BCA

The following are the few Colleges offering the BCA+MCA dual degree course in Madhya Pradesh.
1. Renaissance University Indore
2. IIPS Indore.

The eligibility criteria and admission details related to BCA of Symbiosis Institute of Computer Studies and Research, Pune are given below.
Eligibility criteria : Student passing XII from any stream or equivalent government approved diploma in Engineering/Technology with minimum 50% marks (45% for SC/ST candidates)
SELECTION PROCEDURE : Symbiosis Entrance Test Score, Personal Interaction and Writing Ability Test (PI-WAT)
So from above you are eligible. If you have completed you Engineering Diploma with minimum 50% of marks.

Yes, you are eligible for BCA from St. Xavier College, Ahemdabad. For more details click on the link below.
Good luck.

Yes, government has changed the whole MCA pattern to two year in all the Indian colleges.

You just need to pass in your last qualification as an eligiblity criteria for it at IGNOU.

You may check their website for such specific details.

No, maths is not considered as a compulsory subject when it comes to taking up BCA.

Mathematics or Statistics is mandatory at 10+2 level for the BCA course at NIZAM College. Hence, Non-Mathematics background candidates are not eligible for this course.