🧠 Top 10 Determinants Questions for CBSE Class 12 Board Exam 2025
Are you preparing for the CBSE Class 12 Maths Board Exam 2025? If yes, then mastering the chapter Determinants is a must. It’s not only scoring but also conceptually important for solving problems related to matrices, area of triangles, and properties of algebra.
Below are the Top 10 Determinants Questions selected carefully as per the rationalized syllabus and CBSE board exam pattern. These questions will boost your confidence and prepare you for the type of problems likely to appear in the final paper.
💡 Questions for Practice:
1. Evaluate:
| 1 2 3 |
| 4 5 6 |
| 7 8 9 |
| 1 2 3 |
| 4 5 6 |
| 7 8 9 |
2. If
A = | x 1 1 |
| 1 x 1 |
| 1 1 x |,
find A in terms of x.
| 1 x 1 |
| 1 1 x |,
find A in terms of x.
3. Prove using properties:
| a b c |
| b c a |
| c a b |
= (a + b + c)(a² + b² + c² − ab − bc − ca)
| a b c |
| b c a |
| c a b |
= (a + b + c)(a² + b² + c² − ab − bc − ca)
4. Check if the points (1, 2), (3, 6), and (5, 10) are collinear using determinants.
5. Find the area of triangle with vertices A(1,1), B(4,2), and C(2,3) using determinant method.
6. Show that if
| 1 a a² |
| 1 b b² |
| 1 c c² | = 0, then a, b, c are in A.P.
| 1 b b² |
| 1 c c² | = 0, then a, b, c are in A.P.
7. Find the value of λ for which the determinant vanishes:
| 1 1 1 |
| 2 3 4 |
| 3 5 λ |
| 1 1 1 |
| 2 3 4 |
| 3 5 λ |
8. Prove that if
| 1 x x² |
| 1 y y² |
| 1 z z² | = 0, then x, y, z are not distinct.
| 1 y y² |
| 1 z z² | = 0, then x, y, z are not distinct.
9. Without expanding, show that:
| a a a |
| b b b |
| c c c | = 0
| a a a |
| b b b |
| c c c | = 0
10. Evaluate using cofactor expansion:
| 2 -1 3 |
| 0 4 5 |
| 7 1 -2 |
| 2 -1 3 |
| 0 4 5 |
| 7 1 -2 |
📘 Tips for Scoring High in Determinants:
- Practice questions involving properties like row/column operations and factorization.
- Understand when a determinant is zero – often used to prove collinearity or dependence.
- Be fluent in expanding a 3×3 determinant using cofactor method.
- Revise the area of triangle formula using determinants regularly.
Consistent practice of such questions will help you tackle both MCQs and long-form problems with ease for solutions and queries, visit More-Marks.com.