JEE Mathematics

Properties of Determinants: JEE Questions & Solutions

11 previous-year JEE Mathematics questions on Properties of Determinants, each with a worked step-by-step solution.

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Previous-year questions

  1. 01If A = 2 3 3 5, then the determinant of the matrix A²⁰²⁵ - 3A²⁰²⁴ + A²⁰²³ isMCQMediumJEE 2026
  2. 02Let |A| = 6, where A is a 3 × 3 matrix. If |adj(3adj(A² · adj(2A)))| = 2^m · 3ⁿ, then m + n is equal to:NVAMediumJEE 2026
  3. 03Let f(x)=∫ (7x¹⁰+9x⁸)/(1+x²+2x⁹)² dx, x>0, lim_(x→ 0)f(x)=0, f(1)=1/4. If A= 0 0 1 1/4 f'(1) 1 α² 4 1 and B=adj(adj A) is such that |B|=81,…MCQMediumJEE 2026
  4. 04Let A be a square matrix of order 3 such that det(A) = -2 and det(3 · adj(-6 · adj(3A))) = 2^(m+n) · 3^mn, where m > n. Then 4m + 2n is…NVAMediumJEE 2025
  5. 05Let A = [ a_ij ] = [ log₅ 128 log₄ 5 log₅ 8 log₄ 25 ]. If A_ij is the cofactor of a_ij, C_ij = Σ_(k=1)² a_ik A_jk, and C = [C_ij], then…MCQMediumJEE 2025
  6. 06Let a ∈ ℝ and A be a matrix of order 3 × 3 such that det(A) = -4 and A + I = [ 1 a 1 2 1 0 a 1 2 ] where I is the identity matrix of order…MCQMediumJEE 2025
  7. 07Let A = 2 1 2 6 2 11 3 3 2 and P = 1 2 0 5 0 2 7 1 5. The sum of the prime factors of |P⁻¹AP - 2I| is equal to:MCQMediumJEE 2024
  8. 08If A = √2 1 -1 √2, B = 1 0 1 1, C = ABA^T, and X = A^T C² A, then det(X) is equal to:MCQMediumJEE 2024
  9. 09Let A be a 3 × 3 matrix such that |adj(adj(adj A))| = 12⁴. Then |A⁻¹ adj A| is equal to:MCQMediumJEE 2023
  10. 10Let f(x) = 1 + sin² x cos² x sin 2x sin² x 1 + cos² x sin 2x sin² x cos² x 1 + sin 2x where x ∈ [ π/6, π/3 ]. If α, β are respectively the…MCQMediumJEE 2023
  11. 11If A is a 3×3 matrix and |A| = 2, then |3adj(|3A|A²)| is equal to:MCQMediumJEE 2023

Frequently asked questions

Our bank has 11 previous-year JEE Mathematics questions tagged to Properties of Determinants, drawn from JEE papers between 2023 and 2026, including 3 from 2026 alone. Each comes with a full step-by-step solution.

Properties of Determinants is rated Advanced overall for JEE Mathematics. The PYQs on this page break down as 11 medium.

Of the 11 previous-year questions on Properties of Determinants, 9 are multiple-choice (MCQ) and 2 are numerical-value (NVA) questions.

Based on recent paper analysis, Properties of Determinants is worth about 1 mark in JEE Main. It sits in Matrices & Determinants, a Class 12 Mathematics chapter.

More Matrices & Determinants topics

Solving Linear Equations (Matrix Method)40Algebra of Matrices25Inverse & Adjoint of a Matrix22Determinants Basics16Types of Matrices3

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