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GATE ECE 2010 | Question: 1
The eigenvalues of a skew-symmetric matrix are always zero always pure imaginary either zero or pure imaginary always real
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GATE ECE 2010 | Question: 2
The trigonometric Fourier series for the waveform $f(t)$ shown below contains only cosine terms and zero value for the $dc$ component only cosine terms and a positive value for the $dc$ component only cosine terms and a negative value for the $dc$ component only sine terms and a negative value for the $dc$ component
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GATE ECE 2010 | Question: 3
A function $n(x)$ satisfies the differential equation $\frac{d^{2} n(x)}{d x^{2}}-\frac{n(x)}{L^{2}}=0$ where $L$ is a constant. The boundary conditions are: $\pi(0)=K$ and $n(\infty)=0$. The solution to this equation is $n(x)=K \exp (x / L)$ $n(x)=K \exp (-x / \sqrt{L})$ $n(x)=K^{2} \exp (-x / L)$ $n(x)=K \exp (-x / L)$
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GATE ECE 2010 | Question: 4
For the Iwo-port network shown below, the short-circuit admittance parameter matrix is $\left[\begin{array}{cc}4 & -2 \\ -2 & 4\end{array}\right] \mathrm{S}$ $\left[\begin{array}{cc}1 & -0.5 \\ -0.5 & 1\end{array}\right] S$ ... $\left[\begin{array}{ll}4 & 2 \\ 2 & 4\end{array}\right] S$
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GATE ECE 2010 | Question: 5
For a parallel $\text{RLC}$ circuit, which one of the following statements is $\text{NOT}$ correct? The bandwidth of the circuit decreases if $\mathrm{R}$ is increased The bandwidth of the circuit remains same if $\mathrm{L}$ is increased At resonance, input impedance is a real quantity At resonance, the magnitude of input impedance attains its minimum value
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GATE ECE 2010 | Question: 6
At room temperature a possible value for the mobility of electrons in the inversion layer of a silicon $n$-channel MOSFET is $450 \mathrm{~cm}^2 / \mathrm{V-s}$ $1350 \mathrm{~cm}^2 / \mathrm{V-s}$ $1800 \mathrm{~cm}^2 / \mathrm{V-s}$ $3600 \mathrm{~cm}^2 / \mathrm{V-s}$
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GATE ECE 2010 | Question: 7
Thin gate oxide in a CMOS process is preferably grown using wet oxidation dry oxidation epitaxial deposition ion implantation
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GATE ECE 2010 | Question: 8
In the silicon BJT circuit shown below, assume that the emitter area of transistor $\text{Q1}$ is half that of transistor $\text{Q2.}$ The value of current $I_0$ is approximately $0.5 \mathrm{~mA}$ $2 \mathrm{~mA}$ $9.3 \mathrm{~mA}$ $15 \mathrm{~mA}$
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GATE ECE 2010 | Question: 9
The amplifier circuit shown below uses a silicon transistor. The capacitors $\mathrm{C}_{\mathrm{C}}$ and $\mathrm{C}_{\mathrm{E}}$ can be assumed to be short at signal frequency and the effect of output resistance $\tau_O$ can be ignored. ... and the magnitude of voltage gain $A_v$ decrease Both input resistance $R_i$ and the magnitude of voltage gain $A_{v}$ increase
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GATE ECE 2010 | Question: 10
Assuming the $\text{OP-AMP}$ to be ideal. the voltage gain of the amplifier shown below is $-\frac{\mathrm{R}_2}{\mathrm{R}_1}$ $-\frac{\mathrm{R}_3}{\mathrm{R}_1}$ $-\left(\frac{\mathrm{R}_2 \| \mathrm{R}_3}{\mathrm{R}_1}\right)$ $-\left(\frac{\mathrm{R}_2+\mathrm{R}_3}{\mathrm{R}_1}\right)$
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GATE ECE 2010 | Question: 11
Match the logic gates in Column A with their equivalents in Column B. $\text{P-2, Q-4, R-1, S-3}$ $\text{P-4, Q-2, R-1, S-3}$ $\text{P-2, Q-4, R-3, S-1}$ $\text{P-4, Q-2, R-3, S-1}$
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GATE ECE 2010 | Question: 12
For the output $\text{F}$ to be $1$ in the logic circuit shown, the input combination should be $\mathrm{A}=1, \mathrm{~B}=1, \mathrm{C}=0$ $\text{A = 1, B = 0, C = 0}$ $\mathrm{A}=0, \mathrm{~B}=1, \mathrm{C}=0$ $\text{A = 0, B = 0, C = 1}$
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GATE ECE 2010 | Question: 13
In the circuit shown, the device connected to $\text{Y5}$ can have address in the range $2000 – \mathrm{20FF}$ $\mathrm{2D00} – \mathrm{2DEF}$ $\mathrm{2E00} – \mathrm{2EFF}$ $\text{FD00 - FDFF}$
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GATE ECE 2010 | Question: 14
Consider the $z$-transform $X(z)=5 z^2+4 z^{-1}+3 ; 0<|z|<\infty$. The inverse $z$-transform $x[n]$ is $5 \delta[n+2]+3 \delta[n]+4 \delta[n-1]$ $5 \delta[n-2]+3 \delta[n]+4 \delta[n+1]$ $5 u[n+2]+3 u[n]+4 u[n-1]$ $5 u[n-2]+3 u[n]+4 u[n+1]$
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GATE ECE 2010 | Question: 15
Two discrete time systems with impulse responses $h_t[n]=\delta[n-1]$ and $h_2[n]=\delta[n-2]$ are connected in cascade. The overall impulse response of the cascaded system is $\delta[n-1]+ \delta[n-2]$ $\delta[n-4]$ $\delta[n-3]$ $\delta[n-1] \delta[n-2]$
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GATE ECE 2010 | Question: 16
For an $\mathrm{N}$-point $\mathrm{FFT}$ algorithm with $\mathrm{N}=2^{\text {m}}$, which one of the following statements is $\text{TRUE}?$ It is not possible to construct a signal flow graph with both input and output in ... $2 \mathrm{N}$ node data Computation of a butterfly requires only one complex multiplication
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GATE ECE 2010 | Question: 17
The transfer function $Y(s) / R(s)$ of the system shown is $0$ $\frac{1}{s+1}$ $\frac{2}{s+1}$ $\frac{2}{s+3}$
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GATE ECE 2010 | Question: 18
A system with the transfer function $\frac{Y(s)}{X(s)}=\frac{s}{s+p}$ has an output $y(t)=\cos \left(2 t-\frac{\pi}{3}\right)$ for the input signal $x(t)=p \cos \left(2 t-\frac{\pi}{2}\right)$. Then, the system parameter $’p’$ is $\sqrt{3}$ $\frac{2}{\sqrt{3}}$ $1$ $\frac{\sqrt{3}}{2}$
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GATE ECE 2010 | Question: 19
For the asymptotic Bode magnitude plot shown below, the system transfer function can be $\frac{10 s+1}{0.1 s+1}$ $\frac{100 s+1}{0.1 s+1}$ $\frac{100 \mathrm{s}}{10 \mathrm{s}+1}$ $\frac{0.1 s+1}{10 s+1}$
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GATE ECE 2010 | Question: 20
Suppose that the modulating signal is $m(t)=2 \cos \left(2 \pi f_{m} t\right)$ and the carrier signal is $x_{c}(t)=A_{C} \cos \left(2 \pi f_{c}t\right)$. Which one of the following is a conventional $\text{AM}$ ...
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GATE ECE 2010 | Question: 21
Consider an angle modulated signal $x(t)=6 \cos \left[2 \pi \times 10^{6} t+2 \sin (8000 \pi t)+4 \cos (8000 \pi t)\right] \mathrm{V}$. The average power of $x(t)$ is $10 \mathrm{~W}$ $18 \mathrm{~W}$ $20 \mathrm{~W}$ $28 \mathrm{~W}$
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GATE ECE 2010 | Question: 22
If the scattering matrix $[S]$ of a two port network is \[ [S]=\left[\begin{array}{cc} 0.2 \angle 0^{\circ} & 0.9 \angle 90^{\circ} \\ 0.9 \angle 90^{\circ} & 0.1 \angle 90^{\circ} \end{array}\right] \] then the network is lossless and reciprocal lossless but not reciprocal not lossless but reciprocal neither lossless nor reciprocal
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GATE ECE 2010 | Question: 23
A transmission line has a characteristic impedance of $50 \; \Omega$ and a resistance of $0.1 \; \Omega / \mathrm{m}$. If the line is distortionless, the attenuation constant (in $\mathrm{Np/m})$ is $500$ $5$ $0.014$ $0.002$
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GATE ECE 2010 | Question: 24
Consider the pulse shape $s(t)$ as shown. The impulse response $h(t)$ of the filter matched to this pulse is
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GATE ECE 2010 | Question: 25
The electric field component of a time harmonic plane EM wave traveling in a nonmagnetic lossless dielectric medium has an amplitude of $1 \; \mathrm{V/m}$. If the relative permittivity of the medium is $4$, the magnitude of the time-average power density vector (in $\text{W/m}^{2}$ ) is $\frac{1}{30 \pi}$ $\frac{1}{60 \pi}$ $\frac{1}{120 \pi}$ $\frac{1}{240 \pi}$
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GATE ECE 2010 | Question: 26
If $e^{y}=x^{\frac{1}{x}}$, then $y$ has a maximum at $x=e$ minimum at $x=e$ maximum at $x=e^{-1}$ minimum at $x=e^{-1}$
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GATE ECE 2010 | Question: 27
A fair coin is tossed independently four times. The probability of the event "the number of times heads show up is more than the number of times taits show up" is $\frac{1}{16}$ $\frac{1}{8}$ $\frac{1}{4}$ $\frac{5}{16}$
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GATE ECE 2010 | Question: 28
If $\vec{A}=x y \hat{a}_{4}+x^{2} \hat{a}_{3}$, then $\oint_{c} \vec{A} \cdot d \vec{l}$ over the path shown in the figure is $0$ $\frac{2}{\sqrt{3}}$ $1$ $2 \sqrt{3}$
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GATE ECE 2010 | Question: 29
The residues of a complex function $X(z)=\frac{1-2 z}{z(z-1)(z-2)}$ at its poles are $\frac{1}{2},-\frac{1}{2}$ and $1$ $\frac{1}{2}, \frac{1}{2}$ and $-1$ $\frac{1}{2}, 1$ and $-\frac{3}{2}$ $\frac{1}{2},-1$ and $\frac{3}{2}$
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GATE ECE 2010 | Question: 30
Consider a differential equation $\frac{d y(x)}{d x}-y(x)=x$ with the initial condition $y(0)=0$. Using Euler's first order method with a step size of $0.1$, the value of $y(0.3)$ is $0.01$ $0.031$ $0.0631$ $0.3$
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GATE ECE 2010 | Question: 31
Given $f(t)=\mathscr{L}^{-1}\left[\frac{3 s+1}{s^{3}+4 s^{2}+(K-3) s}\right]$. If $\lim _{t \rightarrow } f(t)=1$, then the value of $K$ is $1$ $2$ $3$ $4$
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GATE ECE 2010 | Question: 32
In the circuit shown, the switch $S$ is open for a long time and is closed at $t=0$. The current $i(t)$ for $t \geq 0$ is $i(t)=0.5-0.125 e^{-1000} \mathrm{~A}$ $i(t)=1.5-0.125 e^{-1000} \mathrm{~A}$ $i(t)=0.5-0.5 e^{-1000} \mathrm{~A}$ $i(t)=0.375 e^{- 1000} \mathrm{~A}$
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GATE ECE 2010 | Question: 33
The current $\mathrm{I}$ in the circuit shown is $\text{-j 1 A}$ $\text{j 1 A}$ $0 \mathrm{~A}$ $20 \mathrm{~A}$
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GATE ECE 2010 | Question: 34
In the circuit shown, the power supplied by the voltage source is $0 \mathrm{~W}$ $5 \mathrm{~W}$ $10 \mathrm{~W}$ $100 \mathrm{~W}$
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GATE ECE 2010 | Question: 35
In a uniformly doped BJT, assume that $N_{E}, N_{H}$ and $N_{C}$ are the emitter, base and collector dopings in $\text{atoms/cm}^{3}$ ... $\mathrm{N}_{\mathrm{H}}<\mathrm{N}_{\mathrm{B}}<\mathrm{N}_{\mathrm{C}}$
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GATE ECE 2010 | Question: 36
Compared to a $p-n$ junction with $\mathrm{N}_{\mathrm{A}}=\mathrm{N}_{\mathrm{D}}=10^{14} / \mathrm{cm}^{3}$, which one of the following statements is $\text{TRUE}$ for a $p-n$ junction ... and depletion capacitance is lower Reverse breakdown voltage is lower and depletion capacitance is higher Reverse breakdown voltage is higher and depletion capacitance is higher
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GATE ECE 2010 | Question: 37
Assuming that all flip-flops are in reset condition initially, the count sequence observed at $Q_{A}$ in the circuit shown is $0010111 \ldots$ $0001011 \ldots$ $0101111 \ldots$ $0110100 \ldots$
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GATE ECE 2010 | Question: 38
The transfer characteristic for the precision rectifier circuit shown below is (assume ideal $\text{OP-AMP}$ and practical diodes)
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GATE ECE 2010 | Question: 39
The Boolean function realized by the logic circuit shown is $F = \sum_{m} (0, 1, 3, 5, 9, 10, 14)$ $F=\sum_{m}(2,3,5,7,8,12,13)$ $F=\sum_{m}(1,2,4,5,11, 14,15)$ $F= \sum_{m}(2,3,5,7,8,9,12)$
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GATE ECE 2010 | Question: 40
For the $8085$ ... $\text{00H}$ $45 \text{H}$ $\text{67H}$ $\text{E7H}$
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