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2722
GATE ECE 2014 Set 1 | GA Question: 8
A train that is $280$ meters long, traveling at a uniform speed, crosses a platform in $60$ seconds and passes a man standing on the platform in $20$ seconds. What is the length of the platform in meters?
A train that is $280$ meters long, traveling at a uniform speed, crosses a platform in $60$ seconds and passes a man standing on the platform in $20$ seconds. What is the...
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2725
GATE ECE 2014 Set 1 | Question: 1
For matrices of same dimension $M, N$ and scalar $c$, which one of these properties DOES NOT ALWAYS hold? $(M^{T})^{T} = M$ $(cM)^{T} = c(M)^{T}$ $(M+N)^{T} = M^{T} + N^{T}$ $MN = NM$
For matrices of same dimension $M, N$ and scalar $c$, which one of these properties DOES NOT ALWAYS hold?$(M^{T})^{T} = M$$(cM)^{T} = c(M)^{T}$$(M+N)^{T} = M^{T} + N^{T}...
1 votes
1 answer
2726
GATE ECE 2014 Set 1 | Question: 2
In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is ________.
In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at r...
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2727
GATE ECE 2014 Set 1 | Question: 3
$C$ is a closed path in the $z$-plane given by $\mid z \mid = 3.$ The value of the integral $\displaystyle{}\oint_{C}\bigg(\dfrac{z^{2}-z+4j}{z+2j}\bigg)dz$ is $-4\pi(1+j2)$ $4\pi(3-j2)$ $-4\pi(3+j2)$ $4\pi(1-j2)$
$C$ is a closed path in the $z$-plane given by $\mid z \mid = 3.$ The value of the integral $\displaystyle{}\oint_{C}\bigg(\dfrac{z^{2}-z+4j}{z+2j}\bigg)dz$ is$-4\pi(1+j2...
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2728
GATE ECE 2014 Set 1 | Question: 4
A real $(4 \times 4)$ matrix $A$ satisfies the equation $A^{2} = I$, where $I$ is the $(4 \times 4)$ identity matrix. The positive eigen value of $A$ is ______.
A real $(4 \times 4)$ matrix $A$ satisfies the equation $A^{2} = I$, where $I$ is the $(4 \times 4)$ identity matrix. The positive eigen value of $A$ is ______.
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2729
GATE ECE 2014 Set 1 | Question: 5
Let $X_{1},X_{2},$ and $X_{3}$ be independent and identically distributed random variables with the uniform distribution on $[0,1].$ The probability $P\{X_{1}\: \text{is the largest}\}$ is ________.
Let $X_{1},X_{2},$ and $X_{3}$ be independent and identically distributed random variables with the uniform distribution on $[0,1].$ The probability $P\{X_{1}\: \text{is ...
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2732
GATE ECE 2014 Set 1 | Question: 8
When the optical power incident on a photodiode is $10\:\mu W$ and the responsivity is $0.8\: A/ W,$ the photocurrent generated $(\text{in} \:\mu A)$ is_______.
When the optical power incident on a photodiode is $10\:\mu W$ and the responsivity is $0.8\: A/ W,$ the photocurrent generated $(\text{in} \:\mu A)$ is_______.
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2733
GATE ECE 2014 Set 1 | Question: 9
In the figure, assume that the forward voltage drops of the $PN$ diode $D_{1}$ and Schottky diode $D_{2}$ are $0.7\: V$ and $0.3\: V,$ ... is ON and $D_{2}$ is OFF both $D_{1}$ and $D_{2}$ are OFF $D_{1}$ is OFF and $D_{2}$ is ON
In the figure, assume that the forward voltage drops of the $PN$ diode $D_{1}$ and Schottky diode $D_{2}$ are $0.7\: V$ and $0.3\: V,$ respectively. If ON denotes conduct...
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2734
GATE ECE 2014 Set 1 | Question: 10
If fixed positive charges are present in the gate oxide of an $n$-channel enhancement type MOSFET, it will lead to a decrease in the threshold voltage channel length modulation an increase in substrate leakage current an increase in accumulation capacitance
If fixed positive charges are present in the gate oxide of an $n$-channel enhancement type MOSFET, it will lead to a decrease in the threshold voltagechannel length modul...
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2735
GATE ECE 2014 Set 1 | Question: 11
A good current buffer has low input impedance and low output impedance low input impedance and high output impedance high input impedance and low output impedance high input impedance and high output impedance
A good current buffer haslow input impedance and low output impedancelow input impedance and high output impedancehigh input impedance and low output impedancehigh input ...
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2736
GATE ECE 2014 Set 1 | Question: 12
In the ac equivalent circuit shown in the figure, if $i_{in}$ is the input current and $R_{F}$ is very large, the type of feedback is voltage-voltage feedback voltage-current feedback current-voltage feedback current-current feedback
In the ac equivalent circuit shown in the figure, if $i_{in}$ is the input current and $R_{F}$ is very large, the type of feedback isvoltage-voltage feedbackvoltage-curre...
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2737
GATE ECE 2014 Set 1 | Question: 13
In the low-pass filter shown in the figure, for a cut-off frequency of $5\:kHz,$ the value of $R_{2}\:(\text{in}\:k\Omega)$ is ______.
In the low-pass filter shown in the figure, for a cut-off frequency of $5\:kHz,$ the value of $R_{2}\:(\text{in}\:k\Omega)$ is ______.
1 votes
2 answers
2739
GATE ECE 2014 Set 1 | Question: 15
The Boolean expression $(X+Y)(X+\overline{Y}) + \overline{(X\;\overline{Y}) + \overline{X}}$ simplifies to $X$ $Y$ $XY$ $X+Y$
The Boolean expression $(X+Y)(X+\overline{Y}) + \overline{(X\;\overline{Y}) + \overline{X}}$ simplifies to$X$$Y$$XY$$X+Y$
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2740
GATE ECE 2014 Set 1 | Question: 16
Five JK flip-flops are cascaded to form the circuit shown in Figure. Clock pulses at a frequency of $1\: MHz$ are applied as shown. The frequency $(\text{in}\:kHz)$ of the waveform at $Q3$ is ________.
Five JK flip-flops are cascaded to form the circuit shown in Figure. Clock pulses at a frequency of $1\: MHz$ are applied as shown. The frequency $(\text{in}\:kHz)$ of th...
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1 answer
2741
GATE ECE 2014 Set 1 | Question: 17
A discrete-time signal $x[n] = \sin(\pi^{2}n),n$ being an integer, is periodic with period $\pi$ periodic with period $\pi^{2}$ periodic with period $\pi/2$ not periodic
A discrete-time signal $x[n] = \sin(\pi^{2}n),n$ being an integer, isperiodic with period $\pi$periodic with period $\pi^{2}$periodic with period $\pi/2$not periodic
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2742
GATE ECE 2014 Set 1 | Question: 18
Consider two real valued signals, $x(t)$ band-limited to $[-500\:Hz,500\:Hz]$ and $y(t)$ band-limited to $[-1\:kHz,1\:kHz].$ For $z(t) = x(t)\cdot y(t),$ the Nyquist sampling frequency (in $kHz$) is _______.
Consider two real valued signals, $x(t)$ band-limited to $[-500\:Hz,500\:Hz]$ and $y(t)$ band-limited to $[-1\:kHz,1\:kHz].$ For $z(t) = x(t)\cdot y(t),$ the Nyquist samp...
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2744
GATE ECE 2014 Set 1 | Question: 20
The forward path transfer function of a unity negative feedback system is given by $G(s) = \frac{K}{(s+2)(s-1)}$. The value of $K$ which will place both the poles of the closed-loop system at the same location, is _______.
The forward path transfer function of a unity negative feedback system is given by $$G(s) = \frac{K}{(s+2)(s-1)}$$. The value of $K$ which will place both the poles of th...
0 votes
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2746
GATE ECE 2014 Set 1 | Question: 22
In a code-division multiple access $(\text{CDMA})$ system with $N = 8$ chips, the maximum number of users who can be assigned mutually orthogonal signature sequences is ________.
In a code-division multiple access $(\text{CDMA})$ system with $N = 8$ chips, the maximum number of users who can be assigned mutually orthogonal signature sequences is _...
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2747
GATE ECE 2014 Set 1 | Question: 23
The capacity of a Binary Symmetric Channel $\text{(BSC)}$ with cross-over probability $0.5$ is ________.
The capacity of a Binary Symmetric Channel $\text{(BSC)}$ with cross-over probability $0.5$ is ________.
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2750
GATE ECE 2014 Set 1 | Question: 26
The Taylor series expansion of $3\sin x + 2 \cos x$ is $2 + 3x-x^{2} – \frac{x^{3}}{2} + \dots$ $2 – 3x + x^{2} – \frac{x^{3}}{2} + \dots$ $2 + 3x + x^{2} + \frac{x^{3}}{2} + \dots$ $2 – 3x – x^{2} + \frac{x^{3}}{2} + \dots$
The Taylor series expansion of $3\sin x + 2 \cos x$ is$2 + 3x-x^{2} – \frac{x^{3}}{2} + \dots$$2 – 3x + x^{2} – \frac{x^{3}}{2} + \dots$$2 + 3x + x^{2} + \frac...
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2752
GATE ECE 2014 Set 1 | Question: 28
The volume under the surface $z(x,y) = x + y$ and above the triangle in the $x – y$ plane defined by $\{0 \leq y \leq x \: \text{and} \: 0 \leq x \leq 12\}$ is _______.
The volume under the surface $z(x,y) = x + y$ and above the triangle in the $x – y$ plane defined by $\{0 \leq y \leq x \: \text{and} \: 0 \leq x \leq 12\}$ is _______....
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2753
GATE ECE 2014 Set 1 | Question: 29
Consider the matrix ... $\alpha$ is a non-negative real number. The value of $\alpha$ for which $\text{det(P)} = 0$ is _______.
Consider the matrix $$J_{6} = \begin{bmatrix} 0&0 &0 &0 &0 &1 \\ 0& 0& 0& 0& 1&0 \\ 0& 0& 0& 1& 0&0 \\ 0&0 & 1& 0&0 &0 \\0 &1 &0 &0 &0 &0 \\1 &0 &0 &0 & 0& 0\end{bmatrix}...
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2754
GATE ECE 2014 Set 1 | Question: 30
A $Y$-network has resistances of $10\Omega$ each in two of its arms, while the third arm has a resistance of $11\Omega.$ In the equivalent $\Delta$ – network, the lowest value (in $\Omega)$ among the three resistances is ______.
A $Y$-network has resistances of $10\Omega$ each in two of its arms, while the third arm has a resistance of $11\Omega.$ In the equivalent $\Delta$ – network, the lowe...
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2756
GATE ECE 2014 Set 1 | Question: 32
A periodic variable $x$ is shown in the figure as a function of time. The root-mean-square (rms) value of $x$ is _______.
A periodic variable $x$ is shown in the figure as a function of time. The root-mean-square (rms) value of $x$ is _______.
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2757
GATE ECE 2014 Set 1 | Question: 33
In the circuit shown in the figure, the value of capacitor $C\:(\text{in}\: mF)$ needed to have critically damped response $i(t)$ is ____.
In the circuit shown in the figure, the value of capacitor $C\:(\text{in}\: mF)$ needed to have critically damped response $i(t)$ is ____.
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2758
GATE ECE 2014 Set 1 | Question: 34
A BJT is biased in forward active mode. Assume $V_{EE} = 0.7\:V, \: kT/q = 25\:mV$ and reverse saturation current $I_{S} = 10^{-13}\:A.$ The transconductance of the BJT (in $mA/V$) is __________
A BJT is biased in forward active mode. Assume $V_{EE} = 0.7\:V, \: kT/q = 25\:mV$ and reverse saturation current $I_{S} = 10^{-13}\:A.$ The transconductance of the BJT ...
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