# Class 12 Mathematics Chapter 4 Determinants MCQ Question with Answer

Determinants Class 12 MCQ is one of the best strategies to prepare for the CBSE Class 12 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more MCQ on Determinants Class 12, which will help them all through their board test.

## Determinants Class 12 MCQ Questions with Answer

Class 12 Maths MCQ with answers are given here to Chapter 4 Determinants. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 12 Mathematics syllabus. By Solving these Class 12 MCQs, you will be able to analyze all of the concepts quickly in the chapter and get ready for the Class 12 Annual exam.

Learn Determinants Class 12 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 12 Mathematics Determinants MCQ with answers given below.

Question 1. If A, B and C are angles of a triangle, then the determinant

$\begin{vmatrix} -1 & CosC & CosB\\ CosC & -1 & CosA\\ CosB & CosA & -1 \end{vmatrix}$

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

A

Question 2. If ,

$\begin{vmatrix} x &2 \\ 18 &x \end{vmatrix}=\begin{vmatrix} 6 &2 \\ 18 &6 \end{vmatrix}$

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

B

Question 3.The value of

$\begin{vmatrix} 1 & a & b+c\\ 1 & b & c+a\\ 1 & c & a+b \end{vmatrix}$

is
(a) 1
(b) 0
(c) a + b
(d) a – b

B

Question 4. 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

B

Question 5. The value of determinant

$\begin{vmatrix} a-b & b+c & a\\ b-c & c+a & b\\ c-a & a+b & c \end{vmatrix}$

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

C

Question 6.If

$\begin{vmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31}& a_{32} & a_{33} \end{vmatrix}$

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

D

Question 7. If f(x) =

$\begin{vmatrix} 0 & x-a & x-b\\ x+a & 0 & x-c\\ x+b &x+c & 0 \end{vmatrix}$

,then

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

C

Question 8.The value of is

$\begin{vmatrix} 1 & \omega & \omega ^{2}\\ \omega & \omega ^{2} & 1\\ \omega ^{2} & \omega & 1 \end{vmatrix}$

(a) 1
(b) –1
(c) 0
(d) ω

C

Question 9. 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|

C

Question 10. There are two values of a which makes determinant Δ =

$\begin{vmatrix} 1 & -2 & 5\\ 2 & a & -1\\ 0 & 4 & 2a \end{vmatrix}$

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

C

Whoever needs to take the CBSE Class 12 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 12 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Determinants Class 12 MCQ are ready by the subject specialists themselves.

Question 11.The value of

$\begin{vmatrix} 1 & a & a^{2}\\ 1 & b & b^{2}\\ 1 & c & c^{2} \end{vmatrix}= \begin{vmatrix} 1 & 1 & 1\\ a & b & c\\ a^{2}& b^{2} & c^{2} \end{vmatrix}$

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

A

Question 12. If x, y, z are all different from zero and

$\begin{vmatrix} 1+x & 1 & 1\\ 1 & 1+y & 1\\ 1 & 1 & 1+z \end{vmatrix}$

= 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

D

Question 13.The value of the determinant

$\begin{vmatrix} x & x+y & x+2y\\ x+2y & x & x+y\\ x+y & x+2y & x \end{vmatrix}$

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

B

Question 14.The value of is
(a) 0
(b) 1
(c) –1
(d) None

A

Question 15.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

D

Question 16. If

$\begin{vmatrix} 2 & 3 & 2\\ x & x & x\\ 4 & 9 & 1 \end{vmatrix}$

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

C

Question 17.If a, b, c are in AP, then the value of determinant Δ =

$\begin{vmatrix} x+2 & x+3 & x+2a\\ x+3 & x+4 & x+2b\\ x+4 & x+5 & x+2c \end{vmatrix}$

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

A

Question 18. 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

D

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