Friday, April 10, 2009

Prof. K.D. Joshi's analysis of JEE math papers

The analysis by Prof. K.D.Joshi (professor of mathematics at IIT-B) of the mathematics portion of JEE-2008 formed the basis of Manoj Mitta's story on the IITs' policy regarding disclosing the answers to the JEE questions this year. In response to my post linking to that story, Sridhar and Niket point out that Prof. Joshi's analysis is available online -- not just for JEE-2008, but JEE's going back to 2003!

I glanced through his analysis of JEE-2008 (pdf). It's an amazing document: his analysis is methodical, meticulous and clear. His love for the subject is evident in every page of that 85+ page document. Where he has problems with the choice of the paper setters, he expresses his anguish that such a choice brings harm to the subject of mathematics itself.

Here is an example from near the end of the document where he takes up "a very unpleasant task ... of analysing the mistakes" in JEE-2008:

... As remarked in the comments to that question [Q. 21(A) of Paper 2], the mistake arises because the word ‘minimum’ is used instead of the phrase ‘local minimum’. Since most good books emphasise the difference between these two concepts, a good candidate relying on such books will be confused on seeing that none of the answers is correct. So, he may simply leave a blank in the answer. There may be some unscrupulous books or teachers who do not distinguish between a ‘minimum’ and a ‘local minimum’. If the idea was that candidates in remote areas who have to depend exclusively on such shoddy sources should not be penalised, then perhaps the answer given in the model answers can be justified as a charity on social but non-mathematical grounds. But why should such charity be at the cost of a good candidate? ...

The real harm caused by the failure of the model answers to do so is not confined only to the good candidates who answered Q.21(A) correctly. A far greater casualty is mathematics itself, because the model answers amount to giving a sancion to wrong mathematics. Next year the IITs will have no moral right to penalise a candidate who confuses ‘minimum’ with ‘local minimum’.


  1. Niket said...


    Its the age-old "fight" where mathematicians insist proofs to be mathematically perfect and complete, whereas engineers are OK with "workable" proofs.

    There are several examples where we use cyclic arguments to prove theorems in engineering math courses, something pure mathematicians will never do.

    For example (co-opting Sridhar's argument): when was the last time you meticulously distinguished between "positive" and "non-negative"?

  2. Anonymous said...

    Losers from a has-been college engaged in useless activities.

  3. Wavefunction said...

    K D Joshi is an old friend of my father's and his great love and talent for mathematics were evident ever since he and my father together went to a private tuition class in school taught by a great teacher, Prof. Godbole, in the (then) small town of Ratnagiri.

    Since some of my research involved investigating energy surfaces of molecules, I am all too aware of the mistake of confusing a minimum with a local minimum!

  4. Badri Seshadri said...

    Prof. Joshi says he has taken the questions from

    I looked around (not thoroughly though) and couldn't find the question papers or the model answers.

    If you come across the links to the above, do post them here.