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GATE ECE 2012 | Question: 65
$A$ and $B$ are friends. They decide to meet between $1:00$pm and $2:00$ pm on a given day. There is a condition that whoever arrives first will not wait for the other for more than $15$ minutes. The probability that they will meet on that day is $1/4$ $1/16$ $7/16$ $9/16$

Milicevic3306 asked in Quantitative Aptitude Mar 25, 2018

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GATE ECE 2012 | Question: 64
The data given in the following table summarizes the monthly budget of an average household. ... $10\%$ $14\%$ $81\%$ $86\%$

Milicevic3306 asked in Quantitative Aptitude Mar 25, 2018

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GATE ECE 2012 | Question: 63
There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number of weighings required to identify the heavier bag is $2$ $3$ $4$ $8$

Milicevic3306 asked in Analytical Aptitude Mar 25, 2018

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GATE ECE 2012 | Question: 62
Raju has $14$ currency notes in his pocket consisting of only Rs. $20$ notes and Rs. $10$ notes. The total money value of the notes is Rs. $230$. The number of Rs. $10$ notes that Raju has is $5$ $6$ $9$ $10$

Milicevic3306 asked in Quantitative Aptitude Mar 25, 2018

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GATE ECE 2012 | Question: 61
One of the legacies of the Roman legions was discipline. In the legions, military law prevailed and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting, even when the odds and conditions were against them. ... seniors. The harsh discipline to which the legions were subjected to led to the odds and conditions being against them.

Milicevic3306 asked in Verbal Aptitude Mar 25, 2018

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GATE ECE 2012 | Question: 60
One of the parts $(A, B, C, D)$ in the sentence given below contains an ERROR. Which one of the following is INCORRECT? I requested that he should be given the driving test today instead of tomorrow. requested that should be given the driving test instead of tomorrow

Milicevic3306 asked in Verbal Aptitude Mar 25, 2018

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GATE ECE 2012 | Question: 59
Which one of the following options is the closest in meaning to the word given below? Latitude Eligibility Freedom Coercion Meticulousness

Milicevic3306 asked in Verbal Aptitude Mar 25, 2018

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GATE ECE 2012 | Question: 57
Choose the most appropriate alternative from the options given below to complete the following sentence: If the tired soldier wanted to lie down, he _______ the mattress out on the balcony. should take shall take should have taken will have taken

Milicevic3306 asked in Verbal Aptitude Mar 25, 2018

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GATE ECE 2012 | Question: 58
Choose the most appropriate word from the options given below to complete the following sentence: Given the seriousness of the situation that he had to face, his ___ was impressive. beggary nomenclature jealousy nonchalance

Milicevic3306 asked in Verbal Aptitude Mar 25, 2018

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GATE ECE 2012 | Question: 56
If $(1.001)^{1259}=3.52$ and $(1.001)^{2062}=7.85,$ then $(1.001)^{3321}=?$ $2.23$ $4.33$ $11.37$ $27.64$

Milicevic3306 asked in Quantitative Aptitude Mar 25, 2018

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GATE ECE 2012 | Question: 53
An infinitely long uniform solid wire of radius $a$ carries a uniform dc current of density $\overrightarrow{j}$. A hole of radius $b$ (b < a) ia now drilled along the length of the wire at a distance $d$ from the center of the wire as shown ... uniform and depends only on $d$ uniform and depends only on $b$ uniform and depends only on both $b$ and $d$ non uniform

Milicevic3306 asked in Electronic Devices Mar 25, 2018

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GATE ECE 2012 | Question: 52
An infinitely long uniform solid wire of radius $a$ carries a uniform dc current of density $\overrightarrow{j}$. The magnetic field at a distance $r$ from the center of the wire is proportional to $r$ for $r\lt a$ and $\frac{1}{r^2}$ for $r\gt a$ $0$ for $r\lt a$ ... $r\lt a$ and $\frac{1}{r}$ for $r\gt a$ $0$ for $r\lt a$ and $\frac{1}{r^2}$ for $r\gt a$

Milicevic3306 asked in Electronic Devices Mar 25, 2018

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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 $a=1,b=2$ $a=3,b=2$ $a=-3,b=-1$ $a=3,b=1$

Milicevic3306 asked in Network Solution Methods Mar 25, 2018

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GATE ECE 2012 | Question: 49
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 $2\:A$ For the same network, with ... $6\:V$ $7\:V$ $8\:V$ $9\:V$

Milicevic3306 asked in Network Solution Methods Mar 25, 2018

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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

Milicevic3306 asked in Network Solution Methods Mar 25, 2018

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GATE ECE 2012 | Question: 50
In the three dimensional view of a silicon n-channel MOS transistor shown below, $\delta=20\:nm$. The transistor is of width $1\: \mu m$. The depletion width formed at every p-n junction is $10\:nm$. The relative permittivities of $Si$ and $SiO_2$, respectively, are ... $0.7\:fF$ $0.7\:pF$ $0.35\:fF$ $0.24\:pF$

Milicevic3306 asked in Analog Circuits Mar 25, 2018

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GATE ECE 2012 | Question: 51
In the three dimensional view of a silicon n-channel MOS transistor shown below, $\delta=20\:nm$. The transistor is of width $1\: \mu m$. The depletion width formed at every p-n junction is $10\:nm$. The relative permittivities of $Si$ and $SiO_2$, respectively, are ... $2\:fF$ $7\:fF$ $2\:pF$ $7\:pF$

Milicevic3306 asked in Analog Circuits Mar 25, 2018

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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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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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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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GATE ECE 2012 | Question: 43
The state transition diagram for the logic circuit shown is

Milicevic3306 asked in Digital Circuits Mar 25, 2018

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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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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 $0$ $\frac{1}{2}$ $1$ $\frac{3}{2}$

Milicevic3306 asked in Continuous-time Signals Mar 25, 2018

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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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25

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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26

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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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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28

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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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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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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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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32

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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33

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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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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35

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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36

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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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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38

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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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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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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