Solution:

$ \begin{aligned} & \text { (i) } x(t)=\sin 2 t+\cos 3 \pi t \\\\ & \text { sol: } w_1=2, w_2=3 \pi \\\\ & \frac{w_1}{w_2}=\frac{2}{3 \pi} \quad \text { (Irrational) } \\\\ &\\ \end{aligned}\\ $

Hence it is non-periodic

$ \begin{aligned} & \text { (ii) } x(t)=\sin 2 \pi t+\cos \sqrt{2} \pi t \\\\ & \text { sol: } \quad w_1=2 \pi, w_2=\sqrt{2} \pi \\\\ & \frac{w_1}{w_2}=\frac{2 \pi}{\sqrt{2} \pi}=\sqrt{2} \text { (Irrational) } \\\\ & \end{aligned} $

Hence it is non-periodic