💬 Discord
Login

Determinants Practice Questions

Class 12 · Mathematics · 1944 free MCQs with instant results and detailed explanations.

1944
Total
645
Easy
900
Medium
399
Hard

Start Practicing Determinants

Take a timed quiz or customize your practice session

Quick Quiz (10 Qs) → Mock Test (25 Qs) ⚙ Customize

Topics in Determinants

Properties of Determinants 604
Applications 470
Minors and Cofactors 397
Adjoint and Inverse 473

Sample Questions from Determinants

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What is the value of the determinant if two rows of a determinant are identical?
A. 0
B. 1
C. 2
D. Undefined
Show Answer & Explanation
Correct Answer: A
When two rows of a determinant are identical, the determinant's value is zero because it indicates that the matrix is not full rank.
Q2
Easy
Which property of determinants states that if two rows are exchanged, the sign of the determinant changes?
A. Row exchange property
B. Column addition property
C. Scalar multiplication property
D. Determinant of transpose property
Show Answer & Explanation
Correct Answer: A
The Row exchange property confirms that swapping two rows in a determinant changes its sign, which is fundamental in determinant theory.
Q3
Easy
Which of the following is true about the determinant of a triangular matrix?
A. It is the product of the diagonal elements.
B. It is always zero.
C. It equals the sum of the diagonal elements.
D. It cannot be computed.
Show Answer & Explanation
Correct Answer: A
The determinant of a triangular matrix (upper or lower) is simply the product of its diagonal entries.
Q4
Medium
Which of the following operations does NOT change the value of the determinant?
A. Interchanging two rows of the matrix
B. Multiplying a row by a non-zero scalar
C. Adding a multiple of one row to another row
D. Adding a multiple of one column to another column
Show Answer & Explanation
Correct Answer: D
Only adding a multiple of one row to another does not change the determinant. However, adding a multiple of one column to another is not a row operation and can change the determinant.
Q5
Medium
If the rows of a 3x3 matrix A are linearly dependent, what can be said about det(A)?
A. det(A) is positive
B. det(A) is negative
C. det(A) is zero
D. det(A) cannot be determined
Show Answer & Explanation
Correct Answer: C
If the rows of a matrix are linearly dependent, the determinant is zero, indicating that the matrix does not have full rank.
Q6
Medium
For a 2x2 matrix A = [[a, b], [c, d]], what is the determinant formula?
A. ad + bc
B. ad - bc
C. ac - bd
D. ab + cd
Show Answer & Explanation
Correct Answer: B
The determinant for a 2x2 matrix is calculated as det(A) = ad - bc.
Q7
Medium
Which property of determinants states that if two rows of a matrix are equal, its determinant is zero?
A. Row interchange property
B. Row addition property
C. Row dependence property
D. Column equivalence property
Show Answer & Explanation
Correct Answer: C
The Row Dependence Property states that if two rows of a matrix are identical, the determinant is zero due to linear dependence.
Q8
Hard
If A is a 3x3 matrix such that |A| = 5 and B is the matrix obtained by interchanging two rows of A, what is |B|?
A. -5
B. 5
C. 10
D. 0
Show Answer & Explanation
Correct Answer: A
Interchanging two rows of a matrix changes the sign of its determinant. Thus, |B| = -|A| = -5.
Q9
Hard
Let A be a square matrix of order 4. If the determinant of A is 0, what can we say about the rank of A?
A. Rank is 4
B. Rank is 3
C. Rank is less than 4
D. Rank is 0
Show Answer & Explanation
Correct Answer: C
A determinant of 0 indicates that the matrix is singular, meaning the rank is less than the order of the matrix, which is 4.
Q10
Hard
If A is a 3x3 matrix given by A = [[2, 3, 1], [4, 1, 0], [0, 5, 2]], what is |A|?
A. 0
B. 1
C. 14
D. 8
Show Answer & Explanation
Correct Answer: C
Calculating the determinant using the rule of Sarrus or cofactor expansion gives |A| = 14.

Showing 10 of 1944 questions. Start a quiz to practice all questions with scoring and timer.

Practice All 1944 Questions →

More Mathematics Chapters

1 Relations and Functions
1660 Qs →
2 Inverse Trigonometric Functions
1949 Qs →
3 Matrices
2241 Qs →
4 Continuity and Differentiability
1849 Qs →
5 Application of Derivatives
1543 Qs →
6 Integrals
2245 Qs →
7 Application of Integrals
1878 Qs →
8 Differential Equations
2519 Qs →

Other Class 12 Subjects

🧬 Biology → 🧪 Chemistry → ⚡ Physics →

Determinants — Class 12 Mathematics Practice Questions Online

This page contains 1944 practice MCQs for the chapter Determinants in Class 12 Mathematics. The questions are organized by difficulty — 645 easy, 900 medium, 399 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 4 topics, giving you comprehensive coverage of the entire chapter.