JEE Main 2022 · 24 Jun · Shift 1, Mathematics question 1

Picture it. $A$ is the closed annulus about $1+i$ with radii 1 and 2. $B$ is the part of the circle $|z-(1-i)|=1$ (centre $1-i$, radius 1) lying in $A$.

Distances. The centres are 2 apart, so points of the circle are at distance between $2-1=1$ and $2+1=3$ from $1+i$. The points with distance in $[1,2]$ form a whole arc (from the nearest point, at distance 1, out to where the distance reaches 2).

Conclusion. An arc has infinitely many points.

(D)