Determinants Case Study Questions Class 12 Maths Chapter 4

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Last Updated on July 21, 2025 by XAM CONTENT

Hello students, we are providing case study questions for class Class 12 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 Class 12 Maths. In this article, you will find case study questions for cbse class Class 12 Maths chapter 4 Determinants.

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

Table of Contents

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Case Study Questions on Determinants

Case Study:
A school is conducting a mathematics quiz competition. There are three participants: Amit, Beena, and Carlos. The marks scored by them in three rounds are shown below:

\[ \begin{array}{|c|c|c|c|} \hline \text{Participant} & \text{Round 1} & \text{Round 2} & \text{Round 3} \\ \hline \text{Amit} & 5 & 7 & 6 \\ \text{Beena} & 8 & 5 & 9 \\ \text{Carlos} & 6 & 8 & 7 \\ \hline \end{array} \]

Let the matrix \( A \) represent the scores:

\[ A = \begin{bmatrix} 5 & 7 & 6 \\ 8 & 5 & 9 \\ 6 & 8 & 7 \end{bmatrix} \]

Calculate the determinant of matrix \( A \), denoted \( |A| \).
If the determinant represents the volume of a parallelepiped formed by the row vectors of \( A \), interpret the meaning of determinant being zero.
Is matrix \( A \) invertible? Justify your answer.
If Amit’s score in the third round changes to 8, form the new matrix \( B \) and calculate \( |B| \).

Solutions:

1. Calculate \( |A| \):

\[ |A| = \begin{vmatrix} 5 & 7 & 6 \\ 8 & 5 & 9 \\ 6 & 8 & 7 \end{vmatrix} \] \[ = 5 \begin{vmatrix} 5 & 9 \\ 8 & 7 \end{vmatrix} – 7 \begin{vmatrix} 8 & 9 \\ 6 & 7 \end{vmatrix} + 6 \begin{vmatrix} 8 & 5 \\ 6 & 8 \end{vmatrix} \] \[ = 5(5 \cdot 7 – 9 \cdot 8) – 7(8 \cdot 7 – 9 \cdot 6) + 6(8 \cdot 8 – 6 \cdot 5) \] \[ = 5(35 – 72) – 7(56 – 54) + 6(64 – 30) \] \[ = 5(-37) – 14 + 204 = -185 – 14 + 204 = \boxed{5} \]

2. Interpretation of zero determinant:
If \( |A| = 0 \), it means the row vectors of matrix \( A \) are linearly dependent, and the volume of the parallelepiped they form is zero. This implies the vectors lie in the same plane. Since \( |A| = 5 \neq 0 \), the volume is non-zero and the vectors are linearly independent.

3. Invertibility:
Matrix \( A \) is invertible if \( |A| \neq 0 \). Since \( |A| = 5 \), matrix \( A \) is invertible.

4. New matrix after correction:

\[ B = \begin{bmatrix} 5 & 7 & 8 \\ 8 & 5 & 9 \\ 6 & 8 & 7 \end{bmatrix} \]

Calculate \( |B| \):

\[ |B| = \begin{vmatrix} 5 & 7 & 8 \\ 8 & 5 & 9 \\ 6 & 8 & 7 \end{vmatrix} \] \[ = 5 \begin{vmatrix} 5 & 9 \\ 8 & 7 \end{vmatrix} – 7 \begin{vmatrix} 8 & 9 \\ 6 & 7 \end{vmatrix} + 8 \begin{vmatrix} 8 & 5 \\ 6 & 8 \end{vmatrix} \] \[ = 5(35 – 72) – 7(56 – 54) + 8(64 – 30) \] \[ = 5(-37) – 14 + 272 = -185 – 14 + 272 = \boxed{73} \]

We hope the given case study questions for Determinants Class Class 12 helps you in your learning.

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Topics from which case study questions may be asked

Determinants of a Square Matrix (Up to 3 × 3)
Properties of Determinants
Cofactors and Minors
Applications of Determinants:

Cramer’s Rule uses determinants to solve linear equations, making it a powerful tool in algebraic and geometric applications.

Frequently Asked Questions (FAQs) on Determinants 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 12 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 Determinants case study questions?

A12: We provide case study questions for CBSE Class 12 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.