Falling standards. An example.

My father pointed me to this, when I met him last week in Hyderabad. Following is the first question in IIT JEE Math Paper.

Q) Let ω be a complex cube root of unity with ω ≠ 1. A fair die is thrown three times. If r1, r2 and r3 are the numbers obtained on the die, then the probability that ω^r1+ ω^r2+ ω^r3 = 0 is
(A) 1/18 (B) 1/9 (C) 2/9 (D) 1/36

How difficult is the question is currently under big debate in circles of Math +1, +2 teachers. Many say “it is a very easy question. A no brainer. Many questions in math paper are like this“. Does this show the falling standards of the IIT JEE?

I have seen the paper. There are many questions which look as if they are deliberately placed in the paper to allow students to score better. We all know with left and right reservations, what this means. There are many other questions like this. For example,

Q) Let p and q be real numbers such that p ≠ 0, p^3 ≠ q and p^3 ≠ − q. If α and β are nonzero complex numbers satisfying α + β = − p and α^3 + β^3 = q, then a quadratic equation having
α/β and β/α as its roots is
(A) (p^3+q)x^2−(p^3+2q)x+(p^3+q)=0 (B) (p^3+q)x^2−(p^3−2q)x+(p^3+q)=0
(C) (p^3−q)x^2−(5p^3−2q)x+(p^3−q)=0 (D) (p^3−q)x2−(5p^3+2q)x+(p^3−q)=0

This question is something which can be answered by even a Standard Eight student with decent understanding of Math in his previous classes. IIT JEE Math paper used to be something which used to have seek a thought process. Only when the thought process is in the right direction (may not be the path the question paper setter would have thought of, but mostly the direction would be the same) one would reach the correct answer.

Appalling standards in setting question papers will only lead to the downfall of the brand name called IIT. When I wrote my IIT JEE final exam, the paper had 15 objective type questions. The time limit was 2 hours. In such a paper, a person like me, with average intelligence couldn’t answer even 7 questions. Some high IQ students I knew could answer almost 12 questions. The best I heard in my circle of friends was 13 questions. There was never time shortage for solving the problem. It was only finding the right direction and applying the right formulae. In contrast, in 2010 paper, with objective type questions only, it seems like there is not much thought process involved. Today JEE paper seems to be more like how EAMCET paper used to be.

Some +1, +2 teachers, including my father, say that “it seems like the IIT JEE paper is being set deliberately with easy questions to allow for students easily pass through the test. But is it really the case? We couldn’t tell. But looking at the policies the government is framing and the changes happening in the academia, we don’t know if we can completely ignore the possibility

Mr. Kapil Sibal is acting like a typical manager in a typical Indian IT company. He is making statements and then asking professors in academia to make them true. This will only hurt the larger brand name of the IITs. He would better be careful!



  1. 🙂 Nostalgia. My memory on complex numbers and probability got rusted. Restless to know the trick behind 1st question. 2nd q is straight enough. 🙂

    Ya, if they want to suck more ppl into IITs maybe they can reduce the cut-off, not the difficulty level. That would hamper the preparation.

  2. I know, right! Its so fresh in memory but then a very distant memory, forgotten and sometimes lost!

    First is quite simple. Only two important properties of cube roots of unity are required. 1+w+w^2 = 0 and w^3 = 1 if w is a cube root of unity and w != 1.

    From my facebook comment with another frnd
    (1,2,3), (2,3,4), (3,4,5), (4,5,6), (5,6,1), (6,1,2), (1,5,3) and (2,4,6) and all combinations of these 3-tuples will lead to 1+w+w^2 which is zero. Rem that all other 3-tuples like (1,4,5) (2,4,5) (1,1,2) etc will not lead to 1+w+w^2…. See More

    There will be 3! = 6 of each of these 3-tuples. So if the die is rolled three times, everytime total posibilities are 6 while chance of getting one particular number is 1.

    So, prob that 1,2,3 will happen consecutively is 1/(6*6*6). There are 6 ways of doing this 3-tuple. So, the prob of having (1,2,3) and all combinations of 3-tuples is 1/36 (coz 6 times 1/216)

    There are 8 ways of doing this. Thus the probability of 1+w+w^2 = 0 is 8/36 = 2/9. Answer is C.

    The second one is something like jujubee. There are more like this. Simply too easy to answer. Heres the link to the complete JEE paper



  3. […] by a long shot. This is not good. The consequences of a low level of difficulty JEE before too [2010, 2011]. The direction in which JEE seems to be headed is precisely the road toward total disaster. […]

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