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GATE2019 EE: 18
If $f=2x^{3}+3y^{2}+4z$, the value of line integral $\int_{c} \text{grad}f \cdot d \textbf{r}$ evaluated over contour $C$ formed by the segments $(3,3,2)\rightarrow(2,3,2)\rightarrow(2,6,2) \rightarrow(2,6,1) $ is___________.
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GATE2019 EE: 19
The current $I$ is flowing in the circuit shown below in amperes (round off to one decimal place) is _________
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GATE2019 EE: 20
A coaxial Cylindrical capacitor is shown in the Figure(i) has dielectric with relative permittivity $\varepsilon_{r1} = 2$. When one – fourth portion of the dielectric is replaced with another dielectric of relative permittivity $\varepsilon_{r2}$, as shown in the Figure(ii), the capacitance is doubled. The value of $\varepsilon_{r2}$ is _________.
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GATE2019 EE: 21
The $Y_{\text{bus}}$ matrix of a twobus power system having two identical parallel lines connected between them in pu is given as $Y_{\text{bus}} = \begin{bmatrix} j8 & j20 \\ j20& j8 \end{bmatrix}$The magnitude of the series reactance of each line in pu (round off upto one decimal place) is__________.
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GATE2019 EE: 22
Five alternators each rated $5$ MVA, $13.2$ kV with $25 \%$ of reactance on its own base are connected in parallel to a busbar. The short circuit level in MVA at the busbar is ____________
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GATE2019 EE: 23
The total impedance of the secondary winding, leads, and burden of a $5$ A CT is $0.01 \: \Omega$. If the fault current is $20$ times the rated primary current of the CT, the VA output of the CT is_________
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GATE2019 EE: 25
The output voltage of a singlephase fullbridge voltage source inverter is controlled by unipolar PWM with one pulse per half cycle. For the fundamental rms Component of the output voltage to be $75 \%$ of DC voltage, the required pulse width in degrees (round off up to one decimal place) is ___________.
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GATE2019 EE: 26
Consider a $2\times 2$ matrix $M=\begin{bmatrix} v_1 & v_2 \end{bmatrix}$, where $v_1$ and $v_2$ are the column vectors. Suppose $M^{1}=\begin{bmatrix} u_1^T \\ u_2^T \end{bmatrix}$, where $u_1^T$ and $u_2^T$ are the row vecotrs. ... $2$ is false Statement $2$ is true and Statement $1$ is false Both the Statements are true Both the statements are false
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GATE2019 EE: 27
The closedloop line integral $\underset{\mid z \mid = 5}{\oint} \frac{z^3 + z^2 + 8}{z+2}dz$ evaluated Counterclockwise, is $+8 j \pi$ $8 j \pi$ $4 j \pi$ $+4 j \pi$
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GATE2019 EE: 28
A periodic function $f(t)$, with a period of $2 \pi$, is represented as its Fourier series, $f(t) = a_0 + \sum_{n=1}^{\infty }a_n \cos nt + \sum_{n=1}^{\infty} b_n \sin nt.$ ... $a_1 = \frac{A}{2}; \: b_1 = 0$ $a_1 = 0; \: b_1 = \frac{A}{\pi}$ $a_1 = 0;b_1 = \frac{A}{2}$
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GATE2019 EE: 29
The asymptotic Bode magnitude plot of a minimum phase transfer function $G(s)$ is shown below. Consider the following two statements. Statement I: Transfer function $G(s)$ ... and statement II is false Statement I is false and statement II is true Both the statements are true Both the statements are false
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GATE2019 EE: 30
The transfer function of a phase lead compensator is given by $D(s) = \frac{3 \bigg( s+ \frac{1}{3T} \bigg)}{ \bigg( s+ \frac{1}{T} \bigg)}$ The frequency (in rad/sec), at which $\angle D(j \omega)$ is maximum, is $\sqrt{\frac{3}{T^2}}$ $\sqrt{\frac{1}{3T^2}}$ $\sqrt{3T}$ $\sqrt{3T^2}$
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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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16
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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17
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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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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19
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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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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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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22
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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23
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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GATE2019 EE: 42
The current $I$ flowing in the circuit shown in amperes is ____________
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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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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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27
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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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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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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30
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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31
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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32
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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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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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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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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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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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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38
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.
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Jul 8, 2018
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39
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
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Numerical Ability
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40
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 $5$ $6$ $9$ $10$
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Mar 24, 2018
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