Practice Test: Gate Electrical Engineering GATE 2017 Paper - Electrical Engineering (EE)

After Rajendra Chola returned from his voyage to Indoneisa, he _______ to visit the temple in Thanjavur.

Rahul, Murali, Srinivas and Arul are seated around a square table. Rahul is sitting to the left of Murali. Srinivas is sitting to the right of Arul. Which of the following pairs are seated opposite each other?

Directions

Q. No. 6 – 10 Carry Two Marks Each

Q.

Six people are seated around a circular table. There are at least two men and two women. There are at least three right-handed persons. Every woman has a left-handed person to her immediate right. None of the women are right-handed. The number of women at the table is

The expression    is equal to.

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25m intervals in this plot. If in a flood, the water level rises to 525m. Which of the villages P,Q,R,S,T get submerged?

Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes the colour white, Gulab and Neel like all the colours. In how many different ways can they choose the shirts so that no one has a shirt with a colour he or she dislikes?

“The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history.”

Which of the following statements best reflects the author‟s opinion?

Directions

Q. No. 11 – 35 Carry One Mark Each

Q.

Consider g(t) = 

Here, represents the largest integer less than or equal to t and  denotes the smallest integer greater than or equal to t. The coefficient of the second harmonic component of the Fourier series representing g(t) is _________.

A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are V_an =220sin (100πt ) V and 
i_a = 10 sin(100πt)A, respectively. Similarly for phase-b the instantaneous voltage and current are  V_tm = 220cos(100πt )V and i_b = 10 cos(100πt)A, respectively.

The total instantaneous power flowing form the source to the load is 

A three-phase, 50Hz, star-connected cylindrical-rotor synchronous machine is running as a motor. The machine is operated from a 6.6 kV grid and draws current at unity power factor (UPF). The synchronous reactance of the motor is 30Ω per phase. The load angle is 30^o. The power delivered to the motor in kW is _______

For a complex number z,

Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the electron and proton. At t=0, the particles are released but are constrained to move along the same straight line. Which of these will collide first?

Let z ( t ) = x ( t )* y ( t ) , where " * " denotes convolution. Let C be a positive real-valued constant. Choose the correct expression for z (ct).

A 3-bus power system is shown in the figure below, where the diagonal elements of Y-bus matrix are Y11 = - j12pu, Y22 = - j15pu and Y33 = - j7pu The per unit values of the line reactances p, q and r shown in the figure are

The equivalent resistance between the terminals A and B is ____ Ω.

The Boolean expression  simplifies to

The following measurements are obtained on a single phase load:

If the power factor is calculated using these measurements, the worst case error in the calculated power factor in percent is ________. 

The transfer function of a system is given by,  Let the output of the system be 

v_o( t ) = V_m sin( ωt + φ) for the input v_i (t) = V sin(ωt) . Then the minimum and maximum 
values of φ (in radians) are respectively

The matrix  has three distinct eigenvalues and one of its eigenvectors is   Which one of the following can be another eigenvector of A?

For the power semiconductor devices IGBT, MOSFET, Diode and Thyristor, which one of the following statements is TRUE?

Consider the unity feedback control system shown. The value of K that results in a phase margin of the system to be 30^o is _______. 

A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic field lines inside the cylinder will

where R is the region shown in the figure and c = 6 x 10^-4. The value of I equals________.

Consider the system with following input-output relation y[n] =  (1 + ( -1)n ) x [ n ]where, x[n] is the input and y[n] is the output. The system is 

The slope and level detector circuit in a CRO has a delay of 100 ns. The start-stop sweep generator has a response time of 50 ns. In order to display correctly, a delay line of

A 3-phase voltage source inverter is supplied from a 600V DC source as shown in the figure below. For a star connected resistive load of 20Ω per phase, the load power for 120^o device conduction, in kW is __________.

A closed loop system has the characteristic equation given by s³ + Ks² + ( K + 2 )s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?

A 4 pole induction machine is working as an induction generator. The generator supply frequency is 60 Hz. The rotor current frequency is 5 Hz. The mechanical speed of the rotor in RPM is

For the circuit shown in the figure below, assume that diodes D₁, D₂ and D₃ are ideal. The DC components of voltages v₁ and v₂, respectively are

A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is _______.

The power supplied by the 25 V source in the figure shown below is ________W.

In the converter circuit shown below, the switches are controlled such that the load voltage v_o(t) is a 400 Hz square wave.

The RMS value of the fundamental component of v_o(t) in volts is _______.

Directions

Q. No. 36 – 65 Carry Two Marks Each

Q.

The output expression for the Karnaugh map shown below is 

A 220 V DC series motor runs drawing a current of 30 A from the supply. Armature and field circuit resistances are 0.4 Ω and 0.1 Ω respectively. The load torque varies as the square of the speed. The flux in the motor may be taken as being proportional to the armature current. To reduce the speed of the motor by 50% the resistance in ohms that should be added in series with the armature is _________. 

The transfer function of the system Y(s)/U(s) whose state-space equations are given below is:

The load shown in the figure is supplied by a 400 V (line to line) 3-phase source (RYB sequence).  The load is balanced and inductive, drawing 3464 VA. When the switch S is in position N, the three watt-meters W₁, W₂ and W₃ read 577.35 W each. If the switch is moved to position Y, the readings of the watt-meters in watts will be:

Two passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port 1.

Given V₁ = A₁V₂ +B₁I₂

          I₁ = C₁V₂+ D₁I₂

          V₂ = A₂V₃ +B₂I₃

         I₂ = C₂V₃ + V₂I₃

A₁ , B₁ , C₁ , D₁ , A₂ , B₂ , C₂ and D₂ are the generalized circuit constants. If the Thevenin equivalent circuit at port 3 consists of a voltage source V_T and impedance Z_T connected in series, then

The circuit shown in the figure uses matched transistors with a thermal voltage V_T = 25mV.
The base currents of the transistors are negligible. The value of the resistance R in kΩ that is required to provide 1 μA bias current for the differential amplifier block shown is ______. 

The figure below shows an uncontrolled diode bridge rectifier supplied form a 220 V, 50 Hz 1-phase ac source. The load draws a constant current I_o = 14A. The conduction angle of the diode D₁ in degrees is___________.

Consider the differential equation 

There exists a unique solution for this differential equation when t belongs to the interval

A separately excited DC generator supplies 150 A to a 145 V DC grid. The generator is running at 800 RPM. The armature resistance of the generator is 0.1 Ω . If the speed of the generator is increased to 1000 RPM, the current in amperes supplied by the generator to the DC grid is

In the circuit shown below, the maximum power transferred to the resistor R is _______ W.

Let a causal LTI system be characterized by the following differential equation, with initial rest condition

Where x(t) and y(t) are the input and output respectively. The impulse response of the system is (u(t) is the unit step function)

The approximate transfer characteristic for the circuit shown below with an ideal operational amplifier and diode will be

The switch in the figure below was closed for a long time. It is opened at t = 0. The current in the inductor of 2 H for t ≥ 0, is

The bus admittance matrix for a power system network is  There is a transmission line, connected between buses 1 and 3, which is represented by the circuit shown in figure.

If this transmission line is removed from service, What is the modified bus admittance matrix?

In the system whose signal flow graph is shown in the figure, U₁(s) and U₂ (s) are inputs. The 
transfer function 

For a system having transfer function    a unit step input is applied at time t=0. 
The value of the response of the system at t=1.5 sec is __________.

The magnitude of magnetic flux density (B) in micro Teslas ( μT ) at the center of a loop of wire wound as a regular hexagon of side length 1m carrying a current (I=1A), and placed in vacuum as shown in the figure is __________. 

The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is 1.5 sinδ , where δ is the rotor angle. The system is operating at the stable equilibrium point with mechanical power equal to 1 pu. If one of the transmission line circuits is removed, the maximum value of δ as the rotor swings, is 1.221 radian. If the expression for electrical power with one transmission line circuit removed is P_max Sinδ , the value of P_max , in pu is 

A 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting): Z_m = (12.50 + j15.75) Ω (main winding), 
 Z_a = (24.50 + j12.75) Ω (auxiliary winding). Neglecting the magnetizing branch the value of the capacitance (in μF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.

A function f(x) is defined   Which one of the following statements is TRUE?

Consider a causal and stable LTI system with rational transfer function H(z). Whose corresponding impulse response begins at n = 0. Furthermore, H(1) = 5/4. The poles of H(z) are   for k = 1,2,3,4. The zeros of H(z) are all at z = 0. Let g[n] = jⁿh[n]. The value of g[8] equals ----.

Only one of the real roots of f ( x ) = x⁶ - x - 1 lies in the interval 1 ≤ x ≤ 2 and bisection method is used to find its value. For achieving an accuracy of 0.001, the required minimum number of iterations is ________.

Two parallel connected, three-phase, 50Hz, 11kV, star-connected synchronous machines A and B, are operating as synchronous condensers. They together supply 50 MVAR to a 11 kV grid. Current supplied by both the machines are equal. Synchronous reactances of machine A and machine B are 1Ω and 3Ω respectively. Assuming the magnetic circuit to be linear, the ratio of excitation current of machine A to that of machine B is ________. 

The positive, negative and zero sequence reactances of a wye-connected synchronous generator are 0.2 pu, 0.2 pu, and 0.1 pu, respectively. The generator is on open circuit with a terminal voltage of 1 pu. The minimum value of the inductive reactance, in  pu, required to be connected between  neutral and ground so that the fault current does not exceed 3.75 pu if a single line to ground fault occurs at the terminals is _______ (assume fault impedance to be zero). 

Let the signal  be passed through an LTI system with frequency 
response H (ω) , as given in the figure below

The Fourier series representation of the output is given as

The logical gate implemented using the circuit shown below where. V₁ and V₂ are inputs (with 0 V as digital 0 and 5 V as digital 1) and V_out is the output is

A load is supplied by a 230 V, 50 Hz source. The active power P and the reactive power Q consumed by the load are such that 1 kW ≤ P ≤ 2kW and 1 kVAR ≤ Q ≤ kVAR . A capacitor connected across the load for power factor correction generates 1 kVAR reactive power. The worst case power factor after power factor correction is

The input voltage V_DC of the buck-boost converter shown below varies from 32 V to 72 V. Assume that all components are ideal, inductor current is continuous, and output voltage is ripple free. The range of duty ratio D of the converter for which the magnitude of the steady state output voltage remains constant at 48 V is

A three-phase, three winding Δ /Δ / Y (1.1kV/6.6kV/400 V) transformer is energized from AC mains at the 1.1 kV side. It supplies 900 kVA load at 0.8 power factor lag from the 6.6 kV winding and 300 kVA load at 0.6 power factor lag from the 400 V winding. The RMS line current in ampere drawn by the 1.1 kV winding from the mains is _______. 

Consider the line integral  where z = x + iy. The line C is shown in the figure below.