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GATE ECE 2015 Set 3 | GA Question: 1
Choose the most appropriate word from the options given below to complete the following sentence. If the athlete had wanted to come first in the race, he ________________ several hours every day. should practise should have practised practised should be practising

Milicevic3306 asked in Verbal Aptitude Mar 28, 2018

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GATE ECE 2015 Set 3 | GA Question: 2
Choose the most suitable one word substitute for the following expression: Connotation of a road or way Pertinacious Viaticum Clandestine Ravenous

Milicevic3306 asked in Verbal Aptitude Mar 28, 2018

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GATE ECE 2015 Set 3 | GA Question: 3
Choose the correct verb to fill in the blank below: Let us __________ introvert alternate atheist altruist

Milicevic3306 asked in Verbal Aptitude Mar 28, 2018

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GATE ECE 2015 Set 3 | GA Question: 4
Find the missing sequence in the letter series below: $A, CD, GHI,?, UVWXY$ $LMN$ $MNO$ $MNOP$ $NOPQ$

Milicevic3306 asked in Analytical Aptitude Mar 28, 2018

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5

GATE ECE 2015 Set 3 | GA Question: 5
If $x>y>1,$ which of the following must be true? $\text{ln } x > \text{ln }y$ $e^{x}>e^{y}$ $y^{x}>x^{y}$ $\cos x> \cos y$ $(i)$ and $(ii)$ $(i)$ and $(iii)$ $(iii)$ and $(iv)$ $(ii)$ and $(iv)$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

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GATE ECE 2015 Set 3 | GA Question: 6
Ran and Shyam shared a secret and promised to each other that it would remain between them. Ram expressed himself in one of the following ways as given in the choices below. Identify the correct way as per standard English. It would remain between you and me. It would remain between I and you. It would remain between you and I. It would remain with me.

Milicevic3306 asked in Verbal Aptitude Mar 28, 2018

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7

GATE ECE 2015 Set 3 | GA Question: 7
In the following question, the first and the last sentence of the passage are in order and numbered $1$ and $6.$ The rest of the passage is split into $4$ parts and numbered as $2,3,4,$ and $5.$ These $4$ parts are not arranged in proper order. Read the sentences ... . Houses look so pretty with lighted lamps all around. $2,5,3,4$ $5,2,4,3$ $3,5,4,2$ $4,5,2,3$

Milicevic3306 asked in Verbal Aptitude Mar 28, 2018

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GATE ECE 2015 Set 3 | GA Question: 8
From a circular sheet of paper of radius $30$ cm, a sector of $10\%$ area is removed. If the remaining part is used to make a conical surface, then the ratio of the radius and height of the cone is ________.

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

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9

GATE ECE 2015 Set 3 | GA Question: 9
$\log \tan1^{\circ}+ \log \tan2^{\circ}+ \dots + \log \tan89^{\circ}$ is $1$ $\frac{1}{\sqrt{2}}$ $0$ $-1$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

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GATE ECE 2015 Set 3 | GA Question: 10
Ms. $X$ will be in Bagdogra from $01/05/2014$ to $20/05/2014$ and from $22/05/2014$ to $31/05/2014.$ On the morning of $21/05/2014,$ she will reach Kochi via Mumbai. Which one of the statements below is logically valid and can be inferred from the above ... May. Ms. $X$ will be only in Kochi for one day in May. Only Ms. $X$ will be in Kochi for one day in May.

Milicevic3306 asked in Analytical Aptitude Mar 28, 2018

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GATE ECE 2015 Set 3 | Question: 1
For $A = \begin{bmatrix} 1 &\tan x \\ -\tan x &1 \end{bmatrix},$ the determinant of $A^{T}A^{-1}$ is $\sec^{2}x$ $\cos 4x$ $1$ $0$

Milicevic3306 asked in Linear Algebra Mar 28, 2018

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12

GATE ECE 2015 Set 3 | Question: 2
The contour on the $x-y$ plane, where the partial derivative of $x^{2} + y^{2}$ with respect to $y$ is equal to the partial derivative of $6y+4x$ with respect to $x$, is $y=2$ $x=2$ $x+y=4$ $x-y=0$

Milicevic3306 asked in Calculus Mar 28, 2018

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13

GATE ECE 2015 Set 3 | Question: 3
If $C$ is a circle of radius $r$ with centre $z_{0},$ in the complex $z$-plane and if $n$ is a non-zero integer, then $\oint _{C}\frac{dz}{(z-z_{0})^{n+1}}$ equals $2\pi n j$ $0$ $\frac{nj}{2\pi}$ $2\pi n$

Milicevic3306 asked in Complex Analysis Mar 28, 2018

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14

GATE ECE 2015 Set 3 | Question: 4
Consider the function $g(t) = e^{-t}\sin(2\pi t)u(t)$ where $u(t)$ is the unit step function. The area under $g(t)$ is ______.

Milicevic3306 asked in Vector Analysis Mar 28, 2018

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15

GATE ECE 2015 Set 3 | Question: 5
The value of $\displaystyle{}\sum_{n=0}^{\infty} n \left(\dfrac{1}{2}\right)^{n}$ is ________.

Milicevic3306 asked in Calculus Mar 28, 2018

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16

GATE ECE 2015 Set 3 | Question: 6
For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals $a-b$ is _______.

Milicevic3306 asked in Network Solution Methods Mar 28, 2018

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GATE ECE 2015 Set 3 | Question: 9
In the circuit shown, the voltage $V_{X}$ (in Volts) is ________.

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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18

GATE ECE 2015 Set 3 | Question: 8
At very high frequencies, the peak output voltage $V_{0}$ (in Volts) is _______.

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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19

GATE ECE 2015 Set 3 | Question: 9
Which one of the following processes is preferred to form the gate dielectric $(SiO_{2})$ of MOSFETs ? Sputtering Molecular beam epitaxy Wet oxidation Dry oxidation

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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20

GATE ECE 2015 Set 3 | Question: 10
If the base width in a bipolar junction transistor is doubled, which one of the following statements will be TRUE? Current gain will increase Unity gain frequency will increase Emitter-base junction capacitance will increase Early Voltage will increase

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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21

GATE ECE 2015 Set 3 | Question: 11
In the circuit shown in the figure, the BJT has a current gain $(\beta)$ of $50.$ For an emitter-base voltage ܸ $V_{EB} = 600\: mV,$ the emitter-collector voltage $V_{EC}$ (in Volts) is _______.

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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22

GATE ECE 2015 Set 3 | Question: 12
In the circuit shown using an ideal opamp, the $3$-dB cut-off frequency (in Hz) is _______.

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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23

GATE ECE 2015 Set 3 | Question: 13
In the circuit shown, assume that diodes $D_{1}$ and $D_{2}$ are ideal. In the steady state condition, the average voltage $V_{ab}$ (in Volts) across the $0.5\: \mu F$ capacitor is ______.

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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24

GATE ECE 2015 Set 3 | Question: 14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset $(\overline{R_{d}}\:\text{input}).$ The counter corresponding to this circuit is a modulo-$5$ binary up counter a modulo-$6$ binary down counter a modulo-$5$ binary down counter a modulo-$6$ binary up counter

Milicevic3306 asked in Network Solution Methods Mar 28, 2018

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25

GATE ECE 2015 Set 3 | Question: 15
In the circuit shown, diodes $D_{1}, D_{2}$ and $D_{3}$ are ideal, and the inputs $E_{1} , E_{2}$ and $E_{3}$ are $“0\: V”$ for logic $‘0’$ and $“10\: V”$ for logic $‘1’$. What logic gate does the circuit represent? $3$-input OR gate $3$-input NOR gate $3$-input AND gate $3$-input XOR gate

Milicevic3306 asked in Number Representations Mar 28, 2018

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26

GATE ECE 2015 Set 3 | Question: 16
Which one of the following $8085$ microprocessor programs correctly calculates the product of two $8$-bit numbers stored in registers $B$ and $C?$ ...

Milicevic3306 asked in Digital Circuits Mar 28, 2018

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27

GATE ECE 2015 Set 3 | Question: 17
The impulse response of an LTI system can be obtained by differentiating the unit ramp response differentiating the unit step response integrating the unit ramp response integrating the unit step response

Milicevic3306 asked in Continuous-time Signals Mar 28, 2018

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28

GATE ECE 2015 Set 3 | Question: 18
Consider a four-point moving average filter defined by the equation $y[n] = \displaystyle{}\sum _{i=0}^{3}\alpha_{i}\:x[n-i].$ ... $\alpha_{1} = \alpha_{2} = 0;\:\alpha_{0} = \alpha_{3}$

Milicevic3306 asked in Analog Circuits Mar 28, 2018

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29

GATE ECE 2015 Set 3 | Question: 19
Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued. The value of $f_{H}\: – f_{L}\:( \text{in}\: Hz)$ is ___________.

Milicevic3306 asked in Control Systems Mar 28, 2018

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30

GATE ECE 2015 Set 3 | Question: 20
The phase margin (in degrees) of the system $G(s) = \dfrac{10}{s(s+10)}$ is _______.

Milicevic3306 asked in Continuous-time Signals Mar 28, 2018

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31

GATE ECE 2015 Set 3 | Question: 21
The transfer function of a first-order controller is given as $G_{C}(s) = \dfrac{K(s+a)}{s+b}$where $K,a$ and ܾ$b$ are positive real numbers. The condition for this controller to act as a phase lead compensator is $a<b$ $a>b$ $K<ab$ $K>ab$

Milicevic3306 asked in Network Solution Methods Mar 28, 2018

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32

GATE ECE 2015 Set 3 | Question: 22
The modulation scheme commonly used for transmission from GSM mobile terminals is $4$-QAM $16$-PSK Walsh-Hadamard orthogonal codes Gaussian Minimum Shift Keying (GMSK)

Milicevic3306 asked in Communications Mar 28, 2018

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33

GATE ECE 2015 Set 3 | Question: 23
A message signal $m(t) = A_{m} \sin(2πf_{m}t)$ is used to modulate the phase of a carrier $A_{c} \cos(2πf_{c}t)$ to get the modulated signal $y(t) = A_{c} \cos(2πf_{c}t + m(t)).$ The bandwidth of $y(t)$ depends on $A_{m}$ but not on $f_{m}$ depends on $f_{m}$ but not on $A_{m}$ depends on both $A_{m}$ and $f_{m}$ does not depend on $A_{m}$ or $f_{m}$

Milicevic3306 asked in Continuous-time Signals Mar 28, 2018

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34

GATE ECE 2015 Set 3 | Question: 24
The directivity of an antenna array can be increased by adding more antenna elements, as a larger number of elements improves the radiation efficiency increases the effective area of the antenna results in a better impedance matching allows more power to be transmitted by the antenna

Milicevic3306 asked in Electromagnetics Mar 28, 2018

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35

GATE ECE 2015 Set 3 | Question: 25
A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with Teflon $(\varepsilon_{r} = 2.1, \tan \delta = 0).$ Which one of the following circuits can represent the lumped element model of a small piece of this cable having length $\Delta z$?

Milicevic3306 asked in Electromagnetics Mar 28, 2018

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36

GATE ECE 2015 Set 3 | Question: 26
The Newton-Raphson method is used to solve the equation $f(x) = x^{3} – 5x^{2} + 6x – 8 = 0.$ Taking the initial guess as $x = 5,$ the solution obtained at the end of the first iteration is __________.

Milicevic3306 asked in Numerical Methods Mar 28, 2018

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37

GATE ECE 2015 Set 3 | Question: 27
A fair die with faces $\{1, 2, 3, 4, 5, 6\}$ is thrown repeatedly till $’3’$ is observed for the first time. Let $X$ denote the number of times the die is thrown. The expected value of $X$ is _______.

Milicevic3306 asked in Probability and Statistics Mar 28, 2018

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38

GATE ECE 2015 Set 3 | Question: 28
Consider the differential equation $\dfrac{\mathrm{d^{2}}x(t) }{\mathrm{d} t^{2}} +3\frac{\mathrm{d}x(t)}{\mathrm{d} t} + 2x(t) = 0. $ Given $x(0) = 20$ and $x(1) = 10/e,$ where $e = 2.718,$ the value of $x(2)$ is ________.

Milicevic3306 asked in Differential Equations Mar 28, 2018

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39

GATE ECE 2015 Set 3 | Question: 29
A vector field $\textbf{D} = 2\rho^{2}\:\textbf{a}_{\rho} + z\: \textbf{a}_{z}$ exists inside a cylindrical region enclosed by the surfaces $\rho =1,z = 0$ and $z = 5.$ Let $S$ be the surface bounding this cylindrical region. The surface integral of this field on $S(∯_{S} \textbf{D.ds})$ is _______.

Milicevic3306 asked in Vector Analysis Mar 28, 2018

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40

GATE ECE 2015 Set 3 | Question: 31
The $ABCD$ parameters of the following $2$-port network are $\begin{bmatrix}3.5 + j2 & 20.5 \\ 20.5 & 3.5-j2 \end{bmatrix} \\$ $\begin{bmatrix}3.5 +j2 & 30.5 \\ 0.5&3.5-j2 \end{bmatrix} \\$ $\begin{bmatrix}10 &2+j0 \\2+j0 &10 \end{bmatrix} \\$ $\begin{bmatrix}7+j4 &0.5 \\ 30.5&7-j4 \end{bmatrix} $

Milicevic3306 asked in Network Solution Methods Mar 28, 2018

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