Final answer:
The inventions that helped the monarchy conquer territories were the cannon and the cross-bow design. The option (3) is correct.
Step-by-step explanation:
The inventions that helped the monarchy conquer territories during the time of political and technological development were both the cannon and the cross-bow design.
These inventions revolutionized warfare and enabled armies to breach stone walls, dismantle protective fortifications, and defeat enemies. The use of cannons played a significant role in the fall of Constantinople and the destruction of castles, consolidating the power of rulers over their territories. Therefore, option (3) is correct.