Dual

https://www.shiksha.com/bba/articles/integrated-mba-programmes-in-india-blogId-15044
Go through the above link. You will get all the details of the good colleges having integrated MBA programme. Choose the college according to your city preference and also checking out the fees and placement record of the colleges.

You may refer to following link for integrated M.Sc PhD at:
http://www.jnu.ac.in/SCIS/programme_of_study.html

Both have pros and cons. MBA is for 2 years but integrated MBA is for 5 years. MBA can be done by someone who has completed his Bachelor's degree in any stream but in integrated MBA one has to study management courses right after 12th. One has to give MBA entrance to do MBA but no entrance exam is needed in integrated MBA to do MBA. Getting into MBA colleges is easy as many colleges are available but there are limited integrated MBA colleges in India.

Some universities provide dual specialisations, but you can take one subject as major and the other as minor.

There is no cut-off but 55% at least recommended. They consider Academic record, Performance during the CT-GE-PI process and overall profile. Please check the FAQ section and contact for further information.
Good Luck.

Balaji college in Pune is one of the good colleges for the same.

As such, there is no entrance exam for integrated BCA +MCA but there are various exams of different colleges and universities for this course.

We had 100% placements in all streams last year. We have a decent faculty for operations. The average package for freshers in operations is about Rs 6 lakh. No we don't have dual specialization but we do get to choose a major specialization and a minor specialization.

NMIMS offers best online MBA with dual specialisation. Other colleges which don't offer dual Specialisation but a good for distance MBA are Symbiosis, Amity, IGNOU and Welingkar.