please solve this question

Exercise 3: The composite signal x(t) = 3 sin(250ft) + 2 cos(500mt), was captured at the input of a measuring device, it will be sampled then processed digitally. 1. Is the rate Fs = 2000 samples/sec a correct choice (justify by calculating the Nyquist frequency)? In so far, consider Fs = 2000 samples / sec. 2. Give the expression of the sampled signal x(n). 3. Calculate the number of samples per period of the sampled signal? 4. Sketch the spectrum of the discrete signal in the interval [0, Fs). 5. Explain what the frequency resolution is, and how it could be improved