Indian Institute of Science Bangalore Answered Questions

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.

You have not mentioned about the rank you obtained in JAM. However, the previous year closing ranks for IITs and IISc are given below for M.Sc. Biotechnology and Integrated M.Sc Ph.D. in your category for an idea.
1. IIT Bombay : 88
2. IIT Roorkee : 227
3. IISc Bangalore (Integrated Ph.D. ): 115
4. IIT Bombay (M.Sc. Ph.D. Dual Degree): 299
5. IIT Kharagpur (Joint M.Sc. - Ph.D) : 241
6. IIT Indore: 241

Yes, physics, chemistry and mathematics is mandatory for B.S. Research programmes of IISc. The eligibility criteria of B.S. Research programme is given below. Eligibility: Candidates who have completed their II PUC / 12th Standard in the same year and those who are expecting to complete their II PUC / 12th Standard 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.

BASIC QUALIFICATION FOR ELIGIBILITY: M.Sc. Or equivalent degree in Physical Sciences/ Mathematical Sciences/ Chemical Sciences/ Biotechnology or BE / B Tech or equivalent degree in any discipline or Graduates of 4-year Bachelor of Science programmes.

The IISc eligibility criteria of IISc BS 2020 is given below:
1. Candidates should have passed class 12th (or equivalent) qualifying examination in 2019. However, those candidates who will be qualifying the examination in 2020 will also be termed eligible.
2. Physics, Chemistry, and Mathematics should have been studied by the candidates as compulsory subjects in the qualifying examination.
3. Those candidates who studied Biology, Electronics, Statistics, Computer Science and more along with Physics, Chemistry and Mathematics will also be eligible for the qualifying exam.
4. Should have scored at least 60% marks or first grade (or equivalent grade) in the 12th standard (or equivalent) examination. So PCB students are not eligible for the IISc BS course. Eligibility criteria of BITS Pilani for Integrated first degree course M.Sc. (Biological Science) is given below. For admission to all the Integrated First-Degree Programmes except B.Pharma. Candidates should have passed the 12th class examination of 10+2 system from a recognized Central or State board or its equivalent with Physics, Chemistry, and Mathematics and adequate proficiency in English. The candidate should have obtained a minimum of aggregate 75% marks in Physics, Chemistry and Mathematics subjects (if he/she has taken Mathematics in BITSAT or a minimum of aggregate 75% marks in Physics, Chemistry and Biology subjects (if he/she has taken Biology in BITSAT in 12th class examination, with at least 60% marks in each of the Physics, Chemistry, and Mathematics / Biology subjects. So PCB Students are not eligible here for Integrated M.Sc. Biological Science. IISER Bhopal eligibility criteria for BS programme is given below ;
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 the 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)BS degree programmes are available only at IISER Bhopal. Also, for applying to any of the BS degree programmes, students must have Mathematics as one of the subjects in class XII examinations. So from above PCB students are not eligible here for BS programme.

The eligibility criteria for Bachelor of Science (Research) Programme is given below. Eligibility criteria : 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. So from above Mathematics is mandatory here for admission.