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2921
GATE ECE 2012 | Question: 6
Consider the given circuit. In the circuit, the race around does not occur occurs when $\text{CLK}=0$ occurs when $\text{CLK}=1$ and $A=B=1$ occurs when $\text{CLK}=1$ and $A=B=0$
Consider the given circuit.In the circuit, the race arounddoes not occuroccurs when $\text{CLK}=0$occurs when $\text{CLK}=1$ and $A=B=1$occurs when $\text{CLK}=1$ and $A=...
Milicevic3306
16.0k
points
154
views
Milicevic3306
asked
Mar 25, 2018
Number Representations
gate2012-ec
digital-circuits
sequential-circuit
flip-flop
+
–
0
votes
0
answers
2922
GATE ECE 2012 | Question: 7
The output $Y$ of a $2-\text{bit}$ comparator is logic $1$ whenever the $2-\text{bit}$ input $A$ is greater than the $2-\text{bit}$ input $B$. The number of combinations for which the output is logic $1$, is $4$ $6$ $8$ $10$
The output $Y$ of a $2-\text{bit}$ comparator is logic $1$ whenever the $2-\text{bit}$ input $A$ is greater than the $2-\text{bit}$ input $B$. The number of combinations ...
Milicevic3306
16.0k
points
83
views
Milicevic3306
asked
Mar 25, 2018
Digital Circuits
gate2012-ec
digital-circuits
+
–
0
votes
0
answers
2923
GATE ECE 2012 | Question: 8
The $i-v$ characteristics of the diode in the circuit given below are $i = \begin{cases} \frac{v-0.07}{500}\:A, & v\ge0.7\:V \\ \:\:\:\:\:\:\:\:0\:A, & v \lt 0.7\:V \end{cases}$ The current in the circuit is $10\:mA$ $9.3\:mA$ $6.67\:mA$ $6.2\:mA$
The $i-v$ characteristics of the diode in the circuit given below are$$i = \begin{cases} \frac{v-0.07}{500}\:A, & v\ge0.7\:V \\ \:\:\:\:\:\:\:\:0\:A, & v \lt 0.7\:V \en...
Milicevic3306
16.0k
points
120
views
Milicevic3306
asked
Mar 25, 2018
Electronic Devices
gate2012-ec
electronic-devices
carrier-transport
+
–
0
votes
0
answers
2924
GATE ECE 2012 | Question: 9
In the following figure, $C_1$ and $C_2$ are ideal capacitors. $C_1$ has been charged to $12\:V$ before the ideal switch $S$ is closed at $t=0$. The current $i(t)$ for all $t$ is zero a step function an exponentially decaying function an impulse function
In the following figure, $C_1$ and $C_2$ are ideal capacitors. $C_1$ has been charged to $12\:V$ before the ideal switch $S$ is closed at $t=0$. The current $i(t)$ for al...
Milicevic3306
16.0k
points
109
views
Milicevic3306
asked
Mar 25, 2018
Electronic Devices
gate2012-ec
electronic-devices
+
–
0
votes
0
answers
2925
GATE ECE 2012 | Question: 10
The average power delivered to an impedance $(4-j3)\:\Omega$ by a current $5\cos(100\pi t+100)\:A$ is $44.2\:W$ $50\:W$ $62.5\:W$ $125\:W$
The average power delivered to an impedance $(4-j3)\:\Omega$ by a current $5\cos(100\pi t+100)\:A$ is$44.2\:W$$50\:W$$62.5\:W$$125\:W$
Milicevic3306
16.0k
points
71
views
Milicevic3306
asked
Mar 25, 2018
Electromagnetics
gate2012-ec
electromagnetics
impedance
+
–
0
votes
0
answers
2926
GATE ECE 2012 | Question: 11
The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}$. The unilateral Laplace transform of $tf(t)$ is $-\frac{s}{(s^2+s+1)^2}$ $-\frac{2s+1}{(s^2+s+1)^2}$ $\frac{s}{(s^2+s+1)^2}$ $\frac{2s+1}{(s^2+s+1)^2}$
The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}$. The unilateral Laplace transform of $tf(t)$ is$-\frac{s}{(s^2+s+1)^2}$$-\frac{2s+1}{(s^2+s+1)^2}$$\frac...
Milicevic3306
16.0k
points
147
views
Milicevic3306
asked
Mar 25, 2018
Network Solution Methods
gate2012-ec
network-solution-methods
laplace-transform
+
–
0
votes
0
answers
2927
GATE ECE 2012 | Question: 2
The power spectral density of a real process $X(t)$ for positive frequencies is shown below. The values of $E[X^2(t)]$ and $ \mid E[X(t)] \mid$, respectively, are $\frac{6000}{\pi}\:,\:0$ $\frac{6400}{\pi}\:,\:0$ $\frac{6400}{\pi}\:,\:\frac{20}{(\pi\sqrt2)}$ $\frac{6000}{\pi}\:,\:\frac{20}{(\pi\sqrt2)}$
The power spectral density of a real process $X(t)$ for positive frequencies is shown below. The values of $E[X^2(t)]$ and $ \mid E[X(t)] \mid$, respectively, are$\frac{6...
Milicevic3306
16.0k
points
111
views
Milicevic3306
asked
Mar 25, 2018
Communications
gate2012-ec
communications
autocorrelation-and-power-spectral-density
+
–
0
votes
0
answers
2928
GATE ECE 2012 | Question: 3
In a baseband communications link, frequencies upto $3500\:Hz$ are used for signaling. Using a raised cosine pulse with $75\%$ excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in the symbols per second is $1750$ $2625$ $4000$ $5250$
In a baseband communications link, frequencies upto $3500\:Hz$ are used for signaling. Using a raised cosine pulse with $75\%$ excess bandwidth and for no inter-symbol in...
Milicevic3306
16.0k
points
90
views
Milicevic3306
asked
Mar 25, 2018
Communications
gate2012-ec
communications
calculation-of-bandwidth
+
–
0
votes
0
answers
2929
GATE ECE 2012 | Question: 4
A plane wave propagating in air with $\overrightarrow{E}=(8\hat{a}_x+6\hat{a}_y+5\hat{a}_z)e^{j(\omega t+3x-4y)}\:V/m$ is incident on a perfectly conducting slab positioned at $x\le0$ . The $\overrightarrow{E}$ ... $(-8\hat{a}_x+6\hat{a}_y-5\hat{a}_z)e^{j(\omega t-3x-4y)}\:V/m$
A plane wave propagating in air with $\overrightarrow{E}=(8\hat{a}_x+6\hat{a}_y+5\hat{a}_z)e^{j(\omega t+3x-4y)}\:V/m$ is incident on a perfectly conducting slab position...
Milicevic3306
16.0k
points
130
views
Milicevic3306
asked
Mar 25, 2018
Electromagnetics
gate2012-ec
electromagnetics
propagation
+
–
0
votes
0
answers
2930
GATE ECE 2012 | Question: 1
The current $i_b$ through the base of a silicon $npn$ transistor is $1+0.1\cos(10000\pi t)\:mA$. At $300\:K$, the $r_\pi$ in the small signal model of the transistor is $250\:\Omega$ $27.5\:\Omega$ $25\:\Omega$ $22.5\:\Omega$
The current $i_b$ through the base of a silicon $npn$ transistor is $1+0.1\cos(10000\pi t)\:mA$. At $300\:K$, the $r_\pi$ in the small signal model of the transistor is$2...
Milicevic3306
16.0k
points
108
views
Milicevic3306
asked
Mar 25, 2018
Electronic Devices
gate2012-ec
electronic-devices
intrinsic-and-extrinsic-silicon
+
–
0
votes
0
answers
2931
GATE ECE 2018 | Question: 55
Let $X\left[ k \right ] = k + 1,0\leq k\leq 7$ be $8$-point $\:\text{DFT}\:$ of a sequence $x[n]$. where $X\left [ k \right ]=\sum_{n=0}^{N-1}x \left [ n \right ]e^{-j2\pi nk/N}$. The value (correct to two decimal places) of $\sum_{n=0}^{3}x \left [ 2n \right ]$ is ________.
Let $X\left[ k \right ] = k + 1,0\leq k\leq 7$ be $8$-point $\:\text{DFT}\:$ of a sequence $x[n]$.where $X\left [ k \right ]=\sum_{n=0}^{N-1}x \left [ n \right ]e^{-j2\pi...
gatecse
1.6k
points
114
views
gatecse
asked
Feb 19, 2018
Calculus
gate2018-ec
numerical-answers
calculus
+
–
0
votes
0
answers
2932
GATE ECE 2018 | Question: 46
In the circuit shown below, a positive edge-triggered $D$ Flip-Flop is used for sampling input data $D_{in}$ using clock $CK$. The XOR gate output $3.3$ volts for logic HIGH and $0$ volts for logic LOW levels. The data bit and clock periods are ... period is $0.3$, the average value (in volts, accurate to two decimal places) of the voltage at node $X$, is _________.
In the circuit shown below, a positive edge-triggered $D$ Flip-Flop is used for sampling input data $D_{in}$ using clock $CK$. The XOR gate output $3.3$ volts for logic H...
gatecse
1.6k
points
247
views
gatecse
asked
Feb 19, 2018
Number Representations
gate2018-ec
numerical-answers
digital-circuits
sequential-circuit
flip-flops
+
–
0
votes
0
answers
2933
GATE ECE 2018 | Question: 47
The logic gates shown in the digital circuit below use strong pull-down $\text{nMOS}$ transistors for LOW logic level at the outputs. When the pull-downs are off, high-value resistors set the output logic levels to HIGH (i.e. the pull-ups are weak). Note that some nodes ... values of $X_{3}X_{2}X_{1}X_{0}$ (out of the $16$ possible values) that give $Y=1$ is ________.
The logic gates shown in the digital circuit below use strong pull-down $\text{nMOS}$ transistors for LOW logic level at the outputs. When the pull-downs are off, high-va...
gatecse
1.6k
points
264
views
gatecse
asked
Feb 19, 2018
Number Representations
gate2018-ec
numerical-answers
digital-circuits
combinational-circuits
logic-gates
+
–
0
votes
0
answers
2934
GATE ECE 2018 | Question: 49
A uniform plane wave traveling in free space and having the electric field ... ) as shown in the figure and there is no reflected wave. The relative permittivity (correct to two decimal places) of the dielectric medium is __________.
A uniform plane wave traveling in free space and having the electric field$$\overrightarrow{E} =\left ( \sqrt{2}\:\hat{a}_{x} -\hat{a}_{z}\right )cos\left [ 6\sqrt{3}\: \...
gatecse
1.6k
points
205
views
gatecse
asked
Feb 19, 2018
Electromagnetics
gate2018-ec
numerical-answers
electromagnetics
plane-waves-and-properties
+
–
0
votes
0
answers
2935
GATE ECE 2018 | Question: 50
The position of a particle $y\left ( t \right )$ is described by the differential equation: $\frac{d^{2}y}{dt^{2}}=-\frac{dy}{dt}-\frac{5y}{4}.$ The initial conditions are $y\left ( 0 \right )=1$ and $\frac{dy}{dt}\mid_{t=0}=0$. The position (accurate to two decimal places) of the particle at $t=\pi$ is _________.
The position of a particle $y\left ( t \right )$ is described by the differential equation:$$\frac{d^{2}y}{dt^{2}}=-\frac{dy}{dt}-\frac{5y}{4}.$$The initial conditions ar...
gatecse
1.6k
points
128
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
numerical-answers
differential-equations
second-order-differential-equation
+
–
0
votes
0
answers
2936
GATE ECE 2018 | Question: 51
The contour $C$ given below is on the complex plane $z=x+j y,$ where $j=\sqrt{-1}.$ The value of the integral $\displaystyle{}\dfrac{1}{\pi j}\oint _{C}\dfrac{dz}{z^{2}-1}$ is _______.
The contour $C$ given below is on the complex plane $z=x+j y,$ where $j=\sqrt{-1}.$ The value of the integral $\disp...
gatecse
1.6k
points
421
views
gatecse
asked
Feb 19, 2018
Complex Analysis
gate2018-ec
numerical-answers
complex-analysis
+
–
0
votes
0
answers
2937
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
129
views
gatecse
asked
Feb 19, 2018
Calculus
gate2018-ec
numerical-answers
calculus
partial-derivatives
+
–
0
votes
0
answers
2938
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
151
views
gatecse
asked
Feb 19, 2018
Network Solution Methods
gate2018-ec
numerical-answers
network-solution-methods
+
–
0
votes
0
answers
2939
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
109
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
2940
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
318
views
gatecse
asked
Feb 19, 2018
Analog Circuits
gate2018-ec
numerical-answers
analog-circuits
+
–
0
votes
0
answers
2941
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
228
views
gatecse
asked
Feb 19, 2018
Analog Circuits
gate2018-ec
numerical-answers
analog-circuits
op-amps
+
–
0
votes
0
answers
2942
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
154
views
gatecse
asked
Feb 19, 2018
Continuous-time Signals
gate2018-ec
numerical-answers
hilbert-transformer
+
–
0
votes
0
answers
2943
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
220
views
gatecse
asked
Feb 19, 2018
Probability and Statistics
gate2018-ec
numerical-answers
probability-and-statistics
propability
random-variable
+
–
0
votes
0
answers
2944
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
145
views
gatecse
asked
Feb 19, 2018
Network Solution Methods
gate2018-ec
numerical-answers
network-solution-methods
transfer-function
+
–
0
votes
0
answers
2945
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
139
views
gatecse
asked
Feb 19, 2018
Analog Circuits
gate2018-ec
numerical-answers
analog-circuits
nmos-transistor
+
–
0
votes
0
answers
2946
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
155
views
gatecse
asked
Feb 19, 2018
Electronic Devices
gate2018-ec
numerical-answers
electronic-devices
+
–
0
votes
0
answers
2947
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
177
views
gatecse
asked
Feb 19, 2018
Digital Circuits
gate2018-ec
numerical-answers
boltzman-constant
doping
digital-circuits
+
–
0
votes
0
answers
2948
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
174
views
gatecse
asked
Feb 19, 2018
Communications
gate2018-ec
gaussian-noise
autocorrelation-and-power-spectral-density
communications
+
–
0
votes
0
answers
2949
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
174
views
gatecse
asked
Feb 19, 2018
Network Solution Methods
gate2018-ec
network-solution-methods
state-equations
+
–
0
votes
0
answers
2950
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
185
views
gatecse
asked
Feb 19, 2018
Electronic Devices
gate2018-ec
electronic-devices
p-n-junction
+
–
0
votes
0
answers
2951
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
262
views
gatecse
asked
Feb 19, 2018
Diode Circuits
gate2018-ec
digital-circuits
rom
+
–
0
votes
0
answers
2952
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
130
views
gatecse
asked
Feb 19, 2018
Analog Circuits
gate2018-ec
analog-circuits
+
–
0
votes
0
answers
2953
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
134
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
differential-equations
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–
0
votes
0
answers
2954
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
115
views
gatecse
asked
Feb 19, 2018
Analog Circuits
gate2018-ec
analog-circuits
+
–
0
votes
0
answers
2955
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
195
views
gatecse
asked
Feb 19, 2018
Analog Circuits
gate2018-ec
numerical-answers
analog-circuits
+
–
0
votes
0
answers
2956
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
155
views
gatecse
asked
Feb 19, 2018
Digital Circuits
gate2018-ec
numerical-answers
digital-circuits
sequential-circuit
flip-flops
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–
0
votes
0
answers
2957
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
118
views
gatecse
asked
Feb 19, 2018
Electronic Devices
gate2018-ec
numerical-answers
electronic-devices
photolithography
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–
0
votes
0
answers
2958
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
156
views
gatecse
asked
Feb 19, 2018
Electromagnetics
gate2018-ec
numerical-answers
impedance
electromagnetics
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–
0
votes
0
answers
2959
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
110
views
gatecse
asked
Feb 19, 2018
Linear Algebra
gate2018-ec
numerical-answers
linear-algebra
system-of-equations
+
–
0
votes
0
answers
2960
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
165
views
gatecse
asked
Feb 19, 2018
Probability and Statistics
gate2018-ec
numerical-answers
probability-and-statistics
probability
random-variable
variance
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