A) 0
B) 25
C) 625
D) None of these
Correct Answer: D
Solution :
\[{{D}_{1}}=\left| \,\begin{matrix} 1 & 15 & 8 \\ 1 & 35 & 9 \\ 1 & 25 & 10 \\ \end{matrix}\, \right|,{{D}_{2}}=\left| \,\begin{matrix} 2 & 15 & 8 \\ 4 & 35 & 9 \\ 8 & 25 & 10 \\ \end{matrix}\, \right|\] \[{{D}_{3}}=\left| \,\begin{matrix} 3 & 15 & 8 \\ 9 & 35 & 9 \\ 27 & 25 & 10 \\ \end{matrix}\, \right|,{{D}_{4}}=\left| \,\begin{matrix} 4 & 15 & 8 \\ 16 & 35 & 9 \\ 64 & 25 & 10 \\ \end{matrix}\, \right|\] \[{{D}_{5}}=\left| \,\begin{matrix} 5 & 15 & 8 \\ 25 & 35 & 9 \\ 125 & 25 & 10 \\ \end{matrix}\, \right|\] Þ \[{{D}_{1}}+{{D}_{2}}+{{D}_{3}}+{{D}_{4}}+{{D}_{5}}=\left| \,\begin{matrix} 15 & 75 & 40 \\ 55 & 175 & 45 \\ 225 & 125 & 50 \\ \end{matrix}\, \right|\] \[=15(3125)-75(-7375)+40(-32500)\] \[=46875+553125-1300000=-700000\] .You need to login to perform this action.
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