Here, you will find all the questions of ISI Entrance Paper 2011 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: Let $x_1, x_2, \cdots , x_n $ be positive reals with $x_1+x_2+\cdots+x_n=1 $. Then show that $ \sum_{i=1}^n \frac{x_i}{2-x_i} \ge \frac{n}{2n-1} $ […]
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It is possible to input Latex in facebook to input math equations. Latex in Facebook Down side is, only viewers using chrome and latex extension installed can view the equations. Other browsers can only see latex code. Anyways, it is better than not having latex at all. Steps: Go to Google Chrome Click on Settings […]
This is a problem from Test of Mathematics, TOMATO problem 6. It is useful for ISI and CMI Entrance Exam. Problem : TOMATO Problem 6 Let $latex x_1 , x_2, ..... , x_{100} $ be positive integers such that $latex x_i + x_{i+1} = k $ for all $latex i $ where $latex k $ […]
This is a problem from Test of Mathematics, TOMATO Problem 106. It is useful for ISI and CMI Entrance Exam. Try out the problem. Problem: TOMATO Objective 106 The term that is independent of x in the expansion of $[\frac{3x^2}{2}-\frac{1}{3x}]^9 $ a) ${{9} \choose {6}}(\frac{1}{3})^3(\frac{3}{2})^6 $ b) ${{9} \choose {5}}(\frac{3}{2})^5(-\frac{1}{3})^4 $ c) ${{9} \choose {3}}(\frac{1}{6})^3 […]
We observe a renewed interest in Math and Basic Science in India after decades of engineering mania. This is a welcome change. The top tier students, in increasing numbers, are opting for such courses. In this article we present some of the institutes which offer world class education in basic science after school.
This is a problem from Test of Mathematics, TOMATO Objective 8, useful for ISI and CMI Entrance. Try out this problem. (by Rahul Roy) Problem: Two trains of equal length L,travelling at speeds v1 and v2 miles per hour in opposite directions,take t seconds to cross each other .then L in feet is: Solution: Total […]
This is a problem from TOMATO Objective 01 based on worker and wages. This problem is helpful for ISI Entrance Exam. Try out the problem. (By Akash Singha Roy) Problem: TOMATO Objective 01 A worker suffers a $20 $ % cut in wages. He regains his original pay by obtaining a rise of (A) $20 […]
This is a problem from TOMATO Objective 94 based on number of divisors. This problem is helpful for ISI Entrance Exam. Try out the problem. (By Akash Singha Roy) Problem: TOMATO Objective 94 Number of divisors of $ 2700 $ Solution: $ 2700 = 2^2 \times 3^3\times 5^2 $ Hence, any divisor of $2700 $ […]
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 […]
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Smallest prime.
Try this beautiful problem from Geometry: Octahedron AMC-10A, 2006. You may use sequential hints to solve the problem
Try this beautiful problem from Probability in Coordinates from AMC-10A, 2003. You may use sequential hints to solve the problem.
Try this beautiful problem from Pre-Regional Mathematics Olympiad, PRMO, 2012 based on Triangle You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Triangle and Trigonometry.
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2013 based on HCF. You may use sequential hints to solve the problem.
Try this beautiful problem from Singapore Mathematics Olympiad based on area of triangle. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2015 based on Theory of Equations.
Try this beautiful problem from American Invitational Mathematics Examination, AIME, 1999 based on Probability in Games. You may use sequential hints.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2000 based on Least Positive Integer.
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
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 […]