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|10 ! 11 ! 12 ! 11 ! 12 ! 13 ! 12 ! 13 ! 14 !|=
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Q. $\begin{vmatrix}10 ! & 11 ! & 12 ! \\ 11 ! & 12 ! & 13 ! \\ 12 ! & 13 ! & 14 !\end{vmatrix}=$
Gujarat CET
Gujarat CET 2018
A
$2(10!. 12!. 13!)$
B
$2(10!. 11!. 12!)$
C
$-2(10 ! .11 ! . 12 !)$
D
$2(10 ! .13 !)$
Solution:
$\begin{vmatrix}1 & 1 & 1 \\ 11 & 12 & 13 \\ 11.12 & 12.13 & 13.14\end{vmatrix}$
$=10 ! 11 ! 12 ! \times \begin{vmatrix}1 & 0 & 1 \\ -1 & -1 & 13 \\ -24 & -26 & 13.14\end{vmatrix}$
$10 ! 11 ! 12 !(26-24)=2.10 ! 11 ! 12 !$