Mathematics Question from JEE Main 2025 · 3 April, Shift 2

Line $L_1$ of slope $2$ and line $L_2$ of slope $\frac{1}{2}$ intersect at the origin $O$. In the first quadrant, $P_1, P_2, \dots, P_{12}$ are $12$ points on line $L_1$ and $Q_1, Q_2, \dots, Q_9$ are $9$ points on line $L_2$. Then the total number of triangles that can be formed having vertices at three of the $22$ points $O$, $P_1, P_2, \dots, P_{12}$, $Q_1, Q_2, \dots, Q_9$, is: