GATE EC question library

Given $\mathrm{G}(s) \mathrm{H}(z)=\frac{\mathrm{K}}{s(s+1)(s+3)}$, the point of intersection of the asymptotes of the root loci with the real axis is

In a $\text{PCM}$ system, if the code word length is increased from $6$ to $8$ bits, the signal to quantization noise ratio improves by the factor

An AM signal is detected using an envelope detector. The carrier frequency and modulating signal frequency are $1 \; \mathrm{MHz}$ and $2 \; \mathrm{kHz}$ respectively. An appropriate value for the time constant of the envelope detector is

An AM signal and a narrow-band FM signal with identical carriers, modulating signals and modulation indices of $0.1$ are added together. The resultant signal can be closely approximated by

In the output of a DM speech encoder, the consecutive pulses are of opposite polarity during time interval $t_{1} < t < t_{2}.$ This indicates that during this interval

The phase velocity of an electromagnetic wave propagating in a hollow metallic rectangular waveguide in the $\mathrm{TE}_{10}$ mode is

Consider a lossless antenna with a directive gain of $+6 \mathrm{~dB}$. If $1 \mathrm{~mW}$ of power is fed to it the total power radiated to the antenna will be

For the lattice circuit shown in the figure, $Z_{a}=j 2 \Omega$ and $Z_{b}=2 \Omega$. The values of the open circuit impedance parameters $Z=\left[\begin{array}{ll}z_{11} & z_{12} \\ z_{21} & z_{22}\end{array}\right]$ are

The circuit shown in the figure has initial current $i_{t}\left(0^{-}\right)=1 \mathrm{~A}$ through the inductor and an initial voltage $v_{c}\left(0^{-}\right)=-1 \mathrm{~V}$ across the capacitor. For input $v(t)=u(t)$, the Laplace transform of the current $i(t)$ for $t \geq 0$ is

Consider the Bode magnitude plot shown in the given figure. The transfer function $\mathrm{H}(s)$ is

The transfer function $H(s)=\frac{V_{0}(s)}{V_{i}(s)}$ of an R-L-C circuit is given by $$H(s)=\frac{10^{6}}{s^{2}+20 s+10^{6}}$$ The Quality factor (Q-factor) of this circuit is

For the circuit shown in the figure, the initial conditions are zero. Its transfer function $$H(s) = \frac{V_{c}(s)}{V_{i}(s)}$$

A system described by the following differential equation $\frac{d^{2} y}{d t^{2}}+3 \frac{d y}{d t}+2 y=x(t)$ is initially at rest. For input $x(t)=2 u(t)$, the output $y(t)$ is

Consider the following statements $\text{S1}$ and $\text{S2}$ $\text{S1} :$ At the resonant frequency the impedance of a series $\mathrm{R}-\mathrm{L}-\mathrm{C}$ circuit is zero. $\text{S2} :$ In a parallel $\mathrm{G}-\mathrm{L}-\mathrm{C}$ circuit, increasing the conductance $\mathrm{G}$ results in increase in its $\mathrm{Q}$ factor. …

In an abrupt $p-n$ junction, doping concentrations on $p$-side and $n$-side are $\mathrm{N}_{\mathrm{A}}=9 \times 10^{16} / \mathrm{cm}^{3}$ and $N_{0}=1 \times 10^{16} / \mathrm{cm}^{3}$ respectively. The $p-n$ junction is reverse biased and the total depletion width is $3 \; \mu \mathrm{m}$. The depletion width on the $p$-side is

The resistivity of a uniformloy doped $n$-type silicon sample is $0.5 \; \Omega-\mathrm{cm}$. If the electron mobility $\left(\mu_{n}\right)$ is $1250 \mathrm{~cm}^{2} / \mathrm{V}$-sec and the charge of an electron is $1.6 \times 10^{-19}$ Coulomb, the donor impurity concentration $\left(\mathrm{N}_{\text{n}}\right)$ in the sample is

Consider an abrupt $p$-junction. Let $V_{\text{in }}$ be the built-in potential of this junction and $\mathrm{V}_{\mathrm{R}}$ be the applied reverse bias. If the junction capacitance $\left(\mathrm{C}_{t}\right)$ is $1 \; \mathrm{pF}$ for $V_{\text{in}}+V_{\mathrm{R}}=1 \mathrm{~V}$, then for …

Consider the following statements $\mathrm{S} 1$ and $\mathrm{S} 2$. $\mathrm{S} 1 :$ The threshold voltage $\left(V_{T}\right)$ of a MOS capacitor decreases with increase in gate oxide thickness $\mathrm{S} 2 :$ The threshold voltage $\left(V_{t}\right)$ of a MOS capacitor decreases with increase in substrate doping concentration Which one of …

The drain of an $n$-channel MOSFET is shorted to the gate so that $V_{G S}=V_{D s}$. The threshold voltage $\left(V_{T}\right)$ of MOSFET is $1 \mathrm{~V}$. If the drain current $\left(\mathrm{I}_{\mathrm{D}}\right)$ is $1 \mathrm{~mA}$ for $\mathrm{V}_{G S}=2 \mathrm{~V}$, then for …

The longest wavelength that can be absorbed by silicon, which has the bandgap of $1.12 \; \mathrm{eV}$, is $1$. If the longest wavelength that can be absorbed by another material is $0.87 \; \mu \mathrm{m}$, then the bandgap of this material is