jee-main 2023 Q62

jee-main · India · session2_15apr_shift1 Complex Numbers Argand & Loci Distance and Region Optimization on Loci
If the set $\left\{ \operatorname { Re } \left( \frac { z - \bar { z } + z \bar { z } } { 2 - 3 z + 5 \bar { z } } \right) : z \in \mathbb { C } , \operatorname { Re } z = 3 \right\}$ is equal to the interval $( \alpha , \beta ]$, then $24 ( \beta - \alpha )$ is equal to
(1) 36
(2) 27
(3) 30
(4) 42
If the set $\left\{ \operatorname { Re } \left( \frac { z - \bar { z } + z \bar { z } } { 2 - 3 z + 5 \bar { z } } \right) : z \in \mathbb { C } , \operatorname { Re } z = 3 \right\}$ is equal to the interval $( \alpha , \beta ]$, then $24 ( \beta - \alpha )$ is equal to\\
(1) 36\\
(2) 27\\
(3) 30\\
(4) 42