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Some General Questions

  1. The first term of a sequence is 2014. Each succeeding term is the sum of the cubes of the digits of the previous term. What is the 2014th term of the sequence?

  2. In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 17. What is the greatest possible perimeter of the triangle?

  3. If real numbers a, b, c, d, e satisfy a + 1 = b + 2 = c + 3 = d + 4 = e + 5 = a + b + c + d + e + 3, what is the value of a^2 + b^2 + c^2 + d^2 + e^2

  4. Let ABCD be a convex quadrilateral with perpendicular diagonals. If AB = 20, BC = 70 and CD = 90, then what is the value of DA?

  5. A natural number k is such that k^2 < 2014 < (k + 1)^2. What is the largest prime factor of k?

  6. Let S be a set of real numbers with mean M. If the means of the sets S∪{15} and S∪{15, 1} are M + 2 and M + 1, respectively, then how many elements does S have?

  7. What is the smallest possible natural number n for which the equation x^2 − nx + 2014 = 0 has integer roots?

  8. In a triangle ABC, X and Y are points on the segments AB and AC, respectively, such that AX : XB = 1 : 2 and AY : Y C = 2 : 1. If the area of triangle AXY is 10 then what is the area of triangle ABC?

  9. Let XOY be a triangle with angleXOY = 90◦ . Let M and N be the midpoints of legs OX and OY , respectively. Suppose that XN = 19 and Y M = 22. What is XY ?

Note by Vishruth Khare
2 years, 4 months ago

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All of these are from the Pre - RMO in Mumbai region, right? Siddhartha Srivastava · 2 years, 4 months ago

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@Siddhartha Srivastava Yes !! Vishruth Khare · 2 years, 4 months ago

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If u have some more question of pre emo send to muramallaswaroop@gmail.com. ..... k? Swaroop M. · 2 years, 4 months ago

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@Swaroop M. sure ... actually I too am hunting for these papers !! :) Vishruth Khare · 2 years, 4 months ago

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@Vishruth Khare This Set has all of the Pre - RMO questions of 2014. You can also find them on the HBCSE's site I think. Siddhartha Srivastava · 2 years, 4 months ago

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@Siddhartha Srivastava thanks ... If you have any more sets or papers of this kind then kindly send me the links or stuff... also HBCSE site copied ... thanks again ..!!! Vishruth Khare · 2 years, 4 months ago

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@Vishruth Khare waiting fr ur email dude....... Swaroop M. · 2 years, 4 months ago

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@Swaroop M. I said I have this pre rmo paper only ...you can check the websites suggested by Siddhartha Srivastava ..... kindly have a look. PS: I've got few more papers regarding class 10 and 11 course ..but i'll mail them to you after my exams are over .. so plz wait till 24th .. Vishruth Khare · 2 years, 4 months ago

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@Vishruth Khare I wanted the papers so am asking since you have fr 10 th and 11 th pls do mail them earliest....pls Swaroop M. · 2 years, 4 months ago

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