JEE Math Practice 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 :
- A.$$(-3,0) \cup\left(\frac{2}{3}, 1\right)$$
- B.$$(-3,0) \cup\left(\frac{1}{3}, 1\right)$$
- C.$$(-3,-1) \cup\left(\frac{1}{3}, 1\right)$$
- D.$$(-3,-1) \cup\left(-\frac{1}{3}, 1\right)$$
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