GATE Electrical Engineering (EE) 2014 Shift 2 Solved Paper

An input signal $\mathit{x}\left(\mathit{t}\right)=2+5\mathit{s}\mathit{i}\mathit{n}\left(100\mathit{\pi }\mathit{t}\right)$  is sampled with a sampling frequency of $400\mathit{H}\mathit{z}$  and applied to the system whose transfer function is represented by
$\frac{\mathit{Y}\left(\mathit{z}\right)}{\mathit{X}\left(\mathit{z}\right)}=\frac{1}{\mathit{N}}\left(\frac{1-{\mathit{z}}^{-\mathrm{N}}}{1-{\mathit{z}}^{-1}}\right)$
where, $\mathit{N}$  represents the number of samples per cycle. The output $\mathit{y}\left[\mathit{n}\right]$  of the system under steady state is