Question

Total number of ordered pairs (x,y) satisfying $|x|+|y|=2,sin\left(\frac{\pi x^2}{3}\right)=1$ is

• A. 2
• B. 3
• C. 4
• D. 6

Answer 1

The correct option is C

4

$|x|+|y|=2\Rightarrow |x|,|y|\in [0,2]sin\left(\frac{\pi x^2}{3}\right)=1\Rightarrow \frac{\pi x^2}{3}=(4n+1)\frac{\pi }{2}\Rightarrow \frac{x^2}{3}=(4n+1)\frac{1}{2}\Rightarrow x^2=(4n+1)\frac{3}{2}=\frac{3}{2}$ [as $|x|\le 2$]
$\Rightarrow |x|=\sqrt{\frac{3}{2}},|y|=2-\frac{\sqrt{3}}{2}\therefore 4$