Introduction:
In the context of slow and inefficient I/O peripherals, the interrupt mechanism plays a crucial role in handling the I/O operations efficiently. The design of the interrupt mechanism should aim to minimize the time required to handle interrupts and maximize the system's responsiveness. Among the given options, the best choice for interrupt handling in this scenario is the vectored interrupt.

Explanation:
1. Polling:
Polling is a simple technique where the processor constantly checks the status of an I/O device to determine if it requires attention. However, in the case of slow and inefficient I/O peripherals, the polling mechanism would waste a significant amount of processing time as the processor would have to wait for the I/O device to respond. This approach is highly inefficient and not suitable for such peripherals.

2. Daisy chaining:
Daisy chaining is a technique where multiple devices are connected in a chain, and each device passes the interrupt signal to the next device until it reaches the processor. While this approach is suitable for handling interrupts from multiple devices, it does not address the issue of slow and inefficient I/O peripherals. It does not provide any mechanism to expedite the interrupt handling process, making it less efficient for this scenario.

3. Vectored Interrupt:
Vectored interrupt is a mechanism where each I/O device is assigned a unique interrupt vector, which contains the address of the corresponding interrupt service routine. When an interrupt occurs, the processor directly jumps to the appropriate interrupt service routine based on the interrupt vector. This approach eliminates the need for the processor to search for the appropriate routine, reducing the interrupt handling time significantly.

4. I/O controller:
While an I/O controller can handle the I/O operations, it does not directly address the issue of interrupt handling for slow and inefficient peripherals. An I/O controller is responsible for managing the data transfer between the processor and the peripheral device, but it may not optimize the interrupt handling process.

Conclusion:
Considering the requirements of handling slow and inefficient I/O peripherals efficiently, the vectored interrupt mechanism is the best choice. It minimizes the interrupt handling time by directly jumping to the appropriate interrupt service routine, thereby ensuring the system's responsiveness and efficient utilization of processor resources.