Recent questions tagged numerical-answers

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41

GATE ECE 2020 | Question: 25
The two sides of a fair coin are labelled as $0$ to $1$. The coin is tossed two times independently. Let $M$ and $N$ denote the labels corresponding to the outcomes of those tosses. For a random variable $X$, defined as $X = \text{min}(M, N)$, the expected value $E(X)$ (rounded off to two decimal places) is ___________.

asked Feb 13, 2020 in Probability and Statistics by jothee (1.8k points) | 73 views

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42

GATE ECE 2020 | Question: 44
In the voltage regulator shown below, $V_{1}$ is the unregulated imput at $15\:V$. Assume $V_{BE}=0.7\:V$ and the base current is negligible for both the $\text{BJTs}$. If the regulated output $V_{O}$ is $9\:V$, the value of $R_{2}$ is ___________$\Omega$

asked Feb 13, 2020 in Analog Circuits by jothee (1.8k points) | 18 views

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43

GATE ECE 2020 | Question: 45
The magnetic field of a uniform plane wave in vacuum is given by $\overrightarrow{H}\left ( x,y,z,t \right )=(\hat{a_{x}}+2\hat{a_{y}}+b\hat{a_{z}})\cos\left ( \omega t+3x-y-z\right ).$ The value of $b$ is ___________.

asked Feb 13, 2020 in Electromagnetics by jothee (1.8k points) | 20 views

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44

GATE ECE 2020 | Question: 46
For a $2$-port network consisting of an ideal lossless transformer, the parameter $S_{21}$ (rounded off to two decimal places) for a reference impedance of $10 \Omega$, is __________.

asked Feb 13, 2020 in Electromagnetics by jothee (1.8k points) | 16 views

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45

GATE ECE 2020 | Question: 47
$S_{PM}(t)$ and $S_{FM}(t)$ as defined below, are the phase modulated and the frequency modlated waveforms, respectively, corresponding to the message signal $m(t)$ ... $S_{PM}(t)$ and $S_{FM}(t)$ are same, then the value of the ratio $\dfrac{K_{p}}{K_{f}}$ is ________ seconds.

asked Feb 13, 2020 in Communications by jothee (1.8k points) | 17 views

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46

GATE ECE 2020 | Question: 48
In a digital communication system, a symbol $S$ randomly chosen from the set $\left \{ s_{1},s_{2},s_{3},s_{4} \right \}$ is transmitted. It is given that $s_{1}=-3,s_{2}=-1,s_{3}=+1$ and $s_{4}=+2$. The received ... decoding when the transmitted symbol $S=s_{i}$. The index $i$ for which the conditional symbol error probability $P_{i}$ is the highest is ___________.

asked Feb 13, 2020 in Communications by jothee (1.8k points) | 15 views

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47

GATE ECE 2020 | Question: 49
A system with transfer function $G\left ( s \right )=\dfrac{1}{\left ( s+1 \right )\left ( s+a \right )},\:\:a> 0$ is subjected to an input $5 \cos3t$. The steady state output of the system is $\dfrac{1}{\sqrt{10}}\cos\left ( 3t-1.892 \right )$. The value of $a$ is _______.

asked Feb 13, 2020 in Network Solution Methods by jothee (1.8k points) | 17 views

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48

GATE ECE 2020 | Question: 50
For the components in the sequential circuit shown below, $t_{pd}$ is the propagation delay, $t_{\text{setup}}$ is the setup-time, and $t_{\text{hold}}$ is the hold time. The maximum clock frequency (rounded off to the nearest integer), at which the given circuit can operate reliably, is _________$\text{MHz}$.

asked Feb 13, 2020 in Digital Circuits by jothee (1.8k points) | 38 views

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49

GATE ECE 2020 | Question: 51
For the solid $S$ shown below, the value of $\underset{S}{\iiint} xdxdydz$ (rounded off to two decimal places) is _______________.

asked Feb 13, 2020 in Calculus by jothee (1.8k points) | 46 views

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50

GATE ECE 2020 | Question: 52
$X\left ( \omega \right )$ is the Fourier transform of $x(t)$ shown below. The value of $\int_{-\infty }^{\infty }\mid X \left ( \omega \right ) \mid ^{2}d \omega$ (rounded off to two decimal places) is ____________

asked Feb 13, 2020 in Continuous-time Signals by jothee (1.8k points) | 19 views

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51

GATE ECE 2020 | Question: 53
The transfer function of a stable discrete-time $\text{LTI}$ system is $H\left ( z \right )=\dfrac{K\left ( z-\alpha \right )}{z+0.5}$, where $K$ and $\alpha$ are real numbers. The value of $\alpha$ (rounded off to one decimal place) with $\mid \alpha \mid > 1$, for which the magnitude response of the system is constant over all frequencies, is ___________.

asked Feb 13, 2020 in Network Solution Methods by jothee (1.8k points) | 20 views

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52

GATE ECE 2020 | Question: 54
$X$ is a random variable with uniform probability density function in the interval $[-2,\:10]$. For $Y=2X-6$, the conditional probability $P\left ( Y\leq 7\mid X\geq 5 \right )$ (rounded off to three decimal places) is __________.

asked Feb 13, 2020 in Probability and Statistics by jothee (1.8k points) | 24 views

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53

GATE ECE 2020 | Question: 55
Consider the following closed loop control system where $G\left ( s \right )=\dfrac{1}{s\left ( s+1 \right )}$ and $C\left ( s \right )=K\dfrac{s+1}{s+3}$. If the steady state error for a unit ramp input is $0.1$, then the value of $K$ is ______________.

asked Feb 13, 2020 in Network Solution Methods by jothee (1.8k points) | 32 views

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54

GATE ECE 2019 | Question: 16
The value of the contour integral $\frac{1}{2\pi j} \oint\left(z+\frac{1}{z}\right)^{2}dz$ evaluated over the unit circle $\mid z \mid=1$ is_______.

asked Feb 12, 2019 in Calculus by Arjun (4.4k points) | 41 views

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55

GATE ECE 2019 | Question: 17
The number of distinct eigenvalues of the matrix $A=\begin{bmatrix} 2&2&3&3\\0&1&1&1\\0&0&3&3\\0&0&0&2 \end{bmatrix}$ is equal to ____________.

asked Feb 12, 2019 in Linear Algebra by Arjun (4.4k points) | 59 views

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56

GATE ECE 2019 | Question: 18
If $X$ and $Y$ are random variables such that $E\left[2X+Y\right]=0$ and $E\left[X+2Y\right]=33$, then $E\left[X\right]+E\left[Y\right]=$___________.

asked Feb 12, 2019 in Probability and Statistics by Arjun (4.4k points) | 38 views

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57

GATE ECE 2019 | Question: 19
The value of the integral $ \displaystyle{}\int_{0}^{\pi} \int_{y}^{\pi}\dfrac{\sin x}{x}dx\: dy ,$ is equal to __________.

asked Feb 12, 2019 in Calculus by Arjun (4.4k points) | 52 views

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58

GATE ECE 2019 | Question: 20
Let $Z$ be an exponential random variable with mean $1$. That is, the cumulative distribution function of $Z$ is given by $F_{Z}(x)= \left\{\begin{matrix} 1-e^{-x}& \text{if}\: x \geq 0 \\ 0& \text{if}\: x< 0 \end{matrix}\right.$ Then $Pr\left(Z>2 \mid Z>1\right),$ rounded off to two decimal places, is equal to ___________.

asked Feb 12, 2019 in Probability and Statistics by Arjun (4.4k points) | 78 views

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59

GATE ECE 2019 | Question: 21
Consider the signal $f(t)=1+2 \cos(\pi t)+3 \sin \left(\dfrac{2\pi}{3}t\right)+4 \cos \left(\dfrac{\pi}{2}t+\dfrac{\pi}{4}\right)$, where $t$ is in seconds. Its fundamental time period, in seconds, is __________.

asked Feb 12, 2019 in Continuous-time Signals by Arjun (4.4k points) | 46 views

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60

GATE ECE 2019 | Question: 22
The baseband signal $m(t)$ shown in the figure is phase-modulated to generate the $PM$ signal $\varphi(t)=\cos(2\pi f_{c}t+ k\:\: m(t)).$ The time $t$ on the $x-$ axis in the figure is in milliseconds. If the ... ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is _________ (rounded off to $2$ decimal places).

asked Feb 12, 2019 in Continuous-time Signals by Arjun (4.4k points) | 103 views

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61

GATE ECE 2019 | Question: 23
Radiation resistance of a small dipole current element of length $l$ at a frequency of $3$ GHz is $3$ ohms. If the length is changed by $1\%$, then the percentage change in the radiation resistance, rounded off to two decimal places, is ________ $\%.$

asked Feb 12, 2019 in Electromagnetics by Arjun (4.4k points) | 51 views

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62

GATE ECE 2019 | Question: 24
In the circuit shown, $V_{s}$ is square wave of period $T$ with maximum and minimum values of $8\: V$ and $-10\: V$, respectively. Assume that the diode is ideal and $R_{1}=R_{2}=50\: \Omega.$ The average value of $V_{L}$ is _______ volts (rounded off to $1$ decimal place).

asked Feb 12, 2019 in Electromagnetics by Arjun (4.4k points) | 78 views

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63

GATE ECE 2019 | Question: 25
In the circuit shown, the clock frequency, i.e., the frequency of the ClK signal, is $12\:kHz$. The frequency of the signal at $Q_{2}$ is _______ kHz.

asked Feb 12, 2019 in Continuous-time Signals by Arjun (4.4k points) | 74 views

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64

GATE ECE 2019 | Question: 41
The $\text{RC}$ circuit shown below has a variable resistance $R(t)$ given by the following expression: $R(t)=R_{0}\left(1-\frac{t}{T}\right) \text{for} \:\: 0 \leq t < T$ where $R_{0}=1\: \Omega,$ and $C=1\:F.$ ... $t=0$ is $1\: A,$ then the current $I(t)$, in amperes, at time $t=T/2$ is __________ (rounded off to $2$ decimal places).

asked Feb 12, 2019 in Electronic Devices by Arjun (4.4k points) | 85 views

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65

GATE ECE 2019 | Question: 42
Consider a unity feedback system, as in the figure shown, with an integral compensator $\dfrac{K}{s}$ and open-loop transfer function $G(s)=\dfrac{1}{s^{2}+3s+2}$ where $K>0.$ The positive value of $K$ for which there are exactly two poles of the unity feedback system on the $j\omega$ axis is equal to ________ (rounded off to two decimal places).

asked Feb 12, 2019 in Network Solution Methods by Arjun (4.4k points) | 24 views

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66

GATE ECE 2019 | Question: 43
Consider the homogenous ordinary differential equation $x^{2}\frac{d^{2}y}{dx^{2}}-3x\frac{dy}{dx}+3y=0, \quad x>0$ with $y(x)$ as a general solution. Given that $y(1)=1 \quad \text{and} \quad y(2)=14$ the value of $y(1.5),$ rounded off to two decimal places, is________.

asked Feb 12, 2019 in Differential Equations by Arjun (4.4k points) | 46 views

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67

GATE ECE 2019 | Question: 44
Let $h[n]$ be a length - $7$ discrete-time finite impulse response filter, given by $h[0]=4, \quad h[1]=3,\quad h[2]=2,\quad h[3]=1,$ $\quad h[-1]=-3, \quad h[-2]=-2, \quad h[-3]=-1,$ and $h[n]$ is zero for $|n|\geq4.$ A ... and $g[n],$ respectively. For the filter that minimizes $E(h,g),$ the value of $10g[-1]+g[1],$ rounded off to $2$ decimal places, is __________.

asked Feb 12, 2019 in Continuous-time Signals by Arjun (4.4k points) | 54 views

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68

GATE ECE 2019 | Question: 45
Let a random process $Y(t)$ be described as $Y(t)=h(t) \ast X(t)+Z(t),$ where $X(t)$ is a white noise process with power spectral density $S_{x}(f)=5$W/Hz. The filter $h(t)$ ... power spectral density as shown in the figure. The power in $Y(t),$ in watts, is equal to _________ $W$ (rounded off to two decimal places).

asked Feb 12, 2019 in Communications by Arjun (4.4k points) | 24 views

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69

GATE ECE 2019 | Question: 46
A voice signal $m(t)$ is in the frequency range $5\:kHz$ to $15\:kHz$. The signal is amplitude-modulated to generated an AM signal $f(t)=A\left(1+m(t)\right)\cos 2\pi f_{c}t,$ where $f_{c}=600\: kHz.$ ... for the encoding. The rate, in Megabits per second (rounded off to $2$ decimal places), of the resulting stream of coded bits is ________ Mbps.

asked Feb 12, 2019 in Communications by Arjun (4.4k points) | 56 views

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70

GATE ECE 2019 | Question: 47
A random variable $X$ takes values $-1$ and $+1$ with probabilities $0.2$ and $0.8$, respectively. It is transmitted across a channel which adds noise $N,$ so that the random variable at the channel output is $Y=X+N$. The noise $N$ is ... probability of error $Pr[ \hat{X} \neq X].$ The minimum probability of error, rounded off to $1$ decimal place, is _________.

asked Feb 12, 2019 in Probability and Statistics by Arjun (4.4k points) | 68 views

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71

GATE ECE 2019 | Question: 48
A Germanium sample of dimensions $1\: cm \times 1\: cm$ is illuminated with a $20\:mW,$ $600\: nm$ laser light source as shown in the figure. The illuminated sample surface has a $100\: nm$ of loss-less Silicon dioxide layer that reflects one-fourth ... bandgap is $0.66\: eV,$ the thickness of the Germanium layer, rounded off to $3$ decimal places, is ________ $\mu m.$

asked Feb 12, 2019 in Electromagnetics by Arjun (4.4k points) | 66 views

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72

GATE ECE 2019 | Question: 49
In an ideal $pn$ junction with an ideality factor of $1$ at $T=300\:K,$ the magnitude of the reverse-bias voltage required to reach $75\%$ of its reverse saturation current, rounded off to $2$ decimal places, is ______ $mV.$ $[k=1.38 \times 10^{-23} JK^{-1}, h=6.625 \times 10^{-34} J-s, q=1.602 \times 10^{-19}C]$

asked Feb 12, 2019 in Electronic Devices by Arjun (4.4k points) | 69 views

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73

GATE ECE 2019 | Question: 50
Consider a long-channel MOSFET with a channel length $1\:\mu m$ and width $10\: \mu m.$ The device parameters are acceptor concentration $N_{A}=5 \times 10^{16}\: cm^{-3},$ electron mobility $\mu_{n}=800\: cm^{2}/V-s,$ ... _______ $mA$ (rounded off to two decimal places.). $[\varepsilon_{0}=8.854 \times 10^{-14}F/cm, \varepsilon_{si} =11.9]$

asked Feb 12, 2019 in Electronic Devices by Arjun (4.4k points) | 31 views

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74

GATE ECE 2019 | Question: 51
A rectangular waveguide of width $w$ and height $h$ has cut-off frequencies for $TE_{10}$ and $TE_{11}$ modes in the ration $1:2$ . The aspect ratio $w/h$, rounded off to two decimal places , is _______.

asked Feb 12, 2019 in Electromagnetics by Arjun (4.4k points) | 36 views

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75

GATE ECE 2019 | Question: 52
In the circuit shown. $V_{s}$ is a $10\:V$ square wave of period, $T=4\: ms$ with $R=500\: \Omega$ and $C= 10\:\mu F.$ The capacitor is initially uncharged at $t=0,$ and the diode is assumed to be ideal. The voltage across the capacitor $(V_{c})$ at $3\:ms$ is equal to _____ volts (rounded off to one decimal place)

asked Feb 12, 2019 in Electronic Devices by Arjun (4.4k points) | 45 views

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76

GATE ECE 2019 | Question: 53
A CMOS inverter, designed to have a mid-point voltage $V_{1}$ equal to half of $V_{dd}.$ as shown in the figure, has the following parameters: $V_{dd}=3V$ $\mu_{n} C_{ox}=100\: \mu A/V^{2}; V_{tn}=0.7\:V $ for $\text{nMOS}$ ... of $\left(\frac{W}{L}\right)_{n}$ to $\left(\frac{W}{L}\right)_{p}$ is equal to _______ (rounded off to $3$ decimal places).

asked Feb 12, 2019 in Electronic Devices by Arjun (4.4k points) | 25 views

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77

GATE ECE 2019 | Question: 54
In the circuit shown, the threshold voltages of the $pMOS\:\: (|V_{tp}|)$ and $nMOS\:\: (V_{tn})$ transistors are both equal to $1\:V.$ All the transistors have the same output resistance $r_{ds}$ of $6\:M\Omega.$ The other ... area. Ignoring the effect of channel length modulation and body bias, the gain of the circuit is ______ (rounded off to $1$ decimal place).

asked Feb 12, 2019 in Electronic Devices by Arjun (4.4k points) | 19 views

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78

GATE ECE 2019 | Question: 55
In the circuit shown, $V_{1}=0$ and $V_{2}=V_{dd}.$ The other relevant parameters are mentioned in the figure. Ignoring the effect of channel length modulation and the body effect, the value of $I_{out}$ is _________ $mA$ (rounded off to $1$ decimal place).

asked Feb 12, 2019 in Communications by Arjun (4.4k points) | 18 views

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79

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

asked Mar 28, 2018 in Calculus by Milicevic3306 (15.8k points) | 30 views

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80

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 _______

asked Mar 28, 2018 in Numerical Methods by Milicevic3306 (15.8k points) | 29 views