This post contains problem from Chennai Mathematics Institute, CMI BSc Math Entrance 2014 Model Problem set. In each problem you have to fill in 4 blanks as directed. Points will be given based only on the filled answer, so you need not explain your answer. Each correct answer gets 1 point and having all 4 […]
This is a problem from ISI BMath 2014 Subjective Solution based on Mulitple roots or Real root. Try to solve this problem. Problem: Multiple roots or real root Let $latex \mathbf { y = x^4 + ax^3 + bx^2 + cx +d , a,b,c,d,e \in \mathbb{R}}$. it is given that the functions cuts the x […]
Let PQR be a triangle. Take a point A on or inside the triangle. Let f(x, y) = ax + by + c. Show that $latex \mathbf { f(A) \le \max { f(P), f(Q) , f(R)} }$ Discussion: Basic idea is this: First we take A on a side, say PQ. We show $latex \mathbf […]
Prove that sum of any 12 consecutive integers cannot be perfect square. Give an example where sum of 11 consecutive integers is a perfect square Discussion: Suppose a, a+1, a+2 , ... , a+ 11 are 12 consecutive integers. Sum of these 12 integers are 6(2a + 11). This is an even integer. If it […]
Here, you will find all the questions of ISI Entrance Paper 2014 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: In a class there are $100$ student. We define $\mathbf { A_i} $ as the number of friends of $\mathbf { i^{th} […]
Overview of Math Olympiads in United States The American Mathematics Competitions (AMC) are the first of a series of competitions in middle school and high school mathematics that lead to the United States team for the International Mathematical Olympiad (IMO). AMC has three levels: AMC 8 - grade 8 and below AMC 10 - grades 10 and […]
This is a subjective problem number 3 from ISI BMath 2011 based on inequality of a product expression. Try out this problem. Problem: Inequality of a product expression For $latex \mathbf{n\in\mathbb{N}}$ prove that $latex \mathbf{\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdots\frac{2n-1}{2n}\leq\frac{1}{\sqrt{2n+1}}}$ Discussion Note that $latex \mathbf{ \frac{2n}{2n+1} \ge \frac{2n-1}{2n} }$ since simple cross multiplication gives $latex \mathbf{ 4n^2 \ge 4n^2 - […]
ISI Entrance Paper BMath 2011 - from Indian Statistical Institute's Entrance Also see: ISI and CMI Entrance Course at Cheenta Given $latex \mathbf{ a,x\in\mathbb{R}}$ and $latex \mathbf{x\geq 0,a\geq 0}$ . Also $latex \mathbf{sin(\sqrt{x+a})=sin(\sqrt{x})}$ . What can you say about a? Justify your answer. Given two cubes R and S with integer sides of lengths r […]
This is a problem number 8 from ISI BMath 2007 based on the Continuity and composition of a function. Try this out. Problem: Continuity and composition of a function Let $ \mathbf{P:\mathbb{R} \to \mathbb{R}}$ be a continuous function such that $P(x)=x$ has no real solution. Prove that $P(P(x))=x$ has no real solution. Discussion: Hunch: There […]
This is a problem number 7 from ISI B.Math 2007 based on an inequality related to (sin x)/x function. Try out this problem. Problem: An inequality related to (sin x)/x function Let $ \mathbf{0\leq \theta\leq \frac{\pi}{2}}$ . Prove that $\mathbf{\sin \theta \geq \frac{2\theta}{\pi}}$. Discussion: We consider the function $ \mathbf{ f(x) = \frac{\sin x }{x} […]
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on Trigonometry and positive integers.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1997 based on Odd and Even integers.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1997 based on Two and Three-digit numbers.
Try this beautiful problem from the Pre-RMO, 2017 based on Geometric Progression and Integers. You may use sequential hints to solve the problem.
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2008 based on Trigonometry. You may use sequential hints to solve the problem.
Try this problem from the Singapore Mathematics Olympiad, SMO, 2010 based on the application of the Pythagoras Theorem. You may use sequential hints.
Try this beautiful problem from Probability in Dice from AMC-10A, 2009. You may use sequential hints to solve the problem.
Try this beautiful Problem from Singapore Mathematics Olympiad, 2012 based on Functional Equations. You may use sequential hints to solve the problem.
Try this beautiful problem from Pre-Regional Mathematics Olympiad, PRMO, 2018 based on Triangles. You may use sequential hints to solve the problem.
Try this beautiful Problem from Singapore Mathematics Olympiad, SMO, 2008 based on Trigonometry. You may use sequential hints to solve the problem.
This is a solution to a problem from American Mathematics Competition (AMC) 8 2020 Problem 18 based on Geometry. AMC 8 2020 Problem 18 Rectangle $A B C D$ is inscribed in a semicircle with diameter $\overline{F E}$ as shown in the figure. Let $D A=16$, and let $F D=A E=9 .$ What is the […]
Mann Shah is a Gold Awardee in HKIMO (Hong Kong International Mathematical Olympiad), AIMO (Asia International Mathematical Olympiad), and SASMO (Singapore and Asian Schools Math Olympiad) 2021. He is a student of Class 7 and also a proud Young Achiever of Cheenta. Cheenta is happy to share the success story of Mann! Mann says, "I […]
Aryabhata is considered the "Father of Mathematics" in India. He is the first ancient Mathematician- Astronomer, whose important work includes "Aryabhatiya" and "Arya-Siddhanta". Today, let's learn 3 lessons from Aryabhata - the 𝗙𝗮𝘁𝗵𝗲𝗿 𝗼𝗳 𝗠𝗮𝘁𝗵𝗲m𝗮𝘁𝗶𝗰𝘀. 𝟭. 𝗛𝗮𝘃𝗲 𝗖𝗼𝘂𝗿𝗮𝗴𝗲 𝘁𝗼 𝗤𝘂𝗲𝘀𝘁𝗶𝗼𝗻 When eclipses were seen as something to be feared, and the concepts of "Rahu" and […]
An interesting problem based on complex numbers and their inversion. This is a Subjective Problem 89 from the Test of Mathematics Book, highly recommended for the ISI and CMI Entrance Exams. Let's check out the problem and solutions in two episodes: Useful Resources Previous Year Problems for ISI and CMI How to use invariance in […]
This post discusses the solutions of Problems from RMO 1994 Question Paper. You may find to solution to some of these. RMO 1994 Problem 1: A leaf is torn from a paperback novel. The sum of the numbers on the remaining pages is 15000. What are the page numbers on the torn leaf. RMO 1994 Problem2: […]
This is the solution to the real analysis from ISI MStat 2020 PSB Problem 8 with designed food for thoughts on hypothesis testing and probability theory.
This is a really interesting problem in the probability theory, which enhances the intuition of independent events, conditional probability and exhaustive events.
Aaditya Dharmen Punatar is a Gold Awardee in NMTC (National Mathematics Talent Contests) and SASMO (Singapore and Asian Schools Math Olmpiad) 2021. He is a student of Class 7 from Euroschool, Airoli and also a proud Young Achiever of Cheenta. Cheenta is happy to share the succes story of Aaditya! Aaditya says, "I love solving […]
This is the solution to the real analysis from IIT JAM MS 2020 Section A Problem 1 with designed food for thoughts.
From the path of falling in love with data and chance. to an examination ISI MStat program is different and unique. We discuss that how ISI MStat program is something more than an exam. We will also discuss how to prepare for the exam.