Binomial Theorem Case Study Questions Class 11 Maths Chapter 7

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Last Updated on July 22, 2025 by XAM CONTENT

Hello students, we are providing case study questions for class 11 Maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 11 Maths. In this article, you will find case study questions for cbse class 11 Maths chapter 7 Binomial Theorem.

Chapter	Binomial Theorem
Type of Questions	Case Study Questions
Nature of Questions	Competency Based Questions
Board	CBSE
Class	11
Subject	Maths
Useful for	Class 12 Studying Students
Answers provided	Yes
Difficulty level	Mentioned
Important Link	Class 11 Maths Chapterwise Case Study

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Case Study Questions on Binomial Theorem

Case Study:
A research team is developing a new algorithm, and its efficiency in processing data is given by the expansion of \( (1 + 2x)^6 \). They are especially interested in certain coefficients for analyzing data patterns. The value of \( x \) can be set experimentally to tune the algorithm.

Questions:

Write the general term (\( T_{r+1} \)) in the expansion of \( (1 + 2x)^6 \) and find the coefficient of \( x^3 \).
Find the middle term(s) in the expansion and provide their values.
If the sum of coefficients in the expansion is interpreted as the algorithm’s total performance score, what is its value? Give justification.
If the coefficient of \( x^k \) is 240, find the value(s) of \( k \).

Solutions:

1. General term and coefficient of \( x^3 \):

\[ T_{r+1} = {6 \choose r} (1)^{6 – r} (2x)^r = {6 \choose r} 2^r x^r \] For \( x^3 \), set \( r = 3 \): \[ T_4 = {6 \choose 3} 2^3 x^3 = 20 \times 8\, x^3 = 160\, x^3 \] So, the coefficient of \( x^3 \) is \(\boxed{160}\).

2. Middle term(s) in the expansion:

Since the power is 6 (even), there are two middle terms: \( \left(\frac{6}{2}+1\right)^{th} \) and \( \left(\frac{6}{2}\right)^{th} \) terms, i.e., 4th and 3rd terms (\( T_4 \) and \( T_3 \)). – For \( r = 2 \): \[ T_3 = {6 \choose 2} 2^2 x^2 = 15 \times 4\, x^2 = 60\, x^2 \] – For \( r = 3 \): \[ T_4 = 160\, x^3 \text{ (already found)} \] So, the middle terms are \( 60x^2 \) and \( 160x^3 \).

3. Sum of coefficients (set \( x = 1 \)):

Sum of coefficients is the value of the expansion at \( x = 1 \): \[ (1 + 2 \times 1)^6 = 3^6 = \boxed{729} \]

4. If the coefficient of \( x^k \) is 240, find possible \( k \):

Coefficient of \( x^k \) in the expansion is \( {6 \choose k} 2^k \). Set equal to 240: \[ {6 \choose k} 2^k = 240 \] Try \( k = 4 \): \[ {6 \choose 4} 2^4 = 15 \times 16 = 240 \] So, \[ \boxed{k = 4} \]

We hope the given case study questions for Binomial Theorem Class 11 helps you in your learning.

Also check

Topics from which case study questions may be asked

Introduction to Binomial Theorem
Binomial Theorem for Positive Integral Indices
General Term in the Binomial Expansion
Middle Term(s) in the Expansion
Properties and Applications of Binomial Coefficients
Pascal’s Triangle
Simple Applications of Binomial Theorem in Problems

Frequently Asked Questions (FAQs) on Binomial Theorem Case Study Questions

Q1: What is a case study question in mathematics?

A1: A case study question in mathematics is a problem or set of problems based on a real-life scenario or application. It requires students to apply their understanding of mathematical concepts to analyze, interpret, and solve the given situation.

Q2: How should students tackle case study questions in exams?

A2: To tackle case study questions effectively, students should:
Read the problem carefully: Understand the scenario and identify the mathematical concepts involved.
Break down the problem: Divide the case study into smaller parts to manage the information better.
Apply relevant formulas and theorems: Use the appropriate mathematical tools to solve each part of the problem.

Q3: Why are case study questions included in the Class 11 Maths curriculum?

A3: Case study questions are included to bridge the gap between theoretical knowledge and practical application. They help students see the relevance of what they are learning and prepare them for real-life situations where they may need to use these mathematical concepts.

Q4: Are there any online resources or tools available for practicing “Binomial Theorem” case study questions?

A12: We provide case study questions for CBSE Class 11 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.