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Question

Let $\mathrm{R}$ be the interior region between the lines $3 x-y+1=0$ and $x+2 y-5=0$ containing the origin. The set of all values of $a$, for which the points $\left(a^2, a+1\right)$ lie in $R$, is :

 $(-3,0) \cup\left(\frac{2}{3}, 1\right)$
$(-3,0) \cup\left(\frac{1}{3}, 1\right)$
$(-3,-1) \cup\left(\frac{1}{3}, 1\right)$
$(-3,-1) \cup\left(-\frac{1}{3}, 1\right)$

Solution

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