Symmetries of Cube (TIFR 2014 problem 20)

Question: Let \(C\) denote the cube \([-1,1]^3\subset \mathbb{R}^3 \). How many rotations are there in \(\mathbb{R}^3\) which take \(C\) to itself? Discussion: Let us label the six faces of the cube by \(F_1,F_2,…,F_6\). Let \(G\) be the set consisting of all...

Last digit of \(97^{2013}\) (TIFR 2014 problem 18)

Question: What is the last digit of \(97^{2013}\)? Discussion: \(97 \equiv -3 (\mod 10 ) \) \(97^2 \equiv (-3)^2 \equiv -1 (\mod 10 ) \) \(97^3 \equiv (-1)\times (-3) \equiv 3 (\mod 10 ) \) \(97^4 \equiv (3)\times (-3) \equiv 1 (\mod 10 ) \). Now, \(2013=4\times 503...

Discrete space (TIFR 2014 problem 15)

Question: \(X\) is a metric space. \(Y\) is a closed subset of \(X\) such that the distance between any two points in \(Y\) is at most 1. Then A. \(Y\) is compact. B. any continuous function from \(Y\to \mathbb{R}\) is bounded. C. \(Y\) is not an open subset of \(X\)...
UCLA full scholarship program – MUMS

UCLA full scholarship program – MUMS

Cheenta Opportunity is an initiative for the benefit of Cheenta Olympiad candidates. We dig up opportunities and resources available all around the world for our students.  University of  California, Los Angles is one of the leading universities in the world. Its...