Top 12 Determinants Questions for Class 12 Board Exam – CBSE 2025
Looking for the best questions on Determinants for Class 12 CBSE Maths Board Exam 2025? You’re in the right place! This post features a curated list of the 12 most important and exam-relevant questions based on the rationalised syllabus of 2025. These questions are tailored to cover all essential concepts — from cofactor expansion to inverse using adjoint — and include a variety of 1-mark, 2-mark, 4-mark, and 6-mark types.
Why Practice Determinants Thoroughly?
Determinants play a crucial role in solving systems of linear equations, understanding properties of matrices, and computing the inverse of a matrix. The CBSE Class 12 Board exam often includes 5 to 7 marks worth of questions from this topic alone.
🔢 Practice Questions – Categorized by Marks
🟢 1-Mark Questions
| 1 2 3 | | 0 1 4 | | 0 0 1 |
A = | a b |
| c d |,
then prove that: det(kA) = k² × det(A).
🟡 2-Mark Questions
x if
| x 1 1 | | 1 x 1 | | 1 1 x | = 0
A = | 1 2 |
| 3 4 |
Find the adjoint of matrix A.
🔵 4-Mark Questions
| a b c | | b c a | | c a b |
| 2 3 1 | | 0 1 4 | | 5 2 0 |
| a b a+b | | c d c+d | | e f e+f | = 0
🔴 6-Mark Questions
A = | 2 1 3 |
| 1 0 2 |
| 3 2 4 |
using the adjoint method.
| x x² 1 | | y y² 1 | | z z² 1 | = (y - x)(z - x)(z - y)
A = | 1 2 3 |
| 4 5 6 |
| 7 8 9 |
Find adj(A) and verify that A × adj(A) = |A| × I
2x + 3y + z = 1 x + y + 2z = 2 3x + 4y + z = 0
📘 Final Tips for Scoring Full Marks in Determinants
- Always use cofactor expansion along the row or column with the most zeros.
- Use properties like row/column interchange, scalar multiplication, and adding multiples for simplification.
- Practice matrix inversion using adjoint at least 5 times before the exam.
- Revise application-based questions such as checking collinearity and solving linear systems.
Mastering these 12 questions can help you tackle any problem that appears in the CBSE Class 12 Maths Board Exam 2025 from the topic of Determinants.