Recent questions tagged gatein-2021 / GO Instrumentation

0 votes

0 answers

1

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

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

2

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

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

3

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

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

4

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

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

5

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

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

6

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

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

7

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

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

8

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

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

9

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

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

10

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

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

11

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

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

12

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$

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

13

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...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

14

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 ...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

15

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...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

16

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 ______________...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

17

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

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

18

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 $T=4\pi ^{2}$

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

19

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...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

20

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...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

21

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...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

22

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...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

23

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...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

24

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 $v_{s}$...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

25

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 __________...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

26

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 ...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

27

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...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

28

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...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

29

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 ...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

30

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...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

31

GATE IN 2021 | Question: 21
An amplitude modulation $\text{(AM)}$ scheme uses tone modulation, with modulation index of $0.6$. The power efficiency of the $\text{AM}$ scheme is ______________ $\%$ (rounded off to one decimal place).

An amplitude modulation $\text{(AM)}$ scheme uses tone modulation, with modulation index of $0.6$. The power efficiency of the $\text{AM}$ scheme is ______________ $\%$ (...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

32

GATE IN 2021 | Question: 22
When the movable arm of a Michelson interferometer in vacuum $(n=1)$ is moved by $325\: \mu m$ , the number of fringe crossings is $1000$. The wavelength of the laser used in nanometers is ___________________.

When the movable arm of a Michelson interferometer in vacuum $(n=1)$ is moved by $325\: \mu m$ , the number of fringe crossings is $1000$. The wavelength of the laser use...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

33

GATE IN 2021 | Question: 23
Consider the function $f\left ( x \right )=-x^{2}+10x+100$. The minimum value of the function in interval $[5,10]$ is ___________.

Consider the function $f\left ( x \right )=-x^{2}+10x+100$. The minimum value of the function in interval $[5,10]$ is ___________.

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

34

GATE IN 2021 | Question: 24
Let $f\left ( z \right )=\dfrac{1}{z^{2}+6z+9}$ defined in the complex plane. The integral $\oint _{c}\:f\left ( z \right )dz$ over the contour of a circle $\text{c}$ with center at the origin and unit radius is _______________.

Let $f\left ( z \right )=\dfrac{1}{z^{2}+6z+9}$ defined in the complex plane. The integral $\oint _{c}\:f\left ( z \right )dz$ over the contour of a circle $\text{c}$ wit...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

35

GATE IN 2021 | Question: 25
The determinant of the matrix $\text{M}$ shown below is _______________. $M=\begin{bmatrix} 1 & 2 & 0 & 0\\ 3 & 4 & 0 & 0\\ 0 & 0 & 4 & 3\\ 0 & 0 & 2 & 1 \end{bmatrix}$

The determinant of the matrix $\text{M}$ shown below is _______________. $$M=\begin{bmatrix} 1 & 2 & 0 & 0\\ 3 & 4 & 0 & 0\\ 0 & 0 & 4 & 3\\ 0 & 0 & 2 & 1 \end{bmatrix}$$...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

36

GATE IN 2021 | Question: 26
$f\left ( Z \right )=\left ( Z-1 \right )^{-1}-1+\left ( Z-1 \right )-\left ( Z-1 \right )^{2}+ \cdots$ is the series expansion of $\frac{-1}{Z\left ( Z-1 \right )}$ for $\left | Z-1 \right |< 1$ $\frac{1}{Z\left ( Z-1 \right )}$ for $\left | Z-1 \right |< 1$ $\frac{1}{\left ( Z-1 \right )^{2}}$ for $\left | Z-1 \right |< 1$ $\frac{-1}{\left ( Z-1 \right )}$ for $\left | Z-1 \right |< 1$

$f\left ( Z \right )=\left ( Z-1 \right )^{-1}-1+\left ( Z-1 \right )-\left ( Z-1 \right )^{2}+ \cdots$ is the series expansion of$\frac{-1}{Z\left ( Z-1 \right )}$ for $...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

37

GATE IN 2021 | Question: 27
A single-phase transformer has maximum efficiency of $98 \%$. The core losses are $\text{80 W}$ and the equivalent winding resistance as seen from the primary side is $0.5 \:\Omega$. The rated current on the primary side is $\text{25 A}$. The percentage of the rated input current at which the maximum efficiency occurs is $35.7\%$ $50.6\%$ $80.5\%$ $100\%$

A single-phase transformer has maximum efficiency of $98 \%$. The core losses are $\text{80 W}$ and the equivalent winding resistance as seen from the primary side is $0....

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

38

GATE IN 2021 | Question: 28
A slip-ring induction motor is expected to be started by adding extra resistance in the rotor circuit. The benefit that is derived by adding extra resistance in the rotor circuit in comparison to the rotor being shorted is The starting torque would be higher The power factor at start will be lower The starting current is higher The losses at starting would be lower

A slip-ring induction motor is expected to be started by adding extra resistance in the rotor circuit. The benefit that is derived by adding extra resistance in the rotor...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

39

GATE IN 2021 | Question: 29
Consider a unity feedback configuration with a plant a $\text{PID}$ controller as shown in the figure. $G\left ( s \right )=\dfrac{1}{\left ( s+1 \right )\left ( s+3 \right )}$ and $C(s)=K\dfrac{\left ( s+3-j \right )\left ( s+3+j \right )}{s}$with $\text{K}$ being scalar. The closed loop is only stable for $K>0$ only stable for $\text{K}$ between $-1$ and $+1$ only stable for $K<0$ stable for all values of $\text{K}$

Consider a unity feedback configuration with a plant a $\text{PID}$ controller as shown in the figure. $G\left ( s \right )=\dfrac{1}{\left ( s+1 \right )\left ( s+3 \rig...

Arjun

2.9k points

Arjun asked Feb 19, 2021

0 votes

0 answers

40

GATE IN 2021 | Question: 30
The output $V_{o}$ of the ideal $\text{OpAmP}$ used in the circuit shown below is $\text{5 V}$. Then the value of resistor $R_{L}$ in kilo ohm $(k \Omega)$ is $2.5$ $5$ $25$ $50$

The output $V_{o}$ of the ideal $\text{OpAmP}$ used in the circuit shown below is $\text{5 V}$. Then the value of resistor $R_{L}$ in kilo ohm $(k \Omega)$ is$2.5$$5$$25$...

Arjun

2.9k points

Arjun asked Feb 19, 2021