Important Practice Problems for CBSE Class 12 Maths Chapter 4: Determinants
FAQs on Important Questions for CBSE Class 12 Maths Chapter 4 - Determinants 2024-25
1. What are the most important questions from Chapter 4 Determinants for CBSE Class 12 as per the 2025-26 syllabus?
- Evaluate 3x3 determinants using properties and expansion.
- Solve linear equations using Cramer's rule for unique solutions.
- Prove specific determinant identities such as the value being zero when rows or columns are identical.
- Application-based HOTS: If a determinant has two rows proportional, what is its value? Justify.
- Find the area of a triangle using determinants given its vertex coordinates.
2. Which topics carry the highest mark weightage in Determinants for the Class 12 board exam?
As per CBSE 2025-26, high-weightage topics in Determinants include:
- Properties and evaluation of 3x3 determinants (3–5 mark questions)
- Application of determinants in solving linear equations (Cramer’s Rule, 4–5 mark questions)
- Area problems using determinants (3-mark)
- Miscellaneous conceptual and proof-based questions (up to 5 marks)
3. What are the conceptual traps students should avoid when solving Class 12 Determinant questions?
Common mistakes include:
- Incorrect sign usage during cofactor expansion.
- Failing to apply properties (like row/column operations) correctly in proofs.
- Assuming a determinant is always non-zero; ignoring the cases of proportional rows/columns.
- Mixing up area formulae when using coordinates.
4. How can students identify frequently asked or expected 5-mark questions from Determinants for CBSE Class 12?
- Review previous years’ board papers and recent sample papers for pattern.
- Look for questions on proof of properties, system of equations, and application-based HOTS.
- Practice questions involving error-spotting in determinants and Cramer’s rule.
- Vedantu’s important questions always tag likely 5-mark problems as per the latest CBSE guidelines.
5. What higher-order thinking skills (HOTS) questions are common in CBSE Class 12 Determinants?
HOTS problems often require:
- Justifying why a determinant is zero, using properties.
- Modifying or constructing new determinants to meet given conditions.
- Comparing methods (expansion vs. property-based) for efficiency.
- Applying determinant results to non-mathematical situations (geometry, physics, economics).
6. Why is understanding the properties of determinants critical for Class 12 exams?
Properties simplify calculation, help prove identities, and are key in solving systems of equations quickly—frequent in 3–5 mark CBSE questions. Mastery ensures faster problem-solving and accuracy under exam pressure.
7. What are common misconceptions students have about Determinants in CBSE 12th Maths?
- Assuming determinant and matrix mean the same (they do not).
- Believing row/column swaps do not affect value—when they change sign.
- Misapplying properties not valid for non-square matrices.
- Thinking determinants always produce unique solutions for equations.
8. How can students maximize scores in Determinants questions during boards?
- Practice each property separately and then in combination.
- Write all steps clearly, especially for expansion and Cramer’s Rule.
- Attempt section-wise important questions as per 2025-26 pattern.
- Focus revision on proof-based and concept-application questions.
9. What are the expected 3-mark questions in Determinants for Class 12 CBSE?
Common 3-markers include:
- Evaluating a 3x3 determinant
- Verifying determinant properties with examples
- Finding area of triangle using coordinates and determinants
10. How are determinants used to solve real-life problems as per NCERT Class 12 syllabus?
- Solving systems of linear equations in business, physics, and engineering
- Calculating area/volume in geometry using coordinates
- Decision-making in economics via input-output models
- Analyzing circuits in electrical engineering
11. What mistakes to avoid in determinant-based application questions in CBSE Class 12?
- Not checking for zero determinants in system of equations—could lead to no or infinite solutions.
- Misplacing sign or value in expansion.
- Neglecting conditions for unique solution (determinant ≠ 0).
12. How should students approach proof-based questions in Determinants for CBSE boards?
First, recall and state the relevant property, then apply it stepwise to the given matrix, ensuring every logical step is shown. Always mark the change/step that leads to the conclusion.
13. What are the exam trends for Determinants important questions in recent CBSE Class 12 board papers?
- Focus on proof of properties and application in equations.
- Increased presence of HOTS and real-life based questions in 3–5 mark ranges.
- Mix of computation and theory, stressing clarity and logical steps.
14. If a determinant of a matrix equals zero, what does it imply for the corresponding system of equations?
It means the system does not have a unique solution: there are either infinitely many solutions or no solution, as per CBSE 2025-26 board logic.
15. What property allows you to conclude a determinant is zero if two rows are equal?
Property of identical rows/columns: If any two rows or columns of a determinant are identical, the value of the determinant is zero. This is frequently tested in 2- and 3-mark questions.
