B.E.

You will have to give the entrance test to get admission in the course. You will have to go through the prospectus of the course provided by the college to know more about the admission procedure, eligibility criteria, fees etc. You can use this link
https://www.shiksha.com/teaching-education/colleges/b-ed-colleges-india?rf=searchWidget&landing=ctp

Hello Nidhi Singh,
Unfortunately the information you sought could not be found. But all the same I would like to advise you that instead of looking for fee concession or scholarships, you should go for education loan that is being offered by many banks.
Best wishes to you.

Hello,It is very nice to know that you are interested in doing your PG in Product Design. I am attaching a link that will give you all the required information that you need. https://www.shiksha.com/design/industrial-product-design/colleges/colleges-india
Best wishes to you.

Apart from the marks, you will also have to take admission and language proficiency tests. The eligibility criteria is based on these.

Hi
You will have to give the JEE exam. Visit this link to know more:
https://www.shiksha.com/engineering/colleges/b-tech-colleges-india

You will have to complete an undergraduate course first to do post graduation in Art direction and production design.

Yes, you can give the CAT exam after completing the course. CAT is a highly competitive exam and you should be thoroughly prepared for the same because you need to secure a very good percentile in order to get a good college of the top ranking. Buy books online or at stores or join a coaching class which can help you sail through it and start preparing right away.