Exam

Yes you can join. Regarding the syllabus, it's available online in the college portal

Top MBA colleges with budget fees-
RV institute of management -75000. Directorate of distance education 8230. Dr Ambedkar institute of technology 3700
Dayanand sagar college of management and information technology 63750. BMS College of engineering 25300. The Oxford college of engineering 70000. Xavier institute of business management studies 50900. government ramnarayan chelleram college of commerce and management -48,000. National institute of retail management 67000.

It all depends on your goal and, indeed, your interest. If your aim is to get a good private job or become a programmer, you're good to go for competitive coding. But suppose your aim is either to do a Master's (Master of Technology), a Ph.D. (Doctor of Philosophy) or to get a job in public sector undertakings. In that case, you must prepare for the Graduate Aptitude Test in Engineering. I hope this will help you.

Any student from any degree in their undergraduate can apply for CAT exam.

The short answer is 'yes'. Even if you are in 3rd year of your college, you can still give CAT exam.

You are eligible to give the CAT exam but still cannot satisfy the 'minimum 50% in graduation' criteria.

It is better to pursue a regular MBA degree rather than a distance degree. Because MBA is one of those degrees which require a lot of regular networking and working. You would not get all of those from a distance degree.

Yes, you have to crack the CAT exam in order to make it into IIMs.

The simple answer is 'no'. If you wish to pursue M. B.A. in I. MS then you have to clear the CAT exam. GATE exam is for those who wants to do M.Tech.