Students of class 12 Mathematics should refer to MCQ Questions Class 12 Mathematics Determinants with answers provided here which is an important chapter in Class 12 Mathematics NCERT textbook. These MCQ for Class 12 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 12 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 12 Mathematics examination

Chapter 4 Determinants MCQ with Answers Class 12 Mathematics

MCQ Questions Class 12 Mathematics Determinants provided below have been prepared by expert teachers of grade 12. These objective questions with solutions are expected to come in the upcoming Standard 12 examinations. Learn the below provided MCQ questions to get better marks in examinations.

Question. If ,

then x is equal to
(a) 6
(b) ± 6
(c) – 6
(d) 0

Question: The value of x obtained from the equation

(a) 0 and – (α+β+y)
(b) 0 and (α+β+y)
(c) 1 and (α-β-y)
(d) 0 and (α²+β²+y²) 

Question: if a+b+c=0 then the solution of the equation

Question: If a, b and c are positive integers, then the

by
(a) x³
(b) x²
(c) (a²+b²+c²)
(d) None of these 

Question: The roots of the equation

(a) -1,-2
(b) -1,2
(c) 1,-2 
(d) 1, 2 

Question: Determinant

(a) sin (x-y)
(b) cos (x-y)
(c) cos (x+y)
(d) xy sin (x-y)

Question: The value of the determinant

(a) n
(b) a
(c) x 

Question: If x, y and z are different from zero and

(a) 0
(b) -1
(c) 1
(d) 2 

Question:

(a) 1
(b) – 1
(c) 0
(d) None of these 

Question: The value of

(a) 0
(b) 1
(c) – 1
(d) None of these

Question: For the values of A, B, C and P, Q, R the value of

(a) 0
(b) cos cos cos A B C
(c) sin sin sin A B C
(d) cos cos cos P 

Question: if

f(50) is equal
(a) 0
(b) 1
(c) 100
(d) – 100   

Question:

(a) 0
(b) 1
(c) 2
(d) 3 

Question: The value of the determinant

Question:

(a) – 1
(b) 0
(c) 1
(d) dependent of a

Question:

(a) depends upon the function f (x)
(b) is 4
(c) is – 4
(d) is zero 

Question:

(a) 1/ 4
(b) 1/ 2
(c) 0
(d) – 1/ 2 

Question:

Question:  The area of a triangle with vertices (-3,0) (3,0)  and (0, k) is 9 s q units. The value of k will be
(a) 9
(b) 3
(c) –9
(d) 6 

Question: If the coordinates of the vertices of an equilateral triangle with sides of length a are (x₁,y₁),(x₂,y2)

(a)a⁴
(b)3a²
(c)5a⁴
(d)3a⁴ 

Question: If the system of equations x+ ky -z=0, 3x-ky-z=0 and x-3y+z=0 has non-zero solution, then k is equal to
(a) – 1
(b) 0
(c) 1
(d) 2 

Question:. The equation of the line joining (1, 2) and (3, 6) using determinants is 
(a) y =x 
(b) 2y= x
(c) 2x= y
(d) x= 3y 

Question: The system of equations 3x-2y+z=0, λx-14y+15z=0, x+2y-3z=0 has a solution other then x=y=z=0 then λ is equal to
(a) 1
(b) 2
(c) 3
(d) 5 

Question: If the equations 2X+ 3Y +1= 0   and ax+2y-b=0 are consistent, then
(a) a- b  = 2
(b) a +b +1
(c) a+ b  = 3
(d) a- b – 8=0 

Question: If the system of equations 2x+3y+5=0,x+ky+5=0 and kx-12y-14=0 be consistent, then value of k is
(a) – 2,12/5
(b) – 1,1/5
(c) – 6.17/5
(d) 6,12/5

Question:

Question:

(a) (2, 4)
(b) [2, 4]
(c) [2, 4)
(d) All of these  D

Question: The maximum value of Δ =

(a) 1/2
(b) √3/2
(c) √2
(d) 2√3/4 

Question: If A, B and C are angles of a triangle, then the determinant,
(a) 0
(b) –1
(c) 1
(d) None of these 

Question: There are two values of a which makes determinant,

(a) 4
(b) 5
(c) – 4
(d) 9 

Question:

(a) 0
(b) –1
(c) 2
(d) 3 

Question: The number of distinct real roots of

(a) 0
(b) 2
(c) 1
(d) 3 

Question:

(a) f (a) = 0
(b) f (b) = 0
(c) f (0) 0 =
(d) f (1)= 0 

Question. The value of

is
(a) 1
(b) 0
(c) a + b
(d) a – b

Question. 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

Question. If A, B and C are angles of a triangle, then the determinant

is equal to
(a) 0
(b) –1
(c) 1
(d) None of these

Question. If 

and Aij is cofactors of aij, then value of D is given by
(a) a11 A31 + a12 A32 + a13 A33
(b) a11 A11 + a12 A21 + a13 A31
(c) a21 A11 + a22 A12 + a23 A13
(d) a11 A11 + a21 A21 + a31 A31

Question. The value of determinant

(a) a3 + b3 + c3
(b) 3bc
(c) a3 + b3 + c3 – 3abc
(d) None of these

Question. The value of is

(a) 1
(b) –1
(c) 0
(d) ω

Question. If f(x) =

,then

(a) f(a) = 0
(b) f(b) = 0
(c) f(0) = 0
(d) f(1) = 0

Question. The value of 

is
(a) (a – b) (b – c) (c – a)
(b) (b – a) (c – b) (c – a)
(c) a (b – c) (c – a)
(d) None of these

Question. If x, y, z are all different from zero and

= 0, then value of x^–1 + y^–1 + z^–1 is
(a) xyz
(b) x–1 y–1 z–1
(c) –x –y –z
(d) –1

Question. Let A be a square matrix of order 3 × 3, then |KA| is equal to
(a) K|A|
(b) K²|A|
(c) K³|A|
(d) 3K|A|

Question. There are two values of a which makes determinant Δ =

,86 then sum of these numbers is
(a) 4
(b) 5
(c) – 4
(d) 9

Question. 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

Question. The value of the determinant

(a) 9×2(x + y)
(b) 9y2(x + y)
(c) 3y2(x + y)
(d) 7×2(x + y)

Question. The value of is
(a) 0
(b) 1
(c) –1
(d) None

Question. If A is a non-singular square matrix of order 3 such that A2 = 3A, then value of |A| is
(a) –3
(b) 3
(c) 9
(d) 27

Question. If

+3 = 0 , then the value of x is
(a) 3
(b) 0
(c) –1
(d) 1

Question. If a, b, c are in AP, then the value of determinant Δ =

(a) 0
(b) 1
(c) x
(d) 2x

We hope the above multiple choice questions for Class 12 Mathematics for Chapter 4 Determinants provided above with answers based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS are really useful for you. Determinants is an important chapter in Class 12 as it provides very strong understanding about this topic. Students should go through the answers provided for the MCQs after they have themselves solved the questions. All MCQs have been provided with four options for the students to solve. These questions are really useful for benefit of class 12 students. Please go through these and let us know if you have any feedback in the comments section.