Recent questions tagged gatein-2022

The input $x(t)$ to a system is related to its output $y(t)$ as$$\frac{dy(t)}{dt} + y(t) = 3x (t-3)u (t-3)$$Here $u(t)$ represents a unit-step function.The transfer funct...

A pneumatic nozzle-flapper system is conventionally used to convert __________Small changes in flapper’s velocity to large changes in output temperatureSmall changes in f...

A periodic function $f(x),$ with period $2,$ is defined as$f(x) = \left\{\begin{matrix} -1 -x & -1 \leq x < 0 \\ 1 – x & 0 < x \leq 1 \end{matrix}\right. $The Fourier ser...

The output of a system $y(t)$ is related to its input $x(t)$ according to the relation $y(t) = x(t) \sin (2 \pi t).$ This system is __________Linear and time-variantNon-l...

A unity-gain negative-feedback control system has a loop-gain $L(s)$ given by$$L(s) = \frac{6}{s(s-5)}$$The closed-loop system is _________Causal and stableCausal and uns...

A sinusoidal carrier wave with amplitude $A_{c}$ and frequency $f_{c}$ is amplitude modulated with a message signal $m(t)$ having frequency $0 < f_{m} \ll f_{c}$ to gener...

A Hall sensor is based on the principle of ___________Photoelectric effectSeebeck effectPiezoelectric effectLorentz force

A signal $x(t)$ is band-limited between $100 \; \text{Hz}$ and $200 \; \text{Hz}.$A signal $y(t)$ is related to $x(t)$ as follows:$$y(t) = x (2t – 5)$$The statement that ...

The figure shows a Chromel-Alumel thermocouple, where the junction $A$ is held at temperature $T_{A},$ and a thermal emf $E_{1}$ is measured using an ideal voltmeter betw...

The resistance of a pure copper wire of length $10 \; \text{cm}$ and diameter $1 \; \text{mm}$ is to be measured. The most suitable method from amongst the choices given ...

The logic block shown has an output $F$ given by ________$A + B$$A \cdot \overline{B}$$A + \overline{B}$$\overline{B}$

In which of the following bridge(s) is the balancing condition frequency-independent?Maxwell bridgeWien bridgeSchering bridgeWheatstone bridge

Given $\text{M} = \begin{bmatrix} 2 & 3 & 7 \\ 6 & 4 & 7 \\ 4 & 6 & 14 \end{bmatrix},$ Which of the following statement(s) is/are correct?The rank of $\text{M}$ is $2$The...

An analog-to-digital converter with resolution $0.01 \; \text{V}$ converts analog signals between $0 \; \text{V}$ to $+10 \; \text{V}$ to an unsigned binary output. The m...

Consider $24$ voice signals being transmitted without latency using time-division multiplexing. If each signal is sampled at $12 \; \text{kHz}$ and represented by an $8$-...

A photodiode is made of a semiconductor with a bandgap of $1.42 \; \text{eV}.$ Given that Plank’s constant is $6.626 \times 10^{-34} \; \text{Js,}$ the speed of light in ...

The global minimum of $x^{3} e^{-|x|}$ for $x \in (-\infty, \infty)$ occurs at $x = $ _________ (round off to one decimal place)

A $\text{440 V, 8 kW, 4-pole, 50 Hz,}$ star-connected induction motor has a full load slip of $0.04.$ The rotor speed (in rpm) at full load is ________ (round off to one ...

The transfer function of a system is:$$\frac{(s+1)(s+3)}{(s+5)(s+7)(s+9)}$$In the state-space representation of the system, the minimum number of state variables (in inte...

A Zener diode is used as a $4 \; \text{V}$ voltage regulator in the circuit shown. Given that the diode requires a minimum current of $4 \; \text{mA}$ for voltage regulat...

A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are re...

In the bandpass filter circuit shown, $R_{0} = 50\; \Omega, L_{0} = 1 \; \text{mH,} \; C_{0} = 10 \; \text{nF.}$ The $\text{Q}$ factor of the filter is _________ (round o...

The Newton-Raphson method is applied to determine the solution of $f(x) = 0$ where $f(x) = x – \cos (x).$ If the initial guess of the solution is $x_{0} = 0,$ the value o...

An $\text{OPAMP}$ has a gain of $10^{4},$ an input impedance of $10 \; \text{M} \Omega$ and an output impedance of $100 \; \Omega.$ The $\text{OPAMP}$ is used in unity-g...

A signal $V_{in} (t)$ shown is applied from $t = 0 \; \text{ms}$ to $t = 6 \; \text{ms}$ to the circuit shown. Given the initial voltage across the capacitor is $0.3 \; \...

The signal flow graph of a system is shown. The expression for $Y(s)/X(s)$ is ___________ $\frac{2G_{1}(s) G_{2}(s) + 2G_{1}(s) G_{3}(s)} {1 + G_{2}(s) + G_{3}(s)}$$2 + G...

Consider the transfer function$$H_{c}(S) = \frac{1}{(s+1)(s+3)}$$Bilinear transformation with a sampling period of $0.1 \; \text{s}$ is employed to obtain the discrete-ti...

A car is moving collinearly with a laser beam emitted by a transceiver. A laser pulse emitted at $t=0 \; \text{s}$ is received back by the transceiver $100 \; \text{ns}$ ...

The signal $x(t) = (t-1)^{2}u(t-1),$ where $u(t)$ is the unit-step function, has the Laplace transform $X(s).$ The value of $X(1)$ is ________$\frac{1}{e}$$\frac{2}{e}$$2...

A proportional-integral-derivative $\text{(PID)}$ controller is employed to stably control a plant with transfer function$$P(s) = \frac{1}{(s+1)(s+2)}$$Now, the proportio...

The Nyquist plot of a stable open-loop system $G (j \omega)$ is plotted in the frequency range $0 \leq \omega < \infty$ as shown. It is found to intersect a unit circle w...

In the small signal circuit shown, the enhancement mode $n$-channel $\text{MOSFET}$ is biased in saturation with transconductance $g_{m}.$ If channel length modulation is...

Consider the differential equation$\dfrac{dy}{dx} + y \ln (y) = 0$If $y(0) = e,$ then $y(1)$ is ___________$e^{e}$$e^{-e}$$e^{(1/e)}$$e^{(-1/e)}$

The digital circuit shown ________is a divide-by-$5$ counteris a divide-by-$7$ counteris a divide-by-$8$ counterdoes not function as a counter due to disjoint cycles of s...

In the small circuit shown, the enhancement mode $n$-channel $\text{MOSFET}$ is biased in saturation with a transconductance $g_{m}.$ A small signal low-frequency voltage...

$A= a_{1}a_{0}$ and $B= b_{1}b_{0}$ are two $2$–bit unsigned binary numbers. If $F(a_{1},a_{0},b_{1},b_{0})$ is a Boolean function such that $F=1$ only when $A>B,$ and $F...

The matrix $\text{A} = \begin{bmatrix} 4 & 3 \\ 9 & -2 \end{bmatrix}$ has eigenvalues $-5$ and $7.$The eigenvectors(s) is/are __________ $\begin{bmatrix} 1\\ 1 \end{bmat...

For the complex number $z= \frac{a+jb}{a-jb},$ where $a>0$ and $b>0.$Which of the following statement(s) is/are true?The phase is $2 \; \tan^{-1}\frac{b}{a}$The phase is ...

Monochromatic light of wavelength $532 \; \text{nm}$ is used to measure the absorption coefficient of a material in a $\text{UV}$-Visible Spectrophotometer. The measured ...