Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Sign change. You may use sequential hints to solve the problem.
Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Sign change. You may use sequential hints to solve the problem.
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Maximum and Minimum Element. You may use sequential hints.
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on function. You may use sequential hints to solve the problem.
Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Graph in Calculus. You may use sequential hints to solve the problem.
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Set of real numbers. You may use sequential hints.
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Number of roots. You may use sequential hints.
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Periodic Function. You may use sequential hints.
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Periodic Function. You may use sequential hints.
Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Negative & Positive Roots. You may use sequential hints to solve the problem.
Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Calculus. You may use sequential hints to solve the problem.
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 […]
In 2021, Cheenta is proud to introduce 5-days-a-week problem solving sessions for Math Olympiad and ISI Entrance.
This post contains problems from Indian National Mathematics Olympiad, INMO 2015. Try them and share your solution in the comments. INMO 2015, Problem 1 Let $A B C$ be a right-angled triangle with $\angle B=90^{\circ} .$ Let $B D$ be the altitude from $B$ on to $A C .$ Let $P, Q$ and $I$ be […]
This post will provide you all the PRMO (Pre-Regional Mathematics Olympiad) 2012 Set A problems and solutions. You may find some solutions with hints too. There are 20 questions in the question paper and question carries 5 marks. Time Duration: 2 hours PRMO 2012 Set A, Problem 1: Rama was asked by her teacher to […]
This post will provide you all the PRMO (Pre-Regional Mathematics Olympiad) 2013 Set A problems and solutions. You may find some solutions with hints too. There are 20 questions in the question paper and question carries 5 marks. Time Duration: 2 hours PRMO 2013 Set A, Problem 1: What is the smallest positive integer $k$ […]
This post will provide you all the PRMO (Pre-Regional Mathematics Olympiad) 2015 Set B problems and solutions. You may find some solutions with hints too. PRMO 2015 Set B, Problem 1: A man walks a certain distance and rides back in $3 \frac{3}{4}$ hours; he could ride both ways in $2 \frac{1}{2}$ hours. How many […]
This post will provide you all the PRMO (Pre-Regional Mathematics Olympiad) 2014 problems and solutions. You may find some solutions with hints too. PRMO 2014, Problem 1: A natural number $k$ is such that $k^{2}<2014<(k+1)^{2}$. What is the largest prime factor of $k ?$ PRMO 2014, Problem 2: The first term of a sequence is […]
IOQM 2021 - Problem 1 Let $ABCD$ be a trapezium in which $AB \parallel CD$ and $AB=3CD$. Let $E$ be the midpoint of the diagonal $BD$. If $[ABCD]= n \times [CDE] $, what is the value of $n$ ? (Here $[\Gamma]$ denotes the area of the geometrical figure $\Gamma$).Answer: 8 Solution: IOQM 2021 - Problem […]