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GATE ECE 2013 | Question: 62
Find the sum to $n$ terms of the series $10+84+ 734 +\dots $ $\frac{9(9^n+1)}{10}+1$ $\frac{9(9^n-1)}{8}+1$ $\frac{9(9^n-1)}{8}+n$ $\frac{9(9^n-1)}{8}+n^2$

Milicevic3306 asked in Quantitative Aptitude Mar 26, 2018

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GATE ECE 2013 | Question: 65
What is the chance that a leap year, selected at random, will contain $53$ Saturdays? $2/7$ $3/7$ $1/7$ $5/7$

Milicevic3306 asked in Quantitative Aptitude Mar 26, 2018

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GATE ECE 2013 | Question: 64
The set of values of $p$ for which the roots of the equation $3x^2+2x+p(p-1)=0$ are of opposite sign is $(-\infty ,0)$ $(0,1)$ $(1,\infty )$ $(0,\infty )$

Milicevic3306 asked in Quantitative Aptitude Mar 26, 2018

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GATE ECE 2013 | Question: 63
Statement: There were different streams of freedom movements in colonial India carried out by the moderates, liberals, radicals, socialists, and so on. Which one of the following is the best inference from the above statement? The ... Nationalism in India emerged in the context of colonialism. Nationalism in India is homogeneous. Nationalism in India is heterogeneous.

Milicevic3306 asked in Verbal Aptitude Mar 26, 2018

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GATE ECE 2013 | Question: 61
A car travels $8 \: km$ in the first quarter of an hour, $6\: km$ in the second quarter and $16\: km$ in the third quarter. The average speed of the car in $km$ per hour over the entire journey is $30$ $36$ $40$ $24$

Milicevic3306 asked in Quantitative Aptitude Mar 26, 2018

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GATE ECE 2013 | Question: 60
They were requested not to $\textbf{quarrel}$ with others. Which one of the following options is the closest in meaning to the word $\textbf{quarrel}$? make out call out dig out fall out

Milicevic3306 asked in Verbal Aptitude Mar 26, 2018

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GATE ECE 2013 | Question: 55
The state diagram of a system is shown below. A system is described by the state-variable equations $\dot{X}= AX+Bu;\:\: y = CX+Du$ The state transition matrix $e^{At}$ ... $\begin{bmatrix} e^{-t}&-te^{-t} \\ 0 &e^{-t} \end{bmatrix}$

Milicevic3306 asked in Others Mar 26, 2018

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GATE ECE 2013 | Question: 59
Complete the sentence: Dare _______________ mistakes. commit to commit committed committing

Milicevic3306 asked in Verbal Aptitude Mar 26, 2018

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GATE ECE 2013 | Question: 58
In the summer of $2012,$ in New Delhi, the mean temperature of Monday to Wednesday was $41^{\circ}C$ and of Tuesday to Thursday was $43^{\circ}C$. If the temperature on Thursday was $15\%$ higher than that of Monday, then the temperature in $^{\circ}C$ on Thursday was $40$ $43$ $46$ $49$

Milicevic3306 asked in Quantitative Aptitude Mar 26, 2018

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GATE ECE 2013 | Question: 57
Statement: You can always give me a ring whenever you need. Which one of the following is the best inference from the above statement? Because I have a nice caller tune. Because I have a better telephone facility. Because a friend in need is a friend indeed. Because you need not pay towards the telephone bills when you give me a ring.

Milicevic3306 asked in Verbal Aptitude Mar 26, 2018

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GATE ECE 2013 | Question: 56
Choose the grammatically CORRECT sentence: Two and two add four. Two and two become four. Two and two are four. Two and two make four.

Milicevic3306 asked in Verbal Aptitude Mar 26, 2018

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GATE ECE 2013 | Question: 54
The state diagram of a system is shown below. A system is described by the state-variable equations $\dot{X}= AX+Bu;\:\: y = CX+Du$ ...

Milicevic3306 asked in Continuous-time Signals Mar 26, 2018

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GATE ECE 2013 | Question: 49
Bits $1$ and $0$ are transmitted with equal probability. At the receiver, the pdf of the respective received signals for both bits are as shown below. The optimum threshold to achieve minimum bit error rate $(BER)$ is $\frac{1}{2} \\$ $\frac{4}{5} \\$ $1\\$ $\frac{3}{2} $

Milicevic3306 asked in Communications Mar 26, 2018

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GATE ECE 2013 | Question: 50
Consider the following figure The current $I_{S}$ in $\text{Amps}$ in the voltage source, and voltage $V_{S}$ in Volts across the current source respectively, are $13, − 20$ $8, − 10$ $− 8, 20$ $− 13, 20$

Milicevic3306 asked in Electronic Devices Mar 26, 2018

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GATE ECE 2013 | Question: 51
Consider the following figure The current in the $1\Omega$ resistor in $\text{Amps}$ is $2$ $3.33$ $10$ $12$

Milicevic3306 asked in Electronic Devices Mar 26, 2018

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GATE ECE 2013 | Question: 52
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...

Milicevic3306 asked in Vector Analysis Mar 26, 2018

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GATE ECE 2013 | Question: 53
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...

Milicevic3306 asked in Vector Analysis Mar 26, 2018

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GATE ECE 2013 | Question: 45
There are four chips each of $1024\:\text{bytes}$ connected to a $16\:\text{bit}$ address bus as shown in the figure below. $RAMs\: 1, 2, 3$ and $4$ ... $0500H-08FFH, 1500H-18FFH, 3500H-38FFH, 5500H-58FFH$ $0800H-0BFFH, 1800H-1BFFH, 2800H-2BFFH, 3800H-3BFFH$

Milicevic3306 asked in Digital Circuits Mar 26, 2018

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GATE ECE 2013 | Question: 48
Bits $1$ and $0$ are transmitted with equal probability. At the receiver, the pdf of the respective received signals for both bits are as shown below. If the detection threshold is $1,$ the $BER$ will be $\frac{1}{2} \\ $ $\frac{1}{4} \\$ $\frac{1}{8} \\$ $\frac{1}{16}$

Milicevic3306 asked in Communications Mar 26, 2018

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GATE ECE 2013 | Question: 47
Let $U$ and $V$ be two independent and identically distributed random variables such that $P(U=+1)=P(U=-1) = \dfrac{1}{2}.$ The entropy $H(U + V)$ in bits is $\frac{3}{4} \\$ $1$ $\frac{3}{2} \\$ $\log_{2}3$

Milicevic3306 asked in Communications Mar 26, 2018

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GATE ECE 2013 | Question: 43
A voltage $1000 \sin\omega t\:\: \text{Volts}$ is applied across $YZ.$ Assuming ideal diodes, the voltage measured across $WX$ in $\text{Volts},$ is $\sin \omega t$ $(\sin \omega t \:+ \mid \sin \omega t \mid)/2$ $(\sin \omega t \: - \mid \sin \omega t \mid)/2$ $0$ for all $t$

Milicevic3306 asked in Analog Circuits Mar 26, 2018

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GATE ECE 2013 | Question: 42
In the circuit shown below, $Q_{1}$ has negligible collector-to-emitter saturation voltage and the diode drops negligible voltage across it under forward bias. If $V_{cc}$ is $+5 V, X$ and $Y$ are digital signals with $0\: V$ as logic $0$ and $V_{cc}$ as logic $1,$ then the Boolean expression for $Z$ is $XY$ $\overline{X}Y$ $X\overline{Y}$ $\overline{XY}$

Milicevic3306 asked in Analog Circuits Mar 26, 2018

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23

GATE ECE 2013 | Question: 44
Three capacitors $C_{1}, C_{2}$ and $C_{3}$ whose values are $10\mu F, 5\mu F,$ and $2\mu F$ respectively, have breakdown voltages of $10V, 5V,$ and $2V$ respectively. For the interconnection shown below, the maximum safe voltage in Volts that can be ... capacitance across the terminals are respectively, $2.8$ and $36$ $7$ and $119$ $2.8$ and $32$ $7$ and $80$

Milicevic3306 asked in Electronic Devices Mar 26, 2018

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GATE ECE 2013 | Question: 46
In the circuit shown below, the silicon $npn$ transistor $Q$ has a very high value of $\beta.$ The required value of $R_{2}$ in $k\Omega$ to produce $I_{C} = 1\: mA$ is $20$ $30$ $40$ $50$

Milicevic3306 asked in Electronic Devices Mar 26, 2018

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25

GATE ECE 2013 | Question: 38
Consider two identically distributed zero-mean random variables $U$ and $V.$ Let the cumulative distribution functions of $U$ and $2V$ be $F(x)$ and $G(x)$ respectively. Then, for all values of $x$ $F(x) - G(x) \leq 0$ $F(x) - G(x) \geq 0$ $(F(x) - G(x)) \cdot x\leq 0$ $(F(x) - G(x)) \cdot x\geq 0$

Milicevic3306 asked in Probability and Statistics Mar 26, 2018

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26

GATE ECE 2013 | Question: 36
A system is described by the differential equation $\dfrac{\mathrm{d}^{2} y}{\mathrm{d} x} + 5\dfrac{\mathrm{d}y }{\mathrm{d} x} + 6y(t) = x(t).$ Let $x(t)$ be a rectangular pulse given by $x(t) = \begin{cases} 1&0<t<2 \\ 0&\text{otherwise} \end{cases}$ ... $\frac{e^{-2s}}{(s+2)(s+3)} \\$ $\frac{1-e^{-2s}}{s(s+2)(s+3)} $

Milicevic3306 asked in Differential Equations Mar 26, 2018

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27

GATE ECE 2013 | Question: 40
The signal flow graph for a system is given below. The transfer function $\dfrac{Y(s)}{U(s)}$ for this system is $\frac{s+1}{5s^{2}+6s+2} \\$ $\frac{s+1}{s^{2}+6s+2} \\$ $\frac{s+1}{s^{2}+4s+2} \\$ $\frac{1}{5s^{2}+6s+2}$

Milicevic3306 asked in Control Systems Mar 26, 2018

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GATE ECE 2013 | Question: 37
A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by $y(t)$ for $t>0,$ when the forcing function is $x(t)$ and the initial condition is $y(0).$ If one wishes to modify the ... forcing function to $j\sqrt{2}x(t)$ change the initial condition to $−2y(0)$ and the forcing function to $−2x(t)$

Milicevic3306 asked in Differential Equations Mar 26, 2018

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GATE ECE 2013 | Question: 41
In the circuit shown below the $\text{op-amps}$ are ideal. Then $V_{\text{out}}$ in $\text{Volts}$ is $4$ $6$ $8$ $10$

Milicevic3306 asked in Analog Circuits Mar 26, 2018

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GATE ECE 2013 | Question: 35
The ac schematic of an $NMOS$ common-source stage is shown in the figure below, where part of the biasing circuits has been omitted for simplicity. For the $n$-channel $MOSFET\: M,$ the transconductance $g_{m} = 1\; mA/V,$ and body effect and ... effect are to be neglected. The lower cutoff frequency in $Hz$ of the circuit is approximately at $8$ $32$ $50$ $200$

Milicevic3306 asked in Electronic Devices Mar 26, 2018

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GATE ECE 2013 | Question: 39
The $\text{DFT}$ of a vector $\begin{bmatrix} a & b & c & d \end{bmatrix}$ is the vector $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}.$ ... $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}$

Milicevic3306 asked in Vector Analysis Mar 26, 2018

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32

GATE ECE 2013 | Question: 29
The open-loop transfer function of a dc motor is given as $\dfrac{\omega(s)}{V_{a}(s)} = \dfrac{10}{1+10s}.$ When connected in feedback as shown below, the approximate value of $K_{a}$ that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is $1$ $5$ $10$ $100$

Milicevic3306 asked in Network Solution Methods Mar 26, 2018

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33

GATE ECE 2013 | Question: 34
The small-signal resistance $(i.e., dV_{B}/dI_{D})$ in $k\Omega$ offered by the $n$-channel $MOSFET\: M$ shown in the figure below, at a bias point of $V_{B} = 2\: V$ is (device data for $M:$ ... $V_{TN} = 1\: V,$ and neglect body effect and channel length modulation effects) $12.5$ $25$ $50$ $100$

Milicevic3306 asked in Electronic Devices Mar 26, 2018

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34

GATE ECE 2013 | Question: 33
The impulse response of a continuous time system is given by $h(t) = \delta(t-1) + \delta(t-3).$ The value of the step response at $t = 2$ is $0$ $1$ $2$ $3$

Milicevic3306 asked in Continuous-time Signals Mar 26, 2018

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GATE ECE 2013 | Question: 31
The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of $0.8.$ An ac voltage $V_{WX1} = 100V$ is applied across $WX$ to get an open circuit voltage $V_{YZ1}$ across $YZ.$ Next, an ac voltage $V_{YZ2}= 100V$ is ... , $125/100$ and $80/100$ $100/100$ and $80/100$ $100/100$ and $100/100$ $80/100$ and $80/100$

Milicevic3306 asked in Electronic Devices Mar 26, 2018

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36

GATE ECE 2013 | Question: 32
Two magnetically uncoupled inductive coils have $Q$ factors $q_{1}$ and $q_{2}$ at the chosen operating frequency. Their respective resistances are $R_{1}$ and $R_{2}.$ When connected in series, their effective $Q$ factor at the same operating frequency is $q_{1} + q_{2}$ ... $(q_{1}R_{2} + q_{2}R_{1})/(R_{1} + R_{2})$

Milicevic3306 asked in Digital Circuits Mar 26, 2018

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37

GATE ECE 2013 | Question: 30
In the circuit shown below, the knee current of the ideal Zener diode is $10\: mA.$ To maintain $5\: V$ across $R_{L},$ the minimum value of $R_{L}$ in $\Omega$ and the minimum power rating of the Zener diode in $mW,$ respectively, are $125$ and $125$ $125$ and $250$ $250$ and $125$ $250$ and $250$

Milicevic3306 asked in Electronic Devices Mar 26, 2018

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38

GATE ECE 2013 | Question: 26
Let $U$ and $V$ be two independent zero mean Gaussian random variables of variances $\dfrac{1}{4}$ and $\dfrac{1}{9}$ respectively. The probability $P(3V\geq 2U)$ is $4/9$ $1/2$ $2/3$ $5/9$

Milicevic3306 asked in Probability and Statistics Mar 26, 2018

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GATE ECE 2013 | Question: 27
Let $A$ be an $m \times n$ matrix and $B$ an $n \times m$ matrix. It is given that determinant $(I_{m} + AB) =$ determinant $(I_{n} + BA),$ where $I_{k}$ is the $k \times k$ identity matrix. Using the above property, the determinant of the matrix given below ... $2$ $5$ $8$ $16$

Milicevic3306 asked in Linear Algebra Mar 26, 2018

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40

GATE ECE 2013 | Question: 28
In the circuit shown below, if the source voltage $V_S = 100\angle 53.13^{\circ}\: V$ then the Thevenin’s equivalent voltage in Volts as seen by the load resistance $R_{L}$ is $100\angle 90^{\circ}$ $800\angle 0^{\circ}$ $800\angle 90^{\circ}$ $100\angle 60^{\circ}$

Milicevic3306 asked in Network Solution Methods Mar 26, 2018

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