Which category of multiplexing randomly allocates time slots to different data signals depending on the rate at which they are being generated from the source?

The correct answer is found in the definition of asynchronous time-division multiplexing (ATDM). This category of multiplexing enables a system to allocate time slots to different data signals in a flexible manner, based on the arrival rate of the data from the various sources. Unlike synchronous time-division multiplexing, which assigns fixed time slots to each signal regardless of whether they are active, ATDM responds dynamically to the demand from each source. This means that if a source generates data more frequently, it may receive more time slots, while a source that generates data less frequently may receive fewer. This efficient use of time slots helps to optimize bandwidth usage in a network.

Dynamic time division multiplexing, while similar in that it may dynamically allocate resources, is not commonly recognized as a distinct category in the same way that asynchronous time-division multiplexing is. The mention of frequency division multiplexing refers to a different technique entirely that uses different frequency bands for different signals and does not involve the time-based allocation being described.