Problem Suppose (a, b) are positive real numbers such that (a \sqrt{a}+b \sqrt{b}=183 . a \sqrt{b}+b \sqrt{a}=182). Find (\frac{9}{5}(a+b)). Hint 1 This problem will use the following elementary algebraic identity: $(x+y)^3=x^3+y^3+3 x^2 y+3 x y^2$ Can you identify what is x and what is y? Hint 2 background_video_pause_outside_viewport="on" tab_text_shadow_style="none" body_text_shadow_style="none"] Set $x=\sqrt{a}, y=\sqrt{b}$. Then the […]
In this post we have discussed AMC 10A 2018 problem number 13.
Tools in Geometry is very useful for pre regional mathematical olympiad, regional mathematical olympiad as well as I.S.I. & C.M.I entrance.
Cheenta is introducing open seminar for students interested in Advanced Mathematics and preparing for Pre-RMO and ISI Entrance Students. Know more..
The fifth problem from I.S.I. B.Stat and B.Math Entrance 2018, has a clever application of this mean value theorem. Watch the video and learn.
I.S.I 2018 Problem 2 Discussion is done based on the idea of ratio of areas of similar triangles is equal to ratio of squares on their corresponding sides.
Find all pairs ( (x,y) ) with (x,y) real, satisfying the equations $$\sin\bigg(\frac{x+y}{2}\bigg)=0~,~\vert x\vert+\vert y\vert=1$$ Discussion: Back to Problems
Here, you will find all the questions of ISI Entrance Paper 2018 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Find all pairs $(x,y)$ with $x,y$ real, satisfying the equations: $\sin(\frac{x+y}{2})=0,\vert x\vert+\vert y\vert=1$ Problem 2: Suppose that $PQ$ and $RS$ are two […]
Injection Principle is an very elegant idea to count objects. This idea is useful for olympiad students as well as for the I.S.I & C.M.I. students.
This post is about the concept of Orthocenter (the intersection point of altitudes) and equal circles. Watch the videos and learn.
Try this beautiful problem from Geometry: Ratio of area of Circles from AMC-10A, 2009, Problem 21. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1988, Question 11, based on Complex plane.
Try this beautiful problem from algebra, based on Quadratic equation from AMC-10A, 2005. You may use sequential hints to solve the problem.
Try this beautiful problem based on Probability in game from AMC-10A, 2005. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2019 based on Covex Cyclic Quadrilateral. You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry: Area of the inner square AMC-10A, 2005, Problem-8. You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry: Ratios of the areas of Triangle and Quadrilateral from AMC-10A. You may use sequential hints to solve the problem.
Try this beautiful problem from PRMO, 2019, problem-19, based on the Ratio of the areas. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on real numbers. Use sequential hints if required.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Digits and Integers.
Try this beautiful Objective Sequence Problem appeared in ISI Entrance 2018 Problem 8. You may use sequential hints to solve it.
This collection of problems and solutions from CMI Entrance 2022 is a work in progress. If you remember the problems, let us know in the comment section. Part A (indicate if each statement is true or false) Problem A1 Let $a_0 , a_1, a_2…..$ be an arithmetic progression such that $a_0$ and $a_1$ are positive […]
Try this beautiful problem based on cube from AMC 8, 2020 Problem 9. You may use sequential hints to solve it.
Try this beautiful Objective Limit Problem appeared in ISI Entrance - 2021. You may use sequential hints to solve it.
Try this problem on circular Motion and angular momentum from NSEP 2015. You may use sequential hints to solve it.
On 28th May 2022, Dr. Ashani Dasgupta is going to guide the students about the Opportunities in College for Mathematics in India and abroad.
On 28th May 2022, Dr. Ashani Dasgupta is going to guide the students to prepare for ISI-CMI Entrances 2023 on the basis of his teaching experience since 2010.
Try this beautiful Problem based on Enumeration from AMC 10A 2021, Problem 20. You may use sequential hints to solve it.
Try this beautiful Problem based on simple Arithmetic appeared in Math Kangaroo (Benjamin) - 2021 Problem 22. You may use sequential hints to solve it.
Try this beautiful 2D Motion Problem based on Projectile Motion from NSEP 2019, Problem 26. You may use sequential hints to solve it.