Determinants MCQs, Class 12 Maths Chapter 4 MCQ Quiz

Determinants MCQ Question Answers for CUET 2026 from Class 12 Maths Chapter 4

To score full marks in the CUET 2026 Maths exam, Practice Class 12 Maths Chapter 4 Determinants MCQ Test any number of times free on our website. These questions have been created by our experts from the latest Class 12 Maths Syllabus and as per latest exam pattern. Multiple Choice Questions (MCQs) are a type of objective assessment in which a person is asked to choose one or more correct answers from a list of available options. An MCQ presents a question along with several possible answers. Most of the exams in India including CUET exam conduct online test to check your knowledge

Class 12 Maths Chapter 4 MCQs

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1. The area of a triangle with vertices (-3, 0) (3, 0) and (0, k) is 9 sq. units. The value of k will be

a.-9

b.0

c.9

d.3

2. If A is a square matrix of order 3 and |A| = 5, then the value of |2A′| is

a.-40

b.-10

c.10

d.40

3. Question

a.-1

b.-2

c.2

d.1

4. If the points (3, -2), (x, 2), (8, 8) are collinear, then find the value of x.

a.4

b.2

c.5

d.3

5. If the points (2, -3), (k, -1) and (0, 4) are collinear, then find the value of 4k.

a.4/7

b.4

c.40/7

d.7/140

6. If A is a square matrix of order 3 and |A| = 7 then |AT| =

a.1/7

b.21

c.3

d.7

7. Question

a.d

b.a

c.c

d.b

8. Which of the following is correct?

a.Determinant is a number associated to a matrix

b.Determinant is a square matrix

c.None of these

d.Determinant is a number associated to a square matrix

9. Solve the following system of equations x – y + z = 4, x – 2y + 2z = 9 and 2x + y + 3z = 1.

a.x = -1, y = -3, z = 2

b.x = 3, y = 6, z = 9

c.x = 2, y = 4, z = 6

d.x = -4, y = -3, z = 2

10. Find the area of the triangle whose vertices are (-2, 6), (3, -6) and (1, 5).

a.15.5 sq. units

b.40 sq. units

c.35 sq. units

d.30 sq. units

11. System of equations AX = B is inconsistent if

a.│B│ = 0

b.│A│ ≠ 0

c.(adj A) B ≠ 0

d.(adj A) B = 0

12. In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has value

a.9

b.1

c.24

d.16

13. If A is an invertible matrix of order 2, then det (A–1) is equal to

a.1/det (A)

b.1

c.0

d.det (A)

14. Which of the following conditions holds true for a system of equations to be consistent?

a.It should have one or more solutions

b.It should have exactly two solutions

c.It should have exactly one solution

d.It should have no solutions

15. The minor Mij of an element aij of a determinant is defined as the value of the determinant obtained after deleting the

a.ith column and jth row of the determinant

b.ith row of the determinant

c.jth row of the determinant

d.ith row and jth column of the determinant

16. Question

a.a singleton

b.a finite set containing two or more elements

c.an infinite set

d.an empty set

17. Given that A is a square matrix of order 3 and |A| = -4, then |adj A| is equal to

a.-4

b.16

c.4

d.-16

18. Question

a.1

b.Zero

c.3

d.2

19. A system of linear equations AX = B is said to be inconsistent, if the system of equations has

a.Trivial Solution

b.Infinite Solutions

c.Unique Solutions

d.No Solution

20. Inverse of a matrix A exists, if

a.| A | = 0

b.Matrix A is non-singular

c.AT = A

d.Matrix A is singular

21. Question

a.a

b.d

c.b

d.c

22. Using determinants, find the equation of the line joining the points (1, 2) and (3, 6).

a.x = 3y

b.y = x

c.y = 2x

d.4x – y = 5

23. If A is a symmetric matrix, then At =

a. |A|

b.Diagonal matrix

c.A

d.12:00 AM

24. If 4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1, then z = …………….

a.-2

b.2

c.3

d.1

25. The area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 sq. units. The value of k will be

a.-9

b.6

c.9

d.3

26. Find the area of the triangle with vertices P(4, 5), Q(4, -2) and R(-6, 2).

a.21 sq. units

b.40 sq. units

c.35 sq. units

d.30 sq. units

27. The area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 sq. units. The value of ‘k’ will be:

a.3

b.9

c.6

d.-9

28. If the points (2, -3), (k, -1) and (0, 4) are collinear, then find the value of 4k.

a.7/140

b.47

c.40/7

d.4

29. If the equations 2x + 3y + z = 0, 3x + y – 2z = 0 and ax + 2y – bz = 0 has non-trivial solution, then

a.a – b = 2

b.a + b = 3

c.a – b – 8 = 0

d.a + b + 1 = 0

30. Question

a.Exactly one value of λ

b.Exactly three values of λ

c.Exactly four values of λ

d.Exactly two values of λ

31. Question

a.c

b.b

c.d

d.a

32. If the area of the triangle is 35 sq. units with vertices (2, -6), (5, 4) and (k, 4). Then k is

a.-12, -2

b.-2

c.12, -2

d.12

33. If A is a square matrix of order 3 and |A| = 5 then |3A| = ?

a.135

b.45

c.32

d.15

34. If the system of equations x + ky – z = 0, 3x – ky – z = 0 & x – 3y + z = 0 has non-zero solution, then k is equal to

a.1

b.-1

c.0

d.2

35. A non-trivial solution of the system of equations x + λy + 2z = 0, 2x + λz = 0, 2λx – 2y + 3z = 0 is given by x : y : z =

a.1 : 2 : -2

b.2 : 1 : -2

c.2 : 1 : 2

d.1 : -2 : 2

36. For a given system of equations if |A|=0 and (adj A)B≠O(zero matrix), then which of the following is correct regarding the solutions of the given equations?

a.there are one or more solutions

b.there will be exactly one solution

c.the solution does not exist

d.there will be exactly two solutions

37. We can add two matrices having real numbers A and B if their

a.columns are same

b.rows are same

c.order is same

d.elements are same

38. Question

a.c

b.b

c.d

d.a

39. Question

a.I

b.A

c.None of these

d.O

40. Question

a.a

b.c

c.d

d.b

41. If A is any square matrix of order 3 x 3 such that |a| = 3, then the value of |adj. A| is?

a.3

b.9

c.13

d.27

To summarize, revising for free using our MCQs on Class 12 Maths Chapter 4 Determinants is highly beneficial for scoring full marks on the CUET 2026 Maths exam. We provide a sophisticated online test platform tailored for unlimited practice through proficiently crafted questions built on the most recent syllabus and exam pattern. Practicing MCQs regularly will boost conceptual understanding as they are significant for objective assessments. Start practicing now to succeed in your CUET 2026 Maths exam!

Also See :

Relations and Functions MCQs Class 12 Chapter 1
Inverse Trigonometric Functions MCQs Class 12 Chapter 2
Matrices MCQs Class 12 Chapter 3
Continuity and Differentiability MCQs Class 12 Chapter 5
Applications of Derivatives MCQs Class 12 Chapter 6
Integrals MCQs Class 12 Chapter 7
Application of the Integrals MCQs Class 12 Chapter 8
Differential Equations MCQs Class 12 Chapter 9
Vectors MCQs Class 12 Chapter 10
Three Dimensional Geometry MCQs Class 12 Chapter 11
Linear Programming MCQs Class 12 Chapter 12
Multiplication Theorem Probability MCQs Class 12 Chapter 13

Determinants MCQs | Class 12 Maths Chapter 4 MCQ Question and Answers

Determinants MCQ Question Answers for CUET 2026 from Class 12 Maths Chapter 4

Class 12 Maths Chapter 4 MCQs

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