GATE 2023 Electrical Engineering
98 questions across 2 sessions
Gate Ee 2023
Consider a lead compensator of the form $$K(s) = {{1 + {s \over a}} \over {1 + {s \over {\beta a}}}},\beta > 1,a > 0$$ The frequency at which this compensator produces maximum phas...
Consider the following equation in a 2-D real-space. $$|{x_1}{|^p} + |{x_2}{|^p} = 1$$ for $$p > 0$$ Which of the following statement(s) is/are true.
The expected number of trials for first occurrence of a "head" in a biased coin is known to be 4. The probability of first occurrence of a "head" in the second trial is __________...
Consider the state-space description of an LTI system with matrices $$A = \left[ {\matrix{ 0 & 1 \cr { - 1} & { - 2} \cr } } \right],B = \left[ {\matrix{ 0 \cr 1 \cr } } \right],C...
A three-phase synchronous motor with synchronous impedance of 0.1+j0.3 per unit per phase has a static stability limit of 2.5 per unit. The corresponding excitation voltage in per...
A three phase 415 V, 50 Hz, 6-pole, 960 RPM, 4 HP squirrel cage induction motor drives a constant torque load at rated speed operating from rated supply and delivering rated output...
A quadratic function of two variables is given as $$f({x_1},{x_2}) = x_1^2 + 2x_2^2 + 3{x_1} + 3{x_2} + {x_1}{x_2} + 1$$ The magnitude of the maximum rate of change of the function...
The bus admittance ($$Y_{bus}$$) matrix of a 3-bus power system is given below. $$\quad\quad$$$$\matrix{ 1 & \quad\quad\quad2\quad\quad & 3 \cr } $$ $$\matrix{ 1 \cr 2 \cr 3 \cr }...
The period of the discrete-time signal $$x[n]$$ described by the equation below is $$N=$$ __________ (Round off to the nearest integer). $$x[n] = 1 + 3\sin \left( {{{15\pi } \over...
A continuous-time system that is initially at rest is described by $${{dy(t)} \over {dt}} + 3y(t) = 2x(t)$$, where $$x(t)$$ is the input voltage and $$y(t)$$ is the output voltage....
The Fourier transform $$X(\omega)$$ of the signal $$x(t)$$ is given by $$X(\omega ) = 1$$, for $$|\omega | $$ = 0$$, for $$|\omega | > {W_0}$$ Which one of the following statements...
The Z-transform of a discrete signal $$x[n]$$ is $$X(z) = {{4z} \over {(z - {1 \over 5})(z - {2 \over 3})(z - 3)}}$$ with $$ROC = R$$. Which one of the following statements is true...
Which of the following statement(s) is/are true?
The discrete-time Fourier transform of a signal $$x[n]$$ is $$X(\Omega ) = (1 + \cos \Omega ){e^{ - j\Omega }}$$. Consider that $${x_p}[n]$$ is a periodic signal of period N = 5 su...
A signal $$x(t) = 2\cos (180\pi t)\cos (60\pi t)$$ is sampled at 200 Hz and then passed through an ideal low pass filter having cut-off frequency of 100 Hz. The maximum frequency p...
In a given 8-bit general purpose micro-controller there are following flags. C-Carry, A-Auxiliary Carry, O-Overflow flag, P-Parity (0 for even, 1 for odd) R$$_0$$ and R$$_1$$ are t...
Rafi told Mary, "I am thinking of watching a film this weekend." The following repots the above statement in indirect speech: Rafi told Mary that he _________ of watching a film th...
Permit : __________ : : Enforce : Relax (By word meaning)
Given a fair six-faced dice where the faces are labelled '1', '2', '3', '4', '5', and '6', what is the probability of getting a '1' on the first roll of the dice and a '4' on the s...
A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco. Based...
Students of all the departments of a college who have successfully completed the registration process are eligible to vote in the upcoming college elections. However, by the time t...
Which one of the options does NOT describe the passage below or follow from it? We tend to think of cancer as a 'modern' illness because its metaphors are so modern. It is a diseas...
the digit in the unit's place of the product $$3^{999}\times7^{1000}$$ is __________.
For a given vector $${[\matrix{ 1 & 2 & 3 \cr } ]^T}$$, the vector normal to the plane defined by $${w^T}x = 1$$ is
Consider a unity-gain negative feedback system consisting of the plant G(s) (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 a...
The following columns present various modes of induction machine operation and the ranges of slip A B Mode of operation Range of Slip a. Running in generator mode p) From 0.0 to 1....
A 10-pole, 50 Hz, 240 V, single phase induction motor runs at 540 RPM while driving rated load. The frequency of induced rotor currents due to backward field is
The expressions of fuel cost of two thermal generating units as a function of the respective power generation $${P_{G1}}$$ and $${P_{G2}}$$ are given as $$\matrix{ {{F_1}({P_{G1}})...
One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation $$\sigma_0$$. The $$\sigma_0$$ i...
A separately excited DC motor rated 400 V, 15 A, 1500 RPM drives a constant torque load at rated speed operating from 400 V DC supply drawing rated current. The armature resistance...
A 50 Hz, 275 kV line of length 400 km has the following parameters: Resistance, R = 0.035 $$\Omega$$/km; Inductance, L = 1 mH/km; Capacitance, C = 0.01 $$\mu$$F/km; The line is rep...
In the following differential equation, the numerically obtained value of $$y(t)$$, at $$t=1$$ is ___________ (Round off to 2 decimal places). $${{dy} \over {dt}} = {{{e^{ - \alpha...
Three points in the x-y plane are ($$-$$1, 0.8), (0, 2.2) and (1, 2.8). The value of the slope of the best fit straight line in the least square sense is _________ (Round off to 2...
Set Master
Rafi told Mary, "I am thinking of watching a film this weekend." The following reports the above statement in indirect speech: Rafi told Mary that he ________ of watching a film th...
Permit : ________ :: Enforce : Relax (By word meaning)
Given a fair six-faced dice where the faces are labelled '1', '2', '3', '4', '5', and '6', what is the probability of getting a '1' on the first roll of the dice and a '4' on the s...
A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco. Based...
How many triangles are present in the given figure?
Students of all the departments of a college who have successfully completed the registration process are eligible to vote in the upcoming college elections. However, by the time t...
Which one of the following options represents the given graph?
Which one of the options does NOT describe the passage below or follow from it? We tend to think of cancer as a 'modern' illness because its metaphors are so modern. It is a diseas...
The digit in the unit's place of the product $3^{999} \times 7^{1000}$ is _________.
A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown. The area of the...
For a given vector w = [1 2 3]$^T$, the vector normal to the plane defined by w$^T$x = 1 is
For the block diagram shown in the figure, the transfer function $\frac{Y(s)}{R(s)}$ is
In the Nyquist plot of the open-loop transfer function $G(s)H(s) = \frac{3s + 5}{s - 1}$ corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of t...
Consider a unity-gain negative feedback system consisting of the plant G(s) (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 a...
The following columns present various modes of induction machine operation and the ranges of slip A Mode of operation a. Running in generator mode b. Running in motor mode c. Plugg...
A 10-pole, 50 Hz, 240 V, single phase induction motor runs at 540 RPM while driving rated load. The frequency of induced rotor currents due to backward field is
A continuous-time system that is initially at rest is described by $\frac{dy(t)}{dt} + 3y(t) = 2x(t)$, where $x(t)$ is the input voltage and $y(t)$ is the output voltage. The impul...
The Fourier transform X($\omega$) of the signal x(t) is given by $X(\omega) = 1$, for $|\omega| W_0$ Which one of the following statements is true?
The Z-transform of a discrete signal x[n] is $X(z) = \frac{4z}{(z-\frac{1}{2})(z-\frac{2}{3})(z-3)}$ with ROC = R. Which one of the following statements is true?
For the three-bus power system shown in the figure, the trip signals to the circuit breakers B1 to B9 are provided by overcurrent relays R1 to R9, respectively, some of which have...
The expressions of fuel cost of two thermal generating units as a function of the respective power generation PG1 and PG2 are given as F1(PG1) = 0.1aP^2_G1 + 40 PG1 + 120 Rs/hour 0...
The four stator conductors (A, A', B and B') of a rotating machine are carrying DC currents of the same value, the directions of which are shown in the figure (i). The rotor coils...
The chopper circuit shown in figure (i) feeds power to a 5 A DC constant current source. The switching frequency of the chopper is 100 kHz. All the components can be assumed to be...
In the figure, the vectors u and v are related as: Au = v by a transformation matrix A. The correct choice of A is
One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation $\sigma_o$. The $\sigma_o$ is es...
A semiconductor switch needs to block voltage V of only one polarity (V > 0) during OFF state as shown in figure (i) and carry current in both directions during ON state as shown i...
Which of the following statement(s) is/are true?
The bus admittance (Ybus) matrix of a 3-bus power system is given below. Considering that there is no shunt inductor connected to any of the buses, which of the following can NOT b...
The value of parameters of the circuit shown in the figure are R1 = 2Ω, R2 = 2Ω, R3 = 3Ω, L = 10 mH, C = 100 μF For time t < 0, the circuit is at steady state with the switch 'K' i...
A separately excited DC motor rated 400 V, 15 A, 1500 RPM drives a constant torque load at rated speed operating from 400 V DC supply drawing rated current. The armature resistance...
For the signals x(t) and y(t) shown in the figure, z(t) = x(t) * y(t) is maximum at t = T₁. Then T₁ in seconds is __________. (Round off to the nearest integer).
For the circuit shown in the figure, V₁ = 8 V, DC and I₁ = 8 A, DC. The voltage Vab in Volts is __________. (Round off to 1 decimal place).
A 50 Hz, 275 kV line of length 400 km has the following parameters: Resistance, R = 0.035 Ω/km; Inductance, L = 1 mH/km; Capacitance, C = 0.01 µF/km; The line is represented by the...
In the following differential equation, the numerically obtained value of y(t), at t =1, is ________ (Round off to 2 decimal places). $\frac{dy}{dt} = \frac{e^{-at}}{2 + at}$, α =...
Three points in the x-y plane are (-1, 0.8), (0, 2.2) and (1, 2.8). The value of the slope of the best fit straight line in the least square sense is ________ (Round off to 2 decim...
The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is
Consider the OP AMP based circuit shown in the figure. Ignore the conduction drops of diodes D1 and D2. All the components are ideal and the breakdown voltage of the Zener is 5 V....
Consider a lead compensator of the form $K(s) = \frac{1 + \frac{s}{a}}{1 + \frac{s}{\beta a}}, \beta > 1, a > 0$ The frequency at which this compensator produces maximum phase lead...
A 3-phase, star-connected, balanced load is supplied from a 3-phase, 400 V (rms), balanced voltage source with phase sequence R-Y-B, as shown in the figure. If the wattmeter readin...
An 8 bit ADC converts analog voltage in the range of 0 to +5 V to the corresponding digital code as per the conversion characteristics shown in figure. For $V_{in} = 1.9922 V$, whi...
The three-bus power system shown in the figure has one alternator connected to bus 2 which supplies 200 MW and 40 MVAr power. Bus 3 is infinite bus having a voltage of magnitude |V...
Consider the following equation in a 2-D real-space. |x1|^p + |x2|^p = 1 for p > 0 Which of the following statement(s) is/are true.
In the figure, the electric field E and the magnetic field B point to x and z directions, respectively, and have constant magnitudes. A positive charge 'q' is released from rest at...
All the elements in the circuit shown in the following figure are ideal. Which of the following statements is/are true?
The expected number of trials for first occurrence of a "head" in a biased coin is known to be 4. The probability of first occurrence of a "head" in the second trial is __________....
Consider the state-space description of an LTI system with matrices A = $\begin{bmatrix} 0 & 1 \ -1 & -2 \end{bmatrix}$, B = $\begin{bmatrix} 0 \ 1 \end{bmatrix}$, C = $\begin{bmat...
A three-phase synchronous motor with synchronous impedance of 0.1+j0.3 per unit per phase has a static stability limit of 2.5 per unit. The corresponding excitation voltage in per...
A three phase 415 V, 50 Hz, 6-pole, 960 RPM, 4 HP squirrel cage induction motor drives a constant torque load at rated speed operating from rated supply and delivering rated output...
The period of the discrete-time signal x[n] described by the equation below is N = ____________ (Round off to the nearest integer). x[n] = 1 + 3sin($\frac{15\pi}{8}n + \frac{3\pi}{...
The discrete-time Fourier transform of a signal x[n] is X($\Omega$) = (1 + cos$\Omega$)e$^{-j\Omega}$. Consider that x$_p$[n] is a periodic signal of period N = 5 such that x$_p$[n...
For the circuit shown, if $i = \sin 1000t$, the instantaneous value of the Thevenin's equivalent voltage (in Volts) across the terminals a-b at time $t = 5$ ms is ________ (Round o...
The admittance parameters of the passive resistive two-port network shown in the figure are $y_{11} = 5 S, y_{22} = 1 S, y_{12} = y_{21} = -2.5 S$. The power delivered to the load...
When the winding c-d of the single-phase, 50 Hz, two winding transformer is supplied from an AC current source of frequency 50 Hz, the rated voltage of 200 V (rms), 50 Hz is obtain...
The circuit shown in the figure is initially in the steady state with the switch K in open condition and K in closed condition. The switch K is closed and K is opened simultaneousl...
The circuit shown in the figure has reached steady state with thyristor 'T' in OFF condition. Assume that the latching and holding currents of the thyristor are zero. The thyristor...
Neglecting the delays due to the logic gates in the circuit shown in figure, the decimal equivalent of the binary sequence [ABCD] of initial logic states, which will not change wit...
In a given 8-bit general purpose micro-controller there are following flags. C-Carry, A-Auxiliary Carry, O-Overflow flag, P-Parity (0 for even, 1 for odd) R0 and R1 are the two gen...
The single phase rectifier consisting of three thyristors T1, T2, T3 and a diode D1 feed power to a 10 A constant current load. T1 and T3 are fired at α = 60° and T2 is fired at α...
The Zener diode in circuit has a breakdown voltage of 5 V. The current gain β of the transistor in the active region in 99. Ignore base-emitter voltage drop VBE. The current throug...
The two-bus power system shown in figure (i) has one alternator supplying a synchronous motor load through a Y-Δ transformer. The positive, negative and zero-sequence diagrams of t...
An infinite surface of linear current density K = 5âx A/m exists on the x-y plane, as shown in the figure. The magnitude of the magnetic field intensity (H) at a point (1,1,1) due...
The closed curve shown in the figure is described by r = 1 + cosθ, where r = √x² + y²; x = rcosθ, y = rsinθ The magnitude of the line integral of the vector field F = -yî + xĵ arou...
A signal x(t) = 2cos(180πt)cos(60πt) is sampled at 200 Hz and then passed through an ideal low pass filter having cut-off frequency of 100 Hz. The maximum frequency present in the...
A balanced delta connected load consisting of the series connection of one resistor (R = 15 Ω) and a capacitor (C = 212.21 µF) in each phase is connected to three-phase, 50 Hz, 415...
A quadratic function of two variables is given as f(x1,x2) = x₁² + 2x₂² + 3x₁ + 3x₂ + x₁x₂ + 1 The magnitude of the maximum rate of change of the function at the point (1,1) is ___...