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If $x, y, z$ are in arithmetic progression with common difference $d$, $x \neq 3d$, and the determinant of the matrix $\begin{bmatrix} 3 & 4\sqrt{2} & x \ 4 & 5\sqrt{2} & y \ 5 & k & z \end{bmatrix}$ is zero, then the value of $k^2$ is
(1) $72$
(2) $12$
(3) $36$
(4) $6$
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