5. Why is finding the r-th term from the end of (a+b)n equivalent to finding the (n-r+2)-th term from the beginning?

This is a shortcut used frequently in RD Sharma solutions to simplify problems. The equivalence exists because of the symmetry of binomial coefficients. The expansion of (a+b)n is symmetric. The coefficients from the beginning (nC0, nC1, ...) are the same as the coefficients from the end (nCn, nCn-1, ...). The r-th term from the end of (a+b)n is the same as the r-th term from the beginning of (b+a)n. By calculation, this corresponds exactly to the (n-r+2)-th term from the beginning of the original expansion (a+b)n, saving you from expanding the whole expression backwards.

RD Sharma Solutions

RD Sharma Class 11 Maths Solutions Chapter 18 - Binomial Theorem

RD Sharma Class 11 Maths Solutions Chapter 18 - Binomial Theorem

Q: 2. What are the key steps to find the general term (Tr+1) in a binomial expansion using the method from RD Sharma Solutions?

To find the general term in the expansion of (x + a)n, RD Sharma solutions follow these steps:Identify the values of 'x', 'a', and 'n' from the given binomial expression.Apply the general term formula: Tr+1 = nCr xn-r ar.Substitute the values of x, a, and n into this formula. The resulting expression is the general term, which can be used to find any term in the expansion by putting in the appropriate value for 'r'.

Q: 3. What is the correct method to determine if a binomial expansion has one or two middle terms, as explained in RD Sharma solutions?

The number of middle terms in the expansion of (x + a)n depends on the value of the index 'n'. The method is as follows:If 'n' is even, there is only one middle term, which is the (n/2 + 1)th term.If 'n' is odd, there are two middle terms: the ((n+1)/2)th term and the ((n+3)/2)th term.RD Sharma solutions use this logic as the first step before calculating the middle term(s).

Q: 7. What is a common mistake when finding a specific term versus its binomial coefficient in Chapter 18 exercises?

A very common pitfall is confusing the 'term' with its 'binomial coefficient'. For the general term Tr+1 = nCr xn-r ar:The binomial coefficient is only the nCr part.The term is the entire expression, including the coefficient and the variables with their powers.When a question asks for the '5th term', you must provide the complete value. If it asks for the 'coefficient of the 5th term', you provide just the numerical coefficient after simplification.

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

The RD Sharma Class 11 Maths Chapter 18 PDF files contain all the important concepts related to the Binomial Theorem. The RD Sharma Solutions for the Chapter - Binomial Theorem are developed by our experienced faculty team at Vedantu. The solutions are created with step-by-step explanations to clarify students’ doubts and also guide them for solving problems confidently. This helps in improving their problem-solving skills, which is important from the examination point of view. For students who wish to learn the right steps of solving such problems, the RD Sharma Solutions of Class 11 Maths Chapter 18 is made available in pdf format. Students can easily download the pdf from the links provided below which is easily accessible.

Class 11 RD Sharma Textbook Solutions for Chapter 18 - Binomial Theorem

An algebraic expression that contains two terms is called a binomial expression. Following are the concepts discussed in this chapter.

Binomial theorem for positive integral index.
Some important conclusions from the binomial theorem.
How to find the general term and middle terms of a binomial expansion.

RD Sharma Solutions for Class 11 Maths Chapter 18 - Binomial Theorem are offered here to help students gain a better understanding of the concepts. Our best faculty team at Vedantu prepared the RD Sharma Class 11 Maths Solutions intending to resolve student doubts as quickly as possible. These solutions also offer students advice on how to solve problems confidently, which aids in the development of their problem-solving abilities, which is critical for exam success.

Exercises in RD Sharma Solutions of Class 11 Maths Chapter 18

The RD Sharma Solutions provide step-by-step solutions to the questions in each of the two exercises in Chapter 18 – Binomial Theorem. Students who want to learn how to solve problems in a simple and systematic way can download RD Sharma Solutions in PDF format for the 2024-25 syllabus.

Exercise 18.1

Exercise 18.2

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

1. How do Vedantu's RD Sharma Solutions for Class 11 Maths Chapter 18 help in solving the exercises?

Vedantu's RD Sharma Solutions for Chapter 18, Binomial Theorem, provide step-by-step methods for every problem in the textbook. They are designed to help you understand the correct approach for different types of questions, from finding a specific term to expanding complex binomials, ensuring your methodology aligns with the CBSE 2025-26 curriculum standards.

2. What are the key steps to find the general term (T_r+1) in a binomial expansion using the method from RD Sharma Solutions?

To find the general term in the expansion of (x + a)ⁿ, RD Sharma solutions follow these steps:

Identify the values of 'x', 'a', and 'n' from the given binomial expression.
Apply the general term formula: T_r+1 = ⁿC_r x^n-r a^r.
Substitute the values of x, a, and n into this formula. The resulting expression is the general term, which can be used to find any term in the expansion by putting in the appropriate value for 'r'.

3. What is the correct method to determine if a binomial expansion has one or two middle terms, as explained in RD Sharma solutions?

The number of middle terms in the expansion of (x + a)ⁿ depends on the value of the index 'n'. The method is as follows:

If 'n' is even, there is only one middle term, which is the (n/2 + 1)^th term.
If 'n' is odd, there are two middle terms: the ((n+1)/2)^th term and the ((n+3)/2)^th term.

RD Sharma solutions use this logic as the first step before calculating the middle term(s).

4. What is the step-by-step process to find the term independent of 'x' in a binomial expansion, as shown in RD Sharma solutions?

Finding the term independent of 'x' means finding the term where the power of 'x' is zero. The standard method used in the solutions is:

Step 1: Write the formula for the general term, T_r+1 = ⁿC_r x^n-r a^r.
Step 2: Simplify the expression to collect all powers of 'x' into a single term, like x^k, where 'k' is an expression involving 'r'.
Step 3: Set the resulting exponent of 'x' to zero (i.e., k = 0) and solve for 'r'.
Step 4: Substitute this integer value of 'r' back into the general term formula to find the required term.

5. Why is finding the r-th term from the end of (a+b)ⁿ equivalent to finding the (n-r+2)-th term from the beginning?

This is a shortcut used frequently in RD Sharma solutions to simplify problems. The equivalence exists because of the symmetry of binomial coefficients. The expansion of (a+b)ⁿ is symmetric. The coefficients from the beginning (ⁿC₀, ⁿC₁, ...) are the same as the coefficients from the end (ⁿC_n, ⁿC_n-1, ...). The r-th term from the end of (a+b)ⁿ is the same as the r-th term from the beginning of (b+a)ⁿ. By calculation, this corresponds exactly to the (n-r+2)-th term from the beginning of the original expansion (a+b)ⁿ, saving you from expanding the whole expression backwards.

6. What key properties of the binomial expansion are essential for solving the problems in RD Sharma Class 11 Chapter 18?

To effectively solve problems in this chapter, you must be familiar with these properties:

The total number of terms in the expansion of (a+b)ⁿ is n+1.
The sum of the powers of 'a' and 'b' in any term is always equal to n.
The binomial coefficients (ⁿC_r) equidistant from the beginning and the end are equal, i.e., ⁿC_r = ⁿC_n-r.
The sum of all binomial coefficients is 2ⁿ.

7. What is a common mistake when finding a specific term versus its binomial coefficient in Chapter 18 exercises?

A very common pitfall is confusing the 'term' with its 'binomial coefficient'. For the general term T_r+1 = ⁿC_r x^n-r a^r:

The binomial coefficient is only the ⁿC_r part.
The term is the entire expression, including the coefficient and the variables with their powers.

When a question asks for the '5th term', you must provide the complete value. If it asks for the 'coefficient of the 5th term', you provide just the numerical coefficient after simplification.

8. How is Pascal's Triangle related to the binomial coefficients (ⁿC_r) used in RD Sharma solutions?

Pascal's Triangle is a visual representation of binomial coefficients. Each entry in the triangle is a value of ⁿC_r. While it is a useful tool for finding coefficients for small powers of n (e.g., n=2, 3, 4) quickly, it becomes impractical for larger powers. RD Sharma solutions primarily use the formula ⁿC_r = n! / (r!(n-r)!) because it is a more powerful and general method that works for any value of 'n' and 'r' encountered in Class 11 exam problems.