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Hi,
The Graduate Aptitude Test in Engineering (GATE) is an examination that primarily tests the comprehensive understanding of various undergraduate subjects in engineering and science.
The score is used for admissions to various post-graduate education programs (e.g. Master of Engineering, Master of Technology, Doctor of Philosophy) in Indian higher education institutes, with financial assistance provided by MHRD and other government agencies.
The following are eligible to take GATE:
1)Bachelor's degree holders in Engineering /Technology/Architecture (4 years after 10+2/ Post-B.Sc./ Post-Diploma) and those who are in the final year of such programs.
2) Master's degree holders in any branch of Science/ Mathematics/Statistics/Computer Applications or equivalent and those who are in the final year of such programs.
3) Candidates in the second or higher year of Four-year integrated master's degree programs (Post-B.Sc.) in Engineering/Technology.
4) Candidates in the fourth or higher year of Five-year integrated master's degree programs or Dual Degree programs in Engineering/Technology
You may also refer: http://www.gate.iitr.ernet.in

As you have done B.Sc in PCM and now you want to pursue your Master's degree in the relevant stream. Before choosing right stream you should know about your interest and dream job you are looking for. Your career option is totally based on these factors as it will provide you satisfaction and stability in your professional front.
Now as courses are concerned, you may go for:
M.Sc in any of the individual subject which you feel you are strong in it because job opportunity varies in Physics, Chemistry or Mathematics. So if you are planning for M.Sc then choose it wisely after analysing job prospects.
You can also go for MBA in various specialisations like international business, HR, Finance, Operations, Retail, Banking, and much more.
You can also move towards pharma industry.
You may move towards Astronomy, it is an emerging field and has a great market demand.
You will be having career in industries like
Agriculture Industry
Testing Laboratories
Forensic Crime Research
Wastewater Plants
Aquariums
Environmental Management and Conservation
Food Institutes
Pharmaceuticals and Biotechnology Industry
Research Firms
Forest Services
Geological Survey Departments
Health Care Providers
Industrial Laboratories
Oil Industry
Biotechnology Firms
Chemical Industry
Educational Institutes
Hospitals
Seed and Nursery Companies
Space Research Institutes
Wildlife and Fishery Departments
So, now do self-analysis as I advise all the students, and then decide what suits you more.
All the best.

It is always suggested to do a technical course through regular mode than distance mode, because it increases your chances of employment and better career opportunities. The best colleges are: Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Bangalore
International Institute of Aerospace Engineering & Management (IIAEM-Jain University), Bangalore
Indian Institute of Science (IISc), Bangalore
Indian Institute of Technology, Bombay IIT Mumbai
Lovely Professional University, (LPU) Punjab
Indian Institute of Technology, Kanpur IIT Kanpur
Indian Institute of Technology, Madras IIT Chennai
Indian Institute of Space Science and Technology, Thiruvananthapuram IIST Thiruvananthapuram
Indian Institute of Technology, Kharagpur IIT Kharagpur
Indian Institute of Engineering Science and Technology, Shibpur (IIEST-S), Howrah
Madras Institute of Technology, Anna University, Chennai
Birla Institute of Technology, Mesra, Ranchi
Defence Institute of Advanced Technology (DIAT/IAT), Pune.