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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Matrices
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The value of $\begin{vmatrix}x&p&q\\p&x&q\\p&q&x\end{vmatrix}$ is

$\begin{array}{1 1}(a)\;x(x-p)(x-q)\\(b)\;(x-p)(x-q)(x+p+q)\\(c)\;(p-q)(x-q)(x-p)\\(d)\;pq(x-p)(x-q)\end{array}$

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1 Answer

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Given :
$\begin{vmatrix}x&p&q\\p&x&q\\p&q&x\end{vmatrix}$
$\Rightarrow x(x^2-q^2)-p(px-pq)+q[pq-px]$
$\Rightarrow x(x-q)(x+q)-p^2(x-q)-pq(x-q)$
$\Rightarrow (x-q)[x^2+xq-p^2-pq]$
$\Rightarrow (x-q)(x-p)(x+p+q)$
Hence (b) is the correct answer.
answered Nov 22, 2013 by sreemathi.v
 

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