Matrices and Determinants JEE Questions PDF with Solution, Practice Now

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Matrices and Determinants JEE Questions Overview

Matrices are a rectangular arrangement of numbers, symbols, or expressions, set out by rows and columns. Matrices are used to solve a system of linear equations, as well as the transform a geometrical figure. It is an important concept of algebra and is often used to solve many algebra questions. Determinants are numbers obtained by performing operations on a square matrix.

A determinant can be used to calculate the inverse of a matrix, solve linear equations by using Cramer’s rule, and check the non-singular properties. In JEE Mains and JEE Advanced, problems on matrices and determinants are a very important part of the algebra syllabus. Matrix and determinant questions in these exams are direct and are often based on basic formulas. However, these questions can get a bit tricky when mixed with important algebra PYQs JEE. 

Practice Matrices and Determinants JEE Questions

Practice questions is the right way to learn matrices and determinants. Start from simple questions on matrices and determinants and gradually attempt more complex ones. Do mixed algebra questions too. Here are some questions similar to those found in exams:

1. If p+q+r = 0 = a+b+c , then the value of the determinant
| pa qb rc |
| qc ra pb |
| rb pc qa | is

A. 0
B. pa + qb + rc
C. 1
D. none of these

2. Let A = BBᵀ + CCᵀ, where B = [ cosθ ; sinθ ], C = [ sinθ ; –cosθ ], θ ∈ R. Then A is

A. [0 0; 0 0]
B. [1 0; 0 1]
C. [0 1; 1 0]
D. [0 0; 0 1]

3. If A, B, C are angles of a triangle, then the value of
| e²ⁱᴬ e⁻ⁱᶜ e⁻ⁱᴮ |
| e⁻ⁱᶜ e²ⁱᴮ e⁻ⁱᴬ |
| e⁻ⁱᴮ e⁻ⁱᴬ e²ⁱᶜ |
Is

A. 1
B. –1
C. –2
D. 4

4. If a, b, c are different, then the value of x satisfying
| 0 x²–a x³–b |
| x²+a 0 x²+c |
| x⁴+b x–c 0 |
Is

A. a
B. b
C. c
D. 0

5. If A = | 3 –3 4; 2 –3 4; 0 –1 1 | then A⁻¹ =

A. A³
B. A²
C. A⁴
D. A

6. Let {D₁, D₂, D₃, …, Dₙ} be the set of third-order determinants that can be made with the distinct non-zero real numbers a₁, a₂, …, aₙ. Then

A. Σ Dᵢ² = 1
B. Σ Dᵢ = 0
C. Dᵢ = Dⱼ ∀ i, j
D. None of these

7. Let A = | 0 0 –1; 0 –1 0; –1 0 0 |. The only correct statement about the matrix A is:

A. A is a zero matrix
B. A² = I, where I is a unit matrix
C. A⁻¹ does not exist
D. A = (–I)I, where I is a unit matrix

8. Let A = [aᵢⱼ]₃×₃ be such that aᵢⱼ = 3 when i=j, 0 otherwise. Then {det(adj(adj A))}/5 equals (where {·} denotes fractional part function):

A. 2/5
B. 1/5
C. 2/3
D. ⅓

9. If | xⁿ xⁿ⁺² x²ⁿ |
 | 1 x² a | = 0, ∀x ∈ R, where n ∈ N,
 | xⁿ⁺⁵ xⁿ⁺⁶ x²ⁿ⁺⁵ |
then value of a is

A. n
B. n–1
C. n+1
D. none of these

10. The value of the determinant
| nCᵣ₋₁ nCᵣ (r+1) nCᵣ₊₁ |
| nCᵣ nCᵣ₊₁ (r+2) nCᵣ₊₂ |
| nCᵣ₊₁ nCᵣ₊₂ (r+3) nCᵣ₊₃ |
Is

A. n² + n – 1
B. 0
C. nCᵣ₋₁ + nCᵣ + nCᵣ₊₁
D. nCᵣ₋₁ + nCᵣ + nCᵣ₊₁

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Matrices and Determinants JEE Questions PDF with Solution

Physics Wallah provides a PDF for matrices and determinants questions for JEE Mains and Advanced. It includes a variety of problems with step-by-step solutions and previous years’ questions. Practicing with this PDF helps students improve speed, accuracy, and problem-solving skills.