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Dear aspirant,
Glad to meet you.
Yes you are eligible.
JMI offers BA, B.Sc, BBA, B.Com, BTTM, BFA, BA-LL.B, B.Ed and B.Li.I.Sc courses in various specializations. The minimum eligibility criteria is 10+2 from a recognized board. Admission to some of the UG courses will be done through Common University Entrance Test (CUET) while admission to the remaining courses will be done through JMI entrance Test.
Selection for the BA (Hons) Hindi, BA (Hons) Sanskrit, BA (Hons) French and Francophone Studies, BA (Hons) Spanish and Latin American Studies, BA (Hons) Economics, BA (Hons) History, BSc in Biotechnology, BVoc (Solar Energy), BSc (Hons) Physics and BA (Hons) Turkish Language & Literature courses will be done on the basis of scores obtained in the Common University Entrance Test (CUET). Candidates must choose the subjects mentioned in the eligibility criteria while appearing for the CUET.
Selection for the remaining courses will be based on the JMI entrance test.
Hope it helps.

Scope for Higher Studies after M.Sc. In Mathematics:
Candidates who have completed M.Sc. In Mathematics can specialize in a particular area according to their interest. Several Master of Philosophy and Doctor of Philosophy courses are available in various areas of Mathematics. Candidates can pursue these courses after meeting the criteria specified for the particular course. Those who have completed any of these courses can find lucrative opportunities in the field of research. Also, they can find many career opportunities in various multinational companies. List of different doctoral level courses that are available after M.Sc. In Mathematics are given below.
Master of Philosophy in Applied Mathematics
Master of Philosophy in Mathematical Science
Master of Philosophy in Mathematics
Master of Philosophy in Maths and Statistics
Doctor of Philosophy in Applied Mathematics
Doctor of Philosophy in Mathematics
Doctor of Philosophy in Maths and Statistics
Career Opportunities after M.Sc. In Mathematics:
M.Sc in Mathematics graduates can find lot of opportunities in Research and Development firms, Economic Research firms, Market Research firms and Manufacturing firms. They can look for the job profiles like Quantitative Risk Analyst, Statistician, Treasury Management Specialist and Demographer in these firms. Those who want to work in public sector can find ample opportunities in various government organizations like Defense Research and Development organisation (DRDO) and Indian Space Research organisation (ISRO). Reputed Software companies offer several career opportunities for these graduates in operation research, software design and programming. Banks and Insurance companies also offer lucrative opportunities for the candidates who have completed their postgraduate degree in Mathematics. They can also work in various government colleges after qualifying SET or NET exam.
Regards.

Some popular entrance exams conducted for admission to B.Sc. Agriculture course are as follows:
ICAR Entrance Exam ICAR AIEEA It is an agriculture entrance exam conducted by Indian Council of Agricultural Research (ICAR) for admission to 15% seats in Agriculture Universities in Bachelor Degree programs and 100% seats in ICAR Deemed to be Universities and NDRI, Karnal
EAMCET- Conducted for admissions in Agriculture colleges and universities in Andhra Pradesh
PAU Entrance Exam- Conducted by Punjab Agricultural University
KEAM- Conducted for agricultural colleges in Kerala
IGKV CET- Conducted by Indira Gandhi Krishi Vishwavidyalaya
It is not possible to list all entrance exams conducted across the country as there are too many. Please let me know if you have a college in mind, so that I may be able to populate relevant details. Regards.

I don't know about South India, but can suggest you the best college in North India. University School of Agricultural Sciences, Chandigarh University is recognised as one among the Top B.Sc. Agriculture Colleges In Punjab, University Institute of Agricultural Sciences (UIAS) is a premier institute delivering quality, research-based agri-business education. We focus on creating holistic yet innovative workforce for the industry. I will recommend you The University School of Agricultural Sciences, Chandigarh University. The various features of UIAS are as follows:UIAS has the state-of-art infrastructure including well-equipped laboratories, extensive farmlands and an operational research management system. UIAS has unique academic model comprised of teaching major, minor and open elective courses and project work. Give a global vision to your career and get ahead with our strong Global alliances. Chandigarh University offers the highest return on investments to the students and their parents. The impeccable placement record of Chandigarh University makes it the most sought after educational institute in North India.