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GATE EE 2017 Set 2

All 65 solved GATE EE 2017 Set 2 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

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 23Medium 36Hard 6

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Choose the option with words that are not synonyms.
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    Question

    Saturn is ________ to be seen on a clear night with the naked eye.
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    Question

    There are five buildings called V, W, X, Y and Z in a row (not necessarily in that order). V is to the West of W. Z is to the East of X and the West of V. W is to the West of Y. Which is the building in the middle?
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    Question

    A test has twenty questions worth 100 marks in total. There are two types of questions. Multiple choice questions are worth 3 marks each and essay questions are worth 11 marks each. How many multiple choice questions does the exam have?
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    Question

    There are 3 red socks, 4 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same colour is
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    Question

    "We lived in a culture that denied any merit to literary works, considering them important only when they were handmaidens to something seemingly more urgent – namely ideology. This was a country where all gestures, even the most private, were interpreted in political terms."
    The author's belief that ideology is not as important as literature is revealed by the word:
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    Question

    There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?
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    Question

    X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number X³ will have
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    Question

    The number of roots of ex+0.5x2−2=0e^x + 0.5x^2 - 2 = 0 in the range [−5,5][-5, 5] is
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    Question

    An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Contour lines are shown at 0.05 bar intervals in this plot.
    If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region, which of the following regions is most likely to have a thunderstorm?

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Electrical Engineering

55
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    Question

    An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is
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    Question

    Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed
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    Question

    The figures show diagrammatic representations of vector fields X⃗\vec{X}, Y⃗\vec{Y}, and Z⃗\vec{Z}, respectively. Which one of the following choices is true?
    Diagrammatic representations of three vector fields X, Y, and Z. Field X is radial, Field Y is circular, and Field Z is a spiral.
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    Question

    The pole-zero plots of three discrete-time systems P, Q and R on the zz-plane are shown below.
    Which one of the following is TRUE about the frequency selectivity of these systems?

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    Question

    If a synchronous motor is running at a leading power factor, its excitation induced voltage (EfE_f) is
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    Question

    When a unit ramp input is applied to the unity feedback system having closed loop transfer function C(s)R(s)=Ks+bs2+as+b,(a>0,b>0,K>0)\frac{C(s)}{R(s)} = \frac{Ks + b}{s^2 + as + b}, (a > 0, b > 0, K > 0), the steady state error will be
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    Question

    The transfer function C(s)C(s) of a compensator is given below.C(s)=(1+s0.1)(1+s100)(1+s)(1+s10)C(s) = \frac{(1 + \frac{s}{0.1})(1 + \frac{s}{100})}{(1 + s)(1 + \frac{s}{10})}The frequency range in which the phase (lead) introduced by the compensator reaches the maximum is
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    Question

    Two resistors with nominal resistance values R1R_1 and R2R_2 have additive uncertainties ΔR1\Delta R_1 and ΔR2\Delta R_2, respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance RR is
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    Question

    A stationary closed Lissajous pattern on an oscilloscope has 3 horizontal tangencies and 2 vertical tangencies for a horizontal input with frequency 3 kHz. The frequency of the vertical input is
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    Question

    For a 3-input logic circuit shown below, the output ZZ can be expressed as

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    Question

    A phase-controlled, single-phase, full-bridge converter is supplying a highly inductive DC load. The converter is fed from a 230 V, 50 Hz, AC source. The fundamental frequency in Hz of the voltage ripple on the DC side is
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    Question

    In the circuit shown, the diodes are ideal, the inductance is small, and I0≠0I_0 \neq 0. Which one of the following statements is true?

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    Question

    A three-phase voltage source inverter with ideal devices operating in 180∘180^\circ conduction mode is feeding a balanced star-connected resistive load. The DC voltage input is VdcV_{dc}. The peak of the fundamental component of the phase voltage is
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    Question

    A 3-phase, 4-pole, 400 V, 50 Hz squirrel-cage induction motor is operating at a slip of 0.02. The speed of the rotor flux in mechanical rad/sec, sensed by a stationary observer, is closest to
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    Question

    The figure shows the per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where α\alpha is a complex number with non-zero real and imaginary parts.
    Per-phase representation of a phase-shifting transformer with impedance Z and ideal transformer with ratio 1:α
    For the given circuit, YbusY_{bus} and ZbusZ_{bus} are bus admittance matrix and bus impedance matrix, respectively, each of size 2×22 \times 2. Which one of the following statements is true?
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    Question

    The figure below shows the circuit diagram of a controlled rectifier supplied from a 230 V,50 Hz230\text{ V}, 50\text{ Hz}, 1-phase voltage source and a 10:110:1 ideal transformer. Assume that all devices are ideal. The firing angles of the thyristors T1T_1 and T2T_2 are 90∘90^\circ and 270∘270^\circ, respectively.

    The RMS value of the current through diode D3D_3 in amperes is _______
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    Question

    Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is _______
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    Question

    Consider a function f(x,y,z)f(x, y, z) given byf(x,y,z)=(x2+y2−2z2)(y2+z2)f(x, y, z) = (x^2 + y^2 - 2z^2)(y^2 + z^2)The partial derivative of this function with respect to xx at the point x=2,y=1x = 2, y = 1 and z=3z = 3 is _______
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    Question

    Let xx and yy be integers satisfying the following equations2x2+y2=342x^2 + y^2 = 34x+2y=11x + 2y = 11The value of (x+y)(x + y) is ______.
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    Question

    Let y2−2y+1=xy^2 - 2y + 1 = x and x+y=5\sqrt{x} + y = 5. The value of x+yx + \sqrt{y} equals ________. (Give the answer up to three decimal places)
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    Question

    For the given 2-port network, the value of transfer impedance z21z_{21} in ohms is ______.

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    Question

    The initial charge in the 1 F1\text{ F} capacitor present in the circuit shown is zero. The energy in joules transferred from the DC source until steady state condition is reached equals ______. (Give the answer up to one decimal place.)

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    Question

    The mean square value of the given periodic waveform f(t)f(t) is ______.
    periodic square waveform graph with values 4 and -2
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    Question

    The nominal-π\pi circuit of a transmission line is shown in the figure.
    nominal-pi circuit diagram with series impedance Z and shunt reactances X
    Impedance Z=100∠80∘ ΩZ = 100\angle 80^\circ\text{ }\Omega and reactance X=3300 ΩX = 3300\text{ }\Omega. The magnitude of the characteristic impedance of the transmission line, in Ω\Omega, is ______. (Give the answer up to one decimal place.)
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    Question

    In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100×100100 \times 100. If there are 20 PV buses in addition to PQ buses and a slack bus, the total number of buses in the system is ________.
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    Question

    Let g(x)={−x,x≤1x+1,x≥1g(x) = \begin{cases} -x, & x \leq 1 \\ x + 1, & x \geq 1 \end{cases} and f(x)={1−x,x≤0x2,x>0f(x) = \begin{cases} 1 - x, & x \leq 0 \\ x^2, & x > 0 \end{cases}. Consider the composition of ff and gg, i.e., (f∘g)(x)=f(g(x))(f \circ g)(x) = f(g(x)). The number of discontinuities in (f∘g)(x)(f \circ g)(x) present in the interval (−∞,0)(-\infty, 0) is:
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    Question

    The value of the contour integral in the complex-plane∮z3−2z+3z−2dz\oint \frac{z^3 - 2z + 3}{z - 2} dzalong the contour ∣z∣=3|z| = 3, taken counter-clockwise is
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    Question

    The eigenvalues of the matrix given below are[0100010−3−4]\begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & -3 & -4 \end{bmatrix}
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    Question

    For the balanced Y-Y connected 3-phase circuit shown in the figure below, the line-line voltage is 208 V rms208\text{ V rms} and the total power absorbed by the load is 432 W432\text{ W} at a power factor of 0.60.6 leading.
    The approximate value of the impedance ZZ is

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    In the circuit shown below, the value of capacitor CC required for maximum power to be transferred to the load is

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    The output y(t)y(t) of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is

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    Question

    A cascade system having the impulse responses h1(n)={1↑,−1}h_1(n) = \{\underset{\uparrow}{1}, -1\} and h2(n)={1↑,1}h_2(n) = \{\underset{\uparrow}{1}, 1\} is shown in the figure below, where symbol ↑\uparrow denotes the time origin.
    Cascade system block diagram showing $x(n) \rightarrow h_1(n) \rightarrow h_2(n) \rightarrow y(n)$
    The input sequence x(n)x(n) for which the cascade system produces an output sequence y(n)={1↑,2,1,−1,−2,−1}y(n) = \{\underset{\uparrow}{1}, 2, 1, -1, -2, -1\} is
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    Question

    A 220 V, 10 kW, 900 rpm separately excited DC motor has an armature resistance Ra=0.02ΩR_a = 0.02 \Omega. When the motor operates at rated speed and with rated terminal voltage, the electromagnetic torque developed by the motor is 70 Nm. Neglecting the rotational losses of the machine, the current drawn by the motor from the 220 V supply is
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    Question

    The root locus of the feedback control system having the characteristic equation s2+6Ks+2s+5=0s^2 + 6Ks + 2s + 5 = 0 where K>0K > 0, enters into the real axis at
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    Question

    The range of KK for which all the roots of the equation s3+3s2+2s+K=0s^3 + 3s^2 + 2s + K = 0 are in the left half of the complex ss-plane is
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    Which of the following systems has maximum peak overshoot due to a unit step input?
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    Question

    For the circuit shown in the figure below, it is given that VCE=VCC2V_{CE} = \frac{V_{CC}}{2}. The transistor has β=29\beta = 29 and VBE=0.7 VV_{BE} = 0.7\text{ V} when the B-E junction is forward biased.
    Transistor circuit diagram
    For this circuit, the value of RBR\frac{R_B}{R} is
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    Question

    For the circuit shown below, assume that the OPAMP is ideal.
    Operational amplifier circuit with feedback and input resistors
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    Question

    The figure below shows a half-bridge voltage source inverter supplying an RL-load with R=40 ΩR = 40\ \Omega and L=(0.3π) HL = \left(\frac{0.3}{\pi}\right)\ H. The desired fundamental frequency of the load voltage is 50 Hz50\ Hz. The switch control signals of the converter are generated using sinusoidal pulse width modulation with modulation index, M=0.6M = 0.6. At 50 Hz50\ Hz, the RL-load draws an active power of 1.44 kW1.44\ kW. The value of DC source voltage VDCV_{DC} in volts is
    Half-bridge voltage source inverter circuit diagram
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    Question

    A person decides to toss a fair coin repeatedly until he gets a head. He will make at most 3 tosses. Let the random variable YY denote the number of heads. The value of var{Y}\text{var}\{Y\}, where var{⋅}\text{var}\{\cdot\} denotes the variance, equals
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    For the network given in figure below, the Thevenin's voltage VabV_{ab} is

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    Question

    A 120 V DC shunt motor takes 2 A at no load. It takes 7 A on full load while running at 1200 rpm. The armature resistance is 0.8 Ω0.8\ \Omega, and the shunt field resistance is 240 Ω240\ \Omega. The no load speed, in rpm, is ________.
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    Question

    A star-connected, 12.5 kW12.5\text{ kW}, 208 V208\text{ V} (line), 3-phase, 60 Hz60\text{ Hz} squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator: R1=0.3ΩR_1=0.3\Omega, R2=0.3ΩR_2=0.3\Omega, X1=0.41ΩX_1=0.41\Omega, X2=0.41ΩX_2=0.41\Omega. Neglect shunt branch in the equivalent circuit. The starting current (in Ampere) for this motor when connected to an 80 V80\text{ V} (line), 20 Hz20\text{ Hz}, 3-phase AC source is ______.
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    Question

    A 25 kVA, 400 V, Δ\Delta-connected, 3-phase, cylindrical rotor synchronous generator requires a field current of 5 A to maintain the rated armature current under short-circuit condition. For the same field current, the open-circuit voltage is 360 V. Neglecting the armature resistance and magnetic saturation, its voltage regulation (in % with respect to terminal voltage), when the generator delivers the rated load at 0.8 pf leading, at rated terminal voltage is ___________.

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    Question

    If the primary line voltage rating is 3.3 kV3.3\text{ kV} (Y side) of a 25 kVA25\text{ kVA}, Y-Δ\Delta transformer (the per phase turns ratio is 5:1), then the line current rating of the secondary side (in Ampere) is ______.
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    Question

    Consider the system described by the following state space representation[x˙1(t)x˙2(t)]=[010−2][x1(t)x2(t)]+[01]u(t)\begin{bmatrix} \dot{x}_1(t) \\ \dot{x}_2(t) \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ 0 & -2 \end{bmatrix} \begin{bmatrix} x_1(t) \\ x_2(t) \end{bmatrix} + \begin{bmatrix} 0 \\ 1 \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}If u(t)u(t) is a unit step input and [x1(0)x2(0)]=[10]\begin{bmatrix} x_1(0) \\ x_2(0) \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \end{bmatrix}, the value of output y(t)y(t) at t=1t = 1 sec (rounded off to three decimal places) is ________.
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    Question

    A 101210 \frac{1}{2} digit timer counter possesses a base clock of frequency 100 MHz100\text{ MHz}. When measuring a particular input, the reading obtained is the same in: (i) Frequency mode of operation with a gating time of one second and (ii) Period mode of operation (in the x 10 ns scale). The frequency of the unknown input (reading obtained) in Hz is ________.
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    In the circuit shown in the figure, the diode used is ideal. The input power factor is __________. (Give the answer up to two decimal places.)

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    Question

    For the synchronous sequential circuit shown below, the output ZZ is zero for the initial conditions QAQBQC=QA′QB′QC′=100Q_A Q_B Q_C = Q'_A Q'_B Q'_C = 100.
    Synchronous sequential circuit consisting of two 3-bit shift registers with feedback and logic gates
    The minimum number of clock cycles after which the output ZZ would again become zero is ___________
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    Question

    In the circuit shown all elements are ideal and the switch SS is operated at 10 kHz10\text{ kHz} and 60%60\% duty ratio. The capacitor is large enough so that the ripple across it is negligible and at steady state acquires a voltage as shown. The peak current in amperes drawn from the 50 V50\text{ V} DC source is __________. (Give the answer up to one decimal place.)

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    Consider an overhead transmission line with 3-phase, 50 Hz50\text{ Hz} balanced system with conductors located at the vertices of an equilateral triangle of length Dab=Dbc=Dca=1mD_{ab} = D_{bc} = D_{ca} = 1\text{m} as shown in figure below. The resistances of the conductors are neglected. The geometric mean radius (GMR) of each conductor is 0.01 m0.01\text{ m}. Neglecting the effect of ground, the magnitude of positive sequence reactance in Ω/km\Omega/\text{km} (rounded off to three decimal places) is __________.

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    A 3-phase, 50 Hz generator supplies power of 3MW at 17.32 kV to a balanced 3-phase inductive load through an overhead line. The per phase line resistance and reactance are 0.25Ω0.25 \Omega and 3.925Ω3.925 \Omega respectively. If the voltage at the generator terminal is 17.87 kV, the power factor of the load is _______.
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    Two generating units rated 300 MW and 400 MW have governor speed regulation of 6% and 4% respectively from no load to full load. Both the generating units are operating in parallel to share a load of 600 MW. Assuming free governor action, the load shared by the larger unit is _______ MW.
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    A 3-phase, 2-pole, 50 Hz, synchronous generator has a rating of 250 MVA, 0.8 pf lagging. The kinetic energy of the machine at synchronous speed is 1000 MJ. The machine is running steadily at synchronous speed and delivering 60 MW power at a power angle of 10 electrical degrees. If the load is suddenly removed, assuming the acceleration is constant for 10 cycles, the value of the power angle after 5 cycles is _______ electrical degrees.
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    A thin soap bubble of radius R=1 cmR = 1\text{ cm}, and thickness a=3.3 μma = 3.3\text{ }\mu\text{m} (a≪Ra \ll R), is at a potential of 1 V1\text{ V} with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop of soap (assuming all the soap is contained in the drop) of radius rr. The volume of the soap in the thin bubble is 4πR2a4\pi R^2 a and that of the drop is 43πr3\frac{4}{3}\pi r^3. The potential in volts, of the resulting single spherical drop with respect to the same reference point at infinity is ________. (Give the answer up to two decimal places.)

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