A square sheet of paper ABCD is so folded that B falls on the mid-point of M of CD. Prove that the crease will divide BC in the ratio 5:3. Discussion: Assuming the side of the square is 's'. Let a part of the crease be 'x' (hence the remaining part is 's-x'). We apply […]
This post contains problems from Indian National Mathematics Olympiad, INMO 2012. Try them and share your solution in the comments. Problem 1 Let ABCD be a quadrilateral inscribed in a circle. Suppose AB =$latex \sqrt {2 + \sqrt {2} } $ and AB subtends 1350 at the center of the circle. Find the maximum possible […]
This post contains problem from Indian National Mathematics Olympiad, INMO 2011. Try them out and share your solution in the comments. Let D, E, F be points on the sides BC, CA, AB respectively of a triangle ABC such that BD = CE = AF and ∠BDF = ∠CED = ∠AFE. Prove that ABC […]
This a problem from from National Board for Higher Mathematics (NBHM) 2013 based on Cyclic Group Problem for M.Sc Students. Which of the following statements are true? Every group of order 11 is cyclic. Every group of order 111 is cyclic. Every group of order 1111 is cyclic. Discussion: Every group of order 11 is […]
Find all triples $latex (p, x, y) $ such that $latex p^x = y^4 + 4 $, where $latex p $ is a prime and $latex x, y $ are natural numbers. Hint 1: p cannot be 2. For if p is 2 then $latex p^x $ is even which implies $latex y^4 + 4 […]
This post contains Indian National Mathematical Olympiad, INMO 2010 questions. Try to solve these problems and share it in the comments. Let ABC be a triangle with circum-circle $ \Gamma $.Let M be a point in the interior of the triangle ABC which is also on the bisector of $ \angle A $. Let AM, […]
This post contains the problems from Indian National Mathematics Olympiad, INMO 2009 Question Paper. Do try to find their solutions. Indian National Mathematics Olympiad (INMO) 2009 Question Paper: Let ABC be a triangle and P be a interior point such that $ \angle BPC $=$ 90^0 $, $ \angle BAP $ = $ \angle BCP […]
Let $ABC$ be a triangle, $I$ its in-centre; $ A_1, B_1, C_1 $ be the reflections of $I$ in BC, CA, AB respectively. Suppose the circumcircle of triangle $ A_1 B_1 C_1 $ passes through A. Prove that $ B_1, C_1, I, I_1 $ are concyclic, where $ I_1 $ is the incentre of triangle […]
This post contains the problems from Indian National Mathematics Olympiad, INMO 2008 Question Paper. Do try to find their solutions. Let $ABC$ be a triangle, $I$ its in-centre; $ A_1, B_1, C_1 $ be the reflections of $I$ in BC, CA, AB respectively. Suppose the circum-circle of triangle $ A_1 B_1 C_1 $ passes through […]
Try this beautiful problem from Geometry: Area of Trapezoid from AMC-10A, 2002. You may use sequential hints to solve the problem.
Try this beautiful problem from AMC-10A, 2004 based on ratio of two triangles.You may use sequential hints to solve the problem.
Try this beautiful problem from Algebra on Quadratic equation from AMC-10A, 2002. You may use sequential hints to solve the problem.
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Arbitrary Arrangement. You may use sequential hints.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Remainders and Functions.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Rational Numbers.
This problem is a simple application of the sequential definition of continuity from ISI MStat 2015 PSB Problem 1.
This is a problem from ISI MStat Examination,2019. This tests one's familiarity with the simple and multiple linear regression model and estimation of model parameters and is based on the Invariant Regression Coefficient.
This is a problem from the ISI MStat Entrance Examination, 2019. This primarily tests one's familiarity with size, power of a test and whether he/she is able to condition an event properly.
Try this beautiful problem from the Pre-RMO, 2017 based on ratio and proportion. You may use sequential hints to solve the problem.