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Hello Sachin,
1) Jobs for aspirants within the public sector are quite ample. There are many firms that are under the aegis of the Indian government that offer aspirants with jobs of high profiles. With the right qualification, a person can get employed as an Agricultural Research Scientist (ARS).
Upon clearing the NET qualification, aspirants can start their career as a lecturer. Besides this, jobs are also available for aspirants as Block Development Officers (BDO) or Agriculture Development Officers (ADO). To get this job, it will be needed by applicants to write an admission test.
2) Public Sector Banking Jobs after B.Sc Agriculture:
Jobs for students of B.Sc Agriculture can be got with banks, insurance companies, and many other areas.
3) Teaching Profession in Government Sector after B.Sc Agriculture:
Aspirants can get employed as teachers with well-known institutions such as the Kerala University, the JNU, Annamalai University and the MG University etc. Those who aspire to get jobs as lecturers shall need to have a Postgraduate level degree in the relevant field in addition to a NET or SET degree.

Yes, you can do it. A candidate is eligible for enrollment to any of the level(s) of the Intermediate (IPC) course on passing the Common Proficiency Test and Senior Secondary Examination (10+2 examination) conducted by an examining body constituted by law in India or an examination recognized by the Central Government as equivalent thereto.
Students who are pursuing their final year graduation course can also register for the Intermediate (IPC) course on provisional basis and such students registration would be regularised and they can commence practical training only on submission of satisfactory proof of having passed graduation examination with the specified percentage of marks within six months from the date of appearance in the final year graduation examination.

There are many higher study options for those who have pursued M.Sc in Computer Science. Higher studies will help you get placed in better positions and will improve your remuneration. Some of those options are given below.
M.Phil in Computer Science
Ph.D in Computer Science
Ph.D in Computer Science and Applications
Ph.D in Computer and Information Science
M.Tech in Computer Science (various streams)
Career Opportunities after M.Sc in Computer Science
Network Administrator
Database Administrator
Software Programmer
QA Tester
Game Developer
Application Developer
Software Marketer
Technical Architect
Technical Analyst
IT Consultant
Web Application Developer
Professor
Systems Engineer
Mainframe Systems Manager
IT Manager
Client-Server Systems Manager
Software Tester
Project Manager
Healthcare Software
CIO
Computer Systems Specialist Supervisor
You can opt for any of these career options or opt for higher studies. The choice is yours.

Selection of the graduate courses ( BE / B.Tech ) is based on merit i.e the marks secured in the final exams of 10+2 and through entrance exams. Entrance to the IIT's is through JEE (Joint Entrance Exam) and for other institutions through their own separate entrance exams and other state level and national level exams. Apart from the IIT's, some other famous institutes also recognize JEE scores for selection.
Currently, students do not have much choice when it comes to genetic engineering colleges. Please use the link provided below for a list of colleges which offer genetic engineering courses in India.
https://www.shiksha.com/engineering/colleges/genetic-engineering-colleges-india