These Determinants Class 12 Important Questions And Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Determinants Class 12 Important Questions And Answers will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.

## Determinants Class 12 Important Questions And Answers

1. If for the non-singular matrix A, A^{2}= I, then find A^{-1}.

(A) A

(B) I

(C) O

(D) None of these

**Answer:** A

2.

(A) -(a – b)(b – c)(c – a)(a^{2} + b^{2} + c^{2})

(B) (a – b)(b – c)(c – a)

(C) (a^{2} + b^{2} + c^{2})

(D) (a – b)(b – c)(c – a)(a^{2} + b^{2} + c^{2})

**Answer:** -(a – b)(b – c)(c – a)(a^{2} + b^{2} + c^{2})

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

(A) y = 2x

(B) x = 3y

(C) y = x

(D) 4x – y = 5

**Answer:** y = 2x

4. The area of the triangle whose vertices are A(5, 4), B(-2, 4) and C(2, -6) is

(A) 15 square units.

(B) 25 square units.

(C) 35 square units.

(D) 45 square units.

**Answer:** 35 square units.

5. Determinant of the 1 x 1 matrix [- 3] is

(A) 3

(B) – 3

(C) 0

(D) none of these

**Answer:** – 3

6. If the equations (a + 1)^{3}x + (a + 2)^{3} y = (a + 3)^{3} (a + 1) x + (a + 2) y = a + 3 and x + y = 1 are consistent, then

(A) a = – 1

(B) a = – 2

(C) a = – 3

(D) none of these.

**Answer:** a = – 2

7. If A is a square matrix of order 2, then det (adj A) is equal to

(A) 1

(B) det A

(C) (det A)^{2}

(D) none of these

**Answer:** det A

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

(A) 2

(B) 3

(C) 4

(D) 5

**Answer:** 5

9. 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) -9

(D) 6

**Answer:** 3

10. If A and B are invertible matrices, then which of the following is not correct?

(A) adj A = |A|.A^{-1}

(B) det (a)^{-1} = [det (a)]^{-1}

(C) (AB)^{-1} = B-1A^{-1}

(D) (A + B)^{-1} = B-1 + A^{-1}

**Answer:** (A + B)^{-1} = B-1 + A^{-1}

11.

(A) 3x² + 4

(B) x(5x + 8)

(C) 3x + 4x²

(D) x(3x + 4)

**Answer:** x(5x + 8)

12. If then k =

(A) 0

(B) 1

(C) 2

(D) 3

**Answer:** 2

13.

(A) (x³ + y³)²

(B) (x² + y²)³

(C) -(x² + y²)³

(D) -(x³ + y³)²

**Answer:** -(x³ + y³)²

14. If x is a complex root of the equation then x^{2007}+ x^{-2007} =

(A) 1

(B) -1

(C) -2

(D) 2

**Answer:** -2

15.

(A) 2

(B) -2

(C) 4

(D) -4

**Answer:** -2

16. If a, b, c are cube roots of unity, then

(A) 0

(B) e

(C) e²

(D) e³

**Answer:** 0

17.

(A) 0

(B) 1

(C) 2

(D) 3

**Answer:** 0

18. If x > 0 and x ≠ 1. y > 0. and y ≠ 1, z > 0 and z ≠ 1 then is equal to

(A) 1

(B) -1

(C) 0

(D) None of these

**Answer:** 0

19. If Δ = then A =

(A) 0

(B) 10

(C) 12

(D) 60

**Answer:** 0

20.

(A) (x – y) (y + z)(z + x)

(B) (x + y) (y – z)(z – x)

(C) (x – y) (y – z)(z + x)

(D) (x – y) (y – z) (z – x)

**Answer:** (x – y) (y – z) (z – x)