GATE 2024 Electrical Engineering
103 questions across 2 sessions
Gate Ee 2024
Simplified form of the Boolean function $$ F(P, Q, R, S)=\bar{P} \bar{Q}+\bar{P} Q S+P \bar{Q} \bar{R} \bar{S}+P \bar{Q} R \bar{S} $$ is
For a two-phase network, the phase voltages $V_p$ and $V_q$ are to be expressed in terms of sequence voltages $V_\alpha$ and $V_\beta$ as $\begin{bmatrix} V_p \\ V_q \end{bmatrix}...
If the following switching devices have similar power ratings, which one of them is the fastest?
A single-phase triac based AC voltage controller feeds a series RL load. The input AC supply is 230 V, 50 Hz. The values of R and L are 10 Ω and 18.37 mH, respectively. The minimum...
Let $X$ be a discrete random variable that is uniformly distributed over the set {$-10, -9, \cdots, 0, \cdots, 9, 10$}. Which of the following random variables is/are uniformly dis...
Consider a vector $\vec{u} = 2\hat{x} + \hat{y} + 2\hat{z}$, where $\hat{x}$, $\hat{y}$, $\hat{z}$ represent unit vectors along the coordinate axes $x$, $y$, $z$ respectively. The...
A 3-phase, 11 kV, 10 MVA synchronous generator is connected to an inductive load of power factor $(\sqrt{3}/2)$ via a lossless line with a per-phase inductive reactance of 5 $\Omeg...
Let $f(t)$ be a real-valued function whose second derivative is positive for $- \infty
Consider the function $f(t) = (\text{max}(0,t))^2$ for $- \infty
Which of the following differential equations is/are nonlinear?
Which of the following options is/are correct for the Automatic Generation Control (AGC) and Automatic Voltage Regulator (AVR) installed with synchronous generators?
In the $(x, y, z)$ coordinate system, three point-charges $Q$, $Q$, and $\alpha Q$ are located in free space at $(-1, 0, 0)$, $(1, 0, 0)$, and $(0, -1, 0)$, respectively. The value...
A 3-phase star connected slip ring induction motor has the following parameters referred to the stator: $R_s = 3\, \Omega,\; X_s = 2\, \Omega,\; X_r' = 2\, \Omega,\; R_r' = 2.5\, \...
A 5 kW, 220 V DC shunt motor has 0.5 $\Omega$ armature resistance including brushes. The motor draws a no-load current of 3 A. The field current is constant at 1 A. Assuming that t...
A single-phase half-controlled bridge converter supplies an inductive load with ripple free load current. The triggering angle of the converter is 60°. The ratio of the rms value o...
A single-phase full bridge voltage source inverter (VSI) feeds a purely inductive load. The inverter output voltage is a square wave in 180° conduction mode. The fundamental freque...
A single-phase full-controlled thyristor converter bridge is used for regenerative braking of a separately excited DC motor with the following specifications: Rated armature voltag...
The input $x(t)$ and the output $y(t)$ of a system are related as $$ y(t) = e^{-t} \int\limits_{-\infty}^{t} e^{\tau} x(\tau) d\tau, \quad - \infty The system is
Consider the discrete-time systems $T_1$ and $T_2$ defined as follows: { $T_1 x[ n ] = x[ 0 ] + x[ 1 ] + \cdots + x[ n ] $} { $T_2 x[ n ] = x[ 0 ] + \frac{1}{2} x[ 1 ] + \cdots + \...
Suppose signal $y(t)$ is obtained by the time-reversal of signal $x(t)$, i.e., $y(t) = x(-t)$, $-\infty
If $u(t)$ is the unit step function, then the region of convergence (ROC) of the Laplace transform of the signal $x(t) = e^{t^2}[u(t-1)-u(t-10)]$ is
Let $X(\omega)$ be the Fourier transform of the signal $x(t) = e^{-t^4} \cos t, \quad -\infty The value of the derivative of $X(\omega)$ at $\, \omega = 0$ is ______ (rounded off t...
The table lists two instrument transformers and their features: Instrument Transformers Features X) Current Transformer (CT) P) Primary is connected in parallel to the grid Y) Pote...
If the Z-transform of a finite-duration discrete-time signal $x[n]$ is $X(z)$, then the Z-transform of the signal $y[n] = x[2n]$ is
If the energy of a continuous-time signal $x(t)$ is $E$ and the energy of the signal $2x(2t - 1)$ is $cE$, then $c$ is _____ (rounded off to 1 decimal place).
The given equation represents a magnetic field strength $\bar{H}(r, \theta, \phi)$ in the spherical coordinate system, in free space. Here, $\hat{r}$ and $\hat{\theta}$ represent t...
A surveyor has to measure the horizontal distance from her position to a distant reference point C. Using her position as the center, a 200 m horizontal line segment is drawn with...
Which one of the following matrices has an inverse?
Which of the following complex functions is/are analytic on the complex plane?
If ‘→’ denotes increasing order of intensity, then the meaning of the words [talk → shout → scream] is analogous to [please → _______ → pander]. Which one of the given options is a...
P and Q have been allotted a hostel room with two beds, a study table, and an almirah. P is an avid bird-watcher and wants to sit at the table and watch birds outside the window. Q...
The decimal number system uses the characters 0, 1, 2, ... , 8, 9, and the octal number system uses the characters 0, 1, 2, ... , 6, 7. For example, the decimal number 12 ( = 1 &ti...
A shopkeeper buys shirts from a producer and sells them at 20% profit. A customer has to pay ₹3,186.00 including 18% taxes, per shirt. At what price did the shopkeeper buy each shi...
Consider the complex function $f(z) = \cos z + e^{z^2}$. The coefficient of $z^5$ in the Taylor series expansion of $f(z)$ about the origin is ______ (rounded off to 1 decimal plac...
If, for non-zero real variables $x$, $y$, and real parameter $a > 1$, $x : y = (a + 1) : (a - 1)$, then, the ratio $(x^2 - y^2) : (x^2 + y^2)$ is
In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks. Following a row ____(i) ______ the shopkeeper ____(ii) ______ the price of a frying p...
The sum of the eigenvalues of the matrix $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}^2$ is ______ (rounded off to the nearest integer).
A three phase, 50 Hz, 6 pole induction motor runs at 960 rpm. The stator copper loss, core loss, and the rotational loss of the motor can be neglected. The percentage efficiency of...
Which one of the following options represents possible voltage polarities in a single phase two winding transformer? Here, $V_p$ is the applied primary voltage, $E_p$ is the induce...
Set Master
If '→' denotes increasing order of intensity, then the meaning of the words [talk → shout → scream] is analogous to [please → ________ → pander]. Which one of the given options is...
P and Q have been allotted a hostel room with two beds, a study table, and an almirah. P is an avid bird-watcher and wants to sit at the table and watch birds outside the window. Q...
The decimal number system uses the characters 0, 1, 2, ..., 8, 9, and the octal number system uses the characters 0, 1, 2, ..., 6, 7. For example, the decimal number 12 (= 1 × 10^1...
A shopkeeper buys shirts from a producer and sells them at 20% profit. A customer has to pay ₹3,186.00 including 18% taxes, per shirt. At what price did the shopkeeper buy each shi...
If, for non-zero real variables x, y, and real parameter a > 1, x: y = (a + 1): (a− 1), then, the ratio (x² - y²): (x² + y²) is
In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks. Following a row ____ (i) ____ the shopkeeper ____ (ii) ____ the price of a frying pan...
In the following figure, CD = 5 cm, BE = 10 cm, AE = 12 cm, ∠DAB = ∠DCB, and ∠DAE = ∠DBC = 90° Points AFCD create a rhombus. The length of BF (in cm) is
The chart below shows the data of the number of cars bought by Millennials and Gen X people in a country from the year 2010 to 2020 as well as the yearly fuel consumption of the co...
The assembly shown below has three teethed circular objects (Pinions) and two teethed flat objects (Racks), which are perfectly mating with each other. Pinions can only rotate cloc...
A surveyor has to measure the horizontal distance from her position to a distant reference point C. Using her position as the center, a 200 m horizontal line segment is drawn with...
Which one of the following matrices has an inverse?
The number of junctions in the circuit is
All the elements in the circuit are ideal. The power delivered by the 10 V source in watts is
The circuit shown in the figure with the switch S open, is in steady state. After the switch S is closed, the time constant of the circuit in seconds is
Suppose signal y(t) is obtained by the time-reversal of signal x(t), i.e., y(t) = x(−t), −∞ < t < ∞. Which one of the following options is always true for the convolution of x(t) a...
If u(t) is the unit step function, then the region of convergence (ROC) of the Laplace transform of the signal x(t) = e^(t^2) [u(t − 1) – u(t − 10)] is
A three phase, 50 Hz, 6 pole induction motor runs at 960 rpm. The stator copper loss, core loss, and the rotational loss of the motor can be neglected. The percentage efficiency of...
Which one of the following options represents possible voltage polarities in a single phase two winding transformer? Here, Vp is the applied primary voltage, Ep is the induced prim...
The figure shows the single line diagram of a 4-bus power network. Branches $b_1$, $b_2$, $b_3$, and $b_4$ have impedances $4z$, $z$, $2z$, and $4z$ per-unit (pu), respectively, wh...
For the block-diagram shown in the figure, the transfer function $\frac{C(s)}{R(s)}$ is
Consider the standard second-order system of the form $\frac{\omega_n^2}{s^2+2\zeta\omega_n s+\omega_n^2}$ with the poles $p$ and $p^*$ having negative real parts. The pole locatio...
Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a first-order pole-only approx...
The table lists two instrument transformers and their features: Instrument Transformers X) Current Transformer (CT) Y) Potential Transformer (PT) Features P) Primary is connected i...
Simplified form of the Boolean function $F(P,Q,R,S) = \overline{P}\overline{Q} + \overline{P}QS + \overline{P}Q\overline{R}\overline{S} + P\overline{Q}\overline{R}\overline{S}$ is
In the circuit, the present value of Z is 1. Neglecting the delay in the combinatorial circuit, the values of S and Z, respectively, after the application of the clock will be
To obtain the Boolean function $F(X,Y) = X\bar{Y} + \bar{X}$, the inputs $PQRS$ in the figure should be
If the following switching devices have similar power ratings, which one of them is the fastest?
A single-phase triac based AC voltage controller feeds a series RL load. The input AC supply is 230 V, 50 Hz. The values of R and L are 10 Ω and 18.37 mH, respectively. The minimum...
Let X be a discrete random variable that is uniformly distributed over the set {-10, -9, ..., 0,..., 9, 10}. Which of the following random variables is/are uniformly distributed?
Which of the following complex functions is/are analytic on the complex plane?
Consider the complex function $f(z) = \cos z + e^{z^2}$. The coefficient of $z^5$ in the Taylor series expansion of $f(z)$ about the origin is ________ (rounded off to 1 decimal pl...
The sum of the eigenvalues of the matrix $A=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}^2$ is ________ (rounded off to the nearest integer).
Let $X(\omega)$ be the Fourier transform of the signal $x(t) = e^{-t^4} \cos t$, $-\infty < t < \infty$. The value of the derivative of $X(\omega)$ at $\omega=0$ is ________ (round...
The incremental cost curves of two generators (Gen A and Gen B) in a plant supplying a common load are shown in the figure. If the incremental cost of supplying the common load is...
A forced commutated thyristorized step-down chopper is shown in the figure. Neglect the ON-state drop across the power devices. Assume that the capacitor is initially charged to 50...
Consider a vector $\bar{u} = 2\hat{x} + \hat{y} + 2\hat{z}$, where $\hat{x}, \hat{y}, \hat{z}$ represent unit vectors along the coordinate axes $x, y, z$ respectively. The directio...
The input $x(t)$ and the output $y(t)$ of a system are related as $y(t) = e^{-t} \int_{-\infty}^{t} e^{\tau} x(\tau) d\tau, \quad -\infty < t < \infty$. The system is
If the Z-transform of a finite-duration discrete-time signal x[n] is X(z), then the Z-transform of the signal y[n] = x[2n] is
A 3-phase, 11 kV, 10 MVA synchronous generator is connected to an inductive load of power factor (√3/2) via a lossless line with a per-phase inductive reactance of 5 Ω. The per-pha...
For the three-bus lossless power network shown in the figure, the voltage magnitudes at all the buses are equal to 1 per unit (pu), and the differences of the voltage phase angles...
A BJT biasing circuit is shown in the figure, where VBE = 0.7 V and β = 100. The Quiescent Point values of VCE and IC are respectively
Let f(t) be a real-valued function whose second derivative is positive for -∞ < t < ∞. Which of the following statements is/are always true?
Consider the function f(t) = (max(0,t))² for -∞ < t < ∞, where max(a, b) denotes the maximum of a and b. Which of the following statements is/are true?
Which of the following differential equations is/are nonlinear?
For a two-phase network, the phase voltages Vₚ and Vq are to be expressed in terms of sequence voltages Vα and Vβ as [Vₚ Vq] = S [Vα Vβ]. The possible option(s) for matrix S is/are
Which of the following options is/are correct for the Automatic Generation Control (AGC) and Automatic Voltage Regulator (AVR) installed with synchronous generators?
Two passive two-port networks P and Q are connected as shown in the figure. The impedance matrix of network P is Zp = [40 Ω 60 Ω; 80 Ω 100 Ω]. The admittance matrix of network Q is...
For the circuit shown in the figure, the source frequency is 5000 rad/sec. The mutual inductance between the magnetically coupled inductors is 5 mH with their self inductances bein...
In the circuit shown, Z₁ = 50∠ – 90° Ω and Z₂ = 200∠ – 30° Ω. It is supplied by a three phase 400 V source with the phase sequence being R-Y-B. Assume the watt meters W₁ and W₂ to...
In the (x, y, z) coordinate system, three point-charges Q, Q, and αQ are located in free space at (-1, 0, 0), (1, 0, 0), and (0, -1, 0), respectively. The value of α for the electr...
The given equation represents a magnetic field strength $\vec{H}(r, \theta, \phi)$ in the spherical coordinate system, in free space. Here, $\hat{r}$ and $\hat{\theta}$ represent t...
If the energy of a continuous-time signal x(t) is E and the energy of the signal 2x(2t − 1) is cE, then c is ________ (rounded off to 1 decimal place).
A 3-phase star connected slip ring induction motor has the following parameters referred to the stator: R_s = 3 Ω, X_s = 2 Ω, X'_r = 2 Ω, R'_r = 2.5 Ω The per phase stator to rotor...
A 5 kW, 220 V DC shunt motor has 0.5 Ω armature resistance including brushes. The motor draws a no-load current of 3 A. The field current is constant at 1 A. Assuming that the core...
The single line diagram of a lossless system is shown in the figure. The system is operating in steady-state at a stable equilibrium point with the power output of the generator be...
Consider the closed-loop system shown in the figure with $G(s) = \frac{K(s^2 - 2s + 2)}{(s^2 + 2s + 5)}$ The root locus for the closed-loop system is to be drawn for $0 \le K < \in...
Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of $G(s)$ has a constant slope of -20 dB/decade at least till 100 rad/sec with the ga...
Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of G(s) are given in the table. The value of the gain K_I (>0)...
In the given circuit, the diodes are ideal. The current I through the diode D1 in milliamperes is ____________ (rounded off to two decimal places).
A difference amplifier is shown in the figure. Assume the op-amp to be ideal. The CMRR (in dB) of the difference amplifier is ________ (rounded off to 2 decimal places).
A single-phase half-controlled bridge converter supplies an inductive load with ripple free load current. The triggering angle of the converter is 60°. The ratio of the rms value o...
A single-phase full bridge voltage source inverter (VSI) feeds a purely inductive load. The inverter output voltage is a square wave in 180° conduction mode. The fundamental freque...
In the DC-DC converter shown in the figure, the current through the inductor is continuous. The switching frequency is 500 Hz. The voltage ($V_o$) across the load is assumed to be...
A single-phase full-controlled thyristor converter bridge is used for regenerative braking of a separately excited DC motor with the following specifications: Rated armature voltag...