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JEE Math Practice Question

The values of $$\alpha$$, for which $$\left|\begin{array}{ccc}1 & \frac{3}{2} & \alpha+\frac{3}{2} \\ 1 & \frac{1}{3} & \alpha+\frac{1}{3} \\ 2 \alpha+3 & 3 \alpha+1 & 0\end{array}\right|=0$$, lie in the interval

  1. A.$$(-2,1)$$
  2. B.$$\left(-\frac{3}{2}, \frac{3}{2}\right)$$
  3. C.$$(-3,0)$$
  4. D.$$(0,3)$$

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