Questions by Arjun / GO Instrumentation

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1

GATE IN 2024 | GA Question: 1
If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [drizzle $\rightarrow$ rain $\rightarrow$ downpour] is analogous to [ $\rightarrow$ quarrel $\rightarrow$ feud]. Which one of the given options is appropriate to fill the blank? bicker bog dither dodge

If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words[drizzle $\rightarrow$ rain $\rightarrow$ downpour] is analogous to [ $\rightarro...

asked Feb 16

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GATE IN 2024 | GA Question: 2
Statements: 1. All heroes are winners. 2. All winners are lucky people. Inferences: I. All lucky people are heroes. II. Some lucky people are heroes. III. Some winners are heroes. Which of the above inferences can be logically deduced from statements 1 and 2 ? Only I and II Only II and III Only I and III Only III

Statements:1. All heroes are winners.2. All winners are lucky people.Inferences:I. All lucky people are heroes.II. Some lucky people are heroes.III. Some winners are hero...

asked Feb 16

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GATE IN 2024 | GA Question: 3
A student was supposed to multiply a positive real number $p$ with another positive real number $q$. Instead, the student divided $p$ by $q$. If the percentage error in the student's answer is $80 \%$, the value of $q$ is $5$ $\sqrt{2}$ $2$ $\sqrt{5}$

A student was supposed to multiply a positive real number $p$ with another positive real number $q$. Instead, the student divided $p$ by $q$. If the percentage error in t...

asked Feb 16

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4

GATE IN 2024 | GA Question: 4
If the sum of the first 20 consecutive positive odd numbers is divided by $20^{2}$, the result is $1$ $20$ $2$ $1 / 2$

If the sum of the first 20 consecutive positive odd numbers is divided by $20^{2}$, the result is$1$$20$$2$$1 / 2$

asked Feb 16

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5

GATE IN 2024 | GA Question: 5
The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) in classes VIII and IX is 450 and 360 , respectively. If the number of girls in classes VIII and IX is the same, then the number of girls in each class is $150$ $200$ $250$ $175$

The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) ...

asked Feb 16

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6

GATE IN 2024 | GA Question: 6
In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks. Yoko Roi stands (i) as an author for standing (ii) as an honorary fellow, after she stood (iii) her writings that stand (iv) the freedom of speech. (i) out (ii) down (iii) in (iv) for (i) down (ii) out (iii) by (iv) in (i) down (ii) out (iii) for (iv) in (i) out (ii) down (iii) by (iv) for

In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks.Yoko Roi stands (i) as an author for standing (ii) as an honorary fellow, af...

asked Feb 16

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GATE IN 2024 | GA Question: 7
Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder. The length of the container is equal to the length of the chalk-sticks. The ratio of the occupied space to the empty space of the container is $5 / 2$ $7 / 2$ $9 / 2$ $3$

Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder.The...

asked Feb 16

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GATE IN 2024 | GA Question: 8
The plot below shows the relationship between the mortality risk of cardiovascular disease and the number of steps a person walks per day. Based on the data, which one of the following options is true? The risk reduction on increasing the steps/day from 0 to 10000 is less than the risk reduction on increasing the ... risk reduction occurs on going from 0 to 5000 . For any 5000 increment in steps/day the largest risk reduction occurs on going from 15000 to 20000 .

The plot below shows the relationship between the mortality risk of cardiovascular disease and the number of steps a person walks per day. Based on the data, which one of...

asked Feb 16

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9

GATE IN 2024 | GA Question: 9
Five cubes of identical size and another smaller cube are assembled as shown in Figure A. If viewed from direction $X$, the planar image of the assembly appears as Figure B. Figure $\mathrm{A}$ Figure B If viewed from direction $Y$, the planar image of the assembly (Figure A) will appear as \begin{tabular}{|l|l|} \hline & \\ \hline & \\ \hline \end{tabular}

Five cubes of identical size and another smaller cube are assembled as shown in Figure A. If viewed from direction $X$, the planar image of the assembly appears as Figure...

asked Feb 16

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GATE IN 2024 | GA Question: 10

Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. The ...

asked Feb 16

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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

asked Feb 19, 2021

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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

asked Feb 19, 2021

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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 ...

asked Feb 19, 2021

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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...

asked Feb 19, 2021

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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...

asked Feb 19, 2021

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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 ...

asked Feb 19, 2021

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17

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...

asked Feb 19, 2021

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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 __...

asked Feb 19, 2021

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19

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{...

asked Feb 19, 2021

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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. ...

asked Feb 19, 2021

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21

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$

asked Feb 19, 2021

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22

GATE IN 2021 | Question: 2
Consider the sequence $x_{n}=0.5x_{n-1}+1,n=1,2, \dots \:\dots$ with $x_0=0$ . Then $\displaystyle \lim_{n\rightarrow \infty} x_n$ is $0$ $1$ $2$ $\infty$

Consider the sequence $x_{n}=0.5x_{n-1}+1,n=1,2, \dots \:\dots$ with $x_0=0$ . Then $\displaystyle \lim_{n\rightarrow \infty} x_n$ is$0$$1$$2$$\infty$

asked Feb 19, 2021

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GATE IN 2021 | Question: 3
An infinitely long line, with uniform positive charge density, lies along the $\text{z}$-axis. In cylindrical coordinate $\left ( r,\varnothing ,z \right )$, at any point $\vec{P}$ not on the $\text{z}$-axis, the direction of the electric field is $\hat{r}$ $\hat{\varnothing }$ $\hat{z }$ $\frac{\left ( \hat{r}+\hat{z} \right )}{\sqrt{2}}$

An infinitely long line, with uniform positive charge density, lies along the $\text{z}$-axis. In cylindrical coordinate $\left ( r,\varnothing ,z \right )$, at any point...

asked Feb 19, 2021

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GATE IN 2021 | Question: 4
The input-output relationship of an $\text{LTI}$ system is given below. For an input $x\left [ n \right ]$ shown below the peak value of the output when $x\left [ n \right ]$ passes through $\text{h}$ is _____________. $2$ $4$ $5$ $6$

The input-output relationship of an $\text{LTI}$ system is given below.For an input $x\left [ n \right ]$ shown belowthe peak value of the output when $x\left [ n \right ...

asked Feb 19, 2021

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25

GATE IN 2021 | Question: 5
In an $\text{ac}$ main, the $\text{rms}$ voltage $V_{ac}$, $\text{rms}$ current $I_{ac}$ and power $W_{ac}$ are measured as: $V_{ac}=100 \: V \pm 1\%, I_{ac} = 1 \: A \pm 1\%$ and $W_{ac}=50 \: W \pm 2\%$(errors are with respect to readings). The percentage error in calculating the power factor using these readings is $1\%$ $2\%$ $3\%$ $4\%$

In an $\text{ac}$ main, the $\text{rms}$ voltage $V_{ac}$, $\text{rms}$ current $I_{ac}$ and power $W_{ac}$ are measured as: $V_{ac}=100 \: V \pm 1\%, I_{ac} = 1 \: A \p...

asked Feb 19, 2021

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26

GATE IN 2021 | Question: 6
Let $u\left ( t \right )$ denote the unit step function. The bilateral Laplace transform of the function $f\left ( t \right )=e^{t}u\left ( -t \right )$ is ________________. $\frac{1}{s-1}$ with real part of $s< 1$ $\frac{1}{s-1}$ with real part of $s> 1$ $\frac{-1}{s-1}$ with real part of $s< 1$ $\frac{-1}{s-1}$ with real part of $s> 1$

Let $u\left ( t \right )$ denote the unit step function. The bilateral Laplace transform of the function $f\left ( t \right )=e^{t}u\left ( -t \right )$ is ______________...

asked Feb 19, 2021

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27

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

asked Feb 19, 2021

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28

GATE IN 2021 | Question: 8
The signal $\sin\left ( \sqrt{2\pi t} \right )$ is periodic with period $T=\sqrt{2\pi }$ not periodic periodic with period $T=2\pi$ periodic with period $T=4\pi ^{2}$

The signal $\sin\left ( \sqrt{2\pi t} \right )$ isperiodic with period $T=\sqrt{2\pi }$not periodic periodic with period $T=2\pi$periodic with period $T=4\pi ^{2}$

asked Feb 19, 2021

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29

GATE IN 2021 | Question: 9
The step response of a circuit is seen to have an oscillatory behavior at the output with oscillations dying down after some time. The correct inference$\text{(s)}$ regarding the transfer function from input to output is/are that it is of at least second order that it has at least one pole-pair that is underdamped that it does not have a real pole that it is a first order system

The step response of a circuit is seen to have an oscillatory behavior at the output with oscillations dying down after some time. The correct inference$\text{(s)}$ regar...

asked Feb 19, 2021

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30

GATE IN 2021 | Question: 10
For a $4$-bit Flash type Analog to Digital Convertor $\text{(ADC)}$ with full scale input voltage range $\text{"V"}$ which of the following statement$\text{(s)}$ is/are true? The $\text{ADC}$ requires $15$ comparators The $\text{ADC}$ requires one $4$ to $2$ priority encoder and $4$ comparators A change in the ... $\text{MSB}$ of the output A change in the input voltage by $\frac{V}{16}$ will always flip the $\text{LSB}$ of the output

For a $4$-bit Flash type Analog to Digital Convertor $\text{(ADC)}$ with full scale input voltage range $\text{"V"}$ which of the following statement$\text{(s)}$ is/are t...

asked Feb 19, 2021

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31

GATE IN 2021 | Question: 11
A $16$-bit microprocessor has twenty address lines ($A_{0}$ to $A_{19}$) and $16$ data lines. The higher eight significant lines of the data bus of the processor are tied to the $8$-data lines of a $16$ Kbyte memory that can store one byte in each of its $\text{16K}$ address locations.The memory chip ... only $A_{19}$ to $A_{14}$ for generating chip select The above chip cannot be interfaced as the width of the data bus of the processor and the memory chip differs

A $16$-bit microprocessor has twenty address lines ($A_{0}$ to $A_{19}$) and $16$ data lines. The higher eight significant lines of the data bus of the processor are tied...

asked Feb 19, 2021

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32

GATE IN 2021 | Question: 12
A single-phase transformer has a magnetizing inductance of $\text{250 mH}$ and a core loss resistance of $300\: \Omega$, referred to primary side. When excited with a $\text{230 V}$, $\text{50 Hz}$ sinusoidal supply at the primary, the power factor of the input current drawn, with secondary on open circuit, is ______ (rounded off to two decimal places).

A single-phase transformer has a magnetizing inductance of $\text{250 mH}$ and a core loss resistance of $300\: \Omega$, referred to primary side. When excited with a $\t...

asked Feb 19, 2021

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33

GATE IN 2021 | Question: 13
Taking $\text{N}$ as positive for clockwise encirclement, otherwise negative, the number of encirclements $\text{N}$ of $(-1,0)$ in the Nyquist plot of $G\left ( s \right )=\dfrac{3}{s-1}$ is _______________.

Taking $\text{N}$ as positive for clockwise encirclement, otherwise negative, the number of encirclements $\text{N}$ of $(-1,0)$ in the Nyquist plot of $G\left ( s \right...

asked Feb 19, 2021

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34

GATE IN 2021 | Question: 14
The diode used in the circuit has a fixed voltage drop of $\text{0.6 V}$ when forward biased. A signal $v_{s}$ is given to the ideal $\text{OpAmp}$ as shown. When $v_{s}$ is at its positive peak, the output $(v_{OA})$ of the $\text{OpAmp}$ in volts is ___________.

The diode used in the circuit has a fixed voltage drop of $\text{0.6 V}$ when forward biased. A signal $v_{s}$ is given to the ideal $\text{OpAmp}$ as shown. When $v_{s}$...

asked Feb 19, 2021

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GATE IN 2021 | Question: 15
The transistor $Q_{1}$ has a current gain $\beta _{1}=99$ and the transistor $Q_{2}$ has a current gain $\beta _{2}=49$. The current $I_{B2}$ in microampere is ______________.

The transistor $Q_{1}$ has a current gain $\beta _{1}=99$ and the transistor $Q_{2}$ has a current gain $\beta _{2}=49$. The current $I_{B2}$ in microampere is __________...

asked Feb 19, 2021

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GATE IN 2021 | Question: 16
A $\text{300 V}$, $\text{5 A}$, $\text{LPF}$ wattmeter has a full scale of $\text{300 W}$. The wattmeter can be used for loads supplied by $\text{300 V ac}$ mains with a maximum power factor of ___________________ (rounded off to one decimal place).

A $\text{300 V}$, $\text{5 A}$, $\text{LPF}$ wattmeter has a full scale of $\text{300 W}$. The wattmeter can be used for loads supplied by $\text{300 V ac}$ mains with a ...

asked Feb 19, 2021

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GATE IN 2021 | Question: 17
A $10$-bits $\text{ADC}$ has a full-scale of $\text{10.230 V}$, when the digital output is $(11\:1111\:1111)_{2}$. The quantization error of the $\text{ADC}$ in millivolt is __________________.

A $10$-bits $\text{ADC}$ has a full-scale of $\text{10.230 V}$, when the digital output is $(11\:1111\:1111)_{2}$. The quantization error of the $\text{ADC}$ in millivolt...

asked Feb 19, 2021

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38

GATE IN 2021 | Question: 18
A strain gage having nominal resistance of $1000\:\Omega$ has a gage factor of $2.5$. If the strain applied to the gage is $100\:\mu m/m$, its resistance in ohm will change to __________________ (rounded off to two decimal places).

A strain gage having nominal resistance of $1000\:\Omega$ has a gage factor of $2.5$. If the strain applied to the gage is $100\:\mu m/m$, its resistance in ohm will chan...

asked Feb 19, 2021

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39

GATE IN 2021 | Question: 19
Given: Density of mercury is $\text{13,600 kg/}$ $m^{3}$ and acceleration due to gravity is $\text{9.81 m/s}^{2}$. Atmospheric pressure is $\text{101 kPa}$. In a mercury $\text{U}$-tube manometer, the difference between the heights of the liquid in the $\text{U}$-tube is $\text{1 cm}$. The differential pressure being measured in pascal is ___________ (rounded off to the nearest integer).

Given: Density of mercury is $\text{13,600 kg/}$ $m^{3}$ and acceleration due to gravity is $\text{9.81 m/s}^{2}$. Atmospheric pressure is $\text{101 kPa}$. In a mercury ...

asked Feb 19, 2021

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GATE IN 2021 | Question: 20
A piezoresistive pressure sensor has a sensitivity of $\text{1 (mV/V) /kPa}$. The sensor is excited with a $\text{dc}$ supply of $\text{10 V}$ and the output is read using a $3$ $^1/_2$ digit $\text{200 mV}$ full-scale digital ultimeter. The resolution of the measurement set-up, in pascal is ________________.

A piezoresistive pressure sensor has a sensitivity of $\text{1 (mV/V) /kPa}$. The sensor is excited with a $\text{dc}$ supply of $\text{10 V}$ and the output is read usin...

asked Feb 19, 2021