NCERT Solutions for Class 11 Maths Chapter 7 Binomial Theorem - PDF Download
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NCERT solutions for class 12 maths chapter 7 are based on Binomial theorem. The binomial theorem is used to assess the numerical values of a number that has been raised to a very high exponent. This chapter is based on the principle that as the index of the expansion increases, the value of the expressions follows a certain formula. In NCERT solutions of chapter 7 students are also introduced to the concept of Pascal's triangle. eSaral's subject experts have solved all the questions and explained all the topics to this chapter in NCERT solution. These solutions are available for free to download at eSaral.
Chapter 7 of class 11 maths covers fundamental topics such as positive integral measures, Pascal's triangle, Binomial theorem for any positive number and certain special cases.
By practicing NCERT solutions for every question in chapter 7, Students can easily achieve high scores in the exams. Each solution is implemented in an easy to understand way, taking into account the level of comprehension of the students.Therefore, it is essential to understand the logic behind each solution and to gain a better grasp of the concepts.
Important Topics covered in Chapter 7 - Binomial Theorem
NCERT solutions for class 11 maths chapter 7 defines the application of binomial theorem. chapter 7 for class 11 maths covers topics like expanding expressions using a binomial theorem and finding a general term and the middle term of an exponential expression.
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7.1 Introduction |
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7.2 Binomial Theorem for Positive Integral Indices |
7.2.1 Binomial Theorem for any Positive Integer n 7.2.2 Some special cases |
7.1 Introduction - The Binomial Theorem is presented to the students as a fundamental concept. It begins with a few examples and definitions so that students can get familiar with solving simple equations before moving on to complex sums.
7.2 Binomial Theorem for Positive Integral Indices
7.2.1 Binomial Theorem for any Positive Integer n
7.2.2 Some special cases
In this section of NCERT Solutions Binomial Theorem, students learn about the different types of expansion.
You need to know about positive integral indices. The binomial theorem shows how many terms are left after expanding (x+a) to the power of n is (n+1).
You will learn how to use different formulas. Referring to the examples mentioned in NCERT solutions provided by eSaral’s subject experts will help you to understand the lesson better.
NCERT Solutions for Class 11 Maths Chapter 7 Exercises
This chapter contains a total of two exercises, including the Miscellaneous exercise.
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Exercise 7.1 |
14 Questions & Solutions |
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Miscellaneous Exercise |
6 Questions & Solutions |
Benefits of Downloading The NCERT Solutions for Class 11 Maths Chapter 7 - Binomial Theorem
NCERT solutions for class 11 chapter 7 Binomial Theorem are a great resource for students who want to do well in their studies. Here, we will discuss the various benefits of downloading and using these solutions.
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NCERT solutions for class 11 maths chapter 7 provide step-wise explanations for all the questions, which helps students to comprehend the concepts clearly.
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The questions in these exercises are presented in an easy and step-wise manner, so you can understand it easily.
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The NCERT solutions for class 11 maths chapter 7 are presented in a straightforward and simple language, enabling students to comprehend the material.
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The NCERT solutions cover various practical problems related to various aspects of Binomial Theorem. By solving these problems, students can improve their problem solving skills and build confidence in their ability to solve similar challenges in exams.
Frequently Asked Questions
Find answers to common questions.
What is the Binomial Theorem in simple terms?
The Binomial Theorem is a formula that expands expressions of the form (a + b)ⁿ into a sum of terms. Each term is of the form ⁿCᵣ · aⁿ⁻ʳ · bʳ. It works for all positive integer values of n and removes the need for repeated manual multiplication. The binomial coefficients in the expansion match the entries in Pascal's triangle.
How many exercises are in Class 11 Maths Chapter 7?
Class 11 Maths Chapter 7 contains two exercises: Exercise 7.1 with 14 questions covering basic expansion and coefficient problems, and one Miscellaneous Exercise with 6 questions testing general term, middle term, and application-based problems. Completing both exercises is important for board exams and JEE Main preparation.
What is the general term in binomial expansion?
The general term of the expansion (a + b)ⁿ is T\_{r+1} = ⁿCᵣ · aⁿ⁻ʳ · bʳ, where r = 0, 1, 2, … n. This formula lets you find any specific term directly without expanding the full expression. Substitute the required value of r to get the term, and set the power of a variable to zero to find the term independent of that variable.
How do I find the middle term in a binomial expansion?
If n is even, there is one middle term: T\_{(n/2)+1}. If n is odd, there are two middle terms: T\_{(n+1)/2} and T\_{(n+3)/2}. Identify n first, check whether it is odd or even, then apply the general term formula with the appropriate value of r. This is a standard 3-mark question in CBSE Class 11 board exams.
What is Pascal's Triangle and how is it related to the Binomial Theorem?
Pascal's triangle is a triangular arrangement of numbers where each entry is the sum of the two entries directly above it. The nth row (starting from row 0) gives the binomial coefficients ⁿC₀, ⁿC₁, ⁿC₂, … ⁿCₙ for the expansion (a + b)ⁿ. It provides a fast visual method to write expansion coefficients for small values of n without computing factorials.