JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Circle

$OB$ is a diameter of the circle and $PQ$ is the chord through $A$ perpendicular to it, so $A$ is the midpoint of $PQ$.
Here $OA=1$ and $OB=13$, so $AB=13-1=12$. The two chords $OB$ and $PQ$ cut at $A$, and therefore

Since $PA=AQ$, $PA=2\sqrt{3}$ and $PQ=4\sqrt{3}$.
In triangle $PQB$ the side $PQ$ is a base and $AB=12$ is the perpendicular distance from $B$ to it, so

The area of triangle $PQB$ is $24\sqrt{3}$ square units.