GATE EC question library

In the derivation of expression for peak percent overshoot, $M_{p}=\exp \left(\frac{-\pi \zeta}{\sqrt{1-\zeta^{2}}}\right) \times 100 \%$, which one of the following conditions is NOT required?

A ramp input applied to an unity feedback system results in $5 \%$ steady state error. The type number and zero frequency gain of the system are respectively

A double integrator plant, $\mathrm{G}(s)=\frac{\mathrm{K}}{s^{2}}, \mathrm{H}(\mathrm{s})=1$ is to be compensated to achieve the damping ratio $\zeta=0.5$, and an undamped natural frequency, $\omega_{n}=5 \; \mathrm{rad/s}$. Which one of the following compensator $G_{e}(s)$ will be suitable?

A $\text{MOS}$ capacitor made using $p$ type substrate is in the accumulation mode. The dominant charge in the channel is due to the presence of

A device with input $x(t)$ and output $y(t)$ is characterized by: $y(t)=x^{2}(t)$. An FM signal with frequency deviation of $90 \; \mathrm{kHz}$ and modulating signal bandwidth of $5 \; \mathrm{kHz}$ is applied to this device. The bandwidth of the output signal is

A signal as shown in the figure is applied to a matched filter. Which of the following does represent the output of this matched filter?

Noise with uniform power spectral density of $\text{N}_{0}$ $\mathrm{W / Hz}$ is passed through a filter $\mathrm{H}(\omega)=2$ exp $\left(-j \omega t_{d}\right)$ followed by an ideal low pass filter of bandwidth $\text{B Hz.}$ The output noise power in Watts is

A carrier is phase modulated (PM) with frequency deviation of $10 \; \mathrm{kHz}$ by a single tone frequency of $1 \; \mathrm{kHz}$. If the single tone frequency is increased to $2 \; \mathrm{kHz}$, assuming that phase deviation remains unchanged, the bandwidth of the PM signal is

An output of a communication channel is a random variable $v$ with the probability density function as shown in the figure The mean square value of $v$ is

Characteristic impedance of a transmission line is $50 \Omega$. Input impedance of the open-circuited line is $Z_{a^{-}}=100+j 150 \Omega$. When the transmission line is short- circuited, then value of the input impedance will be

Common Data Questions 78, 79, 80 Given, $r_{d}=20 \; \mathrm{k} \Omega, \mathrm{I}_{\mathrm{DSS}}=10 \mathrm{~mA}, \mathrm{~V}_{p}=-8 \mathrm{~V}$ $Z_1$ and $Z_0$ of the circuit are respectively

Common Data Questions 78, 79, 80 Given, $r_{d}=20 \; \mathrm{k} \Omega, \mathrm{I}_{\mathrm{DSS}}=10 \mathrm{~mA}, \mathrm{~V}_{p}=-8 \mathrm{~V}$ $\mathrm{I}_{\mathrm{D}}$ and $\mathrm{V}_{\mathrm{DS}}$ under $\mathrm{DC}$ conditions are respectively

Common Data Questions 78, 79, 80 Given, $r_{d}=20 \; \mathrm{k} \Omega, \mathrm{I}_{\mathrm{DSS}}=10 \mathrm{~mA}, \mathrm{~V}_{p}=-8 \mathrm{~V}$ Transconductance in milli-Siemens (mS) and voltage gain of the amplifier are respectively

Statement for Linked Answer Questions 81 a and 81 b: Consider an $8085$ microprocessor system The following program starts at location $0100 \mathrm{H}$. $\begin{array}{l} \text{LXI SP, 00FF} \\ \text{LXI H, 0701} \\ \text{MVI A, 20H} \\ \text{SUB M} \end{array}$ The content of accumulator when the program counter reaches $0109 \mathrm{H}$ is

Statement for Linked Answer Questions 82a and 82b: The dopen loop transfer function of a unity feedback system is given by $$\mathrm{G}(s)=\frac{3 e^{-2}}{s(s+2)}$$ The gain and phase crossover frequencies in $\mathrm{rad} / \mathrm{sec}$ are, respectively

Statement for Linked Answer Questions 83a and 83b: Asymmetric three-level midtread quantizer is to be designed assuming equiprobable occurence of all quantization levels. If the probability density function is divided into three regions as shown in the figure, the value of a in the figure is

Statement of Linked Answer Questions 84a and 84b: Voltage standing wave pattern in a lossless transmission line with characteristic impedance $50 \mathrm{~W}$ and a resistive load is shown in the figure. The value of the load resistance is