# Maths MCQs for Class 12 with Answers Chapter 4 Determinants

## Determinants Class 12 Maths MCQs Pdf

1.

**Answer/Explanation**

Answer: d

Explaination:

2.

**Answer/Explanation**

Answer: a

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

3.

**Answer/Explanation**

Answer: d

Explaination:

4. Let A be a square matrix of order 2 × 2, then |KA| is equal to

(a) K|A|

(b) K²|A|

(c) K^{3}|A|

(d) 2K|A|

**Answer/Explanation**

Answer: b

Explaination:

5.

**Answer/Explanation**

Answer: a

Explaination:

6. Let x, yeR, then the determinant

**Answer/Explanation**

Answer: a

Explaination:

7.

**Answer/Explanation**

Answer: d

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) \(\frac{1}{16}\)

**Answer/Explanation**

Answer: d

Explaination:

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

**Answer/Explanation**

Answer:

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

10.

**Answer/Explanation**

Answer:

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

11.

**Answer/Explanation**

Answer:

Explaination:

sin 30° cos 60° + cos 30° sin 60°

= sin(30° + 60°) = sin 90° = 1.

12.

**Answer/Explanation**

Answer:

Explaination:

18x + 45 – 15x -6 = 0

⇒ 3x = -39

⇒ x = -13.

13. Evaluate the determinant

**Answer/Explanation**

Answer:

Explaination:

14.

**Answer/Explanation**

Answer:

Explaination:

15. Value of determinant

is 0, state true or false.

**Answer/Explanation**

Answer:

Explaination: True, as on performing C_{3} → C_{3} + C_{2} we notice elements of C_{1} and C_{3} are proportional.

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

**Answer/Explanation**

Answer:

Explaination:

17. The determinant

**Answer/Explanation**

Answer:

Explaination:

18. Evaluate the determinant

**Answer/Explanation**

Answer:

Explaination:

19. What is the value of the following determinant?

**Answer/Explanation**

Answer:

Explaination:

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

**Answer/Explanation**

Answer:

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 ______ .

**Answer/Explanation**

Answer:

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.

**Answer/Explanation**

Answer:

Explaination:

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

**Answer/Explanation**

Answer:

Explaination:

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

**Answer/Explanation**

Answer:

Explaination:

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

**Answer/Explanation**

Answer:

Explaination:

26. Find the cofactor of a_{12} of the determinant

**Answer/Explanation**

Answer:

Explaination:

27.

cofactor of the element a_{21} [Foreign 2015]

**Answer/Explanation**

Answer:

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

28. In the determinant

find

(i) minor of element 3

(ii) cofactor of element 5.

**Answer/Explanation**

Answer:

Explaination:

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

**Answer/Explanation**

Answer:

Explaination:

30.

**Answer/Explanation**

Answer:

Explaination:

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

**Answer/Explanation**

Answer:

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.

**Answer/Explanation**

Answer:

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.

**Answer/Explanation**

Answer:

Explaination:

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

**Answer/Explanation**

Answer:

Explaination:

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

**Answer/Explanation**

Answer:

Explaination:

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

**Answer/Explanation**

Answer:

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}

**Answer/Explanation**

Answer:

Explaination:

38.

**Answer/Explanation**

Answer:

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]

**Answer/Explanation**

Answer:

Explaination:

40.

**Answer/Explanation**

Answer:

Explaination: