Check the below NCERT MCQ Questions for Class 12 Maths Chapter 4 Determinants with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Determinants Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

## Q.1 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

## Q.2 If A is any square matrix of order 3 x 3 such that |a| = 3, then the value of |adj. A| is?

(a) 3

(b) 13

(c) 9

(d) 27

## Q.3 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

## Q.4 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

## Q.5 If area of triangle is 35 sq. units with vertices (2, -6), (5, 4) and (k, 4). Then k is

(a) 12

(b) -2

(c) -12, -2

(d) 12, -2

### Q.6 The system of linear equations:

x + λy – z = 0

λr – y – z = 0

x + y – λz = 0

has a non-trivial solution for

(a) Exactly one value of λ

(b) Exactly two values of λ

(c) Exactly three values of λ

(d) Infinitely many values of λ

## Q.7 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

## Q.8 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

## Q.9 The number of values of ‘k’ for which the linear equations:

4x + ky + 2z = 0

kx + 4y + z = 0

2x + 2y + z = 0

possesses a non-zero solution is

(a) 3

(b) 2

(c) 1

(d) zero

### Q.10 If Sis the set of distinct values of ‘h’ for which the following system of linear equations:

x + y + z = 1,

x + ay + z = 1,

ax + by + z = 1

has no solution, then S is

(a) a finite set containing two or more elements

(b) a singleton

(c) an empty set

(d) an infinite set

## Q.11 Which of the following is correct?

(a) Determinant is a square matrix

(b) Determinant is a number associated to a matrix

(c) Determinant is a number associated to a square matrix

(d) None of these

## Q.12 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

## Q.13 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

## Q.14 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

## Q.15 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

## Q.16 If 4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1, then z = *…………….*

*…………….*

(a) 1

(b) 3

(c) -2

(d) 2

## Q.17 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

## Q.18 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

## Q.19 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