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GATE EE 2017 Set 1

All 65 solved GATE EE 2017 Set 1 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.

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Questions

65

Paper marks

100

Question formats

2

MCQ · NAT

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Self-paced

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Difficulty mixEasy 15Medium 42Hard 8

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65 of 65 questions

General Aptitude (GA)

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    Question

    After Rajendra Chola returned from his voyage to Indonesia, he ______ to visit the temple in Thanjavur.
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    Question

    Research in the workplace reveals that people work for many reasons ______.
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    Question

    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?
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    Question

    Find the smallest number yy such that y×162y \times 162 is a perfect cube.
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    Question

    The probability that a kk-digit number does NOT contain the digits 0, 5, or 9 is
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    Question

    "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?
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    Question

    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
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    Question

    The expression (x+y)−∣x−y∣2\frac{(x+y)-|x-y|}{2} is equal to
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    Question

    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?
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    Question

    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 25 m intervals in this plot. If in a flood, the water level rises to 525 m, which of the villages P, Q, R, S, T get submerged?
    A contour map showing villages P, Q, R, S, and T with contour lines labeled 425, 450, 500, and 550.
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Electrical Engineering

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    Question

    The matrix A =[320120−1012032]= \begin{bmatrix} \frac{3}{2} & 0 & \frac{1}{2} \\ 0 & -1 & 0 \\ \frac{1}{2} & 0 & \frac{3}{2} \end{bmatrix} has three distinct eigenvalues and one of its eigenvectors is [101]\begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix}. Which one of the following can be another eigenvector of A?
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    For a complex number zz, lim⁡z→iz2+1z3+2z−i(z2+2)\lim_{z \to i} \frac{z^2 + 1}{z^3 + 2z - i(z^2 + 2)} is
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    Question

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

    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
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    Question

    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=0t = 0, the particles are released but are constrained to move along the same straight line. Which of these will collide first?
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    Question

    The transfer function of a system is given by,Vo(s)Vi(s)=1−s1+s\frac{V_o(s)}{V_i(s)} = \frac{1 - s}{1 + s}Let the output of the system be vo(t)=Vmsin⁡(ωt+ϕ)v_o(t) = V_m \sin(\omega t + \phi) for the input, vi(t)=Vmsin⁡(ωt)v_i(t) = V_m \sin(\omega t). Then the minimum and maximum values of ϕ\phi (in radians) are respectively
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    Question

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

    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
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    Question

    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 van=220sin⁡(100πt)v_{an} = 220 \sin(100\pi t) V and ia=10sin⁡(100πt)i_a = 10 \sin(100\pi t) A, respectively. Similarly for phase-b, the instantaneous voltage and current are vbn=220cos⁡(100πt)v_{bn} = 220 \cos(100\pi t) V and ib=10cos⁡(100πt)i_b = 10 \cos(100\pi t) A, respectively.
    The total instantaneous power flowing from the source to the load is

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    Question

    A 3-bus power system is shown in the figure below, where the diagonal elements of YY-bus matrix are: Y11=−j12 pu,Y22=−j15 puY_{11} = -j12 \text{ pu}, Y_{22} = -j15 \text{ pu} and Y33=−j7 puY_{33} = -j7 \text{ pu}.
    A 3-bus power system diagram showing reactances $p, q, r$ between buses 1, 2, and 3.
    The per unit values of the line reactances p,qp, q and rr shown in the figure are
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    Question

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

    The slope and level detector circuit in a CRO has a delay of 100 ns100 \text{ ns}. The start-stop sweep generator has a response time of 50 ns50 \text{ ns}. In order to display correctly, a delay line of
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    Question

    The Boolean expression AB+ACˉ+BCAB + A\bar{C} + BC simplifies to
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    Question

    For the circuit shown in the figure below, assume that diodes D1D_1, D2D_2 and D3D_3 are ideal.
    The DC components of voltages v1v_1 and v2v_2, respectively are

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    Question

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

    Consider g(t)={t−⌊t⌋,t≥0t−⌈t⌉,otherwiseg(t) = \begin{cases} t - \lfloor t \rfloor, & t \geq 0 \\ t - \lceil t \rceil, & \text{otherwise} \end{cases}, where t∈Rt \in \mathbb{R}. Here, ⌊t⌋\lfloor t \rfloor represents the largest integer less than or equal to tt and ⌈t⌉\lceil t \rceil denotes the smallest integer greater than or equal to tt. The coefficient of the second harmonic component of the Fourier series representing g(t)g(t) is ______.

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    Question

    Let I=c∬Rxy2 dxdyI = c \iint_R xy^2 \, dxdy, where RR is the region shown in the figure and c=6×10−4c = 6 \times 10^{-4}. The value of II equals ________. (Give the answer up to two decimal places.)

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    Question

    The power supplied by the 25 V25\text{ V} source in the figure shown below is ________ W\text{W}.

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    The equivalent resistance between the terminals A and B is ______ Ω\Omega.

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    Question

    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 30 Ω\Omega per phase. The load angle is 30∘30^\circ. The power delivered to the motor in kW is ______.
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    Question

    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 ______ .
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    Question

    Consider the unity feedback control system shown. The value of KK that results in a phase margin of the system to be 30∘30^\circ is ______. (Give the answer up to two decimal places.)

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    Question

    The following measurements are obtained on a single phase load: V=220 V±1%V = 220\text{ V} \pm 1\%, I=5.0 A±1%I = 5.0\text{ A} \pm 1\% and W=555 W±2%W = 555\text{ W} \pm 2\%. If the power factor is calculated using these measurements, the worst case error in the calculated power factor in percent is ______. (Give answer up to one decimal place.)
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    Question

    In the converter circuit shown below, the switches are controlled such that the load voltage vo(t)v_o(t) is a 400 Hz400\text{ Hz} square wave.
    H-bridge converter circuit
    The RMS value of the fundamental component of vo(t)v_o(t) in volts is ______.
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    Question

    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 20Ω20 \Omega per phase, the load power for 120∘120^\circ device conduction, in kW, is ________.

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    A function f(x)f(x) is defined as f(x)={ex,x<1ln⁡x+ax2+bx,x≥1f(x) = \begin{cases} e^x, & x < 1 \\ \ln x + ax^2 + bx, & x \geq 1 \end{cases}, where x∈Rx \in \mathbb{R}. Which one of the following statements is TRUE?
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    Consider the differential equation (t2−81)dydt+5ty=sin⁡(t)(t^2 - 81) \frac{dy}{dt} + 5t y = \sin(t) with y(1)=2πy(1) = 2\pi. There exists a unique solution for this differential equation when tt belongs to the interval
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    Question

    Consider the line integral I=∫C(x2+iy2)dzI = \int_C (x^2 + iy^2) dz, where z=x+iyz = x + iy. The line CC is shown in the figure below.
    A graph in the complex plane showing a straight line path C from the origin (0,0) to the point (1, i).

    The value of I is
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    Question

    Two passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port 1.
    Cascade connection of two-port network 1 and two-port network 2 with ports 1, 2, and 3 labeled.
    GivenV1=A1V2+B1I2V_1 = A_1 V_2 + B_1 I_2I1=C1V2+D1I2I_1 = C_1 V_2 + D_1 I_2V2=A2V3+B2I3V_2 = A_2 V_3 + B_2 I_3I2=C2V3+D2I3I_2 = C_2 V_3 + D_2 I_3A1,B1,C1,D1,A2,B2,C2,A_1, B_1, C_1, D_1, A_2, B_2, C_2, and D2D_2 are the generalized circuit constants. If the Thevenin equivalent circuit at port 3 consists of a voltage source VTV_T and an impedance ZTZ_T, connected in series, then
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    Question

    Let a causal LTI system be characterized by the following differential equation, with initial rest conditiond2ydt2+7dydt+10y(t)=4x(t)+5dx(t)dt\frac{d^2y}{dt^2} + 7 \frac{dy}{dt} + 10y(t) = 4x(t) + 5 \frac{dx(t)}{dt}where, x(t)x(t) and y(t)y(t) are the input and output respectively. The impulse response of the system is (u(t)u(t) is the unit step function)
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    Let the signalx(t)=∑k=−∞+∞(−1)kδ(t−k2000)x(t) = \sum_{k=-\infty}^{+\infty} (-1)^k \delta\left(t - \frac{k}{2000}\right)be passed through an LTI system with frequency response H(ω)H(\omega), as given in the figure below
    Frequency response $H(\omega)$
    The Fourier series representation of the output is given as
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    Question

    In the system whose signal flow graph is shown in the figure, U1(s)U_1(s) and U2(s)U_2(s) are inputs. The transfer function Y(s)U1(s)\frac{Y(s)}{U_1(s)} is

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    Question

    The transfer function of the system Y(s)/U(s)Y(s)/U(s) whose state-space equations are given below is:[x˙1(t)x˙2(t)]=[1220][x1(t)x2(t)]+[12]u(t)\begin{bmatrix} \dot{x}_1(t) \\ \dot{x}_2(t) \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ 2 & 0 \end{bmatrix} \begin{bmatrix} x_1(t) \\ x_2(t) \end{bmatrix} + \begin{bmatrix} 1 \\ 2 \end{bmatrix} u(t)y(t)=[10][x1(t)x2(t)]y(t) = \begin{bmatrix} 1 & 0 \end{bmatrix} \begin{bmatrix} x_1(t) \\ x_2(t) \end{bmatrix}
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    Question

    The load shown in the figure is supplied by a 400 V400\text{ V} (line-to-line), 3-phase source (RYB sequence). The load is balanced and inductive, drawing 3464 VA3464\text{ VA}. When the switch S is in position N, the three watt-meters W1W_1, W2W_2 and W3W_3 read 577.35 W577.35\text{ W} each. If the switch is moved to position Y, the readings of the watt-meters in watts will be:

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    Question

    The approximate transfer characteristic for the circuit shown below with an ideal operational amplifier and diode will be
    Op-amp circuit with a diode in the feedback path and a pull-down resistor
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    Question

    The output expression for the Karnaugh map shown below is
    A 4-variable Karnaugh map for variables AB and CD with 1s at cells (01,00), (01,10), (11,00), (11,11), and (11,10).
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    Question

    The logical gate implemented using the circuit shown below where, V1V_1 and V2V_2 are inputs (with 0 V0\text{ V} as digital 00 and 5 V5\text{ V} as digital 11) and VOUTV_{OUT} is the output, is

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    Question

    The input voltage VDCV_{DC} of the buck-boost converter shown below varies from 32 V32\text{ V} to 72 V72\text{ V}. Assume that all components are ideal, inductor current is continuous, and output voltage is ripple free. The range of duty ratio DD of the converter for which the magnitude of the steady-state output voltage remains constant at 48 V48\text{ V} is

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    Question

    A load is supplied by a 230 V230\text{ V}, 50 Hz50\text{ Hz} source. The active power PP and the reactive power QQ consumed by the load are such that 1 kW≤P≤2 kW1\text{ kW} \leq P \leq 2\text{ kW} and 1 kVAR≤Q≤2 kVAR1\text{ kVAR} \leq Q \leq 2\text{ kVAR}. A capacitor connected across the load for power factor correction generates 1 kVAR1\text{ kVAR} reactive power. The worst case power factor after power factor correction is
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    Question

    The bus admittance matrix for a power system network is[Y]=[−j39.9j20j20j20−j39.9j20j20j20−j39.9] pu. [Y] = \begin{bmatrix} -j39.9 & j20 & j20 \\ j20 & -j39.9 & j20 \\ j20 & j20 & -j39.9 \end{bmatrix} \text{ pu. }
    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?
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    Question

    The switch in the figure below was closed for a long time. It is opened at t=0t = 0. The current in the inductor of 2 H2\text{ H} for t≥0t \geq 0, is
    A circuit diagram containing a $50\text{ V}$ DC source, a $6\text{ }\Omega$ resistor, a switch, a bridge of resistors ($8\text{ }\Omega$, $8\text{ }\Omega$, $32\text{ }\Omega$, $32\text{ }\Omega$, $32\text{ }\Omega$), and a $2\text{ H}$ inductor.
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    Only one of the real roots of f(x)=x6−x−1f(x) = x^6 - x - 1 lies in the interval 1≤x≤21 \leq x \leq 2 and bisection method is used to find its value. For achieving an accuracy of 0.001, the required minimum number of iterations is _______.
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    In the circuit shown below, the maximum power transferred to the resistor R is ________ W.

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    The magnitude of magnetic flux density (B) in micro Teslas (μT\mu T), at the center of a loop of wire wound as a regular hexagon of side length 1 m carrying a current (I=1I=1 A), and placed in vacuum as shown in the figure is ________. (Give the answer up to two decimal places.)

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    Question

    A 375 W, 230 V, 50 Hz, capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting): Zm=(12.50+j15.75)ΩZ_m = (12.50 + j15.75) \Omega (main winding), Za=(24.50+j12.75)ΩZ_a = (24.50 + j12.75) \Omega (auxiliary winding). Neglecting the magnetizing branch, the value of the capacitance (in μF\mu F) to be added in series with the auxiliary winding to obtain maximum torque at starting is ________.
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    Two parallel connected, three-phase, 50Hz, 11 kV, 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 1Ω1\Omega and 3Ω3\Omega, respectively. Assuming the magnetic circuit to be linear, the ratio of excitation current of machine A to that of machine B is ________. (Give the answer up to two decimal places.)
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    A 220 V DC series motor runs drawing a current of 30 A from the supply. Armature and field circuit resistances are 0.4Ω0.4\Omega and 0.1Ω0.1\Omega, 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 ________. (Give the answer up to two decimal places.)
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    A three-phase, three winding Δ/Δ/Y\Delta/\Delta/Y (1.1 kV/6.6 kV/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 ________. (Give the answer up to one decimal place.)
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    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 0.1Ω0.1 \Omega. If the speed of the generator is increased to 1000 RPM, the current in amperes supplied by the generator to the DC grid is ________. (Give the answer up to one decimal place.)
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    For a system having transfer function G(s)=−s+1s+1G(s) = \frac{-s + 1}{s + 1}, a unit step input is applied at time t=0t = 0. The value of the response of the system at t=1.5 sect = 1.5\text{ sec} (rounded off to three decimal places) is _______.
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    Consider a causal and stable LTI system with rational transfer function H(z)H(z), whose corresponding impulse response begins at n=0n = 0. Furthermore, H(1)=54H(1) = \frac{5}{4}. The poles of H(z)H(z) are pk=12exp⁡(j(2k−1)π4)p_k = \frac{1}{\sqrt{2}} \exp(j \frac{(2k - 1)\pi}{4}) for k=1,2,3,4k = 1, 2, 3, 4. The zeros of H(z)H(z) are all at z=0z = 0. Let g[n]=jnh[n]g[n] = j^n h[n]. The value of g[8]g[8] equals _______. (Give the answer up to three decimal places.)
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    The circuit shown in the figure uses matched transistors with a thermal voltage VT=25 mVV_T = 25\text{ mV}. The base currents of the transistors are negligible. The value of the resistance RR in kΩk\Omega that is required to provide 1 μA1\text{ }\mu A bias current for the differential amplifier block shown is ______. (Give the answer up to one decimal place.)

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    The figure below shows an uncontrolled diode bridge rectifier supplied from a 220 V220\text{ V}, 50 Hz50\text{ Hz}, 1-phase ac source. The load draws a constant current Io=14 AI_o = 14\text{ A}. The conduction angle of the diode D1D_1 in degrees (rounded off to two decimal places) is ______.

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    The positive, negative, and zero sequence reactances of a wye-connected synchronous generator are 0.2 pu0.2\text{ pu}, 0.2 pu0.2\text{ pu}, and 0.1 pu0.1\text{ pu}, respectively. The generator is on open circuit with a terminal voltage of 1 pu1\text{ 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 pu3.75\text{ pu} if a single line to ground fault occurs at the terminals is ______ (assume fault impedance to be zero). (Give the answer up to one decimal place.)
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    The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is 1.5sin⁡δ1.5 \sin \delta, where δ\delta is the rotor angle. The system is operating at the stable equilibrium point with mechanical power equal to 11 pu. If one of the transmission line circuits is removed, the maximum value of δ\delta, as the rotor swings, is 1.2211.221 radian. If the expression for electrical power with one transmission line circuit removed is Pmaxsin⁡δP_{max} \sin \delta, the value of PmaxP_{max}, in pu is ______. (Give the answer up to three decimal places.)
    Single line diagram of a power system with a generator, transformer, double circuit line, and infinite bus
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