RD Sharma Class 11 Solutions Chapter 18 - Binomial Theorem (Ex 18.1) Exercise 18.1

The Binomial Theorem can be traced back to the 4th century B.C. and Euclid where one finds the formula for (a + b)². In the 3rd century B.C. the Indian mathematician Pingala introduced the “Pascal’s triangle” giving binomial coefficients in a triangle. Much later, in the 10th century A.D. Indian mathematician ‘Halayudha’ and the Persian mathematician ‘al-Karaji’ also derived similar results as did the 13-th century Chinese mathematician ‘Yang Hui’. 

A polynomial with two terms is generally called a binomial. The Binomial Theorem also known as the Binomial Expansion describes the algebraic expansion of powers of a binomial.

It is the method of expanding an expression that is raised to any finite power. The Binomial Theorem is a very  powerful tool of expansion, which finds its application in various streams of mathematics like algebra, probability  etc.

In the RD Sharma book for Class 11, the students are introduced to the Binomial Theorem. The properties of Binomial coefficients are introduced for easy understanding, after that various terms that are used in the Binomial Expansion are given lastly the Binomial theorem for any index is given with various exercises. Applications of Binomial Theorem and problems related to Binomial Theorem are given in the last section.

Use of Binomial Theorem

The Binomial theorem finds its application in numerous real life tasks. Some of the important uses of Binomial Theorem are listed below.

• The binomial theorem is widely used for Statistical purposes and Probability Analysis. It is very  useful as a tool for such tedious calculations as our economy depends on Statistical and Probability Analysis.

• In advanced mathematics and calculation, the Binomial Theorem is used in finding roots of equations in higher powers. Also, it is used for proving many important equations in physics and mathematics.

• The Binomial Theorem finds its heavy application in the Weather Forecast Services which is very important.

• It is used for ranking up candidates in large numbers.

• It is used in the field of Architecture, and also in estimating the cost of big engineering projects.

• In computing areas, the binomial theorem is very useful such as in the distribution of IP addresses to different computer systems. With the help of binomial theorem, the automatic distribution of IP addresses along with the distribution of virtual IP addresses is possible.

• Economists use the binomial theorem to count probabilities that depend on different factors to predict the way the economy will behave in the next few years. Binomial Theorem makes these predictions possible.

• In design of infrastructure. It allows engineers to calculate the size of the projects and deliver accurate estimates of not only the costs but also time required to construct them.