WBJEE 2025 Matrices and Determinants Practice Questions with Solutions

WBJEE 2025 Matrices and Determinants Practice Questions: Matrices and Determinants are an important part of the 12th-grade curriculum, as well as the WBJEE syllabus 2025. The chapter focuses on concepts of Matrices, Addition and Multiplication of Matrices, and Types of Matrices. The topic covers nearly 5% marks weightage from the WBJEE 2025 Mathematics syllabus PDF. You can expect around 5-7 questions from the Matrices and Determinants chapter alone. Thus, to score full marks in this section and improve your overall rank in the WBJEE exam 2025, you should prepare with WBJEE 2025 Matrices and Determinants practice questions daily. In this article, we have compiled a series of WBJEE 2025 Matrices and Determinants practice questions with solutions after analyzing the previous years' question papers and the most important sub-topics. You can refer to these WBJEE Matrices and Determinants sample questions to prepare for the upcoming WBJEE 2025 exam.  

Also Check: WBJEE 2025 Differential Equations Practice Questions with Solutions

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List of WBJEE 2025 Matrices and Determinants Sub Topics for Exam Preparation

The Matrices and Determinants topic covers around 5% of the total syllabus, making it a scoring area in the WBJEE exam 2025. However, you should have a clear idea of all the sub-topics included in this chapter. From this section, you can expect numerical problems based on multiplication, addition of the matrices, properties of matrices, questions based on the area of a triangle, and linear equation concepts. In the following table, we have detailed all the topics covered in the Matrices and Determinants chapter of the WBJEE 2025 syllabus PDF. You should focus on these topics as the questions may require lengthy calculations and a good understanding of the concepts. 

WBJEE 2025 Matrices and Determinants Expected Weightage

The Matrices and Determinants chapter typically features around 5-7 questions in the WBJEE examination. The marks weightage for Matrices and Determinants lets you know how much time you need to invest in this chapter. Considering the topic carries a comparatively higher weightage in the exam, you should pay more attention to solving WBJEE 2025 Matrices and Determinants daily practice questions once you have finished studying the sub topics. In the following table, we have provided the expected WBJEE 2025 Matrices and Determinants marks weightage for reference.

WBJEE 2025 Matrices and Determinants Practice Questions with Solutions

You should attempt as many WBJEE 2025 Matrices and Determinants practice questions as possible to prepare for the exam effectively. In this section, we have provided a list of WBJEE 2025 Matrices and Determinants practice questions with solutions that are likely to feature in the exam paper. 

Q1. The values of x for which the given matrix will be non-singular are:

Ans. b. For all x other than 2 and -2

Solution:

If matrix A is nonsingular then 

given matrix will be non singular for all x other than 2 and - 2

Q2. If A is a square matrix. Then

a. 

b. 

c. 

d. 

Ans. a.

Solution:

Q3. If A2 – A + I = 0, then the inverse of the matrix A is

a. A – I

b. I – A

c. A + I

d. A

Solution:

A(A – I) = I

A(I – A) = I 

A – 1 = I – A.

Q4. If A and B are square matrices of the same order and AB = 3I, then A – 1 is equal to

a. 3B

b. ⅓ B

c. 3B-1

d. ⅓ B-1

Ans. b. ⅓ B

Q5. If A and B are two matrices such that A + B and AB are both defined, then

a. A and B can be any matrices

b. A, B are square matrices not necessarily of same order

c. A, B are square matrices of the same order

d. Number of columns of A = number of rows of B

Ans. c. A, B are square matrices of the same order

Q6. Let A and B are orthogonal matrices and det A + det B = 0. Then

a. A + B is singular

b. A + B is non singular

c. A + B is orthogonal

d. A + B is skew symmetric

Ans. a. A + B is singular

Q7. If M is a 3 X 3 matrix such that (0, 1, 2) M = (1 0 0), (3, 4 5) M = (0, 1, 0), then (6 7 8) M is equal to

a. (2  1  –2)

b. (0  0  1)

c. (-1 2  0)

d. (9  10  8)

Ans. c. (-1  2  0)

Q8. Let A and B be two non-singular skew-symmetric matrices such that AB = BA, A2B2(ATB)-1(AB-1)T then  is equal to

a. A2

b. -B2

c. -A2

d. AB

Ans. c. -A2

Q9. Let T and U be the set of all orthogonal matrices of order 3 over R and the set of all non-singular matrices of order 3 over R respectively. Let A = {-1, 0, 1}, then

a. There exists a bijective mapping between A and T, U

b. There does not exist a bijective mapping between A and T, U

c. There exists a bijective mapping between A and T but not between A and U

d. There exists a bijective mapping between A and U but not between A and T

Ans. b. There does not exist a bijective mapping between A and T, U

Q10. Let A be a square matrix of order 3 whose all entries are 1 and let I3 be the identity matrix of order 3. Then, the matrix A – 3I3 is

a. Invertible

b. Orthogonal

c. Non-invertible

d. Real Skew Symmetric matrix

In addition to solving these WBJEE 2025 Matrices and Determinants daily practice questions, make a habit of solving mock papers. The more you practice with WBJEE 2025 mock test, the more adept you will get in these topics. With the right preparation approach, you can score full marks in WBJEE Mathematics paper (Paper I). 

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