Hot questions / GO Instrumentation

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161

GATE IN 2022 | Question: 2
A pneumatic nozzle-flapper system is conventionally used to convert __________ Small changes in flapper’s velocity to large changes in output temperature Small changes in flapper’s displacement to large changes in output temperature Small changes in flapper’s velocity to large changes in output pressure Small changes in flapper’s displacement to large changes in output pressure

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

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162

GATE IN 2022 | Question: 6
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 generate the modulated wave $s(t)$ given by $ s(t) = A_{c} [1+m(t)] \cos (2 \pi f_{c}t) $ ... $m(t) = 1.5 \sin (2 \pi f_{m} t)$ $m(t) = 2 \sin (4 \pi f_{m} t)$ $m(t) = 2 \cos (4 \pi f_{m} t)$

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...

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163

GATE IN 2022 | Question: 9
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 between the open ends $\text{B1}$ and $\text{B2},$ both held at temperature $T_{B}.$ Two identical copper wires are introduced between $\text{B1-C1}$ and $\text{B2-C2}$ as shown in the ... reads a thermal emf $E_{2}.$ Then, _________ $E_{1} < E_{2}$ $E_{1} > E_{2}$ $E_{1} = 2E_{2}$ $E_{1} = E_{2}$

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...

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164

GATE IN 2022 | Question: 18
The global minimum of $x^{3} e^{-|x|}$ for $x \in (-\infty, \infty)$ occurs at $x = $ _________ (round off to one decimal place)

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

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165

GATE IN 2022 | Question: 33
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 with center at the origin at the point $P = - 0.77 - 0.64j.$ The points $Q$ and $R$ lie on $G (j \omega)$ and assume values $Q = 14.40 + 0.00j$ ... $\text{GM} = 0.07$ $\text{PM} = - 39.7^{\circ}$ and $\text{GM} = 4.76$ $\text{PM} = - 39.7^{\circ}$ and $\text{GM} = 0.07$

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...

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166

GATE IN 2022 | Question: 7
A Hall sensor is based on the principle of ___________ Photoelectric effect Seebeck effect Piezoelectric effect Lorentz force

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

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167

GATE IN 2022 | Question: 17
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 vacuum is $3 \times 10^{8} \; \text{m/s,}$ and $1 \; \text{eV} = 1.6 \times 10^{-19} \; \text{J,}$ the cut-off wavelength (in nanometers) of the photodiode is _________ (round off to one decimal place)

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 i...

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168

GATE IN 2022 | Question: 48
In the circuit shown, $R_{1} = 100 \; \text{k} \Omega$ and $R_{2} = 1 \; \text{k} \Omega.$ If the base-to-emitter voltage of the $npn$ $\text{BJT}$ is $0.7 \; \text{V}$ and the collector-to-emitter voltage is $5.2 \; \text{V},$ the $\beta$ (current gain) of the $\text{BJT}$ is ___________ (round off to two decimal places)

In the circuit shown, $R_{1} = 100 \; \text{k} \Omega$ and $R_{2} = 1 \; \text{k} \Omega.$ If the base-to-emitter voltage of the $npn$ $\text{BJT}$ is $0.7 \; \text{V}$ a...

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169

GATE IN 2022 | GA Question: 2
A sphere of radius $r$ $\text{cm}$ is packed in a box of cubical shape. What should be the minimum volume (in $\text{cm}^{3}$) of the box that can enclose the sphere? $\frac{r^{3}}{8}$ $r^{3}$ $2r^{3}$ $8r^{3}$

A sphere of radius $r$ $\text{cm}$ is packed in a box of cubical shape. What should be the minimum volume (in $\text{cm}^{3}$) of the box that can enclose the sphere?$\fr...

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170

GATE IN 2022 | GA Question: 6
Rice, a versatile and inexpensive source of carbohydrate, is a critical component of diet worldwide. Climate change, causing extreme weather, poses a threat to sustained availability of rice. Scientists are working on developing Green Super Rice $\text{(GSR)}$, which is resilient under extreme weather conditions ... in an extreme weather, but the quantity of produce is lesser than regular ice Regular rice will continue to provide good yields even in extreme weather

Rice, a versatile and inexpensive source of carbohydrate, is a critical component of diet worldwide. Climate change, causing extreme weather, poses a threat to sustained ...

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171

GATE IN 2022 | Question: 1
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 function of this system is __________ $\dfrac{e^{-3s}}{s+3}$ $\dfrac{3e^{-3s}}{s+1}$ $\dfrac{3e^{- (s/3)}}{s+1}$ $\dfrac{e^{-(s/3)}}{s+3}$

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...

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172

GATE IN 2022 | Question: 38
$A= a_{1}a_{0}$ 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 $F=0$ otherwise, then $F$ can be minimized to the form __________ $a_{1}\overline{b}_{1} + a_{1}a_{0}\overline{b}_{0}$ ... $a_{1}\overline{b}_{1} + a_{1}a_{0}\overline{b}_{0} + a_{0}\overline{b}_{0}b_{1}$

$A= a_{1}a_{0}$ 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 ...

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173

GATE IN 2022 | Question: 3
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 series of this function contains ___________ Both $\cos (n \pi x)$ and $\sin (n \pi x)$ where $ n = 1, 2, 3, \dots $ Only $\sin (n \pi x)$ where $ n = 1, 2, 3, \dots $ Only $\cos (n \pi x)$ where $ n = 1, 2, 3, \dots $ Only $\cos (2n \pi x)$ where $ n = 1, 2, 3, \dots $

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 s...

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174

GATE IN 2022 | Question: 8
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 is always true is _______ $y(t)$ is band-limited between $50 \; \text{Hz}$ and $100 \; \text{Hz}$ $y(t)$ is band-limited between $100 \; \text{Hz}$ and $200 \; \text{Hz}$ $y(t)$ is band-limited between $200 \; \text{Hz}$ and $400 \; \text{Hz}$ $y(t)$ is not band-limited

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 tha...

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175

GATE IN 2022 | Question: 55
In the Wheatstone bridge circuit shown, $R_{1}=1.5 \; \text{k} \Omega$ and $R_{2}=R_{3}=R_{4}=1 \; \text{k} \Omega.$ The switch is initially open and the voltage between the points $\text{C}$ and $\text{D}$ is $V_{CD}.$ Upon closing the switch at $t=0,$ the resistance in the arm $\text{AD}$ chances ... $\left|\dfrac{ \delta V_{CD}}{\delta R_{1}}\right|,$ is __________ (round off to two decimal places)

In the Wheatstone bridge circuit shown, $R_{1}=1.5 \; \text{k} \Omega$ and $R_{2}=R_{3}=R_{4}=1 \; \text{k} \Omega.$ The switch is initially open and the voltage between ...

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176

GATE IN 2022 | Question: 14
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 rank of $\text{M}$ is $3$ The rows of $\text{M}$ are linearly independent The determinant of $\text{M}$ is $0$

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...

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177

GATE IN 2022 | Question: 28
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-time transfer function $H_{d}(z).$ Then $H_{d}(z)$ is __________ $\frac{(1+z^{-1})^{2}} {(19-21z^{-1}) (23-17z^{-1})}$ $\frac{(1-z^{-1})^{2}} {(21-19z^{-1}) (17-23z^{-1})}$ $\frac{(1+z^{-1})^{2}} {(21-19z^{-1}) (23-17z^{-1})}$ $\frac{(1+z^{-1})^{2}} {(21-19z^{-1}) (17-23z^{-1})}$

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...

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178

GATE IN 2022 | Question: 39
The matrix $\text{A} = \begin{bmatrix} 4 & 3 \\ 9 & -2 \end{bmatrix}$ has eigenvalues $-5$ and $7.$ The eigenvectors(s) is/are __________ $\begin{bmatrix} 1\\ 1 \end{bmatrix}$ $\begin{bmatrix} 3\\ 4 \end{bmatrix}$ $\begin{bmatrix} 2\\ -6 \end{bmatrix}$ $\begin{bmatrix} 2\\ 8 \end{bmatrix}$

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...

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179

GATE IN 2022 | GA Question: 1
Inhaling the smoke from a burning _________ could ________ you quickly. tire / tier tire / tyre tyre / tire tyre / tier

Inhaling the smoke from a burning _________ could ________ you quickly.tire / tiertire / tyretyre / tiretyre / tier

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180

GATE IN 2022 | Question: 27
The signal flow graph of a system is shown. The expression for $Y(s)/X(s)$ is ___________ $\frac{2G_{1}(s) G_{2}(s) + 2G_{1}(s) G_{3}(s)} {1 + G_{2}(s) + G_{3}(s)}$ $2 + G_{1}(s) + G_{3}(s) + \frac{G_{2}(s)}{1 + G_{2}(s)}$ $ G_{1}(s) + G_{3}(s) - \frac{G_{2}(s)}{2 + G_{2}(s)}$ $\frac{2G_{1}(s) G_{2}(s) + 2G_{1}(s) G_{3}(s) – G_{1}(s)} {1 + G_{2}(s) + G_{3}(s)}$

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...

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181

GATE IN 2022 | Question: 29
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 $100 \; \text{ns}$ (nanoseconds) later after reflection from the car. A second pulse emitted at $t=0.1 \; \text{s}$ is received back $90 \; \text{ns}$ ... $108 \; \text{kmph,}$ moving towards the transceiver $54 \; \text{kmph,}$ moving away from the transceiver $108 \; \text{kmph,}$ moving away from the transceiver

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 $100 \; \text{ns}$ ...

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182

GATE IN 2022 | GA Question: 10

Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.

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183

GATE IN 2022 | Question: 5
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 stable Causal and unstable Non-causal and stable Non-causal and unstable

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...

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184

GATE IN 2022 | Question: 20
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 integer) necessary is _________

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...

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185

GATE IN 2022 | Question: 51
Consider the function $f(z) = \dfrac{1}{(z+1)(z+2)(z+3)}.$ The residue of $f(z)$ at $z = -1,$ is ___________

Consider the function $f(z) = \dfrac{1}{(z+1)(z+2)(z+3)}.$ The residue of $f(z)$ at $z = -1,$ is ___________

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186

GATE IN 2022 | Question: 34
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 ignored, the small signal impedance looking into the node $\text{P}$ is given by ______________ $R_{S} || R_{L} || g^{-1}_{m}$ $R_{S} || g^{-1}_{m}$ $\left(R_{S} + R_{L}\right) || g^{-1}_{m}$ $\frac{R_{L}g_{m}}{1+R_{S}g_{m}}\left( R_{L} || g^{-1}_{m}\right)$

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...

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187

GATE IN 2022 | Question: 15
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 minimum number of bits (in integer) in the output is _________

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...

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188

GATE IN 2022 | Question: 54
In the circuit shown, the switch is initially closed. It is opened at $t=0 \; \text{s}$ and remains open thereafter. The time (in milliseconds) at which the output voltage $V_{out}$ becomes $\text{LOW}$ is ____________ (round off to three decimal places)

In the circuit shown, the switch is initially closed. It is opened at $t=0 \; \text{s}$ and remains open thereafter. The time (in milliseconds) at which the output voltag...

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189

GATE IN 2022 | Question: 35
Consider the differential equation $\dfrac{dy}{dx} + y \ln (y) = 0$ If $y(0) = e,$ then $y(1)$ is ___________ $e^{e}$ $e^{-e}$ $e^{(1/e)}$ $e^{(-1/e)}$

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)}$

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190

GATE IN 2022 | Question: 45
In the balanced three-phase circuit shown, $C_{0} = 8.2 \; \mu \text{F}$ and the line-to-line $\text{r.m.s.}$ voltage is $440 \; \text{V}$ at $50 \; \text{Hz}.$ The reading on the wattmeter (in watts) is ________ (round off to two decimal places)

In the balanced three-phase circuit shown, $C_{0} = 8.2 \; \mu \text{F}$ and the line-to-line $\text{r.m.s.}$ voltage is $440 \; \text{V}$ at $50 \; \text{Hz}.$ The readi...

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191

GATE IN 2022 | Question: 12
In which of the following bridge(s) is the balancing condition frequency-independent? Maxwell bridge Wien bridge Schering bridge Wheatstone bridge

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

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192

GATE IN 2022 | Question: 19
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 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 ...

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193

GATE IN 2022 | GA Question: 7
A game consists of spinning an arrow around a stationary disk as shown below. When the arrow comes to rest, there are eight equally likely outcomes. It could come to rest in any one of the sectors numbered $1, 2, 3,4, 5, 6, 7$ or $8$ as shown. Two such disks are used in a game where their arrows are independently spun. What is the ... spinning the two disks is equal to 8 after the arrows come to rest? $\dfrac{1}{16}$ $\dfrac{5}{64}$ $\dfrac{3}{32}$ $\dfrac{7}{64}$

A game consists of spinning an arrow around a stationary disk as shown below. When the arrow comes to rest, there are eight equally likely outcomes. It could come to rest...

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194

GATE IN 2022 | Question: 23
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 off to two decimal places)

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...

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195

GATE IN 2022 | Question: 25
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-gain feedback configuration in a voltage buffer circuit. The closed-loop output impedance of the $\text{OPAMP}$ (in milliohms) in the circuit is ___________ (round off to one decimal place)

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...

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196

GATE IN 2022 | Question: 30
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 ________ $\frac{1}{e}$ $\frac{2}{e}$ $2e$ $e^{2}$

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...

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197

GATE IN 2021 | GA Question: 7
Consider two rectangular sheets, Sheet $\text{M}$ and Sheet $\text{N}$ of dimensions $6\:cm \times 4\:cm$ each. $\text{Folding operation 1}$ : The sheet is folded into half by joining the short edges of the current shape. $\text{Folding operation 2}$ : The sheet is folded into half by joining the long edges of the current shape. ... of the final folded shape of Sheet $\text{N}$ to the final folded shape of Sheet $\text{M}$ is _____________. $13:7$ $3:2$ $7:5$ $5:13$

Consider two rectangular sheets, Sheet $\text{M}$ and Sheet $\text{N}$ of dimensions $6\:cm \times 4\:cm$ each.$\text{Folding operation 1}$ : The sheet is folded into hal...

Arjun

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198

GATE IN 2021 | Question: 37
Consider that $\text{X}$ and $\text{Y}$ are independent continuous valued random variables with uniform $\text{PDF}$ given by $X\sim U\left ( 2,3 \right )$ and $Y\sim U\left ( 1,4 \right )$. Then $P\left ( Y\leq X \right )$ is equal to __________________ (rounded off to two decimal places).

Consider that $\text{X}$ and $\text{Y}$ are independent continuous valued random variables with uniform $\text{PDF}$ given by $X\sim U\left ( 2,3 \right )$ and $Y\sim U\l...

Arjun

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199

GATE IN 2021 | GA Question: 2
The mirror image of the above text about the $\text{X}$-axis is

The mirror image of the above text about the $\text{X}$-axis is

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200

GATE IN 2021 | Question: 7
Input-output characteristic of a temperature sensor is exponential for a Thermistor Thermocouple Resistive Temperature Device $\text{(RTD)}$ Mercury thermometer

Input-output characteristic of a temperature sensor is exponential for aThermistorThermocoupleResistive Temperature Device $\text{(RTD)}$Mercury thermometer

Arjun

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