Nyquist rate

The output y(t) of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is

For the signal f(t) = 3 sin8$$\mathrm\pi$$t + 6sin12$$\mathrm\pi$$t + sin14$$\mathrm\pi$$t, the minimum sampling frequency (in Hz) satisfying the Nyquist criterion is _________.

A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency in kHz which is not valid is