Before I tell you, Srinivasa Ramanujan can crack the JEE exam or not. I must tell you something. Once my teacher said,
Never ever fall in love with any subject, nor start hating any particular topic or neglecting it- because it is a paper of all the three subjects, Your specializing or expertise in a particular subject can definitely gives a boost in your rank, but it can never be going to help you in terms of cracking IIT JEE, because in order to crack JEE you need to master in all the three subjects.
So, logically Srinivasa Ramanujan was not an IIT type, because he was not a strong supporter of Bookish Knowledge and He did not get any formal training in the field of mathematics or science.
Acctuly he was the believer of logical Ideas that doesn’t came from the Books. And being blessed in mathematics is the gift of nature, which is only given to someone lucky.
If you think you can became a master in Mathematics like Srinivasa Ramanujan or Shakuntala Devi by Practice or hard work so sorry dear it’s not Possible because the real Mathematics is not in Books as I think- “The Mathematics is the Language of Nature” or in outher words of Albert Einstein-“Pure mathematics is, in its way, the poetry of logical ideas.”
But if you want to crack the competitive exams like Joint Entrance Examination you need to be a Book-worm a geek, Poetry of logical Ideas or exceptional brain not going to help you much- yes I believe that such things definitely helps you in a long run but for JEE- sorry Dear!
So from the my point of view Srinivasa Ramanujan can’t be able to crack IIT JEE. I completely accept the fact that- He completely mastered a book on Advanced Trigonometry written by S. L. Loney by the time he was 13. By that time, he had also discovered sophisticated theorems on his own.
But as I mentioned above in order to crack IIT you need to became a master in all the three subjects and you need to have a bookworm brain more than an exceptional brain.