This is the place where we may discuss various problems and get updates of INMO 19. I expect the students of different states to post some problems discussed in their INMOTC. I will regularly upload some problems and even practice tests for INMO and expect you to do so too. Hope we all do perform well in INMO and many of us may even get selected for INMO

IN MY NEXT POST, I WILL SEND A MOCK TEST A BIT EASIER THAN INMO, AS IT IS JUST THE BEGINNING.
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TopNewest1st Indian National Mathematical Olympiad MOCK 2019 Time: 4 hours Instructions: • Calculators (in any form) and protractors are not allowed. • Rulers and compasses are allowed. • All questions carry equal marks. Maximum marks: 102.

1.A circle passes through the vertex C of a rectangle ABCD and touches its sides AB and AD at M and N respectively If the distance from C to the line segment MN is 5 units, find the area of ABCD.

2.Consider the set {3,5,7,9}. You can choose any 2 numbers a,b and replace them by (4a+3b)/5 and (3a-4b)/5. Prove that you can never get the set {2,3,4,9}.

3.A 3*3 square is said to be a mystic square if i)Its entries are from 1 to 13(both inclusive, repetition allowed) ii)The sum of any row, column or diagonal is always divisible by 13. Find the number of MYSTIC SQUARES.

4.In a triangle ABC, AB=AC and angle A is 20 degrees.D is chosen on AC such that AD=BC.Without using trigonometry, find angle ABD.

5.Let P(x) be a cubic polynomial function with positive coefficients..Prove, if -1≤P(x)≤1 for all x such that -1≤x≤1, prove that sum of coefficients of P(x) is at most 7.

6.Find all functions f:R to R which obey

f((x-y)²)=f(x)²-2xf(y)+f(y)²

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Thanks for the mock test!!! What are you focusing on preparing??? Geometry??

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I want to improve at geometry, but I hate doing it.

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Which state are you from?

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Find all functions f:R→R satisfying the equation f(f(x)) + f(x) = 6x

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ALL THE BEST FOR TOMORROW GUYS AND GIRLS!!!!!!!!!!!

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Same to you!!!!

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How did it go????? How many could you solve????

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None

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How was the inmo?

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Tougher than ever, the fifth question used something called inversion(according to some AOPSers), which has not ever been asked in INMO. Could you solve P6?

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Yeah problem no 6 looked easy but solving it took me complete hour and mind bending brainstorming and I skipped two or three lemmas and messed everything but solved it. Seems they would care to give 2 or 3 marks.

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Do you think that the cut off may be lower this time since as per my experience this year, the paper was relatively tougher

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Yes, the cutoff will be around 35-40

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Hey everyone. I appeared for INMO 2019 and solved P2 and P3. In P6, I managed to provide a "pseudo-proof" that f(x,y) =1. What are my chances of selection? Also, I couldn't solve P1 but I heard many saying that it was the easiest problem. Is this really the case?

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Hey dude........same case over here...........I mean even I have done the EXACT same things except P6, in which I was only able to prove the first part..........Oh well.......Chances are slim...........And Yes, P1 was the easiest......IDK why it did not strike me during the exam........!!!!

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Can you provide a hint for P1?

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Btw, which class are you in?? And from which state??

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I am in 12th class from Rajasthan state. What about you?

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Did you hear that P6 was wrong? What would be impact. Will it be deleted or there could be a reexam??

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Check it on aops

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For p2 I did not use php but some approach that is explicitly not php but just the same thing as that. How much do I expect?

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If it is mathematically correct, you get full

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@Suchir Kaustav @Maalav Mehta Is this the first time this has happened that a question in inmo came wrong? If this did happen before then what was done? Any idea?

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I remember it happened in 1999 and 2011. But no idea what was done

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Reexam is a huge logistical challenge on the part of HBCSE. I think they should increase the number of selections.

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If the ans is wrong and the approach is correct or vice versa how much can one expect??

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If the approach is more than 70 percent correct, you may expect 12 marks. If the answer is correct but obtained by doing some nonsensical stuff, then you may get 2 or 3 marks

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Hey what can be expected cutoff this year??

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RMO coordinator of Gujarat told that according to trend, you are required to solve 3-4 questions

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This time I guess cutoff will be around 40

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What about cut off for merit certificate?

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