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 Number Theory problem from PRMO, 2019, problem-18, based on Ordered Pairs. You may use sequential hints to solve the problem.
Try this beautiful Geometry problem from PRMO, 2019, problem-23, based on finding the maximum area. You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry based on Rectangle Pattern from AMC-10A, 2016, Problem 10. You may use sequential hints to solve the problem.
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 based on calculation of area from AMC 8 2020 Problem 3. You may use sequential hints to solve it.
Try this beautiful Problem based on Number theory from AMC 10A, 2002 Problem 15. You may use sequential hints to solve it.
Try this Problem based on simple Arithmetic appeared in Math Kangaroo (Kadett) 2021 Problem 17. You may use sequential hints to solve it.
Try this beautiful Problem based on Divisibility Problem from AMC 2020 Problem 6. You may use sequential hints to solve it.
Try this Problem based on Divisibility Rules appeared in Math Kangaroo (Ecolier) 2021 Problem 21. You may use sequential hints to solve it.
Try this problem on freely falling body and 1D motion from NSEP 2015 Problem 4. You may use sequential hints to solve it.
Try this beautiful Subjective Matrix Problem appeared in ISI Entrance - 2018. You may use sequential hints to solve it.
Try this beautiful Subjective Sequence Problem appeared in ISI Entrance - 2015 problem 8. You may use sequential hints to solve it.
Try this beautiful Subjective Calculus Problem appeared in ISI Entrance 2019 Problem 2. You may use sequential hints to solve it.
Try this beautiful Problem based on Algebra appeared in Math Kangaroo (Benjamin) 2014 Problem 24. You may use sequential hints to solve it.