A) 1
B) 0
C) ? 1
D) None of these
Correct Answer: B
Solution :
\[D=\left| \,\begin{matrix} \sin px & p\cos px & -{{p}^{2}}\sin px \\ -{{p}^{3}}\cos px & {{p}^{4}}\sin px & {{p}^{5}}\cos px \\ -{{p}^{6}}\sin px & -{{p}^{7}}\cos px & {{p}^{8}}\sin px \\ \end{matrix}\, \right|\] \[={{p}^{9}}\left| \,\begin{matrix} \sin px & p\cos px & -{{p}^{2}}\sin px \\ -\cos px & p\sin px & {{p}^{2}}\cos px \\ -\sin px & -p\cos px & {{p}^{2}}\sin px \\ \end{matrix}\, \right|\] \[=-{{p}^{9}}\,\left| \,\begin{matrix} \sin px & p\cos px & -{{p}^{2}}\sin px \\ \cos px & p\sin px & {{p}^{2}}\cos px \\ \sin px & p\cos px & -{{p}^{2}}\sin px \\ \end{matrix}\, \right|=0.\]
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