List of top Signals and Systems Questions on Sampling Theorem

Let \(x_c(t)\) be any continuous-time periodic signal with period \(T\). It is sampled uniformly with a sampling period \(T_s\) where \(T_s\neq T\), resulting in the discrete sequence
\[ x[n]=x_c(nT_s), \]
where \(n\) is an integer.

Which one of the following statements is correct about \(x[n]\)?

Two analog signals \(x_1(t)\) and \(x_2(t)\) (\(t\) in second) are sampled at a rate \(F_s=40\) Hz, where
\[ x_1(t)=\cos(20\pi t),\ t\geq0,\qquad x_2(t)=\cos(100\pi t),\ t\geq0. \] The first ten samples (starting from \(t=0\)) are considered for the analysis. Which of the following statements is TRUE?