NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.1 Binomial Theorem - PDF Download

NCERT solutions for class 11 maths chapter 7 exercise 7.1 Binomial Theorems are all about the binomial formula and binomial theorem for positive integral indices. Before solving ex 7.1, students need to understand a couple of points that follow from this theorem. Binomial theorem is the process of increasing the power of the sum of two or more binomial expressions. The coefficients of binomial expressions in the expansion process are called binomial coefficients. 

Class 11 maths chapter 7 exercise 7.1 NCERT solutions consists of 14 questions ranging from easy to medium. Students are able to gain a thorough understanding of the topics discussed in this chapter by referring to the NCERT solutions provided by subject experts of eSaral for class 11 maths chapter 7 ex 7.1. These solutions are available here in PDF format to help you with your studies. You can download the free PDF from the official website of eSaral to prepare for your exam. Download the PDF link from the link provided below.

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Topics Covered in Exercise 7.1 Class 11 Mathematics Questions

Ex 7.1 class 11 maths chapter 7 Binomial Theorem is based on the topics like binomial theorem for positive integral indices, binomial theorem for any positive integer n, and some special cases. eSaral’s experienced faculty have explained these topics in detail so that students can get a good grasp of each topic and solve questions related to these topics.

1. Binomial Theorem for Positive Integral Indices

It follows from the binomial theorem of positive integral indices that the total number of the terms in an expansion is one more than that of the index.

The Binomial Theorem has the following properties for positive integral indices.

The following are the main identities:

(a+ b)⁰ = 1          a + b ≠ 0

(a+ b)¹ = a + b

(a+ b)² = a² + 2ab + b²

(a+ b)³ = a³ + 3a²b + 3ab² + b³

(a+ b)⁴ = (a + b)³ (a + b) = a⁴ + 4a³b + 6a²b²+ 4ab³ + b⁴

In these expansions, we observe the following: 

(I) The total number of terms in the expansion is one more than the index.

(II) Powers of the first quantity ‘a’ go on decreasing by 1 whereas the powers of the second quantity ‘b’ increase by 1, in the successive terms.

(III) In each term of the expansion, the sum of the indices of a and b is the same and is equal to the index of a + b.

Pascal’s Triangle

The coefficients of the expansions are arranged in an array. This array is called Pascal’s triangle. Expansions for the higher powers of a binomial are also possible by using Pascal’s triangle.

2. Binomial theorem for any positive integer n

The binomial theorem for any positive integer n is 

$(a+b)^n={ }^n c_0 a^n+{ }^n c_1 a^{n-1} b+{ }^n c_2 a^{n-2} b^2+\ldots+{ }^n c_{n-1} a \cdot b^{n-1}+{ }^n c_n b^n$

3. Some special cases - You will also learn some special cases of binomial expansion by proving some identities and binomial expansion.

Tips for Solving Exercise 7.1 Class 11 Chapter 7 Binomial Theorem

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.1 The binomial theorem has various types of problems which you can solve if you follow the tips provided by subject experts of eSaral. Here are some of them.

1. Some questions are based on formulas so you must learn the binomial formula to solve these types of questions.
2. Some of the questions are more complex, like word problems. You need to figure out what the question is asking you to do and then do the calculations accordingly.
3. You must go through all the related theorems of binomial to build a strong foundation of the concepts.

Importance of Solving ex 7.1 Class 11 Maths Chapter 7 Binomial Theorem 

Students will get a lot of benefits of solving questions of ex 7.1 class 11 maths chapter 7 binomial theorem. eSara has provided some of the advantages of solving ex 7.1 chapter 7 that are mentioned below.

1. The NCERT solutions for class 11 math chapter 7 ex 7.1 are explained in a simple way that every student can understand.
2. Ex 7.1 class 11 maths ch 7 talks about binomial theorem for positive integral indices which is elaborated precisely by our expert faculty of eSaral. This will help you to solve questions with proper understanding.
3. NCERT solutions class 11 maths chapter 7 ex 7.1 includes important questions, examples and revision notes. By practicing these solutions and examples will improve your problem solving skills and boost your self-confidence.
4. These solutions are also available in PDF format which can be downloaded from the eSaral website and can be used for finding the answers accurately of all the questions asked in ex 7.1.

Frequently Asked Questions

Question 1. What is binomial theorem according to NCERT solutions class 11 maths chapter 7 ex 7.1?

Answer 1. The binomial theorem is defined as the algebraically process of expanding the power of the sum of two or more binomials. The coefficients of a binomial term in the expansion process are known as binomial coefficients. The introductory sections of these chapters provide accurate definitions of various aspects of the binomial theorems. Binomial theorem for class 11 NCERT solutions PDF can help students to study easily and update with all the information that may be included in their exams. Learning the binomial theorem concepts will be simpler with NCERT solutions PDF on eSaral.

Question 2. Do I have to solve all the questions provided in NCERT solutions class 11 maths chapter 7 ex 7.1?

Answer 2. Yes, it’s important to answer all questions because they cover a wide range of topics and concepts, which will help you get a good idea of what kind of questions you might be asked from these topics. These questions also assist you in understanding how different questions can be formulated from the same topic. Each question should be thoroughly practiced by you. You can find all the concepts and questions in step by step manner related to this exercise on the eSaral website.