A signal x(t) is multiplied by rectangular pulse train c(t)

A signal x(t) is multiplied by rectangular pulse train c(t) as shown below:
x(t) would be recovered from the product x(t) c(t) by using an ideal LPF if X (j_ω) = 0 for—

In order to avoid aliasing f_s > 2f_m
or

2π	≥ 2ω_m
T

where ω_m is the maximum frequency of x(t) and T is period of C (t), i.e. T = 10^{– 3}
and

2π	> 2ω_m
10⁻³

or ω_m < 1000π
Therefore, X (jω) = 0 for ω < 1000
Hence alternative (C) is the correct choice.