Here's the RMO 2015 question paper of west bengal region, which was held on 6th december, in I.S.I. Kolkata.
circles and with centers and respectively, are such that lies on Let be a point on and let be the midpoint of Let be another point on such that Then prove that the midpoint of lies on SOLUTION: Here
Let be a quadratic polynomial where are real numbers. Suppose be an of positive integers. Prove that are integers. SOLUTION:Here
Show that there are infinitely many triples of positive integers, such that SOLUTION:Here
Suppose objects are placed along a circle at equal distances. In how many ways can objects be chosen from among them so that no two of the three chosen objects are adjacent nor diametrically opposite. SOLUTION:Here
Let be a triangle with circumcircle and incenter Let the internal angle bisectors of meet in respectively. Let intersect at and in Let intersect in Suppose the quadrilateral is a kite; that is, and Prove that is an equilateral triangle. SOLUTION:Here
Show that there are infinitely many positive real numbers, which are not integers, such that is an integer. (Here, is the fractional part of For example ) SOLUTION:Here