23put \theta _{b}=0 , \theta _{a}=\pi
then clearly ang vel = 0
hence options a,b are eliminated , and c,d are still dere
now put \theta _{b}= \theta _{a}=\frac{\pi }{2}
now
\upsilon _{a/b}= v_{a}-v_{b}
since they are in the same direction, eqn is true even for magnitude )
hence ang vel of A relative to B is simply \frac{\upsilon _{a/b}}{r}=\frac{ v_{a}-v_{b}}{r}
but this will be in the clockwise direction , hence in anticlockwise direction it will be \frac{ v_{b}-v_{a}}{r}
and out of c,d c gives correct ans
sorry for my nonconceptual method [4]but i really solved ds in 25 secs [3]