Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Derivative of Function. Derivative of Function Problem (B.Stat Objective Question ) Let f(x)=x[x] where [x] denotes the greatest integer smaller than or equal to x where x is not an integer, what...

Try this beautiful problem from the Pre-RMO, 2017, Question 25, based on Area of a triangle. Area of triangles – PRMO 2017, Question 25 Let ABCD be a rectangle and let E and F be points on CD and BC respectively such that area (ADE) =16, area (CEF) =9, and area...

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1988 based on function. Function Problem – AIME I, 1988 For any positive integer k, let \(f_1(k)\) denote the square of the sum of the digits of k. For \(n \geq 2\), let...

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1988 based on Fibonacci sequence. Fibonacci sequence Problem – AIME I, 1988 Find a if a and b are integers such that \(x^{2}-x-1\) is a factor of \(ax^{17}+bx^{16}+1\)....

Try this beautiful problem from the Pre-RMO, 2017, Question 23, based on Solving Equation. Solving Equation – PRMO 2017, Question 23 Suppose an integer r, a natural number n and a prime number p satisfy the equation \(7x^{2}-44x+12=p^{n}\). Find the largest...