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RMO 2015 UP region

Open discussion for UP RMO 2015.. Please solve the following questions

Note by Rishik Jain
9 months, 3 weeks ago

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the same paper came for south bihar as well. ( i am in 10th) i solved q.1,2,3 and 6 correctly. in 3 i took all the cases but just missed to mention 2 of the 8 solutions. and for the combi question(q.5) i wrote 32c3 - 16*30 - (something i don't remember) + 64 = some big number as result of a calculation mistake. what can be my marks. Akash Deep · 9 months, 3 weeks ago

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@Akash Deep Aakash did you gave the tallentex exam 2015 from B D public school ? I think we both were sitting together . Wasif Jawad Hussain · 9 months, 3 weeks ago

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@Wasif Jawad Hussain yes i gave it, i recall u r also a fitjeean Akash Deep · 9 months, 3 weeks ago

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@Akash Deep Yes you are right Wasif Jawad Hussain · 9 months, 3 weeks ago

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@Akash Deep In the combi question I too missed the answer by 32. I subtracted 16x28 instead of 16x26.... Ankit Kumar Jain · 9 months, 3 weeks ago

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How many of your answers were correct Prakher Gaushal · 9 months, 3 weeks ago

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@Prakher Gaushal I attempted 5 and in which 2 are perfectly correct and 2 with little mistakes and the other one I am expecting it to be correct. Easha Manideep D · 9 months, 3 weeks ago

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@Prakher Gaushal I attempted 3.5, and am expecting 42-46. Swapnil Das · 9 months, 3 weeks ago

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@Swapnil Das Same here . Raven Herd · 9 months, 3 weeks ago

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Even my state Jharkhand had the same paper... Ankit Kumar Jain · 9 months, 3 weeks ago

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@Ankit Kumar Jain no it didn't have the same one Gyanendra Prakash · 1 month ago

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@Ankit Kumar Jain Rajasthan also had the same . Raven Herd · 9 months, 3 weeks ago

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Answer to question no.4

Initially count the number of ways you can select 3 objects from 32. - 32C3

Then subtract the ways in which diametrically opposite pairs exist none of them are adjacent - 16.26

Then subtract the ways in which adjacent pairs exist none of which are diametrically opposite. - 32.28

Then also subtract which are both diametrically opp and adjacent - 16.4

Hence totally 32.31.5 - 16.26 - 32.28 - 16.4 Easha Manideep D · 9 months, 3 weeks ago

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Well I am in class 11 Prakher Gaushal · 9 months, 3 weeks ago

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Approximately 55 Prakher Gaushal · 9 months, 3 weeks ago

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@Prakher Gaushal It is said to be 34 here in class 9. Swapnil Das · 9 months, 3 weeks ago

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@Prakher Gaushal Huh..Strange. Does it vary with region and class of the candidate? Swapnil Das · 9 months, 3 weeks ago

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What do you think will be the cutoff? Swapnil Das · 9 months, 3 weeks ago

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What was the answer of Q.4? Prakher Gaushal · 9 months, 3 weeks ago

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Hi,I am also from U.P(Varanasi). I did 2 questions correct but missed one case in ques.3 ,got only 1 answer in ques.6(there are 5) and doubtful about ques.4 How much did you solve:) Siddharth Singh · 9 months, 3 weeks ago

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Even Rajasthan RMO had same paper. Akshat Sharda · 9 months, 3 weeks ago

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@Akshat Sharda chhattisgarh also had the same paper Vaibhav Prasad · 9 months, 3 weeks ago

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Answer to question 6. Let \[a=m+\frac{b}{c}\] where \(m\) is any integer and \[0<b<c\] . Then \[a(a-3{a})=( m+\frac{b}{c})( m-2\frac{b}{c}) \] \[m^{2}-\frac{bm}{c}+\frac{2b^{2}}{c^{2}}\]. \[m^{2}-\frac{2b^{2}-bcm}{c^{2}}\] Now, \(m\) is an integer . Let's consider \[ \frac{2b^{2}-bcm}{c^{2}}=k\] where \(k\) is an integer . After solving we get \[\frac{b}{c}=\frac{m+_{-}\sqrt{m^{2}+8k}}{4}\].....(I) But \[\frac{b}{c}<1\]....(II) Now putting value of \(\frac{b}{c}\) from (I) to (II). We get \[m+k<2\] Therefore there are infinitely many integers \(m,k\) such that \[m+k<2\]. Hence proved. Shivam Jadhav · 9 months, 3 weeks ago

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@Shivam Jadhav Don't you think \(m\) must be equal to \(4\). Akshat Sharda · 9 months, 3 weeks ago

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@Shivam Jadhav m should equal 4 Rishik Jain · 9 months, 3 weeks ago

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@Rishik Jain Hey when will cutoff be declared? Swapnil Das · 9 months, 3 weeks ago

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