The total number of ordered pairs `(x , y)` satisfying `|x|+|y|=2,sin((pix^2)/3)=1,` is equal to 2 (b) 3 (c) 4 (d) 6

Options

A. 2
B. 3
C. 4
D. 6

Answer

C

Explanation

`|x|+|y|=2, sin ((pi x^(2))/3)=1`
`rArr |x|, |y| in [0, 2], (pi x^(2))/3=(4n+1) pi/2, n in Z`
`rArr x^(2)=(3(4n+1))/2=3/2`, as `|x| le 2`
`rArr |a|=sqrt(3/2), |y|=4-sqrt(3/2)`
Thus, there are four ordered pairs.