GATE EC 2014 Question Paper (16-Feb-2014) (Shift 1)

Consider the multiplexer based logic circuit shown in the figure.



Which one of the following Boolean functions is realized by the circuit?

Let $x\left(t\right)=cos10\pi t+\cos \left(30\pi t\right)$ be sampled at 20Hz and reconstructed using an ideal LPF with f${}_c$ of 20Hz. The frequency/frequencies present in reconstructed signal is/are

For an all pass system $H\left(z\right)=\frac{z^{-1}-b}{1-a{z}^{-1}}$ If Rₑ(a)≠0, I${}_m$ (a)≠0, then b equals.

A modulated signal is y(t) = m(t) cos (40000 πt), where the baseband signal m(t) has frequency components less than 5 kHz only. The minimum required rate (in kHz) at which y(t) should be sampled to recover m(t) is ______.

Consider the following block diagram



Transfer function $\frac{C\left(s\right)}{R\left(s\right)}$ is