This is a subjective problem from TOMATO based on inequality. Problem: Inequality Problem If $ {\displaystyle{a}}$ and $latex {\displaystyle{b}}$ are positive real numbers such that, $ {\displaystyle{a + b = 1}}$, prove that,$ {\displaystyle{\left(a + {\frac{1}{a}}\right)^2 + \left(b + {\frac{1}{b}}\right)^2 {\ge} {\frac{25}{2}}}}$. Solution: $ {\displaystyle{\left(a + {\frac{1}{a}}\right)^2 + \left(b + {\frac{1}{b}}\right)^2 {\ge} {\frac{25}{2}}}}$$ {\displaystyle{\Leftrightarrow}}$ $ […]
This is a Test of Mathematics Solution Subjective 80 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem If $ {a, b, c}$ […]
This is a collection of some revision notes. They include topics discussed in first three sessions of Combinatorics Course at Cheenta (Faculty: Ashani Dasgupta). combinatorics 1(work sheet) Study of symmetry in geometry is greatly facilitated by combinatorial methods There are 6 symmetries of an equilateral triangle (=3! permutations of 3 things) There are 8 symmetries […]
This is Problem number 7 from the ISI Subjective Entrance Exam based on the Arithmetic Sequence of reciprocals. Try to solve the problem. Let $ m_1, m_2 , ... , m_k $ be k positive numbers such that their reciprocals are in A.P. Show that $ k< m_1 + 2 $ . Also find such […]
This is problem from Chennai Mathematical Institute, CMI 2015 based on Divisibility of product of consecutive numbers. Try it out! a be a positive integer from set {2, 3, 4, … 9999}. Show that there are exactly two positive integers in that set such that 10000 divides a*a-1. Put $ n^2 -1 $ in place of 9999. […]
In a circle, AB be the diameter.. X is an external point. Using straight edge construct a perpendicular to AB from X If X is inside the circle then how can this be done Discussion: Teacher: What fascinates me about CMI problems is that they are at once fundamental and beautiful in nature. This problem […]
This post contains Chennai Mathematical Institute, CMI, 2015 Objective, and Subjective Problems and Solutions. Please contribute problems and solutions in the comments. Objective For all finite word strings comprising A and B only, A string is arranged by dictionary order. eg. ABAA For any arbitrary string w, with another string y<w, there cannot always exist […]
This post contains problems from Indian Statistical Institute, ISI 2015 MMath Entrance Subjective Problems. Try to solve the problems. If you know any other problem, please put it in the comment section. Let $ (a_k) $ be a sequence in (0, 1) . Prove that $ a_k to 0 $ if $ \displaystyle{ \frac{1}{n} \sum […]
This post contains solutions of Indian Statistical Institute, ISI 2015 BStat - BMath Objective Problems. Try to solve them. This is a work in progress. Candidates, please submit objective problems in the comments section (even if you partially remember them). If you do not remember the options, that is fine too. We can work with […]
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. this is a work in progress. post problems, solutions and correction in the comment section Problem 1: Let $ y = x^2 + ax […]