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GATE EE 2015 Set 1

All 65 solved GATE EE 2015 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

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 22Medium 38Hard 5

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Didn't you buy ________ when you went shopping?
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    Question

    Which of the following options is the closest in meaning to the sentence below?
    She enjoyed herself immensely at the party.
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    Question

    Which one of the following combinations is incorrect?
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    Question

    Based on the given statements, select the most appropriate option to solve the given question.
    If two floors in a certain building are 9 feet apart, how many steps are there in a set of stairs that extends from the first floor to the second floor of the building?
    Statements:
    (I) Each step is 3/4 foot high.
    (II) Each step is 1 foot wide.
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    Question

    Given Set A = {2,3,4,5}\{2, 3, 4, 5\} and Set B = {11,12,13,14,15}\{11, 12, 13, 14, 15\}, two numbers are randomly selected, one from each set. What is the probability that the sum of the two numbers equals 16?
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    Question

    Select the alternative meaning of the underlined part of the sentence.
    The chain snatchers took to their heels when the police party arrived.
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    Question

    The given statement is followed by some courses of action. Assuming the statement to be true, decide the correct option.
    Statement:
    There has been a significant drop in the water level in the lakes supplying water to the city.
    Course of action:
    (I) The water supply authority should impose a partial cut in supply to tackle the situation.
    (II) The government should appeal to all the residents through mass media for minimal use of water.
    (III) The government should ban the water supply in lower areas.
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    Question

    The pie chart below has the breakup of the number of students from different departments in an engineering college for the year 2012. The proportion of male to female students in each department is 5:4. There are 40 males in Electrical Engineering. What is the difference between the numbers of female students in the Civil department and the female students in the Mechanical department?

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    Question

    The probabilities that a student passes in Mathematics, Physics and Chemistry are mm, pp, and cc respectively. Of these subjects, the student has 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Following relations are drawn in mm, pp, cc:
    (I) p+m+c=27/20p + m + c = 27/20
    (II) p+m+c=13/20p + m + c = 13/20
    (III) (p)×(m)×(c)=1/10(p) \times (m) \times (c) = 1/10
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    Question

    The number of students in a class who have answered correctly, wrongly, or not attempted each question in an exam, are listed in the table below. The marks for each question are also listed. There is no negative or partial marking.
    Q No.MarksAnswered CorrectlyAnswered WronglyNot Attempted
    1221176
    2315272
    3111294
    4223183
    5531121
    What is the average of the marks obtained by the class in the examination?
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Electrical Engineering

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    Question

    A random variable XX has probability density function f(x)f(x) as given below:f(x)={a+bxfor 0<x<10otherwisef(x) = \begin{cases} a + bx & \text{for } 0 < x < 1 \\ 0 & \text{otherwise} \end{cases}If the expected value E[X]=2/3E[X] = 2/3, then Pr[X<0.5]Pr[X < 0.5] is ___________.
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    Question

    If a continuous function f(x)f(x) does not have a root in the interval [a,b][a, b], then which one of the following statements is TRUE?
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    Question

    If the sum of the diagonal elements of a 2×22 \times 2 matrix is −6-6, then the maximum possible value of determinant of the matrix is ________.
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    Question

    Consider a function f⃗=1r2r^\vec{f} = \frac{1}{r^2} \hat{r}, where rr is the distance from the origin and r^\hat{r} is the unit vector in the radial direction. The divergence of this function over a sphere of radius RR, which includes the origin, is
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    Question

    When the Wheatstone bridge shown in the figure is used to find the value of resistor RxR_x, the galvanometer GG indicates zero current when R1=50 ΩR_1 = 50\ \Omega, R2=65 ΩR_2 = 65\ \Omega and R3=100 ΩR_3 = 100\ \Omega. If R3R_3 is known with ±5%\pm 5\% tolerance on its nominal value of 100 Ω100\ \Omega, what is the range of RxR_x in Ohms?

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    Question

    A (0-50 A) moving coil ammeter has a voltage drop of 0.1 V across its terminals at full scale deflection. The external shunt resistance (in milliohms) needed to extend its range to (0 – 500 A) is _________.
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    Question

    Of the four characteristics given below, which are the major requirements for an instrumentation amplifier?
    P. High common mode rejection ratio
    Q. High input impedance
    R. High linearity
    S. High output impedance
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    Question

    In the following chopper, the duty ratio of switch S is 0.4. If the inductor and capacitor are sufficiently large to ensure continuous inductor current and ripple free capacitor voltage, the charging current (in Ampere) of the 5 V battery, under steady-state, is_______.

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    Question

    A moving average function is given by y(t)=1T∫t−Ttu(τ)dτy(t) = \frac{1}{T} \int_{t-T}^{t} u(\tau) d\tau. If the input uu is a sinusoidal signal of frequency 12T\frac{1}{2T} Hz, then in steady state, the output yy will lag uu (in degree) by ______.
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    Question

    The impulse response g(t)g(t) of a system, GG, is as shown in Figure (a). What is the maximum value attained by the impulse response of two cascaded blocks of GG as shown in Figure (b)?
    (a) Impulse response g(t) as a unit pulse from 0 to 1; (b) Two blocks of G in cascade
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    Question

    Consider a one-turn rectangular loop of wire placed in a uniform magnetic field as shown in the figure. The plane of the loop is perpendicular to the field lines. The resistance of the loop is 0.4Ω0.4 \Omega, and its inductance is negligible. The magnetic flux density (in Tesla) is a function of time, and is given by B(t)=0.25sin⁡ωtB(t) = 0.25 \sin \omega t, where ω=2π×50\omega = 2\pi \times 50 radian/second. The power absorbed (in Watt) by the loop from the magnetic field is ______.

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    Question

    A steady current II is flowing in the −x-x direction through each of two infinitely long wires at y=±L2y = \pm \frac{L}{2} as shown in the figure. The permeability of the medium is μ0\mu_0. The B⃗\vec{B}-field at (0,L,0)(0, L, 0) is
    Two infinitely long wires at y = -L/2 and y = L/2 carrying current I into the page (-x direction), with x, y, z axes
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    Question

    Consider the circuit shown in the figure. In this circuit R=1 kΩR = 1\ \text{k}\Omega, and C=1 μFC = 1\ \mu\text{F}. The input voltage is sinusoidal with a frequency of 50 Hz, represented as a phasor with magnitude ViV_i and phase angle 0 radian as shown in the figure. The output voltage is represented as a phasor with magnitude VoV_o and phase angle δ\delta radian. What is the value of the output phase angle δ\delta (in radian) relative to the phase angle of the input voltage?
    Op-amp circuit: input vi through capacitors C to inverting and non-inverting inputs, R from non-inverting input to ground, feedback R, output vo
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    Question

    In the given circuit, the silicon transistor has β=75\beta = 75 and a collector voltage VC=9V_C = 9 V. Then the ratio of RBR_B and RCR_C is ________.
    NPN transistor with RC from 15 V to collector (Vc) and RB from collector to base, emitter grounded
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    Question

    In the 4×14 \times 1 multiplexer, the output FF is given by F=A⊕BF = A \oplus B. Find the required input 'I3I2I1I0I_3 I_2 I_1 I_0'.

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    Question

    Consider a HVDC link which uses thyristor based line-commutated converters as shown in the figure. For a power flow of 750 MW750\ \text{MW} from System 1 to System 2, the voltages at the two ends, and the current, are given by: V1=500 kV,V2=485 kVV_1 = 500\ \text{kV}, V_2 = 485\ \text{kV} and I=1.5 kAI = 1.5\ \text{kA}. If the direction of power flow is to be reversed (that is, from System 2 to System 1) without changing the electrical connections, then which one of the following combinations is feasible?
    HVDC link diagram showing System 1 and System 2 connected via converters and a transmission line with resistance.
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    Question

    Base load power plants are
    P: wind farms.
    Q: run-of-river plants.
    R: nuclear power plants.
    S: diesel power plants.
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    Question

    The voltages developed across the 3 Ω3\ \Omega and 2 Ω2\ \Omega resistors shown in the figure are 6 V6\ V and 2 V2\ V respectively, with the polarity as marked. What is the power (in Watt) delivered by the 5 V5\ V voltage source?

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    Question

    For the given circuit, the Thevenin equivalent is to be determined. The Thevenin voltage, VThV_{Th} (in Volt), seen from terminal AB is ___________

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    Question

    An inductor is connected in parallel with a capacitor as shown in the figure.

    As the frequency of current ii is increased, the impedance (ZZ) of the network varies as
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    Question

    A separately excited DC generator has an armature resistance of 0.1Ω0.1 \Omega and negligible armature inductance. At rated field current and rated rotor speed, its open-circuit voltage is 200V200 V. When this generator is operated at half the rated speed, with half the rated field current, an uncharged 1000μF1000 \mu F capacitor is suddenly connected across the armature terminals. Assume that the speed remains unchanged during the transient. At what time (in microsecond) after the capacitor is connected will the voltage across it reach 25V25 V?
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    Question

    The self inductance of the primary winding of a single phase, 50Hz50 Hz, transformer is 800mH800 mH, and that of the secondary winding is 600mH600 mH. The mutual inductance between these two windings is 480mH480 mH. The secondary winding of this transformer is short circuited and the primary winding is connected to a 50Hz50 Hz, single phase, sinusoidal voltage source. The current flowing in both the windings is less than their respective rated currents. The resistance of both windings can be neglected. In this condition, what is the effective inductance (in mH) seen by the source?
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    Question

    The primary mmf is least affected by the secondary terminal conditions in a
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    Question

    A Bode magnitude plot for the transfer function G(s)G(s) of a plant is shown in the figure. Which one of the following transfer functions best describes the plant?

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    Question

    For the signal-flow graph shown in the figure, which one of the following expressions is equal to the transfer function Y(s)X2(s)∣X1(s)=0\frac{Y(s)}{X_2(s)} \mid_{X_1(s)=0} ?

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    Question

    The maximum value of "aa" such that the matrix (−30−21−100a−2)\begin{pmatrix} -3 & 0 & -2 \\ 1 & -1 & 0 \\ 0 & a & -2 \end{pmatrix} has three linearly independent real eigenvectors is
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    Question

    A solution of the ordinary differential equation d2ydt2+5dydt+6y=0\frac{d^2y}{dt^2} + 5\frac{dy}{dt} + 6y = 0 is such that y(0)=2y(0) = 2 and y(1)=−1−3ee3y(1) = -\frac{1-3e}{e^3}. The value of dydt(0)\frac{dy}{dt}(0) is ________.
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    Question

    The signum function is given bysgn(x)={x∣x∣;x≠00;x=0sgn(x) = \begin{cases} \frac{x}{|x|}; & x \neq 0 \\ 0; & x = 0 \end{cases}The Fourier series expansion of sgn(cos⁡(t))sgn(\cos(t)) has
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    Question

    Two players, A and B, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player A starts the game, the probability that A wins the game is
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    Question

    An unbalanced DC Wheatstone bridge is shown in the figure. At what value of pp will the magnitude of V0V_0 be maximum?

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    Question

    The circuit shown is meant to supply a resistive load RLR_L from two separate DC voltage sources. The switches S1 and S2 are controlled so that only one of them is ON at any instant. S1 is turned on for 0.2 ms0.2\text{ ms} and S2 is turned on for 0.3 ms0.3\text{ ms} in a 0.5 ms0.5\text{ ms} switching cycle time period. Assuming continuous conduction of the inductor current and negligible ripple on the capacitor voltage, the output voltage VoV_o (in Volt) across RLR_L is ________.

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    Question

    A self commutating switch SW, operated at duty cycle δ\delta is used to control the load voltage as shown in the figure
    Boost chopper: Vdc source, inductor L with vL marked, self-commutating switch SW with duty cycle delta, diode D, capacitor C with vC and load R_L
    Under steady state operating conditions, the average voltage across the inductor and the capacitor respectively, are
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    Question

    The single-phase full-bridge voltage source inverter (VSI), shown in figure, has an output frequency of 50 Hz50\text{ Hz}. It uses unipolar pulse width modulation with switching frequency of 50 kHz50\text{ kHz} and modulation index of 0.70.7. For Vin=100 V DCV_{in} = 100\text{ V DC}, L=9.55 mHL = 9.55\text{ mH}, C=63.66 μFC = 63.66\text{ μF}, and R=5 Ω R = 5\text{ Ω }, the amplitude of the fundamental component in the output voltage VoV_o (in Volt) under steady-state is ________.

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    Question

    A 3-phase 50 Hz50\text{ Hz} square wave (6-step) VSI feeds a 3-phase, 4 pole induction motor. The VSI line voltage has a dominant 5th5^{th} harmonic component. If the operating slip of the motor with respect to fundamental component voltage is 0.040.04, the slip of the motor with respect to 5th5^{th} harmonic component of voltage is ________.
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    Question

    Consider a discrete time signal given byx[n]=(−0.25)nu[n]+(0.5)nu[−n−1]x[n] = (-0.25)^n u[n] + (0.5)^n u[-n - 1]The region of convergence of its Z-transform would be
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    Question

    A parallel plate capacitor is partially filled with glass of dielectric constant 4.04.0 as shown below. The dielectric strengths of air and glass are 30 kV/cm30\text{ kV/cm} and 300 kV/cm300\text{ kV/cm}, respectively. The maximum voltage (in kilovolts), which can be applied across the capacitor without any breakdown, is ______.

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    Question

    The figure shows a digital circuit constructed using negative edge triggered J-K flip flops. Assume a starting state of Q2Q1Q0=000Q_2Q_1Q_0=000. This state Q2Q1Q0=000Q_2Q_1Q_0=000 will repeat after ______ number of cycles of the clock CLK.

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    Question

    f(A,B,C,D)=ΠM(0,1,3,4,5,7,9,11,12,13,14,15)f(A, B, C, D) = \Pi M(0,1,3,4,5,7,9,11,12,13,14,15) is a maxterm representation of a Boolean function f(A,B,C,D)f(A, B, C, D) where AA is the MSB and DD is the LSB. The equivalent minimized representation of this function is
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    Question

    The op-amp shown in the figure has a finite gain A=1000A = 1000 and an infinite input resistance. A step-voltage Vi=1 mVV_i = 1\text{ mV} is applied at the input at time t=0t = 0 as shown. Assuming that the operational amplifier is not saturated, the time constant (in millisecond) of the output voltage VoV_o is

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    Question

    An 8-bit, unipolar Successive Approximation Register type ADC is used to convert 3.5 V to digital equivalent output. The reference voltage is +5 V. The output of the ADC, at the end of 3rd clock pulse after the start of conversion, is
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    Question

    Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in Rs/MWh along with the generation limits for the two units are given below:C1(P1)=0.01P12+30P1+10C_1(P_1) = 0.01 P_1^2 + 30 P_1 + 10 ; 100 MW≤P1≤150 MW100\text{ MW} \leq P_1 \leq 150\text{ MW}
    C2(P2)=0.05P22+10P2+10C_2(P_2) = 0.05 P_2^2 + 10 P_2 + 10 ; 100 MW≤P2≤180 MW100\text{ MW} \leq P_2 \leq 180\text{ MW}The incremental cost (in Rs/MWh) of the power plant when it supplies 200 MW is ________.
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    Question

    Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].
    Assertion: Fast decoupled load flow method gives approximate load flow solution because it uses several assumptions.
    Reason: Accuracy depends on the power mismatch vector tolerance.
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    Question

    A 50 Hz50\text{ Hz} generating unit has HH-constant of 2 MJ/MVA2\text{ MJ/MVA}. The machine is initially operating in steady state at synchronous speed, and producing 1 pu1\text{ pu} of real power. The initial value of the rotor angle δ\delta is 5∘5^\circ, when a bolted three phase to ground short circuit fault occurs at the terminal of the generator. Assuming the input mechanical power to remain at 1 pu1\text{ pu}, the value of δ\delta in degrees, 0.020.02 second after the fault is ________.
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    Question

    A sustained three-phase fault occurs in the power system shown in the figure. The current and voltage phasors during the fault (on a common reference), after the natural transients have died down, are also shown. Where is the fault located?
    One-line diagram with two parallel transmission lines between two sources, points P, Q, R, S and currents I1-I4 marked, together with the phasor diagram of V1, V2 and I1-I4 during the fault
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    Question

    The circuit shown in the figure has two sources connected in series. The instantaneous voltage of the AC source (in Volt) is given by v(t)=12sin⁡tv(t) = 12 \sin t. If the circuit is in steady state, then the rms value of the current (in Ampere) flowing in the circuit is ______.

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    Question

    In a linear two-port network, when 10 V10\text{ V} is applied to Port 1, a current of 4 A4\text{ A} flows through Port 2 when it is short-circuited. When 5 V5\text{ V} is applied to Port 1, a current of 1.25 A1.25\text{ A} flows through a 1 Ω1\ \Omega resistance connected across Port 2. When 3 V3\text{ V} is applied to Port 1, the current (in Ampere) through a 2 Ω2\ \Omega resistance connected across Port 2 is ______.
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    In the given circuit, the parameter kk is positive, and the power dissipated in the 2 Ω2\ \Omega resistor is 12.5W12.5\text{W}. The value of kk is ______.

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    Question

    A separately excited DC motor runs at 1000 rpm1000\text{ rpm} on no load when its armature terminals are connected to a 200 V200\text{ V} DC source and the rated voltage is applied to the field winding. The armature resistance of this motor is 1 Ω1\text{ }\Omega. The no-load armature current is negligible. With the motor developing its full load torque, the armature voltage is set so that the rotor speed is 500 rpm500\text{ rpm}. When the load torque is reduced to 50%50\% of the full load value under the same armature voltage conditions, the speed rises to 520 rpm520\text{ rpm}. Neglecting the rotational losses, the full load armature current (in Ampere) is _______.
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    Question

    A DC motor has the following specifications: 10 hp10\text{ hp}, 37.5 A37.5\text{ A}, 230 V230\text{ V}; flux/pole =0.01 Wb= 0.01\text{ Wb}, number of poles =4= 4, number of conductors =666= 666, number of parallel paths =2= 2. Armature resistance =0.267 Ω= 0.267\text{ }\Omega. The armature reaction is negligible and rotational losses are 600 W600\text{ W}. The motor operates from a 230 V230\text{ V} DC supply. If the motor runs at 1000 rpm1000\text{ rpm}, the output torque produced (in Nm) is _______.
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    A 200/400 V200/400\text{ V}, 50 Hz50\text{ Hz}, two-winding transformer is rated at 20 kVA20\text{ kVA}. Its windings are connected as an auto-transformer of rating 200/600 V200/600\text{ V}. A resistive load of 12 Ω12\text{ }\Omega is connected to the high voltage (600 V600\text{ V}) side of the auto-transformer. The value of equivalent load resistance (in Ohm) as seen from low voltage side is _______.
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    Question

    Two single-phase transformers T1T_1 and T2T_2 each rated at 500 kVA500\text{ kVA} are operated in parallel. Percentage impedances of T1T_1 and T2T_2 are (1+j6)(1 + j6) and (0.8+j4.8)(0.8 + j4.8), respectively. To share a load of 1000 kVA1000\text{ kVA} at 0.80.8 lagging power factor, the contribution of T2T_2 (in kVA) is ________.
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    Question

    In the signal flow diagram given in the figure, u1u_1 and u2u_2 are possible inputs whereas y1y_1 and y2y_2 are possible outputs. When would the SISO system derived from this diagram be controllable and observable?

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    The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at (2−j3)(2 - j3). List all the poles and zeroes.
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    Find the transfer function Y(s)X(s)\frac{Y(s)}{X(s)} of the system given below.

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    Question

    The open loop poles of a third order unity feedback system are at 0,−1,−20, -1, -2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be KK. Now suppose we introduce a zero in the open loop transfer function at −3-3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?
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