Exam

- With an MSc in Mathematics and B.Ed., there are quite a few government exams from which you can choose depending on your hobbies and career aspirations. Here are some of the best ones for you: Teacher Eligibility Tests (TET):

B.Ed indeed paves the path to appearing for the TET. You can go for the state-level or even central-level exams (CTET) to become a teacher in schools. Eligibility: Generally subject-specific B.Ed plus passing the TET would make you a primary or secondary private school teacher.

State Civil Services Examination (SCT):

If you dream of working in administration, then state civil services of SDM, DSP, or any other administrative post are worth going for. This math background especially would come into play during logical reasoning and general studies portions of the exams.

Indian Statistical Service (ISS):

If someone has a strong math background, then Indian Statistical Service would be the best option for him. It is conducted by UPSC for Indian government statistical department positions. Eligibility: A postgraduate degree in statistics or mathematics with special emphasis upon statistics.

SSC (Staff Selection Commission) exams:

Several SSC exams, for instance, all SSC CGL exams (Combined Graduate Level), are quite suitable for you. The SSC CGL boasts job positions in government departments that, by virtue of your educational background based on math, will be crucial specifically on departments requiring quantitative analysis, statistics, or data analysis. 
Eligibility: A graduate degree from a recognised university, otherwise you easily qualify with your M.Sc in Math.

Most universities in India will not allow students to give a B.Tech in Computer Science entry without writing the entrance exam. But, there are exceptions, like some private universities or institutions that give direct admissions through non-entrance tests management or institutional quota. Hence, your avenues here are:

Private Universities: Most of the private universities, including VIT and Shiv Nadar University, SRM University, offer direct admissions through their own entrance tests (like VITEEE, SRMJEEE, etc.) or on merit. If you were to qualify based on eligibility criteria and score well in your 12th board exams (through Physics, Chemistry, and Mathematics), then you could qualify for direct admission.

Management Quota: There are several private engineering colleges which have seats under management quota and provide admissions without entrance exams. Generally, these seats are more expensive compared to merit seats. Visit the specific college to get more details.

State or National Level Exams: Under this category, although there are colleges that do not require specific entrance tests for B.Tech in CS, public universities and almost all reputed colleges (like IITs, NITs, and IIITs) insist on JEE Main, JEE Advanced, or other state-level exams such as Andhra Pradesh EAPCET or TS EAMCET.

Merit-Based Admission: Some colleges are also known to offer admission in the B.Tech based on Class 12 marks-the actual number of such colleges is less, and those will mostly be private or insignificant colleges.

Thus, it is clear that while you do have chances for direct admission into some private institutions, the entrance exam is generally needed to study B.Tech in CS at almost all of the well-known colleges.

You complete an Electrical and Electronics Engineering (EEE) Diploma after completing 10th grade; it does not mean that you have done any graduation. A Diploma is mainly for 3 years and imparts very basic knowledge and skills in a particular branch of engineering. This is technical qualification at the undergraduate level but not equivalent to B.Tech/B.E., which is a full-fledged undergraduate degree after 4 years.

After completing a Diploma in EEE, you may do the following for further studies:

Lateral entry into B.Tech- Once you have completed your diploma, you can apply for a lateral entry into the second year of a B.Tech programme in Electrical or Electronics Engineering. This is a common path for Diploma holders to obtain a full-fledged engineering qualification.

Working as an Associate Technician or Junior Engineer- This Diploma can also allow entry to various industrial sectors within a technician or an associated junior engineering role, although the size of the working area may be less than a graduate degree.

To conclude, it can be said that a Diploma of EEE gives you practical knowledge but is not equivalent to an entire engineering graduation level.