## RD Sharma Solutions for Class 11 Maths Chapter 18 - Free PDF Download

## FAQs on RD Sharma Class 11 Maths Solutions Chapter 18 - Binomial Theorem

1. Why binomial theorem is used?

The binomial theorem (or binomial expansion) is a result of the expansion of the powers of binomials or sums of two terms. The theorem and its generalizations are used to prove results and solve problems in combinatorics, algebra, calculus, and many other areas of mathematics.

2. How do you expand the power of a binomial?

To expand the power of binomial we should use binomial expansion formula.

There are (n+1) terms in the expansion of (x+y)

^{n}The degree of each term is n.

The powers of x start with n and decrease to 0.

The powers of y start with 0 and increase to n.

The coefficients are symmetric.

3. What is the binomial expression?

A binomial expression is an algebraic expression containing two terms that are joined by either addition or subtraction sign. For example, (x + y) and (2 – x) are examples of binomial expressions.

4. What is the Binomial Theorem of class 11 of RD Sharma?

The binomial theorem was first mentioned in the 4th century BC by Euclids, a great Greek mathematician. The binomial theorem explains how to expand the algebraic statement (x + y)^{n} to a sum of terms using individual exponents of variables x and y. A numeric value called coefficient is assigned to each term in a binomial expansion.

The expanded value of an algebraic expression of the form (x + y)^{n} is found using the binomial theorem. Finding the value of (x + y)^{n}, (a + b + c)^{n} is simple and maybe done simply by multiplying the exponent value by the number of times. The binomial theorem, on the other hand, can be used to find the expanded version of (x + y)^{17} or other expressions with greater exponential values. This binomial theorem expansion's exponent value can be a fraction of a negative number. We restrict our explanations to only non-negative values in this case. Let's look at the terms and attributes of the coefficients in this binomial expansion in more detail.

5. What are the properties of Binomial Theorem according to Class 11 RD Sharma Chapter 18?

The properties of Binomial Theorem are

(n + 1) is the number of coefficients in the binomial expansion of (x + y)

^{n}.In the expansion of (x+y)

^{n}, there are (n+1) words.In the (x+y)

^{n}expansion, x^{n}and y^{n}are the first and last terms, respectively.The powers of x decline from n to 0 as the expansion progresses, while the powers of y grow from 0 to n.

The coefficients of binomial expansion are organized in a triangle known as Pascal's triangle. The binomial theorem formula summarizes the pattern that has emerged.

The r

^{th}term from the end of the binomial expansion of (x + y)^{n}equals (n – r + 2)^{th}term from the beginning.If n is even, the middle term in (x + y)

^{n}is (n/2)+1, but if n is odd, the middle terms are (n+1)/2 and (n+3)/2.

6. What is the importance of the RD Sharma solution of Chapter 18?

The RD Sharma Solutions Class 11 Chapter 18 Binomial Theorem is available for free download at Vedantu. Students can remove their questions and solve problems more quickly by practicing these solutions. Students can acquire new strategies for answering a question in a variety of ways, providing them with an advantage in exam preparation.

The study of fundamental topics such as Positive Integral Indices, Pascal's Triangle, Binomial theorem for any positive integer, and other special examples are covered in Chapter 18 of the Maths textbook. Students can easily achieve good exam scores by studying the RD Sharma Solutions for all of the problems in the textbook. Each problem is solved step by step, taking into account the pupils' level of knowledge. As a result, it's critical to comprehend the logic behind each answer and gain a greater understanding of the topics.

7. Is RD Sharma Solutions for Class 11 Maths Chapter 18 Binomial theorem available on Vedantu?

Yes. It is available On the Vedantu website. On our Vedantu website, students can find all of RD Sharma's class 11 Maths solutions, which can help them improve their exam marks. Solutions will teach you how to use a formula, and with enough practice, you'll be able to apply it to your work. They can be downloaded for free in PDF format by students. All students will benefit from Vedantu's supplemental study aids, which will help them better understand formulas and concepts as well as practice. For students who want to clarify their concerns and improve their learning, there are live sessions with subject specialists as well as doubt clearing sessions.

8. Is chapter 18- Binomial Theorem of RD Sharma, important for class 11 students?

The Binomial Theorem is a simple approach to expand a binomial statement with big powers (that are raised to). This theorem has applications in Permutations and Combinations, Probability, Matrices, and Mathematical Induction, and is a very important topic (part) in algebra. This theorem is very significant for you if you are studying for competitive tests for university admission or jobs because it is a basic and important area of algebra. This chapter will teach you a shortcut for finding (x + y)n without having to multiply the binomial by itself n times.

Some real-life applications of the binomial theorem are-

In Statistical and Probability Analysis, the binomial theorem is frequently employed.

The Binomial Theorem is used in advanced mathematics and calculating to determine the roots of equations in higher powers.

It's also used to prove a lot of significant physics and math equations.

It is quite beneficial, as our economy is heavily reliant on statistical and probability analyses.