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2882
GATE ECE 2012 | Question: 54
The transfer function of a compensator is given as $G_c(s)=\frac{s+a}{s+b}$ $G_c(s)$ is a lead compensator if $a=1,b=2$ $a=3,b=2$ $a=-3,b=-1$ $a=3,b=1$
The transfer function of a compensator is given as$$G_c(s)=\frac{s+a}{s+b}$$$G_c(s)$ is a lead compensator if$a=1,b=2$$a=3,b=2$$a=-3,b=-1$$a=3,b=1$
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2883
GATE ECE 2012 | Question: 55
The transfer function of a compensator is given as $G_c(s)=\frac{s+a}{s+b}$ The phase of the above lead compensator is maximum at $\sqrt{2}$ rad/s $\sqrt{3}$ rad/s $\sqrt{6}$ rad/s $\frac{1}{\sqrt{3}}$ rad/s
The transfer function of a compensator is given as$$G_c(s)=\frac{s+a}{s+b}$$The phase of the above lead compensator is maximum at$\sqrt{2}$ rad/s$\sqrt{3}$ rad/s$\sqrt{6}...
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2884
GATE ECE 2012 | Question: 42
Let $y[n]$ denote the convolution of $h[n]$ and $g[n]$, where $h[n]=(\frac{1}{2})^nu[n]$ and $g[n]$ is a casual sequence. If $y[0]=1$ and $y[1]=\frac{1}{2}$, then $g[1]$ equals $0$ $\frac{1}{2}$ $1$ $\frac{3}{2}$
Let $y[n]$ denote the convolution of $h[n]$ and $g[n]$, where $h[n]=(\frac{1}{2})^nu[n]$ and $g[n]$ is a casual sequence. If $y[0]=1$ and $y =\frac{1}{2}$, then $g $ equa...
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2885
GATE ECE 2012 | Question: 43
The state transition diagram for the logic circuit shown is
The state transition diagram for the logic circuit shown is
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2886
GATE ECE 2012 | Question: 44
The voltage gain $A_v$ of the circuit shown below is $\mid A_v \mid\approx 200$ $\mid A_v\mid \approx 100$ $ \mid A_v \mid \approx 20$ $\mid A_v \mid \approx 10$
The voltage gain $A_v$ of the circuit shown below is$\mid A_v \mid\approx 200$$\mid A_v\mid \approx 100$$ \mid A_v \mid \approx 20$$\mid A_v \mid \approx 10$
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2887
GATE ECE 2012 | Question: 45
If $V_A-V_B=6\:V$, then $V_C-V_D$ is $-5\:V$ $2\:V$ $3\:V$ $6\:V$
If $V_A-V_B=6\:V$, then $V_C-V_D$ is$-5\:V$$2\:V$$3\:V$$6\:V$
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2888
GATE ECE 2012 | Question: 46
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1,6]$ is $21$ $25$ $41$ $46$
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1,6]$ is$21$$25$$41$$46$
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2889
GATE ECE 2012 | Question: 47
Given that $A=\begin{bmatrix} -5 &-3 \\ 2 &0\end{bmatrix}$ and $I=\begin{bmatrix} 1 & 0 \\ 0 &1\end{bmatrix}$, the value of $A^3$ is $15\:A+12\:I$ $19\:A+30\:I$ $17\:A+15\:I$ $17\:A+21\:I$
Given that$A=\begin{bmatrix} -5 &-3 \\ 2 &0\end{bmatrix}$ and $I=\begin{bmatrix} 1 & 0 \\ 0 &1\end{bmatrix}$, the value of $A^3$ is$15\:A+12\:I$$19\:A+30\:I$$17\:A+15\:I$...
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2891
GATE ECE 2012 | Question: 35
The direction of vector $A$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\triangledown.A=0$ is $-2$ $2$ $1$ $0$
The direction of vector $A$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\triangledown....
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2892
GATE ECE 2012 | Question: 37
In the CMOS circuit shown, electron and hole mobilities are equal, and $M1$ and $M2$ are equally sized. The device $M1$ is in the linear region if $V_{in}\lt 1.875\:V$ $1.875\:V\lt V_{in}\lt 3.125\:V$ $V_{in}\gt 3.125\:V$ $0\lt V_{in}\lt 5\:V$
In the CMOS circuit shown, electron and hole mobilities are equal, and $M1$ and $M2$ are equally sized. The device $M1$ is in the linear region if$V_{in}\lt 1.875\:V$$1.8...
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2899
GATE ECE 2012 | Question: 29
The input $x(t)$ and output $y(t)$ of a system are related as $y(t)=\underset{-\infty}{\int}x(\tau)\cos(3\tau)d\tau$. The system is time-invariant and stable stable and not time-invariant time-invariant and not stable not time-invariant and not stable
The input $x(t)$ and output $y(t)$ of a system are related as $y(t)=\underset{-\infty}{\int}x(\tau)\cos(3\tau)d\tau$. The system istime-invariant and stablestable and not...
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2900
GATE ECE 2012 | Question: 30
The feedback system shown below oscillates at $2\:rad/s$ when $K=2$ and $a=0.75$ $K=3$ and $a=0.75$ $K=4$ and $a=0.5$ $K=2$ and $a=0.5$
The feedback system shown below oscillates at $2\:rad/s$ when$K=2$ and $a=0.75$$K=3$ and $a=0.75$$K=4$ and $a=0.5$$K=2$ and $a=0.5$
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2901
GATE ECE 2012 | Question: 31
The Fourier transform of a signal $h(t)$ is $H(j\omega)=(2\cos\omega)(\sin2\omega)/\omega$. The value of $h(0)$ is $\frac{1}{4}$ $\frac{1}{2}$ $1$ $2$
The Fourier transform of a signal $h(t)$ is $H(j\omega)=(2\cos\omega)(\sin2\omega)/\omega$. The value of $h(0)$ is$\frac{1}{4}$$\frac{1}{2}$$1$$2$
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2902
GATE ECE 2012 | Question: 32
The state variable description of an LTI system is given by ... $a_1\neq 0,a_2=0,a_3\neq 0$ $a_1=0,a_2\neq0,a_3\neq 0$ $a_1=0,a_2\neq0,a_3=0$ $a_1\neq 0,a_2\neq0,a_3=0$
The state variable description of an LTI system is given by$$\begin{pmatrix} \dot{x_1}\\ \dot{x_2}\\ \dot{x_3} \end{pmatrix}=\begin{pmatrix} 0 & a_1 & 0\\ 0 & 0 & a_2\\a_...
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2903
GATE ECE 2012 | Question: 33
Assuming both the voltage sources are in phase, the value of $R$ for which maximum power is transferred from circuit $A$ to circuit $B$ is $0.8\:\Omega$ $1.4\:\Omega$ $2\:\Omega$ $2.8\:\Omega$
Assuming both the voltage sources are in phase, the value of $R$ for which maximum power is transferred from circuit $A$ to circuit $B$ is$0.8\:\Omega$$1.4\:\Omega$$2\:\O...
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2904
GATE ECE 2012 | Question: 34
Consider the differential equation $\frac{d^2y(t)}{dt^2}+2\frac{dy(t)}{dt}+y(t)=\delta(t)$ with $y(t)\big|_{t=0^-}=-2$ and $\frac{dy}{dt}\big|_{t=0^-}=0$. The numerical value of $\frac{dy}{dt}\big|_{t=0^+}$ is $-2$ $-1$ $0$ $1$
Consider the differential equation$\frac{d^2y(t)}{dt^2}+2\frac{dy(t)}{dt}+y(t)=\delta(t)$ with $y(t)\big|_{t=0^-}=-2$ and $\frac{dy}{dt}\big|_{t=0^-}=0$.The numerical val...
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2905
GATE ECE 2012 | Question: 20
A system with transfer function $G(s)=\frac{(s^2+9)(s+2)}{(s+1)(s+3)(s+4)}$ is excited by $\sin(\omega t)$. The steady-state output of the system is zero at $\omega=1\:rad/s$ $\omega=2\:rad/s$ $\omega=3\:rad/s$ $\omega=4\:rad/s$
A system with transfer function$$G(s)=\frac{(s^2+9)(s+2)}{(s+1)(s+3)(s+4)}$$is excited by $\sin(\omega t)$. The steady-state output of the system is zero at$\omega=1\:rad...
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2906
GATE ECE 2012 | Question: 21
The impedance looking into nodes $1$ and $2$ in the given circuit is $50\:\Omega$ $100\:\Omega$ $5\:k\Omega$ $10.1\:k\Omega$
The impedance looking into nodes $1$ and $2$ in the given circuit is$50\:\Omega$$100\:\Omega$$5\:k\Omega$$10.1\:k\Omega$
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2907
GATE ECE 2012 | Question: 22
In the circuit shown below, the current through the inductor is $\frac{2}{1+j}\:A$ $\frac{-1}{1+j}\:A$ $\frac{1}{1+j}\:A$ $0\:A$
In the circuit shown below, the current through the inductor is$\frac{2}{1+j}\:A$$\frac{-1}{1+j}\:A$$\frac{1}{1+j}\:A$$0\:A$
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2908
GATE ECE 2012 | Question: 23
Given $f(z)=\frac{1}{z+1}-\frac{2}{z+3}$. If $C$ is a counterclockwise path in the z-plane such that $\mid z+1 \mid=1$, the value of $\frac{1}{2\pi j}\oint_cf(z)dz$ is $-2$ $-1$ $1$ $2$
Given $f(z)=\frac{1}{z+1}-\frac{2}{z+3}$. If $C$ is a counterclockwise path in the z-plane such that $\mid z+1 \mid=1$, the value of $\frac{1}{2\pi j}\oint_cf(z)dz$ is$-2...
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2909
GATE ECE 2012 | Question: 24
Two independent random variables $X$ and $Y$ are uniformly distributed in the interval $[-1,1]$. The probability that max$[X,Y]$ is less than $\frac{1}{2}$ is $\frac{3}{4}$ $\frac{9}{16}$ $\frac{1}{4}$ $\frac{2}{3}$
Two independent random variables $X$ and $Y$ are uniformly distributed in the interval $[-1,1]$. The probability that max$[X,Y]$ is less than $\frac{1}{2}$ is$\frac{3}{4}...
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2910
GATE ECE 2012 | Question: 25
If $x=\sqrt{-1}$, then the value of $x^x$ is $e^{\frac{-\pi}{2}}$ $e^{\frac{\pi}{2}}$ $x$ $1$
If $x=\sqrt{-1}$, then the value of $x^x$ is$e^{\frac{-\pi}{2}}$$e^{\frac{\pi}{2}}$$x$$1$
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2912
GATE ECE 2012 | Question: 12
With initial condition $x(1)=0.5$, the solution of the differential equation, $t\frac{dx}{dt}+x=t$ is $x=t-\frac{1}{2}$ $x=t^2-\frac{1}{2}$ $x=\frac{t^2}{2}$ $x=\frac{t}{2}$
With initial condition $x(1)=0.5$, the solution of the differential equation,$$t\frac{dx}{dt}+x=t$$ is$x=t-\frac{1}{2}$$x=t^2-\frac{1}{2}$$x=\frac{t^2}{2}$$x=\frac{t}{2}$...
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2913
GATE ECE 2012 | Question: 13
The diodes and capacitors in the circuit shown are ideal. The voltage $v(t)$ across the diode $D1$ is $\cos(\omega t)-1$ $\sin(\omega t)$ $1-\cos(\omega t)$ $1-\sin(\omega t)$
The diodes and capacitors in the circuit shown are ideal. The voltage $v(t)$ across the diode $D1$ is$\cos(\omega t)-1$$\sin(\omega t)$$1-\cos(\omega t)$$1-\sin(\omega t)...
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2914
GATE ECE 2012 | Question: 14
In the circuit shown $Y=\overline{A} \overline{B}+\bar{C}$ $Y=(A+B)C$ $Y=(\overline{A}+\overline{B})\overline{C}$ $Y=AB+C$
In the circuit shown$Y=\overline{A} \overline{B}+\bar{C}$$Y=(A+B)C$$Y=(\overline{A}+\overline{B})\overline{C}$$Y=AB+C$
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2917
GATE ECE 2012 | Question: 17
The radiation pattern of an antenna in spherical co-ordinates is given by $F(\theta)=\cos^4\theta\:\:\:;\:\:\:0\le \theta\le \frac{\pi}{2}$ The directivity of the antenna is $10\:dB$ $12.6\:dB$ $11.5\:dB$ $18\:dB$
The radiation pattern of an antenna in spherical co-ordinates is given by$$F(\theta)=\cos^4\theta\:\:\:;\:\:\:0\le \theta\le \frac{\pi}{2}$$The directivity of the antenna...
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2918
GATE ECE 2012 | Question: 18
If $x[n]=(\frac{1}{3})^{|n|}-(\frac{1}{2})^{|n|}u[n]$, then the region of convergence (ROC) of its Z-transform in the Z-plane will be $\frac{1}{3}\lt |z|\lt 3$ $\frac{1}{3}\lt |z|\lt \frac{1}{2}$ $\frac{1}{2}\lt |z|\lt 3$ $\frac{1}{3}\lt |z|$
If $x[n]=(\frac{1}{3})^{|n|}-(\frac{1}{2})^{|n|}u[n]$, then the region of convergence (ROC) of its Z-transform in the Z-plane will be$\frac{1}{3}\lt |z|\lt 3$$\frac{1}{3}...
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