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2081
GATE ECE 2015 Set 1 | Question: 25
A vector $\overrightarrow{P}$ is given by $\overrightarrow{P} = x^3y\overrightarrow{a}_x - x^2y^2\overrightarrow{a}_y - x^2 yz \overrightarrow{a}_z$. Which one of the statements is TRUE? $\overrightarrow{P}$ is ... irrotational, but not solenoidal $\overrightarrow{P}$ is neither solenoidal, nor irrotational $\overrightarrow{P}$ is both solenoidal and irrotational
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2082
GATE ECE 2015 Set 1 | Question: 28
Which one of the following graphs describes the function $f(x)=e^{-x}(x^2+x+1)$?
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Calculus
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2083
GATE ECE 2015 Set 1 | Question: 29
The maximum area (in square units) of a rectangle whose vertices lie on the eclipse $x^2+4y^2=1$ is __________.
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Calculus
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2084
GATE ECE 2015 Set 1 | Question: 30
The damping ratio of a series RLC circuit can be expressed as $\frac{R^2C}{2L} \\$ $\frac{2L}{R^2C} \\$ $\frac{R}{2} \sqrt{\frac{C}{L}} \\$ $\frac{2}{R} \sqrt{\frac{L}{C}}$
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Network Solution Methods
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2085
GATE ECE 2015 Set 1 | Question: 31
In the circuit shown, switch SW is closed at $t=0$. Assuming zero initial conditions, the value of $v_c(t)$ (in Volts) at $t=1$ sec is _________.
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Continuous-time Signals
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gate2015-ec-1
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2086
GATE ECE 2015 Set 1 | Question: 32
In the given circuit, the maximum power (in Watts) that can be transferred to the load $R_L$ is ________.
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Network Solution Methods
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maximum-power-transfer
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2087
GATE ECE 2015 Set 1 | Question: 33
The built-in potential of an abrupt p-n junction is $0.75$ V. If its junction capacitance $(C_J)$ at a reverse bias $(V_R)$ of $1.25 \: V$ is $5$ pF, the value of $C_J$ (in pF) when $V_R = 7.25 \: V$ is ________.
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Electronic Devices
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gate2015-ec-1
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p-n-junction
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2088
GATE ECE 2015 Set 1 | Question: 34
A MOSFET in saturation has a drain current of $1$ mA for $V_{DS} =0.5 \: V$. If the channel length modulation coefficient is $0.05 \: V^{-1}$, the output resistance (in $k \Omega$) of the MOSFET is ___________.
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Analog Circuits
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33
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gate2015-ec-1
numerical-answers
analog-circuits
mosfet
0
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0
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2089
GATE ECE 2015 Set 1 | Question: 35
For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are $1 \times 10^{17} \:cm^{-3}$ and $1 \times 10^{15} \: cm^{-3}$, respectively. The lifetimes of electrons in P region and holes in N ... $nA/cm^2$) injected from P region to N region is __________.
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Electronic Devices
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electronic-devices
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2090
GATE ECE 2015 Set 1 | Question: 36
The Boolean expression $F(X,Y,Z) = \overline{X} \: Y \: \overline{Z}+ X \: \overline{Y} \: \overline{Z}+ X \: Y \: \overline{Z} + X \: Y \: Z$ ... $(X+\overline{Y}+\overline{Z})(\overline{X}+Y+Z)(\overline{X}+\overline{Y}+Z)(X + Y + Z)$
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Digital Circuits
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gate2015-ec-1
boolean-algebra
digital-circuits
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2091
GATE ECE 2015 Set 1 | Question: 37
All the logic gates shown in the figure have a propagation delay of $20$ ns. Let $A=C=0$ and $B=1$ until time $t=0$. At $t=0$, all the inputs flip (i.e., $A=C=1$ and $B=0$) and remain in that state. For $t>0$, output $Z=1$ for a duration (in ns) of ________.
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Electromagnetics
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gate2015-ec-1
numerical-answers
electromagnetics
propagation
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0
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2092
GATE ECE 2015 Set 1 | Question: 38
A $3$-input majority gate is defined by the logic function $M(a,b,c)=ab+bc+ca$. Which one of the following gates is represented by the function $M(\overline{M(a,b,c)}, M(a,b,\overline{c}),c)$? $3$-input NAND gate $3$-input XOR gate $3$-input NOR gate $3$-input XNOR gate
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Digital Circuits
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gate2015-ec-1
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2093
GATE ECE 2015 Set 1 | Question: 39
For the NMOSFET in the circuit shown, the threshold voltage is $V_{th}$, where $V_{th}>0$. The source voltage $V_{SS}$ is varied from $0$ to $V_{DD}$. Neglecting the channel length modulation, the drain current $I_D$ as a function of $V_{SS}$ is represented by
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Analog Circuits
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25
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analog-circuits
mosfet
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0
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2094
GATE ECE 2015 Set 1 | Question: 40
In the circuit shown, assume that the opamp is ideal. The bridge output voltage $V_0$ (in mV) for $\delta=0.05$ is __________
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Analog Circuits
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28
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gate2015-ec-1
numerical-answers
analog-circuits
op-amps
0
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0
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2095
GATE ECE 2015 Set 1 | Question: 41
The circuit shown in the figure has an ideal opamp. The oscillation frequency and the condition to sustain the oscillations, respectively, are $\frac{1}{CR}$ and $R_1=R_2 \\ $ $\frac{1}{CR}$ and $R_1=4R_2 \\ $ $\frac{1}{2CR}$ and $R_1=R_2 \\ $ $\frac{1}{2CR}$ and $R_1=4R_2 $
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Analog Circuits
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op-amps
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2096
GATE ECE 2015 Set 1 | Question: 42
In the circuit shown, $I_1=80$ mA and $I_2=4$ mA. Transistors $T_1$ and $T_2$ are identical. Assume that the thermal voltage $V_T$ is $26$ mV at $27^{\circ}C$. At $50^{\circ}C$, the value of the voltage $V_{12}=V_1 - V_2$ (in mV) is _______.
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Diode Circuits
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60
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gate2015-ec-1
numerical-answers
0
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0
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2097
GATE ECE 2015 Set 1 | Question: 43
Two sequences $\begin{bmatrix}a, & b, & c \end{bmatrix}$ and $\begin{bmatrix}A, & B, & C \end{bmatrix}$ ... $\begin{bmatrix}p, & q, & r \end{bmatrix} = \begin{bmatrix} c, & b, & a \end{bmatrix}$
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Linear Algebra
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gate2015-ec-1
linear-algebra
matrices
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2098
GATE ECE 2015 Set 1 | Question: 44
For the discrete-time system shown in the figure, the poles of the system transfer function are located at $2,3 \\$ $\frac{1}{2},3 \\$ $\frac{1}{2}, \frac{1}{3} \\$ $2, \frac{1}{3}$
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Network Solution Methods
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40
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gate2015-ec-1
network-solution-methods
transfer-function
0
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0
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2099
GATE ECE 2015 Set 1 | Question: 45
The pole-zero diagram of a casual and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity $4$. The impulse response of the system is $h[n]$. If $h[0]=1$, we can conclude $h[n]$ is real for all $n$ $h[n]$ is purely imaginary for all $n$ $h[n]$ is real for only even $n$ $h[n]$ is purely imaginary for only odd $n$
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Continuous-time Signals
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Milicevic3306
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61
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gate2015-ec-1
continuous-time-signals
poles-and-zeros
0
votes
0
answers
2100
GATE ECE 2015 Set 1 | Question: 46
The open-loop transfer function of a plant in a unity feedback configuration is given as $G(s) = \frac{K(s+4)}{(s+8)(s^2-9)}$. The value of the gain $K(>0)$ for which $-1+j2$ lies on the root locus is _________.
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Network Solution Methods
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Milicevic3306
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30
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gate2015-ec-1
numerical-answers
network-solution-methods
diodes
transfer-function
0
votes
0
answers
2101
GATE ECE 2015 Set 1 | Question: 47
A lead compensator network includes a parallel combination of $R$ and $C$ in the feed-forward path. If the transfer function of the compensator is $G_c(s)=\frac{s+2}{s+4}$, the value of $RC$ is ___________.
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Network Solution Methods
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Milicevic3306
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41
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gate2015-ec-1
numerical-answers
network-solution-methods
transfer-function
0
votes
0
answers
2102
GATE ECE 2015 Set 1 | Question: 48
A plant transfer function is given as $G(s)= \bigg( K_p+ \frac{K_1}{s} \bigg) \frac{1}{s(s+2)}$. When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is $K_p>\frac{K_1}{2}>0 \\$ $2K_1>K_p>0 \\$ $2K_1<K_p \\$ $2K_1>K_p$
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Network Solution Methods
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Milicevic3306
15.8k
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64
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gate2015-ec-1
network-solution-methods
transfer-function
0
votes
0
answers
2103
GATE ECE 2015 Set 1 | Question: 49
The input $X$ to the Binary Symmetric Channel (BSC) shown in the figure is $’1’$ with probability $0.8$. The cross-over probability is $1/7$. If the received bit $Y=0$, the conditional probability that $’1’$ was transmitted is ____________
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Probability and Statistics
Mar 28, 2018
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95
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gate2015-ec-1
numerical-answers
probability-and-statistics
probability
0
votes
0
answers
2104
GATE ECE 2015 Set 1 | Question: 50
The transmitted signal in a GSM system is of $200$ kHz bandwidth and $8$ users share a common bandwidth using TDMA. If at a given time $12$ users are talking in a cell, the total bandwidth of the signal received by the base station of the cell will be at least (in kHz) ___________.
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Communications
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47
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gate2015-ec-1
numerical-answers
communications
time-divison-multiple-accessamplifiers
0
votes
0
answers
2105
GATE ECE 2015 Set 1 | Question: 51
In the system shown in Figure (a), $m(t)$ is a low-pass signal with bandwidth $W$ Hz. The frequency response of the band-pass filter $H(f)$ is shown in Figure (b). If it is desired that the output signal $z(t)=10x(t)$, the maximum value of $W$ (in Hz) should be strictly less than _____________.
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Continuous-time Signals
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57
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gate2015-ec-1
numerical-answers
signals-and-systems
continuous-time-signals
0
votes
0
answers
2106
GATE ECE 2015 Set 1 | Question: 52
A source emits bit $0$ with probability $\frac{1}{3}$ and bit $1$ with probability $\frac{2}{3}$. The emitted bits are communicated to the receiver. The receiver decides for either $0$ or $1$ based on the received value $R$. It is given that the ... $0$ $1/12$ $1/9$ $1/6$
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Probability and Statistics
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Milicevic3306
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76
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gate2015-ec-1
probability-and-statistics
probability
probability-density-function
0
votes
0
answers
2107
GATE ECE 2015 Set 1 | Question: 53
The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression ... and $b=0.033 \: m$. The mode of propagation inside the waveguide is $TM_{12}$ $TM_{21}$ $TE_{21}$ $TE_{12}$
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Electromagnetics
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Milicevic3306
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56
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gate2015-ec-1
electromagnetics
propagation
0
votes
0
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2108
GATE ECE 2015 Set 1 | Question: 54
The electric field intensity of a plane wave traveling in free space is given by the following expression $\textbf{E}(x,t)=\textbf{a}_y \: 24 \: \pi \: \: \cos(\omega t - k_0 x) \: \: (V/m)$ ... $x+y=1$. The total time-averaged power (in mW) passing through the square area is _____________.
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Vector Analysis
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Milicevic3306
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44
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gate2015-ec-1
numerical-answers
vector-analysis
0
votes
0
answers
2109
GATE ECE 2015 Set 1 | Question: 55
Consider a uniform plane wave with amplitude $(E_0)$ of $10 \: V/m$ and $1.1$ GHz frequency travelling in air, and incident normally on a dielectric medium with complex relative permittivity $(\varepsilon _r)$ ... electric field component (in V/m) after it has travelled a distance of $10$ cm inside the dielectric region is ____________.
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Vector Analysis
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Milicevic3306
15.8k
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54
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gate2015-ec-1
numerical-answers
vector-analysis
0
votes
0
answers
2110
GATE ECE 2014 Set 4 | GA Question: 1
Which of the following options is the closest in meaning to the word underlined in the sentence below? In a democracy, everybody has the freedom to disagree with the government. dissent descent decent decadent
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Verbal Aptitude
Mar 26, 2018
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15.8k
points
41
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gate2014-ec-4
verbal-ability
most-appropriate-word
0
votes
0
answers
2111
GATE ECE 2014 Set 4 | GA Question: 2
After the discussion, Tom said to me, 'Please revert!'. He expects me to _________. retract get back to him move in reverse retreat
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Verbal Aptitude
Mar 26, 2018
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Milicevic3306
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points
37
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gate2014-ec-4
verbal-ability
most-appropriate-word
0
votes
0
answers
2112
GATE ECE 2014 Set 4 | GA Question: 3
While receiving the award, the scientist said, "I feel vindicated". Which of the following is closest in meaning to the word ‘vindicated’? punished substantiated appreciated chastened
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Verbal Aptitude
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15.8k
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38
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gate2014-ec-4
verbal-ability
most-appropriate-word
0
votes
0
answers
2113
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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Quantitative Aptitude
Mar 26, 2018
by
Milicevic3306
15.8k
points
44
views
gate2014-ec-4
numerical-ability
functions
0
votes
0
answers
2114
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
Mar 26, 2018
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15.8k
points
49
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gate2014-ec-4
numerical-ability
arithmetic-series
numerical-answers
0
votes
0
answers
2115
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
Mar 26, 2018
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15.8k
points
56
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gate2014-ec-4
analytical-aptitude
logical-reasoning
sequence-series
0
votes
0
answers
2116
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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15.8k
points
50
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gate2014-ec-4
logical-reasoning
sequence-series
0
votes
0
answers
2117
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
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by
Milicevic3306
15.8k
points
47
views
gate2014-ec-4
numerical-ability
data-interpretation
0
votes
0
answers
2118
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
Mar 26, 2018
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Milicevic3306
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points
38
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gate2014-ec-4
numerical-ability
data-interpretation
pie-chart
0
votes
0
answers
2119
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
Mar 26, 2018
by
Milicevic3306
15.8k
points
39
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gate2014-ec-4
numerical-ability
couting
0
votes
0
answers
2120
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
Mar 26, 2018
by
Milicevic3306
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points
43
views
gate2014-ec-4
calculus
taylor-series
convergence
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