JEE MAIN - Mathematics Bengali (2022 - 29th July Evening Shift - No. 12)
Let $$S = \{ z = x + iy:|z - 1 + i| \ge |z|,|z| < 2,|z + i| = |z - 1|\} $$. Then the set of values of $$x$$, for which $$w = 2x + iy \in S$$ for some $$y \in R$$ is
$$\left( { - \sqrt 2 ,{1 \over {2\sqrt 2 }}} \right]$$
$$\left( { - {1 \over {\sqrt 2 }},{1 \over 4}} \right]$$
$$\left( { - \sqrt 2 ,{1 \over 2}} \right]$$
$$\left( { - {1 \over {\sqrt 2 }},{1 \over {2\sqrt 2 }}} \right]$$
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