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201
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$
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203
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 ...
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206
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
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207
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}$
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212
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...
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213
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}$...
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214
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 __________...
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215
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 ...
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216
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...
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217
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...
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220
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 ______________ $\%$ (...
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221
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...
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222
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 ___________.
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224
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}$$...
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229
GATE IN 2021 | Question: 30
The output $V_{o}$ of the ideal $\text{OpAmP}$ used in the circuit shown below is $\text{5 V}$. Then the value of resistor $R_{L}$ in kilo ohm $(k \Omega)$ is $2.5$ $5$ $25$ $50$
The output $V_{o}$ of the ideal $\text{OpAmP}$ used in the circuit shown below is $\text{5 V}$. Then the value of resistor $R_{L}$ in kilo ohm $(k \Omega)$ is$2.5$$5$$25$...
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230
GATE IN 2021 | Question: 31
Boolean function $\text{F}$ of three variable $\text{X, Y,}$ and $\text{Z}$ ... $F\left ( X, Y, Z \right )={X}' {Z}' + Y {Z}'$ $F\left ( X, Y, Z \right )={X}' {Y}' Z + XYZ$
Boolean function $\text{F}$ of three variable $\text{X, Y,}$ and $\text{Z}$ is given as$F\left ( X, Y, Z \right )=\left ( {X}' + Y + Z \right )\cdot \left ( X + {Y}' + {Z...
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236
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 $\left | A^{4}-5A^{3}+6A^{2}+2I \right |=$ _______________.
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240
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...
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