JEE (Advanced) 2008 Paper-1

Instructions

Let A, B, C be three sets of complex numbersas defined below
$$A = \left\{z : Imz \geq 1\right\}$$
$$B = \left\{z : \mid z - 2 - i \mid = 3\right\}$$
$$C = \left\{z : Re((1 - i)z) = \sqrt{2}\right\}$$

Question 21

The number of elements in the set $$A \bigcap B \bigcap C$$ is


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