August 22, 2019 M CUBE: Math-e-Matics by Maheshwari INMO, INMO Do there exist three distant positive real numbers a,b,c such that the numbers a,b,c, b+c-a, a+b-c and a+b+c form a 7-term arithmetic progression in some order? INMO 2002
August 22, 2019August 22, 2019 M CUBE: Math-e-Matics by Maheshwari INMO, INMO Do there exists 100 lines in the plane, no three of them concurrent, such that they intersect exactly in 2002 points? INMO 2002
August 22, 2019September 20, 2019 M CUBE: Math-e-Matics by Maheshwari INMO, INMO Determine the least positive value taken by the expression a^3+b^3+c^3-3abc as a,b,c vary over all positive integers. Find also all triples (a,b,c) for which least value is attained INMO 2002
August 21, 2019 M CUBE: Math-e-Matics by Maheshwari INMO, INMO Let R denote the set of all real numbers. Find all functions f : R → R satisfying the condition f(x + y) = f(x)f(y)f(xy) for all x, y in R INMO 2001
August 21, 2019August 21, 2019 M CUBE: Math-e-Matics by Maheshwari INMO, INMO All possible 6 digit numbers, in each of which the digits occur in non-increasing order (from left to right, eg: 877550) are written as a sequence in increasing order. Find the 2005-th number in this sequence. INMO 2005
August 21, 2019August 21, 2019 M CUBE: Math-e-Matics by Maheshwari INMO Let M be the mid-point of side BC of a triangle ABC. Let the median AM intersect the in-circle of ABC at K and L, K being nearer to A than L. If AK=KL=LM, prove that the sides of the triangle ABC are in the ratio 5:10:13 in the same order. INMO 2005
August 21, 2019 M CUBE: Math-e-Matics by Maheshwari INMO Let ABC be a triangle and D be the mid-point of side BC. Suppose ∠DAB = ∠BCA and ∠DAC = 15 . Show that ∠ADC is obtuse. Further, if O is the circumcentre of ADC, prove that triangle AOD is equilateral. INMO 2001 OR OR
August 21, 2019 M CUBE: Math-e-Matics by Maheshwari INMO Show that the equation: x^2+y^2+z^2=(x-y)(y-z)(z-x) has infinitely many solutions in integers x,y,z. INMO 2001
M CUBE: MatheMatics by Maheshwari 