JEE Main 2027 Matrices & Determinants Questions: Previous Year Questions, Weightage & Important Topics

In JEE Mains, Matrices and Determinants are always featured in the numerical value section as well as in the MCQs. The questions from this section can be tricky as well as lengthy. Therefore, students must practice JEE Mains Matrices & Determinants questions with a strategy. Check complete details below.

JEE Mains 2027 Matrices and Determinants Questions

JEE Mains 2027 Matrices & Determinants Questions: In JEE Mains, Matrices and Determinants is one of the highest-yield, most reliable scoring chapters in Mathematics, consistently accounting for 6% to 10% of the total Maths section. It is one of the high weightage topics for JEE Mains 2027. Students preparing for JEE Mains, should take this chapter seriously and prepare it with dedication. This chapter frequently features 2 questions (1 MCQ + 1 Numerical Value Question) on average in each shift of the exam.

Key Highlights for JEE Main Matrices and Determinants

After the analysis of the past 5 year JEE Main question papers, Shiksha experts have the following observations for the Determinants and Matrices questions:

• Consistent appearance each year: Matrices and Determinants consistently contribute 2 to 3 questions (8 to 12 marks) across every single JEE Main shift without exception. Every paper has at least one question testing linear systems and frequently has at least one calculation-heavy problem in Section B (Numerical section).
• Most repeated concept: The single most frequent concept is solving non-homogeneous systems of linear equations with parameters to identify conditions for infinite, unique, or no solutions. This is closely followed by chained adjoint determinant identities and evaluating higher matrix powers.
• Lengthy vs Tricky:
  • Lengthy: Step-by-step evaluations of Cramer's rule and multi-step adjoint expansions that are simple in method but calculation-heavy.
  • Tricky: Matrices and determinants with built-in shortcuts - like odd skew-symmetrics, hidden symmetries, and quick Cayley-Hamilton reductions.

Also Check: JEE Main Vector & 3D Questions 2027

JEE Mains 2027 Matrices and Determinants Questions

From below, candidates can download the JEE Main questions for the Matrices and Determinants chapters. These questions have been curated from the past 5 year JEE Mains question papers.

(1) 6

(2) 72

(3) 36

(4) 12

 

(1) 1

(2) 2

(3) 3

(4) 0

 

(1) 7π12, 11π12

(2) π6, 5π6

(3) π12, π6

(4) 5π12, 7π12

 

Q4. Let α, β, γ be the real roots of the equation x³ + ax² + bx + c = 0, (a, b, c ∈ ℝ and a, b ≠ 0). If the system of equations (in u, v, w) given by αu + βv + γw = 0, βu + γv + αw = 0, γu + αv + βw = 0 has non-trivial solutions, then the value of a²b is:

(1) 5

(2) 3

(3) 1

(4) 0

 

Q5. Define a relation R over a class of n × n real matrices A and B as "ARB iff there exists a non-singular matrix P such that PAP^-1 = B". Then which of the following is true?

(1) R is reflexive, symmetric but not transitive

(2) R is symmetric, transitive but not reflexive

(3) R is reflexive, transitive but not symmetric

(4) R is an equivalence relation

 

Q6. Let the system of linear equations
4x + λy + 2z = 0
2x - y + z = 0
μx + 2y + 3z = 0, λ, μ ∈ ℝ
have a non-trivial solution. Then which of the following is true?

(1) μ = 6, λ ∈ ℝ

(2) μ = -6, λ ∈ ℝ

(3) λ = 2, μ ∈ ℝ

(4) λ = 3, μ ∈ ℝ

 

(1) -2

(2) 4

(3) 0

(4) 2

 

Q8. For a 3 × 3 matrix M, let trace(M) denote the sum of all diagonal elements of M. Let A be a 3 × 3 matrix such that |A| = 12 and trace(A) = 3. If B = adj(adj(2A)), then the value of |B| + trace(B) equals:

(1) 174

(2) 132

(3) 56

(4) 280

 

Q9. If the system of linear equations
x + y + 2z = 6
2x + 3y + az = a + 1
-x - 3y + bz = 2b
where a, b ∈ ℝ has infinitely many solutions, then 7a + 3b is equal to:

(1) 9

(2) 22

(3) 16

(4) 12

 

Q10. Let A = [a_ij] and B = [b_ij] be two 3 × 3 real matrices such that b_ij = (3)^(i+j-2) a_ji where i, j = 1, 2, 3. If the determinant of B is 81, then the determinant of A is:

(1) 13

(2) 19

(3) 181

(4) 3

JEE Main Matrices and Determinants Weightage: 5-Year Trend Analysis (2021 to 2026)

Check below the overall weightage of Determinants and Matrices in JEE Mains exam from 2026 to 2021:

JEE Mains Determinants and Matrices Concept-Wise Weightage (2021 to 2026)

From subtopics or concepts under the matrices and determinants chapters from JEE Main syllabus, there are a few that are repeated the most over the years. Linear systems dominate (around 40%), followed by adjoint/inverse identities (around 24%) and matrix powers (around 17%). Determinant evaluations and special matrix properties make up the remaining 19% of questions. Check details below.

Preparation Strategy for Determinants and Matrices for JEE Main 2027

Below are some tips to ace the determinants and matrices chapter of JEE Mains 2027:

Phase-Wise Study Plan

• Phase 1: Foundational Algebra & Properties (3-4 Days)
  • Master matrix multiplication, transpose, trace properties, and basic determinant expansions
  • Familiarise yourself with types of matrices
• Phase 2: High-Yield Core Topics (5-6 Days)
  • System of Linear Equations (Cramer’s Rule)
  • Adjoint & Inverse Identities
• Phase 3: Advanced Tricks & Speed Techniques (3-4 Days)
  • Cayley-Hamilton Theorem: Practice forming characteristic equations to reduce higher powers without manual multiplication.
  • Matrix Induction: Identify recurrence patterns in triangular or trigonometric matrices

PYQ Strategy

Practice the questions from the following concepts:

High Probability JEE Main 2027 Matrices & Determinants Questions

The following types of questions can appear in JEE Main 2027 exam: