The number of ordered pairs $(x, y)$ of real numbers satisfying $4 x^{2} - 4 x + 2 = {sin}^{2} y$ and $x^{2} + y^{2} \leq 3$ will be

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Solution

The correct option is B
2

Since ${sin}^{2} y ϵ [0, 1]$

$\Rightarrow 0 \leq 4 x^{2} - 4 x + 2 \leq 1$

$\Rightarrow 0 \leq 4 x^{2} - 4 x + 1 \leq 0$

$\Rightarrow 0 \leq (2 x - 1)^{2} \leq 0$

$∴ x = \frac{1}{2}$

$\Rightarrow {sin}^{2} y = 1 \Rightarrow y = \pm \frac{π}{2}$

So, ordered pairs are $(\frac{1}{2}, \frac{π}{2})$ and $(\frac{1}{2}, - \frac{π}{2})$

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