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281
GATE2020 IN: 49
A circuit consisting of capacitors, DC voltage source and an amplifier having a voltage gain G=-5 is shown in the figure. The effective capacitance across the nodes A and B $\text{(in $\mu$F, rounded off to one decimal place)}$ is ________
A circuit consisting of capacitors, DC voltage source and an amplifier having a voltage gain G=-5 is shown in the figure. The effective capacitance across the nodes A and...
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282
GATE2020 IN: 50
Consider the following state variable equations: $\dot{x_1}(t)=x_2(t)$ $\dot{x_2}(t)=-6x_1(t)-5x_2(t)$ The initial conditions are $x_1(0)=0 \:and\: x_2(0)=1.$ At $t=1$ second, the value of $x_2(1)$ $\text{(rounded off to two decimal places)}$ is ___________
Consider the following state variable equations:$\dot{x_1}(t)=x_2(t)$$\dot{x_2}(t)=-6x_1(t)-5x_2(t)$The initial conditions are $x_1(0)=0 \:and\: x_2(0)=1.$ At $t=1$ secon...
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283
GATE2020 IN: 51
Assume the diodes in the circuit shown are ideal. The current $I_X$ flowing through the $3\: k\Omega$ resistor $\text{(in mA, rounded off to one decimal place)}$ is ___________
Assume the diodes in the circuit shown are ideal. The current $I_X$ flowing through the $3\: k\Omega$ resistor $\text{(in mA, rounded off to one decimal place)}$ is _____...
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286
GATE2020 IN: 54
In the Maxwell-Wien bridge shown, the detector D reads zero when $C_1=100 nF$ and $R_1=100 k\Omega$. The Q factor of the coil is ______
In the Maxwell-Wien bridge shown, the detector D reads zero when $C_1=100 nF$ and $R_1=100 k\Omega$. The Q factor of the coil is ______
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287
GATE2020 IN: 55
The loop transfer function of a negative feedback system is $ G(s)H(s)=\frac{2(s+1)}{s^2}$. The phase margin of the system $\text{(in degrees, rounded off to one decimal place)}$ is __________
The loop transfer function of a negative feedback system is $ G(s)H(s)=\frac{2(s+1)}{s^2}$. The phase margin of the system $\text{(in degrees, rounded off to one decimal ...
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291
GATE2020: 4
In the circuit shown below, the safe maximum value for the current $I$ is _______ $\text{1.0 A}$ $\text{0.5 A}$ $\text{0.1 A}$ $\text{0.05 A}$
In the circuit shown below, the safe maximum value for the current $I$ is _______$\text{1.0 A}$$\text{0.5 A}$$\text{0.1 A}$$\text{0.05 A}$
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292
GATE2020: 5
A differentiator has a transfer function whose phase increases linearly with frequency magnitude remains constant magnitude increases linearly with frequency magnitude decreases linearly with frequency
A differentiator has a transfer function whosephase increases linearly with frequencymagnitude remains constantmagnitude increases linearly with frequencymagnitude decrea...
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293
GATE2020: 6
A phase lead network has the transfer function $G(S)=\frac{1+0.2s}{1+0.05s}$. The angular frequency at which the maximum phase shift for the network occurs is _____________ $10\;rad/s$ $20\;rad/s$ $100\;rad/s$ $200\;rad/s$
A phase lead network has the transfer function $G(S)=\frac{1+0.2s}{1+0.05s}$. The angular frequency at which the maximum phase shift for the network occurs is ___________...
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294
GATE2020: 7
If the diodes in the circuit shown are ideal and the breakdown voltage $V_z$ of the Zener diode is $5\;V$ the power dissipated in the $100\;\Omega$ resistor (in watts) is __________. $0$ $1$ $25/100$ $225/100$
If the diodes in the circuit shown are ideal and the breakdown voltage $V_z$ of the Zener diode is $5\;V$ the power dissipated in the $100\;\Omega$ resistor (in watts) is...
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296
GATE2020: 9
A $Q$ meter is best suited for the measurement of the ___________ Quality factor of a capacitance Distributed capacitance of a coil quality factor of piezoelectric sensor Turns-ratio of a transformer
A $Q$ meter is best suited for the measurement of the ___________Quality factor of a capacitanceDistributed capacitance of a coilquality factor of piezoelectric sensorTur...
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299
GATE2020: 12
The boolean operation performed by the following circuit at the output O is _______ $O=S_1\oplus S_0$ $O=S_1\bullet \overline{S_0}$ $O=S_1+S_0$ $O=S_0\bullet \overline{S_1}$
The boolean operation performed by the following circuit at the output O is _______$O=S_1\oplus S_0$$O=S_1\bullet \overline{S_0}$$O=S_1+S_0$$O=S_0\bullet \overline{S_1}$
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300
GATE2020: 13
Consider the signal $x[n]=\sin(2\pi n)u[n]$, where $u[n]= \left\{ \begin{array}{rcl} 1 & n=0,1,2,3\dots \\ 0 & otherwise\end{array}\right. $ The period of this signal $x[n]$ is ___________. $4$ $3$ $2$ $1$
Consider the signal $x[n]=\sin(2\pi n)u[n]$, where $u[n]= \left\{ \begin{array}{rcl} 1 & n=0,1,2,3\dots \\ 0 & otherwise\end{array}\right. $The period of this signal $x[n...
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301
GATE2020: 14
The closed loop transfer function of a control system is given by $\frac{C(s)}{R(s)}=\frac{1}{s+1}$. for the input $r(t)=\sin\;t$ the steady state response $c(t)$ is ___________ $1$ $\frac{1}{\sqrt{2}} \cos t$ $\frac{1}{\sqrt{2}} \sin (t+\frac{\pi}{4})$ $\frac{1}{\sqrt{2}} \sin (t-\frac{\pi}{4})$
The closed loop transfer function of a control system is given by $\frac{C(s)}{R(s)}=\frac{1}{s+1}$. for the input $r(t)=\sin\;t$ the steady state response $c(t)$ is ____...
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302
GATE2020: 15
Let $f(z)=\frac{1}{z+a},a>0.$ the value of the integral $\oint f(z)dz$ over a circle $C$ with center $(-a,0)$ and radius $R>0$ evaluated in the anti-clockwise direction is ____________ $0$ $2\pi i$ $-2\pi i$ $4\pi i$
Let $f(z)=\frac{1}{z+a},a>0.$ the value of the integral $\oint f(z)dz$ over a circle $C$ with center $(-a,0)$ and radius $R>0$ evaluated in the anti-clockwise direction i...
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304
GATE2020: 17
Assuming ideal opamps, the output voltage at $V_1$ in the figure shown (in volts) is __________
Assuming ideal opamps, the output voltage at $V_1$ in the figure shown (in volts) is __________
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305
GATE2020: 18
Three $400\;\Omega$ resistors are connected in delta and powered by a $400\;V\;(rms), \;50\;Hz,$ balanced symmetrical $R-Y-B$ sequence, three-phase three-wire mains. The rms value of the line current $\text{(in amperes, rounded off to one decimal place)}$ is __________.
Three $400\;\Omega$ resistors are connected in delta and powered by a $400\;V\;(rms), \;50\;Hz,$ balanced symmetrical $R-Y-B$ sequence, three-phase three-wire mains. The ...
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306
GATE2020: 19
Consider the signal $x(t)=e^{-|t|}$. Let $X(j\omega)=\int_{-\infty}^{\infty} x(t)e^{-j\omega t} dt$ be the Fourier transform of $x(t)$. The value of $X(j0) $is _________
Consider the signal $x(t)=e^{-|t|}$. Let $X(j\omega)=\int_{-\infty}^{\infty} x(t)e^{-j\omega t} dt$ be the Fourier transform of $x(t)$. The value of $X(j0) $is _________
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307
GATE2020: GA: 1
He is known for his unscrupulous ways. He always sheds ___________ tears to deceive people. fox’s crocodile’s crocodile fox
He is known for his unscrupulous ways. He always sheds ___________ tears to deceive people.fox’scrocodile’scrocodilefox
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308
GATE2020: GA: 2
Jofra Archer, the England fast bowler, is _____________ than accurate. more fast faster less faster more faster
Jofra Archer, the England fast bowler, is _____________ than accurate.more fastfasterless fastermore faster
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309
GATE2020: GA: 3
Select the word that fits the analogy: $\text{Build : Building :: Grow :}$ _______________ Grown Grew Growth Growed
Select the word that fits the analogy:$\text{Build : Building :: Grow :}$ _______________GrownGrewGrowthGrowed
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311
GATE2020: GA: 5
Define $[x]$ as the greatest integer less than or equal to $x$, for each $x \; \in \; [-\infty,\infty]$. If $y=[x],$ then area under $y$ for $x \; \in \; [1,4]$ is ____________. $1$ $3$ $4$ $6$
Define $[x]$ as the greatest integer less than or equal to $x$, for each $x \; \in \; [-\infty,\infty]$. If $y=[x],$ then area under $y$ for $x \; \in \; [1,4]$ is _____...
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314
GATE2020: GA: 8
The sum of the first $n$ terms in the sequence $\text{8, 88, 888, 8888,$\dots$}$ is __________. $\frac{81}{80}(10^n-1)+\frac{9}{8}n$ $\frac{81}{80}(10^n-1)-\frac{9}{8}n$ $\frac{80}{81}(10^n-1)+\frac{8}{9}n$ $\frac{80}{81}(10^n-1)-\frac{8}{9}n$
The sum of the first $n$ terms in the sequence $\text{8, 88, 888, 8888,$\dots$}$ is __________.$\frac{81}{80}(10^n-1)+\frac{9}{8}n$$\frac{81}{80}(10^n-1)-\frac{9}{8}n$$\f...
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315
GATE2020: GA: 9
Select the graph that schematically represents $\text{BOTH} \;y=x^m$ and $y=x^{1/m}$ properly in the interval $0\leq x\leq 1$, for integer values of $m$, where $m>1$.
Select the graph that schematically represents $\text{BOTH} \;y=x^m$ and $y=x^{1/m}$ properly in the interval $0\leq x\leq 1$, for integer values of $m$, where $m>1$.
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317
GATE2017: 31
A series $R-L-C$ circuit is excited with an a.c. voltage source. The quality factor $(Q)$ of the circuit is given as $Q=30$. The amplitude of current in $\text{ampere}$ at upper half-power frequency will be _________.
A series $R-L-C$ circuit is excited with an a.c. voltage source. The quality factor $(Q)$ of the circuit is given as $Q=30$. The amplitude of current in $\text{ampere}$ a...
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318
GATE2017: 32
In the circuit diagram, shown in the figure, $S_1$ was closed and $S_2$ was open for a very long time. At $t=0,\;S_1$ is opened and $S_2$ is closed. The voltage across the capacitor, in volt, at $t=5\mu s$ is _________.
In the circuit diagram, shown in the figure, $S_1$ was closed and $S_2$ was open for a very long time. At $t=0,\;S_1$ is opened and $S_2$ is closed. The voltage across th...
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319
GATE2017: 33
Consider two discrete-time signals: $x_1(n)$={1,1} and $x_2(n)$={1,2} , for $n=0,1$. The Z-transform of the convoluted sequence $x(n)=x_1(n)^*x_2(n)$ is $1+2z^{-1}+3z^{-2}$ $z^2+3z+2$ $1+3z^{-1}+2z^{-2}$ $z^{-2}+3z^{-3}+2z^{-4}$
Consider two discrete-time signals:$x_1(n)$={1,1} and $x_2(n)$={1,2} , for $n=0,1$.The Z-transform of the convoluted sequence $x(n)=x_1(n)^*x_2(n)$ is$1+2z^{-1}+3z^{-2}$$...
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320
GATE2017: 34
Three $DFT$ coefficients, out of five $DFT$ coefficients of a five-point reall sequence are given as: $X(0)=4$, $X(1)=1-j1$ and $X(3)=2+j2$. The zeroth value of the sequence $x(n), \;x(0)$,is $1$ $2$ $3$ $4$
Three $DFT$ coefficients, out of five $DFT$ coefficients of a five-point reall sequence are given as: $X(0)=4$, $X(1)=1-j1$ and $X(3)=2+j2$. The zeroth value of the seque...
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