MCQ
જો $\begin{vmatrix}1&w^n&w^{2n}\\w^n&w^{2n}&1\\w^{2n}&1&w^n\end{vmatrix}= .......$
- ✓$0$
- B$1$
- C$w$
- D$w^2$
$\rightarrow w$ એ $1$ નું ઘનમૂળ છે તેથી ${w^3} = 1,\,{w^{3n}} = {1^n} = 1$
$D=\begin{vmatrix}1 & \ \omega^n & \ \omega^{2n} \\\omega^n & \omega^{2n} & 1 \\\omega^{2n} & 1 & \omega^n \end{vmatrix}$
$=1( \omega^{3n} - 1)- \omega^n(\omega^{2n}-\omega^{2n})+ \omega^{2n}(\omega^{n}-\omega^{4n})$
$=1(1-1)- \omega^n(0)+ \omega^{3n}(1-\omega^{3n})$
$=0-0+0$
$=0$
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$\begin{gathered}
f\left( x \right) = \left[ \begin{gathered}
{\cos ^{ - 1}}\left( \mu \right) + {x^2},0 < x < 1 \hfill \\
4x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,x \geqslant 1 \hfill \\
\end{gathered} \right.,f\left( x \right) \hfill \\
\hfill \\ \end{gathered}$ જેને $x =$ $1$ આગળ સ્થાનીય ન્યુન્તમ કિમત મળે તો $\mu$ ની ક્યા અંતરાલમા મળે ?