Recent questions / GO Electronics

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2761

GATE ECE 2014 Set 1 | Question: 37
In the voltage regulator circuit shown in the figure, the op-amp is ideal. The BJT has $V_{BE} = 0.7\:V$ and $\beta = 100,$ and the zener voltage is $4.7\:V.$ For a regulated output of $9\:V,$ the value of $R$ (in $\Omega)$ is ______.

In the voltage regulator circuit shown in the figure, the op-amp is ideal. The BJT has $V_{BE} = 0.7\:V$ and $\beta = 100,$ and the zener voltage is $4.7\:V.$ For a regul...

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2762

GATE ECE 2014 Set 1 | Question: 38
In the circuit shown the op-amp has finite input impedance, infinite voltage gain, and zero input offset voltage. The output voltage $V_{out}$ is $-I_{2}(R_{1} + R_{2})$ $I_{2}R_{2}$ $I_{1}R_{2}$ $-I_{1}(R_{1} + R_{2})$

In the circuit shown the op-amp has finite input impedance, infinite voltage gain, and zero input offset voltage. The output voltage $V_{out}$ is $-I_{2}(R_{1} + R_{2})$$...

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2763

GATE ECE 2014 Set 1 | Question: 39
For the amplifier shown in the figure, the BJT parameters are $V_{BE} = 0.7\:V, \beta = 200,$ and thermal voltage $V_{T} = 25\:mV.$ The voltage gain $(v_{0}/v_{i})$ of the amplifier is ______.

For the amplifier shown in the figure, the BJT parameters are $V_{BE} = 0.7\:V, \beta = 200,$ and thermal voltage $V_{T} = 25\:mV.$ The voltage gain $(v_{0}/v_{i})$ of th...

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2764

GATE ECE 2014 Set 1 | Question: 40
The output $F$ in the digital logic circuit shown in the figure is $F = \overline{X}\:Y\:Z + X\:\overline{Y}\:Z$ $F = \overline{X}\:Y\:\overline{Z} + X\:\overline{Y}\:\overline{Z}$ $F = \overline{X}\:\overline{Y}\:Z + X\:Y\:Z$ $F = \overline{X}\:\overline{Y}\:\overline{Z} + X\:Y\:Z$

The output $F$ in the digital logic circuit shown in the figure is$F = \overline{X}\:Y\:Z + X\:\overline{Y}\:Z$$F = \overline{X}\:Y\:\overline{Z} + X\:\overline{Y}\:\over...

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2765

GATE ECE 2014 Set 1 | Question: 41
Consider the Boolean function $F(w,x,y,z) = wy + xy + \overline{w}\:xyz + \overline{w}\:\overline{x}\:y + xz + \overline{x}\:\overline{y}\:\overline{z}.$ Which one of the following is the complete set of essential prime implicants? $w,y,xz,\overline{x}\:\overline{z}$ $w,y,xz$ $y, \overline{x}\:\overline{y}\:\overline{z}$ $y,xz,\overline{x}\:\overline{z}$

Consider the Boolean function $F(w,x,y,z) = wy + xy + \overline{w}\:xyz + \overline{w}\:\overline{x}\:y + xz + \overline{x}\:\overline{y}\:\overline{z}.$ Which one of th...

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2766

GATE ECE 2014 Set 1 | Question: 42
The digital logic shown in the figure satisfies the given state diagram when $Q1$ is connected to input $A$ of the XOR gate. Suppose the XOR gate is replaced by an XNOR gate. Which one of the following options preserves the state diagram? Input $A$ is ... $A$ is connected to $\overline{Q1}$ and $S$ is complemented Input $A$ is connected to $\overline{Q1}$

The digital logic shown in the figure satisfies the given state diagram when $Q1$ is connected to input $A$ of the XOR gate.Suppose the XOR gate is replaced by an XNOR ga...

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2767

GATE ECE 2014 Set 1 | Question: 43
Let $x[n] = \bigg( – \dfrac{1}{9}\bigg)^{n}u(n) \:– \bigg( – \dfrac{1}{3}\bigg)^{n}u(-n-1).$ The Region of Convergence (ROC) of the $z$-transform of $x[n]$ is $\mid z \mid > \frac{1}{9} \\$ is $\mid z \mid < \frac{1}{3} \\$ is $\frac{1}{3}>\mid z \mid > \frac{1}{9} \\$ does not exist

Let $x[n] = \bigg( – \dfrac{1}{9}\bigg)^{n}u(n) \:– \bigg( – \dfrac{1}{3}\bigg)^{n}u(-n-1).$ The Region of Convergence (ROC) of the $z$-transform of $x[n]$is $\mid ...

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2768

GATE ECE 2014 Set 1 | Question: 44
Consider a discrete time periodic signal $x[n] = \sin(\frac{\pi n}{s}).$ Let $a_{k}$ be the complex Fourier series coefficients of $x[n].$ The coefficients $\{a_{k}\}$ are non-zero when $k = Bm\: \pm 1,$ where $m$ is any integer. The value of $B$ is ______.

Consider a discrete time periodic signal $x[n] = \sin(\frac{\pi n}{s}).$ Let $a_{k}$ be the complex Fourier series coefficients of $x[n].$ The coefficients $\{a_{k}\}$ ar...

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2769

GATE ECE 2014 Set 1 | Question: 45
A system is described by the following differential equation, where $u(t)$ is the input to the system and $y(t)$ is the output of the system. $y(t) + 5y(t) = u(t)$ When $y(0) = 1$ and $u(t)$ is a unit step function, $y(t)$ is $0.2 + 0.8e^{-5t}$ $0.2 - 0.2e^{-5t}$ $0.8 + 0.2e^{-5t}$ $0.8 - 0.8e^{-5t}$

A system is described by the following differential equation, where $u(t)$ is the input to the system and $y(t)$ is the output of the system.$$y(t) + 5y(t) = u(t)$$When $...

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2770

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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2771

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 ______.

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2772

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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2773

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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2774

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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2775

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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2776

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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2777

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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2778

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...

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2779

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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2780

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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2781

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...

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2782

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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2783

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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2784

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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2785

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.

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2786

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...

Milicevic3306

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2787

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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2788

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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2789

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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2790

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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2791

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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2792

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, −...

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2793

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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2794

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

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2795

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

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2796

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...

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2797

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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2798

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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2799

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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2800

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...

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