Mathematics

TIFR runs a graduate programme leading to the award of Ph.D, Integrated M.Sc-Ph.D as well as M.Sc degree in subjects such as: Mathematics, Physics, Chemistry, Biology, Computer & System Sciences (including Communications and Applied Probability) and Science Education. It is conducted at the Mumbai campus and various National Centres of TIFR. You are eligible for integrated PhD program in Maths. You will have to appear for the entrance test and interview to seek admission in Integrated PhD program in Maths at TIFR. There is no minimum CGPA as eligibility criteria. You may refer to following link for further details:
http://univ.tifr.res.in/gs2017/index.html

Yes, there are no restrictions on students to prepare for JEE provided they fulfil the criteria for JEE exams. The eligibility for JEE is as follows:
Basic eligibility:
Nationality: Candidates must be an Indian citizen.
NRIs, PIOs, OCIs & Foreign national candidates can also apply.
Number of Attempts: Candidates can apply for JEE Mains exam only three times. This attempt limit will be counted from 2017.
Aadhaar Card is compulsory to apply for this exam.
Age criteria:
Age limit: Candidates whose date of birth falls on or after 1st October 1993 (for general and OBC candidates) are eligible to apply.
Relaxation: If candidates belong to a reserved category like SC, ST and PwD category then the date of birth falls on or after 1st October 1988 are eligible for JEE Mains.
Candidates note down that the date of birth mentioned in the Secondary Education Board/University will be considered only for appearing in the exam.
Qualification criteria:
Qualifying exam: Candidates must qualify their 10+2 or equivalent examination from a recognized board.
Subjects: Candidates must have to take a minimum of 5 subjects in 12th/equivalent examination. Candidates appearing for JEE Mains 2018 must have passed class 12th with Physics, Chemistry & Mathematics in order to apply.
Passing marks: There is no prescribed percentage to appear in the examination. Candidates having passing marks can also apply.
Only for admission to NITs, IIITs and CFTIs, candidates should secure minimum 75% marks (65% for SC/ST students) in the qualifying examination or must be in the top 20 percentile in class 12th examination conducted by the respective boards.
Appearing candidates: If a candidate appears in class 12th or equivalent class in 2018 then he/she is also eligible for JEE Mains 2018.
NIOS candidates can also apply for this exam.
Diploma holders: To appear in JEE Advanced, a Diploma holder can apply in JEE Mains 2018, but their rank & score in JEE Mains will not be considered for admission in NITs & CFTIs.
No board marks will be taken into account for calculating JEE Mains score from the year 2017 onwards.