# Let $\mid x\mid$ represent the greatest integer less than or equal to $x$ then the value of the determinant $\begin{vmatrix}e & \pi & \pi^{2}-6 \\ \pi & \pi^{2}-6 & e \\ \pi^{2}-6 & e & \pi \end{vmatrix}$ is

$(a)\;-8\qquad(b)\;8\qquad(c)\;10\qquad(d)\;None\;of\;these$

Given :
$\begin{vmatrix}[e]&[\pi]&[\pi^2-6] \\ [\pi]&[\pi^2-6]&[e] \\ [\pi^2-6]&[e]&[\pi]\end{vmatrix}$
$\Rightarrow \begin{vmatrix}2&3&3\\3&3&2\\3&2&3\end{vmatrix}$
$2(9-4)-3(9-6)+3(6-9)$
$\Rightarrow 10-9-9$
$\Rightarrow -8$
edited Mar 26, 2014 by balaji