A post on homological triangles... topic of our math camp August 2014 (in Scotland)
A post on homological triangles... topic of our math camp August 2014 (in Scotland)
a and b are two numbers having the same no. of digits and same sum of digits (=28). Can one be a multiple of the other? a is not equal to b. (courtesy Abhra Abir Kundu) Is $latex e^x-sinx $ a polynomial ? (courtesy Tias Kundu) Find the number of onto function from set A containing […]
This post contains an interesting problem from ISI BMath 2014 based on the jump of a frog and the lotus. Solve and enjoy this problem. Problem: Jump of a frog Problem n (> 1) lotus leafs are arranged in a circle. A frog jumps from a particular leaf by the following rule: It always moves […]
This is a problem from CMI Entrance 2014 based on Map from a power set to n-set. Problem: Map from a power set to n-set (1) Let A = {1, ... , k} and B = {1, ... , n}. Find the number of maps from A to B . (2) Define $latex \mathbf{ P_k […]
This is a problem from Chennai Mathematical Institute, CMI Entrance 2014 based on area of a region. Try to solve it. Problem: Area of a region $latex \mathbf{ A= {(x, y), x^2 + y^2 \le 144 , \sin(2x+3y) le 0 } } $ . Find the area of A. Discussion: $latex \mathbf{ x^2 + y^2 […]
Let $latex \mathbf{ x \in \mathbb{R} , x^{2014} - x^{2004} , x^{2009} - x^{2004} in \mathbb{Z} }$ . Then show that x is an integer. (Hint: First show that x is a rational number)Discussion: $latex \mathbf{ x^{2014} - x^{2004} - x^{2009} + x^{2004} = x^{2014} - x^{2009} = x^{2009}(x^{5} - 1 ) }$ is an […]
This post contains problem from Chennai Mathematics Institute, CMI 2014 B.Sc. Entrance Paper. Try to solve them out. Help us to add and rectify problems and solutions to this paper. We are collecting problems from student feed back. 4 Point Problems Find the minimum value for x for which $latex \mathbf{ 50!/ (24)^n }$ is […]
This post contains problem from Chennai Mathematics Institute, CMI BSc Math Entrance 2014 Model Problem set. In each problem you have to fill in 4 blanks as directed. Points will be given based only on the filled answer, so you need not explain your answer. Each correct answer gets 1 point and having all 4 […]
This is a problem from ISI BMath 2014 Subjective Solution based on Mulitple roots or Real root. Try to solve this problem. Problem: Multiple roots or real root Let $latex \mathbf { y = x^4 + ax^3 + bx^2 + cx +d , a,b,c,d,e \in \mathbb{R}}$. it is given that the functions cuts the x […]
Let PQR be a triangle. Take a point A on or inside the triangle. Let f(x, y) = ax + by + c. Show that $latex \mathbf { f(A) \le \max { f(P), f(Q) , f(R)} }$ Discussion: Basic idea is this: First we take A on a side, say PQ. We show $latex \mathbf […]
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on Right Rectangular Prism.
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 the American Invitational Mathematics Examination I, AIME I, 1995 based on Pyramid with Square base.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on Repeatedly Flipping a Fair Coin.
Try this beautiful problem from the Pre-RMO, 2019 based on Sum of digits. You may use sequential hints to solve the problem.
Try this beautiful problem from Geometry: Sectors in Circle from AMC-10A, 2012. You may use sequential hints to solve the problem
Try this beautiful problem from Algebra: Sum of whole numbers from AMC-10A, 2012. You may use sequential hints to solve the problem
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2009 based on Trigonometry Simplification. You may use sequential hints.
Try this beautiful problem from Geometry: Area of quadrilateral from AMC-10A, 2020. You may use sequential hints to solve the problem.