### 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 …

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

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

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 Cheenta Notes in Mathematics Adding infinitely many positive quantities, you may end up having something finite. …

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 …

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

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

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

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

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