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If the value of the determinant $\left|\begin{array}{lll}a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c\end{array}\right|$ is positive, where $\mathrm{a} \neq \mathrm{b} \neq \mathrm{c}$, then the value of abc
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is greater than-8
$\left|\begin{array}{lll}\mathrm{a} & 1 & 1 \\ 1 & \mathrm{~b} & 1 \\ 1 & 1 & \mathrm{c}\end{array}\right|>0$
$\Rightarrow a(b c-1)-1(c-1)+1(1-b)>0$
$\Rightarrow a b c-a-c+1+1-b>0$
$\Rightarrow a b c+2-(a+b+c)>0$
$\Rightarrow a b c>(a+b+c)-2$
Let; $\mathrm{a}=-1 ; \mathrm{b}=0 \& \mathrm{c}=1$
Then; $0>-2$ [which is correct $]$ Hence, $\mathrm{abc}=0$
$\therefore$ After considering all the option; (b) is correct option.s
$\Rightarrow a(b c-1)-1(c-1)+1(1-b)>0$
$\Rightarrow a b c-a-c+1+1-b>0$
$\Rightarrow a b c+2-(a+b+c)>0$
$\Rightarrow a b c>(a+b+c)-2$
Let; $\mathrm{a}=-1 ; \mathrm{b}=0 \& \mathrm{c}=1$
Then; $0>-2$ [which is correct $]$ Hence, $\mathrm{abc}=0$
$\therefore$ After considering all the option; (b) is correct option.s
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