Let's discuss a problem based on the maximum height of water in a tank with a hole. Try the problem yourself first and then read the solution. The Problem: Maximum Height of Water A large tank is filled with water of (70 cm^3/s). A hole of cross-section (0.25cm^2) is punched at the bottom of the […]
Let's discuss a problem based on efflux velocity of fluid through a small orifice in a tube. Try it yourself first, then read the solution.
Let's discuss a problem and find out the work done by a force acting on the piston. First, try the problem and then read the solution. The Problem: A cylinder filled with water of volume (V) is fitted with a piston and placed horizontally. There is a hole of cross-sectional area (s) at the other […]
The central theme of the thousand flowers program is: connected ideas and connected problems. We will illustrate the idea using some examples. But before we do so, let's point out the theoretical motivation behind such a program. It is greatly borrowed from the pedagogical experiments of Rabindranath Thakur. (Reference: https://bn.m.wikisource.org/wiki/বিশ্বভারতী). One of his major criticisms of […]
Let's discuss the problem based on losing seconds where we find the depth below the earth's surface. Try yourself and then read the solution. The Problem: Losing Seconds Taking the earth's radius as (6400 Km) and assuming that the value of (g) inside the earth is proportional to the distance from the earth's centre, at […]
Here is a video post that discusses the roots of a polynomial problem from RMO 2017 problem 3. Watch, learn and enjoy the video. Some useful links: RMO Problems RMO 2002 Problem 1 - Video
In this post, we have discussed a problem based on the time period of a rolling cylinder. Try the problem yourself first, then read the solution. The Problem: Time Period of a Rolling Cylinder A solid uniform cylinder of radius (r) rolls without sliding along the inside the surface of a hollow cylinder of radius […]
TIFR 2014 Problem 5 Solution has been written for TIFR entrance preparation series. A problem on maps for bounded sequence from Real analysis.
Let's solve the Regional Mathematics Olympiad Problem, RMO 2017 from Goa and Maharashtra. Try the problems and check your solutions here. (\ 1).((\ 16) marks)Consider a chessboard of size (\ 8) units(\ \times8) units (i.e., each small square on the board has a side length of (\ 1) unit).Let (\ S) be the set of […]
Here are the questions asked in Regional Math Olympiad 2017 and their solutions. Try to solve it first and then see the solutions. Looking for just the problems? Download the PDF here. RMO 2017, Problem 1: Let AOB be a given angle less than \( 180^o \) and let P be an interior point of […]