[shripadk]

Yes you are right in a way. Lets put it into perspective: The total number of students who gave their 12th final board exams was 1.43 crore in 2017 (https://www.india.com/education/board-examinations-2017-over...). That is roughly 14.3 million students. This is an aggregation across all boards: ICSE, CBSE and various State Boards. Let us assume that the same number of students gave their board exams in 2018 as well (I am sure the number is higher but I can't find stats for it).

Now not all of these 14.3 million students appear for IIT JEE. Only 7% of these (1 million) appear for JEE. But since you talk about "eligible student", all the 14.3 million are eligible. But many don't even bother to take it because (as you mentioned) they know they don't stand a chance. Many of them are not interested in Engineering and are interested in Medical. These students take up NEET (which is equally tough). The remaining move on to do Arts, Commerce or any other stream with an aim to either do an MBA (through CAT), become a CA, LLB (for law) or pursue Civil Services (UPSC - as tough or some say even tougher than IIT JEE). The outliers are those that do not follow any of these well trodden paths: these are few and far between. So in reality only 7% of those eligible students appear for IIT JEE and then 1% of those appearing get selected.

The other fact you need to consider is that the Government of India expanded the number of IITs from the earlier 7 (as of 2001) to now 23 (as of 2018) and increased the total number of seats from 4500 to 12000. So an approx 3x jump in the number of seats keeping in mind the total number of aspirants taking the exam. So the pass percentage remains roughly the same year-on-year. I am sure if you now take 30% of the total eligible population (from your example), viz. 4.29 million students appearing for the exam, the percentage that pass will further decrease (from 1% to 0.28%). Because students are ranked and IIT seats that are fixed (around 12000) are filled rank-wise.