MCA

No, you can't do it after completing B.Sc. You can get admission in MCA in NITs. For Masters, you must have a graduation degree.

For 3-years full time MCA course in Pune, you need Bachelors degree in any stream from recognized university and mathematics as a subject in 12th class/SSC. For lateral entry in MCA, you need either BCA or B.Sc (IT/CS) degree. Also, you have to clear the entrance exam like MAH-MCA CET.

MCA and B.Tech CSE are preferable educational qualifications for developer and tester roles in IT companies. Majority of MCA graduates work in IT industry or IT department of business enterprises. There are ample opportunities for bright software professionals to work abroad. Nowadays, long term onsite assignments are scarce but there are good opportunities for short term onsite assignments.

Yes, you can do.
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Unless you are able to clear BCA, you may not able to either MCA or MBA. You are advised to concentrate in clearing your BCA backlogs.

Yes definitely, if you want, you can pursue MCA from NIT since, you have done B.Sc in maths. But the condition is that you have to qualify NIMCET examination to pursue MCA from any of the 11 NITs providing the same. The NIMCET is a National Level Entrance Test conducted by NITs for admission to the MCA course offered by NITs. Only if you are capable of qualifying the exam with a good rank, you will be able to get an admission in the NITs.

Yes, there is no specific subject graduation is done on. You can do your graduation and get into civil services. One of the challenging task to get through civil jobs.

Everything has its own way to go. Without completing 12th if you say I want to MCA that's a joke. But your under the right path do your BCA and forward go on to do MCA. It's relevant to your option choosen and one of the best courses to.