How to Solve a Math Problem? A very common question. Here is how to understand the anatomy of a problem and also why problem-solving is important. Artificial Intelligence, Raychaudhuri Mathematics Award, PreRMO Have you read Polya's 'How to Solve It'? This is a pioneering work on problem-solving strategies. Why is this important? […]
Here are the problems and their corresponding solutions from BStat Hons Objective Admission Test 2005. Try it yourself and then read the solutions.
Dear students, I hope you are doing well. French mathematician Yves Meyer won the Abel Prize for his work in Wavelet theory. You may read more about his work in the words of celebrated mathematician Terence Tao here. Presently I am reading a cult classic by Hilbert: Geometry and Imagination. In introductory […]
Here, you will find all the questions of ISI Entrance Paper 2016 from Indian Statistical Institute's B.Stat Entrance. You will also get the solutions soon of all the previous year problems. Problem 1: In a sports tournament of $n$ players, each pair of players plays exactly one match against each other. There are no draws. […]
Mathematicians love fixed point theorems. Brouwer fixed point theorem is one such result. It states that "for any continuous function f mapping a compact convex set into itself there is a point a such that f(a) = a." We are interested in one such fixed point theorem. Consider maps (continuous functions) from [latex] S^n \to S^n [/latex] […]
In this post, the notes in Mathematics are based on inversion and price change. Notes in Mathematics A Cheenta Newsletter Hello friend, Suppose there is a lion inside a round field (not at the center). The field has a boundary wall. You are standing outside the field. How can the lion catch you? […]
Try this problem from TOMATO Objective 288, useful for ISI BStat, BMath Entrance Exam based on finding big remainder in a small way. Problem: Tomato objective 288 The remainder R(x) obtained by dividing the polynomial [latex]x^{100}[/latex] by the polynomial [latex]x^2-3x+2[/latex] is (A) [latex]2^{100}-1[/latex] (B) [latex](2^{100}-1)x-(2^{99}-1)[/latex] (C) [latex]2^{100}x-3(2^{100})[/latex] (D) [latex](2^{100}-1)x+(2^{99}-1)[/latex] SOLUTION: (B) The the divisor is […]
Problem: If the roots of the equation ${(x-a)(x-b)}$+${(x-b)(x-c)}$+${(x-c)(x-a)}$=$0$, (where a,b,c are real numbers) are equal , then (A) $b^2-4ac=0$ (B) $a=b=c$ (C) a+b+c=0 (D) none of foregoing statements is correct Answer: $(B)$ ${(x-a)(x-b)}$+${(x-b)(x-c)}$+${(x-c)(x-a)}$=$0$ => $x^2-{(a+b)}x$+$ab+x^2-{(b+c)}x$+$bc+x^2-{(c+a)}x+ca$=$0$ => $3x^2-2{(a+b+c)}x$+$(ab+bc+ca)$=$0$ discriminant, of the equation is => $4{(a+b+c)^2}$-$4.3{(ab+bc+ca)}$=$0$ => $a^2+b^2+c^2+2(ab+bc+ca)$-$3(ab+bc+ca)$=$0$ => $a^2+b^2+c^2$-$(ab+bc+ca)$=$0$ => $a=b=c$ So, option (B) is correct.