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 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.
Try this beautiful problem from Pattern based on Triangle from AMC-10A, 2003. You may use sequential hints to solve the problem
Try this beautiful problem from Number theory based on divisibility from AMC-10A, 2003. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2011 based on Rectangles and sides.
MLE is an important algorithm to find an estimate. Method of Moments is too. But they are often same. When are they same? What is so common between them? Let's explore.
This problem is an application of the smoothng property of expectation and variance and compares the mse of two sample survey schemes inlcuding SRSWR and SRSWOR. Let's enjoy this problem 9 of ISI MStat 2020.
Try these AMC 8 Algebra Questions and check your knowledge! AMC 8, 2025, Problem 7 On the most recent exam on Prof. Xochi's class, 5 students earned a score of at least \(95 \%\),13 students earned a score of at least \(90 \%\),27 students earned a score of at least \(85 \%\),50 students earned a […]
MLE is an important algorithm to find an estimate. Sufficiency is a good small sample property. So, how are they related? Is MLE always a function of sufficient statistic? Let's explore.
This problem is an application of the multinomial distribution, sufficiency and beautiful application of probabilistic algebraic argument. Let's enjoy this problem 6 of ISI MStat 2020.
Your Math-Mail from Cheenta Dear students, Let the world engage in rat race. We will focus on deep and beautiful learning. Here is a beautiful problem that we worked on this week. Suppose there are 5 points spread in 1 by 1 square field. The points can be at the corners, on the edges or […]
A beautiful geometry problem from INMO 2021 (problem 5). Learn how to use angle chasing to find center of a circle.
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.
Are you preparing for ISI MStat Entrance Exams? Here is the list of useful books for ISI MStat Entrance Exam based on the syllabus.
Are you ready for IIT JAM MS 2022? Check it out with a Free Diagnostic Test prepared by Cheenta Statistics & Analytics Department! Other Useful Resources for You