1.1 Some Corner Cases We’ve almost covered the essence of combinatorics that are needed at a beginner’s level to start studying this beautiful topic. This will be the last editorial of this module for those of you who’d not like to pursue any advanced studies in this chapter. There’ll be another editorial on this topic… Continue reading
Tag: Engineering
Week -11 | Combinatorics – 2
1.1 Basic Cases and Circular Permutations In the last lecture we considered the basic concepts of permutations and combinations. Let’s consider a couple of examples further to ease the process of understanding these. Ex -1 Find the number of permutations of the word ‘TRIANGLE’. How many of these permutations start with ‘T’ and end with… Continue reading
Week – 10 | Combinatorics – 1
1.1 Introduction Combinatorics, in a way, deals with the art of counting, and thus, a lot of problems in this regard will be dealing with counting the number of arrangements of a particular sequence. As trivial as it may sound, this branch of mathematics has been widely used in various fields like economics, physics and… Continue reading
Week – 10 | Inequalities – 4
Q-1) For the minimum value of is __ Q-2) If be the sides of a triangle, then the minimum value of is a) b) c) d) Q-3) For positive reals , is always a) b) c) d) Q-4) For positive reals in H.P which of the follwing… Continue reading
Week -9 | Inequalities – 3
Q-1) Define with for . Show that for all positive integers Solution: Using the AM-HM Inequality we have The RHS on simplification becomes . This is known as the famous Nesbitt’s Inequality Q-2) Find the maximum value of with . Solution: Set and . We thus have , and we need the maximum value of . Applying the… Continue reading