Let . Let attains minimum and maximum values, respectively, at and . If , where and are integers, then the value of is equal to:

26 Explanation: Solution Region : Circle aur line . Point : . Humne se ke points ki distance check karni hai. Finding (Minimum) : Center se ki distance . circle ki boundary par hoga: . . Finding (Maximum) : Line aur circle ke intersection points: . Points are and . Distance . Distance . Lekin circle ka sabse door wala point (agar line constraint na hoti) hota, jo satisfy nahi karta. Isliye maximum distance intersection point par check karte hain: . Final Calculation : . . . Correct Answer: 26

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JEE 2022 — Mathematics PYQ

JEE | Mathematics | 2022

Let $S = \{z \in C : |z - 2| \le 1, z(1 + i) + \bar{z}(1 - i) \le 2\}$ . Let $|z - 4i|$ attains minimum and maximum values, respectively, at $z_1 \in S$ and $z_2 \in S$ . If $5(|z_1|^2 + |z_2|^2) = \alpha + \beta\sqrt{5}$ , where $\alpha$ and $\beta$ are integers, then the value of $\alpha + \beta$ is equal to:

JEE 2022 — Mathematics PYQ

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