Dual

No dear. You can't get admission in integrated B.Sc & B.Ed. You can get admission in B.Sc Or B.Ed.
Good luck!

M.Sc. Integrated M.Sc. B.Ed is there at CUCET. For more details, please go through this link- https://www.shiksha.com/science/cucet-exam.

Please visit this link for the M.Sc courses that are available in Tezpur University. https://www.shiksha.com/university/tezpur-university-tezu-269/courses/msc-bc.

A dual degree means you will be getting your two degrees (B.Tech an M.Tech) separately, which means you will get a B.Tech Degree after 4-year course and then an M.Tech Degree after 2-year course. Whereas for an integrated course, you will get both your degrees after pursuing a 5-year course for B.Tech + M.Tech.

Obviously, Thapar Institute of Technology, because it has good rating and you will have a royal life in your college days. Because, both are chemical engineering that's why I am preferring you Thapar Institute of Technology.

You can refer to this link for details: https://www.shiksha.com/university/tezpur-university/tuee-exam-syllabus?course=991.

Yes, it is very much possible for you to do so. There are a couple of colleges offering this integrated course including IIM-Indore. Also, as for the entrance exams, it really depends on the college you are applying for. Usually, the exams one needs to give for pursuing an MBA at Iims is CAT. The other exams are GMAT XAT. It really just depends on the college you choose you go to.

It is most likely to take place on June 22, 2019.
Good luck!

It is generally a 2 year course.