What should bc thc cut-off frequency (in Hz) of the LPF to recover the continuous time sign. from its sampkd version,now,many samples will be there in 0.5 s?

Ql. The following signal is sairqded at .H7. and no alioing happens. Answer the following by showing all the calculations.  x(t)= 10 sin(2001rt + tr/2) + 15 cos + 7 sin(5001rt + zr) (a) What should be the possible values of to (in rad/s)?
(b) What is the sampling interval (in ms)?
(c) What should bc thc cut-off frequency (in Hz) of the LPF to recover the continuous time sign. from its sampkd version,
(d) now,many samples will be there in 0.5 s?
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(e) What will be the Nyquist rate it rad/s)?

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