If D_p = | , * 20 c p& 15 &8 p^2 & 35 &9 p^3 & 25 & 10 , |, then … - Vidyadip

MCQ

If ${D_p} = \left| {\,\begin{array}{*{20}{c}}p&{15}&8\\{{p^2}}&{35}&9\\{{p^3}}&{25}&{10}\end{array}\,} \right|$, then ${D_1} + {D_2} + {D_3} + {D_4} + {D_5} = $

A
$0$
B
$25$
C
$625$
✓
$- 700000$

✓

Answer

Correct option: D.

$- 700000$

d
(d) ${D_1} = \left| {\,\begin{array}{*{20}{c}}1&{15}&8\\1&{35}&9\\1&{25}&{10}\end{array}\,} \right|,{D_2} = \left| {\,\begin{array}{*{20}{c}}2&{15}&8\\4&{35}&9\\8&{25}&{10}\end{array}\,} \right|$

${D_3} = \left| {\,\begin{array}{*{20}{c}}3&{15}&8\\9&{35}&9\\{27}&{25}&{10}\end{array}\,} \right|,{D_4} = \left| {\,\begin{array}{*{20}{c}}4&{15}&8\\{16}&{35}&9\\{64}&{25}&{10}\end{array}\,} \right|$

${D_5} = \left| {\,\begin{array}{*{20}{c}}5&{15}&8\\{25}&{35}&9\\{125}&{25}&{10}\end{array}\,} \right|$

==> ${D_1} + {D_2} + {D_3} + {D_4} + {D_5} = \left| {\,\begin{array}{*{20}{c}}{15}&{75}&{40}\\{55}&{175}&{45}\\{225}&{125}&{50}\end{array}\,} \right|$

$ = 15(3125) - 75( - 7375) + 40( - 32500)$

$ = 46875 + 553125 - 1300000 = - 700000$ .

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