GATE 2019 Electrical Engineering
76 questions across 2 sessions
Gate Ee 2019
Given two sets X = {1, 2, 3} and Y = {2, 3, 4}, we construct a set Z of all possible fractions where the numerators belong to set X and the denominators belong to set Y. The produc...
How many integers are there between 100 and 1000 all of whose digits are even?
The passengers were angry __________ the airline staff about the delay.
It takes two hours for a person X to mow the lawn. Y can mow the same lawn in four hours. How long (in minutes) will it take X and Y, if they work together to mow the lawn?
The ratio of the number of boys and girls who participated in an examination is 4 : 3. The total percentage of candidates who passed the examination is 80 and the percentage of a g...
Newspapers are a constant source of delight and recreation for me. The _____ trouble is that I read _______ many of them.
A 0.1 μF capacitor charged to 100 V is discharged through a 1 kΩ resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to...
The missing number in the given sequence 343, 1331, _______, 4913 is
I am not sure if the bus that has been booked will be able to ______ all the students
Consider five people- Mitra, Ganga, Rekha, Lakshmi and Sana, Ganga is taller than both Rekha and Lakshmi. Lakshmi is taller than Sana. Mita is taller than Ganga. Which of the follo...
An award-winning study by a group of researchers suggests that men are as prone to buying on impulse as women but women feel more guilty about shopping. Which one of the following...
Set Master
I am not sure if the bus that has been booked will be able to ________ all the students.
The inverse Laplace transform of H(s) = $\frac{s+3}{s^2+2s+1}$ for t ≥ 0 is
M is a 2 x 2 matrix with eigenvalues 4 and 9. The eigenvalues of M² are
The passengers were angry ________ the airline staff about the delay.
The partial differential equation $\frac{\partial^2u}{\partial t^2} - c^2 (\frac{\partial^2u}{\partial x^2} + \frac{\partial^2u}{\partial y^2}) = 0$; where c ≠ 0 is known as
The missing number in the given sequence 343, 1331, ______, 4913 is
Which one of the following functions is analytic in the region |z| ≤ 1?
It takes two hours for a person X to mow the lawn. Y can mow the same lawn in four hours. How long (in minutes) will it take X and Y, if they work together to mow the lawn?
The mean-square of a zero-mean random process is $\frac{kT}{C}$, where k is Boltzmann's constant, T is the absolute temperature, and C is a capacitance. The standard deviation of t...
Newspapers are a constant source of delight and recreation for me. The ________ trouble is that I read ________ many of them.
A system transfer function is H(s) = $\frac{a_1s^2+b_1s+c_1}{a_2s^2+b_2s+c_2}$. If $a_1 = b_1 = 0$, and all other coefficients are positive, the transfer function represents a
How many integers are there between 100 and 1000 all of whose digits are even?
The symbols, a and T, represent positive quantities, and u(t) is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-inva...
The ratio of the number of boys and girls who participated in an examination is 4:3. The total percentage of candidates who passed the examination is 80 and the percentage of girls...
A 5 kVA, 50 V/100 V, single-phase transformer has a secondary terminal voltage of 95 V when loaded. The regulation of the transformer is
An award-winning study by a group of researchers suggests that men are as prone to buying on impulse as women but women feel more guilty about shopping. Which one of the following...
A six-pulse thyristor bridge rectifier is connected to a balanced three-phase, 50 Hz AC source. Assuming that the DC output current of the rectifier is constant, the lowest harmoni...
Given two sets X = {1, 2, 3} and Y = {2, 3, 4}, we construct a set Z of all possible fractions where the numerators belong to set X and the denominators belong to set Y. The produc...
Consider five people - Mita, Ganga, Rekha, Lakshmi and Sana. Ganga is taller than both Rekha and Lakshmi. Lakshmi is taller than Sana. Mita is taller than Ganga. Which of the follo...
The parameter of an equivalent circuit of a three-phase induction motor affected by reducing the rms value of the supply voltage at the rated frequency is
A three-phase synchronous motor draws 200 A from the line at unity power factor at rated load. Considering the same line voltage and load, the line current at a power factor of 0.5...
In the circuit shown below, the switch is closed at t = 0. The value of $\theta$ in degrees which will give the maximum value of DC offset of the current at the time of switching i...
The output response of a system is denoted as y(t), and its Laplace transform is given by $Y(s) = \frac{10}{s(s^2+s+100\sqrt{2})}$. The steady state value of y(t) is
The open loop transfer function of a unity feedback system is given by $G(s) = \frac{\pi e^{-0.25s}}{s}$. In G(s) plane, the Nyquist plot of G(s) passes through the negative real a...
The characteristic equation of a linear time-invariant (LTI) system is given by $\Delta(s) = s^4 + 3s^3 + 3s^2 + s + k = 0$. The system is BIBO stable if
Given, Vgs is the gate-source voltage, Vds is the drain source voltage, and Vth is the threshold voltage of an enhancement type NMOS transistor, the conditions for transistor to be...
A current controlled current source (CCCS) has an input impedance of 10 Ω and output impedance of 100 kΩ. When this CCCS is used in a negative feedback closed loop with a loop gain...
If f = 2x³ + 3y² + 4z, the value of line integral ∫c gradf ⋅ dr evaluated over contour C formed by the segments (-3, -3, 2)→(2, -3, 2)→(2, 6, 2)→(2, 6, -1) is
The current I flowing in the circuit shown below in amperes (round off to one decimal place) is
A co-axial cylindrical capacitor shown in Figure (i) has dielectric with relative permittivity εr1 = 2. When one-fourth portion of the dielectric is replaced with another dielectri...
The Ybus matrix of a two-bus power system having two identical parallel lines connected between them in pu is given as Ybus = [-j8 j20] [j20 -j8] The magnitude of the series reacta...
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 _________.
The total impedance of the secondary winding, leads, and burden of a 5 A CT is 0.01 Ω. If the fault current is 20 times the rated primary current of the CT, the VA output of the CT...
The rank of the matrix, M = [0 1 1] [1 0 1], [1 1 0] is _________.
The output voltage of a single-phase full bridge voltage source inverter is controlled by unipolar PWM with one pulse per half cycle. For the fundamental rms component of output vo...
Consider a 2 × 2 matrix M = [v₁ v₂], where, v₁ and v₂ are the column vectors. Suppose M⁻¹ = [u₁ᵀ; u₂ᵀ], where u₁ᵀ and u₂ᵀ are the row vectors. Consider the following statements: St...
The closed loop line integral ∮_{|z|=5} (z³ + z² + 8)/(z + 2) dz evaluated counter-clockwise, is
A periodic function f(t), with a period of 2π, is represented as its Fourier series, f(t) = a₀ + Σ_{n=1}^∞ aₙ cos nt + Σ_{n=1}^∞ bₙ sin nt. If f(t) = { A sin t, 0 ≤ t ≤ π; 0, π < t...
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) has three po...
The transfer function of a phase lead compensator is given by D(s) = 3(s+1/(3T))/(s+1/T) The frequency (in rad/sec), at which ∠D(jω) is maximum, is
Consider a state-variable model of a system [ẋ1; ẋ2] = [[0, 1]; [-α, -2β]] * [x1; x2] + [[0]; [α]] * r y = [1, 0] * [x1; x2] where y is the output, and r is the input. The damping...
A moving coil instrument having a resistance of 10 Ω, gives a full-scale deflection when the current is 10 mA. What should be the value of the series resistance, so that it can be...
The enhancement type MOSFET in the circuit below operates according to the square law. $\mu_n C_{ox} = 100 \mu A/V^2$, the threshold voltage (V_T) is 500 mV. Ignore channel length...
In the circuit below, the operational amplifier is ideal. If V_1 = 10 mV and V_2 = 50 mV, the output voltage (V_out) is
The output expression for the Karnaugh map shown below is
In the circuit shown below, X and Y are digital inputs, and Z is a digital output. The equivalent circuit is a
A DC-DC 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 25...
The line currents of a three-phase four wire system are square waves with amplitude of 100 A. These three currents are phase shifted by 120° with respect to each other. The rms val...
If A = 2xi + 3yj + 4zk and u = x² + y² + z², then div(uA) at (1, 1, 1) is _________.
The probability of a resistor being defective 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...
A 0.1 µF capacitor charged to 100 V is discharged through a 1 KΩ resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to...
The current I flowing in the circuit shown below in amperes is _________.
The voltage across and the current through a load are expressed as follows v(t) = -170 sin (377t - $\frac{\pi}{6}$) V i(t) = 8 cos (377t + $\frac{\pi}{6}$) A The average power in w...
The magnetic circuit shown below has uniform cross-sectional 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 negl...
A single-phase 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)...
A 220 V DC shunt motor takes 3 A at no-load. It draws 25 A when running at full-load at 1500 rpm. The armature and shunt resistances are 0.5 Ω and 220 Ω, respectively. The no-load...
A delta-connected, 3.7 kW, 400 V(line), three-phase, 4-pole, 50-Hz squirrel-cage induction motor has the following equivalent circuit parameters per phase referred to the stator: R...
A 220 V (line), three-phase, Y-connected, synchronous motor has a synchronous impedance of (0.25 + j2.5) Ω/phase. The motor draws the rated current of 10 A at 0.8 pf leading. The r...
A three-phase 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 µF/km per phase. The line is under open circuit...
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 w...
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...
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 µF. The critical value...
In a DC-DC 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...
A fully-controlled three-phase bridge converter is working from a 415 V, 50 Hz AC supply. It is supplying constant current of 100 A at 400 V to a DC load. Assume large inductive sm...
A single-phase fully-controlled 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 single-phase AC suppl...