This is a problem from TOMATO Objective 21 based on positive integers. This problem is helpful for ISI Entrance Exam. Try out the problem. Problem: TOMATO Objective 21 Suppose x & y are positive integers, x>y, and 3x+4y & 2x+3y when divided by 5, leave remainders 2&3 respectively. It follows that when (x-y) is divided […]
Let's understand one-one function and differentiability with the help of a problem. Try it yourself before reading the solution. Let f be real valued, differentiable on (a, b) and $ f'(x) \ne 0 $ for all $ x \in (a, b) $. Then f is 1-1. True Discussion: Suppose f is not 1-1. Then there […]
Lets understand direct product of two subgroups with the help of a problem. This problem is useful for College Mathematics.
Let's understand Fixed Point of continuous bounded function with the help of a problem. This problem is useful for College Mathematics.
Given any integer $n \ge 2 $ , we can always find an integer m such that each of the n-1 consecutive integers m + 2, m + 3,..., m + n are composite. True Discussion: Take m=n!. Then the consecutive integers n! + 2 , n! + 3 , ... n! + n are […]
Let's discuss a problem based on Least Value of a Sum of Complex Numbers. Try to solve it yourself before reading the solution. Problem: Least Value of a Sum of Complex Numbers If $ z_1 , z_2 , z_3 , z_4 \in \mathbb{C} $ satisfy $ z_1 + z_2 + z_3 + z_4 = 0 […]
A lamp is placed on the ground 100 feet away from a wall. A man six feet tall is walking at a speed of 10 ft/sec from the lamp to the nearest point on the wall. When he is midway between the lamp and the wall, the rate of change in the length of his shadow is (in ft/ sec)?
View the other sections of this test. Algebra || Geometry Try a online trial session of Cheenta I.S.I. M.Math, IIT JAM, TIFR Entrance Program. Mail us at helpdesk@cheenta.com View the other sections of this test. Algebra || Geometry Try a online trial session of Cheenta I.S.I. M.Math, IIT JAM, TIFR Entrance Program. Mail us at […]
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2019 based on Equations and Complex numbers.
Try this beautiful problem from American Invitational Mathematics Examination, AIME, 2009 based on Probability of tossing a coin.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2009 based on Equations with a number of variables.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2010 based on Probability of divisors.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2015 from Geometry based on Area of Equilateral Triangle.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2015 based on Probability. You may use sequential hints.
Try this beautiful problem from the Pre-RMO, 2019 based on Two Arrangements. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2012 based on Arrangement of Digits. You may use sequential hints.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2012 based on Complex Numbers and prime.
Try this beautiful problem from American Invitational Mathematics Examination I, AIME I, 2009 based on geometric sequence. Use hints to solve the problem.
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
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 $r =2$. […]
This is a work in progress. Please come back soon for more updates. We are adding problems, solutions and discussions on INMO (Indian National Math Olympiad 2021) INMO 2021, Problem 1 Suppose $r \geq 2$ is an integer, and let $m_{1}, n_{1}, m_{2}, n_{2}, \cdots, m_{r}, n_{r}$ be $2 r$ integers such that $$|m_{i} n_{j}-m_{j} […]
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 […]