This is a problem from Test of Mathematics, TOMATO problem 6. It is useful for ISI and CMI Entrance Exam. Problem : TOMATO Problem 6 Let $latex x_1 , x_2, ..... , x_{100} $ be positive integers such that $latex x_i + x_{i+1} = k $ for all $latex i $ where $latex k $ […]
This is a problem from Test of Mathematics, TOMATO Problem 106. It is useful for ISI and CMI Entrance Exam. Try out the problem. Problem: TOMATO Objective 106 The term that is independent of x in the expansion of $[\frac{3x^2}{2}-\frac{1}{3x}]^9 $ a) ${{9} \choose {6}}(\frac{1}{3})^3(\frac{3}{2})^6 $ b) ${{9} \choose {5}}(\frac{3}{2})^5(-\frac{1}{3})^4 $ c) ${{9} \choose {3}}(\frac{1}{6})^3 […]
We observe a renewed interest in Math and Basic Science in India after decades of engineering mania. This is a welcome change. The top tier students, in increasing numbers, are opting for such courses. In this article we present some of the institutes which offer world class education in basic science after school.
This is a problem from Test of Mathematics, TOMATO Objective 8, useful for ISI and CMI Entrance. Try out this problem. (by Rahul Roy) Problem: Two trains of equal length L,travelling at speeds v1 and v2 miles per hour in opposite directions,take t seconds to cross each other .then L in feet is: Solution: Total […]
This is a problem from TOMATO Objective 01 based on worker and wages. This problem is helpful for ISI Entrance Exam. Try out the problem. (By Akash Singha Roy) Problem: TOMATO Objective 01 A worker suffers a $20 $ % cut in wages. He regains his original pay by obtaining a rise of (A) $20 […]
This is a problem from TOMATO Objective 94 based on number of divisors. This problem is helpful for ISI Entrance Exam. Try out the problem. (By Akash Singha Roy) Problem: TOMATO Objective 94 Number of divisors of $ 2700 $ Solution: $ 2700 = 2^2 \times 3^3\times 5^2 $ Hence, any divisor of $2700 $ […]
This is a problem from TOMATO Objective 21 based on positive integers. This problem is helpful for ISI Entrance Exam. Try out the problem. Problem: TOMATO Objective 21 Suppose x & y are positive integers, x>y, and 3x+4y & 2x+3y when divided by 5, leave remainders 2&3 respectively. It follows that when (x-y) is divided […]
Let's understand one-one function and differentiability with the help of a problem. Try it yourself before reading the solution. Let f be real valued, differentiable on (a, b) and $ f'(x) \ne 0 $ for all $ x \in (a, b) $. Then f is 1-1. True Discussion: Suppose f is not 1-1. Then there […]
Lets understand direct product of two subgroups with the help of a problem. This problem is useful for College Mathematics.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Function of Complex numbers.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Squares and Triangles.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on A Parallelogram and a Line.
Try this beautiful problem from the Pre-RMO, 2019 based on Triangle and Integer. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2019 based on Area of Triangle and Integer. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2008 based on Cones and circle.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2001 based on Incentre and Triangle.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Smallest prime.
Try this beautiful problem from Geometry: Octahedron AMC-10A, 2006. You may use sequential hints to solve the problem
Try this beautiful problem from Probability in Coordinates from AMC-10A, 2003. You may use sequential hints to solve the problem.