Recent questions tagged gate2016-ec-2

A discrete memoryless source has an alphabet $\left \{ a_{1},a_{2}, a_{3},a_{4}\right \}$ with corresponding probabilities $\left \{ \frac{1}{2}, \frac{1}{4},\frac{1}{8},...

A speech signal is sampled at $8$ $kHz$ and encoded into $PCM$ format using $8$ bits/sample. The $PCM$ data is transmitted through a baseband channel via $4$-level $PAM$....

A uniform and constant magnetic field $\textbf{B}=\hat{z}B$ exists in the $\hat{z}$ direction in vacuum. A particle of mass $m$ with a small charge $q$ is introduced into...

Let the electric field vector of a plane electromagnetic wave propagating in a homogeneous medium be expressed as $\textbf{E}=\hat{x}E_{x}e^{-j(\omega t-\beta z)},$ where...

Light from free space is incident at an angle $\theta _{i}$ to the normal of the facet of a step-index large core optical fibre. The core and cladding refractive indices ...

The ordinary differential equation $$\frac{dx}{dt}=-3x+2, \text{ with }x(0) = 1$$ is to be solved using the forward Euler method. The largest time step that can be used t...

Suppose $C$ is the closed curve defined as the circle $x^{2}+y^{2}=1$ with $C$ oreinted anti-clockwise. The value of $\oint$ ( $xy^{2}$ $dx$ + $ x^{2}y$ $dy$ )over the cu...

Two random variables $X$ and $Y$ are distributed according to $$f_{X,Y}(x,y)=\begin{cases} (x+y),& 0\leq x\leq 1,&0\leq y\leq 1\\ 0, & \text{otherwise.} \end{cases}$$ The...

The matrix $A=\begin{bmatrix} a & 0 &3 &7 \\ 2& 5&1 &3 \\ 0& 0& 2 &4 \\ 0&0 & 0 &b \end{bmatrix}$ has $\text{det}(A) = 100$ and $\text{trace}(A) = 14$. The value of $\mid...

In the given circuit, each resistor has a value equal to $1\Omega$. What is the equivalent resistance across the terminals $a$...

In the circuit shown in the figure, the magnitude of the current (in amperes) through $R_{2}$ is ____

A continuous-time filter with transfer function $H\left ( s \right )= \frac{2s+6}{s^{2}+6s+8}$ is converted to a discrete-time filter with transfer function $G\left ( z\r...

The Discrete Fourier Transform (DFT) of the $4$-point sequence$x\left [ n \right ]=\left \{ x\left [ 0 \right ],x\left [ 1 \right ], x\left [ 2 \right ], x\left [ 3 \righ...

The switch $S$ in the circuit shown has been closed for a long time. It is opened at $t = 0$ and remains open after that. Assume that the diode has zero reverse current a...

A voltage $V_{G}$ is applied across a $MOS$ capacitor with metal gate and $p$-type silicon substrate at $T=300$ $K$. The inversion carrier density (in number of carriers ...

Consider avalanche breakdown in a silicon $p^{+}n$ junction. The $n$-region is uniformly doped with a donor density $N_{D}.$ Assume that breakdown occurs when the magnitu...

Consider a region of silicon devoid of electrons and holes, with an ionized donor density of $N_{d}^{+}=10^{17} cm^{-3}.$ The electric field at $x = 0$ is $0\: V/cm$ and ...

Consider a long-channel $NMOS$ transistor with source and body connected together. Assume that the electron mobility is independent of $V_{GS}$ and $V_{DS}.$ Given,$g_{m}...

The figure shows a half-wave rectifier with a $475 \: \mu F$ filter capacitor. The load draws a constant current $I_{o}= 1 \: A$ from the rectifier. The figure also shows...

In the opamp circuit shown, the Zener diodes $Z1$ and $Z2$ clamp the output voltage $V_{0}$ to $+5V$ or $-5 V$. The switch $S$ is initially closed and is opened at time $...

An opamp has a finite open loop voltage gain of $100$. Its input offset voltage $V_{ios}(=+5mV)$ is modeled as shown in the circuit below. The amplifier is ideal in all o...

An $8$ Kbyte ROM with an active low Chip Select input $\left (\overline{CS}\right )$ is to be used in an $8085$ microprocessor based system. The ROM should occupy the add...

In an $N$ bit flash ADC, the analog voltage is fed simultaneously to $2^{N}-1$ comparators. The output of the comparators is then encoded to a binary format using digita...

The state transition diagram for a finite state machine with states $A$, $B$ and $C$, and binary inputs $X$, $Y$ and $Z$, is shown in the figure. ...

In the feedback system shown below $G\left ( s \right )=\frac{1}{\left ( s^{2}+2s \right )}$. The step response of the closed-loop system should have minimum settling tim...

In the feedback system shown below $G\left ( s \right )=\frac{1}{\left ( s+1 \right )\left (s+2 \right )\left ( s+3 \right )}.$ The positive v...

An information source generates a binary sequence $\left \{ \alpha _{n} \right \}$. $\alpha _{n}$ can take one of the two possible values $-1$ and $+1$ with equal probabi...

An ideal band-pass channel $500 \: Hz –2000 \:Hz$ is deployed for communication. A modem is designed to transmit bits at the rate of $4800$ bits/s using $16-QAM$. The rol...

Consider a random process $X\left ( t \right )=3V(t)-8,$ where $V(t)$ is a zero mean stationary random process with autocorrelation $R_{v}\left ( \tau \right )=4e^{-5\mid...

A binary communication system makes use of the symbols “zero” and “one”. There are channel errors. Consider the following events:$\begin{array}{ll} x_{0}& : & \text{a “z...