Distance

There is no university for distance B.Tech.

To get placements, you should join a regular college.

Hi Anirban,
Yes, you can do that. You can choose among:
1. Anna University.
2. Manipal.
3. IMT Center for Distance Learning.

Yes, you can take admission in MBA finance also through distance. The criteria is graduation, which you have completed. You just need to apply in colleges which provides distance MBA in finance and they will conduct exams semester wise.

Yes, you can do that because to pursue class 12th from distance, you are not required to submit original leaving certificate.

From my point of view, GITAM University would be a better option for you.

Hello Amit,
I understand and appreciate your interest in pursuing MBA in finance. In my opinion, IGNOU is the best option for MBA in finance by distance learning. It's course material and content is of international standards. Fee is Rs 1500 per subject. MBA is of 21 courses including finance electives. It is one of cheapest MBA in India.
Alternatively, you can refer to the link below for more colleges providing MBA in finance by distance learning:
https://goo.gl/rBxUvY
I hope this answers your question to your satisfaction. If so, kindly upvote this answer. If you have any further questions, kindly revert.