The number of pair (x,y) satisfying 4x²-4x+2=sin²y and x²+y²≤3 are

a.0

b.2

c.4

d.none of these

Hi Menka,

Please note the minimum value that the Q.Expression can take is 1 (when x=1/2).

So y^2 ≤ 3-1/4 = 11/4.

and for this sin^2 y = 1, so y = Π/2, -Π/2.

So there are two pairs viz. (1/2,Π/2) and (1/2,-Π/2)

Hence Option (B).

Hope that helps.

Best Regards,

Ashwin (IIT Madras).