Class 12 Mathematics — Chapter 4: Determinants
66 practice questions · 22 Easy · 22 Medium · 22 Hard
Practise Class 12 Mathematics Chapter 4, "Determinants", with 66 NCERT-aligned multiple-choice questions. The set is split into 22 Easy, 22 Medium and 22 Hard questions, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams, JEE Main and JEE Advanced.
"Determinants" is one of the chapters where problem-solving speed, formula recall and step-by-step reasoning really pays off. Each MCQ on this chapter is timed and uses exam-grade marking (+2 correct, −1 wrong, 0 skipped), training the same accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Determinants, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 12 Mathematics mastery score. A few sample questions are shown below; sign in free to practise all 66.
Key concepts: Determinants (Class 12 Mathematics)
This chapter covers determinants and their properties, the adjoint and inverse of a matrix, and using determinants to solve systems of linear equations.
- Determinant
- A scalar associated with a square matrix; for a 2×2 matrix [[a,b],[c,d]] it is ad − bc.
- Properties
- Swapping two rows changes the sign; a common factor of a row can be taken out; equal rows make the determinant 0.
- Area & singular matrices
- The area of a triangle with given vertices uses a determinant; a matrix is singular (no inverse) when its determinant is 0.
- Adjoint and inverse
- The adjoint is the transpose of the cofactor matrix; A⁻¹ = adj(A)/|A|, defined only when |A| ≠ 0.
- Solving linear systems
- For AX = B, X = A⁻¹B (matrix method); Cramer's rule uses determinants. Consistency depends on |A|.
Key formulas — Determinants
💡 Exam tips for Determinants
- A system AX = B has a unique solution only when |A| ≠ 0 (non-singular).
- Take out common factors from rows/columns first to simplify a determinant before expanding.
Sample questions
Area of triangle with vertices (x₁, y₁), (x₂, y₂), (x₃, y₃):
Determinant form.
det([[1, 0, 0], [0, 2, 0], [0, 0, 3]]) =
Diagonal product.
det([[a, b, c], [b, c, a], [c, a, b]]) factors as:
Standard factorisation.
Determinants — FAQs
What are the key concepts in Class 12 Mathematics Determinants?+
This chapter covers determinants and their properties, the adjoint and inverse of a matrix, and using determinants to solve systems of linear equations. Key ideas include Determinant, Properties, Area & singular matrices, Adjoint and inverse, Solving linear systems.
What does Class 12 Mathematics Chapter 4 (Determinants) cover on XamBaaz?+
It covers 66 NCERT-aligned MCQs on "Determinants" — 22 Easy, 22 Medium and 22 Hard — each with a timed quiz and an instant explanation, suitable for CBSE Board exams, JEE Main and JEE Advanced.
Are these "Determinants" questions free to practise?+
Yes — sign in with Google to practise "Determinants" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "Determinants" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
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