সংখ্যাতত্ত্ব লেখাটিতে আমরা Pythagorean triplet বা পিথাগোরীয়ান ত্রয়ী নিয়ে আলোচনা করা হয়েছে ।
সংখ্যাতত্ত্ব লেখাটিতে আমরা Pythagorean triplet বা পিথাগোরীয়ান ত্রয়ী নিয়ে আলোচনা করা হয়েছে ।
Problem: Problem on Asteroid Let PQ be a line segment of a fixed length L with it's two ends P and Q sliding along the X axis and Y-axis respectively. Complete the rectangle OPRQ where O is the origin. Show that the locus of the foot of the perpendicular drawn from R on PQ is […]
This is a Test of Mathematics Solution Subjective 128 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Problem Draw the graph (on plain paper) of f(x)= min { |x| -1, |x-1| - […]
Try this Arithmetic Mean - Geometric Mean Subjective Problem number 82 from TOMATO. Problem: Arithmetic Mean - Geometric Mean Let $ {a, b, c, d}$ be positive real numbers such that $ {abcd = 1}$. Show that, $ {\displaystyle{(1 + a)(1 + b)(1 + c)(1 + d) {\ge} {16}}}$ Solution: $ {{\sum{a}} = a + […]
This is a subjective problem from TOMATO based on inequality. Problem: Inequality Problem If $ {\displaystyle{a}}$ and $latex {\displaystyle{b}}$ are positive real numbers such that, $ {\displaystyle{a + b = 1}}$, prove that,$ {\displaystyle{\left(a + {\frac{1}{a}}\right)^2 + \left(b + {\frac{1}{b}}\right)^2 {\ge} {\frac{25}{2}}}}$. Solution: $ {\displaystyle{\left(a + {\frac{1}{a}}\right)^2 + \left(b + {\frac{1}{b}}\right)^2 {\ge} {\frac{25}{2}}}}$$ {\displaystyle{\Leftrightarrow}}$ $ […]
This is a Test of Mathematics Solution Subjective 80 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance. Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta Problem If $ {a, b, c}$ […]
This is a collection of some revision notes. They include topics discussed in first three sessions of Combinatorics Course at Cheenta (Faculty: Ashani Dasgupta). combinatorics 1(work sheet) Study of symmetry in geometry is greatly facilitated by combinatorial methods There are 6 symmetries of an equilateral triangle (=3! permutations of 3 things) There are 8 symmetries […]
This is Problem number 7 from the ISI Subjective Entrance Exam based on the Arithmetic Sequence of reciprocals. Try to solve the problem. Let $ m_1, m_2 , ... , m_k $ be k positive numbers such that their reciprocals are in A.P. Show that $ k< m_1 + 2 $ . Also find such […]