सारणिक $\left|\begin{array}{ll}\cos 50^{\circ} & \sin 10^{\circ} \\ \sin 50^{\circ} & \cos 10^{\circ}\end{array}\right|$ का मान है $-$
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$(C) \ \frac{1}{2}$
$\cos 50^{\circ} \cos 10^{\circ}-\sin 10^{\circ} \sin 50^{\circ}$
$=\cos \left(50^{\circ}+10^{\circ}\right)$
$=\cos 60^{\circ}=\frac{1}{2}$
अतः सही विकल्प $(C)$ है।
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यदि मैट्रिक्स $P=\left[\begin{array}{ccc}1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & 2 & 4\end{array}\right]$ के अवयव $p_{i j}$ के लिए सहखण्डज $C_{i j}$ से व्यक्त हो तो $C _{31} \cdot C _{23}$ का मान है-