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GATE ECE 2016 Set 2 | GA Question: 1
Based on the given statements, select the appropriate option with respect to grammar and usage. Statements The height of Mr. $X$ is $6$ feet. The height of Mr. $Y$ is $5$ feet. Mr. $X$ is longer than Mr. $Y$. Mr. $X$ is more elongated than Mr. $Y$. Mr. $X$ is taller than Mr. $Y$. Mr. $X$ is lengthier than Mr. $Y$.

Milicevic3306 asked in Verbal Aptitude Mar 28, 2018

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GATE ECE 2016 Set 2 | GA Question: 2
The students ___________ the teacher on the teachers’ day for twenty years of dedicated teaching. facilitated felicitated fantasized facillitated

Milicevic3306 asked in Verbal Aptitude Mar 28, 2018

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GATE ECE 2016 Set 2 | GA Question: 3
After India’s cricket world cup victory in $1985$, Shrotria who was playing both tennis and cricket till then, decided to concentrate only on cricket. And the $\underline{\text{rest is history}}$. What does the underlined phrase mean in this context? history will rest in peace rest is recorded in history books rest is well known rest is archaic

Milicevic3306 asked in Verbal Aptitude Mar 28, 2018

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GATE ECE 2016 Set 2 | GA Question: 4
Given ($9$ inches)$^{1/2}=(0.25$ yards)$^{1/2}$, which one of the following statements is $TRUE$? $3$ inches $= 0.5$ yards $9$ inches $= 1.5$ yards $9$ inches $= 0.25$ yards $81$ inches $= 0.0625$ yards

Milicevic3306 asked in Analytical Aptitude Mar 28, 2018

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GATE ECE 2016 Set 2 | GA Question: 5
$S$, $M$, $E$ and $F$ are working in the shifts in a team to finish a project. $M$ works with twice the efficiency of others but for half as many days as $E$ worked. $S$ amd $M$ have $6$ hour shifts in a day, whereas $E$ and $F$ have $12$ hours shifts. What is the ratio of contribution of $M$ to contribute of $E$ in the project? $1:1$ $1:2$ $1:4$ $2:1$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

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GATE ECE 2016 Set 2 | GA Question: 6
The Venn diagram shows the preference of the students population for leisure activities. From the data given, the number of students who like to read books or play sports is _____. $44$ $51$ $79$ $108$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

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GATE ECE 2016 Set 2 | GA Question: 7
Social science disciplines were existence in an amorphous form until the colonial period when they were institutionalized. In varying degrees, they were intended to further the colonial interest. In the time of globalization and the economic rise ... science disciplines must maintain disciplinary boundaries ii only i and iii only ii and iv only iii and iv only

Milicevic3306 asked in Verbal Aptitude Mar 28, 2018

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GATE ECE 2016 Set 2 | GA Question: 8
Two and a quarter hours back, when seen in a mirror, the reflection of a wall clock without umber markings seemed to show $1.30$. What is the actual current time shown by the clock? $8.15$ $11.15$ $12.15$ $12.45$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

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GATE ECE 2016 Set 2 | GA Question: 9
$M$ and $N$ start from the same location. $M$ travels $10$ km east ad then $10$ km North-East. $N$ travels $5$ km South and then $4$ km South-East. What is the shortest distance (in km) between $M$ and $N$ at the end of their travel? $18.60$ $22.50$ $20.61$ $25.00$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

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GATE ECE 2016 Set 2 | GA Question: 10
A wire of length $340$ mm is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of $1:2$. What is the length of the square (in mm) such that the combined area of the square and the rectagle is a $\textbf{MINIMUM?}$ $30$ $40$ $120$ $180$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

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11

GATE ECE 2016 Set 2 | Question: 1
The value of $x$ for which the matrix $A= \begin{bmatrix} 3& 2 &4 \\ 9& 7 & 13\\ -6&-4 &-9+x \end{bmatrix}$ has zero as an eigenvalue is ________

Milicevic3306 asked in Linear Algebra Mar 28, 2018

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GATE ECE 2016 Set 2 | Question: 2
Consider the complex valued function $f(z)=2z^{3}+b\mid z \mid^{3}$ where $z$ is a complex variable. The value of $b$ for which function $f(z)$ is analytic is _________

Milicevic3306 asked in Complex Analysis Mar 28, 2018

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13

GATE ECE 2016 Set 2 | Question: 3
As $x$ varies from $-1$ to $+3$, which one of the following describes the behaviour of the function $f(x)=x^{3}-3x^{2}+1?$ $f(x)$ increases monotonically. $f(x)$ increases, then decreases and increases again. $f(x)$ decreases, then increases and decreases again. $f(x)$ increases and then decreases.

Milicevic3306 asked in Calculus Mar 28, 2018

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14

GATE ECE 2016 Set 2 | Question: 4
How many distinct value of $x$ satisfy the equation $\sin(x)=x/2$, where $x$ is in radians? $1$ $2$ $3$ $4$ or more

Milicevic3306 asked in Calculus Mar 28, 2018

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15

GATE ECE 2016 Set 2 | Question: 5
Consider the time-varying vector $\textbf{I}=\hat{x}15\cos(\omega t)+\hat{y}5\sin(\omega t)$ in Cartesian coordinates, where $\omega> 0$ is a constant. When the vector magnitude $\mid \textbf{I} \mid$ is at its minimum value, the angle $\theta$ that $\textbf{I}$ makes with the $x$ axis (in degrees, such that $ 0\leq \theta \leq 180)$ ________

Milicevic3306 asked in Vector Analysis Mar 28, 2018

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16

GATE ECE 2016 Set 2 | Question: 6
In the circuit shown below, $V_{s}$ is a constant voltage source and $I_{L}$ is a constant current load. The value of $I_{L}$ that maximizes the power absorbed by the constant current load is $\frac{V_{S}}{4R} \\$ $\frac{V_{S}}{2R} \\$ $\frac{V_{S}}{R} \\$ $\infty$

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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GATE ECE 2016 Set 2 | Question: 7
The switch has been in position $1$ for a long time and abruptly changes to position $2$ at $t = 0$. If time $t$ is in seconds, the capacitor voltage $V_{C}$ (in volts) for $t > 0$ is given by $4\left ( 1- \text{ exp }\left ( -t/0.5 \right ) \right )$ ... $4\left ( 1-\text{ exp }\left ( -t/0.6 \right ) \right )$ $10 -6 \text{ exp }\left ( -t/0.6 \right )$

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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18

GATE ECE 2016 Set 2 | Question: 8
The figure shown an $RLC$ circuit with a sinusoidal current source. At resonance, the ratio $\mid I_{L} \mid / \mid I_{R} \mid$, i.e., the ratio of the magnitudes of the inductor current phasor and the resistor current phasor, is ________

Milicevic3306 asked in Network Solution Methods Mar 28, 2018

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19

GATE ECE 2016 Set 2 | Question: 9
The $z$-parameter matrix for the two-port network shown is $\begin{bmatrix} 2j\omega &j\omega \\ j\omega & 3+2j\omega \end{bmatrix},$ where the entries are in $\Omega$. Suppose $Z_{b}\left ( j\omega \right )=R_{b}+j\omega .$ Then the value of $R_{b}$ (in $\Omega$) equals ________

Milicevic3306 asked in Control Systems Mar 28, 2018

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20

GATE ECE 2016 Set 2 | Question: 10
The energy of the signal $x(t)= \frac{\sin(4\pi t)}{4\pi t}$ is ________

Milicevic3306 asked in Continuous-time Signals Mar 28, 2018

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21

GATE ECE 2016 Set 2 | Question: 11
The Ebers-Moll model of a $BJT$ is valid only in active mode only in active and saturation modes only in active and cut-off modes in active, saturation and cut-off modes

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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22

GATE ECE 2016 Set 2 | Question: 12
A long-channel $NMOS$ transistor is biased in the linear region with $V_{DS}=50$ $m$ $V$ and is used as a resistance. Which one of the following statement is $NOT$ correct? If the device width $W$ is increased, the resistance ... decreases. If the device length $L$ is increased, the resistance increases. If $V_{GS}$ is incresed, the resistance increases.

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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23

GATE ECE 2016 Set 2 | Question: 13
Assume that the diode in the figure has $V_{on}=0.7 \:V$, but it otherwise ideal. The magnitude of the current $i_{2}$ in mA) is equal to _________

Milicevic3306 asked in Electronic Devices Mar 28, 2018

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24

GATE ECE 2016 Set 2 | Question: 14
Resistor $R_{1}$ in the circuit below has been adjusted so that $I_{1}=1$ $mA$. The bipolar transistors $Q1$ and $Q2$ are perfectly matched and have very high current gain, so their base currents are negligible. The supply voltage $V_{cc}$ is $6$ $V$. The thermal ... $KT/q$ is $26$ $mV$. The value of $R_{2}$ (in $\Omega)$ for which $I_{2}=100\mu A$ is _________

Milicevic3306 asked in Electronic Devices Mar 28, 2018

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25

GATE ECE 2016 Set 2 | Question: 15
Which one of the following statements is correct about an ac-coupled common-emitter amplifier operating in the mid-band region? The device parasitic capacitances behave like open circuits, whereas coupling and bypass capacitances ... The device parasitic capacitances behave like short circuits, whereas coupling and bypass capacitances behave like open circuits.

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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26

GATE ECE 2016 Set 2 | Question: 16
Transistor geometries in a $CMOS$ inverter have been adjusted to meet the requirement for worst case charge and discharge times for driving a load capacitor $C$. This design is to be converted to that of a $NOR$ circuit in the same ... should not be changed. Widths of $PMOS$ transistors should be unchanged, while widths of $NMOS$ transistors should be halved.

Milicevic3306 asked in Electronic Devices Mar 28, 2018

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27

GATE ECE 2016 Set 2 | Question: 17
Assume that all the digital gates in the circuit shown in the figure are ideal, the resistor $R=10\Omega$ and the supply voltage is $5\:V$. The $D$ flip-flops $D_{1} \:, D_{2} \:, D_{3} \:, D_{4}$ and $D_{5}$ are initialized with ... $0$, respectively. The clocks has a $30\%$ duty cycle. The average power dissipated (in $mW$) in the resistor $R$ is _________

Milicevic3306 asked in Number Representations Mar 28, 2018

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28

GATE ECE 2016 Set 2 | Question: 18
A $4:1$ multiplexer is to be used for generating the output carry of a full adder. $A$ and $B$ are the bits to be added while $C_{in}$ is the input carry and $C_{out}$ is the output carry. $A$ and $B$ are to be used as the select bits with $A$ being the more significant select ... $I_{3}=C_{in}$ $I_{0}=0, I_{1}=C_{in},I_{2}=1$ and $I_{3}=C_{in}$

Milicevic3306 asked in Number Representations Mar 28, 2018

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29

GATE ECE 2016 Set 2 | Question: 19
The response of the system $G(s)=\frac{s-2}{(s+1)(s+3)}$ to the unit step input $u(t)$ is $y(t)$. The value of $\frac{dy}{dt}$ at $t=0^{+}$ is _________

Milicevic3306 asked in Differential Equations Mar 28, 2018

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30

GATE ECE 2016 Set 2 | Question: 20
The number and direction of encirclements around the point $-1+j0$ in the complex plane by the Nyquist plot of $G(s)=\frac{1-s}{4+2s}$ is zero. one,anti-clockwise. one, clockwise. two, clockwise.

Milicevic3306 asked in Control Systems Mar 28, 2018

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31

GATE ECE 2016 Set 2 | Question: 21
A discrete memoryless source has an alphabet $\left \{ a_{1},a_{2}, a_{3},a_{4}\right \}$ with corresponding probabilities $\left \{ \frac{1}{2}, \frac{1}{4},\frac{1}{8},\frac{1}{8}\right \}.$ The minimum required average codeword length in bits to represent this source for error-free reconstruction is _________

Milicevic3306 asked in Probability and Statistics Mar 28, 2018

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32

GATE ECE 2016 Set 2 | Question: 22
A speech signal is sampled at $8$ $kHz$ and encoded into $PCM$ format using $8$ bits/sample. The $PCM$ data is transmitted through a baseband channel via $4$-level $PAM$. The minimum bandwidth (in $kHz$) required for transmission is _________

Milicevic3306 asked in Communications Mar 28, 2018

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33

GATE ECE 2016 Set 2 | Question: 23
A uniform and constant magnetic field $\textbf{B}=\hat{z}B$ exists in the $\hat{z}$ direction in vacuum. A particle of mass $m$ with a small charge $q$ ... . Circular motion in the $xy$ plane. Linear motion in the $\hat{z}$ direction. Linear motion in the $\hat{x}$ direction.

Milicevic3306 asked in Electromagnetics Mar 28, 2018

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34

GATE ECE 2016 Set 2 | Question: 24
Let the electric field vector of a plane electromagnetic wave propagating in a homogeneous medium be expressed as $\textbf{E}=\hat{x}E_{x}e^{-j(\omega t-\beta z)},$ where the propogation constant $\beta$ ... of the wave. The group velocity of the wave. The phase velocity of the wave. The power flux through the $z=0$ plane.

Milicevic3306 asked in Electromagnetics Mar 28, 2018

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35

GATE ECE 2016 Set 2 | Question: 25
Light from free space is incident at an angle $\theta _{i}$ to the normal of the facet of a step-index large core optical fibre. The core and cladding refractive indices are $n _{1}=1.5$ and $n _{2}=1.4$, respectively. The maximum value of $\theta _{i}$ (in degrees) for which the incident light will be guided in the core of the fibre is _________

Milicevic3306 asked in Electromagnetics Mar 28, 2018

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GATE ECE 2016 Set 2 | Question: 26
The ordinary differential equation $\frac{dx}{dt}=-3x+2, \text{ with }x(0) = 1$ is to be solved using the forward Euler method. The largest time step that can be used to solve the equation without making the numerical solution unstable is _________

Milicevic3306 asked in Differential Equations Mar 28, 2018

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37

GATE ECE 2016 Set 2 | Question: 27
Suppose $C$ is the closed curve defined as the circle $x^{2}+y^{2}=1$ with $C$ oreinted anti-clockwise. The value of $\oint$ ( $xy^{2}$ $dx$ + $ x^{2}y$ $dy$ )over the curve $C$ equals _________

Milicevic3306 asked in Complex Analysis Mar 28, 2018

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38

GATE ECE 2016 Set 2 | Question: 28
Two random variables $X$ and $Y$ are distributed according to $f_{X,Y}(x,y)=\begin{cases} (x+y),& 0\leq x\leq 1,&0\leq y\leq 1\\ 0, & \text{otherwise.} \end{cases}$ The probability $P(X+Y\leq 1)$ is ________

Milicevic3306 asked in Probability and Statistics Mar 28, 2018

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GATE ECE 2016 Set 2 | Question: 29
The matrix $A=\begin{bmatrix} a & 0 &3 &7 \\ 2& 5&1 &3 \\ 0& 0& 2 &4 \\ 0&0 & 0 &b \end{bmatrix}$ has $\text{det}(A) = 100$ and $\text{trace}(A) = 14$. The value of $\mid a-b \mid$ is ________

Milicevic3306 asked in Linear Algebra Mar 28, 2018

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40

GATE ECE 2016 Set 2 | Question: 33
The Discrete Fourier Transform (DFT) of the $4$-point sequence $x\left [ n \right ]=\left \{ x\left [ 0 \right ],x\left [ 1 \right ], x\left [ 2 \right ], x\left [ 3 \right ] \right \}= \left \{ 3,2,3,4 \right \}$ ... $\left | \frac{X_{1}\left [ 8 \right ]}{X_{1}\left [ 11 \right ]} \right |$ is _________

Milicevic3306 asked in Continuous-time Signals Mar 28, 2018

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