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Hi Rohan,
Yes, you are eligible to appear for the CET exam.
It is important and necessary to understand difference between the two tests.
The Common Admission Test (CAT) is a computer based test held in India. This test scores a person on the bases of quantitative ability, data interpretation, verbal ability and logical reasoning. The Indian Institutes of Management (IIMs) started this exam and use the test for selecting students for their business administration programs.
CET Common Entrance Test is conducted in Maharashtra to give the admission in MBA/MMS/PGDBM/PGDBA courses. The exam is conducted by Directorate of Technical Education (DTE), Maharashtra.
CAT is a test designed to select only top percent from a large pool of students. As a result, it is a conceptual test, which is a good mix of moderate to difficult questions and where selection of questions is crucial.
On the contrary, CET is a test to have uniform distribution on both sides of normal curve. As a result, CET is designed as a speed-based test, which consists of easy to moderate questions.
Again, in CAT one has to perform across all sections covering various areas of expertise
In CET there is no sectional cut-offs. Randomly distributed questions make things difficult if you want to attempt your preferred area of expertise across the test. Also, there is no negative marking in this exam.

I am currently pursuing MBA and PGDEM course from FABS, and I would be the right person to tell you about FABS. Fazlani Academy of Business Sciences (previously Fazlani Altius Business School & popularly known as 'FABS') is an autonomous center of Corporate Excellence and Leadership. Infrastructure in FABS is absolutely world class, it gives you the feeling of corporate environment and culture is the best part of this institute, which differentiate FABS from other institute of management. It is a highly equipped Digital can. Learning & Development helps us to groom ourselves and develop our inner qualities. Pre-placement is the biggest differentiate between FABS and other Management institutes, you get admission only after placement, and 9 months paid internship is a part of the programme. FABS provides best of best faculty members from well know Dun&Bradstreet institute to the students and the faculty are all Corporate practitioner with years of corporate experience behind them. One thing that absolutely helped me grow a lot, it is the Corporate Thursday. On corporate Thursdays, CEOs & Directors of top companies visit our campus and talk and discuss about relevant topics, this helps students to learn a lot more about the corporate world and real problems and solutions in small and big organisations. I would recommend you to visit and see and understand for yourself.

Hi,
List of colleges offering B.E Mechanical in Mumbai are:
https://www.shiksha.com/search/?q=B.E+Mechanical&qer=0|0|0|0|0|621,1473,3498,4573,1172,3494,4576,4574,1106,4572,3493,3499,331,4575,1936,1938,587,3497,1073,1934,1935,1937,1933,638,604,3496,1040,680,3495,1932,1139,4571,4577|under-graduate-degree|0|0&sa=^0^0^0^0^0&ts=399927&rf=searchwidget
Kindly filter out the branch / college / location as desired from the above link.
Every institute has its own course specific fee structure. In order to know the exact fee, it would be always advisable to browse through the official website of the institute where you wish to apply.
Always remember, you should pursue a stream/course based on two things:
-your career goal
-the type of job you want to do
Please feel free to discuss more.
Wish you luck.

For BCA, it's not compulsory to have Mathematics in 10+2. The basic educational qualification eligibility criteria for the course is that the candidate must have passed 10+2 with any stream from any recognized board with at least 50% marks.
It is very good for a person who further wants to make his/her future in field of computer programming and software developing. A person with BCA degree can easily get job in the big IT companies. A BCA student can also go for further studies like for MCA or MBA. It is worth doing if u do it from a good college.
The BCA is an undergraduate degree course in computer applications for duration of 3 years. After completing BCA, a student can go for MCA which is a master course in computer application and is considered equivalent to engineering course (B.Tech).
The demand of IT professionals is increasing not only in India but also in abroad. After the completion of the course, the student can find a job in reputed IT companies like IBM, Oracle, Infosys, and Google. The student can work as a system engineer, junior programmer, web developer or as a system administrator. This field provides you ample opportunities to make your career not only in private sector but also in the public sector. The government organization like NIC, Indian Army, Indian Air Force and India Navy also recruit large number of computer professionals for their IT department. After the completion of the course a students work profile may include:
Some best BCA colleges are listed below:
Indian school of Mines, Dhanbad
Birla Institute of Technology, Mesra
SRM University, Chennai
Geeta University, Panipat
Manipal Institute of Technology
Dehradun Institute of Technology, dehradun
Petroleum University, Dehradun

Hello Jyoti,
There are few things which need to be keep in mind before joining a course from any institute.
1. Are you getting a PGD or MBA Degree? Although, they are considered equivalent but technically both are different and MBA have more value than any PGD.
2. Is your University recognized? UGC, DEB and AIU are basic recognition required.
3. What flexibility you are getting? App based learning, live interactive lectures and career advisory are basic facilities.
4. Placement Support provided or not? Straight and forward saying no university can guarantee your placement, as companies pay for skills not for Degree you are holding.
Welingkar and IMT, both are providing you with a PG Diploma as they are just institutes. So, better to go with a university rather than institute.