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2161
GATE ECE 2014 Set 4 | GA Question: 4
Let $f(x,y)=x^n y^m=P$. If $x$ is doubled and $y$ is halved, the new value of $f$ is $2^{n-m}P$ $2^{m-n}P$ $2(n-m)P$ $2(m-n)P$
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2162
GATE ECE 2014 Set 4 | GA Question: 5
In a sequence of $12$ consecutive odd numbers, the sum of the first $5$ numbers is $425$. What is the sum of the last $5$ numbers in the sequence?
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Quantitative Aptitude
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gate2014-ec-4
numerical-ability
arithmetic-series
numerical-answers
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0
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2163
GATE ECE 2014 Set 4 | GA Question: 6
Find the next term in the sequence: $13M, 17Q, 19S$, ___ $21W$ $21V$ $23W$ $23V$
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Analytical Aptitude
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gate2014-ec-4
analytical-aptitude
logical-reasoning
sequence-series
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0
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2164
GATE ECE 2014 Set 4 | GA Question: 7
If $\text{‘KCLFTSB’}$ stands for ‘best of luck’ and $\text{‘SHSWDG’}$ stands for ‘good wishes’, which of the following indicates ‘ace the exam’? $\text{MCHTX}$ $\text{MXHTC}$ $\text{XMHCT}$ $\text{XMHTC}$
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Verbal Aptitude
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50
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gate2014-ec-4
logical-reasoning
sequence-series
0
votes
0
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2165
GATE ECE 2014 Set 4 | GA Question: 8
Industrial consumption of power doubled from $2000$-$2001$ to $2010$-$2011$. Find the annual rate of increase in percent assuming it to be uniform over the years. $5.6$ $7.2$ $10.0$ $12.2$
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Quantitative Aptitude
Mar 26, 2018
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Milicevic3306
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gate2014-ec-4
numerical-ability
data-interpretation
0
votes
0
answers
2166
GATE ECE 2014 Set 4 | GA Question: 9
A firm producing air purifiers sold $200$ units in $2012$. The following pie chart presents the share of raw material, labour, energy, plant & machinery, and transportation costs in the total manufacturing cost of the firm in $2012$. The ... all other expenses increased by $20 \%$. What is the percentage increase in total cost for the company in $2013$?
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Quantitative Aptitude
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15.8k
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38
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gate2014-ec-4
numerical-ability
data-interpretation
pie-chart
0
votes
0
answers
2167
GATE ECE 2014 Set 4 | GA Question: 10
A five digit number is formed using the digits $1,3,5,7$ and $9$ without repeating any of them. What is the sum of all such possible five digit numbers? $6666660$ $6666600$ $6666666$ $6666606$
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Quantitative Aptitude
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Milicevic3306
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39
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gate2014-ec-4
numerical-ability
couting
0
votes
0
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2168
GATE ECE 2014 Set 4 | Question: 1
The series $\Sigma_{n=0}^{\infty} \frac{1}{n!}$ converges to $2 \text{ ln } 2$ $\sqrt{2}$ $2$ $e$
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Calculus
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43
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gate2014-ec-4
calculus
taylor-series
convergence
0
votes
0
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2169
GATE ECE 2014 Set 4 | Question: 2
The magnitude of the gradient for the function $f(x,y,z) = x^2 +3y^2 +z^3$ at the point $(1,1,1)$ is ___________.
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Vector Analysis
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43
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gate2014-ec-4
numerical-answers
vector-analysis
gradient
0
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0
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2170
GATE ECE 2014 Set 4 | Question: 3
Let $X$ be a zero mean unit variance Gaussian random variable. $E[ \mid X \mid ]$ is equal to __________
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Vector Analysis
Mar 26, 2018
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Milicevic3306
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54
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gate2014-ec-4
numerical-answers
vector-analysis
gausss-theorem
random-variable
0
votes
0
answers
2171
GATE ECE 2014 Set 4 | Question: 4
If $a$ and $b$ are constants, the most general solution of the differential equation $\frac{d^2x}{dt^2}+2 \frac{dx}{dt}+x=0$ is $ae^{-t}$ $ae^{-t} + bte^{-t}$ $ae^t+bte^{-t}$ $ae^{-2t}$
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Differential Equations
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Milicevic3306
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37
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gate2014-ec-4
differential-equations
0
votes
0
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2172
GATE ECE 2014 Set 4 | Question: 5
The directional derivative of $f(x,y)= \frac{xy}{\sqrt{2}} (x+y)$ at $(1,1)$ in the direction of the unit vector at an angle of $\frac{\pi}{4}$ with $y$-axis, is given by _________.
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Vector Analysis
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Milicevic3306
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45
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gate2014-ec-4
vector-analysis
numerical-answers
0
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0
answers
2173
GATE ECE 2014 Set 4 | Question: 6
The circuit shown in the figure represents a voltage controlled voltage source voltage controlled current source current controlled current source current controlled voltage source
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Analog Circuits
Mar 26, 2018
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Milicevic3306
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37
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gate2014-ec-4
analog-circuits
0
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0
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2174
GATE ECE 2014 Set 4 | Question: 7
The magnitude of current (in mA) through the resistor $R_2$ in the figure shown is __________
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Electronic Devices
Mar 26, 2018
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Milicevic3306
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37
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gate2014-ec-4
numerical-answers
electronic-devices
0
votes
0
answers
2175
GATE ECE 2014 Set 4 | Question: 8
At $T=300 \:K$, the band gap and the intrinsic carrier concentration of GaAs are $1.42$ eV and $10^6 \: cm^{-3}$, respectively. In order to generate electron hole pairs in GaAs, which one of the wavelength $(\lambda_C)$ ranges of incident radiation, is most suitable? (Given ... $1.62 \: \mu m < \lambda _C < 6.62 \: \mu m$
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Electromagnetics
Mar 26, 2018
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Milicevic3306
15.8k
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36
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gate2014-ec-4
electromagnetics
plank's-constant
0
votes
0
answers
2176
GATE ECE 2014 Set 4 | Question: 9
In the figure, $\text{ln }(\rho _i)$ is plotted as a function of $1/T$, where $\rho_i$ is the intrinsic resistivity of silicon, $T$ is the temperature, and the plot is almost linear. The slope of the line can be used to estimate band gap ... the sum of electron and hole mobility in silicon $(\mu _n + \mu _p)^{-1}$ intrinsic carrier concentration of silicon $(n_i)$
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Electronic Devices
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gate2014-ec-4
electronic-devices
intrinsic-and-extrinsic-silicon
0
votes
0
answers
2177
GATE ECE 2014 Set 4 | Question: 10
The cut-off wavelength (in $\mu m$) of light that can be used for intrinsic excitation of a semiconductor material of bandgap $E_g = 1.1 \: eV$ is ______________
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Electronic Devices
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Milicevic3306
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32
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gate2014-ec-4
numerical-answers
electronic-devices
0
votes
0
answers
2178
GATE ECE 2014 Set 4 | Question: 11
If the emitter resistance in a common-emitter voltage amplifier is not bypassed, it will reduce both the voltage gain and the input impedance reduce the voltage gain and increase the input impedance increase the voltage gain and reduce the input impedance reduce both the voltage gain and the input impedance
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Electromagnetics
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Milicevic3306
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39
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gate2014-ec-4
electromagnetics
impedance
0
votes
0
answers
2179
GATE ECE 2014 Set 4 | Question: 12
Two silicon diodes, with a forward voltage drop of $0.7 \: V$, are used in the circuit shown in the figure. The range of input voltage $V_i$ for which the output voltage $V_o=V_i$, is $-0.3 \:V < V_i < 1.3 \: V$ $-0.3 \:V < V_i < 2 \: V$ $-1.0 \:V < V_i < 2.0 \: V$ $-1.7 \:V < V_i < 2.7 \: V$
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Electronic Devices
Mar 26, 2018
by
Milicevic3306
15.8k
points
36
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gate2014-ec-4
electronic-devices
intrinsic-and-extrinsic-silicon
0
votes
0
answers
2180
GATE ECE 2014 Set 4 | Question: 13
The circuit shown represents a bandpass filter a voltage controlled oscillator an amplitude modulator a monostable multivibrator
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Analog Circuits
Mar 26, 2018
by
Milicevic3306
15.8k
points
52
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gate2014-ec-4
analog-circuits
oscillator
0
votes
0
answers
2181
GATE ECE 2014 Set 4 | Question: 14
For a given sample-and-hold circuit, if the value of the hold capacitor is increased, then droop rate decreases and acquisition time decreases droop rate decreases and acquisition time increases droop rate increases and acquisition time decreases droop rate increases and acquisition time increases
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Digital Circuits
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Milicevic3306
15.8k
points
28
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gate2014-ec-4
digital-circuits
sample-and-hold-circuits
0
votes
0
answers
2182
GATE ECE 2014 Set 4 | Question: 15
In the circuit shown in the figure, if $C=0$, the expression for $Y$ is $Y=A \overline{B} + \overline{A}B$ $Y=A+B$ $Y=\overline{A} + \overline{B}$ $Y=A \: B$
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Digital Circuits
Mar 26, 2018
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Milicevic3306
15.8k
points
55
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gate2014-ec-4
digital-circuits
combinational-circuits
logic-gates
0
votes
0
answers
2183
GATE ECE 2014 Set 4 | Question: 16
The output $(Y)$ of the circuit shown in the figure is $\overline{A} + \overline{B} +C$ $A + \overline{B} \cdot \overline{C} + A \cdot \overline{C}$ $\overline{A} +B+\overline{C}$ $A \cdot B \cdot \overline{C}$
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Digital Circuits
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Milicevic3306
15.8k
points
84
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gate2014-ec-4
digital-circuits
0
votes
0
answers
2184
GATE ECE 2014 Set 4 | Question: 17
A Fourier transform pair is given by $\left ( \frac{2}{3} \right ) \: u[n+3] \overset{FT}{\Leftrightarrow} \frac{Ae^{-j6 \pi f}}{1- (\frac{2}{3} ) e^{-j2 \pi f}}$ where $u[n]$ denotes the unit step sequence. The values of $A$ is ____________
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Continuous-time Signals
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Milicevic3306
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46
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gate2014-ec-4
numerical-answers
continuous-time-signals
signals-and-systems
fourier-transform
0
votes
0
answers
2185
GATE ECE 2014 Set 4 | Question: 18
A real-valued signal $x(t)$ limited to the frequency band $\mid f \mid \leq \frac{W}{2}$ is passed through a linear time invariant system whose frequency response is $H(f) = \begin{cases} e^{-j 4 \pi f}, & \mid f \mid \leq \frac{W}{2} \\ 0, & \mid f \mid > \frac{W}{2} \end{cases}.$ The output of the system is $x(t+4)$ $x(t-4)$ $x(t+2)$ $x(t-2)$
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Continuous-time Signals
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72
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gate2014-ec-4
continuous-time-signals
linear-time-invariant-systems
0
votes
0
answers
2186
GATE ECE 2014 Set 4 | Question: 19
The sequence $x[n] = 0.5^n \: u[n]$, where $u[n]$ is the unit step sequence, is convolved with itself to obtain $y[n]$. Then $\Sigma_{n= -\infty}^{+ \infty} y[n]$ is _________.
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Continuous-time Signals
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Milicevic3306
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points
64
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gate2014-ec-4
numerical-answers
continuous-time-signals
to-be-tagged
0
votes
0
answers
2187
GATE ECE 2014 Set 4 | Question: 20
In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a $4$th order all-pole system? $-80$ dB/decade $-40$ dB/decade $+40$ dB/decade $+80$ dB/decade
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Control Systems
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46
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gate2014-ec-4
control-systems
bode-and-root-locus-plots
0
votes
0
answers
2188
GATE ECE 2014 Set 4 | Question: 21
For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is $16$ $4$ $2$ $1$
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Network Solution Methods
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Milicevic3306
15.8k
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49
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gate2014-ec-4
network-solution-methods
to-be-tagged
0
votes
0
answers
2189
GATE ECE 2014 Set 4 | Question: 22
If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier or future calls, the probability distribution function of the total number of calls in a fixed time interval will be Poisson Gaussian Exponential Gamma
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Vector Analysis
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Milicevic3306
15.8k
points
93
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gate2014-ec-4
vector-analysis
gauss's-theorem
0
votes
0
answers
2190
GATE ECE 2014 Set 4 | Question: 23
In a double side-band (DSB) full carrier AM transmission system, if the modulation index is doubled, then the ratio of total sideband power to the carrier power increases by a factor of __________.
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Communications
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Milicevic3306
15.8k
points
44
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gate2014-ec-4
numerical-answers
communications
amplitude-modulation
0
votes
0
answers
2191
GATE ECE 2014 Set 4 | Question: 24
For an antenna radiating in free space, the electric field at a distance of $1$ km is found to be $12 \: mV/m$. Given that intrinsic impedance of the free space is $120 \pi \: \Omega$, the magnitude of average power density due to this antenna at a distance of $2$ km from the antenna (in $nW/m^2$) is _________.
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Electromagnetics
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by
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54
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gate2014-ec-4
numerical-answers
electromagnetics
impedance
0
votes
0
answers
2192
GATE ECE 2014 Set 4 | Question: 25
Match column A with column B. ... $ 1 \rightarrow R; \: 2 \rightarrow Q; \: 3 \rightarrow P;$
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Electromagnetics
Mar 26, 2018
by
Milicevic3306
15.8k
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50
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gate2014-ec-4
electromagnetics
0
votes
0
answers
2193
GATE ECE 2014 Set 4 | Question: 26
With initial values $y(0) =y’(0)=1$, the solution of the differential equation $\frac{d^2y}{dx^2}+4 \frac{dy}{dx}+4y=0$ at $x=1$ is ________
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Differential Equations
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by
Milicevic3306
15.8k
points
42
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gate2014-ec-4
numerical-answers
differential-equations
0
votes
0
answers
2194
GATE ECE 2014 Set 4 | Question: 27
Parcels from sender S to receiver R pass sequentially through two-post offices. Each post-office has a probability $\frac{1}{5}$ of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post office is _________
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Probability and Statistics
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by
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15.8k
points
63
views
gate2014-ec-4
numerical-answers
probability-and-statistics
probability
0
votes
0
answers
2195
GATE ECE 2014 Set 4 | Question: 28
The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}$. Which one of the following is the unilateral Laplace transform of $g(t) = t \cdot f(t)$? $\frac{-s}{(s^2+s+1)^2}$ $\frac{-(2s+1)}{(s^2+s+1)^2}$ $\frac{s}{(s^2+s+1)^2}$ $\frac{2s+1}{(s^2+s+1)^2}$
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Network Solution Methods
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by
Milicevic3306
15.8k
points
58
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gate2014-ec-4
network-solution-methods
laplace-transform
0
votes
0
answers
2196
GATE ECE 2014 Set 4 | Question: 29
For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the triangle, the angle between the hypotenuse and the side is $12^{\circ}$ $36^{\circ}$ $60^{\circ}$ $45^{\circ}$
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Calculus
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15.8k
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41
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gate2014-ec-4
calculus
maxima-minima
0
votes
0
answers
2197
GATE ECE 2014 Set 4 | Question: 30
The steady state output of the circuit shown in the figure is given by $y(t)=A(\omega) \sin (\omega t + \phi ( \omega))$. If the amplitude $\mid A (\omega ) \mid =0.25$, then the frequency $\omega$ is $\frac{1}{\sqrt{3} \: R \: C}$ $\frac{2}{\sqrt{3} \: R \: C}$ $\frac{1}{R \: C}$ $\frac{2}{R \: C}$
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Network Solution Methods
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Milicevic3306
15.8k
points
43
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gate2014-ec-4
network-solution-methods
steady-state
0
votes
0
answers
2198
GATE ECE 2014 Set 4 | Question: 31
In the circuit shown in the figure, the value of $v_0(t)$ (in Volts) for $t \to \infty$ is ___________
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Network Solution Methods
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Milicevic3306
15.8k
points
28
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gate2014-ec-4
numerical-answers
network-solution-methods
0
votes
0
answers
2199
GATE ECE 2014 Set 4 | Question: 32
The equivalent resistance in the infinite ladder network shown in the figure, is $R_e$. The value of $R_e/R$ is __________
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Network Solution Methods
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Milicevic3306
15.8k
points
32
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gate2014-ec-4
numerical-answers
network-solution-methods
ladder-network
0
votes
0
answers
2200
GATE ECE 2014 Set 4 | Question: 33
For the two-port network shown in the figure, the impedance (Z) matrix (in $\Omega$) is $\begin{bmatrix} 6 & 24 \\ 42 & 9 \end{bmatrix}$ $\begin{bmatrix} 9 & 8 \\ 8 & 24 \end{bmatrix}$ $\begin{bmatrix} 9 & 6 \\ 6 & 24 \end{bmatrix}$ $\begin{bmatrix} 42 & 6 \\ 6 & 60 \end{bmatrix}$
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Electromagnetics
Mar 26, 2018
by
Milicevic3306
15.8k
points
38
views
gate2014-ec-4
electromagnetics
impedance
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