Which valve type can be operated manually and provides on/off control?

The choice of a ball valve as the correct answer reflects its design and functionality. A ball valve has a spherical disc, or "ball," that controls the flow of fluid through the valve. When the handle is turned, the ball rotates to either allow fluid to pass through or to block the flow completely, providing a very reliable on/off control.

Ball valves are typically easy to operate manually and offer a quick shut-off capability with minimal resistance to flow when in the open position. Their tight sealing properties make them ideal for applications where leak-proof performance is critical. This allows for efficient control over fluid flow with a simple quarter turn of the handle.

In contrast, a check valve is designed to prevent backflow and does not offer manual control, while a gate valve is designed to fully open or close the flow but requires more rotation and can be less efficient in smaller lines. A butterfly valve, while capable of on/off control, involves a rotating disc that can be less effective at providing a complete seal compared to a ball valve. Hence, the ball valve stands out as the best option for manually operated on/off control.