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GATE201843
Let $f(x) = 3x^37x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to one decimal place).
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Feb 19, 2018
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GATE201844
Let $A= \begin{bmatrix} 1 & 0 & 1 \\ 1 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix}$ and $B=A^3A^24A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$ is _______ (up to $1$ decimal place).
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GATE201845
The capacitance of an airfilled parallelplate capacitor is $60$ pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes $86$ pF. Neglecting the fringing effects, the relative permittivity of the dielectric is ___________ (up to $2$ decimal places)
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4
GATE201839
The signal energy of he continuoustime signal $x(t)=[(t1)u(t1)][(t2)u(t2)][(t3)u(t3)]+[(t4)u(t4)]$ is $11/3$ $7/3$ $1/3$ $5/3$
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5
GATE201840
The Fourier transform of a continuoustime signal $x(t)$ is given by $X(\omega) = \frac{1}{(10+j \omega)^2}, – \infty < \omega < \infty$, where $j = \sqrt{1}$ and $\omega$ denoes frequency. Then the value of $\mid \text{ln } x(t) \mid$ at $t=1$ is _________ (up to $1$ decimal place). ($\text{ln}$ denotes the logarithm base $e$)
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6
GATE201841
In the circuit shown in the figure, the bipolar junction transistor (BJT) has a current gain $\beta = 100$. The baseemitter voltage drop is a constant, $V_{BE}=0.7 \: V$. The value of the Thevenin equivalent resistance $R_{Th}$ (in $\Omega$) as shown in the figure is _________ (up to $2$ decimal places)
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7
GATE201842
As shown in the figure, $C$ is the arc from the point $(3,0)$ to the point $(0,3)$ on the circle $x^2+y^2=9$. The value of the integral $\int_C (y^2+2yx) dx +(2xy+x^2)dy$ is ________ (up to $2$ decimal places).
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8
GATE201832
The equivalent impedance $Z_{eq}$ for the infinite ladder circuit shown in the figure is $\text{j} 12 \: \Omega$ $\text{j} 12 \: \Omega$ $\text{j} 13 \: \Omega$ $13 \: \Omega$
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Feb 19, 2018
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9
GATE201833
Consider a system governed by the following equations $ \frac{dx_1(t)}{dt} = x_2(t)x_1(t) \\ \frac{dx_2(t)}{dt} = x_1(t)x_2(t)$ The initial conditions are such that $x_1(0)<x_2(0)< \infty$. Let $x_{1f}= \underset{t \to \infty}{\lim} x_1(t)$ ... is true? $x_{1f}<x_{2f}<\infty$ $x_{2f}<x_{1f}<\infty$ $x_{1f}<=_{2f}<\infty$ $x_{1f}=x_{2f}=\infty$
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Feb 19, 2018
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GATE201834
The number of roots of the polynomial, $s^7+s^6+7s^5+14s^4+31s^3+73s^2+25s+200$, in the open left half of the complex plane is $3$ $4$ $5$ $6$
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Feb 19, 2018
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11
GATE201835
If $C$ is a circle $\mid z \mid=4$ and $f(z)=\frac{z^2}{(z^23z+2)^2}$, then $\underset{C}{\oint} f(z) dz$ is $1$ $0$ $1$ $2$
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GATE201836
Which one of the following statements is true about the digital circuit shown in the figure It can be used for dividing input frequency by $3$ It can be used for dividing input frequency by $5$ It can be used for dividing input frequency by $7$ It cannot be reliably used as a frequency divider due to disjoint internal cycles
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13
GATE201837
Digital input signals A, B, C with A as the MSB and C as the LSB are used to realize the Boolean function $F=m_0+m_2+m_3+m_5+m_7$, where $m_i$ denotes the $i$ th minterm. In addition, $F$ has a don’t care for $m_1$. The simplified expression for $F$ is given by $\overline{A} \: \overline{C} + \overline{B} C + AC$ $\overline{A}+C$ $\overline{C}+A$ $\overline{A} C + BC + A \overline{C}$
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14
GATE201838
Consider the two continuoustime signals defined below: ... is greater than the energy of $x_1[n]$ $x_1[n]$ and $x_2[n]$ have equal energies Neither $x_1[n]$ nor $x_2[n]$ is a finiteenergy signal
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Feb 19, 2018
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15
GATE201828
The positive, negative and zero sequence impedances of a three phase generator are $Z_1, Z_2$ and $Z_0$ respectively. For a linetoline fault with fault impedance $Z_f$, the fault current is $I_{f1}= kI_f$, where $I_f$ is the fault current with zero fault impedance. The relation between $Z_f$ ... $Z_f=\frac{(Z_1+Z_2)k}{1k} \\$ $Z_f=\frac{(Z_1+Z_2)k}{1+k}$
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Feb 19, 2018
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16
GATE201829
Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator $G_1$ and $G_2$ are $Q_{G1}$ and $Q_{G2}$ respectively. The per unit values of $Q_{G1}$, $Q_{G2}$ ... $6.34, \: 10.00, \: 1.34$ $6.34, \: 11.34, \: 2.68$ $5.00, \: 11.34, \: 1.34$
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Feb 19, 2018
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17
GATE201830
The perunit power output of a salientpole generator which is connected to an infinite bus, is given by the expression, $P=1.4 \sin \delta + 0.15 \sin 2 \delta$, where $\delta$ is the load angle. NewtonRaphson method is used to calculate the value of $\delta$ ... (in degree) at the end of the first iteration is $15^{\circ}$ $28.28^{\circ}$ $28.74^{\circ}$ $31.20^{\circ}$
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Feb 19, 2018
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18
GATE201831
A DC voltage source is connected to a series $LC$ circuit by turning on the switch S at time $t=0$ as shown in the figure. Assume $i(0)=0$, $v(0)=0$. Which one of the following circular loci represents the plot of $i(t)$ versus $v(t)$?
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19
GATE201824
A separately excited dc motor has an armature resistance $R_a =0.05 \: \Omega$. The field excitation is kept constant. At an armature voltage of $100$ V, the motor produces a torque of $500$ Nm at zero speed. Neglecting all mechanical losses, the noload speed of the motor (in $\text{radian /s}$) for an armature voltage of $150$ V is ____________ (up to $2$ decimal places).
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20
GATE201825
Consider a unity feedback system with forward transfer function given by $G(s) = \frac{1}{(s+1)(s+2)}$ The steadystate error in the output of the system for a unitstep input is _______ (up to $2$ decimal places).
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21
GATE201826
A transformer with toroidal core of permeability $\mu$ is shown in the figure. Assuming uniform flux density across the circular core crosssection of radius $r < < R$, and neglecting any leakage flux, the best estimate for the mean radius $R$ is $\frac{\mu V r^2 N_P^2 \omega}{I} \\ $ ... $\frac{\mu V r^2 N_P^2 \omega}{2I} \\ $ $\frac{\mu I r^2 N_P^2 \omega}{2V} $
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Feb 19, 2018
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22
GATE201827
A $01$ Ampere moving iron ammeter has an internal resistance of $50 \: m \Omega$ and inductance of $0.1 \: mH$. A shunt coil is connected to extend its range to $010$ Ampere for all operating frequencies. The time constant in milliseconds and resistance in $m \Omega$ of the shunt coil respectively are $2, \: 5.55$ $2, \: 1$ $2.18, \: 0.55$ $11.1, \: 2$
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Feb 19, 2018
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23
GATE201816
A continuoustime input signal $x(t)$ is an eigenfunction of an LTI system, if the output is $k \: x(t)$, where $k$ is an eigenvalue $k \: e^{j \omega t} \: x(t)$, where $k$ is an eigenvalue and $e^{j \omega t}$ is a complex exponential signal ... $k \: H(\omega)$, where $k$ is an eigenvalue and $H(\omega)$ is a frequency response of the system
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24
GATE201817
Consider a nonsingular $2 \times 2$ square matrix $\textbf{A}$. If $\textit{trace}(\textbf{A})=4$ and $\textit{trace}(\textbf{A}^2)=5$, the determinant of the matrix $\textbf{A}$ is _________ (up to $1$ decimal place).
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25
GATE201818
Let $f$ be a realvalued function of a real variable defined as $f(x)=x – [x]$, where $[x]$ denotes the largest integer less than or equal to $x$. The value of $\int_{0.25}^{1.25} f(x) dx$ is _______ (up to $2$ decimal places).
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26
GATE201819
In the twoport nework shown, the $h_{11}$ parameter $\bigg($ where, $h_{11} = \frac{V_1}{I_1}$, when $V_2=0 \bigg)$ in ohms is _________ (up to $2$ decimal places).
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27
GATE201820
The series impedance matrix of a short threephase transmission line in phase coordinates is $\begin{bmatrix} Z_s & Z_m & Z_m \\ Z_m & Z_s & Z_m \\ Z_m & Z_m & Z_s \end{bmatrix}$. If the positive sequence impedance is $(1+j \: 10) \Omega$, and the ... $(4+j \: 31) \Omega$, then the imaginary part of $Z_m$ (in $\Omega$) is ___________ (up to $2$ decimal places).
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28
GATE201821
The positive, negative and zero sequence impedances of a $125$ MVA, threephase, $15.5$ kV, stargounded, $50$ Hz generator are $j0.1$ pu, $j0.05$ pu and $j0.01$ pu respectively on the machine rating base. The machine is unloaded and working at the rated ... $b$phase to ground fault (in kA) is __________ (up to $2$ decimal places).
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29
GATE201822
A $1000 \times 1000$ bus admittance matrix for an electric power system has $8000$ nonzero elements. The minimum number of branches (transmission lines and transformers) in this system are _________ (up to $2$ decimal places).
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30
GATE201823
The waveform of the current drawn by a semiconverter from a sinusoidal AC voltage source is shown in the figure. If $I_0=20$ A, the rms value of fundamental component of the current is ________ A (up to $2$ decimal places).
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31
GATE201815
The opamp shown in the figure is ideal. The input impedance $\frac{v_{\text{in}}}{i_{\text{in}}}$ is given by $Z \frac{R_1}{R_2}$ $ – Z \frac{R_2}{R_1}$ $Z$ $ – Z \frac{R_1}{R_1 + R_2}$
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32
GATE20188
In the figure, the voltages are $v_1(t)=100 \cos (\omega t)$, $v_2(t)=100 \cos (\omega t + \pi /18)$ and $v_3(t)=100 \cos (\omega t + \pi / 36)$. The circuit is in sinusoidal steady state, and $R< < \omega L$. $P_1$, $P_2$ and $P_3$ are the average power outputs ... $P_1 <0$, $P_2>0$, $P_3>0$ $P_1 <0$, $P_2>0$, $P_3<0$ $P_1 > 0$, $P_2<0$, $P_3>0$
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33
GATE20189
Match the transfer functions of the secondorder systems with the nature of the systems given below. ... PI, QII, RIII PII, QI, RIII PIII, QII, RI PIII, QI, RII
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34
GATE201810
A positive charge of $1$ nC is placed at $(0,0,0.2)$ where all dimensions are in meters. Consider the $xy$ plane to be a conducting ground plane. Take $\epsilon_0 = 8.85 \times 10^{12}$ F/m. The $Z$ component of the E field at $(0,0,0.1)$ is closest to $899.18$ V/m $899.18$ V/m $999.09$ V/m $999.09$ V/m
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35
GATE201811
Let $f$ be a realvalued function of a real variable defined as $f(x)=x^2$ for $x \geq 0$, and $f(x)=x^2$ for $x<0$. Which one of the following statements is true? $f(x)$ is discontinuous at $x=0$ $f(x)$ is continuous but not ... $x=0$ $f(x)$ is differentiable but its first derivative is not differentiable at $x=0$
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36
GATE201812
The value of the directional derivative of the function $\Phi (x,y,z) = xy^2 +yz^2+zx^2$ at the point $(2,1,1)$ in the direction of the vector $\textbf{p}= \textbf{i} +2 \textbf{j} + 2 \textbf{k}$ is $1$ $0.95$ $0.93$ $0.9$
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37
GATE201813
The value of the integral $\oint _c \frac{z+1}{z^24} dz$ in counter clockwise direction around a circle $C$ of radius $1$ with center at the point $z=2$ is $\frac{\pi i}{2} \\ $ $2 \pi i\\$ $ – \frac{\pi i}{2}\\$ $2 \pi i$
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38
GATE201814
In the logic circuit shown in the figure, $Y$ is given by $Y=ABCD$ $Y=(A+B)(C+D)$ $Y=A+B+C+D$ $Y=AB+CD$
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39
GATE20182
In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is $0$ $45$ $60$ $90$
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GATE20183
A single phase fully controlled rectifier is supplying a load with an antiparallel diode as shown in the figure. All switches and diodes are ideal. Which one of the following is true for instantaneous load voltage and current? $v_o \geq 0$ & $i_o<0$ $v_o < 0$ & $i_o <0$ $v_o \geq 0$ & $i_o \geq 0$ $v_0 < 0$ & $i_o\geq 0$
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