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 AMC-10A, 2004 based on Triangle. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Points of Equilateral triangle.
Try this beautiful problem from the Pre-RMO, 2017 based on ratio and proportion. You may use sequential hints to solve the problem.
Try this beautiful problem from Number Theory based on largest possible value from AMC-10A, 2004. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Complex roots and equations.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Length and Inequalities.
Try this beautiful problem from the Pre-RMO, 2017 based on Trigonometry & natural numbers. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1994 based on Right angled triangle.
Try this beautiful problem from Probability: positive factors AMC-10A, 2003. You may use sequential hints to solve the problem
Try this beautiful problem from AMC 10A, 2007 based on Numbers on cube. You may use sequential hints to solve the problem.