Let ABC be an acute angled scalene triangle with circumcenter O orthocenter H. If M is the midpoint of BC, then show that AO and HM intersect at the circumcircle of ABC. Let n be a positive integer such that 2n + 1 and 3n + 1 are both perfect squares. Show that 5n + […]
1. Let ABC be a triangle. Let D, E, F be points on the segments BC, CA and AB such that AD, BE and CA concur at K. Suppose $latex (\frac{BD}{DC} = \frac{BF}{FA})$ and ∠ADB = ∠AFC. Prove that ∠ABE = ∠CAD. Solution: Diagram Given: ABC be any triangle. AD, BE and CF are drawn […]
ABCD is a quadrilateral and P, and Q are mid-points of CD, and AB respectively. Let AP, DQ meet at X, and BP, CQ meet at Y . Prove that area of ADX + area of BCY = area of quadrilateral PXQY The number of ways in which three non-negative integers \( n_1, n_2, n_3 […]
Try this beautiful problem from AMC-10A, 2004 based on Triangle. You may use sequential hints to solve the problem.
This problem is an easy application in calculus using the basic ideas of curve sketching. This is the problem 1 from ISI MStat 2019 PSB.
This is a problem from ISI MStat Examination,2018.
It involves construction of a most powerful test of size alpha using Neyman Pearson Lemma. The aim is to find its critical region in terms of quantiles of a standard distribution.
This problem is a cute application of joint distribution and conditional probability. This is the problem 5 from ISI MStat 2018 PSB.
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Binomial Expression. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Right angled triangle.
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Perfect square and Positive Integer. You may use sequential hints.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Complex roots and equations.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Length and Inequalities.
Try this beautiful problem from the Pre-RMO, 2017 based on Trigonometry & natural numbers. You may use sequential hints to solve the problem.