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

The general form of the complementary function of a differential equation is given by $y(t)=(At+B)e^{-2t}$, where $A$ and $B$ are real constants determined by the initial condition. The corresponding differential equation is ________.

In the context of Bode magnitude plots, $40$ dB/decade is the same as ________.

In the feedback control system shown in the figure below $G(s)=\frac{6}{s(s+1)(s+2)}$

R(s), Y(s), and E(s) are the Laplace transforms of r(t), y(t), and e(t), respectively. If the input r(t) is a unit step function, then ________.

A digital communication system transmits through a noiseless bandlimited channel $[-WW]$. The received signal $z(t)$ at the output of the receiving filter is given by $z(t)={\sum }_{n}b[n]x(t-nT)$ where $b[n]$ are the symbols and $x(t)$ is the overall system response to a single symbol. The received signal is sampled at $t=mT$. The Fourier transform of $x(t)$ is $X(f)$. The Nyquist condition that $X(f)$ must satisfy for zero intersymbol interference at the receiver is ________.

Consider a lossless transmission line terminated with a short circuit as shown in the figure below. As one moves towards the generator from the load, the normalized impedances $Z_{inA}$, $Z_{inB}$, $Z_{inC}$, and $Z_{inD}$ (indicated in the figure) are _____________