MCQ
The value of $^{15}{C_3}{ + ^{15}}{C_{13}}$ is
- ✓$^{16}{C_3}$
- B$^{30}{C_{16}}$
- C$^{15}{C_{10}}$
- D$^{15}{C_{15}}$
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$S_1=\{z \in C:|z|<4\}, S_2=\left\{z \in C: \operatorname{Im}\left[\frac{z-1+\sqrt{3} i}{1-\sqrt{3} i}\right]>0\right\} \text { and } $
$S_3:\{z \in C: \operatorname{Re} z>0\} .$
$1.$ Area of $S=$
$(A)$ $\frac{10 \pi}{3}$ $(B)$ $\frac{20 \pi}{3}$ $(C)$ $\frac{16 \pi}{3}$ $(D)$ $\frac{32 \pi}{3}$
$2.$ $\min _{z \in S}|1-3 i-z|=$
$(A)$ $\frac{2-\sqrt{3}}{2}$ $(B)$ $\frac{2+\sqrt{3}}{2}$ $(C)$ $\frac{3-\sqrt{3}}{2}$$(D)$ $\frac{3+\sqrt{3}}{2}$
Give the answer question $1$ and $2$