Question

If $\left[x\right]$ stands greatest integer $\le x$ then the value of $\left|\begin{array}{ccc}\left[e\right]& \left[\pi \right]& [{\pi }^2-6]\\ \left[\pi \right]& {\pi }^2-6& \left[e\right]\\ [{\pi }^2-6]& \left[e\right]& \left[\pi \right]\end{array}\right|$ equals

• A. -8
• B. 8
• C. -1
• D. 1

Answer 1

Answer: (A)

-8

$\pi =3.14---\left[\pi \right]=3$
$e=2-----\left[e\right]=2$
$9<{\pi }^2<10[{\pi }^2-6]=3$
$\Rightarrow \left|\begin{array}{ccc}2& 3& 3\\ 3& 3& 2\\ 3& 2& 3\end{array}\right|$
$R_1\to R_1-R_2$
$\Rightarrow \left|\begin{array}{ccc}-1& 0& 1\\ 3& 3& 2\\ 3& 2& 3\end{array}\right|$
$c_1\to c_1-c_2$
$\Rightarrow \left|\begin{array}{ccc}0& 0& 1\\ 5& 3& 2\\ 6& 2& 3\end{array}\right|$
expand along $R_1$
$\Rightarrow -8$