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 […]
Here, you will find all the questions of ISI Entrance Paper 2017 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1 : Let the sequence \( \{ a_n\} _{n \ge 1 } \) be defined by $$ a_n = \tan n \theta $$ […]
Try this beautiful problem from Algebra, based on Sum of two digit numbers from PRMO 2016. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-Regional Mathematics Olympiad, PRMO, 2014, based on finding side of Triangle. You may use sequential hints.
Try this beautiful problem from Geometry: The area of a trapezoid from AMC-8 (2003). You may use sequential hints to solve the problem.
Try this beautiful problem from AMC 8, 2003, problem no-22 based on Largest area. You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry, based on Cube from AMC-10A, 2007. You may use sequential hints to solve the problem
Try this problem from Geometry: Ratios of the areas of Triangle and Quadrilateral from AMC-10A, 2005 You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2012 based on Angles and Triangles.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2012 based on Digits and Numbers.
Try this beautiful problem from Geometry based on Try this beautiful problem from Algebra based on Largest Common Divisor . from PRMO 2014. You may use sequential hints to solve the problem.
Try this beautiful problem from ALGEBRA: Greatest Common Divisor AMC-10A, 2018. You may use sequential hints to solve the problem