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3081

GATE ECE 2017 Set 1 | Question: 49
The Nyquist plot of the transfer function $G(s)=\frac{K}{(s^{2}+2s+2)(s+2)}$ does not encircle the point $(-1+j0)$ for $K=10$ but does encircle the point $(-1+j0)$ for $K=100$. Then the closed loop system (having unity gain feedback) is stable ... $K=10$ and unstable for $K=100$ unstable for $K=10$ and stable for $K=100$ stable for $K=10$ and unstable for $K=100$

The Nyquist plot of the transfer function$$G(s)=\frac{K}{(s^{2}+2s+2)(s+2)}$$does not encircle the point $(-1+j0)$ for $K=10$ but does encircle the point $(-1+j0)$ for $K...

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3082

GATE ECE 2017 Set 1 | Question: 35
In the circuit shown, the voltage $V_{IN}(t)$ is described by: $V_{IN}(t)=\begin{cases} 0, & \text{for } t< 0 \\ 15 \text{Volts} & \text{for } t\geq 0 \end{cases}$ where $t$ is in seconds. The time (in seconds) at which the current $I$ in the circuit will reach the value $2$ Amperes is ___________.

In the circuit shown, the voltage $V_{IN}(t)$ is described by: $$V_{IN}(t)=\begin{cases} 0, & \text{for } t< 0 \\ 15 \text{Volts} & \text{for } t\geq 0 \end{cases}$$wher...

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3083

GATE ECE 2017 Set 1 | Question: 19
Consider a stable system with transfer function,$G(s)=\frac{s^{p}+b_{1}s^{p-1}+\dots +b_{p}}{s^{q}+a_{1}s^{q-1}+\dots +a_{q}}$, where $b_1, \dots ,b_p$ and $a_1, \dots ,a_q$ are real valued constants.The slope of the Bode log magnitude curve of $G(s)$ ... of values for $p$ and $q$ is $p=0$ and $q=3$ $p=1$ and $q=7$ $p=2$ and $q=3$ $p=3$ and $q=5$

Consider a stable system with transfer function,$$G(s)=\frac{s^{p}+b_{1}s^{p-1}+\dots +b_{p}}{s^{q}+a_{1}s^{q-1}+\dots +a_{q}}$$, where $b_1, \dots ,b_p$ and $a_1, \dots ...

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3084

GATE ECE 2017 Set 1 | Question: 10
An $n^+-n$ Silicon device is fabricated with uniform and non-degenerate donor doping concentrations of $N_{D1}=1\times 10^{18}cm^{-3}$ and $N_{D2}=1\times 10^{15}cm^{-3}$ corresponding to the $n^+$ and $n$ regions respectively. At the operational temperature $T$, ... of the build-in potential of this device? $0.748 \: V$ $0.460 \: V$ $0.288 \: V$ $0.173 \: V$

An $n^+-n$ Silicon device is fabricated with uniform and non-degenerate donor doping concentrations of $N_{D1}=1\times 10^{18}cm^{-3}$ and $N_{D2}=1\times 10^{15}cm^{-3}$...

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3085

GATE ECE 2017 Set 1 | Question: 29
Which one of the following is the general solution of the first order differential equation $\frac{dy}{dx}=(x+y-1)^{2},$ where $x,y$ are real? $y=1+x+\tan^{-1}(x+c)$, where $c$ is a constant $y=1+x+\tan(x+c)$, where $c$ is a constant $y=1-x+\tan^{-1}(x+c)$, where $c$ is a constant $y=1-x+\tan(x+c)$, where $c$ is a constant

Which one of the following is the general solution of the first order differential equation $$\frac{dy}{dx}=(x+y-1)^{2},$$ where $x,y$ are real?$y=1+x+\tan^{-1}(x+c)$, wh...

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3086

GATE ECE 2017 Set 1 | Question: 32
Two discrete-time signals $x[n]$ and $h[n]$ are both non-zero only for $n=0,1,2$, and are zero otherwise .It is given that $x[0]=1, \: x[1]=2, \: x[2]=1, \: h[0]=1$ Let $y[n]$ be the linear convolution of $x[n]$ and $h[n]$. Given that $y[1]=3$ and $y[2]=4$, the value of the expression $(10y[3]+y[4])$ is__________.

Two discrete-time signals $x[n]$ and $h[n]$ are both non-zero only for $n=0,1,2$, and are zero otherwise .It is given that$$x[0]=1, \: x =2, \: x =1, \: h[0]=1$$ Let $y[n...

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3087

GATE ECE 2017 Set 1 | Question: 31
Let $x(t)$ be a continuous time periodic signal with fundamental period $T=1$ seconds.Let ${a_{k} }$ be the complex Fourier series coefficients of $x(t)$, where $k$ is integer valued. Consider the following statements about $x(3t)$: The complex ... one of the following is correct? Only II and III are true Only I and III are true Only III is true Only I is true

Let $x(t)$ be a continuous time periodic signal with fundamental period $T=1$ seconds.Let ${a_{k} }$ be the complex Fourier series coefficients of $x(t)$, where $k$ is in...

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3088

GATE ECE 2017 Set 1 | GA Question: 5
Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusion can be deduced from the preceding sentences? At least one bench is a table At least one shelf is a bench At least one chair is a table All benches are chairs Only $\text{i}$ Only $\text{ii}$ Only $\text{ii}$ and $\text{iii}$ Only $\text{iv}$

Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusion can be deduced from the preceding sentences?At least one bench...

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3089

GATE ECE 2017 Set 1 | Question: 41
For the DC analysis of the Common-Emitter amplifier shown, neglect the base current and assume that the emitter and collector currents are equal. Given that $V_{T}=25mV,V_{BE}=0.7V$, and the BJT output resistance $r_{o}$ is practically infinite. Under these conditions, the midband voltage gain magnitude, $A_{v}=\mid v_{o}/v_{i} \mid $, V/V is ____________.

For the DC analysis of the Common-Emitter amplifier shown, neglect the base current and assume that the emitter and collector currents are equal. Given that $V_{T}=25mV,V...

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3090

GATE ECE 2017 Set 1 | Question: 30
Starting with $x=1$, the solution of the equation $x^{3}+x=1$, after two iterations of Newton-Raphson’s method (up to two decimal places) is__________.

Starting with $x=1$, the solution of the equation $x^{3}+x=1$, after two iterations of Newton-Raphson’s method (up to two decimal places) is__________.

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3091

GATE ECE 2017 Set 1 | Question: 26
Let $f(x)=e^{x+x^{2}}$ for real $x$ . From among the following, choose the Taylor series approximation of $f(x)$ around $x=0$, which includes all powers of $x$ less than or equal to $3$. $1 + x + x^{2} + x^{3} $ $1 + x +\frac{3}{2} x^{2} + x^{3} $ $1 + x +\frac{3}{2} x^{2} + \frac{7}{6}x^{3} $ $1 + x +3 x^{2} + 7x^{3} $

Let $f(x)=e^{x+x^{2}}$ for real $x$ . From among the following, choose the Taylor series approximation of $f(x)$ around $x=0$, which includes all powers of $x$ less than...

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3092

GATE ECE 2017 Set 1 | Question: 53
An optical fiber is kept along the $\hat{z}$ direction. The refractive indices for the electric fields along $\hat{x}$ and $\hat{y}$ directions in the fiber are $n_{x}=1.5000$ and $n_{y}=1.5001$, ... is circularly polarized at the input of the fiber, the minimum propagation distance after which it becomes linearly polarized, in centimeters,is______________.

An optical fiber is kept along the $\hat{z}$ direction. The refractive indices for the electric fields along $\hat{x}$ and $\hat{y}$ directions in the fiber are $n_{x}=1....

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3093

GATE ECE 2017 Set 1 | GA Question: 4
$40 \%$ of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is $120$ $144$ $160$ $212$

$40 \%$ of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is$120$$144$$160$$212$

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3094

GATE ECE 2017 Set 1 | GA Question: 9
There are $3$ Indians and $3$ Chinese in a group of $6$ people. How many subgroups of this group can we choose so that every subgroup has at least one Indian? $56$ $52$ $48$ $44$

There are $3$ Indians and $3$ Chinese in a group of $6$ people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?$56$$52$$48$...

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3095

GATE ECE 2017 Set 1 | Question: 43
Which one of the following gives the simplified sum of products expression for the Boolean function $F=m_{0}+m_{2}+m_{3}+m_{5}$, where $m_{0},m_{2},m_{3}$ and $m_{5}$ are minterms corresponding to the inputs $A,B$ and $C$ with $A$ as the $MSB$ and ... $\overline{A} BC+\overline{A} \: \overline{C}+A \overline{B}C$

Which one of the following gives the simplified sum of products expression for the Boolean function $F=m_{0}+m_{2}+m_{3}+m_{5}$, where $m_{0},m_{2},m_{3}$ and $m_{5}$ are...

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3096

GATE ECE 2017 Set 1 | Question: 39
In the figure shown, the $npn$ transistor acts as a switch. For the input $V_{in}(t)$ as shown in the figure, the transistor switches between the cut-off and saturation regions of operation, when $T$ is large. Assume collector-to-emitter ... $(\alpha)$ of the transistor for the switching should be __________.

In the figure shown, the $npn$ transistor acts as a switch.For the input $V_{in}(t)$ as shown in the figure, the transistor switches between the cut-off and saturation re...

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3097

GATE ECE 2017 Set 1 | GA Question: 8
Trucks ($10$ m long) and cars ($5$ m long) go on a single lane bridge. There must be a gap of at least $20$ m after each truck and a gap of at least $15$ m after each car. Trucks and cars travel at a speed of $36$ km/h. If cars and trucks go alternately, what is the maximum number of vehicles that can use the bridge in one hour? $1440$ $1200$ $720$ $600$

Trucks ($10$ m long) and cars ($5$ m long) go on a single lane bridge. There must be a gap of at least $20$ m after each truck and a gap of at least $15$ m after each car...

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3098

GATE ECE 2017 Set 1 | GA Question: 7
S, T, U, V, W, X, Y and Z are seated around a circular table .T’s neighbors are Y and V. Z is seated third to the left of T and second to the right of S. U’s neighbors are S and Y; and T and W are not seated opposite each other .Who is third to the left of V? X W U T

S, T, U, V, W, X, Y and Z are seated around a circular table .T’s neighbors are Y and V. Z is seated third to the left of T and second to the right of S. U’s neighbo...

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3099

GATE ECE 2017 Set 1 | GA Question: 2
I __________ made arrangements had I _________informed earlier. could have, been would have, being had, have had been, been

I __________ made arrangements had I _________informed earlier.could have, beenwould have, beinghad, havehad been, been

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3100

GATE ECE 2017 Set 1 | Question: 21
Let $\left ( X_{1},X_{2} \right )$ be independent random variables. $\left ( X_{1} \right )$ has mean $0$ and variance $1$, while $\left ( X_{2} \right )$ has mean $1$ and variance $4$. The mutual information $I\left (X_{1},X_{2} \right )$ between $X1$ and $X2$ in bits is_______.

Let $\left ( X_{1},X_{2} \right )$ be independent random variables. $\left ( X_{1} \right )$ has mean $0$ and variance $1$, while $\left ( X_{2} \right )$ has mean $1$ an...

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3101

GATE ECE 2017 Set 1 | Question: 51
Let $X(t)$ be a wide sense stationary random process with the power spectral density $S_{X}(f)$ as shown in Figure (a), where $f$ is in Hertz$(Hz)$. The random process $X(t)$ ... Select the correct option: only I is true only II and III are true only I and II are true only I and III are true

Let $X(t)$ be a wide sense stationary random process with the power spectral density $S_{X}(f)$ as shown in Figure (a), where $f$ is in Hertz$(Hz)$. The random process $X...

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3102

GATE ECE 2017 Set 1 | Question: 13
A good transconductance amplifier should have High input resistance and low output resistance Low input resistance and high output resistance High input and output resistance Low input and output resistance

A good transconductance amplifier should haveHigh input resistance and low output resistanceLow input resistance and high output resistanceHigh input and output resistanc...

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3103

GATE ECE 2017 Set 1 | GA Question: 3
In the summer, water consumption is known to decrease overall by $25 \%$. A Water Board official states that in the summer household consumption decreases by $20 \%$, while other consumption increases by $70 \%$. Which of the following statement is ... is $1/17$ The ratio of household to other consumption is $17/8$ There are errors in the official's statement.

In the summer, water consumption is known to decrease overall by $25 \%$. A Water Board official states that in the summer household consumption decreases by $20 \%$, whi...

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3104

GATE ECE 2017 Set 1 | Question: 38
As shown, two Silicon (Si) abrupt $p-n$ junction diodes are fabricated with uniform donor doping concentrations of $ N_{D1}=10^{14} cm^{-3} $ and $N_{D2}=10^{16}cm^{-3}$ in the $n$-regions of the diodes, and uniform acceptor ... in potentials of the diodes, the ratio $C_{2}/C_{1}$ of their reverse bias capacitance for the same applied reverse bias, is _________.

As shown, two Silicon (Si) abrupt $p-n$ junction diodes are fabricated with uniform donor doping concentrations of $ N_{D1}=10^{14} cm^{-3} $ and $N_{D2}=10^{16}cm^{-3}$ ...

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