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I.S.I. and C.M.I. Entrance Corner

Efficiency of Heat Engine

A heat engine absorbs heat of \(10^5Kcal\) from a source, which is at \(127^\circ\) and rejects a part of heat …

Power Consumption of Electric Heater (KVPY ’10)

An electric heater coonsists of a nichrome coil and under \(220V\) consuming \(1KW\) power. Part of its coil burned out …

Complete-Not Compact (TIFR 2013 problem 23)

Question: True/False? Let \(X\) be complete metric space such that distance between any two points is less than 1. Then …

Parallel Plate Capacitor using Paper Sheets

Suppose you are to construct a parallel plate capacitor of \(1\mu F\) by using paper sheets of thickness \(0.05mm\) as …

Understanding the Infinitesimal

Understanding the Infinitesimal¬† Cheenta Notes in Mathematics ¬† Adding infinitely many positive quantities, you may end up having something finite. …

Differentiability at origin (I.S.I. B.Stat, B.Math Subjective 2017)

Problem: Suppose \( f : \mathbb{R} \to \mathbb{R} \) is a function given by $$ f(x) = \left\{\def\arraystretch{1.2}% \begin{array}{@{}[email protected]{\quad}[email protected]{}} 1 …

Region close to center (I.S.I. B.Stat, B.Math Subjective 2017, Problem 4)

Problem: Let S be the square formed by the four vertices (1, 1), (1, -1), (-1, 1), and (-1, -1). …

Number theoretic function (I.S.I. B.Stat, B.Math 2017 Subjective 5)

Problem Let \( g: \mathbb{N} \to \mathbb{N} \) with g(n) being the product of the digits of n. Prove that …

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