Sine rule is an important rule relating to the sides and angles of any triangle. Here is a Subjective problem no. 120 from TOMATO. Try it. Problem: Sine Rule and Triangle (i) If $ A + B +C = n \pi $ and $ s=2 $, show that $ \sin 2A + \sin 2B + […]
Sine rule is an important rule relating to the sides and angles of any triangle. Here is a Subjective problem no. 120 from TOMATO. Try it. Problem: Sine Rule and Triangle (i) If $ A + B +C = n \pi $ and $ s=2 $, show that $ \sin 2A + \sin 2B + […]
This is a subjective problem from TOMATO based on Graphing integer value function. Problem: Graphing integer value function Let [x] denote the largest integer (positive, negative or zero) less than or equal to x. Let $ y= f(x) = [x] + \sqrt{x - [x]} $ and $ s=2 $ be defined for all real numbers […]
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 […]
Try this beautiful problem from the Pre-RMO, 2017 based on Altitudes of triangle. You may use sequential hints to solve the problem.
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2012 based on Probability. You may use sequential hints to solve the problem.
Try this beautiful problem from Algebra, based on Sum of digits from AMC-10A, 2020. You may use sequential hints to solve the problem
Try this beautiful problem from Number theory based on Integer from AMC-10A, 2020. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2017 based on Average and Integers. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Row of Pascal Triangle.
Try this beautiful problem from the Pre-RMO, 2017 based on Geometric Progression. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Digits and Order.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Ratio and Inequalities.
Try this beautiful problem from Pre-Regional Mathematics Olympiad, PRMO, 2017 based on Time & Work. You may use sequential hints to solve the problem.