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RMO-2015 Karnataka region


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Note by Svatejas Shivakumar
1 year, 6 months ago

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Answer to question 3.\[a^{2}-b^{2}=c(b-a)\] This implies \[a+b+c=0 ...or... a=b\] Case 1\[a+b+c=0\] Solutions are \[(a,b,c)=(2,0,-2),(-2,0,2),(0,2,-2),(0,-2,2),(2,2,0),(2,-2,0),(-2,2,0),(-2,-2,0).\] Case 2\[a=b \] Therefore \[(a,b,c)=(2,2,0),(-2,-2,0).\]. Shivam Jadhav · 1 year, 6 months ago

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@Shivam Jadhav There is also two more solutions when a=b, (1,1,-3) and (-1,-1,3) Svatejas Shivakumar · 1 year, 6 months ago

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@Shivam Jadhav Two more solutions! (4,4,3) and (-4,-4,-3) Ranjana Kasangeri · 1 year, 6 months ago

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@naitik sanghavi @Ranjana Kasangeri @Ganesh Ayyappan @Kush Singhal @easha manideep d Official answer key has been declared click here. Svatejas Shivakumar · 1 year, 6 months ago

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@Svatejas Shivakumar Thanks !!! Naitik Sanghavi · 1 year, 6 months ago

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@Svatejas Shivakumar Thanks but can you please search key for RMO telangana region. I am too busy ok. THANKS!!! Easha Manideep D · 1 year, 6 months ago

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@Svatejas Shivakumar thanks Ganesh Ayyappan · 1 year, 6 months ago

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@Svatejas Shivakumar Thanx :D Kush Singhal · 1 year, 6 months ago

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@Kush Singhal How many did you solve? Do you have any idea what is the cut-off and when the results will be declared? Svatejas Shivakumar · 1 year, 6 months ago

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@Svatejas Shivakumar I think I got none :/ Kush Singhal · 1 year, 6 months ago

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Check Answer key by Resonance !! Naitik Sanghavi · 1 year, 6 months ago

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@Naitik Sanghavi Can you send the link please? Svatejas Shivakumar · 1 year, 6 months ago

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@Svatejas Shivakumar pccp.resonance.ac.in Naitik Sanghavi · 1 year, 6 months ago

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In 6th one the difference between two consecutive squares must be greater than 125. Then you can find step of sqrt m becomes step of sqrt of m + 125 which the smaller square in which m, m+125 lies. I gave a hint.

ENJOY!!!! Easha Manideep D · 1 year, 6 months ago

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@Easha Manideep D hi ... i had the same idea .. and proceeded in the same direction for Q6 ... i got 72 such integers ... is my answer right??

aand cud sum1 post a link where i can get full detailed solution for this paper .... Ganesh Ayyappan · 1 year, 6 months ago

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Oh by the way results came out. Go to isi Bangalore website and check out Kush Singhal · 1 year, 6 months ago

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For 3rd break into cases like @Shivam Jadhav did. But he forgot some cases, the two cases gets 8 and 6 subcases more for a+b+c=0 and a=b respectively . Saarthak Marathe · 1 year, 6 months ago

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How many questions do u need to get right to get qualify? Tarush Govil · 1 year, 6 months ago

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Answer to 4th one is 40C3 - 20.34 - 40.36 Easha Manideep D · 1 year, 6 months ago

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In Q 6, according to me, total no. of values of m are 8. 63^2 to 70^2. Verified. In Q3, even i have written permutations of (2,-2,0), total 6. But it's wrong. Someone pls do Q1 and 5. I wasted a lot of time on 1, have done something but couldn't conclude my answer. Pls do those 2 questions. Anoushka Gupta · 1 year, 6 months ago

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Comment deleted Dec 11, 2015

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@Svatejas Shivakumar My solution for 4th!(Tell mewhat is wrong in my solution)-(I'm writing in short) There are 40 ways to select 1st object! There are 36 ways to select 2nd! And ,32 ways to select the 3rd! In total there are 40×36×32=46080 ways!! Naitik Sanghavi · 1 year, 6 months ago

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@Naitik Sanghavi There is a mistake. If the second object is two places away from the first object, you count the restricted object twice. Sorry. Good luck for getting selected. Svatejas Shivakumar · 1 year, 6 months ago

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@Svatejas Shivakumar So this case can be taken separately!and then we can solve ?? Naitik Sanghavi · 1 year, 6 months ago

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@Naitik Sanghavi Also I don't think you can multiply 40 and 36 and so on because there will be several cases in which you choose the Same object. I just realized that repetitions are not allowed as they are placed around a circle. Hard luck. Svatejas Shivakumar · 1 year, 6 months ago

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@Svatejas Shivakumar Yes, even I realized just after writing this comment, hard luck. Anoushka Gupta · 1 year, 6 months ago

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When will the results be out? Shashank Rammoorthy · 1 year, 6 months ago

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The 6th question's answer is 73 I think... Kush Singhal · 1 year, 6 months ago

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@Kush Singhal Well, may be its 72! Please add the list of numbers if you can! Ranjana Kasangeri · 1 year, 6 months ago

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@Ranjana Kasangeri I got it wrong :( It's 72... Kush Singhal · 1 year, 6 months ago

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@Kush Singhal How? Shashank Rammoorthy · 1 year, 6 months ago

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@Shashank Rammoorthy Count the number of integers greater than a square above \(63^2\) and which is strictly lesser than the next square by 125... Kush Singhal · 1 year, 6 months ago

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Please tell your answers to 3,4,6 questions!! Naitik Sanghavi · 1 year, 6 months ago

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Comment deleted Dec 11, 2015

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@Svatejas Shivakumar But 40 c 3 =9880 Adarsh Kumar · 1 year, 6 months ago

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@Adarsh Kumar In 4th ,my answer is 46080 Naitik Sanghavi · 1 year, 6 months ago

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Comment deleted Dec 07, 2015

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@Svatejas Shivakumar But your number is too large.Just look at your number once. Adarsh Kumar · 1 year, 6 months ago

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Comment deleted Jan 13, 2016

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@Svatejas Shivakumar I solved 3 perfectly but have a doubt in the combi one,if that is correct then 4. Adarsh Kumar · 1 year, 6 months ago

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@Adarsh Kumar Did you also have the same paper? Svatejas Shivakumar · 1 year, 6 months ago

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@Adarsh Kumar You solved 3 perfectly ,you will surely appear for INMO!0 Naitik Sanghavi · 1 year, 6 months ago

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@Svatejas Shivakumar How many did you solved? Harsh Shrivastava · 1 year, 6 months ago

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@Harsh Shrivastava Completely left question no.1 and did question no.5 with less than 5 minutes left :( Svatejas Shivakumar · 1 year, 6 months ago

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@Harsh Shrivastava solved 3 not sure about question no.4 Svatejas Shivakumar · 1 year, 6 months ago

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@Svatejas Shivakumar Which 3? Harsh Shrivastava · 1 year, 6 months ago

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@Harsh Shrivastava What do you think would be the cutoff for this paper? Svatejas Shivakumar · 1 year, 6 months ago

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@Svatejas Shivakumar I think minimum would be 34-40,and maximum 45-51! Naitik Sanghavi · 1 year, 6 months ago

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@Naitik Sanghavi So is 34 like 2 questions fully right? Shashank Rammoorthy · 1 year, 6 months ago

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@Shashank Rammoorthy yes Svatejas Shivakumar · 1 year, 6 months ago

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@Naitik Sanghavi How many did you solve? Svatejas Shivakumar · 1 year, 6 months ago

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@Svatejas Shivakumar In 3,i left one case where a=b! Naitik Sanghavi · 1 year, 6 months ago

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@Svatejas Shivakumar I solved 3,4,6 3rd is right!(One case left) 6th is half (or less than that)Wrong! 4th don't know Naitik Sanghavi · 1 year, 6 months ago

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@Naitik Sanghavi You too had the same paper! Svatejas Shivakumar · 1 year, 6 months ago

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@Svatejas Shivakumar Each region had very similar paper!! Naitik Sanghavi · 1 year, 6 months ago

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@Svatejas Shivakumar Yes but I'm from Gujarat Naitik Sanghavi · 1 year, 6 months ago

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@Harsh Shrivastava How about you? Svatejas Shivakumar · 1 year, 6 months ago

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@Harsh Shrivastava 2,3,6 Svatejas Shivakumar · 1 year, 6 months ago

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