Last Updated on April 21, 2025 by XAM CONTENT
Hello students, we are providing assertion reason questions for class 12. Assertion Reason questions are the new question format that is introduced in CBSE board. The resources for assertion reason questions are very less. So, to help students we have created chapterwise assertion reason questions for class 12 maths. In this article, you will find assertion reason questions for CBSE Class 12 Maths Chapter 4 Determinants. It is a part of Assertion Reason Questions for CBSE Class 12 Maths Series.
| Chapter | Determinants |
| Type of Questions | Assertion Reason Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 12 |
| Subject | Maths |
| Useful for | Class 12 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 12 Maths Chapterwise Assertion Reason |
Assertion Reason Questions on Determinants
Directions: Each of the following questions consists of two statements: an Assertion (A) and a Reason (R). Answer them by selecting the correct option:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.
Q1. Assertion (A): If a determinant has two identical rows, its value is zero.
Reason (R): Interchanging two rows of a determinant changes its sign.
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Difficulty Level: Moderate
Q2. Assertion (A): If the rows and columns of a $3 \times 3$ determinant are multiplied by a constant $k$, the determinant is multiplied by $k^6$.
Reason (R): When all rows and all columns are multiplied by a scalar $k$, the determinant is multiplied by $k^n$, where $n$ is the order of the determinant.
Answer: (c) A is false, but $R$ is true.
Difficulty Level: Tough
Q3. Assertion (A): If $A$ is a singular matrix, then $A^{-1}$ does not exist.
Reason (R): A matrix is singular if its determinant is zero.
Answer: (a) Both $A$ and $R$ are true, and $R$ is the correct explanation of $A$.
Difficulty Level: Moderate
Q4. Assertion (A): If $\operatorname{adj}(A)=0$, then matrix $A$ must be singular.
Reason (R): A matrix has no inverse if its adjugate is the zero matrix.
Answer: (b) Both A and $R$ are true, but $R$ is not the correct explanation of $A$.
Difficulty Level: Moderate
Q5. Assertion (A): The value of a determinant remains unchanged if each element of a row is replaced by the sum of itself and a multiple of the corresponding elements of another row.
Reason (R): A row operation that adds a multiple of one row to another does not change the value of a determinant.
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Difficulty Level: Tough
Also check
- Probability Class 12 Assertion Reason Questions Maths Chapter 13
- Linear Programming Class 12 Assertion Reason Questions Maths Chapter 12
- Three Dimensional Geometry Class 12 Assertion Reason Questions Maths Chapter 11
- Vectors Class 12 Assertion Reason Questions Maths Chapter 10
- Differential Equations Class 12 Assertion Reason Questions Maths Chapter 9
- Applications of the Integrals Class 12 Assertion Reason Questions Maths Chapter 8
- Integrals Class 12 Assertion Reason Questions Maths Chapter 7
- Applications of Derivatives Class 12 Assertion Reason Questions Maths Chapter 6
- Continuity and Differentiability Class 12 Assertion Reason Questions Maths Chapter 5
- Determinants Class 12 Assertion Reason Questions Maths Chapter 4
- Matrices Class 12 Assertion Reason Questions Maths Chapter 3
- Inverse Trigonometric Functions Class 12 Assertion Reason Questions Maths Chapter 2
- Relations and Functions Class 12 Assertion Reason Questions Maths Chapter 1
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Topics from which assertion reason questions may be asked
- Determinant Properties
- Area of Triangle
- Cramer’s Rule
- Inverse using Adjoint
Determinants are essential in finding matrix properties and solving linear systems.
Assertion reason questions from the above given topic may be asked.
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Frequently Asked Questions (FAQs) on Determinants Assertion Reason Questions Class 12
Q1: What does the chapter ‘Determinants’ cover?
A1: It builds key concepts related to determinants and prepares you for logical reasoning-based questions.
Q2: What are assertion reason questions?
A2: These consist of two statements: an assertion and a reason. Students need to determine their correctness and relationship.
Q3: Why practice assertion reason questions in Determinants?
A3: They strengthen core concepts and boost confidence in tackling tricky scenarios from determinants.
Q4: Are assertion reason questions part of CBSE board exams?
A4: Yes, they are included under competency-based formats to test depth of understanding.
