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Recent questions tagged numerical-answers

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161
GATE2019 IN: 17
In the circuit shown below, maximum power is transferred to the load resistance R${_L}$, when R${_L}$ = $\_\_\_\_$ $\Omega$.
In the circuit shown below, maximum power is transferred to the load resistance R${_L}$, when R${_L}$ = $\_\_\_\_$ $\Omega$.
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162
GATE2019 IN: 24
A pitot-static tube is used to estimate the velocity of an incompressible fluid of density 1 kg/m$^{3}$. If the pressure differences measured by the tube is 200 N/m$^{2}$, the velocity of the fluid, assuming the pitot-tube coefficient to be 1.0, is $\_\_\_\_$m/s.
A pitot-static tube is used to estimate the velocity of an incompressible fluid of density 1 kg/m$^{3}$. If the pressure differences measured by the tube is 200 N/m$^{2}$...
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165
GATE2019 IN: 44
In the circuit shown below, a step input voltage of magnitude 5 V is applied at node A at time t = 0. If the capacitor has no charge for t $\leq$ 0, the voltage at node P at t=6 ${\mu}$s is $\_\_\_\_$ V.(Answer should be rounded off to two decimal places)
In the circuit shown below, a step input voltage of magnitude 5 V is applied at node A at time t = 0. If the capacitor has no charge for t $\leq$ 0, the voltage at node P...
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166
GATE2019 IN: 45
In the circuit shown below, the angular frequency $\omega$ at which the current is in phase with the voltage is $\_\_\_\_\_\_$ rad/s.
In the circuit shown below, the angular frequency $\omega$ at which the current is in phase with the voltage is $\_\_\_\_\_\_$ rad/s.
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167
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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168
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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169
GATE2019 IN: 48
A discrete- time signal x[n] = e$^{j(\frac{5\pi}{3})n}$ + e$^{j(\frac{\pi}{4})n}$ is down-sampled to the signal x${_d}[n]$ such that x${_d}[n]$ = x[4n]. The fundamental period of the down-sampled signal x${_d}[n]$ is $\_\_\_\_\_\_$.
A discrete- time signal x[n] = e$^{j(\frac{5\pi}{3})n}$ + e$^{j(\frac{\pi}{4})n}$ is down-sampled to the signal x${_d}[n]$ such that x${_d}[n]$ = x[4n]. The fundamental...
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170
GATE2019 IN: 49
In a control system with unity gain feedback, the transfer function of the loop-gain function is L(S) = 9e$^{-0.1s}$/S. The phase margin of the loop-gain function L(S) is ${\_\_\_\_}$ degree
In a control system with unity gain feedback, the transfer function of the loop-gain function is L(S) = 9e$^{-0.1s}$/S. The phase margin of the loop-gain function L(S) is...
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171
GATE2019 IN: 50
In the circuit shown below, all transistors are n-channel enhancement mode MOSFETs. They are identical and are biased to operate in saturation mode. Ignoring channel length modulation, the output voltage V${_o}{_u}{_t}$ is ${\_\_\_\_\_}$ V.
In the circuit shown below, all transistors are n-channel enhancement mode MOSFETs. They are identical and are biased to operate in saturation mode. Ignoring channel leng...
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172
GATE2019 IN: 51
In the circuit shown below, all OPAMPS are ideal. The current I = 0 A when the resistance R = $\_\_\_\_\_$ k$\Omega$
In the circuit shown below, all OPAMPS are ideal. The current I = 0 A when the resistance R = $\_\_\_\_\_$ k$\Omega$
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177
GATE 2016 - 1
A straight line of the form $y=mx+c$ passes through the origin and the point $(x,y)$ =$(2,6)$. The value of $m$ is _____.
A straight line of the form $y=mx+c$ passes through the origin and the point $(x,y)$ =$(2,6)$. The value of $m$ is _____.
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178
GATE2016-2
$\underset{n\rightarrow \infty }{\lim}\:\left(\sqrt{n^2+n}-\sqrt{n^2+1}\right)$ is __________.
$\underset{n\rightarrow \infty }{\lim}\:\left(\sqrt{n^2+n}-\sqrt{n^2+1}\right)$ is __________.
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180
GATE2016-6
Three currents $i_1, i_2$ and $i_3$ meet at a node as shown in the figure below. If $i_1=3\cos(\omega t)$ ampere, $i_2=4\sin(\omega t)$ ampere and $i_3=I_3\cos(\omega t+\theta)$ ampere, the value of $I_3$ in $\text{ampere}$ is $\_\_\_\_\_\_\_.$
Three currents $i_1, i_2$ and $i_3$ meet at a node as shown in the figure below. If $i_1=3\cos(\omega t)$ ampere, $i_2=4\sin(\omega t)$ ampere and $i_3=I_3\cos(\omega t+\...
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181
GATE2016-7
An air cored coil has a $Q$ of $5$ at a frequency of $100$ kHz. The $Q$ of the coil at $20$ kHz (neglecting skin effect) will be ________.
An air cored coil has a $Q$ of $5$ at a frequency of $100$ kHz. The $Q$ of the coil at $20$ kHz (neglecting skin effect) will be ________.
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182
GATE2016-8
A current $i(t)$ shown in the figure below is passed through a $\text{1 F}$ capacitor that had zero initial charge. The voltage across the capacitor for $t>2s$ in $volt$ is $\_\_\_\_\_\_\_$.
A current $i(t)$ shown in the figure below is passed through a $\text{1 F}$ capacitor that had zero initial charge. The voltage across the capacitor for $t>2s$ in $volt$ ...
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183
GATE2016-9
The signal $x[n]$ shown in the figure below is convolved with itself to get $y[n]$. The value of $y[-1]$ is $\_\_\_\_\_\_\_\_.$
The signal $x[n]$ shown in the figure below is convolved with itself to get $y[n]$. The value of $y[-1]$ is $\_\_\_\_\_\_\_\_.$
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184
GATE2016-10
In the circuit shown below $ (v_1+v_2) =[1\; \sin(2\pi10000t)] + 1\;\sin(2\pi30000t)] \;V.$ The $RMS$ value of the current through the resistor $R$ will be minimum if the value of the capacitor $C$ in $\text{microfarad}$ is ____________.
In the circuit shown below $ (v_1+v_2) =[1\; \sin(2\pi10000t)] + 1\;\sin(2\pi30000t)] \;V.$ The $RMS$ value of the current through the resistor $R$ will be minimum if th...
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185
GATE2016-11
If $X(s)$, the Laplace transform of signal $x(t)$ is given by $X(s) = \frac{(s+2)}{(s+1)(s+3)^2}$, then the value of $x(t)$ as $t\rightarrow \infty$ is ______.
If $X(s)$, the Laplace transform of signal $x(t)$ is given by $X(s) = \frac{(s+2)}{(s+1)(s+3)^2}$, then the value of $x(t)$ as $t\rightarrow \infty$ is ______.
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186
GATE2016-12
The number of times the Nyquist plot of $G(s)= \frac{s-1}{s+1}$ will encircle the origin clockwise is _______.
The number of times the Nyquist plot of $G(s)= \frac{s-1}{s+1}$ will encircle the origin clockwise is _______.
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187
GATE2016-14
The input $i(t)$ = $2\sin(3t+\pi)$ is applied to a system whose transfer function $G(s)=\frac{8}{(s+10)^2}$. The amplitude of the output of the system is _______.
The input $i(t)$ = $2\sin(3t+\pi)$ is applied to a system whose transfer function $G(s)=\frac{8}{(s+10)^2}$.The amplitude of the output of the system is _______.
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188
GATE2016-15
The diode $D$ used in the circuit below is ideal. The voltage drop $V_{ab}$ across the $1\;k\Omega$ resistor in $\text{volt}$ is $\_\_\_\_\_\_\_\_.$
The diode $D$ used in the circuit below is ideal. The voltage drop $V_{ab}$ across the $1\;k\Omega$ resistor in $\text{volt}$ is $\_\_\_\_\_\_\_\_.$
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189
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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191
GATE2016-23
A peizo-electric type pressure sensor has a sensitivity of $\text{1 mV/kPa}$ and a bandwidth of $\text{300 Hz to 300 kHz.}$ For a constant (dc) pressure of $\text{100 kPa}$, the steady state output of the sensor in $\text{mllivolt}$ is $\_\_\_\_\_\_\_.$
A peizo-electric type pressure sensor has a sensitivity of $\text{1 mV/kPa}$ and a bandwidth of $\text{300 Hz to 300 kHz.}$ For a constant (dc) pressure of $\text{100 kPa...
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192
GATE2016-26
Let $f: [-1,1]\rightarrow \mathbb{R}$, where $f(x)=2x^3-x^4-10$. The minimum value of $f(x)$ is $\_\_\_\_\_\_\_.$
Let $f: [-1,1]\rightarrow \mathbb{R}$, where $f(x)=2x^3-x^4-10$. The minimum value of $f(x)$ is $\_\_\_\_\_\_\_.$
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193
GATE2016-28
Consider the matrix $A= \begin{pmatrix} 2 & 1 & 1\\ 2& 3& 4\\ -1& -1 & -2 \end{pmatrix} $ whose eigenvalues are $1, -1$ and $3$. Then Trace of $(A^3-3A^2)$ is $\_\_\_\_\_\_.$
Consider the matrix $A= \begin{pmatrix} 2 & 1 & 1\\ 2& 3& 4\\ -1& -1 & -2 \end{pmatrix} $ whose eigenvalues are $1, -1$ and $3$. Then Trace of $(A^3-3A^2)$ is $\_\_\_\_\_...
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194
GATE2016-30
The value of the integral $\displaystyle{}\frac{1}{2\pi j}\int_c \frac{Z^2+1}{Z^2-1}dz$ where $z$ is a complex number and $C$ is a unit circle with center at $1+0j$ in the complex plane is $\_\_\_\_\_\_\_\_.$
The value of the integral $\displaystyle{}\frac{1}{2\pi j}\int_c \frac{Z^2+1}{Z^2-1}dz$ where $z$ is a complex number and $C$ is a unit circle with center at $1+0j$ in th...
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195
GATE2016-31
The current $I_X$ in the circuit given below in $\text{milliampere}$ is $\_\_\_\_\_\_\_.$
The current $I_X$ in the circuit given below in $\text{milliampere}$ is $\_\_\_\_\_\_\_.$
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196
GATE2016-32
In the circuit shown below, $V_s=101\angle 0V, R=10\Omega$ and $\omega L=100\Omega$. The current $I_s$ is in phase with $V_s$. The magnitude of $I_s$ in $\text{milliampere}$ is $\_\_\_\_\_\_\_\_.$
In the circuit shown below, $V_s=101\angle 0V, R=10\Omega$ and $\omega L=100\Omega$. The current $I_s$ is in phase with $V_s$. The magnitude of $I_s$ in $\text{milliamper...
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199
GATE2016-35
The voltage $v(t)$ shown below is applied to the given circuit. $v(t)=3V$ for $t<0$ and $v(t)=6V$ for $t>0$. The value of current $i(t)$ at $t=1s$, in ampere is ____________.
The voltage $v(t)$ shown below is applied to the given circuit. $v(t)=3V$ for $t<0$ and $v(t)=6V$ for $t>0$. The value of current $i(t)$ at $t=1s$, in ampere is _________...
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200
GATE2016-37
The fundamental period $N_0$ of the discrete-time sinusoid $x[n]=\sin \left (\frac {301}{4}\pi n \right)$ is ____________.
The fundamental period $N_0$ of the discrete-time sinusoid $x[n]=\sin \left (\frac {301}{4}\pi n \right)$ is ____________.
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