B.Sc

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

Students who have scored above 60 percent marks in their finals, can apply for the Master's degree courses in biology. Some leeway is offered in marks for students of the SC/ST categories. However, all the students need to write an admission test. Those who clear this successfully are called for an interview. There are various higher study options available for an aspirant with a B.Sc in Biology degree. Some of the important higher study options in Biology that are chosen by the candidates who wish for a higher study in this field include the following:
Master of Science in Biology
Master of Science in Biological Sciences
Master of Science in Applied Biology
Master of Science in Conservation Biology
Master of Science in Computational Biology
Master of Science in Environmental Biology
Master of Science in Environmental Microbiology
Master of Philosophy in Plant Molecular Biology
Master of Philosophy in Plant Biology and Plant Biotechnology
Doctor of Philosophy in Biological Sciences
Doctor of Philosophy in Plant Molecular Biology
Post Graduate Diploma in Computational Biology
Master of Business Administration

As far as I know, there is no part time IIT JAM. You will have to devote yourself to the exam if you want to secure a passing grade in the exam and qualify for M.Tech or M.Sc.
JAM 2018 eligibility criteria:
The common criteria across institutes for each programme are:
JAM eligibility criteria is common for each program across institutes for appearing in the postgraduate science admission test.
The candidates should have secured at least 55% in subjects including languages and subsidiaries of all the years combined. Those, however, belonging to SC/ST and OBC categories need to secure at least 50 percent marks in the subjects.
Candidates need to note that equivalence of marks in case of grades in letter/CGPA (and not in percentage of marks) will be decided by the participating institutes of JAM.
As per the JAM eligibility criteria 2018, candidates will need to submit their proof of qualifying degree examinations by September 30th, 2018 to the admitting institute. However, upon failing to do so will lead to cancellation of their candidature.

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.

Further studies:
Valid Diploma certificate holders may pursue relevant Bachelor's degree course. B.Sc degree can then be followed up with PG degree or PG Diploma courses.
Graduates have a handful of PG courses to choose from. M.Sc and PG Diploma courses can be used to specialize in disciplines such as:
Clinical Nutrition
Paediatric Nutrition
Public Health Nutrition
Food Science/Technology
Sports Nutrition/Dietetics
Gerontological Nutrition
Renal Nutrition
Diverse job opportunities exist in front of nutritionists and dieticians in India. Both Government and private sector job opportunities are available in front of them.
Talking about Government sector, some of the well known recruiters include:
Government hospitals
Community health centres
Government Schemes and Missions (ICDS, NHRM, etc.)
Government Organizations (FNB, ICMR, Public Health Foundation, etc.)
Government R&D units
Government nursing homes
Government Nutrition Education Institutes
Coming to the private sector, some of the well known recruiters include:
Private clinics and hospitals
Nursing homes
NGOs
Food products manufacturing firms
Pharmaceutical firms
Private R&D units
Private Nutrition Education Institutes
Health clubs
Fitness centres
Sports centres and franchises
Hotels