Multiple choice (Determinants)

Choose and write the correct option in the following question:(Class 12 determinants multiple choice question)

1.) $\begin{vmatrix} x & 2\\ 18 & x \end{vmatrix} = \begin{vmatrix} 6 & 2 \\ 18 & 6\end{vmatrix}$ , then x is equal to

(a) 6 (b) ±6

Answer:(b)

2.) 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

Answer (b)

3.) 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

Answer (c)

4.) 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

Answer (c)

5.) If $C_{ij}$ denotes the cofactor of element $P_{ij}$ of the matrix $\begin{vmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & 2 & 4\end{vmatrix}$ , then the value of $C_{31},C_{23}$ is

(a) 5 (b) 24

Answer (a)

6.) If x = -4 is a root of $\begin{vmatrix} x & 2 & 3 \\ 1 & x & 1 \\ 3 & 2 & x\end{vmatrix}=0$ , then the sum of the other rwo roots is

(a) 4 (b) -3

Answe (a)

7.) If for a matrix $\begin{bmatrix} \alpha & -2 \\ -2 & \alpha \end{bmatrix},|A^3| = 125$ , then the value of α is

(a) ±3 (b) -3

Answer (a)

8.) If $A = \begin{vmatrix} -2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2\end{vmatrix}$ , then the value of $|adj A|$ is

(a) 64 (b) 16

Answer (a)

9.) If A is square matrix of order 3, such that $A(adj A) = 10I$ , then $|adj A|$ is equal to

(a) 1 (b) 10

Answer (c)

10.) If $B.\begin{bmatrix}1 & -2 \\ 1 & 4\end{bmatrix} = \begin{bmatrix}6 & 0 \\ 0 & 6\end{bmatrix}$

(a) $\begin{bmatrix}4 & 2 \\ 1 & 1\end{bmatrix}$

(b) $\begin{bmatrix}4 & 2 \\ -1 & 1\end{bmatrix}$

(d) I

Answer (b)

11.) The sum of the products of elements of any row with the co-factors of corresponding elements equal to

(a) Cofactor sum (b) Value of the derminant

Answer (b)

12.) The matrix $\begin{bmatrix}5 & 10 & 3 \\ -2 & -4 & 6\\ -1 & -2 & b\end{bmatrix}$ is singular matrix, if the value of b is

(a) -3 (b) 3

Answe (d)

13.) If x, y, z are non zero real numbers, then the inverse of matrix $\begin{bmatrix} x & 0 & 0\\ 0 & y & 0 \\ 0 & 0 & z \end{bmatrix}$ is

(a) $\begin{bmatrix} x^{-1} & 0 & 0\\ 0 & y^{-1} & 0 \\ 0 & 0 & z^{-1} \end{bmatrix}$

(b) $xyz\begin{bmatrix} x^{-1} & 0 & 0\\ 0 & y^{-1} & 0 \\ 0 & 0 & z^{-1} \end{bmatrix}$

(d) $\frac{1}{xyz}\begin{bmatrix} 1 & 0 & 0\\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$

Answer (a)

14.) If $A = \begin{bmatrix} 1 & \tan x \\ -\tan x & 1 \end{bmatrix}$ then the value of $A^TA^{-1}$ is

(a) $\begin{bmatrix} \cos 2x & -\sin 2x \\ \sin 2x & \cos 2x\end{bmatrix}$

(b) $\begin{bmatrix} \cos x & \sin x \\ 1 & 0\end{bmatrix}$

(d) Zero matrix

Answer (a)

15.) The value of $(A^{-1})^T$ is

(a) $(A^T)^{-1}$ (b) $A^{-1}$

Answer (a)

16.) If A is an invertible matrix of order 2, then $(detA^{-1})$ is equal to

(a) det A (b) $\frac{1}{det A}$

Answer (b)

17.) If A is singular matrix, then A(adj A) is

(a) Null matrix (b) Scalar matrix

Answer (a)

18.) Using matrix method to solve the following system of equations: 5x – 7y = 2, 7x – 5y = 3, value of x, y is

(a) x = 11/24, y = 1/24 (b) x = -11/24, y = 1/24

Answer (a)

19.) If A is square matrix of order 3×3 such that |A| = 2, then the value of $|adj(adj A)|$ is

(a) -16 (b) 16

Answer (b)

20.) If A and B are invertible matrices, then which of the following is NOT correct.

(a) $adj A = |A|.A^{-1}$ (b) $det(A^{-1}) = [det (A)]^{-1}$

Answer (d)

Multiple choice (Determinants)

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