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241
GATE2015-12
The value of $\oint \frac{1}{Z^2} dZ,$ where the contour is the unit circle traversed clockwise, is $-2\pi i$ $0$ $2\pi i$ $4\pi i$
The value of $\oint \frac{1}{Z^2} dZ,$ where the contour is the unit circle traversed clockwise, is$-2\pi i$$0$$2\pi i$$4\pi i$
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242
GATE2015-39
The current in amperes through the resistor $R$ in the circuit shown in the figure is ______________ $A$.
The current in amperes through the resistor $R$ in the circuit shown in the figure is ______________ $A$.
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244
GATE2013-40
A signal $V_i(t)=10+10\sin 100\pi t+10\sin 4000 \pi t+10\sin 100000\pi t$ is supplied to a filter circuit (shown below) made up of ideal op-amps. The least attenuated frequency component in the output will be $\text{0 Hz}$ $\text{50 Hz}$ $\text{2 kHz}$ $\text{50 kHz}$
A signal $V_i(t)=10+10\sin 100\pi t+10\sin 4000 \pi t+10\sin 100000\pi t$ is supplied to a filter circuit (shown below) made up of ideal op-amps. The least attenuated fre...
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246
GATE2012-38
The feedback system shown below oscillates at $2\;\text{rad/s}$ when $K=2$ and $a=0.75$ $K=3$ and $a=0.75$ $K=4$ and $a=0.5$ $K=2$ and $a=0.5$
The feedback system shown below oscillates at $2\;\text{rad/s}$ when$K=2$ and $a=0.75$$K=3$ and $a=0.75$$K=4$ and $a=0.5$$K=2$ and $a=0.5$
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248
GATE IN 2022 | Question: 24
The Newton-Raphson method is applied to determine the solution of $f(x) = 0$ where $f(x) = x – \cos (x).$ If the initial guess of the solution is $x_{0} = 0,$ the value of the next approximation $x_{1}$ is ________ (round off to two decimal places)
The Newton-Raphson method is applied to determine the solution of $f(x) = 0$ where $f(x) = x – \cos (x).$ If the initial guess of the solution is $x_{0} = 0,$ the value...
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250
GATE IN 2021 | GA Question: 8
Five line segments of equal lengths, $\text{PR, PS, QS, QT}$ and $\text{RT}$ are used to form a star as shown in the figure above. The value of $\theta$, in degrees, is _______________ $36$ $45$ $72$ $108$
Five line segments of equal lengths, $\text{PR, PS, QS, QT}$ and $\text{RT}$ are used to form a star as shown in the figure above.The value of $\theta$, in degrees, is __...
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251
GATE IN 2021 | Question: 14
The diode used in the circuit has a fixed voltage drop of $\text{0.6 V}$ when forward biased. A signal $v_{s}$ is given to the ideal $\text{OpAmp}$ as shown. When $v_{s}$ is at its positive peak, the output $(v_{OA})$ of the $\text{OpAmp}$ in volts is ___________.
The diode used in the circuit has a fixed voltage drop of $\text{0.6 V}$ when forward biased. A signal $v_{s}$ is given to the ideal $\text{OpAmp}$ as shown. When $v_{s}$...
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252
GATE IN 2021 | Question: 23
Consider the function $f\left ( x \right )=-x^{2}+10x+100$. The minimum value of the function in interval $[5,10]$ is ___________.
Consider the function $f\left ( x \right )=-x^{2}+10x+100$. The minimum value of the function in interval $[5,10]$ is ___________.
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253
GATE IN 2021 | Question: 52
In the bridge circuit shown, the voltmeter $\text{V}$ showed zero when the value of the resistors are: $R_{1}=100\:\Omega$, $R_{2}=110\:\Omega$, and $R_{3}=90\:\Omega$. If $\left ( R_{1}/R_{2} \right )=\left ( R_{A}/R_{B} \right )$, the value of $R_{4}$ is ohm is ________.
In the bridge circuit shown, the voltmeter $\text{V}$ showed zero when the value of the resistors are: $R_{1}=100\:\Omega$, $R_{2}=110\:\Omega$, and $R_{3}=90\:\Omega$. I...
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255
GATE2019 IN: 15
In a single-mode optical fiber, the zero-dispersion wavelength refers to the wavelength at which the material dispersion is zero. waveguide dispersion is zero. sum of material dispersion and waveguide dispersion is zero. material dispersion and waveguide dispersion are simultaneously zero.
In a single-mode optical fiber, the zero-dispersion wavelength refers to the wavelength at which the material dispersion is zero.waveguide dispersion is zero.sum of mater...
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256
GATE2019 IN: 46
The transfer function relating the input x(t) to the output y(t) of a system is given by G(s) = 1/(s + 3). A unit-step input is applied to the system at time t = 0. Assuming that y(0) = 3, the value of y(t) at time t = 1 is $\_\_\_\_$ (Answer should be rounded off to two decimal places)
The transfer function relating the input x(t) to the output y(t) of a system is given by G(s) = 1/(s + 3). A unit-step input is applied to the system at time t = 0. Assum...
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257
GATE2013-2
If the A-matrix of the state space model of a $SISO$ linear time invariant system is rank deficient, the transfer function of the system must have a pole with a positive real part a pole with a negative real part a pole with a positive imaginary part a pole at the origin
If the A-matrix of the state space model of a $SISO$ linear time invariant system is rank deficient, the transfer function of the system must have a pole with a positive ...
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263
GATE IN 2022 | Question: 18
The global minimum of $x^{3} e^{-|x|}$ for $x \in (-\infty, \infty)$ occurs at $x = $ _________ (round off to one decimal place)
The global minimum of $x^{3} e^{-|x|}$ for $x \in (-\infty, \infty)$ occurs at $x = $ _________ (round off to one decimal place)
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268
GATE2020: 17
Assuming ideal opamps, the output voltage at $V_1$ in the figure shown (in volts) is __________
Assuming ideal opamps, the output voltage at $V_1$ in the figure shown (in volts) is __________
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269
GATE2017: 40
Assuming the opamp shown in the figure to be ideal, the frequency at which the magnitude of $V_\circ$ will be $95\%$ of the magnitude of $V_{in}$ is ______________$kHz$.
Assuming the opamp shown in the figure to be ideal, the frequency at which the magnitude of $V_\circ$ will be $95\%$ of the magnitude of $V_{in}$ is ______________$kHz$.
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273
GATE2015-27
Let 3+4j be a zero of a fourth order linear-phase $FIR$ filter. The complex number which is $NOT$ a zero of this filter is $3-4j$ $\frac{3}{25}+\frac{4}{25}j$ $\frac{3}{25}-\frac{4}{25}j$ $\frac{1}{3}-\frac{1}{4}j$
Let 3+4j be a zero of a fourth order linear-phase $FIR$ filter. The complex number which is $NOT$ a zero of this filter is$3-4j$$\frac{3}{25}+\frac{4}{25}j$$\frac{3}{25}-...
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274
GATE2015-59
In the potentiometer circuit shown in the figure, the expression for $V_X$ is ____________. $(1-2\alpha)V$ $(1-\alpha)V$ $(\alpha-1)V$ $\alpha V$
In the potentiometer circuit shown in the figure, the expression for $V_X$ is ____________.$(1-2\alpha)V$$(1-\alpha)V$$(\alpha-1)V$$\alpha V$
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275
GATE2014-22
The resistance and inductance of an inductive coil are measured using an AC bridge as shown in the figure. The bridge is to be balanced by varying the impedance $Z_2$. For obtaining balance, $Z_2$ should consist of element(s): $R$ and $C$ $R$ and $L$ $L$ and $C$ Only $C$
The resistance and inductance of an inductive coil are measured using an AC bridge as shown in the figure. The bridge is to be balanced by varying the impedance $Z_2$.For...
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277
GATE2013-21
Consider a delta connection of resistors and its equivalent star connection as shown. If all elements of the delta connection are scaled by a factor k, k>0, the elements of the corresponding star equivalent will be scaled by a factor of $k^2$ $k$ $\frac{1}{k}$ $\sqrt{k}$
Consider a delta connection of resistors and its equivalent star connection as shown. If all elements of the delta connection are scaled by a factor k, k>0, the elements ...
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280
GATE2018IN: 46
The Boolean function $F(X, Y)$ realized by the given circuit is $\overline{X} Y + X \overline{Y}$ $\overline{X} \;\overline{Y}+ X Y$ $X + Y$ $\overline{X}\cdot \overline{Y}$
The Boolean function $F(X, Y)$ realized by the given circuit is $\overline{X} Y + X \overline{Y}$$\overline{X} \;\overline{Y}+ ...
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