Correct Answer - 4
Let `P-=(2sqrt(3)cos theta, 2 sin theta)`
and `Q-=(2sqrt(3)cos((pi)/(2)+theta),2sin((pi)/(2)+theta))`
or `Q-=(-2sqrt(2)sin theta, 2 cos theta)`
`(PQ)^(2)=8(cos theta+sin theta)^(2)+4(sin theta-cos theta)^(2)=12+4 sin 2 theta`
`:. (PQ)_("max")=4`