A legendary question from the toughest exam

This legendary question from India's JEE Advanced test is so hard that most people would not even attempt it. Only 78 out of 161,319 were able to correctly solve it.

solution by kludg
Other solutions
Jee Advanced 2019 report
Q11, 2019 JEE Advanced Mathematics Paper 2
Dice
Iitduser, CC BY-SA 4.0 via Wikimedia Commons

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[jnswiwh]

With on average 3 minutes per question, through a 6 hour gauntlet
the correct answer to this question is "skip, lets see if there will be time left to loop back around"

[ai]

What makes this question hard is not the math—it's the incredibly confusing wording.

[StatsJedi]

At the pause, the definition of (A, B) is totally unclear. No wonder so few got it correct.

[AdrianColley]

I would have skipped this question because its phenomenal vagueness is not worth spending exam time on decoding. A must be a set, because |A| is defined only on sets, but it's also an "event associated with S"; which can't indicate the natural meaning of an element of S, because A's cardinality is greater than 1. Whoever wrote that question should have had their work reviewed before it went to print.

[GaurangAgrawal]

I started watching your channel in 8th grade and I was always amazed by how you solved JEE Problems. Especially the ones involving logarithms. Ofc, I wasn't able to understand anything at that time, but now that I am preparing for JEE, It's time to correctly solve this problem in order to check my preparation 😅.

Loved these years with you and your way teaching mathematical concepts. Looking for more in the future

Edit: Nah This question was from my least favourite topic Permutations, Combination and Probability... I am currently re-studying those topics to understand them better.

[lefthanded]

You find the true smart folks by asking hard questions in an easy format rather than by asking easy questions in a hard format 👍🏻

[sergniko]

I paused video to understand the question

[pablocopello]

A mathematical problem begins when it is clear what is being asked. Before that, we have a problem like in this case. Does JEE tests evaluate the knowledge/capacity in it's target topics, or evaluate the capacity to guess what it's questions pretend to ask?

[arthatiara]

what im thinking when presh said there were only 78 students,
"did they have enough time to finish other questions???"😂

[fun-damentals]

i feel like the problem itself is actually rather simple. its the fancy mathematical terms and confusing wording that makes it difficult to understand

[makokx]

Imagine getting through that whole thing then messing up the final addition. lol

[ravirajshelar]

The 2019 paper is always going to be on the top 5 hardest papers in JEE Advanced History😂. Also in jee advanced papers students generally leave questions related to permuations and combinations a lot as compared to other topics.

[leogreaves]

It’s always a treat when I get an upload notification from you.

[Kounomura]

The strict mathematical language can be so abstract, even in the formulation of the simplest problems, that it directly scares off those who want to get to know the beauties of mathematics. Above all, in education, much more care should be taken to make every mathematical problem as close as possible to an imaginable situation. Once the listeners have understood the essence of the matter through this, it is then possible to continue with the more abstract and generalized version. In the case of the above test, it is not possible to know exactly who they wanted to select in the first place. Those who switch quickly or who have a large overview, even if it is not that deep.

[dhananjaysawant]

1:14 for a second I thought that was the math problem

[chiragmidha]

I am glad that the Jee exam is recognized as one of the touhgest exams in the world. I gave the test in 2017 and because of that I am still able to follow these math videos, even though I haven't studied math in a while now. Also regarding the percentage of people who got the correct answer. Population of India is huge so a big majority of test takers don't really prepare to that level, however to even give the Jee advance test, you have to get more than certain rank in Jee Mains (an easier version test, (you only have 2 minutes per question in this exam but the questions are easier)). The point that I am trying to make is people who even attempt the Jee advance test have already gotten really scores in the main test.

[olerask]

I guessed 1523.
I read the sample space as rolling a dice, and the independent events as rolling TWO dice. I then had to calculate the sum of all products of binomial coefficients (6, a)*(6, b) under the condition 1<=b<a.
Without the condition the product sum is (2^6)^2=4096.
The cases a=b, sums to the binomial koefficient (2*6, 6)=12!/(6!6!)=924.
To meet the condition b<a, I simply divides the difference by 2, and gets (4096-924)/2=1586.
To secure 1<=b, I must also subtract the cases with b=0, which are 2^6=64, giving 1586-64=1522. But I have already subtracted the case where both a and b equals zero (both are the empty set), and thus add 1, to get my final answer 1523.

[Gyan-fxzx]

Thanks for making this video on my suggestion.

[aayushprasad]

Our Jee advanced 2024 exam after 7 days. Wishing all the best to all jee adv 2024 aspirant !

[muthiah]

I am an Indian student and preparing for this one . Wish good luck for me.