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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. · 9 months, 3 weeks ago

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

yes i gave it, i recall u r also a fitjeean · 9 months, 3 weeks ago

Yes you are right · 9 months, 3 weeks ago

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

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

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. · 9 months, 3 weeks ago

I attempted 3.5, and am expecting 42-46. · 9 months, 3 weeks ago

Same here . · 9 months, 3 weeks ago

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

no it didn't have the same one · 1 month ago

Rajasthan also had the same . · 9 months, 3 weeks ago

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 · 9 months, 3 weeks ago

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

Approximately 55 · 9 months, 3 weeks ago

It is said to be 34 here in class 9. · 9 months, 3 weeks ago

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

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

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

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:) · 9 months, 3 weeks ago

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

chhattisgarh also had the same paper · 9 months, 3 weeks ago

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. · 9 months, 3 weeks ago

Don't you think $$m$$ must be equal to $$4$$. · 9 months, 3 weeks ago

m should equal 4 · 9 months, 3 weeks ago