Recent questions without answers / GO Instrumentation

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161

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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162

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 ...

Lakshman Bhaiya

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163

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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164

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 ...

Lakshman Bhaiya

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165

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 ...

Lakshman Bhaiya

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166

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, ...

Lakshman Bhaiya

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167

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...

Lakshman Bhaiya

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168

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)...

Lakshman Bhaiya

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169

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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170

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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171

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...

Lakshman Bhaiya

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172

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...

Lakshman Bhaiya

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173

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...

Lakshman Bhaiya

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174

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...

Lakshman Bhaiya

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175

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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176

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...

Lakshman Bhaiya

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177

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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178

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...

Lakshman Bhaiya

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179

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 ...

Lakshman Bhaiya

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180

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

Lakshman Bhaiya

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181

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...

Lakshman Bhaiya

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182

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...

Lakshman Bhaiya

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183

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...

Lakshman Bhaiya

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184

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 ...

Lakshman Bhaiya

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185

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 ...

Lakshman Bhaiya

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186

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...

Lakshman Bhaiya

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187

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 =...

Lakshman Bhaiya

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188

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...

Lakshman Bhaiya

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189

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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190

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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191

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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192

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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193

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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194

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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195

GATE IN 2021 | GA Question: 6
$\text{Statement:}$ Either $\text{P}$ marries $\text{Q}$ or $\text{X}$ marries $\text{Y}$ Among the options below, the logical $\text{NEGATION}$ of the above statement is : $\text{P}$ does not marry $\text{Q}$ and $\text{X}$ marries $\text{Y}$ Neither $\text{P}$ marries $\text{Q}$ nor $\text{X}$ marries $\text{Y}$ $\text{X}$ does not marry $\text{Y}$ and $\text{P}$ marries $\text{Q}$ $\text{P}$ marries $\text{Q}$ and $\text{X}$ marries $\text{Y}$

$\text{Statement:}$ Either $\text{P}$ marries $\text{Q}$ or $\text{X}$ marries $\text{Y}$Among the options below, the logical $\text{NEGATION}$ of the above statement is ...

Arjun

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196

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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197

GATE IN 2021 | GA Question: 8
Five line segments of equal lengths, $\text{PR, PS, QS, QT}$ and $\text{RT}$ are used to form a star as shown in the figure above. The value of $\theta$, in degrees, is _______________ $36$ $45$ $72$ $108$

Five line segments of equal lengths, $\text{PR, PS, QS, QT}$ and $\text{RT}$ are used to form a star as shown in the figure above.The value of $\theta$, in degrees, is __...

Arjun

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198

GATE IN 2021 | GA Question: 9
A function, $\lambda$, is defined by $\lambda \left ( p,q \right )=\left\{\begin{matrix} \left ( p-q \right )^{2} , & \text{if} \:p\geq q, \\ p+q, &\text{if} \: p< q.\end{matrix}\right.$ The value of the expression $\dfrac{\lambda \left ( -\left (- 3+2 \right ),\left ( -2+3 \right ) \right )}{\left ( -\left ( -2+1 \right ) \right )}$ is: $-1$ $0$ $\frac{16}{3}$ $16$

A function, $\lambda$, is defined by$\lambda \left ( p,q \right )=\left\{\begin{matrix} \left ( p-q \right )^{2} , & \text{if} \:p\geq q, \\ p+q, &\text{if} \: p< q.\end{...

Arjun

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199

GATE IN 2021 | GA Question: 10

Humans have the ability to construct worlds entirely in their minds, which don't exist in the physical world. So far as we know, no other species possesses this ability. ...

Arjun

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200

GATE IN 2021 | Question: 1
Consider the row vectors $v=(1,0)$ and $w=(2,0)$. The rank of the matrix $M=2v^{T}v+3w^{T}w$, where the superscript $\text{T}$ denotes the transpose, is $1$ $2$ $3$ $4$

Consider the row vectors $v=(1,0)$ and $w=(2,0)$. The rank of the matrix $M=2v^{T}v+3w^{T}w$, where the superscript $\text{T}$ denotes the transpose, is$1$$2$$3$$4$

Arjun

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