This post contains problem from Chennai Mathematics Institute, CMI 2014 B.Sc. Entrance Paper. Try to solve them out. Help us to add and rectify problems and solutions to this paper. We are collecting problems from student feed back. 4 Point Problems Find the minimum value for x for which $latex \mathbf{ 50!/ (24)^n }$ is […]
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 […]
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Right angled triangle.
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