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721
GATE2019 IN: 47
The output of a continuous-time system y(t) is related to its input x(t) as y(t) = x(t) + $\frac{1}{2}$x(t-1). If the Fourier transforms of x(t) and y(t) are x($\omega$) and y($\omega$) respectively. and |x(0)|$^2$ = 4, the value of |y(0)|$^2$ is $\_\_\_\_$
The output of a continuous-time system y(t) is related to its input x(t) as y(t) = x(t) + $\frac{1}{2}$x(t-1). If the Fourier transforms of x(t) and y(t) are x($\omega$) ...
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722
GATE2016-16
In the circuit given below, the opamp is ideal. The output voltage $V_o$ in volt is $\_\_\_\_\_\_\_\_.$
In the circuit given below, the opamp is ideal. The output voltage $V_o$ in volt is $\_\_\_\_\_\_\_\_.$
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725
GATE2014-37
Assuming an ideal op-amp in linear range of operation, the magnitude of the transfer impedance $\frac{V_0}{i}$ in $M\Omega$ of the current to voltage converter shown in the figure is ___________.
Assuming an ideal op-amp in linear range of operation, the magnitude of the transfer impedance $\frac{V_0}{i}$ in $M\Omega$ of the current to voltage converter shown in t...
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726
GATE2013-41
The signal flow graph for a system is given below. The transfer function $\frac{Y(s)}{U(s)}$ for this system is given as $\frac{s+1}{5s^2+6s+2}$ $\frac{s+1}{s^2+6s+2}$ $\frac{s+1}{s^2+4s+2}$ $\frac{1}{5s^2+6s+2}$
The signal flow graph for a system is given below. The transfer function $\frac{Y(s)}{U(s)}$ for this system is given as $\frac{s+1}{5s^2+6s+2}$$\frac{s+1}{s^2+6s+2}$ $\f...
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727
GATE2013-13
The type of the partial differential equation $\frac{\partial f}{\partial t}=\frac{\partial^2 f}{\partial x^2}$ is Parabolic Elliptic Hyperbolic Nonlinear
The type of the partial differential equation $\frac{\partial f}{\partial t}=\frac{\partial^2 f}{\partial x^2}$ isParabolicEllipticHyperbolicNonlinear
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729
GATE2012-60
Choose the most appropriate word from the options given below to complete the following sentence: $\text{Given the seriousness of the situation that he had to face, his ___ was impressive}$. beggary nomenclature jealousy nonchalance
Choose the most appropriate word from the options given below to complete the following sentence:$\text{Given the seriousness of the situation that he had to face, his __...
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730
GATE2012-55
If $R_L=5\;\Omega,$ the approximate power consumption in the load is $700\;\text{W}$ $750\;\text{W}$ $800\;\text{W}$ $850\;\text{W}$
If $R_L=5\;\Omega,$ the approximate power consumption in the load is $700\;\text{W}$$750\;\text{W}$$800\;\text{W}$$850\;\text{W}$
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731
GATE2012-54
The power factor of the load is $0.45$ $0.50$ $0.55$ $0.60$
The power factor of the load is$0.45$$0.50$$0.55$$0.60$
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735
GATE2020 IN: 51
Assume the diodes in the circuit shown are ideal. The current $I_X$ flowing through the $3\: k\Omega$ resistor $\text{(in mA, rounded off to one decimal place)}$ is ___________
Assume the diodes in the circuit shown are ideal. The current $I_X$ flowing through the $3\: k\Omega$ resistor $\text{(in mA, rounded off to one decimal place)}$ is _____...
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736
GATE2020: 9
A $Q$ meter is best suited for the measurement of the ___________ Quality factor of a capacitance Distributed capacitance of a coil quality factor of piezoelectric sensor Turns-ratio of a transformer
A $Q$ meter is best suited for the measurement of the ___________Quality factor of a capacitanceDistributed capacitance of a coilquality factor of piezoelectric sensorTur...
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737
GATE2020: 13
Consider the signal $x[n]=\sin(2\pi n)u[n]$, where $u[n]= \left\{ \begin{array}{rcl} 1 & n=0,1,2,3\dots \\ 0 & otherwise\end{array}\right. $ The period of this signal $x[n]$ is ___________. $4$ $3$ $2$ $1$
Consider the signal $x[n]=\sin(2\pi n)u[n]$, where $u[n]= \left\{ \begin{array}{rcl} 1 & n=0,1,2,3\dots \\ 0 & otherwise\end{array}\right. $The period of this signal $x[n...
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738
GATE2020: GA: 9
Select the graph that schematically represents $\text{BOTH} \;y=x^m$ and $y=x^{1/m}$ properly in the interval $0\leq x\leq 1$, for integer values of $m$, where $m>1$.
Select the graph that schematically represents $\text{BOTH} \;y=x^m$ and $y=x^{1/m}$ properly in the interval $0\leq x\leq 1$, for integer values of $m$, where $m>1$.
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739
GATE2017: 36
The block diagram of a closed-loop control system is shown in the figure. The values of $K$ and $K_p$ are such that the system has a damping ratio of $0.8$ and an undamped natural frequency $\omega_n$ of $\text{4 rad/s}$ respectively. The value of $K_p$ will be__________________.
The block diagram of a closed-loop control system is shown in the figure. The values of $K$ and $K_p$ are such that the system has a damping ratio of $0.8$ and an undampe...
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741
GATE2017: 28
The following table lists an $n^{th}$ order polynominal $f(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0$ and the forward differences evaluated at equally spaced values of $x$. The order of the polynominal is $1$ $2$ $3$ $4$
The following table lists an $n^{th}$ order polynominal $f(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0$ and the forward differences evaluated at equally spaced values of $x$. T...
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742
GATE2017: 11
If a continuous-time signal $x(t)=\cos(2\pi t)$ is sampled at $ \text{4 Hz}$, the value of the discrete-time sequence $x(n)$ at $n=5$ is $-0.707$ $-1$ $0$ $1$
If a continuous-time signal $x(t)=\cos(2\pi t)$ is sampled at $ \text{4 Hz}$, the value of the discrete-time sequence $x(n)$ at $n=5$ is$-0.707$$-1$$0$$1$
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743
GATE2016-19
In the digital circuit given below, $F$ is $XY+Y\overline{Z}$ $XY+\overline{Y}Z$ $\overline{X}\overline{Y}+Y\overline{Z}$ $XZ+\overline{Y}$
In the digital circuit given below, $F$ is$XY+Y\overline{Z}$$XY+\overline{Y}Z$$\overline{X}\overline{Y}+Y\overline{Z}$$XZ+\overline{Y}$
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744
GATE2016-41
An ideal opamp is used to realize a difference amplifier circuit given below having a gain of $10$. If $x=0.025$, the $CMRR$ of the circuit in $dB$ is $\_\_\_\_\_\_\_\_$.
An ideal opamp is used to realize a difference amplifier circuit given below having a gain of $10$. If $x=0.025$, the $CMRR$ of the circuit in $dB$ is $\_\_\_\_\_\_\_\_$....
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745
GATE2015-32
A system with transfer function $G(S)=\frac{1}{s^2+1} $ has zero initial conditions. The percentage overshoot in its step response is ______________ $\%$.
A system with transfer function $G(S)=\frac{1}{s^2+1} $ has zero initial conditions. The percentage overshoot in its step response is ______________ $\%$.
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746
GATE2015-43
The output frequency of an $LC$ tank oscillator employing a capacitive sensor acting as the capacitor of the tank is $100\;kHz$. If the sensor capacitance increases by $10\% $, the output frequency in kilohertz becomes ____________ $kHz.$
The output frequency of an $LC$ tank oscillator employing a capacitive sensor acting as the capacitor of the tank is $100\;kHz$. If the sensor capacitance increases by $1...
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747
GATE2015-65
The resolving power of a spectrometer consisting of a collimator, a grating and a telescope can be increased by increasing the angular magnification of the telescope increasing the period of the grating decreasing the period of the grating decreasing the slit-width of the collimator
The resolving power of a spectrometer consisting of a collimator, a grating and a telescope can be increased byincreasing the angular magnification of the telescopeincrea...
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749
GATE2014-14
The amplifier in the figure has gain of $-10$ and input resistance of $50\;k\Omega$. The values of $R_i$ and $R_f$ are: $R_i=500\;k\Omega, R_f=50\;k\Omega$ $R_i=50\;k\Omega, R_f=500\;k\Omega$ $R_i=5\;k\Omega, R_f=10\;k\Omega$ $R_i=50\;k\Omega, R_f=200\;k\Omega$
The amplifier in the figure has gain of $-10$ and input resistance of $50\;k\Omega$. The values of $R_i$ and $R_f$ are:$R_i=500\;k\Omega, R_f=50\;k\Omega$$R_i=50\;k\Omega...
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750
GATE2014-24
In order to remove respiration related motion artifacts from an $ECG$ signal, the following filter should be used: low-pass filter with $f_c=0.5\;Hz$ high-pass filter with $f_c=0.5\;Hz$ high-pass filter with $f_c=49.5\;Hz$ band-pass filter with passband between $0.1\;Hz$ and $0.5\;Hz$
In order to remove respiration related motion artifacts from an $ECG$ signal, the following filter should be used:low-pass filter with $f_c=0.5\;Hz$high-pass filter with ...
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751
GATE2014-25
In a time-of-flight mass spectrometer if $q$ is the charge and $m$ the mass of the ionized species, then the time of flight is proportional to $\frac{\sqrt m}{\sqrt q}$ $\frac{\sqrt q}{\sqrt m}$ $\frac{m}{\sqrt q}$ $\frac{q}{\sqrt m}$
In a time-of-flight mass spectrometer if $q$ is the charge and $m$ the mass of the ionized species, then the time of flight is proportional to$\frac{\sqrt m}{\sqrt q}$$\f...
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752
GATE2014-28
For the matrix $A$ satisfying the equation given below, the eigenvalues are $[A] \begin {bmatrix} 1&2&3\\7&8&9\\4&5&6\end{bmatrix}=\begin {bmatrix} 1&2&3\\4&5&6\\7&8&9\end{bmatrix}$ $(1,-j,j)$ $(1,1,0)$ $(1,1,-1)$ $(1,0,0)$
For the matrix $A$ satisfying the equation given below, the eigenvalues are$$[A] \begin {bmatrix} 1&2&3\\7&8&9\\4&5&6\end{bmatrix}=\begin {bmatrix} 1&2&3\\4&5&6\\7&8&9\en...
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753
GATE2013-61
Find the sum to $n$ terms of the series $10+84+734+….$ $\frac{9(9^n+1)}{10}+1$ $\frac{9(9^n-1)}{8}+1$ $\frac{9(9^n-1)}{8}+n$ $\frac{9(9^n-1)}{8}+n^2$
Find the sum to $n$ terms of the series $10+84+734+….$$\frac{9(9^n+1)}{10}+1$$\frac{9(9^n-1)}{8}+1$$\frac{9(9^n-1)}{8}+n$$\frac{9(9^n-1)}{8}+n^2$
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754
GATE2013-25
The bode plot of a transfer function $G(s)$ is shown in the figure below. The gain $(20\;log|G(s)|)$ is $32$ dB and $-8$ dB at $1$ rad/s and $10$ rad/s respectively. The phase is negative for all $\omega$. Then $G(s)$ is $\frac{39.8}{s}$ $\frac{39.8}{s^2}$ $\frac{32}{s}$ $\frac{32}{s^2}$
The bode plot of a transfer function $G(s)$ is shown in the figure below.The gain $(20\;log|G(s)|)$ is $32$ dB and $-8$ dB at $1$ rad/s and $10$ rad/s respectively. The p...
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755
GATE2012-28
The direction of vector $\text{A}$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla.$ $\text{A=0}$ is $-2$ $2$ $1$ $0$
The direction of vector $\text{A}$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla....
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757
GATE2012-3
Two independent random variables $\text{X}$ and $\text{Y}$ are uniformly distributed in the interval $[-1, 1]$. The probability that max$\text{[X, Y]}$ is less than $1/2$ is $3/4$ $9/16$ $1/4$ $2/3$
Two independent random variables $\text{X}$ and $\text{Y}$ are uniformly distributed in the interval $[-1, 1]$. The probability that max$\text{[X, Y]}$ is less than $1/2$...
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758
GATE IN 2023 | Question: 7
Match the Exclusive-$\text{OR (XOR)}$ operations $\text{(i)}$ to $\text{(iv)}$ with the results $\text{(p)}$ to $\text{(s),}$ where $X$ ... $\text{(i) - (p), (ii) - (s), (iii) - (q), (iv) - (r)}$ $\text{(i) - (q), (ii) - (p), (iii) - (s), (iv) - (r)}$
Match the Exclusive-$\text{OR (XOR)}$ operations $\text{(i)}$ to $\text{(iv)}$ with the results $\text{(p)}$ to $\text{(s),}$ where $X$ is a Boolean input.$$\begin{array}...
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