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GATE ECE 2016 Set 3 | GA Question: 1
An apple costs Rs.$10$. An onion costs Rs.$8$. Select the most suitable sentence with respect to grammar and usage. The price of an apple is greater than an onion. The price of an apple is more than onion. The price of an apple is greater than that of an onion. Apples are more costlier than onions.

Milicevic3306 asked in Verbal Aptitude Mar 28, 2018

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GATE ECE 2016 Set 3 | GA Question: 2
The Buddha said, “Holding on to anger is like grasping a hot coal with the intent of throwing it at someone else; you are the one who gets burnt. ” Select the word below which is closest in meaning to the word underlined above. burning igniting clutching flinging

Milicevic3306 asked in Verbal Aptitude Mar 28, 2018

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GATE ECE 2016 Set 3 | GA Question: 3
$M$ has a son $Q$ and a daughter $R.$ He has no other children. $E$ is the mother of $P$ and daughter-in-law of $M.$ How is $P$ related to $M?$ $P$ is the son-in-law of $M$ $P$ is the grandchild of $M$ $P$ is the daughter-in-law of $M$ $P$ is the grandfather of $M$

Milicevic3306 asked in Analytical Aptitude Mar 28, 2018

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GATE ECE 2016 Set 3 | GA Question: 4
The number that least fits this set$:(324,441,97$ and $64)$ is $324$ $441$ $97$ $64$

Milicevic3306 asked in Analytical Aptitude Mar 28, 2018

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GATE ECE 2016 Set 3 | GA Question: 5
It takes $10$s and $15$s, respectively, for two trains traveling at a different constant speeds to completely pass a telegraph post. The length of the first train is $120$ m and that of the second train is $150$ m. The magnitude of the difference in the speeds of the two trains (in m/s) is _________ $2.0$ $10.0$ $12.0$ $22.0$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

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GATE ECE 2016 Set 3 | GA Question: 6
The velocity $V$ of a vehicle along a straight line is measured in m/s and plotted as shown with respect to time in seconds. At the end of the $7$ seconds, how much will the odometer reading increase by (in m)? $0$ $3$ $4$ $5$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

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GATE ECE 2016 Set 3 | GA Question: 7
The overwhelming number of people infected with rabies in India has been flagged by the World Health Organization as a source of concern. It is estimated that inoculating $70\%$ of pets and stray dogs against rabies can lead to a significant ... be eradicated in India by vaccinating $70\%$ of stray dogs. Stray dogs are the main source of rabies worldwide.

Milicevic3306 asked in Analytical Aptitude Mar 28, 2018

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GATE ECE 2016 Set 3 | GA Question: 8
A flat is shared by four first-year undergraduate students. They agreed to allow the oldest of them to enjoy some extra space in the flat. Manu is two months older than Sravan, who is three months younger than Trideep. Pavan is one month older than Sravan. Who should occupy the extra space in the flat? Manu Sravan Trideep Pavan

Milicevic3306 asked in Analytical Aptitude Mar 28, 2018

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GATE ECE 2016 Set 3 | GA Question: 9
Find the area bounded by the lines $3x+2y=14$, $2x-3y=5$ in the first quadrant. $14.95$ $15.25$ $15.70$ $20.35$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

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GATE ECE 2016 Set 3 | GA Question: 10
A straight line is fit to a data set $(\text{ln }x,y).$ This line intercepts the abscissa at $\text{ln } x =0.1$ and has a slope of $-0.02$. What is the value of $y$ at $x=5$ from the fit? $-0.030$ $-0.014$ $0.014$ $0.030$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

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11

GATE ECE 2016 Set 3 | Question: 1
Consider a $2\times2$ sqaure matrix $\textbf{A}= \begin{bmatrix} \sigma &x\\ \omega &\sigma \end{bmatrix},$ where $x$ is unknown. If the eigen values of the matrix $\textbf{A}$ are $(\sigma + j\omega)$ and $(\sigma - j\omega)$, then $x$ is equal to $+j\omega$ $-j\omega$ $+\omega$ $-\omega$

Milicevic3306 asked in Linear Algebra Mar 28, 2018

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12

GATE ECE 2016 Set 3 | Question: 2
For $f(z)= \large\frac{\sin(z)}{z^2}$, the residue of the pole at $z = 0$ is _______

Milicevic3306 asked in Complex Analysis Mar 28, 2018

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13

GATE ECE 2016 Set 3 | Question: 3
The probability of getting a “head” in a single toss of a biased coin is $0.3$. The coin is tossed repeatedly till a head is obtained. If the tosses are independent, then the probability of getting “head” for the first time in the fifth toss is _______

Milicevic3306 asked in Probability and Statistics Mar 28, 2018

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14

GATE ECE 2016 Set 3 | Question: 4
The integral $\int\limits_{0}^{1}\large\frac{dx}{\sqrt{(1-x)}}$ is equal to _______

Milicevic3306 asked in Calculus Mar 28, 2018

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15

GATE ECE 2016 Set 3 | Question: 5
Consider the first order initial value problem $y’= y+2x-x^2 ,\ y(0)=1,\ (0 \leq x < \infty)$ with exact solution $y(x) = x^2 + e^x$. For $x = 0.1$, the percentage difference between the exact solution and the solution obtained using a single iteration of the second-order Runga-Kutta method with step-size $h=0.1$ is _______

Milicevic3306 asked in Numerical Methods Mar 28, 2018

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16

GATE ECE 2016 Set 3 | Question: 6
Consider the signal $x(t) = \cos(6\pi t) + \sin (8\pi t)$, where $t$ is in seconds. The Nyquist sampling rate (in samples/second) for the signal $y(t) = x(2t + 5)$ is $8$ $12$ $16$ $32$

Milicevic3306 asked in Control Systems Mar 28, 2018

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17

GATE ECE 2016 Set 3 | Question: 7
If the signal $x(t) = \large \frac{\sin(t)}{\pi t}$*$\large \frac{\sin(t)}{\pi t}$ with $*$ denoting the convolution operation, then $x(t)$ is equal to $\large\frac{\sin(t)}{\pi t}$ $\large\frac{\sin(2t)}{2\pi t}$ $\large\frac{2\sin(t)}{\pi t}$ $\bigg(\frac{\sin(t)}{\pi t}\bigg)^2$

Milicevic3306 asked in Network Solution Methods Mar 28, 2018

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18

GATE ECE 2016 Set 3 | Question: 8
A discrete-time signal $x[n] = \delta[n – 3] + 2 \delta[n – 5]$ has $z$-transform $X(z)$. If $Y(z) = X(-z)$ is the $z$-transform of another signal $y[n]$, then $y[n] = x[n]$ $y[n] = x[-n]$ $y[n] = -x[n]$ $y[n] = -x[-n]$

Milicevic3306 asked in Continuous-time Signals Mar 28, 2018

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19

GATE ECE 2016 Set 3 | Question: 9
In the RLC circuit shown in the figure, the input voltage is given by $v_i(t) = 2\cos (200t) + 4\sin (500t).$ The output voltage $v_o(t)$ is $\cos (200t) + 2\sin (500t)$ $2\cos (200t) + 4\sin (500t)$ $\sin (200t) + 2\cos (500t)$ $2\sin (200t) + 4\cos (500t)$

Milicevic3306 asked in Network Solution Methods Mar 28, 2018

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20

GATE ECE 2016 Set 3 | Question: 10
The $I-V$ characteristics of three types of diodes at the room temperature, made of semiconductors $X, Y$ and $Z$, are shown in the figure. Assume that the diodes are uniformly doped and identical in all respects except their materials. If $E_{gX}$,$E_{gY}$ ... $E_{gX}=E_{gY}=E_{gZ}$ $E_{gX}<E_{gY}<E_{gZ}$ no relationship among these band gaps exists.

Milicevic3306 asked in Number Representations Mar 28, 2018

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21

GATE ECE 2016 Set 3 | Question: 11
The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of this MOS is in inversion accumulation depletion flat band

Milicevic3306 asked in Electronic Devices Mar 28, 2018

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22

GATE ECE 2016 Set 3 | Question: 12
The figure shows the $I-V$ characteristics of a solar cell illuminated uniformly with solar light of power $100\ mW/cm^2$. The solar cell has an area of $3\ cm^2$ and a fill factor of $0.7$. The maximum efficiency (in $\%$) of the device is _______

Milicevic3306 asked in Electronic Devices Mar 28, 2018

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23

GATE ECE 2016 Set 3 | Question: 13
The diodes $D1$ and $D2$ in the figure are ideal and the capacitors are identical. The product $RC$ is very large compared to the time period of the ac voltage. Assuming that the diodes do not breakdown in the reverse bias, the output voltage $V_o$(in volt) at the steady state is _______

Milicevic3306 asked in Network Solution Methods Mar 28, 2018

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24

GATE ECE 2016 Set 3 | Question: 14
Consider the circuit shown in the figure. Assuming $V_{EE1} = V_{EE2} = 0.7$ volt, the value of the dc voltage $V_{C2}$(in volt) is _______

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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25

GATE ECE 2016 Set 3 | Question: 15
In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the output pin $3$ is _______

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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26

GATE ECE 2016 Set 3 | Question: 16
In an $8085$ microprocessor, the contents of the accumulator and the carry flag are $A7$ (in hex) and $0$, respectively. If the instruction $RLC$ is executed, then the contents of the accumulator (in hex) and the carry flag, respectively, will be $4E$ and $0$ $4E$ and $1$ $4F$ and $0$ $4F$ and $1$

Milicevic3306 asked in Digital Circuits Mar 28, 2018

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27

GATE ECE 2016 Set 3 | Question: 17
The logic functionality realized by the circuit shown below is $OR$ $XOR$ $NAND$ $AND$

Milicevic3306 asked in Number Representations Mar 28, 2018

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28

GATE ECE 2016 Set 3 | Question: 18
The minimum number of $2$-input $NAND$ gates required to implement a $2$-input $XOR$ gate is $4$ $5$ $6$ $7$

Milicevic3306 asked in Digital Circuits Mar 28, 2018

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29

GATE ECE 2016 Set 3 | Question: 19
The block diagram of a feedback control system is shown in the figure. The overall closed-loop gain of $G$ of the system is $G = \large\frac{G_1G_2}{1+G_1H_1} \\$ $G = \large\frac{G_1G_2}{1+G_1G_2+G_1H_1} \\$ $G = \large\frac{G_1G_2}{1+G_1G_2H_1} \\$ $G = \large\frac{G_1G_2}{1+G_1G_2+G_1G_2H_1}$

Milicevic3306 asked in Control Systems Mar 28, 2018

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30

GATE ECE 2016 Set 3 | Question: 20
For the unity feedback control system shown in the figure, the open-loop transfer function $G(s)$ is given as $G(s) = \frac{2}{s(s+1)}$ The steady state error $e_{ss}$ due to a unit step input is $0$ $0.5$ $1.0$ $\infty$

Milicevic3306 asked in Control Systems Mar 28, 2018

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31

GATE ECE 2016 Set 3 | Question: 21
For a superheterodyne receiver, the intermediate frequency is $15\ MHz$ and the local oscillator frequency is $3.5\ GHz$. If the frequency of the received signal is greater than the local oscillator frequency, then the image frequency (in $MHz$) is _______

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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32

GATE ECE 2016 Set 3 | Question: 22
An analog baseband signal, bandlimited to $100\ Hz$, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities $p_1 = p_4 = 0.125$ and $p_2 = p_3$. The information rate (bits/sec) of the message source is _______

Milicevic3306 asked in Control Systems Mar 28, 2018

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33

GATE ECE 2016 Set 3 | Question: 23
A binary baseband digital communication system employs the signal $p(t) = \begin{cases}\large\frac{1}{\sqrt T_s},&0\leq t\leq T_s \\ \: 0, & \text{otherwise} \end{cases}$ for transmission of bits. The graphical representation of the matched filter output $y(t)$ for this signal will be

Milicevic3306 asked in Communications Mar 28, 2018

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34

GATE ECE 2016 Set 3 | Question: 24
If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be right-handed circularly polarized left-handed circularly polarized elliptically polarized with a tilt angle of $45^ \circ$ horizontally polarized

Milicevic3306 asked in Electromagnetics Mar 28, 2018

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35

GATE ECE 2016 Set 3 | Question: 25
Faraday's law of electromagnetic induction is mathematically described by which one of the following equations? $\nabla\ \bullet \overrightarrow{B} = 0$ $\nabla\ \bullet \overrightarrow{D} = \rho_V$ ...

Milicevic3306 asked in Electromagnetics Mar 28, 2018

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36

GATE ECE 2016 Set 3 | Question: 26
The particular solution of the initial value problem given below is $\frac{d^2y}{dx^2}+12\frac{dy}{dx}+36y=0\hspace{0.3cm} \text{ with } \hspace{0.3cm}y(0)=3\hspace{0.3cm} \text{ and }\hspace{0.3cm} \frac{dy}{dx} \bigg| _{x=0} =-36$ $(3-18x)e^{-6x}$ $(3+25x)e^{-6x}$ $(3+20x)e^{-6x}$ $(3-12x)e^{-6x}$

Milicevic3306 asked in Differential Equations Mar 28, 2018

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37

GATE ECE 2016 Set 3 | Question: 27
If the vectors $e_1=(1,0,2)$, $e_2=(0,1,0)$ and $e_3=(-2,0,1)$ form an orthogonal basis of the three-dimensional real space $\mathbb{R}^3$, then the vector $\textbf{u}=(4,3,-3)\in \mathbb{R}^3 $ can be expressed as $\textbf{u}=-$ ... \frac{2}{5}$e_1+3e_2+$\large\frac{11}{5}$e_3 \\$ $\textbf{u}=-$\large\frac{2}{5}$e_1+3e_2-$\large\frac{11}{5}$e_3$

Milicevic3306 asked in Vector Analysis Mar 28, 2018

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38

GATE ECE 2016 Set 3 | Question: 28
A triangle in the $xy$-plane is bounded by the straight lines $2x=3y, \: y=0$ and $x=3$. The volume above the triangle and under the plane $x+y+z=6$ is _______

Milicevic3306 asked in Vector Analysis Mar 28, 2018

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39

GATE ECE 2016 Set 3 | Question: 29
The values of the integral $\large\frac{1}{2\pi j}\oint_c\frac{e^z}{(z-2)} \small dz$ along a closed contour $c$ in anti-clockwise direction for the point $z_0=2$ inside the contour $c$, and the point $z_0=2$ outside the contour $c$, respectively,are $(i)2.72, \: (ii) 0$ $(i)7.39, \: (ii) 0$ $(i)0, \: (ii) 2.72$ $(i)0, \: (ii) 7.39$

Milicevic3306 asked in Complex Analysis Mar 28, 2018

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GATE ECE 2016 Set 3 | Question: 31
The ROC (region of convergence) of the $z$-transform of a discrete-time signal is represented by the shaded region in the $z$-plane. If the signal $x[n]=(2.0)^{\mid n\mid},-\infty<n<+\infty$, then the ROC of its $z$-transform is represented by

Milicevic3306 asked in Numerical Methods Mar 28, 2018

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