The correct answer is: B. Contains only the 3 kHz component.
A signal containing only two frequency components (3 kHz and 6 kHz) is sampled at the rate of 8 kHz. This means that the signal is converted into a series of numbers, each of which represents the amplitude of the signal at a particular point in time. The sampling rate is 8 kHz, which means that the signal is sampled 8,000 times per second.
The signal is then passed through a low pass filter with a cut-off frequency of 8 kHz. A low pass filter allows frequencies below the cut-off frequency to pass through, while frequencies above the cut-off frequency are attenuated. In this case, the cut-off frequency is 8 kHz, so the filter will allow the 3 kHz component to pass through, while the 6 kHz component will be attenuated.
The output of the filter will therefore contain only the 3 kHz component. The 6 kHz component will have been attenuated by the filter and will not be present in the output.
Option A is incorrect because the output of the filter is not an undistorted version of the original signal. The 6 kHz component has been attenuated by the filter and is not present in the output.
Option C is incorrect because the output of the filter contains only the 3 kHz component, not the 3 kHz component and a spurious component of 2 kHz.
Option D is incorrect because the output of the filter contains only the 3 kHz component, not both the components of the original signal and two spurious components of 2 kHz and 5 kHz.