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121
GATE ECE 2016 Set 2  Question: 28
Two random variables $X$ and $Y$ are distributed according to $f_{X,Y}(x,y)=\begin{cases} (x+y),& 0\leq x\leq 1,&0\leq y\leq 1\\ 0, & \text{otherwise.} \end{cases}$ The probability $P(X+Y\leq 1)$ is ________
asked
Mar 28, 2018
in
Probability and Statistics
by
Milicevic3306
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25
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gate2016ec2
numericalanswers
probabilityandstatistics
probability
probabilitydensityfunction
0
votes
0
answers
122
GATE ECE 2016 Set 2  Question: 34
The switch $S$ in the circuit shown has been closed for a long time. It is opened at $t = 0$ and remains open after that. Assume that the diode has zero reverse current and zero forward voltage drop. The steady state magnitude of the capacitor voltage $V_{c}$ (in volts) is ______
asked
Mar 28, 2018
in
Network Solution Methods
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Milicevic3306
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18
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gate2016ec2
numericalanswers
networksolutionmethods
diodes
steadystate
0
votes
0
answers
123
GATE ECE 2016 Set 2  Question: 37
Consider a region of silicon devoid of electrons and holes, with an ionized donor density of $N_{d}^{+}=10^{17} cm^{3}.$ The electric field at $x = 0$ is $0\: V/cm$ and the electric field at $x=L$ is $50$ $kV/cm$ in the positive $x$ direction, ... $\epsilon _{r}=11.7$ for silicon, the value of $L$ in $nm$ is ___________
asked
Mar 28, 2018
in
Electronic Devices
by
Milicevic3306
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25
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gate2016ec2
numericalanswers
electronicdevices
silicon
0
votes
0
answers
124
GATE ECE 2016 Set 2  Question: 38
Consider a longchannel $NMOS$ transistor with source and body connected together. Assume that the electron mobility is independent of $V_{GS}$ and $V_{DS}.$ ... $and$ $g_{d}=\frac{\partial I_{D}}{\partial V_{DS}}$ The threshold voltage (in volts) of the transistor is _________
asked
Mar 28, 2018
in
Analog Circuits
by
Milicevic3306
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15.8k
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86
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gate2016ec2
numericalanswers
analogcircuits
nmostransistor
0
votes
0
answers
125
GATE ECE 2016 Set 2  Question: 39
The figure shows a halfwave rectifier with a $475 \: \mu F$ filter capacitor. The load draws a constant current $I_{o}= 1 \: A$ from the rectifier. The figure also shows the input voltage $V_{i}$, the output voltage $V_{C}$ and the peaktopeak voltage ... an amplitude of $10 \: V$ and a period of $1 \: ms$. The value of the ripple $u$ (in volts) is _________
asked
Mar 28, 2018
in
Electronic Devices
by
Milicevic3306
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15.8k
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42
views
gate2016ec2
numericalanswers
electronicdevices
0
votes
0
answers
126
GATE ECE 2016 Set 2  Question: 40
In the opamp circuit shown, the Zener diodes $Z1$ and $Z2$ clamp the output voltage $V_{0}$ to $+5V$ or $5 V$. The switch $S$ is initially closed and is opened at time $t=0$. The time $t=t_{1}$ (in seconds) at which $V_{0}$ changes state is ________
asked
Mar 28, 2018
in
Electronic Devices
by
Milicevic3306
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15.8k
points)

11
views
gate2016ec2
numericalanswers
electronicdevices
zenerdiode
0
votes
0
answers
127
GATE ECE 2016 Set 2  Question: 41
An opamp has a finite open loop voltage gain of $100$. Its input offset voltage $V_{ios}(=+5mV)$ is modeled as shown in the circuit below. The amplifier is ideal in all other respects. $V_{\text{input}}$ is $25 \: mV$. The output voltage (in millivolts) is _________
asked
Mar 28, 2018
in
Analog Circuits
by
Milicevic3306
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15.8k
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11
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gate2016ec2
numericalanswers
analogcircuits
opamps
0
votes
0
answers
128
GATE ECE 2016 Set 2  Question: 45
In the feedback system shown below $G\left ( s \right )=\frac{1}{\left ( s^{2}+2s \right )}$. The step response of the closedloop system should have minimum settling time and have no overshoot. The required value of gain $k$ to achieve this is __________
asked
Mar 28, 2018
in
Analog Circuits
by
Milicevic3306
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15.8k
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9
views
gate2016ec2
numericalanswers
analogcircuits
feedback
0
votes
0
answers
129
GATE ECE 2016 Set 2  Question: 46
In the feedback system shown below $G\left ( s \right )=\frac{1}{\left ( s+1 \right )\left (s+2 \right )\left ( s+3 \right )}.$ The positive value of $k$ for which the gain margin of the loop is exactly $0$ dB and the phase margin of the loop is exactly zero degree is _________
asked
Mar 28, 2018
in
Analog Circuits
by
Milicevic3306
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15.8k
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30
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gate2016ec2
numericalanswers
analogcircuits
feedback
0
votes
0
answers
130
GATE ECE 2016 Set 2  Question: 47
The asymptotic Bode phase plot of $G\left ( s \right )=\frac{k}{\left ( s+0.1 \right )\left ( s+10 \right )\left ( s+p_{1} \right )},$ with $k$ and $p_{1}$ both positive, is shown below. The value of $p_{1}$ is _______
asked
Mar 28, 2018
in
Control Systems
by
Milicevic3306
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15.8k
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15
views
gate2016ec2
numericalanswers
controlsystems
bodeandrootlocusplots
0
votes
0
answers
131
GATE ECE 2016 Set 2  Question: 48
An information source generates a binary sequence $\left \{ \alpha _{n} \right \}$. $\alpha _{n}$ can take one of the two possible values $1$ and $+1$ with equal probability and are statistically independent and identically distributed. This sequence is precoded ... there is a null at $f=\frac{1}{3T}$ in the power spectral density of $X(t)$, then $k$ is ________
asked
Mar 28, 2018
in
Communications
by
Milicevic3306
(
15.8k
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536
views
gate2016ec2
numericalanswers
autocorrelationandpowerspectraldensity
communications
0
votes
0
answers
132
GATE ECE 2016 Set 2  Question: 49
An ideal bandpass channel $500 \: Hz –2000 \:Hz$ is deployed for communication. A modem is designed to transmit bits at the rate of $4800$ bits/s using $16QAM$. The rolloff factor of a pulse with a raised cosine spectrum that utilizes the entire frequency band is __________
asked
Mar 28, 2018
in
Communications
by
Milicevic3306
(
15.8k
points)

23
views
gate2016ec2
numericalanswers
communications
0
votes
0
answers
133
GATE ECE 2016 Set 2  Question: 50
Consider a random process $X\left ( t \right )=3V(t)8,$ where $V(t)$ is a zero mean stationary random process with autocorrelation $R_{v}\left ( \tau \right )=4e^{5\mid \tau \mid}.$ The power in $X(t)$ is _________
asked
Mar 28, 2018
in
Communications
by
Milicevic3306
(
15.8k
points)

19
views
gate2016ec2
numericalanswers
communications
autocorrelationandpowerspectraldensity
0
votes
0
answers
134
GATE ECE 2016 Set 2  Question: 51
A binary communication system makes use of the symbols zero and one . There are channel errors. Consider the following events: ... in bits that you obtain when you learn which symbol has been received (while you know that a zero has been transmitted) is _________
asked
Mar 28, 2018
in
Communications
by
Milicevic3306
(
15.8k
points)

20
views
gate2016ec2
numericalanswers
communications
0
votes
0
answers
135
GATE ECE 2016 Set 2  Question: 54
A microwave circuit consisting of lossless transmission lines $T_{1}$ and $T_{2}$ is shown in the figure. The plot shows the magnitude of the input reflection coefficient $\Gamma$ as a function of frequency $f$. The phase velocity of the signal in the transmission lines is $2\times 10^{8}$ $m/s$. The length $L$ (in meters) of $T_{2}$ is _________
asked
Mar 28, 2018
in
Electromagnetics
by
Milicevic3306
(
15.8k
points)

11
views
gate2016ec2
numericalanswers
electromagnetics
transmissionlines
0
votes
0
answers
136
GATE ECE 2016 Set 1  Question: 2
The second moment of a Poissondistributed random variable is $2$. The mean of the random variable is _____
asked
Mar 28, 2018
in
Probability and Statistics
by
Milicevic3306
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15.8k
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17
views
gate2016ec1
numericalanswers
probabilityandstatistics
probability
poissondistribution
randomvariable
0
votes
0
answers
137
GATE ECE 2016 Set 1  Question: 10
A continuoustime sinusoid of frequency $33 Hz$ is multiplied with a periodic Dirac impulse train of frequency $46Hz$. The resulting signal is passed through an ideal analog lowpass filter with a cutoff frequency of $23Hz$. The fundamental frequency (in $Hz$) of the output is _______
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)

15
views
gate2016ec1
numericalanswers
continuoustimesignals
tobetagged
0
votes
0
answers
138
GATE ECE 2016 Set 1  Question: 14
The following signal $V_i$ of peak voltage $8 \: V$ is applied to the noninverting terminal of an ideal Opamp.The transistor has $V_{EE}=0.7 \: V$, $\beta=100; \: V_{LED}=1.5 \: V$, $V_{CC}=10 \: V$ and $ – V_{CC}= – 10 \:V$. The number of times the LED glows is ________
asked
Mar 28, 2018
in
Analog Circuits
by
Milicevic3306
(
15.8k
points)

22
views
gate2016ec1
numericalanswers
analogcircuits
opamps
0
votes
0
answers
139
GATE ECE 2016 Set 1  Question: 21
Consider binary data transmission at a rate of $56$ kbps using baseband binary pulse amplitude modulation (PAM) that is designed to have a raisedcosine spectrum. The transmission bandwidth (in kHz) required for a rolloff factor of $0.25$ is ________
asked
Mar 28, 2018
in
Communications
by
Milicevic3306
(
15.8k
points)

32
views
gate2016ec1
numericalanswers
communications
modulation
0
votes
0
answers
140
GATE ECE 2016 Set 1  Question: 22
A superheterodyne receiver operates in the frequency range of $58$ MHz – $68$ MHz. The intermediate frequency $f_{IF}$ and local oscillator frequency $f_{LO}$ are chosen such that $f_{IF} \leq f_{LO}$. It is required that the image frequencies fall outside the $58$ MHz – $68$ MHz band. The minimum required $f_{IF}$ (in MHz) is _________
asked
Mar 28, 2018
in
Analog Circuits
by
Milicevic3306
(
15.8k
points)

18
views
gate2016ec1
numericalanswers
analogcircuits
oscillator
0
votes
0
answers
141
GATE ECE 2016 Set 1  Question: 23
The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude modulated signal $s(t) = 5 \cos1600 \pi t + 20 \cos 1800 \pi t + 5 \cos 2000 \pi t$. The value of the modulation index is _________
asked
Mar 28, 2018
in
Network Solution Methods
by
Milicevic3306
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15.8k
points)

20
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gate2016ec1
numericalanswers
networksolutionmethods
sinusoidalsignal
0
votes
0
answers
142
GATE ECE 2016 Set 1  Question: 24
Concentric spherical shells of radii $2$m, $4$m, and $8$ m carry uniform surface charge densities of $20 \: nC/m^2$, $ – 4 \: nC/m^2$ and $\rho_s$ respectively. The value of $\rho_s$ ($nC/m^2$) required to ensure that the electric flux density $\overrightarrow D$ = $\overrightarrow 0$ at radius $10$ m is ________
asked
Mar 28, 2018
in
Communications
by
Milicevic3306
(
15.8k
points)

15
views
gate2016ec1
numericalanswers
tobetagged
communications
0
votes
0
answers
143
GATE ECE 2016 Set 1  Question: 26
The integral $\frac{1}{2\pi} \iint_D(x+y+10) \,dx\,dy$, where $D$ denotes the disc: $x^2+y^2\leq 4$,evaluates to _________
asked
Mar 28, 2018
in
Calculus
by
Milicevic3306
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15.8k
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12
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gate2016ec1
numericalanswers
calculus
definiteintegrals
0
votes
0
answers
144
GATE ECE 2016 Set 1  Question: 27
A sequence $x[n]$ is specified as $\begin{bmatrix}x[n] \\x[n – 1]\end{bmatrix}=\begin{bmatrix}1&1\\1&0\end{bmatrix}^n\begin{bmatrix}1\\0\end{bmatrix}$,for $n \geq 2$. The initial conditions are $x[0] = 1$, $x[1] = 1$, and $x[n] = 0$ for $n < 0$. The value of $x[12]$ is _________
asked
Mar 28, 2018
in
Linear Algebra
by
Milicevic3306
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15.8k
points)

15
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gate2016ec1
numericalanswers
linearalgebra
matrices
0
votes
0
answers
145
GATE ECE 2016 Set 1  Question: 28
In the following integral, the contour $C$ encloses the points $2 \pi j$ and $ 2\pi j$ $\frac{1}{2\pi}\oint_C\frac{\sin z}{(z2\pi j)^3} \,dz$ The value of the integral is _________
asked
Mar 28, 2018
in
Complex Analysis
by
Milicevic3306
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15.8k
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20
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gate2016ec1
numericalanswers
complexanalysis
0
votes
0
answers
146
GATE ECE 2016 Set 1  Question: 29
The region specified by $\{ (\rho,\varphi,z):3 \leq\rho\leq 5,\frac{\pi}{8}\leq\varphi\leq\frac{\pi}{4}, \: 3\leq z\leq4.5\}$ in cylindrical coordinates has volume of _________
asked
Mar 28, 2018
in
Vector Analysis
by
Milicevic3306
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15.8k
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24
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gate2016ec1
numericalanswers
vectoranalysis
0
votes
0
answers
147
GATE ECE 2016 Set 1  Question: 33
An AC voltage source $V = 10 \sin(t)$ volts is applied to the following network. Assume that $R_1 = 3 k\Omega$, $R_2 = 6 k\Omega$ and $R_3 = 9k\Omega$, and that the diode is ideal. RMS current $I_{rms}$(in mA) through the diode is _______
asked
Mar 28, 2018
in
Analog Circuits
by
Milicevic3306
(
15.8k
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17
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gate2016ec1
numericalanswers
analogcircuits
0
votes
0
answers
148
GATE ECE 2016 Set 1  Question: 34
In the circuit shown in the figure, the maximum power (in watt) delivered to the resistor $R$ is _______
asked
Mar 28, 2018
in
Analog Circuits
by
Milicevic3306
(
15.8k
points)

31
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gate2016ec1
numericalanswers
analogcircuits
0
votes
0
answers
149
GATE ECE 2016 Set 1  Question: 35
Consider the signal $x[n] = 6 \delta[n + 2] + 3 \delta[n + 1] + 8 \delta[n] + 7 \delta[n  1] + 4 \delta[n  2]$ If $X(e^{jw})$ is the discretetime Fourier transform of $x[n]$, then $\frac{1}{\pi} \int\limits_{\pi}^{\pi} X(e^{jw}) \sin^2(2\omega) d\omega$ is equal to _______
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)

14
views
gate2016ec1
numericalanswers
continuoustimesignals
signalsandsystems
fouriertransform
0
votes
0
answers
150
GATE ECE 2016 Set 1  Question: 36
Consider a silicon $pn$ junction with a uniform acceptor doping concentration of $10^{17} cm^{3}$ on the $p$side and a uniform donor doping concentration of $10^{16}cm^{3}$ on the $n$ ... $nC \: cm^{2}$) in the depletion region on the $p$side is _________
asked
Mar 28, 2018
in
Electronic Devices
by
Milicevic3306
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15.8k
points)

22
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gate2016ec1
numericalanswers
electronicdevices
pnjunction
0
votes
0
answers
151
GATE ECE 2016 Set 1  Question: 37
Consider an $n$channel metal oxide semiconductor field effect transistor (MOSFET) with a gatetosource voltage of $1.8$ V. Assume that $\frac{W}{L}=4$, $\mu_NC_{ox}= 70 \times 10^{6} AV^{2}$ ... channel length modulation parameter is $0.09 \: V^{1}$. In the saturation region, the drain conductance (in micro siemens) is _________
asked
Mar 28, 2018
in
Electronic Devices
by
Milicevic3306
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15.8k
points)

13
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gate2016ec1
numericalanswers
electronicdevices
mosfet
0
votes
0
answers
152
GATE ECE 2016 Set 1  Question: 38
The figure below shows the doping distribution in a $p$type semiconductor in log scale. The magnitude of the electric field (in $kV/cm$) in the semiconductor due to non uniform doping is _________
asked
Mar 28, 2018
in
Electronic Devices
by
Milicevic3306
(
15.8k
points)

28
views
gate2016ec1
numericalanswers
digitalcircuits
semiconductor
0
votes
0
answers
153
GATE ECE 2016 Set 1  Question: 40
An ideal opamp has voltage sources $V_1, V_3, V_5, \dots, V_{N1}$ connected to the noninverting input and $V_2, V_4, V_6, \dots, V_N$ connected to the inverting input as shown in the figure below $(+V_{CC}= 15$ volt, $  V_{CC} =  15$ volt ... $N$ approaches infinity, the output voltage (in volt) is _________
asked
Mar 28, 2018
in
Analog Circuits
by
Milicevic3306
(
15.8k
points)

9
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gate2016ec1
numericalanswers
analogcircuits
opamps
0
votes
0
answers
154
GATE ECE 2016 Set 1  Question: 41
A $pin$ photodiode of responsivity $0.8 \: A/W$ is connected to the inverting input of an ideal opamp as shown in the figure, $+V_{CC}= 15 V, \: – V_{CC} = – 15 V$, Load resistor $R_L=10k\Omega$. If $10 \mu W$ of power is incident on the photodiode, then the value of the photocurrent(in $\mu A$) through the load is _________
asked
Mar 28, 2018
in
Electronic Devices
by
Milicevic3306
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15.8k
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13
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gate2016ec1
numericalanswers
electronicdevices
photodiode
0
votes
0
answers
155
GATE ECE 2016 Set 1  Question: 45
The openloop transfer function of a unityfeedback control system is $G(s)= \frac{K}{s^2+5s+5}$. The value of $K$ at the breakaway point of the feedback contol system’s rootlocus plot is _________
asked
Mar 28, 2018
in
Network Solution Methods
by
Milicevic3306
(
15.8k
points)

14
views
gate2016ec1
numericalanswers
networksolutionmethods
transferfunction
bodeandrootlocusplots
0
votes
0
answers
156
GATE ECE 2016 Set 1  Question: 46
The openloop transfer function of a unity feedback control system is given by $G(s)= \frac{K}{s(s+2)}$. For the peak overshoot of the closedloop system to a unit step input to be $10 \%$, the value of $K$ is _________
asked
Mar 28, 2018
in
Network Solution Methods
by
Milicevic3306
(
15.8k
points)

13
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gate2016ec1
numericalanswers
networksolutionmethods
transferfunction
0
votes
0
answers
157
GATE ECE 2016 Set 1  Question: 47
The transfer function of a linear time invariant system is given by $H(s) = 2s^4 – 5s^3 + 5s 2$. The number of zeroes in the right half of the $s$plane is _________
asked
Mar 28, 2018
in
Network Solution Methods
by
Milicevic3306
(
15.8k
points)

10
views
gate2016ec1
numericalanswers
networksolutionmethods
transferfunction
0
votes
0
answers
158
GATE ECE 2016 Set 1  Question: 48
Consider a discrete memoryless source with alphabet $S = \{s_0,s_1,s_2,s_3,s_4, \dots \}$ and respective probabilities of occurence $P = \bigg\{ \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \dots \bigg\}$. The entropy of the source (in bits) is _________
asked
Mar 28, 2018
in
Probability and Statistics
by
Milicevic3306
(
15.8k
points)

21
views
gate2016ec1
numericalanswers
probabilityandstatistics
probability
0
votes
0
answers
159
GATE ECE 2016 Set 1  Question: 49
A digital communication system uses a repetition code for channel encoding/decoding. During transmission, each bit is repeated three times ($0$ is transmitted as $000$, and $1$ is transmitted as $111$). It is assumed that the source puts ... a $1$. Assuming a binary symmetric channel with crossover probability $p=0.1$, the average probability of error is _________
asked
Mar 28, 2018
in
Communications
by
Milicevic3306
(
15.8k
points)

59
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gate2016ec1
numericalanswers
digitalcommunications
communications
0
votes
0
answers
160
GATE ECE 2016 Set 1  Question: 53
Two lossless Xband horn antennas are separated by a distance of $200 \lambda$. The amplitude reflection coefficients at the terminals of the transmitting and receiving antennas are $0.15$ and $0.18$,respectively. The maximum directives of ... are perfectly aligned and polarization matched, the power ( in mW) delivered to the load at the receiver is _________
asked
Mar 28, 2018
in
Electromagnetics
by
Milicevic3306
(
15.8k
points)

18
views
gate2016ec1
numericalanswers
electromagnetics
antennas
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