Binomial Theorem is one of the easiest and important chapters of Algebra in the syllabus of IIT JEE, AIEEE and other engineering examinations. The beginners sometimes find it difficult as this topic is very new to them. The other reason is that the concepts of Combinations are also used in Binomial Theorem. This chapter can be said to be one of the easiest as it has very few twists and turns.
This chapter deals with the fundamental concepts of Binomial theorem as developed from elementary ideas. Binomial theorem deals with expansion of two terms with respect to any index. However, according to IIT JEE syllabus, we will deal with index of positive integer specially. The applications of Binomial Theorem are rampant in almost every part of Algebra in general and Permutation and Combination and Probability in particular.
The chapter begins with the Introduction to Binomial Theorem which is followed by the Properties of the Binomial Theorem. Binomial Coefficients are the most important topic of Binomial theorem. The sum of the Binomial coefficients, the coefficient of a particular term, greatest Binomial coefficient etc. has been discussed at length. However, some important results have been given at the end which is supplemented by the application of Binomial Expression. Solved examples as usual are very useful as they can reappear in the examination with slight modification.
Topics Covered under Binomial Theorem for a positive integral index are:-
Binomial Theorem is important from the perspective of scoring high in IIT JEE as there are few fixed pattern on which a number Multiple Choice Questions are framed on this topic. If we consider the chapters of Binomial Theorem, Permutations and Combinations, and Probability together we can say that a good understanding of the concept can help a student to get 10-20 marks varying from one examination to the other. AIEEE and other engineering examinations definitely have 3-5 questions every year directly or indirectly based on these topics. It is very important to master these concepts at early stage as this forms the basis of your preparation for IIT JEE and AIEEE.