Questions by Milicevic3306 / GO Electronics

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641

GATE ECE 2014 Set 1 | Question: 46
Consider the state space model of a system, as given below ... The system is controllable and observable uncontrollable and observable uncontrollable and unobservable controllable and unobservable

Consider the state space model of a system, as given below$\begin{bmatrix} x_{1}\\x_{2} \\x_{3} \end{bmatrix} \begin{bmatrix} -1 &1 &0 \\ 0& -1 &0 \\ 0 & 0 & -2 \end{bmat...

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asked Mar 25, 2018

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642

GATE ECE 2014 Set 1 | Question: 47
The phase margin in degrees of $G(s) = \dfrac{10}{(s+0.1)(s+1)(s+10)}$ calculated using the asymptotic Bode plot is ______.

The phase margin in degrees of $G(s) = \dfrac{10}{(s+0.1)(s+1)(s+10)}$ calculated using the asymptotic Bode plot is ______.

106 views

asked Mar 25, 2018

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643

GATE ECE 2014 Set 1 | Question: 48
For the following feedback system $G(s) = \dfrac{1}{(s+1)(s+2)}.$ The $2\%$-settling time of the step response is required to be less than $2$ seconds. Which one of the following compensators $C(s)$ achieves this? $3\bigg(\dfrac{1}{s+5}\bigg) \\$ $5\bigg(\dfrac{0.03}{s} + 1\bigg) \\$ $2(s+4) \\$ $4\bigg(\dfrac{s+8}{s+3}\bigg)$

For the following feedback system $G(s) = \dfrac{1}{(s+1)(s+2)}.$ The $2\%$-settling time of the step response is required to be less than $2$ seconds.Which one of the fo...

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asked Mar 25, 2018

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644

GATE ECE 2014 Set 1 | Question: 49
Let $X$ be a real-valued random variable with $E[X]$ and $E[X^{2}]$ denoting the mean values of $X$ and $X^{2},$ respectively. The relation which always holds true is $(E[X])^{2}>E[X^{2}]$ $E[X^{2}]\geq (E[X])^{2}$ $E[X^{2}] = (E[X])^{2}$ $E[X^{2}] > (E[X])^{2}$

Let $X$ be a real-valued random variable with $E[X]$ and $E[X^{2}]$ denoting the mean values of $X$ and $X^{2},$ respectively. The relation which always holds true is$(E[...

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asked Mar 25, 2018

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645

GATE ECE 2014 Set 1 | Question: 50
Consider a random process $X(t) = \sqrt{2}\sin(2\pi t + \varphi),$ where the random phase $\varphi$ is uniformly distributed in the interval $[0,2\pi].$ The auto-correlation $E[X(t_{1})X(t_{2})]$ is $\cos(2\pi(t_{1} + t_{2}))$ $\sin(2\pi(t_{1} - t_{2}))$ $\sin(2\pi(t_{1} + t_{2}))$ $\cos(2\pi(t_{1} - t_{2}))$

Consider a random process $X(t) = \sqrt{2}\sin(2\pi t + \varphi),$ where the random phase $\varphi$ is uniformly distributed in the interval $[0,2\pi].$ The auto-correlat...

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asked Mar 25, 2018

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646

GATE ECE 2014 Set 1 | Question: 51
Let $Q(\sqrt{\gamma})$ be the BER of a BPSK system over an AWGN channel with two-sided noise power spectral density $N_{0}/2.$ The parameter $\gamma$ is a function of bit energy and noise power spectral density. A system with two independent and identical ... both the channels. If the BER of this system is $Q( b \sqrt{\gamma})$ then the value of $b$ is _____.

Let $Q(\sqrt{\gamma})$ be the BER of a BPSK system over an AWGN channel with two-sided noise power spectral density $N_{0}/2.$ The parameter $\gamma$ is a function of bit...

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asked Mar 25, 2018

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647

GATE ECE 2014 Set 1 | Question: 52
A fair coin is tossed repeatedly until a ‘Head’ appears for the first time. Let $L$ be the number of tosses to get this first ‘Head’. The entropy $H(L)$ in bits is _____.

A fair coin is tossed repeatedly until a ‘Head’ appears for the first time. Let $L$ be the number of tosses to get this first ‘Head’. The entropy $H(L)$ in bits i...

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asked Mar 25, 2018

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648

GATE ECE 2014 Set 1 | Question: 53
In spherical coordinates, let $\hat{a_{\theta}},\hat{a_{\phi}}$ denote unit vectors along the $\theta,\phi$ directions. $\textbf{E} = \dfrac{100}{r}\sin\theta \cos (\omega t - \beta r)\hat{a_{\theta}}\: V/m$ ... free space. The average power $(W)$ crossing the hemispherical shell located at $r = 1\:km,0\leq \theta \leq \pi/2$ is ______.

In spherical coordinates, let $\hat{a_{\theta}},\hat{a_{\phi}}$ denote unit vectors along the $\theta,\phi$ directions.$$\textbf{E} = \dfrac{100}{r}\sin\theta \cos (\omeg...

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asked Mar 25, 2018

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649

GATE ECE 2014 Set 1 | Question: 54
For a parallel plate transmission line, let $v$ be the speed of propagation and $Z$ be the characteristic impedance. Neglecting fringe effects, a reduction of the spacing between the plates by a factor of two results in halving of $v$ and no change in $Z$ no changes in $v$ and halving of $Z$ no change in both $v$ and $Z$ halving of both $v$ and $Z$

For a parallel plate transmission line, let $v$ be the speed of propagation and $Z$ be the characteristic impedance. Neglecting fringe effects, a reduction of the spacin...

97 views

asked Mar 25, 2018

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650

GATE ECE 2014 Set 1 | Question: 55
The input impedance of a $\dfrac{\lambda}{8}$ section of a lossless transmission line of characteristic impedance $50\: \Omega$ is found to be real when the other end is terminated by a load $Z_{L} (=R + jX)\Omega.$ If $X$ is $30\:\Omega ,$ the value of $R ( \text{in} \:\Omega )$ is _______.

The input impedance of a $\dfrac{\lambda}{8}$ section of a lossless transmission line of characteristic impedance $50\: \Omega$ is found to be real when the other end is...

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asked Mar 25, 2018

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651

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

What is the chance that a leap year, selected at random, will contain $53$ Saturdays?$2/7$$3/7$$1/7$$5/7$

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asked Mar 25, 2018

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652

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 $(-\infty ,0)$ $(0,1)$ $(1,\infty )$ $(0,\infty )$

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 )$

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asked Mar 25, 2018

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653

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.

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 fo...

112 views

asked Mar 25, 2018

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654

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

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$

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asked Mar 25, 2018

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655

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 $30$ $36$ $40$ $24$

A car travels $8 \: km$ in the first quarter of an hour, $6\: km$ in the second quarter and $16\: km$ in the thirdquarter. The average speed of the car in $km$ per hour ...

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asked Mar 25, 2018

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656

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

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 outcall outdig ...

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asked Mar 25, 2018

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657

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

Complete the sentence:Dare _______________ mistakes.committo commitcommittedcommitting

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asked Mar 25, 2018

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658

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 $40$ $43$ $46$ $49$

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 T...

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asked Mar 25, 2018

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659

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.

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.Bec...

120 views

asked Mar 25, 2018

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660

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.

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.

110 views

asked Mar 25, 2018

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661

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 $e^{At}$ ... $\begin{bmatrix} e^{-t}&-te^{-t} \\ 0 &e^{-t} \end{bmatrix}$

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 $e^{At}$ ...

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asked Mar 25, 2018

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662

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

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-variable equations of the sy...

199 views

asked Mar 25, 2018

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663

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 $\vec{E_{t}}$ ...

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 $\vec{E_{t}}$ ...

166 views

asked Mar 25, 2018

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664

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 $\vec{E_{t}}$ ...

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 $\vec{E_{t}}$ ...

146 views

asked Mar 25, 2018

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665

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

Consider the following figure The current in the $1\Omega$ resistor in $\text{Amps}$ is$2$$3.33$ $10$ $12$

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asked Mar 25, 2018

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666

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 $13, − 20$ $8, − 10$ $− 8, 20$ $− 13, 20$

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, −...

181 views

asked Mar 25, 2018

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667

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} $

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 threshol...

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asked Mar 25, 2018

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668

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} \\ $ $\frac{1}{4} \\$ $\frac{1}{8} \\$ $\frac{1}{16}$

Bits $1$ and $0$ are transmitted with equal probability. At the receiver, the pdf of the respective receivedsignals for both bits are as shown below.If the detection thre...

126 views

asked Mar 25, 2018

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669

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 $\frac{3}{4} \\$ $1$ $\frac{3}{2} \\$ $\log_{2}3$

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} ...

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asked Mar 25, 2018

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670

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 $20$ $30$ $40$ $50$

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$2...

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asked Mar 25, 2018

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671

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 $4$ ... $0500H-08FFH, 1500H-18FFH, 3500H-38FFH, 5500H-58FFH$ $0800H-0BFFH, 1800H-1BFFH, 2800H-2BFFH, 3800H-3BFFH$

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 $4$ respectively are mapp...

232 views

asked Mar 25, 2018

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672

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 $80$

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. Fo...

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asked Mar 25, 2018

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673

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 $t$

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...

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asked Mar 25, 2018

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674

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 $XY$ $\overline{X}Y$ $X\overline{Y}$ $\overline{XY}$

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}...

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asked Mar 25, 2018

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675

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

In the circuit shown below the $\text{op-amps}$ are ideal. Then $V_{\text{out}}$ in $\text{Volts}$ is$4$$6$$8$$10$

158 views

asked Mar 25, 2018

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676

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 $\frac{s+1}{5s^{2}+6s+2} \\$ $\frac{s+1}{s^{2}+6s+2} \\$ $\frac{s+1}{s^{2}+4s+2} \\$ $\frac{1}{5s^{2}+6s+2}$

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} \\$$\...

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asked Mar 25, 2018

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677

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

The $\text{DFT}$ of a vector $\begin{bmatrix} a & b & c & d \end{bmatrix}$ is the vector $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}.$ consider the...

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asked Mar 25, 2018

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678

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 $x$ $F(x) - G(x) \leq 0$ $F(x) - G(x) \geq 0$ $(F(x) - G(x)) \cdot x\leq 0$ $(F(x) - G(x)) \cdot x\geq 0$

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. ...

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asked Mar 25, 2018

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679

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 $−2x(t)$

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 functi...

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asked Mar 25, 2018

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680

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)} $

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 rectangul...

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asked Mar 25, 2018