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2721

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$ $\mid A_v \mid \approx 10$

Milicevic3306 asked in Analog Circuits Mar 25, 2018

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2722

GATE ECE 2012 | Question: 45
If $V_A-V_B=6\:V$, then $V_C-V_D$ is $-5\:V$ $2\:V$ $3\:V$ $6\:V$

Milicevic3306 asked in Others Mar 25, 2018

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2723

GATE ECE 2012 | Question: 46
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1,6]$ is $21$ $25$ $41$ $46$

Milicevic3306 asked in Calculus Mar 25, 2018

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2724

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 $15\:A+12\:I$ $19\:A+30\:I$ $17\:A+15\:I$ $17\:A+21\:I$

Milicevic3306 asked in Linear Algebra Mar 25, 2018

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2725

GATE ECE 2012 | Question: 48
With $10\:V$ dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: $1\: \Omega$ connected at port B draws a current of $3\:A$ $2.5\: \Omega$ connected at port B draws a current of $2\:A$ With $10\: V$ dc connected at ... $\frac{3}{7}\: A$ $\frac{5}{7}\: A$ $1\: A$ $\frac{9}{7}\: A$

Milicevic3306 asked in Network Solution Methods Mar 25, 2018

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2726

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 $-2$ $2$ $1$ $0$

Milicevic3306 asked in Vector Analysis Mar 25, 2018

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2727

GATE ECE 2012 | Question: 36
A fair coin is tossed till head appears for the first time. The probability that the number of required tosses is odd, is $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$ $\frac{3}{4}$

Milicevic3306 asked in Probability and Statistics Mar 25, 2018

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2728

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 $V_{in}\lt 1.875\:V$ $1.875\:V\lt V_{in}\lt 3.125\:V$ $V_{in}\gt 3.125\:V$ $0\lt V_{in}\lt 5\:V$

Milicevic3306 asked in Electronic Devices Mar 25, 2018

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2729

GATE ECE 2012 | Question: 38
A binary symmetric channel (BSC) has a transition probability of $\frac{1}{8}$. If the binary transmit symbol $X$ is such that $P(X=0)\:=\:\frac{9}{10}$, then the probability of error for an optimum receiver will be $\frac{7}{80}$ $\frac{63}{80}$ $\frac{9}{10}$ $\frac{1}{10}$

Milicevic3306 asked in Probability and Statistics Mar 25, 2018

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2730

GATE ECE 2012 | Question: 39
The signal $m(t)$ as shown is applied both to a phase modulator (with $k_p$ as the phase constant) and a frequency modulator (with $k_f$ as the frequency constant) having the same carrier frequency. The ratio $\frac{k_p}{k_f}$ (in $rad/Hz$) for the same maximum phase deviation is $8\pi$ $4\pi$ $2\pi$ $\pi$

Milicevic3306 asked in Communications Mar 25, 2018

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2731

GATE ECE 2012 | Question: 40
The magnetic field along the propagation direction inside a rectangular waveguide with the cross-section shown in the figure is $H_Z=3\:\cos(2.094\times10^2x)\:\cos(2.618\times10^2y)\:\cos(6.283\times10^{10}t-\beta z)$ The phase velocity $v_p$ of the wave inside the waveguide satisfies $v_p\gt c$ $v_p=c$ $0\lt v_p\lt c$ $v_p=0$

Milicevic3306 asked in Electromagnetics Mar 25, 2018

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2732

GATE ECE 2012 | Question: 41
The circuit shown is a low pass filter with $f_{3\:dB}=\frac{1}{(R_1+R_2)C}\: rad/s$ high pass filter with $f_{3\:dB}=\frac{1}{R_1C}\: rad/s$ low pass filter with $f_{3\:dB}=\frac{1}{R_1C}\: rad/s$ high pass filter with $f_{3\:dB}=\frac{1}{(R_1+R_2)C}\: rad/s$

Milicevic3306 asked in Continuous-time Signals Mar 25, 2018

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2733

GATE ECE 2012 | Question: 27
A BPSK scheme operating over an AWGN channel with noise power spectral density of $\frac{N_o}{2}$, uses equiprobable signals $s_1(t)=\sqrt{\frac{2E}{T}}\sin(\omega_ct)$ and $s_2(t)=-\sqrt{\frac{2E}{T}}\sin(\omega_ct)$ over the symbol interval $(0,T)$. If the local oscillator ... $Q(\sqrt{\frac{E}{N_o}})$ $Q(\sqrt{\frac{E}{2N_o}})$ $Q(\sqrt{\frac{E}{4N_o}})$

Milicevic3306 asked in Communications Mar 25, 2018

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2734

GATE ECE 2012 | Question: 28
A trasmission line with a characteristic impedance of $100\:\Omega$ is used to match a $50\:\Omega$ section to a $200\:\Omega$ section. If the matching is to be done both at $429\:MHz$ and $1\:GHz$, the length of the transmission line can be approximately $82.5\:cm$ $1.05\:m$ $1.58\:m$ $1.75\:m$

Milicevic3306 asked in Electromagnetics Mar 25, 2018

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2735

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

Milicevic3306 asked in Analog Circuits Mar 25, 2018

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2736

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 $a=0.5$

Milicevic3306 asked in Analog Circuits Mar 25, 2018

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2737

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 $\frac{1}{4}$ $\frac{1}{2}$ $1$ $2$

Milicevic3306 asked in Continuous-time Signals Mar 25, 2018

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2738

GATE ECE 2012 | Question: 32
The state variable description of an LTI system is given by ... $a_1\neq 0,a_2=0,a_3\neq 0$ $a_1=0,a_2\neq0,a_3\neq 0$ $a_1=0,a_2\neq0,a_3=0$ $a_1\neq 0,a_2\neq0,a_3=0$

Milicevic3306 asked in Continuous-time Signals Mar 25, 2018

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2739

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 $0.8\:\Omega$ $1.4\:\Omega$ $2\:\Omega$ $2.8\:\Omega$

Milicevic3306 asked in Analog Circuits Mar 25, 2018

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2740

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 $-2$ $-1$ $0$ $1$

Milicevic3306 asked in Differential Equations Mar 25, 2018

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2741

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 $\omega=1\:rad/s$ $\omega=2\:rad/s$ $\omega=3\:rad/s$ $\omega=4\:rad/s$

Milicevic3306 asked in Network Solution Methods Mar 25, 2018

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2742

GATE ECE 2012 | Question: 21
The impedance looking into nodes $1$ and $2$ in the given circuit is $50\:\Omega$ $100\:\Omega$ $5\:k\Omega$ $10.1\:k\Omega$

Milicevic3306 asked in Electromagnetics Mar 25, 2018

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2743

GATE ECE 2012 | Question: 22
In the circuit shown below, the current through the inductor is $\frac{2}{1+j}\:A$ $\frac{-1}{1+j}\:A$ $\frac{1}{1+j}\:A$ $0\:A$

Milicevic3306 asked in Others Mar 25, 2018

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2744

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 $-2$ $-1$ $1$ $2$

Milicevic3306 asked in Vector Analysis Mar 25, 2018

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2745

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 $\frac{3}{4}$ $\frac{9}{16}$ $\frac{1}{4}$ $\frac{2}{3}$

Milicevic3306 asked in Probability and Statistics Mar 25, 2018

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2746

GATE ECE 2012 | Question: 25
If $x=\sqrt{-1}$, then the value of $x^x$ is $e^{\frac{-\pi}{2}}$ $e^{\frac{\pi}{2}}$ $x$ $1$

Milicevic3306 asked in Calculus Mar 25, 2018

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2747

GATE ECE 2012 | Question: 26
The source of a silicon ($n_i=10^{10}\:per\:cm^3$) n-channel MOS transistor has an area of $1\:sq\:\mu m$ and a depth of $1\:\mu m$. If the dopant density in the source is $10^{19}/cm^3$, the number of holes in the source region with the above volume is approximately $10^7$ $100$ $10$ $0$

Milicevic3306 asked in Electronic Devices Mar 25, 2018

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2748

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 $x=t-\frac{1}{2}$ $x=t^2-\frac{1}{2}$ $x=\frac{t^2}{2}$ $x=\frac{t}{2}$

Milicevic3306 asked in Differential Equations Mar 25, 2018

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2749

GATE ECE 2012 | Question: 13
The diodes and capacitors in the circuit shown are ideal. The voltage $v(t)$ across the diode $D1$ is $\cos(\omega t)-1$ $\sin(\omega t)$ $1-\cos(\omega t)$ $1-\sin(\omega t)$

Milicevic3306 asked in Analog Circuits Mar 25, 2018

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2750

GATE ECE 2012 | Question: 14
In the circuit shown $Y=\overline{A} \overline{B}+\bar{C}$ $Y=(A+B)C$ $Y=(\overline{A}+\overline{B})\overline{C}$ $Y=AB+C$

Milicevic3306 asked in Others Mar 25, 2018

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2751

GATE ECE 2012 | Question: 15
A source alphabet consists of $N$ symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by a small amount $\varepsilon$ and decreases that of the second by $\varepsilon$. After encoding, the entropy of the source increases remains the same increases only if $N=2$ decreases

Milicevic3306 asked in Probability and Statistics Mar 25, 2018

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2752

GATE ECE 2012 | Question: 16
A coaxial cable with an inner diameter of $1\:mm$ and outer diameter of $2.4\:mm$ is filled with a dielectric of relative permittivity $10.89$. Given $\mu_0=4\pi\times10^{-7}\:H/m$, $\varepsilon_0=\frac{10^{-9}}{36\pi}\:F/m$, the characteristic impedance of the cable is $330\:\Omega$ $100\:\Omega$ $143.3\:\Omega$ $43.4\:\Omega$

Milicevic3306 asked in Electromagnetics Mar 25, 2018

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2753

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 $10\:dB$ $12.6\:dB$ $11.5\:dB$ $18\:dB$

Milicevic3306 asked in Electromagnetics Mar 25, 2018

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2754

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 $\frac{1}{3}\lt |z|\lt 3$ $\frac{1}{3}\lt |z|\lt \frac{1}{2}$ $\frac{1}{2}\lt |z|\lt 3$ $\frac{1}{3}\lt |z|$

Milicevic3306 asked in Numerical Methods Mar 25, 2018

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2755

GATE ECE 2012 | Question: 19
In the sum of products function $f(X,Y,Z)=\sum(2,3,4,5)$, the prime implicants are $\overline{X}Y,X\overline{Y}$ $\overline{X}Y,X\overline{Y}\overline{Z},X\overline{Y}Z$ $\overline{X}Y\overline{Z},\overline{X}YZ,X\overline{Y}$ $\overline{X}Y\overline{Z},\overline{X}YZ,X\overline{Y}\overline{Z},X\overline{Y}Z$

Milicevic3306 asked in Digital Circuits Mar 25, 2018

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2756

GATE ECE 2012 | Question: 5
The electric field of a uniform plane electromagnetic wave in free space, along the positive $x$ direction, is given by $\overrightarrow{E}=10(\hat{a}_y+j\hat{a}_z)e^{-j\:25x}$. The frequency and polarization of the wave, respectively, are $1.2\:GHz$ and left circular $4\:Hz$ and left circular $1.2\:GHz$ and right circular $4\:Hz$ and right circular

Milicevic3306 asked in Electromagnetics Mar 25, 2018

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2757

GATE ECE 2012 | Question: 6
Consider the given circuit. In the circuit, the race around does not occur occurs when $\text{CLK}=0$ occurs when $\text{CLK}=1$ and $A=B=1$ occurs when $\text{CLK}=1$ and $A=B=0$

Milicevic3306 asked in Number Representations Mar 25, 2018

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2758

GATE ECE 2012 | Question: 7
The output $Y$ of a $2-\text{bit}$ comparator is logic $1$ whenever the $2-\text{bit}$ input $A$ is greater than the $2-\text{bit}$ input $B$. The number of combinations for which the output is logic $1$, is $4$ $6$ $8$ $10$

Milicevic3306 asked in Digital Circuits Mar 25, 2018

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2759

GATE ECE 2012 | Question: 8
The $i-v$ characteristics of the diode in the circuit given below are $i = \begin{cases} \frac{v-0.07}{500}\:A, & v\ge0.7\:V \\ \:\:\:\:\:\:\:\:0\:A, & v \lt 0.7\:V \end{cases}$ The current in the circuit is $10\:mA$ $9.3\:mA$ $6.67\:mA$ $6.2\:mA$

Milicevic3306 asked in Electronic Devices Mar 25, 2018

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2760

GATE ECE 2012 | Question: 9
In the following figure, $C_1$ and $C_2$ are ideal capacitors. $C_1$ has been charged to $12\:V$ before the ideal switch $S$ is closed at $t=0$. The current $i(t)$ for all $t$ is zero a step function an exponentially decaying function an impulse function

Milicevic3306 asked in Electronic Devices Mar 25, 2018

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