The given question asks us to determine the output of a J-K flip-flop with J = 1 and K = 1, given a 20 kHz clock input. Let's analyze the behavior of a J-K flip-flop and understand why the correct answer is option 'D' - A 10 kHz square wave.

J-K Flip-Flop Behavior:
A J-K flip-flop is a sequential logic device that has two inputs, J and K, and two outputs, Q and Q̅. The flip-flop is clocked by an external clock signal (in this case, a 20 kHz clock input). The J and K inputs determine the behavior of the flip-flop.

- When J = 0 and K = 0, the flip-flop remains in its current state (Q and Q̅ do not change).
- When J = 0 and K = 1, the flip-flop is reset, and Q = 0 and Q̅ = 1.
- When J = 1 and K = 0, the flip-flop is set, and Q = 1 and Q̅ = 0.
- When J = 1 and K = 1, the flip-flop toggles its state. If Q = 0, it will change to 1, and if Q = 1, it will change to 0.

Analysis:
In this question, J = 1 and K = 1, which means that the input to the J-K flip-flop will always be in the toggle state.

- Initially, let's assume that the Q output is 0.
- When the clock input rises from low to high, the J-K flip-flop will toggle its state, and the Q output will become 1.
- When the clock input falls from high to low, the J-K flip-flop will toggle its state again, and the Q output will become 0.
- This toggling process will repeat for each rising and falling edge of the clock signal.

Frequency Analysis:
The given clock input is a 20 kHz signal. Since the J-K flip-flop toggles its state for each rising and falling edge of the clock, the frequency of the Q output will be half of the clock frequency.

- Therefore, the frequency of the Q output will be 20 kHz / 2 = 10 kHz.

Conclusion:
Based on the analysis, the correct answer to the question is option 'D' - A 10 kHz square wave. The J-K flip-flop with J = 1 and K = 1 will produce a square wave output with a frequency of 10 kHz, which is half the frequency of the clock input.