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Hello subid
It demands a comprehensive and in depth knowledge of hundreds of concept in Physics, Chemistry and Mathematics. Whether a typical student can prepare for the exam in a year or not depends on his grasping power, the hard work he puts in etc. Most students who make it are students who are able to crack the examination immediately post grade 12. Which means they were well prepared in 2 years. (11th and 12th, though yes some students take up foundation courses right after grade 6). Now there is a section which could not make it by a whisker, for several reasons including, lack of proper guidance, hardwork, training, resources etc. Among other options some of them choose to drop a year and prepare for JEE again. But let me inform you a very small percentage of this crowd makes the cut after one year. No. One year is no sufficient, if you were under prepared, you are not clear on most concepts and walk into a coaching with almost no knowledge. Making it without a coaching in such cases makes it harder. Thank you.

Hi, there is a really big difference between Invention and Research, but I got the gist. Data Analysis isn't a research area pursued by CS guys, as it's well said
Engineering grads care about, which algorithm or Model fix's better while a Statistical needs to why as well. The ratio in our country is over 100:1 because everyone knows Maths ain't easy, and Statistics in particular is too much for most. But a lot of college have Ph.D. prof. who push the student in BE to do some research which lead them in research directions, so it's your choice either CS or Mathematics in B.Sc. Or B.Tech. But in either of the Choices you have to visit the college website and see how many prof, have don't research and how many research papers the college sets every year. If you can put on an Entrance Exam, I might be able to fill in for the college list as well.