# INMO 2019 Discussion

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.

Note by Maalav Mehta
3 weeks, 4 days ago

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1st 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

- 3 weeks, 4 days ago

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

- 3 weeks, 3 days ago

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

- 3 weeks, 3 days ago

Well, you can start off with some problem solving on AOPS..........BUT, if u want to learn new stuff, the wikis on Brilliant are REALLY good ones...........

- 3 weeks, 3 days ago

Also, if u hate doing it, then focus on something which you like doing and prepare that.......:)

- 3 weeks, 3 days ago

Which state are you from?

- 3 weeks, 3 days ago

I am from Noida..........(UP region).....You???

- 3 weeks, 3 days ago

Gujarat

- 3 weeks, 3 days ago

When is your INMOTC and which teachers are coming?

- 3 weeks, 3 days ago

WHOAH!!!! You have an INMOTC???!!! That is great dude.........yahan pe to aisa kuch inform nhi kara hai!! lol............

- 3 weeks, 3 days ago

You may ask your coordinator to arrange some camp or you may enquire in neighbouring states if they allow outside students

- 3 weeks, 2 days ago

All the best for tomorrow

- 2 days, 6 hours ago

Thanks!!!! Same to you!!

- 2 days, 6 hours ago

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

- 2 weeks, 5 days ago

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

- 2 days, 6 hours ago

Same to you!!!!

- 2 days, 6 hours ago

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

- 1 day, 11 hours ago

None

- 1 day, 9 hours ago

Really?

- 1 day, 9 hours ago

Yes

- 1 day, 9 hours ago

What do you expect from a class 9 student?

- 1 day, 9 hours ago

How was the inmo?

- 1 day, 8 hours ago

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?

- 1 day, 8 hours ago

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.

- 1 day, 7 hours ago

How did you solve it?

- 1 day, 7 hours ago

No exotic methods just little brainstorming , some examples, inducing them ,predicting the power rule and then proved.😃

- 1 day, 6 hours ago

Bro, the last question is incorrect and in the solution of Allen faculties, they have found a counter example

- 13 hours ago

Yes me too saw today my answer is as not Allen's solution buy I used the continuity of the function too. So seems wrong now.

- 7 hours ago

The power rule assumed by me was wrong as I thought only about rational numbers didn't seek for irrational ones.

- 7 hours ago

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

- 1 day, 8 hours ago

Yes, the cutoff will be around 35-40

- 1 day, 8 hours ago

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?

- 12 hours ago

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........!!!!

- 11 hours ago

Can you provide a hint for P1?

- 11 hours ago

Well, Allen has already posted their solutions, but my method was using a lot of trigonometry...........You know, Sine rule and Cosine rule........and that took me too long.....

- 11 hours ago

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

- 11 hours ago

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

- 11 hours ago

Ohhh I am in class 11th.......Uttar Pradesh........

- 11 hours ago

So, you are giving JEE???

- 11 hours ago

Yep

- 11 hours ago

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

- 8 hours ago

Check it on aops

- 8 hours ago

What do u think? HBCSE will delete the qn?

- 8 hours ago

Probably, but that is not correct as many would have spent hours on the question without knowing that it is incorrect

- 7 hours ago

What could be the cut off? I guess, it should be around 40-45.

- 7 hours ago

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?

- 7 hours ago

If it is mathematically correct, you get full

- 7 hours ago

@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?

- 7 hours ago

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

- 7 hours ago

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

- 7 hours ago

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

- 1 day, 8 hours ago

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

- 1 day, 8 hours ago

Hey what can be expected cutoff this year??

- 1 day, 10 hours ago

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

- 1 day, 9 hours ago

This time I guess cutoff will be around 40

- 1 day, 8 hours ago

What about cut off for merit certificate?

- 8 hours ago