MCQ
Let $[.]$ , $ \{.\} $ and $sgn$$(.)$ denotes greatest integer function, fractional part function and signum function respectively, then value of determinant
$\left| {\begin{array}{*{20}{c}}
{\left[ \pi \right]}&{amp(1 + i\sqrt 3 )}&1 \\
1&0&2 \\
{\operatorname{sgn} ({{\cot }^{ - 1}}x)}&1&{\{ \pi \} }
\end{array}} \right|$ is-
- A$ - 6 + \frac{{5\pi }}{3} - \frac{{{\pi ^2}}}{3}$
- ✓$\frac{{5\pi }}{3} - \frac{{{\pi ^2}}}{3} - 5$
- C$\frac{{5\pi }}{3} + \frac{{{\pi ^2}}}{3} + 6$
- D$ - 5 + \frac{{{\pi ^3}}}{3} - \frac{{5{\pi ^2}}}{3}$
