# Maths MCQs for Class 12 with Answers Chapter 4 Determinants

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 4 Determinants. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Determinants MCQs Pdf with Answers to know their preparation level.

## Determinants Class 12 Maths MCQs Pdf

1.

Explaination:

2.

Explaination: (a), Δ = 6(-1)- 1(1) = -7.

3.

Explaination:

4. Let A be a square matrix of order 2 × 2, then |KA| is equal to
(a) K|A|
(b) K²|A|
(c) K3|A|
(d) 2K|A|

Explaination:

5.

Explaination:

6. Let x, yeR, then the determinant

Explaination:

7.

Explaination: (d), as value of determinant is sum of the product of elements of any row and column and then- respective cofactor.

8. A and B are invertible matrices of the same order such that |(AB)-1| = 8, If |A| = 2, then |B| is
(a) 16
(b) 4
(c) 6
(d) $$\frac{1}{16}$$

Explaination:

9. Determinant is a number associated to a matrix, state true or false.

Explaination: False, as determinant is a number associated to a square matrix.

10.

Explaination: (a + ib) (a – ib) – (c + id) (c – id) = a² + b² – c² – d².

11.

Explaination:
sin 30° cos 60° + cos 30° sin 60°
= sin(30° + 60°) = sin 90° = 1.

12.

Explaination:
18x + 45 – 15x -6 = 0
⇒ 3x = -39
⇒ x = -13.

13. Evaluate the determinant

Explaination:

14.

Explaination:

15. Value of determinant

is 0, state true or false.

Explaination: True, as on performing C3 → C3 + C2 we notice elements of C1 and C3 are proportional.

16. If A is a matrix of order 3 × 3, then |KA| = _______ .

Explaination:

17. The determinant

Explaination:

18. Evaluate the determinant

Explaination:

19. What is the value of the following determinant?

Explaination:

20. If for any 2 × 2 square matrix A, A(adj A)

Explaination:

21. If area of a triangle with vertices (3, 2), (-1,4) and (6, k) is 7 sq units, then possible values of k are ______ .

Explaination:

22. The points (a + 5, a – 4), (a – 2, a + 3) and (a, a) are non-collinear for any value of a. State true or false.

Explaination:

23. Find the area of the triangle with vertices (-1, 2), (4, 0) and (3, 9).

Explaination:

24. Find the value of x, such that the points (0, 2), (1, x) and (3, 1) are collinear.

Explaination:

25. Show that points A(a, b + c), B(b, c + a) and C(c, a + b) are collinear. [NCERT]

Explaination:

26. Find the cofactor of a12 of the determinant

Explaination:

27.

cofactor of the element a21 [Foreign 2015]

Explaination: Cofactor of a2l = (-1)3 (18 – 21) = 3

28. In the determinant
find
(i) minor of element 3
(ii) cofactor of element 5.

Explaination:

29. If A and B are invertible matrices of the same order (AB)-1 is _____ .

Explaination:

30.

Explaination:

31. A is invertible matrix of order 3 × 3 and |A| = 9, then value of |A-1|is

Explaination:

32. If the value of a third order determinant is 7, then the value of a determinant formed by replacing each element by its cofactor will be 49. State true or false.

Explaination: True, as |adj.A| = |A|<sup>n-1</sup>, A is matrix of order 3 × n

33. Inverse of matrix

exists, state true or false.

Explaination:

34. For what value of k, the matrix $$\left[\begin{array}{ll}{k} & {2} \\ {3} & {4}\end{array}\right]$$ has no inverse?

Explaination:

35. Write A-1 for A = $$\left[\begin{array}{ll}{2} & {5} \\ {1} & {3}\end{array}\right]$$ [Delhi 2011]

Explaination:

36. Given a square matrix A of order 3 × 3, such that |A| = 12, find the value of |A. adj A|. [HOTS]

Explaination:
|A adj A| = |A|3 as matrix A is of order 3 × 3.
∴ |A adj A| = |A|3 = (12)3 = 1728

37. If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A-1) = (det A)k

Explaination:

38.

Explaination:

39. If for any 2 × 2 square matrix A, A(adj A) = $$\left[\begin{array}{ll}{8} & {0} \\ {0} & {8}\end{array}\right]$$, then write the value of |A|. [Delhi 2017]