It has been widely claimed (e.g., CBS Sixty Minutes) that IITs are the most selective universities in the world -- each year about 300k applicants compete for about 4000 spots. To enter the most competitive (e.g., EECS) departments, applicants must score amongst the top few hundred! I know several theoretical physicists in the US who were "toppers" on the IIT-JEE (Joint Entrance Exam), including one who placed first in all of India his year ("first ranker")! Perhaps ironically, the first ranker didn't attend IIT -- he chose Caltech instead.
Despite the hype (see below) Sinha seems to think IIT is roughly comparable to other elite national universities like University of Tokyo, Seoul National University or Taiwan National University. Note he estimates the effective population base (the number of people who have access to first world educational resources in K-12) of India as only comparable to that of Japan (about 125 million; see here for a similar estimate by a well-known physicist). The estimates that lead to the conclusion that IIT is the most competitive in the world usually normalize to the entire Indian population of nearly 1 billion. I would say that China's effective population (in this sense) is around 200-300 million people (and growing rapidly), so perhaps Beida (Beijing University) and Tsinghua are the most competitive universities in the world.
I'd be interested in the opinions of other IIT graduates! Here is some detailed discussion of the JEE exam by an IIT-Kanpur professor (link provided by a commenter). The professor suggests that the test is too hard: beyond the first few hundred or thousand rankers, noise dominates signal (i.e., even many admitted students have very low absolute scores, in which luck may have played a role).
"This is IIT Bombay. Put Harvard, MIT and Princeton together, and you begin to get an idea of the status of this school in India." (Lesley Stahl, co-anchor on CBS 60 Minutes)
"And it's hard to think of anything like IIT anywhere in the world. It is a very unique institution." (Bill Gates, Microsoft)
"Per capita, IIT has produced more millionaires than any other undergraduate institution." (Salon Magazine)
Sinha on IIT acceptance rate:
Admission to IITs is extremely difficult. Only the top 2 percent of the applicants are admitted and to get into a decent department, about half a percent is a reasonable corresponding figure. Here I will explore whether IITs are the hardest school to get into and later I will check if high selectivity results in higher quality. "Hard" facts will be supplied when they become available.
Extremely low Acceptance Rate?
Having results of a single entrance examination determine whether one would be accepted or not is a common feature among the educational institutions in East Asian countries. I worked in Japan for six years and therefore being somewhat familiar with them will compare Japanese figures with that of IITs. All figures ae based on certain assumptions.
Selective Admissions in Japan
While it might not make the CBS news, Tokyo University, or Todai, an abbreviated form of Tokyo Daigaku is the place Japanese moms start thinking of to send their children for undergraduate studies before they are even born. There are 8 national universities like the Tokyo university, Todai being the most coveted one, and a few prestigious private schools like the Keio and Waseda, and these are the schools where almost every graduating school senior hopes to get into. Among technical schools Tokyo Institute of Technology (part of those 8 national universities) leads the pack. Each year news of a few students committing suicide on failing to secure admission into one of these schools is not uncommon.
Tokyo University admits fewer than 1500. My guess is that all the top private universities and the eight national universities combined admit fewer than 15000 applicants. How many students applied for these seats? About one and a half million which is about the total number of graduating seniors. Means about one percent!
Applicant Pool Size
'Wait a minute' I can hear you saying. Unlike in Japan where almost everyone takes the test to get into an an university, in India not everybody applies to IITs. Most of the applicants who take the JEE are quite good, there being a self-selection process. In response I will point out that if we compare the potential applicant pools, the following factors stand out:
IIT JEE is taken mostly by middle class applicants from urban areas with total population about 125 million. Japan has about same population with lower percentage of test-takers compared to that of India because of lower birth rates. There almost all eligible seniors take the test to get into these prestigious universities, meaning the potential applicant pools are almost equal.
Engineering schools like Tokyo Institute of Technlogy and various engineering departments in other universities are more selective than the average department. Assume those to be twice as selective.
IITs accept about 3500 of applicants. Given the above assumptions it is about (15000/2)/3500 = two times more selective than the average engineering department in these Japanese universities.
Take Tokyo University for comparision. An overwhelming majority of the grduating seniors choose Todai as their first choice. This means that Tokyo University is about twice (3500/1500) as selective as the IITs and more likely at least four times as selective than the IITs when engineering departments are compared.
Quality of Potential Applicant Pools
Japanese seniors in schools perform near the top in international tests in sciences and mathematics. (Seniors from Korea, Hong Kong and Singapore perform equally well.) Indians are not included in most comparison studies but there seems to be some evidence that the average Indian students would have performed near the average, probably somewhat below it. Moreover, after graduation many Japanese students take time off to study for the entrance exam and their dedication has to be seen to be believed. It leads me to believe that their potential applicant pool of of higher quality.
Other Asian Countries like Korea, Singapore, Hongkong, China?
It may be assumed that the student quality and the selection rates are similar to that in Japan, if not better. Means it appears that IITs, however difficult they are to get into, could be overshadowed by institutions in neighboring countries with more difficult admission standards.
There is a difference though. While graduates of universities like Tokyo are quietly working hard to bring their countries up to top and compete with the West, India with its population of a billion or so, through its IIT and other engineering college graduates, seems destined to become a country where the developed world can chooose its low-cost subcontractors to do the jobs they don't want to do or have a shortage of workers.
Admissions in the USA
While it seems true that admission rate at IITs is less than even the most selective US school like the CalTech, it does not mean IIT recruits students of higher caliber. In a country like the USA, educational resources were well developed and the enrollment capacity for engineering majors is kept about the same as the number of seniors intending to enter those programs, if not more. It means less desparation. Moreover, there are lot of top-notch schools schools of about equal caliber which decreases their selectivity figures. My guess is that the top 50 engineering schools in the USA exceed IITs in almost all respect and another 100 or so other schools are not far behind.