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

Orbit of Planet (KVPY ’10)

A planet of mass \(m\) is moving around a star of mass \(M\) and radius \(R\) in a circular orbit …

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 …

Right angled triangle in a circle (B.Stat 2017, subjective 2)

Problem: Consider a circle of radius 6 as given in the diagram below. Let B, C, D and E be …

Sequence of tangents (I.S.I. B.Stat and B.Math 2017, subjective problem 1)

Problem: Let the sequence \( \{ a_n\} _{n \ge 1 } \) be defined by $$ a_n = \tan n …

I.S.I. B.Stat and B.Math Entrance 2017

Let the sequence \( \{ a_n\} _{n \ge 1 } \) be defined by $$ a_n = \tan n \theta …

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