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The frequency of the clock signal applied to the rising edge triggered D flip-flop shown in figure is 10 kHz. The frequency of the signal available at Q is?

1. 5 Khz
2. 10 Khz
3. 1 Khz
4. 0.5 Khz
0
5 Khz

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Here Time Period of Signal at Q will get Doubled, hence frequency is halved. See my solution below.

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The answer I got is 3 but it’s given as 5 and in the solution they are mentioning that the no. of flip flops here are defined by the sequence not the no. of states??
The following sequential circuit has initial state $QAQB = 00$ with one input $X$ and one output $Z.$ What is the minimum input sequence which takes the machine to state $11?$ $(A) 00$ $(B) 10$ $(C) 11$ $(D)$ State $11$ is not reachable