020 are eligible to apply for admissions. Candidates will be admitted to IISER only through following three channels.
1. Kishore Vaigyanik Protsahan Yojana (KVPY) channel
2. Joint Entrance Examination (JEE-Advanced) of the Indian Institutes of Technology
3. State and Central Boards Channel (SCB)
The details about SCB channel are given below.
Students who have passed 10+2 level with science stream in 2019 or 2020 are eligible to apply for admissions and appear for IAT 2020. However, they will be considered for admissions to the degree programmes only if they obtain the cut-off marks specified for their board.
Students applying through SCB channel will have to appear in the IISER Aptitude Test (IAT) which will be conducted at various centres across the country.
So from above IAT is necessary for admission. Hence its better to perform well in JEE Advanced for getting admission here. Otherwise go for IAT because you can meet the CBSE cutoff criteria.

Yes, Mathematics at 12th is mandatory for Bachelor of Science (Research) Programme at IISc Bangalore. The eligibility criteria is given below:
ELIGIBILITY: Candidates who have completed their II PUC / 12th Standard in 2019 and those who are expecting to complete their II PUC / 12th Standard in 2020 are eligible to apply. The candidates must have studied Physics, Chemistry and Mathematics as main subjects during their II PUC / 12th Standard.
Candidates who have studied Biology, Statistics, Electronics, Computer Science, etc., in addition to Physics, Chemistry and Mathematics are also eligible to apply. The candidates must have secured a first class or 60% or equivalent grade (relaxed to pass class for SC/ST candidates) in the II PUC / 12th Standard examination.