You have an inclination to qualify for IAS and hence your objective should be to opt for such papers in IAS examination which will help you in raising your scores in the said examination irrespective of non-inclusion of such papers at your Bachelor degree stage.
You have indicated your inclination for Mathematics and Physics and as such you are interested in Engineering course, but one thing I want to make it clear that these two subjects would be the part of curriculum up to the fourth semester only and for the rest of semesters (up to the eighth semester) other subjects would be covered having equal importance in respect of earning impressive marks. So you can see that your objective is met partially with respect to your interest.
BBA - a degree in management is quite good where you have to apply the logical concept in enhancing your business skill. Preparation of such subjects would not be that much time consuming if you are sincerely involved in your studies.
Now coming for the preparation of IAS Examination, you need to choose papers in such a way so as to get maximum marks with your available time and in that way, you can concentrate on your chosen papers with the allocation of reasonable time. I would like to add one interesting point that an aspirant having chosen Geography, Philosophy and History etc have outperformed in the IAS examination despite the fact that these papers were not included in one's degree examination.
I would not discourage you for your inclination for Mathematics and Physics but you should be acquainted with the vastness of the course especially Mathematics where you would come across innumerable formulas and their applications while solving the problems. You have to have excellent command in Vectors, Differential - calculus, Integral - calculus, Differential - equation, Electricity and Magnetism, Algebra, Solid Coordinate Geometry etc (the list is endless) and for attaining impressive marks in this paper would take your lot of time and so the preparation of other papers would be affected. Needless to say, Physics, too, is a vast subject covering the details of many natural phenomena such as Mechanics, Heat, light, Sound, Electronics etc where you need to have maximum concentration so that you can excel well.
So your strategy for preparation should be somewhat different - choose the papers wisely where you can secure high marks with the less time consumption. You have to allocate your timing for current events, general English and application of Grammar and essay writing where your skills are to be tested apart from the optional papers chosen in the IAS examination and hence an intelligent planning would be the key to your success in such a competitive Examination.