Let me start with Priscilla Jebaraj's story in The Hindu:
At large coaching centres such as those in Kota, students effectively drop out of the school system in order to prepare for JEE. They can then scrape through their board examinations to meet the 60 per cent minimum criteria, without having actually attended school for two years.
This can result in a skewed education, which shows up once the student gets to IIT. IIT-M director M.S. Ananth tells the story of a student who arrived at IIT without having mastered the concept of integration despite it being part of the higher secondary mathematics curriculum. He had failed to study it since he felt only three marks were allotted to the topic under JEE.
I couldn't believe it when I read that stuff about a student entering an IIT without knowing anything about integral calculus. Within a day, I got this view confirmed by another friend from an IIT who went on to complain about large holes in many students' background -- which were probably due to their strategy of selective preparation.
[BTW, this is not peculiar to JEE; recently, a colleague told us about a couple of students who didn't know any mathematics and still managed good ranks in GATE. And they are in a math-heavy engineering field! ]
Frankly, I hadn't thought about this angle before; after thinking about it a bit, it actually makes sense. By any objective yardstick, JEE is a brutally tough exam -- so tough, in fact, that you could get 30 to 40 percent and still find yourself among the rank-holders (especially if you really do well in one of the subjects).
For some students, then, it is certainly rational to cut down on preparing for stuff that's difficult -- and focus more on things for which they have a flair. It's also possible that coaching schools encourage them to put this strategy into practice.
A Board exam -- conducted, for example, by CBSE -- this would be an absolutely disastrous strategy if you want to be among the among the top-rankers. This is because top-rankers in these exams typically have over 90 percent -- and you can't get 90+ percent by ignoring even 20 or 30 percent of the syllabus.
Put this down as yet another 'unintended consequence' of the design choice by the IITs to go with a 'tough' version of JEE. It's this very 'tough-ness' that allows this particular method of gaming the exam to work.