## NCERT Solutions for Class 12 Maths Chapter 4 MCQ’s with Answers

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## NCERT **Maths MCQs for Class 12 Question and Answers Chapter 4 Determinants PDF**

### Q1. 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|

Option b – K²|A|

### Q2. 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)1/16

Option d – 1/16

### Q3. Determinant is a number associated to a matrix, state true or false.

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

### Q4. 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.

Option True, as |adj.A| = |A|^{n-1}, A is matrix of order 3 × n

### Q5. Given a square matrix A of order 3 × 3, such that |A| = 12, find the value of |A. adj A|.

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

### Q6. 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

Option b – 3

### Q7. 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

Option d – 5

### Q8. 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

Option a – y = 2x

### Q9. 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) 1 : -2 : 2

(c) 2 : 1 : 2

(d) 2 : 1 : -2

Option d – 2 : 1 : -2

### Q10. If for the non-singular matrix A, A2 = I, then find A-1.

(a) A

(b) I

(c) O

(d) None of these

Option a – A

### Q11. If 4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1, then z = *__*

*__*

(a) 1

(b) 3

(c) -2

(d) 2

Option d – 2

### Q12. 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 + 1 = 0

(c) a + b = 3

(d) a – b – 8 = 0

Option a – a – b = 2

### Q13. 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 = -1, y = -3, z = 2

(c) x = 2, y = 4, z = 6

(d) x = 3, y = 6, z = 9

Option b – x = -1, y = -3, z = 2

### Q14. 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

Option c – 1

### Q15. Find the area of the triangle with vertices P(4, 5), Q(4, -2) and R(-6, 2).

(a) 21 sq. units

(b) 35 sq. units

(c) 30 sq. units

(d) 40 sq. units

Option b – 35 sq. units

### Q16. If the points (a1, b1), (a2, b2) and(a1 + a2, b1 + b2) are collinear, then

(a) a1b2 = a2b1

(b) a1 + a2 = b1 + b2

(c) a2b2 = a1b1

(d) a1 + b1 = a2 + b2

Option a – a1b2 = a2b1

### Q17. If the points (2, -3), (k, -1) and (0, 4) are collinear, then find the value of 4k.

(a) 4

(b) 7/140

(c) 47

(d) 40/7

Option d – 40/7

### Q18. Find the area of the triangle whose vertices are (-2, 6), (3, -6) and (1, 5).

(a) 30 sq. units

(b) 35 sq. units

(c) 40 sq. units

(d) 15.5 sq. units

Option d – 15.5 sq. units

### Q19. 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

Option b – 3

### Q20. 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

Option d – (A + B)-1 = B-1 + A-1

We hope that the given** NCERT MCQ** **Questions for Class 12 Mathematics Chapter 4 Determinants** **Free Pdf download** will help you in gaining knowledge on the subject.