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GATE2019 EE: 31
Consider a statevariable model of a system $\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ \alpha &  2 \beta \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} + \begin{bmatrix} 0 \\ \alpha \end{bmatrix} r $ ... $\omega_n = \sqrt{\beta}$ $\xi = \sqrt{\beta} $; $\omega_n = \sqrt{\alpha} $
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GATE2019 EE: 32
A moving coil instrument having a resistance of $10 \: \Omega$, gives a fullscale deflection when the current is $10$ mA. What should be the value of the series resistance, so that it can be used as a voltmeter for measuring potential difference up to $100$ V? $9 \: \Omega$ $99 \: \Omega$ $990 \: \Omega$ $9990 \: \Omega$
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GATE2019 EE: 33
The enhancement type MOSFET in the circuit below operates according to the square law. $\mu _nC_{ox} =100 \: \mu A /V^2$, the threshold voltage $(V_T)$ is $500$ mV. Ignore channel length modulation. The output voltage $V_{\text{out}}$ is $100$ mV $500$ mV $600$ mV $2$ V
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4
GATE2019 EE: 34
In the circuit below, the operational amplifier is ideal. If $V_1=10$ mV and $V_2=50$ mV, he output voltage $(V_{\text{out}})$ is $100$ mV $400$ mV $500$ mV $600$ mV
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5
GATE2019 EE: 35
The output expression for the Karnaugh map shown below is $Q \bar{R} +S$ $Q \bar{R} + \bar{S}$ $QR+S$ $Q R +\bar{S}$
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6
GATE2019 EE: 36
In the circuit shown below, $X$ and $Y$ are digital inputs, and $Z$ is a digital output. The Equivalent circuit is a NAND gate NOR gate XOR gate XNOR gate
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Feb 12
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7
GATE2019 EE: 37
A DCDC buck converter operates in continuous conduction mode. It has $48$ V input voltage, and it feeds a resistive load of $24 \: \Omega$. The switching frequency of the converter is $250$ Hz. If switchon duration is $1$ ms, the load power is $6$ W $12$ W $24$ W $48$ W
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8
GATE2019 EE: 38
The line currents of a threephase four wire system are square waves with amplitude of $100$ A. These three currents are phase shifted by $120^{\circ}$ with respect to each other. The rms value of neutral current is $0$ A $\frac{100}{\sqrt{3}}$ A $100$ A $300$ A
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9
GATE2019 EE: 39
If $\textbf{A}= 2x \textbf{i} + 3y \textbf{j} +4z \textbf{k}$ and $u=x^2+y^2+z^2$, then $\text{div} \big(u \textbf{A} \big)$ at $(1,1,1)$ is _______
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10
GATE2019 EE: 40
The probability of a resistor being deflective is $0.02$. There are $50$ such resistors in a circuit. The probability of two or more defective resistors in the circuit (round off to two decimal places) is _______________
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11
GATE2019 EE: 41
A $0.1 \mu F$ capacitor charged to $100$ V is discharged through a $1 \: k \Omega$ resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to $1$ V is _________
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12
GATE2019 EE: 42
The current $I$ flowing in the circuit shown in amperes is ____________
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13
GATE2019 EE: 43
The voltage across and the current through a load are expressed as follows $v(t)=170 \sin \bigg( 377t \frac{\pi}{6} \bigg) V$ $i(t) =8 \cos \bigg( 377t + \frac{\pi}{6} \bigg) A$ The average power in watts (round off to one decimal place) consumed by the load is _________.
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14
GATE2019 EE: 44
The magnetic circuit shown below has uniform crosssectional area and air gap of $0.2$ cm. The mean path length of the core is $40$ cm. Assume that leakage and fringing fluxes are negligible. When the core relative permeability is assumed to be infinite, the ... to be $1000$ (linear), the flux density in tesla (round off to three decimal places) calculated in the air gap is _______
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15
GATE2019 EE: 45
A singlephase transformer of rating $25$ kVA, supplies a $12$ kW load at power factor of $0.6$ lagging. The additional load at unity power factor in kW (round off to two decimal places) that may be added before this transformer exceeds its rated kVA is ________
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16
GATE2019 EE: 46
A $220$ V DC shunt motor takes $3$ A at noload. It draws $25$ A when running at fullload at $1500$ rpm. The armature and shunt resistance are $0.5 \: \Omega$ and $220 \: \Omega$, respectively. The noload speed in rpm (round off to two decimal places) is _____.
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Feb 12
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17
GATE2019 EE: 47
A deltaconnected, $3.7$ kW, $400$ V(line), threephase, $4$pole, $50$Hz squirrelcage induction moor has the following equivalent circuit parameters per phase referred to the stator: $R_1=5.39 \: \Omega$, $R_2=5.72 \: \Omega$ ... in amperes (round off to two decimal places) when it is connected to a $100$ V(line), $10$ Hz, threephase AC source is _______
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Feb 12
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18
GATE2019 EE: 48
A $220$ V(line), threephase, Yconnected, synchronous motor has a synchronous impedance of $(0.25+j2.5) \: \Omega/\text{phase}$. The motor draws the rated current of $10$ A at $0.8$ pf leading. The rms value of linetoline internal voltage in volts (round off to two decimal places) is _________
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19
GATE2019 EE: 49
A threephase $50$ Hz, $400$ kV transmission line is $300$ km long. The line inductance is $1$ mH/km per phase, and the capacitance is $0.01 \: \mu F/km$ per phase. The line is under open circuit condition at the receiving end and energized with $400$ kV at the sending end, the receiving end line voltage in kV (round off to two decimal places) will be _________
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20
GATE2019 EE: 50
A $30$ kV, $50$ Hz, $50$ MVA generator has the positive, negative, and zero sequence reactances of $0.25$ pu, $0.15$ pu, and $0.05$ pu, respectively. The neutral of the generator is grounded with a reactance so that the fault ... bolted threephase fault at the generator terminal are equal. The value of grounding reactance in ohms (round off to one decimal place) is ___________
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21
GATE2019 EE: 51
In the single machine infinite bus system shown below, the generator is delivering the real power of $0.8$ pu at $0.8$ power factor lagging to the infinite bus. The power angle of the generator in degrees (round off to one decimal place) is _________
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22
GATE2019 EE: 52
In a $132$ kV system, the series inductance up to the point of circuit breaker location is $50$ mH. The shunt capacitance at the circuit breaker terminal is $0.05 \: \mu F$. The critical value of resistance in ohms required to be connected across the circuit breaker contacts which will give no transient oscillation is ______
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23
GATE2019 EE: 53
In a DCDC boost converter, the duty ratio is controlled to regulate the output voltage at $48$ V. The input DC voltage is $24$ V. The output power is $120$ W. The switching frequency is $50$ kHz. Assume ideal components and a very ... converter operates at the boundary between continuous and discontinuous conduction modes. The value of the boost inductor (in $\mu H$) is ________
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24
GATE2019 EE: 54
A fullycontrolled threephase bridge converter is working from a $415$ V, $50$ Hz AC supply. It is supplying constant current of $100$ A a $400$ V to a DC load. Assume large inductive smoothing and neglect overlap. The rms value of the AC line current in amperes (round off to two decimal places) is _______
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25
GATE2019 EE: 55
A singlephase fullycontrolled thyristor converter is used to obtain an average voltage of $180$ V with $10$ A constant current to feed a DC load. It is fed from singlephase AC supply of $230$ V, $50$ Hz. Neglect the source impedance. The power factor (round off to two decimal places) of AC mains is _________
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26
Gate EE2014
For a peridic square wave ,which one of the following statements is TRUE? 1). The fourieF series coefficients do not exist 2).The Fourier series coefficients exist but the reconstruction converges at most point. I know the correct answer is 2). But I need some explanation.
asked
Jul 8, 2018
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Signals and Systems
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Shaurya khare
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130
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27
GATE201263
Raju has $14$ currency notes in his pocket consisting of only Rs. $20$ notes and Rs. $10$ notes. The total money value of the notes is Rs. $230$. The number of Rs. $10$ notes that Raju has is $5$ $6$ $9$ $10$
asked
Mar 24, 2018
in
Numerical Ability
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Andrijana3306
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1.4k
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gate2012ee
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28
GATE201264
There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number of weighings required to identify the heavier bag is $2$ $3$ $4$ $8$
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Mar 24, 2018
in
Numerical Ability
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Andrijana3306
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1.4k
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gate2012ee
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29
GATE201265
The data given in the following table summarizes the monthly budget of an average household. ... $\textbf{NOT}$ spent on savings is $10\%$ $14\%$ $81\%$ $86\%$
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Mar 24, 2018
in
Numerical Ability
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Andrijana3306
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1.4k
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gate2012ee
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30
GATE201257
If $(1.001)^{1259}=3.52$ and $(1.001)^{2062}=7.85,$ then $(1.001)^{3321}=?$ $2.23$ $4.33$ $11.37$ $27.64$
asked
Mar 24, 2018
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Numerical Ability
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Andrijana3306
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1.4k
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gate2012ee
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31
GATE201258
Choose the most appropriate alternative from the options given below to complete the following sentence: $\textbf{If the tired soldier wanted to lie down, he _______ the mattress out on the balcony.}$ should take shall take should have taken will have taken
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Mar 24, 2018
in
Verbal Ability
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Andrijana3306
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32
GATE201259
Choose the most appropriate word from the options given below to complete the following sentence: $\textbf{Given the seriousness of the situation that he had to face, his _______was impressive.}$ beggary nomenclature jealousy nonchalance
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Mar 24, 2018
in
Verbal Ability
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Andrijana3306
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gate2012ee
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33
GATE201260
Which one of the following options is the closest in meaning to the word given below? $\textbf{Latitude}$ Eligibility Freedom Coercion Meticulousness
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Mar 24, 2018
in
Verbal Ability
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Andrijana3306
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gate2012ee
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34
GATE201261
$A$ and $B$ are friends. They decide to meet between 1:00 pm and 2:00 pm on a given day. There is a condition that whoever arrives first will not wait for the other for more than $15$ minutes. The probability that they will meet on that day is $1/4$ $1/16$ $7/16$ $9/16$
asked
Mar 24, 2018
in
Numerical Ability
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Andrijana3306
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1.4k
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gate2012ee
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0
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35
GATE201262
One of the legacies of the Roman legions was discipline. In the legions, military law prevailed and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting, even when the odds and conditions were against them. Which one ... their seniors. The harsh discipline to which the legions were subjected to led to the odds and conditions being against them.
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Mar 24, 2018
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Verbal Ability
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Andrijana3306
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gate2012ee
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36
GATE201250
With $10$ V dc connected at port A in the linear nonreciprocal twoport network shown below, the following were observed: $1 \: \Omega$ connected at port B draws a current of $3$ A $2.5 \: \Omega$ connected at port B draws a current of $2$ A For the same network, with $6$ V dc ... $8$ V dc is connected to port A, the open circuit voltage at port B is $6$ V $7$ V $8$ V $9$ V
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Mar 24, 2018
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37
GATE201251
With $10$ V dc connected at port A in the linear nonreciprocal twoport network shown below, the following were observed: $1 \: \Omega$ connected at port B draws a current of $3$ A $2.5 \: \Omega$ connected at port B draws a current of $2$ A With $10$ V dc connected at port A, the current drawn by $7 \: \Omega$ connected at port B is $3/7$ A $5/7$ A $1$ A $9/7$ A
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38
GATE201252
In the circuit shown, the three voltmeter readings are $V_1 =220$ V, $V_2=122$ V, $V_3=136$ V. The power factor of the load is $0.45$ $0.50$ $0.55$ $0.60$
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Mar 24, 2018
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39
GATE201253
In the circuit shown, the three voltmeter readings are $V_1 =220$ V, $V_2=122$ V, $V_3=136$ V. If $R_L=5 \: \Omega$, the approximate power consumption in the load is $700$ W $750$ W $800$ W $850$ W
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40
GATE201254
The transfer function of a compensator is given as $G_c(s) = \frac{s+a}{s+b}$ $G_c(s)$ is a lead compensator if $a=1, \: b=2$ $a=3, \: b=2$ $a=3, \: b=1$ $a=3, \: b=1$
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Mar 24, 2018
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