BW = n × 2f_m + (n − 1)guard band

To accommodate 7 AM broadcast signals simultaneously within a bandwidth of 70 kHz, we need to determine the maximum modulation frequency that each station must be limited to. Let's break down the problem step by step:

1. Total bandwidth available:
The total bandwidth available is 70 kHz.

2. Guard band:
A guard band of 5 kHz is present, which means we need to subtract this from the total bandwidth.

Total bandwidth available after considering the guard band = 70 kHz - 5 kHz = 65 kHz.

3. Number of broadcast signals:
We need to accommodate 7 AM broadcast signals within the available bandwidth.

4. Bandwidth per signal:
To find the bandwidth per signal, we divide the total available bandwidth by the number of broadcast signals.

Bandwidth per signal = 65 kHz / 7 = 9.29 kHz.

5. Maximum modulation frequency:
The maximum modulation frequency is half the bandwidth per signal, as per the Nyquist theorem.

Maximum modulation frequency = 9.29 kHz / 2 = 4.64 kHz.

6. Accounting for upper and lower sidebands:
In AM modulation, both upper and lower sidebands are present. Therefore, we need to consider the bandwidth occupied by both sidebands.

Bandwidth occupied by both sidebands = 4.64 kHz + 4.64 kHz = 9.28 kHz.

7. Maximum modulation frequency per station:
To find the maximum modulation frequency per station, we subtract the bandwidth occupied by both sidebands from the bandwidth per signal.

Maximum modulation frequency per station = 9.29 kHz - 9.28 kHz = 0.01 kHz.

8. Conversion to kHz:
Finally, we convert the maximum modulation frequency per station from Hz to kHz.

Maximum modulation frequency per station = 0.01 kHz = 0.01 kHz * 1000 Hz/kHz = 10 Hz.

Therefore, the maximum modulation frequency that each station must be limited to is 0.01 kHz or 10 Hz. However, none of the given options match this result, so the correct answer may be a typo or there may be additional information missing from the question.