GATE EC 2024 Question Paper (11-Feb-2024) (Shift 1)

The propagation delay of the $2\times 1$ MUX shown in the circuit is 10 ns. Consider the propagation delay of the inverter as 0 ns.

If S is set to 1 then the output Y is ____________.

The sequence of states ($Q_1{Q}_0$) of the given synchronous sequential circuit is ____________

Let $z$ be a complex variable. If $f(z)=\frac{\sin (\pi z)}{z^2(z-2)}$ and $C$ is the circle in the complex plane with $|z|=3$ then ${\oint }_{C}f(z)dz$ is

Consider two continuous time signals $x(t)$ and $y(t)$ as shown below

If $X(f)$ denotes the Fourier transform of $x(t)$, then the Fourier transform of $y(t)$ is _________

A source transmits a symbol $s$, taken from $\{-4,0,4\}$ with equal probability, over an additive white Gaussian noise channel. The received noisy symbol $r$ is given by $r=s+w$, where the noise $w$ is zero mean with variance 4 and is independent of $s$.
Using $Q(x)=\frac{1}{\sqrt{2\pi }}{\int }_x^{\infty }{e}^{-\frac{t^2}{2}}dt$, the optimum symbol error probability is _________