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 6 Permutation and Combinations.
| Chapter | Permutation and Combinations |
| 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 |
Case Study Questions on Permutation and Combinations
Case Study 1:A school library is arranging 5 different science books and 3 different maths books on a shelf. All science books must be together and all maths books must be together, but the block of science books and the block of maths books can be placed in any order.
Questions:
- In how many distinct ways can all the 8 books be arranged on the shelf under these conditions?
- If only the science books must be together (maths books can be anywhere), how many ways can the books be arranged?
1. Both science and maths books together (as groups):
Let the block of science books (\( S \)) and the block of maths books (\( M \)) each be considered as single items. They can be arranged in \( 2! \) ways (S-M or M-S). Within the science block, there are 5 books; so \( 5! \) ways. Within the maths block, \( 3! \) ways. \[ \text{Total ways} = 2! \times 5! \times 3! = 2 \times 120 \times 6 = 1,440 \]2. Only science books together:
Treat 5 science books as one block (\( S \)), so \( 3 + 1 = 4 \) items (block S and 3 maths books). These 4 items can be arranged in \( 4! \) ways. The 5 science books within their block can be arranged in \( 5! \) ways. \[ \text{Total ways} = 4! \times 5! = 24 \times 120 = 2,880 \]Case Study 2:
A teacher wants to form a committee of 4 students from a class of 10 boys and 8 girls. The committee must have at least 2 girls.
Questions:
- In how many ways can the committee be formed?
- In how many ways can the committee be formed if the committee must have exactly 2 girls?
1. At least 2 girls in the committee:
This can be broken into cases:Case I: 2 girls and 2 boys. \[ {8 \choose 2} \times {10 \choose 2} = 28 \times 45 = 1,260 \] Case II: 3 girls and 1 boy. \[ {8 \choose 3} \times {10 \choose 1} = 56 \times 10 = 560 \] Case III: 4 girls. \[ {8 \choose 4} = 70 \] Total ways: \[ 1,260 + 560 + 70 = \boxed{1,890} \]
2. Exactly 2 girls in the committee:
Choose 2 girls from 8 and 2 boys from 10: \[ {8 \choose 2} \times {10 \choose 2} = 28 \times 45 = \boxed{1,260} \]We hope the given case study questions for Permutation and Combinations Class 11 helps you in your learning.
Also check
- Sequences and Series Case Study Questions Class 11 Maths Chapter 8
- Binomial Theorem Case Study Questions Class 11 Maths Chapter 7
- Permutation and Combinations Case Study Questions Class 11 Maths Chapter 6
- Linear Inequalities Case Study Questions Class 11 Maths Chapter 5
- Complex Numbers and Quadratic Equations Case Study Questions Class 11 Maths Chapter 4
- Trigonometric Functions Case Study Questions Class 11 Maths Chapter 3
- Relations and Functions Case Study Questions Class 11 Maths Chapter 2
- Sets Case Study Questions Class 11 Maths Chapter 1
Topics from which case study questions may be asked
- Introduction to Permutations and Combinations
- Fundamental Principle of Counting
- Permutations – Definition and Formula
- Permutations of Objects (Distinct and Repeated)
- Factorial Notation and its Properties
- Circular Permutations
- Combinations – Definition and Formula
- Properties of Combinations
- Applications of Permutations and Combinations in Solving Problems
Frequently Asked Questions (FAQs) on Permutation and Combinations 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 “Permutation and Combinations” 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.
