Recent questions tagged gatein-2022 / GO Instrumentation

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41

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...

Lakshman Bhaiya

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Lakshman Bhaiya asked Mar 20, 2022

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42

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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Lakshman Bhaiya asked Mar 20, 2022

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43

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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Lakshman Bhaiya asked Mar 20, 2022

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44

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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Lakshman Bhaiya asked Mar 20, 2022

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45

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...

Lakshman Bhaiya

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46

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...

Lakshman Bhaiya

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Lakshman Bhaiya asked Mar 20, 2022

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47

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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Lakshman Bhaiya asked Mar 20, 2022

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48

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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Lakshman Bhaiya asked Mar 20, 2022

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49

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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50

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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51

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 ___________

Lakshman Bhaiya

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52

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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53

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...

Lakshman Bhaiya

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54

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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Lakshman Bhaiya asked Mar 20, 2022

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55

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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56

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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Lakshman Bhaiya asked Mar 20, 2022

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57

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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Lakshman Bhaiya asked Mar 20, 2022

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58

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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Lakshman Bhaiya asked Mar 20, 2022

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59

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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Lakshman Bhaiya asked Mar 20, 2022

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60

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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Lakshman Bhaiya asked Mar 20, 2022

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61

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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Lakshman Bhaiya asked Mar 20, 2022

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62

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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Lakshman Bhaiya asked Mar 20, 2022

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63

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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Lakshman Bhaiya asked Mar 20, 2022

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64

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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65

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.

Lakshman Bhaiya

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Lakshman Bhaiya asked Mar 20, 2022