- A$0$
- ✓$\sqrt{2}$
- C2
- D1
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$z^5=1$ then value of $\left| {\begin{array}{*{20}{c}}
{{e^\alpha }}&{{e^{2\alpha }}}&{{e^{3\alpha + 1}}}&{ - {e^{ - \delta }}} \\
{{e^\beta }}&{{e^{2\beta }}}&{{e^{3\beta + 1}}}&{ - {e^{ - \delta }}} \\
{{e^\gamma }}&{{e^{2\gamma }}}&{{e^{3\gamma + 1}}}&{ - {e^{ - \delta }}}
\end{array}} \right|$
$f(x) = \left\{ {\begin{array}{*{20}{c}}
{x + 2,}&{if\,\,x\,\, < \,\,1}\\
{0,}&{if\,\,\,x = 1}\\
{x - 2,}&{if\,\,x\,\, > \,\,1}
\end{array}} \right.$
$( S 1):|(\overrightarrow{ a } \times \overrightarrow{ b })+(\overrightarrow{ c } \times \overrightarrow{ b })|-|\overrightarrow{ c }|=6(2 \sqrt{2}-1)$
$( S 2): \angle ABC =\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)$. Then
$x+y+z=2$
$2 x+4 y-z=6$
$3 x+2 y+\lambda z=\mu$ has infinitely many solutions, then