Practice Test: Gate Electrical Engineering GATE 2018 Paper

For what values of �� given below is  an integer?

Functions F(a, b) and G(a, b) are defined as follows:   represents the absolute value of ��. What would be the value of G(F(1, 3), G(1, 3))?

An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9, one upper case and one lower case character from the English alphabet. How many distinct passwords are possible?

In a certain code, AMCF is written as EQGJ and NKUF is written as ROYJ. How will DHLP be written in that code?

A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the probability that the group accompanying the teacher contains more girls than boys?

A designer uses marbles of four different colours for his designs. The cost of each marble is the same, irrespective of the colour. The table below shows the percentage of marbles of each colour used in the current design. The cost of each marble increased by 25%. Therefore, the designer decided to reduce equal numbers of marbles of each colour to keep the total cost unchanged. What is the percentage of blue marbles in the new design? 

P, Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only one set of oars. The following additional facts are available.
(i) The boat held two persons on each of the three forward trips across the lake and one person on each of the two return trips.
(ii) P is unable to row when someone else is in the boat.
(iii) Q is unable to row with anyone else except R.
(iv) Each person rowed for at least one trip.
(v) Only one person can row during a trip.
Who rowed twice?

A single-phase 100 kVA, 1000 V / 100 V, 50 Hz transformer has a voltage drop of 5% across its series impedance at full load. Of this, 3% is due to resistance. The percentage regulation of the transformer at full load with 0.8 lagging power factor is

In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is

A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. Which one of the following is true for instantaneous load voltage and current?
 

Four power semiconductor devices are shown in the figure along with their relevant terminals. The device(s) that can carry dc current continuously in the direction shown when gated appropriately is (are)

Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of the other (both positive), then the power factor of the load is

Consider a lossy transmission line with V₁ and V₂ as the sending and receiving end voltages, respectively. Z and X are the series impedance and reactance of the line, respectively.  The steady-state stability limit for the transmission line will be

The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph is

In the figure, the voltages are The circuit is in sinusoidal steady state, and �� << ����. ��₁, ��₂ and ��₃ are the average power outputs. Which one of the following statements is true?

Match the transfer functions of the second-order systems with the nature of the systems given below.

A positive charge of 1 nC is placed at (0, 0, 0.2) where all dimensions are in metres. Consider the x - y plane to be a conducting ground plane. Take 12 ε₀= 8.85X10^-12 F/m. The z component of the E field at (0, 0, 0.1) is closest to

Let f be a real-valued function of a real variable defined as f ( x) = x 2 for x ≥ 0 , and 2f ( x) =- x² for x < 0 . Which one of the following statements is true?

The value of the directional derivative of the function at the point (2, -1, 1) in the direction of the vector is

The value of the integral in counter clockwise direction around a circle C of radius 1 with center at the point z = −2 is

In the logic circuit shown in the figure, Y is given by

The op-amp shown in the figure is ideal. The input impedance  is given by

A continuous-time input signal x(t) is an eigenfunction of an LTI system, if the output is

Consider a non-singular 2×2 square matrix A . If trace(A) = 4 and trace (A ² ) = 5 , the determinant of the matrix A is  _________(up to 1 decimal place).

Let  f be a real-valued function of a real variable defined as denotes the largest integer less than or equal to x. The value of   is _______ (up  to 2 decimal places).

In the two-port network shown, the h 11 parameter is _____________ (up to 2 decimal places).

The series impedance matrix of a short three-phase transmission line in phase coordinates is . If the positive sequence impedance is , and the zero sequence is , then the imaginary part of is ______(up to 2 decimal places).

The positive, negative and zero sequence impedances of a 125 MVA, three-phase, 15.5 kV, star-grounded, 50 Hz generator are j0.1 pu,⁡j0.05 pu and j0.01 pu respectively on the machine rating base. The machine is unloaded and working at the rated terminal voltage.  If the grounding impedance of the generator is j0.01 pu, then the magnitude of fault current for a b-phase to ground fault (in kA) is __________ (up to 2 decimal places).

A 1000 × 1000 bus admittance matrix for an electric power system has 8000 non-zero elements. The minimum number of branches (transmission lines and transformers) in this system are _____ (up to 2 decimal places).

The waveform of the current drawn by a semi-converter from a sinusoidal AC voltage source is shown in the figure. If I₀ = 20 A, the rms value of fundamental component of the current is ___________A (up to 2 decimal places).

A separately excited dc motor has an armature resistance R_a = 0.05⁡Ω. The field excitation is kept constant. At an armature voltage of 100 V, the motor produces a torque of 500 Nm at zero speed. Neglecting all mechanical losses, the no-load speed of the motor (in radian/s) for an armature voltage of 150 V is _____  (up to 2 decimal places).

Consider a unity feedback system with forward transfer function given by

The steady-state error in the output of the system for a unit-step input is _________(up to 2 decimal places).

A transformer with toroidal core of permeability m is shown in the figure. Assuming uniform flux density across the circular core cross-section of radius  and neglecting any leakage flux, the best estimate for the mean radius R is

A 0-1 Ampere moving iron ammeter has an internal resistance of 50 mΩ and inductance of 0.1 mH. A shunt coil is connected to extend its range to 0-10 Ampere for all operating frequencies. The time constant in milliseconds and resistance in mΩ of the shunt coil respectively are

The positive, negative and zero sequence impedances of a three phase generator are Z₁, Z₂ and Z₀ respectively. For a line-to-line fault with fault impedance Z_f ,⁡the fault current is⁡ I_f1 = kI_f , where I_f is the fault current with zero fault impedance. The relation between Z_f and k is

Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator G₁ and G₂ are QG₁ and QG₂ respectively. The per unit values of QG₁, QG₂, and line reactive power loss (Q_loss) respectively are 

The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, �� = 1.4 sin �� + 0.15 sin 2��, where �� is the load angle. NewtonRaphson method is used to calculate the value of �� for �� = ⁡0.8 pu.  If the initial guess is 30°, then its value (in degree) at the end of the first iteration is

A DC voltage source is connected to a series L-C circuit by turning on the switch S at time t = 0 as shown in the figure. Assume i(0) = 0,v(0)= 0 . Which one of the following circular loci represents the plot of i(t ) versus v(t ) ?

The equivalent impedance Z_eq for the infinite ladder circuit shown in the figure is

Consider a system governed by the following equations

The initial conditions are such that 

Which one of the following is true?

Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation as
s⁵+s⁴+4s³+4s²+4s+4=0

If C ⁡is a circle |z| = 4 and 

Which one of the following statements is true about the digital circuit shown in the figure

Digital input signals A, B, C with A as the MSB and C as the LSB are used to realize the Boolean function  ⁡minterm. In addition, �� has a don’t care for ��₁. The simplified expression for �� is given by

Consider the two continuous-time signals defined below:

These signals are sampled with a sampling period of T = 0.25 seconds to obtain discretetime signals x₁[n] and x₂ [n] , respectively. Which one of the following statements is true?

The signal energy of the continuous-time signal

The Fourier transform of a continuous-time signal x(t) is given by
 denotes frequency. Then the value of   at t =1 is ___________ (up to 1 decimal place). ( ln denotes the logarithm to base e )

In the circuit shown in the figure, the bipolar junction transistor (BJT) has a current gain β = 100. The base-emitter voltage drop is a constant, v_EE = 0.7⁡��. The value of the Thevenin equivalent resistance R_Th (in Ω) as shown in the figure is ______ (up to 2 decimal places).

As shown in the figure, C is the arc from the point (3,0) to the point (0,3) on the circle x² + y² = 9. The value of the integral (up to 2 decimal places).

Let The maximum value of f (x) over the interval [0, 2] is _______ (up to 1 decimal place).

Let   where I is the 3X3 identity matrix. The determinant of B is ________ (up to 1 decimal place).

The capacitance of an air-filled parallel-plate capacitor is 60 pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes 86 pF. Neglecting the fringing effects, the relative permittivity of the dielectric is _____________ (up to 2 decimal places).

The unit step response y(t) of a unity feedback system with open loop transfer function 
  is shown in the figure. The value of K is _______ (up to 2 decimal places).

A three-phase load is connected to a three-phase balanced supply as shown in the figure. If (angles are considered positive in the anti-clockwise direction), the value of R for zero current in the neutral wire is ___________Ω (up to 2 decimal places).

The voltage across the circuit in the figure, and the current through it, are given by the following expressions:

where �� = 100⁡�� ⁡radian/s. If the average power delivered to the circuit is zero, then the value of �� (in Ampere) is  _____ (up to 2 decimal places).

A phase controlled single phase rectifier, supplied by an AC source, feeds power to an R-L-E load as shown in the figure. The rectifier output voltage has an average value given 
by volts and α is the firing angle. If the power delivered to the lossless battery is 1600 W, α in degree is________ (up to 2 decimal places).

The figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of 100 V. The converters have inductors of identical value. The load resistance is 1 Ω. The capacitor voltage has negligible ripple. Both converters operate in the continuous conduction mode. The switching frequency is 1 kHz, and the switch control signals are as shown. The circuit operates in the steady state. Assuming that the converters share the load equally, the average value of i_S1 , the current of switch S1 (in Ampere), is _____ (up to 2 decimal places).

A 3-phase  transformer has primary (high voltage side) resistance per phase of 0.3 Ω and secondary (low voltage side) resistance per phase of 0.02 Ω. Iron loss of the transformer is 10 kW. The full load % efficiency of the transformer operated at unity power factor is _______ (up to 2 decimal places).

A 200 V DC series motor, when operating from rated voltage while driving a certain load, draws 10 A current and runs at 1000 r.p.m. The total series resistance is 1 Ω. The magnetic circuit is assumed to be linear. At the same supply voltage, the load torque is increased by 44%. The speed of the motor in r.p.m. (rounded to the nearest integer) is ________ .

A dc to dc converter shown in the figure is charging a battery bank, B2 whose voltage is constant at 150 V. B1 is another battery bank whose voltage is constant at 50 V. The value of the inductor, L is 5 mH and the ideal switch, S is operated with a switching frequency of 5 kHz with a duty ratio of 0.4. Once the circuit has attained steady state and assuming the diode D to be ideal, the power transferred from B1 to B2 (in Watt) is ___________ (up to 2 decimal places).

The equivalent circuit of a single phase induction motor is shown in the figure, where the parameters are  is the slip. At no-load, the motor speed can be approximated to be the synchronous speed. The no-load lagging power factor of the motor is___________ (up to 3 decimal places).

 The voltage v(t) across the terminals a and b as shown in the figure, is a sinusoidal voltage having a frequency �� = 100 radian/s. When the inductor current i(t) is in phase with the voltage v(t), the magnitude of the impedance Z (in Ω) seen between the terminals a and b is ________ (up to 2 decimal places).