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

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

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

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

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

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

a.It should have exactly two solutions

b.It should have no solutions

c.It should have exactly one solution

d.It should have one or more solutions

3. Question

a.1

b.-2

c.-1

d.2

4. 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.0

c.1

d.2

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

a.ith row and jth column of the determinant

b.ith row of the determinant

c.jth row of the determinant

d.ith column and jth row of the determinant

6. Inverse of a matrix A exists, if

a.AT = A

b.| A | = 0

c.Matrix A is non-singular

d.Matrix A is singular

7. 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.24

b.16

c.9

d.1

8. 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.the solution does not exist

b.there will be exactly two solutions

c.there are one or more solutions

d.there will be exactly one solution

9. Question

a.d

b.a

c.b

d.c

10. Question

a.3

b.1

c.2

d.Zero

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

a.-2

b.3

c.2

d.1

12. Question

a.A

b.O

c.None of these

d.I

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

a.47

b.4

c.7/140

d.40/7

14. 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

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

a.columns are same

b.elements are same

c.rows are same

d.order is same

16. Question

a.d

b.a

c.b

d.c

17. 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.0

b.3

c.9

d.-9

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

a.13

b.3

c.9

d.27

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

a.4x – y = 5

b.x = 3y

c.y = x

d.y = 2x

20. Question

a.d

b.c

c.b

d.a

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

a.35 sq. units

b.15.5 sq. units

c.30 sq. units

d.40 sq. units

22. Question

a.c

b.d

c.b

d.a

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

a.45

b.15

c.135

d.32

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

a.3

b.4

c.2

d.5

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

a.21

b.7

c.1/7

d.3

26. 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 + 1 = 0

d.a – b – 8 = 0

27. Which of the following is correct?

a.Determinant is a number associated to a matrix

b.Determinant is a number associated to a square matrix

c.Determinant is a square matrix

d.None of these

28. 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.2 : 1 : 2

b.2 : 1 : -2

c.1 : -2 : 2

d.1 : 2 : -2

29. 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.3

c.6

d.9

30. 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.3

d.9

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

a.1/det (A)

b.det (A)

c.0

d.1

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.12

c.-12, -2

d.-2

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

a.-4

b.4

c.-16

d.16

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

a.Diagonal matrix

b.A

c. |A|

d.12:00 AM

35. 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.No Solution

d.Unique Solutions

36. System of equations AX = B is inconsistent if

a.│A│ ≠ 0

b.(adj A) B ≠ 0

c.(adj A) B = 0

d.│B│ = 0

37. Question

a.an empty set

b.an infinite set

c.a singleton

d.a finite set containing two or more elements

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

a.7/140

b.4

c.40/7

d.4/7

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

a.40 sq. units

b.35 sq. units

c.30 sq. units

d.21 sq. units

40. Question

a.b

b.c

c.a

d.d

41. Question

a.Exactly three values of λ

b.Exactly two values of λ

c.Exactly one value of λ

d.Exactly four values of λ

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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