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Question

Total number of ordered pairs (x,y) satisfying |x|+|y|=2, sin(πx23)=1 is


A

2

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B

3

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C

4

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D

6

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Solution

The correct option is C

4


|x|+|y|=2 |x|,|y|[0,2]sin(πx23)=1πx23=(4n+1)π2x23=(4n+1)12x2=(4n+1)32=32 [as |x|2]
|x|=32,|y|=2324


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