You may want to look into the first part
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.
Problem: Let the sequence \( { a_n} _{n \ge 1 } \) be defined by \(a_n = \tan n \theta \) where \( \tan \theta = 2 \). Show that for all n \( a_n \) is a rational number which can be written with an odd denominator. Discussion: This is simple induction. The claim […]
Try this beautiful problem from Geometry: Hexagon from AMC-10A, 2010. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2017 based on Altitudes of triangle. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Digits and Rationals.
Try this beautiful problem from the Pre-RMO, 2017 based on GP and 2-digit number. You may use sequential hints to solve the problem.
Try this beautiful problem from PRMO, 2018 based on Geometry. You may use sequential hints to solve the problem.
Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Quadratic Equation. You may use sequential hints to solve the problem.
Try this beautiful problem from Algebra, based on Sum of digits from AMC-10A, 2020. You may use sequential hints to solve the problem
Try this beautiful problem from Number theory based on Integer from AMC-10A, 2020. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2017 based on Average and Integers. You may use sequential hints to solve the problem.
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2012 based on Probability. You may use sequential hints to solve the problem.