CAT

Hi,
CAT exam is not important for every B-school but top 10 B-schools do accept CAT score, apart from them you can appear for MAT , XAT, NMAT, SNAP or GMAT and then you can apply for MBA admission.
All the best.

With valid CAT score, you are eligible for admission in all IIMs. You will be required to fill admission form in other non IIM colleges which use CAT score for admission.

In Pune, you can join TIME institute or Pankaj Gandhi Academy (PGA).

Your previous background will simplify your preparation to a large extent. If your academic record is satisfactory, you find the going easy for you.

Hi Dear,
There is nothing so called as syllabus. The questions would be from aptitude, reasoning, English and GK.
You would be able to prepare for it better if you purchase quantitative aptitude book from R. S. Agarwal and keep yourself updated about the current affairs. Also, download some previous year's questions and practice.

You need to appear for one of the entrance exams like CAT, MAT, XAT and CMAT and based on your scores, you can apply for individual colleges. You can also take the UPTU entrance exams for management.
I, however, would advise you to look for some good colleges (Tier-1) like IMI New Delhi, MDI Gurgaon etc., but to get into these colleges you need to appear in CAT and score above 80 percentile. So, take a wise decision.

Hi,
You can either download it from the internet or can purchase it from a bookshop. There are many publishers, Arihant being an example.

Yes, other than CAT you can appear for MAT, XAT, CMAT, ATMA, SNAP, NMAT, etc. All have their respective official websites. Do check them from time to time, browse through MBA education portals. These exams also get published in English newspapers.

Yes, there is negative marking.

Yes, why not. but Institutes like JBIMS are the most sought after MBA institutes after IIMs so you need to be among the top percentile holders in CAT or XAT to get admission there.