Let $ A = \left\{ x \in (0, \pi) \mid - \log\left(\frac{2}{\pi}\right)\sin x + \log\left(\frac{2}{\pi}\right)\cos x = 2 \right\} $ and

\[ B = \left\{ x \geq 0 : \sqrt{x}(\sqrt{x - 4}) - 3\sqrt{x - 2} + 6 = 0 \right\}. \]

Then $ n(A \cup B) $ is equal to:

Question

Let $z$ be the complex number satisfying $|z - 5| \le 3$ and having maximum positive principal argument. Then $34 \left| \frac{5z - 12}{5iz + 16} \right|^2$ is equal to :

Answer 1

The set $ A $ is determined by simplifying the provided equation and identifying the $ x $ values that satisfy it. Subsequently, the set $ B $ is derived from its given equation. Once the elements of both sets are established, $ n(A \cup B) $, which represents the cardinality of the union of sets $ A $ and $ B $, is computed. Final Answer: $ n(A \cup B) = 4 $.

Let \( A = \left\{ x \in (0, \pi) \mid - \log\left(\frac{2}{\pi}\right)\sin x + \log\left(\frac{2}{\pi}\right)\cos x = 2 \right\} \) and

\[ B = \left\{ x \geq 0 : \sqrt{x}(\sqrt{x - 4}) - 3\sqrt{x - 2} + 6 = 0 \right\}. \]

Then \( n(A \cup B) \) is equal to:

Show Hint

The Correct Option is D

Solution and Explanation

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Questions Asked in JEE Main exam

Let \( A = \left\{ x \in (0, \pi) \mid - \log\left(\frac{2}{\pi}\right)\sin x + \log\left(\frac{2}{\pi}\right)\cos x = 2 \right\} \) and \[ B = \left\{ x \geq 0 : \sqrt{x}(\sqrt{x - 4}) - 3\sqrt{x - 2} + 6 = 0 \right\}. \] Then \( n(A \cup B) \) is equal to: