Let us learn about Stirling Numbers of First Kind. Watch video and try the problems related to Math Olympiad Combinatorics
Let us learn about Stirling Numbers of First Kind. Watch video and try the problems related to Math Olympiad Combinatorics
Suppose $r\geq 2$ is an integer, and let $m_{1},n_{1},m_{2},n_{2} \cdots ,m_{r},n_{r}$ be $2r$ integers such that$$|m_{i}n_{j}−m_{j}n_{i}|=1$$for any two integers $i$ and $j$ satisfying $1\leq i <j <r$. Determine the maximum possible value of $r$. Solution: Let us consider the case for $r =2$. Then $|m_{1}n_{2} - m_{2}n_{1}| =1$.......(1) Let us take $m_{1} =1, n_{2} =1, m_{2} =0, n_{1} =0$. Then, clearly the condition holds for $r =2$. […]
Suppose we have a triangle $ABC$. Let us extend the sides $BA$ and $BC$. We will draw the incircle of this triangle. How to draw the incircle? Here is the construction. Draw any two angle bisectors, say of angle $A$ and angle $B$ Mark the intersection point $I$. Drop a perpendicular line from I to […]
This year Cheenta Statistics Department has done a survey on the scores in each of the sections along with the total score in IIT JAM MS. Here is the secret for you! We have normalized the score to understand in terms of percentage. There are three questions, we ask The general performance for the IIT […]
Here are the problems and their corresponding solutions from B.Math Hons Objective Admission Test 2008. Problem 1 : Let $a, b$ and $c$ be fixed positive real numbers. Let $u_{n}=\frac{n^{2} a}{b+n^{2} c}$ for $n \geq 1$. Then as $n$ increases, (A) $u_{n}$ increases;(B) $u_{n}$ decreases;(C) $u_{n}$ increases first and then decreases;(D) none of the above […]
Here are the problems and their corresponding solutions from B.Math Hons Objective Admission Test 2007. Problem 1 : The number of ways of going up $7$ steps if we take one or two steps at a time is (A) $19$ ;(B) $20$;(C) $21$ ;(D) $22$ . Problem 2 : Consider the surface defined by $x^{2}+2 […]
Here, you will find all the questions of ISI Entrance Paper 2011 from Indian Statistical Institute's B. Math Entrance. You will also get the solutions soon of all the previous year problems. Problem 1 : Let $a \geq 0$ be a constant such that $\sin (\sqrt{x+a})=\sin (\sqrt{x})$ for all $x \geq 0 .$ What can […]
Here, you will find all the questions of ISI Entrance Paper 2010 from Indian Statistical Institute's B. Math Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Prove that in each year, the $13$ th day of some month occurs on a Friday. Problem 2: In the accompanying […]
Here, you will find all the questions of ISI Entrance Paper 2009 from Indian Statistical Institute's B. Math Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Let $x, y, z$ be non-zero real numbers. Suppose $\alpha, \beta, \gamma$ are complex numbers such that $|\alpha|=|\beta|=|\gamma|=1 .$ If $x+y+z=0=\alpha […]
Here, you will find all the questions of ISI Entrance Paper 2008 from Indian Statistical Institute's B. Math Entrance. You will also get the solutions soon of all the previous year problems. Problem 1 : Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function. Suppose $$f(x)=\frac{1}{t} \int_{0}^{t}(f(x+y)-f(y)) d y$$ for all $x \in \mathbb{R}$ and […]
39 Cheenta students qualified for IOQM 2024 (RMO cut-off). About 130 kids students appeared in the contest from Cheenta this year making the success rate about 30%. This remarkable achievement is the result of months of dedicated effort. Most of these students regularly participated in Here are some of the qualified students who additionally qualified […]
Problems and Solutions from IOQM 2024, the first level of Math Olympiad in India.
PART - A Problem 1 Let $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}=\frac{m}{n}$, where $m$ and $n$ are positive integers with no common divisors other than 1 . The highest power of 7 that divides $m$ is A. 0B. 1C. 2D. 3 Problem 2 Five spherical balls of diameter 10 cm each fit inside a closed cylindrical tin with internal diameter […]
Problem 1 Saket wanted to add two 2-digit numbers. But he multiplied them and got 629 as the answer. The sum of the two 2-digit numbers is a)56b) 52c) 54d) 46 Problem 2 The sum of three integers is 1 . Their product is 36 . The greatest of these three numbers is a) 12b) […]
Question 01 If $x^2+x=1$, then the value of $\frac{x^7+34}{x+2}$ is equal to a) 7b) 1c) 13d) 17 Question 02 The angle between the hour hand and the minute hand of a clock at the time $9: 38 \mathrm{pm}$ is a) $60^{\circ}$b) $61^{\circ}$c) $59^{\circ}$d) $62^{\circ}$ Question 03 In the adjoining figure, $A O B$ is a […]
Question 01 There is a 6-digit number in which the first and the fourth digit from the first are the same, the second and the fifth digit from the first are the same and the third and the sixth digit from the first are the same. Then the number is always a) A square numberb) […]
Times of India Story features Cheenta students and India's growing prowess in mathematical Olympiads.
Learn about the concept of Locus problem in Geometry of Math Olympiad
Try out this beautiful problems from Australian Mathematics Competitions past paper 2020.
Here is the Australian Mathematics Competition (2021) Middle Primary Division question and enhance your problem-solving abilities