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2881
GATE ECE 2018 | Question: 52
Let $r=x^{2}+y-z$ and $z^{3}-xy+yz+y^{3}=1.$ Assume that $x$ and $y$ are independent variables. At $\left( x,y,z \right)=\left ( 2,-1,1 \right ),$ the value (correct to two decimal places) of $\dfrac{\partial r}{\partial x}$ is _________ .
Let $r=x^{2}+y-z$ and $z^{3}-xy+yz+y^{3}=1.$ Assume that $x$ and $y$ are independent variables. At $\left( x,y,z \right)=\left ( 2,-1,1 \right ),$ the value (correct to t...
gatecse
1.6k
points
121
views
gatecse
asked
Feb 19, 2018
Calculus
gate2018-ec
numerical-answers
calculus
partial-derivatives
+
–
0
votes
0
answers
2882
GATE ECE 2018 | Question: 53
Consider the network shown below with $R_{1}=1\:\Omega,R_{2}=2\:\Omega$ and $R_{3}=3\:\Omega.$ The network is connected to a constant voltage source of $11\:V$. The magnitude of the current (in amperes, accurate to two decimal places ) through the source is _________.
Consider the network shown below with $R_{1}=1\:\Omega,R_{2}=2\:\Omega$ and $R_{3}=3\:\Omega.$ The network is connected to a constant voltage source of $11\:V$. ...
gatecse
1.6k
points
148
views
gatecse
asked
Feb 19, 2018
Network Solution Methods
gate2018-ec
numerical-answers
network-solution-methods
+
–
0
votes
0
answers
2883
GATE ECE 2018 | Question: 54
A band limited low-pass signal $x(t)$ of bandwidth $5\:kHz$ is sampled at a sampling rate $f_{s}$.The signal $x(t)$ is reconstructed using the reconstruction filter $H(f)$ whose magnitude response is shown below: The minimum sampling rate $f_{s}(\text{in}\: kHz)$ for perfect reconstruction of $x(t)$ is ________.
A band limited low-pass signal $x(t)$ of bandwidth $5\:kHz$ is sampled at a sampling rate $f_{s}$.The signal $x(t)$ is reconstructed using the reconstruction filter $H(f)...
gatecse
1.6k
points
103
views
gatecse
asked
Feb 19, 2018
Continuous-time Signals
gate2018-ec
numerical-answers
continuous-time-signals
signals-and-systems
sampling-theorem
+
–
0
votes
0
answers
2884
GATE ECE 2018 | Question: 37
A $dc$ current of $26\:\mu A$ flows through the circuit shown. The diode in the circuit is forward biased and it has an ideality factor of one. At the quiescent point, the diode has a junction capacitance of $0.5\:nF$. Its neutral region ... $\mu A$, correct to one decimal place) is __________.
A $dc$ current of $26\:\mu A$ flows through the circuit shown. The diode in the circuit is forward biased and it has an ideality factor of one. At the quiescent point, th...
gatecse
1.6k
points
310
views
gatecse
asked
Feb 19, 2018
Analog Circuits
gate2018-ec
numerical-answers
analog-circuits
+
–
0
votes
0
answers
2885
GATE ECE 2018 | Question: 38
An op-amp based circuit is implemented as shown below. In the above circuit, assume the op-amp to be ideal. The voltage (in volts, correct to one decimal place) at node $A$, connected to the negative input of the op-amp as indicated in the figure is ________.
An op-amp based circuit is implemented as shown below. In the above circuit, assume the op-amp to be ideal. The voltage (in volt...
gatecse
1.6k
points
215
views
gatecse
asked
Feb 19, 2018
Analog Circuits
gate2018-ec
numerical-answers
analog-circuits
op-amps
+
–
0
votes
0
answers
2886
GATE ECE 2018 | Question: 39
The input $4\sin c(2t)$ is fed to a Hilbert transformer to obtain $y( t),$ as shown in the figure below: Here $\sin c \left ( x\right )=\dfrac{\sin\left ( \pi x \right )}{\pi x}.$ The value (accurate to two decimal places) of $\int ^{\infty }_{-\infty } \mid y( t ) \mid ^{2}dt$ is ________.
The input $4\sin c(2t)$ is fed to a Hilbert transformer to obtain $y( t),$ as shown in the figure below: Here $\sin c \left...
gatecse
1.6k
points
148
views
gatecse
asked
Feb 19, 2018
Continuous-time Signals
gate2018-ec
numerical-answers
hilbert-transformer
+
–
0
votes
0
answers
2887
GATE ECE 2018 | Question: 40
A random variable $X$ takes values $-0.5$ and $0.5$ with probabilities $\dfrac{1}{4}$ and $\dfrac{3}{4}$, respectively. The noisy observation of $X\:\text{is}\:Y=X+Z,$ where $Z$ ... $\alpha$ (accurate to two decimal places) is ________.
A random variable $X$ takes values $-0.5$ and $0.5$ with probabilities $\dfrac{1}{4}$ and $\dfrac{3}{4}$, respectively. The noisy observation of $X\:\text{is}\:Y=X+Z,$ wh...
gatecse
1.6k
points
210
views
gatecse
asked
Feb 19, 2018
Probability and Statistics
gate2018-ec
numerical-answers
probability-and-statistics
propability
random-variable
+
–
0
votes
0
answers
2888
GATE ECE 2018 | Question: 41
For a unity feedback control system with the forward path transfer function $G\left ( s \right )=\dfrac{K}{s\left ( s+2 \right )}$The peak resonant magnitude $M_{r}$ of the closed-loop frequency response is $2$. The corresponding value of the gain $\text{K}$ (correct to two decimal places) is _________.
For a unity feedback control system with the forward path transfer function$$G\left ( s \right )=\dfrac{K}{s\left ( s+2 \right )}$$The peak resonant magnitude $M_{r}$ of ...
gatecse
1.6k
points
136
views
gatecse
asked
Feb 19, 2018
Network Solution Methods
gate2018-ec
numerical-answers
network-solution-methods
transfer-function
+
–
0
votes
1
answer
2889
GATE ECE 2018 | Question: 42
The figure below shows the Bode magnitude and phase plots of a stable transfer function $G\left ( s \right )=\dfrac{n_{0}}{s^{3}+d_{2}s^{2}+d_{1}s+d_{0}}.$ Consider the negative unity feedback configuration with gain $k$ in the feedforward path. The closed loop is stable for $k < k_{0}.$ The maximum value of $k_{0}$ is _________.
The figure below shows the Bode magnitude and phase plots of a stable transfer function $G\left ( s \right )=\dfrac{n_{0}}{s^{3}+d_{2}s^{2}+d_{1}s+d_{0}}.$Consider the ne...
gatecse
1.6k
points
462
views
gatecse
asked
Feb 19, 2018
Network Solution Methods
gate2018-ec
numerical-answers
network-solution-methods
transfer-function
+
–
0
votes
0
answers
2890
GATE ECE 2018 | Question: 43
In the circuit shown below, the $(W/L)$ value for $M_{2}$ is twice that for $M_{1}$. The two $\text{nMOS}$ transistors are otherwise identical. The threshold voltage $V_{T}$ for both transistors is $1.0\:V$. Note that $V_{GS}$ for $M_{2}$ ... $V_{x}$ is ________.
In the circuit shown below, the $(W/L)$ value for $M_{2}$ is twice that for $M_{1}$. The two $\text{nMOS}$ transistors are otherwise identical. The threshold voltage $V_{...
gatecse
1.6k
points
130
views
gatecse
asked
Feb 19, 2018
Analog Circuits
gate2018-ec
numerical-answers
analog-circuits
nmos-transistor
+
–
0
votes
0
answers
2891
GATE ECE 2018 | Question: 44
A solar cell of area $1.0\:cm^{2},$ operating at $1.0$ sun intensity, has a short circuit current of $20\: mA$, and an open circuit voltage of $0.65\: V$. Assuming room temperature operation and thermal equivalent voltage of $26\: mV$, the open circuit voltage (in volts, correct to two decimal places) at $0.2$ sun intensity is _________.
A solar cell of area $1.0\:cm^{2},$ operating at $1.0$ sun intensity, has a short circuit current of $20\: mA$, and an open circuit voltage of $0.65\: V$. Assuming room t...
gatecse
1.6k
points
150
views
gatecse
asked
Feb 19, 2018
Electronic Devices
gate2018-ec
numerical-answers
electronic-devices
+
–
0
votes
0
answers
2892
GATE ECE 2018 | Question: 45
A junction is made between $p^{-Si}$ with doping density $N_{A1}=10^{15}cm^{-3}$ and $p^{Si}$ with doping density $N_{A2}=10^{17}cm^{-3}.$ Given: Boltzmann constant $k=1.38\times 10^{-23}J\cdot K^{-1},$ electronic charge ... the magnitude of the built-in potential (in volts, correct to two decimal places) across this junction will be __________.
A junction is made between $p^{-Si}$ with doping density $N_{A1}=10^{15}cm^{-3}$ and $p^{Si}$ with doping density $N_{A2}=10^{17}cm^{-3}.$ Given: Boltzmann constant $k=1....
gatecse
1.6k
points
169
views
gatecse
asked
Feb 19, 2018
Digital Circuits
gate2018-ec
numerical-answers
boltzman-constant
doping
digital-circuits
+
–
0
votes
0
answers
2893
GATE ECE 2018 | Question: 28
Consider a white Gaussian noise process $\text{N(t)}$ with two-sided power spectral density $S_{N}\left ( f \right )=0.5\:W/Hz$ as input to a filter with impulse response $0.5e^{-t^{2}/2}$ (where $t$ is in seconds) resulting in output $Y(t)$. The power in $Y(t)$ in watts is $0.11$ $0.22$ $0.33$ $0.44$
Consider a white Gaussian noise process $\text{N(t)}$ with two-sided power spectral density $S_{N}\left ( f \right )=0.5\:W/Hz$ as input to a filter with impulse response...
gatecse
1.6k
points
168
views
gatecse
asked
Feb 19, 2018
Communications
gate2018-ec
gaussian-noise
autocorrelation-and-power-spectral-density
communications
+
–
0
votes
0
answers
2894
GATE ECE 2018 | Question: 29
The state equation and the output equation of a control system are given below: $\dot{x}=\begin{bmatrix} -4 & -1.5\\ 4& 0 \end{bmatrix}x+\begin{bmatrix} 2\\ 0 \end{bmatrix}u,$ $y=\begin{bmatrix} 1.5 & 0.625 \end{bmatrix}x.$ The transfer function representation of the ... $\dfrac{4s+1.5}{s^{2}+4s+6}$ $\dfrac{6s+5}{s^{2}+4s+6}$
The state equation and the output equation of a control system are given below:$\dot{x}=\begin{bmatrix} -4 & -1.5\\ 4& 0 \end{bmatrix}x+\begin{bmatrix} 2\\ 0 \end{bmatrix...
gatecse
1.6k
points
167
views
gatecse
asked
Feb 19, 2018
Network Solution Methods
gate2018-ec
network-solution-methods
state-equations
+
–
0
votes
0
answers
2895
GATE ECE 2018 | Question: 30
Red (R), Green(G) and Blue (B) Light Emitting Diodes (LEDs) were fabricated using $\text{p-n}$ junctions of three different inorganic semiconductors having different band-gaps. The built-in voltages of red,green and blue diodes are $V_{R}$, $V_{G}$ and $V_{B},$respectively. Assume donor ... $V_{R}<V_{G}<V_{B}$ $V_{R}=V_{G}=V_{B}$ $V_{R}>V_{G}<V_{B}$
Red (R), Green(G) and Blue (B) Light Emitting Diodes (LEDs) were fabricated using $\text{p-n}$ junctions of three different inorganic semiconductors having different band...
gatecse
1.6k
points
163
views
gatecse
asked
Feb 19, 2018
Electronic Devices
gate2018-ec
electronic-devices
p-n-junction
+
–
2
votes
1
answer
2896
GATE ECE 2018 | Question: 31
A four-variable Boolean function is realized using $4\times 1$ multiplexers as shown in the figure. The minimized expression for $\text{F(U,V,W,X)}$ is $\left ( UV+\overline{U}\:\overline{V}\right )\overline{W}$ ... $\left ( U\:\overline{V}+\overline{U}\:V\right )\left (\overline{W}\: \overline{X}+\overline{W}\:X\right )$
A four-variable Boolean function is realized using $4\times 1$ multiplexers as shown in the figure.The minimized expression for $\text{F(U,V,W,X)}$ is $\left ( UV+\overli...
gatecse
1.6k
points
484
views
gatecse
asked
Feb 19, 2018
Number Representations
gate2018-ec
digital-circuits
combinational-circuits
multiplexers
+
–
0
votes
0
answers
2897
GATE ECE 2018 | Question: 32
A $2\times 2$ ROM array is built with the help of diodes as shown in the circuit below. Here $W0$ and $W1$ are signals that select the word lines and $B0$ and $B1$ are signals that are output of the sense amps based on the stored data corresponding to the ... $\begin{bmatrix} 1 &0 \\ 1&0 \end{bmatrix}$ $\begin{bmatrix} 1 &1 \\ 0&0 \end{bmatrix}$
A $2\times 2$ ROM array is built with the help of diodes as shown in the circuit below. Here $W0$ and $W1$ are signals that select the word lines and $B0$ and $B1$ are si...
gatecse
1.6k
points
253
views
gatecse
asked
Feb 19, 2018
Diode Circuits
gate2018-ec
digital-circuits
rom
+
–
0
votes
0
answers
2898
GATE ECE 2018 | Question: 33
The distance (in meters) a wave has to propagate in a medium having a skin depth of $0.1\:m$ so that the amplitude of the wave attenuates by $20\:dB$, is $0.12$ $0.23$ $0.46$ $2.3$
The distance (in meters) a wave has to propagate in a medium having a skin depth of $0.1\:m$ so that the amplitude of the wave attenuates by $20\:dB$, is $0.12$$0.23$$0.4...
gatecse
1.6k
points
125
views
gatecse
asked
Feb 19, 2018
Analog Circuits
gate2018-ec
analog-circuits
+
–
0
votes
0
answers
2899
GATE ECE 2018 | Question: 34
A curve passes through the point $\left ( x=1,y=0 \right )$ and satisfies the differential equation $\dfrac{\mathrm{dy} }{\mathrm{d} x}=\dfrac{x^{2}+y^{2}}{2y}+\dfrac{y}{x}.$ The equation that describes the curve is $\ln\left (1+\dfrac{y^{2}}{x^{2}}\right)=x-1$ ... $\ln\left (1+\dfrac{y}{x}\right)=x-1$ $\dfrac{1}{2}\ln\left (1+\dfrac{y}{x}\right)=x-1$
A curve passes through the point $\left ( x=1,y=0 \right )$ and satisfies the differential equation $\dfrac{\mathrm{dy} }{\mathrm{d} x}=\dfrac{x^{2}+y^{2}}{2y}+\dfrac{y}{...
gatecse
1.6k
points
127
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
differential-equations
+
–
0
votes
0
answers
2900
GATE ECE 2018 | Question: 35
For the circuit given in the figure, the voltage $V_{c}$ (in volts) across the capacitor is $1.25\sqrt{2}\sin\left ( 5t-0.25\pi \right )$ $1.25\sqrt{2}\sin\left ( 5t-0.125\pi \right )$ $2.5\sqrt{2}\sin\left ( 5t-0.25\pi \right )$ $2.5\sqrt{2}\sin\left ( 5t-0.125\pi \right )$
For the circuit given in the figure, the voltage $V_{c}$ (in volts) across the capacitor is $1.25\sqrt{2}\sin\left ( 5t-0.25\pi \...
gatecse
1.6k
points
107
views
gatecse
asked
Feb 19, 2018
Analog Circuits
gate2018-ec
analog-circuits
+
–
0
votes
0
answers
2901
GATE ECE 2018 | Question: 36
For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) $0.5$ second after closing the switch is _______.
For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) $0.5$ second after closing the switch is _______.
gatecse
1.6k
points
187
views
gatecse
asked
Feb 19, 2018
Analog Circuits
gate2018-ec
numerical-answers
analog-circuits
+
–
0
votes
0
answers
2902
GATE ECE 2018 | Question: 19
A traffic signal cycles from $\text{ GREEN to YELLOW, YELLOW to RED and RED to GREEN.}$ In each cycle, $\text{GREEN}$ is turned on for $70$ seconds,$\text{YELLOW}$ is turned on for $5$ seconds and the $\text{RED}$ is turned on $75$ ... $5$ second period. The minimum number of flip-flops required to implement this $\text{FSM}$ is _________.
A traffic signal cycles from $\text{ GREEN to YELLOW, YELLOW to RED and RED to GREEN.}$ In each cycle, $\text{GREEN}$ is turned on for $70$ seconds,$\text{YELLOW}$ is tur...
gatecse
1.6k
points
153
views
gatecse
asked
Feb 19, 2018
Digital Circuits
gate2018-ec
numerical-answers
digital-circuits
sequential-circuit
flip-flops
+
–
0
votes
0
answers
2903
GATE ECE 2018 | Question: 20
There are two photolithography systems: one with light source of wavelength $\lambda _{1}=156\:nm$ (System $1$) and another with light source of wavelength $\lambda _{2}=325\:nm$ (System $2$). Both photolithography systems are otherwise identical. If ... $L_{min2}$ respectively, the ratio $L_{min1}/L_{min2}$ (correct to two decimal places) is __________.
There are two photolithography systems: one with light source of wavelength $\lambda _{1}=156\:nm$ (System $1$) and another with light source of wavelength $\lambda _{2}=...
gatecse
1.6k
points
115
views
gatecse
asked
Feb 19, 2018
Electronic Devices
gate2018-ec
numerical-answers
electronic-devices
photolithography
+
–
0
votes
0
answers
2904
GATE ECE 2018 | Question: 21
A lossy transmission line has resistance per unit length $R=0.05\:\Omega/m.$ The line is distortionless and has characteristic impedance of $50\:\Omega.$ The attenuation constant (in $\text{Np/m}$, correct to three decimal places) of the line is ________.
A lossy transmission line has resistance per unit length $R=0.05\:\Omega/m.$ The line is distortionless and has characteristic impedance of $50\:\Omega.$ The attenuation ...
gatecse
1.6k
points
148
views
gatecse
asked
Feb 19, 2018
Electromagnetics
gate2018-ec
numerical-answers
impedance
electromagnetics
+
–
0
votes
0
answers
2905
GATE ECE 2018 | Question: 22
Consider matrix $A=\begin{bmatrix} k & 2k\\ k^{2}-k & k^{2} \end{bmatrix}$ and vector $x=\begin{bmatrix} x_{1}\\ x_{2} \end{bmatrix}.$ The number of distinct real value of $k$ for which the equation $Ax=0$ has infinitely many solutions is _________.
Consider matrix $A=\begin{bmatrix} k & 2k\\ k^{2}-k & k^{2} \end{bmatrix}$ and vector $x=\begin{bmatrix} x_{1}\\ x_{2} \end{bmatrix}.$ The number of distinct real value o...
gatecse
1.6k
points
103
views
gatecse
asked
Feb 19, 2018
Linear Algebra
gate2018-ec
numerical-answers
linear-algebra
system-of-equations
+
–
0
votes
0
answers
2906
GATE ECE 2018 | Question: 23
Let $X_{1},\:X_{2},\:X_{3}$ and $X_{4}$ be independent normal random variable with zero mean and unit variance. The probability that $X_{4}$ is the smallest among the four is ________.
Let $X_{1},\:X_{2},\:X_{3}$ and $X_{4}$ be independent normal random variable with zero mean and unit variance. The probability that $X_{4}$ is the smallest among the fou...
gatecse
1.6k
points
157
views
gatecse
asked
Feb 19, 2018
Probability and Statistics
gate2018-ec
numerical-answers
probability-and-statistics
probability
random-variable
variance
+
–
0
votes
0
answers
2907
GATE ECE 2018 | Question: 24
Taylor series expansion of $f\left ( x \right )=\int ^{x}_{0}e^{-\left ( \frac{t^{2}}{2} \right )}dt$ around $x=0$ has the form $f\left ( x \right )={a}_{0}+a_{1}x+a_{2}x^{2}+...$ The coefficient $a_{2}$ (correct to two decimal places) is equal to ________.
Taylor series expansion of $f\left ( x \right )=\int ^{x}_{0}e^{-\left ( \frac{t^{2}}{2} \right )}dt$ around $x=0$ has the form $$f\left ( x \right )={a}_{0}+a_{1}x+a_{2}...
gatecse
1.6k
points
186
views
gatecse
asked
Feb 19, 2018
Calculus
gate2018-ec
numerical-answers
calculus
taylor-series
+
–
0
votes
0
answers
2908
GATE ECE 2018 | Question: 25
The $\text{ABCD}$ matrix for a two-port network is defined by: $\begin{bmatrix} V_{1}\\ I_{1} \end{bmatrix}=\begin{bmatrix} A &B \\ C& D \end{bmatrix}\begin{bmatrix} V_{2}\\ -I_{2} \end{bmatrix}$ The parameter $\text{B}$ for the given two-port network (in ohms, correct to two decimal places) is _________.
The $\text{ABCD}$ matrix for a two-port network is defined by:$$\begin{bmatrix} V_{1}\\ I_{1} \end{bmatrix}=\begin{bmatrix} A &B \\ C& D \end{bmatrix}\begin{bmatrix} V_{2...
gatecse
1.6k
points
219
views
gatecse
asked
Feb 19, 2018
Network Solution Methods
gate2018-ec
numerical-answers
two-port-network
network-solution-methods
+
–
0
votes
0
answers
2909
GATE ECE 2018 | Question: 26
The circuit shown in the figure is used to provide regulated voltage $(5 V)$ across the $1\: k\Omega$ resistor. Assume that the Zener diode has a constant reverse breakdown voltage for a current range, starting from a minimum required Zener current, $I_{Z min}=2\:mA$ to its ... $10\:mW$ $100\:\Omega$ and $40\:mW$ $100\:\Omega$ and $10\:mW$ $186\:\Omega$ and $40\:mW$
The circuit shown in the figure is used to provide regulated voltage $(5 V)$ across the $1\: k\Omega$ resistor. Assume that the Zener diode has a constant reverse breakdo...
gatecse
1.6k
points
116
views
gatecse
asked
Feb 19, 2018
Electronic Devices
gate2018-ec
electronic-devices
zener-diode
+
–
0
votes
0
answers
2910
GATE ECE 2018 | Question: 27
Let $c\left ( t \right )=A_{c} \cos \left ( 2\pi f_{c}t\right )$ and $m\left ( t \right )=\cos \left ( 2\pi f_{m}t\right )$. It is given that $f_{c}>> 5f_{m}.$ The signal $c\left ( t \right )+m\left ( t \right )$ is applied to ... wave. If it is desired to have the sideband power of the AM wave to be half of the carrier power, then $a/b$ is $0.25$ $0.5$ $1$ $2$
Let $c\left ( t \right )=A_{c} \cos \left ( 2\pi f_{c}t\right )$ and $m\left ( t \right )=\cos \left ( 2\pi f_{m}t\right )$. It is given that $f_{c}> 5f_{m}.$ The signal ...
gatecse
1.6k
points
109
views
gatecse
asked
Feb 19, 2018
Communications
gate2018-ec
communications
amplitude-modulation
+
–
0
votes
0
answers
2911
GATE ECE 2018 | Question: 10
The points $\text{P, Q, and R}$ shown on the Smith chart (normalized impedance chart) in the following figure represent: $\text{P: Open Circuit, Q: Short Circuit, R: Matched Load}$ $\text{P: Open Circuit, Q: Matched Load, R: Short Circuit}$ $\text{P: Short Circuit, Q: Matched Load, R: Open Circuit}$ $\text{P: Short Circuit, Q: Open Circuit, R: Matched Load}$
The points $\text{P, Q, and R}$ shown on the Smith chart (normalized impedance chart) in the following figure represent: $\text{P: Open Circu...
gatecse
1.6k
points
151
views
gatecse
asked
Feb 19, 2018
Electromagnetics
gate2018-ec
electromagnetics
impedance
+
–
0
votes
0
answers
2912
GATE ECE 2018 | Question: 11
Let $\text{M}$ be a real $4\times 4$ matrix. Consider the following statements: $S1: M $ has $4$ linearly independent eigenvectors. $S2: M$ has $4$ distinct eigenvalues. $S3: M$ is non-singular (invertible). Which one among the following is TRUE? $S1$ implies $S2$ $S1$ implies $S3$ $S2$ implies $S1$ $S3$ implies $S2$
Let $\text{M}$ be a real $4\times 4$ matrix. Consider the following statements:$S1: M $ has $4$ linearly independent eigenvectors.$S2: M$ has $4$ distinct eigenvalues. $S...
gatecse
1.6k
points
119
views
gatecse
asked
Feb 19, 2018
Linear Algebra
gate2018-ec
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
2913
GATE ECE 2018 | Question: 12
Let $f\left ( x,y \right )=\dfrac{ax^{2}+by^{2}}{xy},$ where $a$ and $b$ are constants. If $\dfrac{\partial f}{\partial x}=\dfrac{\partial f}{\partial y}$ at $x = 1$ and $y = 2$, then the relation between $a$ and $b$ is $a=\dfrac{b}{4}$ $a=\dfrac{b}{2}$ $a=2b$ $a=4b$
Let $f\left ( x,y \right )=\dfrac{ax^{2}+by^{2}}{xy},$ where $a$ and $b$ are constants. If $\dfrac{\partial f}{\partial x}=\dfrac{\partial f}{\partial y}$ at $x = 1$ and ...
gatecse
1.6k
points
109
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
differential-equations
partial-differential-equations
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–
0
votes
0
answers
2914
GATE ECE 2018 | Question: 13
A discrete-time all-pass system has two of its poles at $0.25\angle 0^{\circ}$ and $2\angle 30^{\circ}$. Which one of the following statements about the system is TRUE? It has two more poles at $0.5\angle 30^{\circ}$ and ... response is two-sided. It has constant phase response over all frequencies. It has constant phase response over the entire $\text{z-plane}$.
A discrete-time all-pass system has two of its poles at $0.25\angle 0^{\circ}$ and $2\angle 30^{\circ}$. Which one of the following statements about the system is TRUE?It...
gatecse
1.6k
points
151
views
gatecse
asked
Feb 19, 2018
Continuous-time Signals
gate2018-ec
continuous-time-signals
impulse-response
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–
0
votes
0
answers
2915
GATE ECE 2018 | Question: 14
Let $\text{x(t)}$ be a periodic function with period $\text{T = 10}$.The Fourier series coefficients for this series are denoted by $a_{k},$ that is $x\left ( t \right )=\sum ^{\infty }_{k=-\infty }a_{k}e^{jk\:\frac{2\pi }{T}t}$ The same function $x(t)$ can also ... $\sum _{k=-\infty}^{\infty } \mid b_{k} \mid$ is equal to $256$ $64$ $16$ $4$
Let $\text{x(t)}$ be a periodic function with period $\text{T = 10}$.The Fourier series coefficients for this series are denoted by $a_{k},$ that is$$x\left ( t \right )=...
gatecse
1.6k
points
234
views
gatecse
asked
Feb 19, 2018
Continuous-time Signals
gate2018-ec
continuous-time-signals
signals-and-systems
fourier-transform
+
–
0
votes
2
answers
2916
GATE ECE 2018 | Question: 15
Consider the following amplitude modulated signal: $s\left ( t \right )=\cos\left ( 2000\:\pi t \right )+4\cos\left ( 2400\:\pi t \right )+ \cos\left ( 2800\:\pi t \right ).$The ratio (accurate to three decimal places) of the power of the message signal to the power of the carrier signal is _________.
Consider the following amplitude modulated signal:$$s\left ( t \right )=\cos\left ( 2000\:\pi t \right )+4\cos\left ( 2400\:\pi t \right )+ \cos\left ( 2800\:\pi t \right...
gatecse
1.6k
points
280
views
gatecse
asked
Feb 19, 2018
Communications
gate2018-ec
numerical-answers
communications
amplitude-modulation
+
–
0
votes
0
answers
2917
GATE ECE 2018 | Question: 16
Consider a binary channel code in which each codeword has a fixed length of $5\: bits$. The Hamming distance between any pair of distinct codewords in this code is at least $2$. The maximum number of codewords such a code can contain is __________.
Consider a binary channel code in which each codeword has a fixed length of $5\: bits$. The Hamming distance between any pair of distinct codewords in this code is at le...
gatecse
1.6k
points
150
views
gatecse
asked
Feb 19, 2018
Communications
gate2018-ec
numerical-answers
communications
hamming-codes
+
–
0
votes
0
answers
2918
GATE ECE 2018 | Question: 17
A binary source generates symbols $X\in \left \{ -1,1 \right \}$ which are transmitted over a noisy channel.The probability of transmitting $X=1$ is $0.5.$ Input to the threshold detector is $R=X+N$ ... is shown below. If the detection threshold is zero, then the probability of error (correct to two decimal places) is __________.
A binary source generates symbols $X\in \left \{ -1,1 \right \}$ which are transmitted over a noisy channel.The probability of transmitting $X=1$ is $0.5.$ Input to the t...
gatecse
1.6k
points
138
views
gatecse
asked
Feb 19, 2018
Communications
gate2018-ec
numerical-answers
probability-density-function
communications
+
–
0
votes
0
answers
2919
GATE ECE 2018 | Question: 18
A $\text{p-n}$ step junction diode with a contact potential of $0.65\:V$ has a depletion width of $1\:\mu m$ at equilibrium. The forward voltage (in volts, correct to two decimal places) at which this width reduces to $0.6\:\mu m$ is __________.
A $\text{p-n}$ step junction diode with a contact potential of $0.65\:V$ has a depletion width of $1\:\mu m$ at equilibrium. The forward voltage (in volts, correct to two...
gatecse
1.6k
points
130
views
gatecse
asked
Feb 19, 2018
Electronic Devices
gate2018-ec
numerical-answers
electronic-devices
p-n-junction
+
–
0
votes
0
answers
2920
GATE ECE 2018 | Question: 1
Two identical $\text{nMOS}$ transistors $M_{1}$ and $M_{2}$ are connected as shown below. The circuit is used as an amplifier with the input connected between $\text{G and S}$ terminals and the output taken between $D\: \text{and}\: S$ terminals. $V_{bias}$ and $V_{D}$ are ... $g_{m}\approx g_{m1} \:\:\text{and}\:\: r_{o}\approx r_{o2}$
Two identical $\text{nMOS}$ transistors $M_{1}$ and $M_{2}$ are connected as shown below. The circuit is used as an amplifier with the input connected between $\text{G an...
gatecse
1.6k
points
175
views
gatecse
asked
Feb 19, 2018
Electronic Devices
gate2018-ec
analog-circuits
nmos-transistor
amplifier
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–
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