In I.S.I.'s B.Stat Entrance 2005, the following problem appeared: Problem: Let $$ f(x) = \int_0^1 |t-x|t dt $$ for all real x. Sketch the graph of f(x). What is the minimum value of f(x)? Here is the first installment of a discussion on that. Part 1 Part 2 [button url="https://cheenta.com/graphing-an-integral-part-2/" class="" bg="" hover_bg="" size="0px" color="" […]
You may want to look into the first part
Let's discuss a problem and know how to find the power consumption of electric heater. Try the problem and read the solution here. The Problem: An electric heater coonsists of a nichrome coil and under (220V) consuming (1KW) power. Part of its coil burned out and it was reconnected after cutting off the burnt portion. […]
Try this problem 23 from TIFR 2013 named - Complete not compact. Question: TIFR 2013 problem 23 True/False? Let \(X\) be complete metric space such that distance between any two points is less than 1. Then \(X\) is compact. Hint: What happens if you take discrete space? Discussion: Discrete metric space as we know it […]
Try this problem, useful for Physics Olympiad based on Constructing Parallel Plate Capacitor. The Problem: Constructing Parallel Plate Capacitor Suppose you are to construct a parallel plate capacitor of (1\mu F) by using paper sheets of thickness (0.05mm) as dielectric and a number of circular parallel metal foils connected alternately. If the dielectric constant of […]
Understanding the Infinitesimal Cheenta Notes in Mathematics Let's discuss a beautiful idea related to progress in mathematics and understanding the infinitesimal. Adding infinitely many positive quantities, you may end up having something finite. Greeks did not understand this very well. Archimedes had some ideas. Kerala school of mathematics under the leadership of Madhavacharya made […]
Try this problem from ISI B.Stat, B.Math Subjective Entrance Exam, 2017 Problem no. 3 based on Differentiability at origin. Problem: Differentiability at origin Suppose \( f : \mathbb{R} \to \mathbb{R} \) is a function given by $$f(x) = \left\{\def\arraystretch{1.2}%\begin{array}{@{}c@{\quad}l@{}}1 & \text{if x=1}\\ e^{(x^{10} -1)} + (x-1)^2 \sin \left (\frac {1}{x-1} \right ) & \text{if} x […]
Try this problem from ISI B.Stat, B.Math Subjective Entrance Exam, Problem 4 based on Region close to the center. Problem: Let S be the square formed by the four vertices (1, 1), (1, -1), (-1, 1), and (-1, -1). Let the region R be the set of points inside S which are closer to the […]
Try this beautiful problem from ISI BStat 2017 Subjective 2 based on right-angled triangle in a circle. Understand, solve, and learn.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Head Tail Problem.
Try this beautiful problem from Geometry:Radius of a circle.AMC-10A, 2003. You may use sequential hints to solve the problem
Try this beautiful problem from algebra, based on Sum of the digits from AMC-10A, 2007. You may use sequential hints to solve the problem
Try this beautiful problem from Geometry based on medians of triangle from PRMO 2018. You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry based on Hexagon from AMC-10A, 2014. You may use sequential hints to solve the problem
Try this beautiful sum of Co-ordinates based on co-ordinate Geometry from AMC-10A, 2014. You may use sequential hints to solve the problem.
Try this beautiful problem from Algebra based on positive integers from PRMO 2019. You may use sequential hints to solve the problem.
Try this beautiful problem from Singapore Mathematical Olympiad, SMO, 2010 - Problem 7 based on the combination of equations.
Try this beautiful problem from PRMO, 2019, problem-17, based on Largest Possible Value Problem. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2019 based on the Diameter of a circle. You may use sequential hints to solve the problem.
Try this beautiful Recurrence Problem based on Chessboard from IOQM 2022, Part A, Problem 9. You may use sequential hints to solve it.
Try this beautiful Problem on Trigonometry from PRMO -2018.You may use sequential hints to solve the problem.
This is a work in progress. Please come back for the solutions. You can also suggest your solutions in the comment section Objective Section Answer Key Problem 1 -> A Problem 7 -> C 13. Problem 19 -> B Problem 25 -> C Problem 2 -> D 8. Problem 14 -> C Problem 20 -> […]
Tools for middle school children and their parents. How to help kids fall in love with mathematical science and prepare them for math and sciecnce olympiads, ISI, CMI Entrances and other contests in the long run?
The BStat and BMath Entrance of ISI Entrance is ‘different’ from IIT JEE or other engineering entrances. It tests creativity and ingenuity of the problem solver that requires more than mechanical application of formulae. Many of these problems are inspired from erstwhile Soviet Union math contests and other math olympiads. The entrance has two sections: […]
Three out four Indian awardees in the prestigious European Girls Math Olympiad have Cheenta connections. Here is the success story.
Learn about Hermite Identity for Math Olympiad, ISI CMI Entrances. It involves a beautiful application of periodicity of functions.
NMTC 2010 Primary Stage 1 Question 1 $\mathrm{n}, \mathrm{a}$ are natural numbers each greater than 1 . If $a+a+a+a+\ldots+a=2010$, and there are $n$ terms on the left hand side, then the number of ordered pairs $(a, n)$ is NMTC 2019 Primary Stage 1 Question 10 Sum of the odd numbers from 1 to 2019 both […]
NMTC 2019 Stage 1 Sub junior Question 10 How many positive integers smaller than 400 can you get as a sum of eleven consecutive positive integers? NMTC 2019 Stage 1 Sub junior Question 11 Let $x, y$ and $z$ be positive real numbers and let $x \geq y \geq z$ so that $x+y+z=20.1$. Which of […]
We meet in an informal discussion session with Cheenta students Aryan Kalia (Harvard University) and Anushka Aggarwal (MIT). A few selected students will join over Google Meet for a direct interaction. We will also take in questions from Youtube and Facebook Chat. Aryan Kalia had outstanding scores in American Math Competition. He also did a […]