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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, 10 months ago

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## Comments

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All of these are from the Pre - RMO in Mumbai region, right?

- 2 years, 10 months ago

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Yes !!

- 2 years, 10 months ago

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If u have some more question of pre emo send to muramallaswaroop@gmail.com. ..... k?

- 2 years, 10 months ago

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sure ... actually I too am hunting for these papers !! :)

- 2 years, 10 months ago

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This Set has all of the Pre - RMO questions of 2014. You can also find them on the HBCSE's site I think.

- 2 years, 10 months ago

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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 ..!!!

- 2 years, 10 months ago

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waiting fr ur email dude.......

- 2 years, 10 months ago

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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 ..

- 2 years, 10 months ago

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I wanted the papers so am asking since you have fr 10 th and 11 th pls do mail them earliest....pls

- 2 years, 10 months ago

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