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161

GATE IN 2022 | Question: 31
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 proportional gain is increased by a factor of $2,$ the integral gain is increased by a factor of $3,$ and the derivative gain is left unchanged ... -state error in tracking a ramp reference signal _________ Remains unchanged Decreases by a factor of $2$ Decreases by a factor of $3$ Decreases by a factor of $5$

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...

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162

GATE IN 2022 | Question: 32
A resistor ladder digital-to-analog converter $\text{(DAC)}$ receives a digital input that results in the circuit having the state as shown in the figure. For this digital input, the Thevenin voltage, $V_{th},$ and Thevenin resistance, $R_{th},$ as seen at the output node are _________ $V_{th} = 0.5 \; \text{V}, R_{th} = 1 \; \text{k}\Omega$ ... $V_{th} = 1 \; \text{V}, R_{th} = 1 \; \text{k}\Omega$ $V_{th} = 1 \; \text{V}, R_{th} = 2 \; \text{k}\Omega$

A resistor ladder digital-to-analog converter $\text{(DAC)}$ receives a digital input that results in the circuit having the state as shown in the figure. For this digita...

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163

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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164

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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165

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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166

GATE IN 2022 | Question: 36
The digital circuit shown ________ is a divide-by-$5$ counter is a divide-by-$7$ counter is a divide-by-$8$ counter does not function as a counter due to disjoint cycles of states

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...

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167

GATE IN 2022 | Question: 37
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 $v_{d}$ injected at the supply terminal results in a small signal voltage fluctuation $v_{o}$ at the output. If the channel length modulation of the $\text{MOSFET}$ is ignored, the small signal gain ... $\dfrac{-g_{m}R_{o}}{1+2g_{m}R_{o}}$ $\left(\dfrac{g_{m}R_{o}}{2} + \dfrac{3}{2}\right)^{-1}$

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...

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168

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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169

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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170

GATE IN 2022 | Question: 40
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 $ \; \tan^{-1}\frac{2b}{a}$ The magnitude is $1$ The magnitude is $\sqrt{\frac{a^{2}+b^{2}}{a^{2}-b^{2}}}$

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 ...

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171

GATE IN 2022 | Question: 41
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 light intensity after transmission through a $1 \; \text{cm}$ thick sample of the material is $0.414 \; \text{mW/cm}^{2}.$ ... $0.186 \; \text{mW/cm}^{2}.$ The absorption coefficient $(\text{in cm}^{-1})$ of the material is ____________ (round off to two decimal places)

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 ...

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172

GATE IN 2022 | Question: 42
In the circuit shown, the load is driven by a sinusoidal ac voltage source $V_{1} =100 \; \angle 0^{\circ} \; \text{V}$ at $50 \; \text{Hz}.$ Given $R_{1}=20 \; \Omega, C_{1} = \left(\frac{1000}{\pi}\right) \mu \text{F, L}_{1} = \left(\frac{20}{\pi}\right) \; \text{mH} $ and $R_{2} = 4 \; \Omega,$ the power factor is _________ (round off to one decimal place)

In the circuit shown, the load is driven by a sinusoidal ac voltage source $V_{1} =100 \; \angle 0^{\circ} \; \text{V}$ at $50 \; \text{Hz}.$ Given $R_{1}=20 \; \Omega, ...

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173

GATE IN 2022 | Question: 43
In a unity-gain feedback control system, the plant $P(s) = \frac{0.001}{s(2s+1)(0.01s+1)}$ is controlled by a lag compensator $C(s) = \frac{s+10}{s+0.1}$ The slope $(\text{in dB/decade})$ of the asymptotic Bode magnitude plot of the loop gain at $\omega = 3 \; \text{rad/s}$ is _________ (in integer)

In a unity-gain feedback control system, the plant$$P(s) = \frac{0.001}{s(2s+1)(0.01s+1)}$$is controlled by a lag compensator$$C(s) = \frac{s+10}{s+0.1}$$The slope $(\tex...

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174

GATE IN 2022 | Question: 44
Given Circuit $\text{A}$ with currents $I_{1}$ and $I_{2}$ as shown, the current $I_{3}$ in Circuit $\text{B}$ (in amperes), is _________ (round off to one decimal place)

Given Circuit $\text{A}$ with currents $I_{1}$ and $I_{2}$ as shown, the current $I_{3}$ in Circuit $\text{B}$ (in amperes), is _________ (round off to one decimal place)...

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175

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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176

GATE IN 2022 | Question: 46
The circuit shown is driven by a sinusoidal input voltage, $V_{in},$ resulting in the output voltage, $V_{out}.$ The frequency (in kilohertz) at which the voltage gain is $0$ dB is _________ (round off to two decimal places)

The circuit shown is driven by a sinusoidal input voltage, $V_{in},$ resulting in the output voltage, $V_{out}.$ The frequency (in kilohertz) at which the voltage gain is...

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177

GATE IN 2022 | Question: 47
A conducting semi-circular loop of radius $R=0.1 \; \text{m}, $ with its diameter centered at the origin, rotates in the $x-y$ plane about the origin with a constant angular velocity, $\omega= 20 \; \text{rad/s},$ as shown. A magnetic field of magnitude $B=2T$ and normal to $x-y$ plane exists in ... loop has a resistance of $2 \; \Omega,$ and negligible inductance, the peak-to-peak current (in milliamperes) in the loop is ___________ (round off to one decimal place)

A conducting semi-circular loop of radius $R=0.1 \; \text{m}, $ with its diameter centered at the origin, rotates in the $x-y$ plane about the origin with a constant angu...

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178

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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179

GATE IN 2022 | Question: 49
A capacitor is constructed using two concentric spheres and air as the dielectric medium (permittivity of air $= 8.854 \times 10^{-12} \; \text{F/m}.)$ The radii of the inner and outer spheres are $a = 10 \; \text{cm}$ and $b = 15 \; \text{cm},$ respectively .The capacitance (in picofarads) is ___________ (round off to $2$ decimal places)

A capacitor is constructed using two concentric spheres and air as the dielectric medium (permittivity of air $= 8.854 \times 10^{-12} \; \text{F/m}.)$ The radii of the i...

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180

GATE IN 2022 | Question: 50
A $1 \; \text{kHz}$ sine-wave generator having an internal resistance of $50 \; \Omega$ generates an open-circuit voltage of $10 \; \text{V}_{\text{p-p}}.$ When a capacitor is connected across the output terminals, the voltage drops to $8 \; \text{V}_{\text{p-p}}$. The capacitance of the capacitor (in microfarads) is _________________ (round off to two decimal places)

A $1 \; \text{kHz}$ sine-wave generator having an internal resistance of $50 \; \Omega$ generates an open-circuit voltage of $10 \; \text{V}_{\text{p-p}}.$ When a capacit...

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181

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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182

GATE IN 2022 | Question: 52
In the circuit shown, the capacitance $C_{0}=10 \; \mu \text{F}$ and inductance $\text{L}_{0} = 1 \; \text{mH}$ and the diode is ideal. The capacitor is initially charged to $10 \; \text{V}$ and the current in the inductor is initially zero. If the switch is closed at $t=0 \; \text{s},$ the voltage $V_{c}(t)$ (in volts) across the capacitor at $t=0.5 \; \text{s}$ is (round off to one decimal place)

In the circuit shown, the capacitance $C_{0}=10 \; \mu \text{F}$ and inductance $\text{L}_{0} = 1 \; \text{mH}$ and the diode is ideal. The capacitor is initially charged...

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183

GATE IN 2022 | Question: 53
The bridge shown is balanced when $R_{1}=100 \; \Omega , R_{2}=210 \; \Omega, C_{2}=2.9 \; \mu\text{F},$ and $R_{4}=50 \; \Omega.$ The $2\;\text{kHz}$ sine-wave generator supplies a voltage of $10 \; \text{V}_{\text{p-p}}.$ The value of $\text{L}_{3}$ (in millihenry) is __________ (round off to two decimal places)

The bridge shown is balanced when $R_{1}=100 \; \Omega , R_{2}=210 \; \Omega, C_{2}=2.9 \; \mu\text{F},$ and $R_{4}=50 \; \Omega.$ The $2\;\text{kHz}$ sine-wave generator...

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184

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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185

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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186

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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187

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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188

GATE IN 2022 | GA Question: 3
Pipes $\text{P}$ and $\text{Q}$ can fill a storage tank in full with water in $10$ and $6$ minutes, respectively. Pipe $\text{R}$ draws the water out from the storage tank at a rate of $34$ litres per minute. $\text{P, Q and R}$ operate at a constant rate. If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously, what is the capacity of the storage tank (in litres)? $26.8$ $60.0$ $120.0$ $127.5$

Pipes $\text{P}$ and $\text{Q}$ can fill a storage tank in full with water in $10$ and $6$ minutes, respectively. Pipe $\text{R}$ draws the water out from the storage tan...

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189

GATE IN 2022 | GA Question: 4
Six persons $\text{P, Q, R, S, T and U}$ are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements: $\text{P}$ sits next to $\text{S}$ and $\text{T}$. $\text{Q}$ sits diametrically opposite to $\text{P}$. The shortest distance between $\text{S}$ and $\text{R}$ is equal to the ... is a neighbor of $\text{U}$ and $\text{S}$ $\text{R}$ and $\text{T}$ $\text{R}$ and $\text{U}$ $\text{P}$ and $\text{S}$

Six persons $\text{P, Q, R, S, T and U}$ are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements:$\text...

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190

GATE IN 2022 | GA Question: 5
A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially. What is the minimum number of doors that need to be opened in order to go from the point $\text{P}$ to the point $\text{Q}?$ $4$ $3$ $2$ $1$

A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially.What is the minimum number of doors that need ...

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191

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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192

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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193

GATE IN 2022 | GA Question: 8
Consider the following inequalities. $3p \:– q < 4$ $3q \:– p < 12$ Which one of the following expressions below satisfies the above two inequalities? $p + q < 8$ $p + q = 8$ $8 \leq p + q < 16$ $p + q \geq 16$

Consider the following inequalities.$3p \:– q < 4$$3q \:– p < 12$Which one of the following expressions below satisfies the above two inequalities?$p + q < 8$$p + q =...

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194

GATE IN 2022 | GA Question: 9
Given below are three statements and four conclusions drawn based on the statements. Statement $1:$ Some engineers are writers. Statement $2:$ No writer is an actor. Statement $3:$ All actors are engineers. Conclusion $\text{I}:$ Some writers are engineers. Conclusion $\text{II}:$ All engineers are actors. Conclusion ... are correct Only conclusion $\text{I}$ and conclusion $\text{III}$ are correct Either conclusion $\text{III}$ or conclusion $\text{IV}$ is correct

Given below are three statements and four conclusions drawn based on the statements.Statement $1:$ Some engineers are writers.Statement $2:$ No writer is an actor.Stateme...

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195

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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196

GATE IN 2021 | GA Question: 1
Getting to the top is ______________ than staying on top. more easy much easy easiest easier

Getting to the top is ______________ than staying on top.more easymuch easyeasiesteasier

Arjun

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197

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

Arjun

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198

GATE IN 2021 | GA Question: 3
In a company, $35\%$ of the employees drink coffee, $40\%$ of the employees drink tea and $10\%$ of the employees drink both tea and coffee. What $\%$ of employees drink neither tea nor coffee? $15$ $25$ $35$ $40$

In a company, $35\%$ of the employees drink coffee, $40\%$ of the employees drink tea and $10\%$ of the employees drink both tea and coffee. What $\%$ of employees drink ...

Arjun

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199

GATE IN 2021 | GA Question: 4
$\bigoplus$ and $\bigodot$ are two operators on numbers $\text{p}$ and $\text{q}$ such that $p \bigoplus q=\dfrac{p^{2}+q^{2}}{pq}$ and $p \bigodot q=\dfrac{p^{2}}{q}$; If $x\bigoplus y=2\bigodot 2$, then $x=$ $\frac{y}{2}$ $y$ $\frac{3y}{2}$ $2y$

$\bigoplus$ and $\bigodot$ are two operators on numbers $\text{p}$ and $\text{q}$ such that $p \bigoplus q=\dfrac{p^{2}+q^{2}}{pq}$ and $p \bigodot q...

Arjun

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200

GATE IN 2021 | GA Question: 5
Four persons $\text{P, Q, R}$ and $\text{S}$ are to be seated in a row, all facing the same direction, but not necessarily in the same order. $\text{P}$ and $\text{R}$ cannot sit adjacent to each other. $\text{S}$ should be seated to the right of $\text{Q}$. The number of distinct seating arrangements possible is: $2$ $4$ $6$ $8$

Four persons $\text{P, Q, R}$ and $\text{S}$ are to be seated in a row, all facing the same direction, but not necessarily in the same order. $\text{P}$ and $\text{R}$ ca...

Arjun

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Arjun asked Feb 19, 2021