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# If $x,y,z$ are all positive and are the $p$th, $q$th and $r$th terms of a geometric progression respectively, then the value of the determinant $\begin{vmatrix} \log x & p & 1 \\ \log z & r &1 \\ \log z & r & 1 \end{vmatrix}=$

$\begin {array} {1 1} (1)\;\log\; xyz & \quad (2)\;(p-1)(q-1)(r-1) \\ (3)\;pqr & \quad (4)\;0 \end {array}$

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answered Nov 7, 2013 by