GATE EC question library

A $0$ to $6$ counter consists of $3$ flip flops and a combination circuit of $2$ input gate(s). The combination circuit consists of

The Fourier series expansion of a real periodic signal with fundamental frequency $\mathrm{f}_0$ is given by $$g_p(t)=\sum_{n=-\infty}^{\infty} c_n e^{j 2 \pi n f_\omega t}$$ It is given that $c_3=3+j 5$. Then $c_{-3}$ is

Let $x(t)$ be the input to a linear, time-invariant system. The required output is $4 x(t-2)$. The transfer function of the system should be

A sequence $x(n)$ with the z-transform $X(z)=z^4+z^2-2 z+2-3 z-4$ is applied as an input to a linear, time-invariant system with the impulse response $h(n)=2 \delta(n-3)$ where $$\delta(n)= \begin{cases}1, & n=0 \\ 0, & \text{ otherwise }\end{cases}$$ The output at $n=4$ is

The figure shows the Nyquist plot of the open-loop transfer function $\mathrm{G}(\mathrm{s}) \mathrm{H}(s)$ of a system. If $\mathrm{G}(s) \mathrm{H}(\mathrm{s})$ has one right-hand pole, the closed-loop system is

A PD controller is used to compensate a system. Compared to the uncompensated system, the compensated system has

The input to a coherent detector is DSB-SC signal plus noise. The noise at the detector output is

The noise at the input to an ideal frequency detector is white. The detector is operating above threshold. The power spectral density of the noise at the output is

At a given probability of error, binary coherent $\text{FSK}$ is inferior to binary coherent $\text{PSK}$ by

The unit of $\nabla \times \mathrm{H}$ is

The depth of penetration of electromagnetic wave in a medium having conductivity $\sigma$ at a frequency of $1 \; \mathrm{MHz}$ is $25 \mathrm{~cm}$. The depth of penetration at a frequency of $4 \; \mathrm{MHz}$ will be

Twelve $1 \; \Omega$ resistance are used as edges to form a cube. The resistance between two diagonally opposite corners of the cube is

The circuit for $\text{Q. 33-34}$ are given in the figure. For both are the questions, assume that the switch $S$ is in position $1$ for a long time and thrown to position $2$ at $t=0$. At $t=0+$, the current $i_{1}$ is

The circuit for $\text{Q. 33-34}$ are given in the figure. For both are the questions, assume that the switch $S$ is in position $1$ for a long time and thrown to position $2$ at $t=0$. $I_{1}(s)$ and $I_{2}(s)$ are the Laplace transforms of $i_{1}(t)$ and $i_{2}(t)$ respectively. The equations for the loop currents $I_{1}(s)$ and …

An input voltage $v(t)=10 \sqrt{2} \cos \left(t+10^{\circ}\right)+10 \sqrt{3}$ $\cos \left(2 t+10^{\circ}\right) \mathrm{V}$ is applied to a series combination of resistance $R=1 \Omega$ and an inductance $L=1H$. The resulting steady-state current $i(t)$ in ampere is

The driving-point impedance $Z(s)$ of a network has the pole-zero locations as shown in the figure. If $Z(0)=3$, then $Z(s)$ is

The impedance parameters $Z_{11}$ and $Z_{12}$ of the two-port network in the figure are

An $n$-type silicon bar $0.1 \mathrm{~cm}$ long and $100 \; \mu \mathrm{m}^{2}$ in cross-sectional area has a majority carrier concentration of $5 \times 1020 / \mathrm{m}^{3}$ and the carrier mobility is $0.13 \mathrm{~m}^{0} / \mathrm{V}-s$ at $300 \mathrm{~K}$. If the charge of an electron is $1.6 \times 10^{-19}$ coulomb, then the …

The electron concentration in a sample of uniformly doped $n$-type silicon at $300 \mathrm{~K}$ varies linearly from $10^{17} / \mathrm{cm}^{3}$ at $x=0$ to $6 \times 10^{16} / \mathrm{cm}^{3}$ at $x=2 \; \mu \mathrm{m}$. Assume a situation that electrons are supplied to keep this concentration gradient constant with time. If electronic charge is …

Match items in Group $1$ with items in Group $2,$ most suitably. $$\begin{array}{ll} \textbf{Group 1} & \textbf{Group 2} \\ \text{P LED} & \text{1 Heavy doping} \\ \text{Q Avalanche photodiode} & \text{2 Coherent radiation} \\ \text{R Tunnel diode} & \text{3 Spontaneous emission} \\ \text{S LASER} & \text{Current gain} \end{array}$$