jee-main 2024 Q61

jee-main · India · session2_05apr_shift2 Complex Numbers Argand & Loci Intersection of Loci and Simultaneous Geometric Conditions

Let $S _ { 1 } = \{ z \in C : | z | \leq 5 \} , S _ { 2 } = \left\{ z \in C : \operatorname { Im } \left( \frac { z + 1 - \sqrt { 3 } i } { 1 - \sqrt { 3 } i } \right) \geq 0 \right\}$ and $S _ { 3 } = \{ z \in C : \operatorname { Re } ( z ) \geq 0 \}$. Then the area of the region $S _ { 1 } \cap S _ { 2 } \cap S _ { 3 }$ is :
(1) $\frac { 125 \pi } { 12 }$
(2) $\frac { 125 \pi } { 4 }$
(3) $\frac { 125 \pi } { 24 }$
(4) $\frac { 125 \pi } { 6 }$

Let $S _ { 1 } = \{ z \in C : | z | \leq 5 \} , S _ { 2 } = \left\{ z \in C : \operatorname { Im } \left( \frac { z + 1 - \sqrt { 3 } i } { 1 - \sqrt { 3 } i } \right) \geq 0 \right\}$ and $S _ { 3 } = \{ z \in C : \operatorname { Re } ( z ) \geq 0 \}$. Then the area of the region $S _ { 1 } \cap S _ { 2 } \cap S _ { 3 }$ is :\\
(1) $\frac { 125 \pi } { 12 }$\\
(2) $\frac { 125 \pi } { 4 }$\\
(3) $\frac { 125 \pi } { 24 }$\\
(4) $\frac { 125 \pi } { 6 }$

Paper Questions

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