JEE Math Practice Question
Let $$S_1=\{z \in \mathbf{C}:|z| \leq 5\}, S_2=\left\{z \in \mathbf{C}: \operatorname{Im}\left(\frac{z+1-\sqrt{3} i}{1-\sqrt{3} i}\right) \geq 0\right\}$$ and $$S_3=\{z \in \mathbf{C}: \operatorname{Re}(z) \geq 0\}$$. Then the area of the region $$S_1 \cap S_2 \cap S_3$$ is :
- A.$$\frac{125 \pi}{24}$$
- B.$$\frac{125 \pi}{6}$$
- C.$$\frac{125 \pi}{12}$$
- D.$$\frac{125 \pi}{4}$$
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