What is the value of \( \dfrac{11!-10!}{9!}\)? (A) 99 (B) 100 (C) 110 (D) 121 (E) 132 For what value of \( x \) does \( 10^x \cdot 100^{2x} = 1000^5 \)? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 For every dollar Ben spent on bagels, David spent 25 cents less. Ben paid $12.50 more than David. […]
Try the solution of problem from RMO (Regional Mathematical Olympiad) 2015 Problem 1 based on Triangle. Problem: Triangle Problem Two circles $latex \Gamma $ and $latex \Sigma $, with centers O and O', respectively, are such that O' lies on $latex \Gamma $. Let A be a point on $latex \Sigma $, and let M […]
Try this problem from RMO 2015 from Chennai Region based on Integer Solution of Polynomial. Problem: Integer Solution of Polynomial Solve the equation $latex y^3 + 3y^2 + 3y = x^3 + 5x^2 - 19x + 20 &s=2 $ for positive integers x, y. Discussion: $latex y^3 + 3y^2 + 3y = x^3 + 5x^2 […]
This is a problem from RMO 2015 Mumbai Region based on inequality. Problem: RMO 2015 Mumbai Region Let x, y, z be real numbers such that $ x^2 + y^2 + z^2 - 2xyz = 1 $ and $ s=2$ . Prove that $ (1+x)(1+y)(1+z) \le 4 + 4xyz $ and $ s=2$ Discussion Note […]
This is a problem from RMO 2015 from Mumbai Region based on Cyclic Quadrilaterals and Incenters. Problem: RMO 2015 Mumbai Region Let ABC be a right angled triangle with $ \angle B = 90^0 $ and $ s=2 $ and let BD be the altitude from B on to AC. Draw $ DE \perp AB […]
This is a problem from Regional Mathematics Olympiad, RMO 2015 Mumbai Region based on Polynomial with positive integers. Try to solve it. Site title Title Primary category Separator Problem: Let P(x) be a polynomial whose coefficients are positive integers. If P(n) divides P(P(n) -2015) for every natural number n, prove that P(-2015) = 0. Discussion: Let […]
This is a problem from the Regional Mathematics Olympiad, RMO 2015 Mumbai Region based on the Number of Three-digit numbers. Try to solve it. Problem: Number of Three-digit numbers Determine the number of 3 digit numbers in base 10 having at least one 5 and at most one 3. Discussion: (Suggested by Shuborno Das in […]
This is a problem from the Regional Mathematics Olympiad, RMO 2015 Mumbai Region based on Diagonal of a Quadrilateral. Try to solve it. Problem: Diagonal of a Quadrilateral Let ABCD be a convex quadrilateral with AB = a, BC = b, CD = c and DA = d. Suppose $ a^2 + b^2 + c^2 […]
This is a problem from Regional Mathematics Olympiad, RMO 2015 Chennai Region based on the Minimal value problem. Try to solve it. Problem: Minimal value problem Find the minimum value of $ \displaystyle { \frac{ ( x + \frac{1}{x} )^6 - ( x^6 + \frac{1}{x^6}) - 2}{(x+\frac{1}{x})^3 + (x^3 + \frac{1}{x^3} )} } $ and […]
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Algebraic value.
Try this beautiful problem from Probability based on dice from AMC-10A, 2011. You may use sequential hints to solve the problem
Try this beautiful problem from Geometry: Area of Region in a Circle from AMC-10A, 2011, Problem -18. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1990 based on Positive solution.
Try this beautiful problem from Algebra based smallest positive value from PRMO 2019. You may use sequential hints to solve the problem.
Try this beautiful problem from combinatorics based on Regular Polygon from PRMO 2019. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2019 based on Greatest Integer. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1996 based on Parallelogram Problem.
Try this beautiful problem from PRMO, 2019, problem-12, based on Integer Problem. You may use sequential hints to solve the problem.
Try this beautiful problem from TOMATO useful for ISI B.Stat Entrance based on Graph in Calculus. You may use sequential hints to solve the problem.