The value of $x$ if $\begin{vmatrix} x & x+2 \\ x-2 & x \end{vmatrix}$ is : (a) $x^2$ (b) $+4$ (c) $0$ (d) $1$

The value of x if x x+2 x-2 x is : (a) x² (b) +4 (c) 0 (d) 1

Question 20 of 47

x

(a)

x^2

(b)

+4

(c)

0

(d)

1

Puducherry TnboardTamil Nadu HSC First Year (DGE) Commerce Board 2020MCQ· 1mImportance★★★★★

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Evaluating the $2\times2$ determinant gives $x^2-(x+2)(x-2)=x^2-(x^2-4)=4$ , so its value is $4$ .

For a $2\times2$ determinant $\begin{vmatrix} a & b \\ c & d \end{vmatrix}=ad-bc$ . Here $a=x,\;b=x+2,\;c=x-2,\;d=x$ :

$\begin{vmatrix} x & x+2 \\ x-2 & x \end{vmatrix} = (x)(x) - (x+2)(x-2).$ …