Science

Hi Karan,
Firstly, It depends upon the cutoff marks for your shortlisting in these branches. To get an idea, please go through this link:
http://www.bitsadmission.com/cutoffscores2017.aspx
For the understanding of the difference, between the two branches, both have origin in Electrical Engineering. But in detail, Electronics and Instrumentation Engineering deals with Electrical technology and machines, circuit analysis, electronics, electromagnetism, electrical engineering materials, instrumentation etc while ECE consist of analog transmission, basic electronics, solid state devices, microprocessors, digital and analog communication, analog integrated circuits, manufacturing of electronic devices, circuits etc. BITS Goa and Hyderabad are both at par with each other with the aspect of these branches.
Best wishes.

Improvement depends on your current status. Whether you are a beginner or average or good enough, it depends on that. But there is nothing to get scared of, because you are not expected to be a Pandit in mathematics, you just have to clear cut off with some good marks, unless you have a goal to be a top ranker. However, I am suggesting my ways to improve your mathematics for banking exams. If you are a beginner, then clear your basics first (For arithmetic). You can solve NCERT maths books from class 8 to 10 if you too weak. If you are moderately comfortable with maths, then you can simply start with S. Hand (R. S. Agarwal) books on quantitative aptitude. They are good enough. Try to improve your calculations by learning tables upto 20, squares and cubes upto 20. Learn short tricks from YouTube tutorials. If you are average and wanting to become even better, then focus on calculations, try to improve speed by short tricks. If you are serious about mathematics, then you can go for Arun sharma CAT book for quantitative aptitude. There are 3 levels of difficulty (LOD), it is more than sufficient if you can solve LOD 1 and 2 for bank exams. Solve more numberof different types of DI from books and online. Finally, solve mock tests papers. Try to find out what you find easy and comfortable to score with. Practice everything 15 days before your exam but the last 15 days, focus on the accuracy of the strength of yours. Experts already know how to score well ! So no advice to them.
Good luck.