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Straight Lines

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Let \(R\) 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 :

[JEE Main 2024, 27 Jan (Shift 2)]

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

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

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

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

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