JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(\mathrm{A}=\{x \in(0, \pi) -\left\{\frac{\pi}{2}\right\}: \log _{(2 / \pi)}|\sin x|+\log _{(2 / \pi)}|\cos x|=2\}\) and \(\mathrm{B}=\{x \geqslant 0: \sqrt{x}(\sqrt{x}-4)-3|\sqrt{x}-2|+6=0\}\). Then \(\mathrm{n}(\mathrm{A} \cup \mathrm{B})\) is equal to :
- A 4
- B 8
- C 6
- D 2
Answer & Solution
Correct Answer
(B) 8
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{A}: \log _{2 \pi}|\sin \mathrm{x}|+\log _{2 \pi}|\cos \mathrm{x}|=2 \\ & \Rightarrow \log _{2 \pi}(|\sin \mathrm{x} \cdot \cos \mathrm{x}|)=2 \\ & \Rightarrow|\sin 2 \mathrm{x}|=\frac{8}{\pi^2}\end{aligned}\) Number of solution 4…
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