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Recent questions tagged numerical-answers
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41
GATE IN 2022 | Question: 20
The transfer function of a system is: $\frac{(s+1)(s+3)}{(s+5)(s+7)(s+9)}$ In the state-space representation of the system, the minimum number of state variables (in integer) necessary is _________
The transfer function of a system is:$$\frac{(s+1)(s+3)}{(s+5)(s+7)(s+9)}$$In the state-space representation of the system, the minimum number of state variables (in inte...
Lakshman Bhaiya
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Lakshman Bhaiya
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42
GATE IN 2022 | Question: 21
A Zener diode is used as a $4 \; \text{V}$ voltage regulator in the circuit shown. Given that the diode requires a minimum current of $4 \; \text{mA}$ for voltage regulation, the maximum current (in milliamperes) permitted to flow through the load $R_{L}$ is __________ (round off to one decimal place)
A Zener diode is used as a $4 \; \text{V}$ voltage regulator in the circuit shown. Given that the diode requires a minimum current of $4 \; \text{mA}$ for voltage regulat...
Lakshman Bhaiya
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43
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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Lakshman Bhaiya
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44
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
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45
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
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46
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
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47
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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Lakshman Bhaiya
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48
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
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49
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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50
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
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51
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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Lakshman Bhaiya
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Mar 20, 2022
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52
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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Lakshman Bhaiya
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53
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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54
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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55
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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Lakshman Bhaiya
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56
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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57
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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58
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
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Arjun
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59
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
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Arjun
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60
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
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Arjun
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61
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
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Arjun
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62
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
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Arjun
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63
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
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Arjun
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64
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
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Arjun
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65
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
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66
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
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67
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
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68
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
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69
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
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Arjun
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Feb 19, 2021
Calculus
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calculus
maxima-minima
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70
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
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Arjun
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Analysis of complex variables
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71
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
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Arjun
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Feb 19, 2021
Linear Algebra
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linear-algebra
matrices
determinant
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72
GATE IN 2021 | Question: 37
Consider that $\text{X}$ and $\text{Y}$ are independent continuous valued random variables with uniform $\text{PDF}$ given by $X\sim U\left ( 2,3 \right )$ and $Y\sim U\left ( 1,4 \right )$. Then $P\left ( Y\leq X \right )$ is equal to __________________ (rounded off to two decimal places).
Consider that $\text{X}$ and $\text{Y}$ are independent continuous valued random variables with uniform $\text{PDF}$ given by $X\sim U\left ( 2,3 \right )$ and $Y\sim U\l...
Arjun
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Arjun
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Probability and Statistics
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probability-and-statistics
probability
probability-density-function
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73
GATE IN 2021 | Question: 38
Given $A=\begin{pmatrix} 2 & 5\\ 0 & 3 \end{pmatrix}$. The value of the determinant $\left | A^{4}-5A^{3}+6A^{2}+2I \right |=$ _______________.
Given $A=\begin{pmatrix} 2 & 5\\ 0 & 3 \end{pmatrix}$. The value of the determinant $\left | A^{4}-5A^{3}+6A^{2}+2I \right |=$ _______________.
Arjun
2.9k
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Arjun
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Linear Algebra
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determinant
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74
GATE IN 2021 | Question: 39
The figure below shows an electrically conductive bar of square cross-section resting on a plane surface. The bar of mass of $\text{1 kg}$ has a depth of $\text{0.5 m}$ along the $\text{y}$ direction. The coefficient of friction between the bar and the surface is $0.1$. Assume the acceleration due to gravity to be ... onto the bar and is maintained. When the bar has moved by $\text{1 m}$, its speed in metre per second is ___________ (rounded off to one decimal place).
The figure below shows an electrically conductive bar of square cross-section resting on a plane surface. The bar of mass of $\text{1 kg}$ has a depth of $\text{0.5 m}$ a...
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75
GATE IN 2021 | Question: 41
An air cored coil having a winding resistance of $10\: \Omega$ is connected in series with a variable capacitor $C_{x}$. The series circuit is excited by a $\text{10 V}$ sinusoidal voltage source of angular frequency $1000$ rad/$\text{s}$. As the value of the capacitor is varied, a maximum voltage of $\text{30 V}$ was observed across it. Neglecting skin-effect, the value of the inductance of the coil in millihenry is ___________.
An air cored coil having a winding resistance of $10\: \Omega$ is connected in series with a variable capacitor $C_{x}$. The series circuit is excited by a $\text{10 V}$ ...
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Arjun
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76
GATE IN 2021 | Question: 42
A household fan consumes $\text{60 W}$ and draws a current of $\text{0.3125 A (rms)}$ when connected to a $\text{230 V (rms) ac }$, $\text{50 Hz}$ single phase mains. The reactive power drawn by the fan in $\text{VAr}$ is _______________________ (rounded off to the nearest integer).
A household fan consumes $\text{60 W}$ and draws a current of $\text{0.3125 A (rms)}$ when connected to a $\text{230 V (rms) ac }$, $\text{50 Hz}$ single phase mains. The...
Arjun
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Arjun
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77
GATE IN 2021 | Question: 43
Given $y\left ( t \right )=e^{-3t}u\left ( t \right )\ast u\left ( t+3 \right )$, where $\ast$ denotes convolution operation. The value of $y\left ( t \right )$ as $t\rightarrow \infty$ is ___________________ (rounded off to two decimal places).
Given $y\left ( t \right )=e^{-3t}u\left ( t \right )\ast u\left ( t+3 \right )$, where $\ast$ denotes convolution operation. The value of $y\left ( t \right )$ as $t\rig...
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GATE IN 2021 | Question: 44
The input signal shown below is passed through the filter with the following taps The number of non-zero output samples is ________________.
The input signal shown belowis passed through the filter with the following tapsThe number of non-zero output samples is ________________.
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GATE IN 2021 | Question: 45
A sinusoid $\left ( \sqrt{2} \sin t \right ) \: \mu \left ( t \right )$, where $\mu \left ( t \right )$ is the step input, is applied to a system with transfer-function $G\left ( s \right )=\dfrac{1}{s+1}$. The amplitude of the steady state output is __________.
A sinusoid $\left ( \sqrt{2} \sin t \right ) \: \mu \left ( t \right )$, where $\mu \left ( t \right )$ is the step input, is applied to a system with transfer-function $...
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GATE IN 2021 | Question: 46
Consider a system with transfer-function $G\left ( s \right )=\dfrac{2}{s+1}$. A unit step function $\mu \left ( t \right )$ is applied to the system, which results in an output $y\left ( t \right )$. If $e\left ( t \right )=y\left ( t \right )-\mu \left ( t \right ),$ then $ \lim\limits_{t\rightarrow \infty }e\left ( t \right )$ is ___________________.
Consider a system with transfer-function $G\left ( s \right )=\dfrac{2}{s+1}$. A unit step function $\mu \left ( t \right )$ is applied to the system, which results in an...
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