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GATE EE 2023 Set 1

All 65 solved GATE EE 2023 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

3

MCQ · NAT · MSQ

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 12Medium 37Hard 16

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Rafi told Mary, “I am thinking of watching a film this weekend.”
    The following reports the above statement in indirect speech:
    Rafi told Mary that he _______ of watching a film that weekend.
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    Question

    Permit : _______ : : Enforce : Relax
    (By word meaning)
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    Question

    Given a fair six-faced dice where the faces are labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and ‘6’, what is the probability of getting a ‘1’ on the first roll of the dice and a ‘4’ on the second roll?
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    Question

    A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco.
    Based only on the information in the above passage, which one of the following options can be logically inferred with certainty?
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    Question

    How many triangles are present in the given figure?
    A geometric figure composed of multiple triangles within a larger parallelogram-like shape.
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    Question

    Students of all the departments of a college who have successfully completed the registration process are eligible to vote in the upcoming college elections. However, by the time the due date for registration was over, it was found that suprisingly none of the students from the Department of Human Sciences had completed the registration process.
    Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?
    (i) All those students who would not be eligible to vote in the college elections would certainly belong to the Department of Human Sciences.
    (ii) None of the students from departments other than Human Sciences failed to complete the registration process within the due time.
    (iii) All the eligible voters would certainly be students who are not from the Department of Human Sciences.
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    Question

    Which one of the following options represents the given graph?
    Graph of a function f(x) showing odd symmetry, passing through the origin, and decaying to zero as x approaches positive or negative infinity.
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    Question

    Which one of the options does NOT describe the passage below or follow from it?
    We tend to think of cancer as a ‘modern’ illness because its metaphors are so modern. It is a disease of overproduction, of sudden growth, a growth that is unstoppable, tipped into the abyss of no control. Modern cell biology encourages us to imagine the cell as a molecular machine. Cancer is that machine unable to quench its intial command (to grow) and thus transform into an indestructible, self-propelled automaton.
    [Adapted from The Emperor of All Maladies by Siddhartha Mukherjee]
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    Question

    The digit in the unit’s place of the product 3999×710003^{999} \times 7^{1000} is _______.
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    Question

    A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown.
    The area of the shaded region is _______ cm2cm^2.

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Electrical Engineering

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    Question

    For a given vector w=[1 2 3]T\mathbf{w} = [1 \ 2 \ 3]^T, the vector normal to the plane defined by wTx=1\mathbf{w}^T\mathbf{x} = 1 is
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    Question

    For the block diagram shown in the figure, the transfer function Y(s)R(s)\frac{Y(s)}{R(s)} is

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    Question

    In the Nyquist plot of the open-loop transfer function G(s)H(s)=3s+5s−1G(s)H(s) = \frac{3s + 5}{s - 1} corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at

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    Question

    Consider a unity-gain negative feedback system consisting of the plant G(s)G(s) (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 and 1, respectively. For a unit step reference input, the final values of the controller output and the plant output, respectively, areG(s)=1s−1G(s) = \frac{1}{s - 1}
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    Question

    The following columns present various modes of induction machine operation and the ranges of slip
    A (Mode of operation)B (Range of Slip)
    a. Running in generator modep) From 0.0 to 1.0
    b. Running in motor modeq) From 1.0 to 2.0
    c. Plugging in motor moder) From -1.0 to 0.0
    The correct matching between the elements in column A with those of column B is
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    Question

    A 10-pole, 50 Hz, 240 V, single phase induction motor runs at 540 RPM while driving rated load. The frequency of induced rotor currents due to backward field is
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    Question

    A continuous-time system that is initially at rest is described bydy(t)dt+3y(t)=2x(t),\frac{dy(t)}{dt} + 3y(t) = 2x(t),where x(t)x(t) is the input voltage and y(t)y(t) is the output voltage. The impulse response of the system is
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    Question

    The Fourier transform X(ω)X(\omega) of the signal x(t)x(t) is given byX(ω)=1, for ∣ω∣<WoX(\omega) = 1, \text{ for } |\omega| < W_o=0, for ∣ω∣>W0= 0, \text{ for } |\omega| > W_0Which one of the following statements is true?
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    Question

    The ZZ-transform of a discrete signal x[n]x[n] isX(z)=4z(z−15)(z−23)(z−3)with ROC=R.X(z) = \frac{4z}{\left(z-\frac{1}{5}\right)\left(z-\frac{2}{3}\right)(z-3)} \quad \text{with } ROC = R.Which one of the following statements is true?
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    Question

    For the three-bus power system shown in the figure, the trip signals to the circuit breakers B1B_1 to B9B_9 are provided by overcurrent relays R1R_1 to R9R_9, respectively, some of which have directional properties also. The necessary condition for the system to be protected for short circuit fault at any part of the system between bus 1 and the R-L loads with isolation of minimum portion of the network using minimum number of directional relays is
    Single-line diagram of three buses. A generator connects to Bus 1 through breaker B9. Line 1 joins Bus 1 and Bus 2 with breakers B1 at Bus 1 and B3 at Bus 2; Line 2, parallel to it, has breakers B2 at Bus 1 and B4 at Bus 2. Line 3 joins Bus 2 and Bus 3 with breakers B5 at Bus 2 and B7 at Bus 3. An R-L load is connected at Bus 2 through B6 and another at Bus 3 through B8.
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    Question

    The expressions of fuel cost of two thermal generating units as a function of the respective power generation PG1P_{G1} and PG2P_{G2} are given as
    F1(PG1)=0.1aPG12+40PG1+120F_1(P_{G1}) = 0.1aP_{G1}^2 + 40 P_{G1} + 120 Rs/hour
    F2(PG2)=0.2PG22+30PG2+100F_2(P_{G2}) = 0.2P_{G2}^2 + 30 P_{G2} + 100 Rs/hour
    0 MW≤PG1≤350 MW0 \text{ MW} \leq P_{G1} \leq 350 \text{ MW}
    0 MW≤PG2≤300 MW0 \text{ MW} \leq P_{G2} \leq 300 \text{ MW}
    where aa is a constant. For a given value of aa, optimal dispatch requires the total load of 290 MW to be shared as PG1=175 MWP_{G1} = 175 \text{ MW} and PG2=115 MWP_{G2} = 115 \text{ MW}. With the load remaining unchanged, the value of aa is increased by 10% and optimal dispatch is carried out. The changes in PG1P_{G1} and the total cost of generation, F(=F1+F2)F (= F_1 + F_2) in Rs/hour will be as follows
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    Question

    The four stator conductors (AA, A′A', BB and B′B') of a rotating machine are carrying DC currents of the same value, the directions of which are shown in the figure (i). The rotor coils a−a′a-a' and b−b′b-b' are formed by connecting the back ends of conductors ‘aa’ and ‘a′a'’ and ‘bb’ and ‘b′b'’, respectively, as shown in figure (ii). The e.m.f. induced in coil a−a′a-a' and coil b−b′b-b' are denoted by Ea−a′E_{a-a'} and Eb−b′E_{b-b'}, respectively. If the rotor is rotated at uniform angular speed ω\omega rad/s in the clockwise direction then which of the following correctly describes the Ea−a′E_{a-a'} and Eb−b′E_{b-b'}?
    Figure i, cross-sectional view: stator conductors A at top and B at bottom carry current into the page, cross symbol; A prime at right and B prime at left carry current out of the page, dot symbol. Rotor conductors sit inside: a at top, a prime at bottom, b at right, b prime at left. A curved arrow labeled omega shows clockwise rotation. Figure ii, rotor winding connection diagram: two separate coils, one formed by conductors a and a prime and one by b and b prime, each with its back ends joined and two open terminals.
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    Question

    The chopper circuit shown in figure (i) feeds power to a 5 A5\text{ A} DC constant current source. The switching frequency of the chopper is 100 kHz100\text{ kHz}. All the components can be assumed to be ideal. The gate signals of switches S1S_1 and S2S_2 are shown in figure (ii). Average voltage across the 5 A5\text{ A} current source is
    Figure i: 20 V DC source, positive at top, across two series switches; upper switch S1 with antiparallel diode D1, lower switch S2 with antiparallel diode D2, diode cathodes toward the positive rail. A 5 A current source, arrow pointing down, is connected from the midpoint of S1 and S2 to the bottom rail. Figure ii: gate signal of S1 versus time in microseconds is High from 0 to 3, Low from 3 to 10, High again from 10 to about 13; gate signal of S2 is Low from 0 to 5, High from 5 to 8, Low from 8 to about 13, High again from about 13 to 18. Time axis marks 0, 3, 5, 8, 10.
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    Question

    In the figure, the vectors u\mathbf{u} and v\mathbf{v} are related as: Au=v\mathbf{Au} = \mathbf{v} by a transformation matrix A\mathbf{A}. The correct choice of A\mathbf{A} is
    Two vectors drawn from the origin 0, 0 in the x-y plane: vector u ends at the point 4, 3 and vector v ends at the point 5, 0 on the horizontal axis.
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    Question

    One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation σo\sigma_o. The σo\sigma_o is estimated by randomly drawing out 10,000 numbers of samples (xnx_n). The estimates σ^1,σ^2\hat{\sigma}_1, \hat{\sigma}_2 are computed in the following two ways.σ^12=110000∑n=110000xn2σ^22=19999∑n=110000xn2\hat{\sigma}_1^2 = \frac{1}{10000} \sum_{n=1}^{10000} x_n^2 \quad \hat{\sigma}_2^2 = \frac{1}{9999} \sum_{n=1}^{10000} x_n^2Which of the following statements is true?
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    Question

    A semiconductor switch needs to block voltage VV of only one polarity (V>0V > 0) during OFF state as shown in figure (i) and carry current in both directions during ON state as shown in figure (ii). Which of the following switch combination(s) will realize the same?
    Switch requirements showing unipolar voltage blocking and bidirectional current conduction
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    Question

    Which of the following statement(s) is/are true?
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    Question

    The bus admittance (YbusY_{bus}) matrix of a 3-bus power system is given below.
    123
    1−j15-j15j10j10j5j5
    2j10j10−j13.5-j13.5j4j4
    3j5j5j4j4−j8-j8
    Considering that there is no shunt inductor connected to any of the buses, which of the following can NOT be true?
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    Question

    The value of parameters of the circuit shown in the figure are
    R1=2Ω,R2=2Ω,R3=3Ω,L=10 mH,C=100μFR_1 = 2 \Omega, R_2 = 2 \Omega, R_3 = 3 \Omega, L = 10 \text{ mH}, C = 100 \mu\text{F}
    For time t<0t < 0, the circuit is at steady state with the switch ‘K’ in closed condition. If the switch is opened at t=0t = 0, the value of the voltage across the inductor (VLV_L) at t=0+t = 0^+ in Volts is ____________ (Round off to 1 decimal place).

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    Question

    A separately excited DC motor rated 400 V, 15 A, 1500 RPM drives a constant torque load at rated speed operating from 400 V DC supply drawing rated current. The armature resistance is 1.2Ω1.2 \Omega. If the supply voltage drops by 10% with field current unaltered then the resultant speed of the motor in RPM is ____________ (Round off to the nearest integer).
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    Question

    For the signals x(t)x(t) and y(t)y(t) shown in the figure, z(t)=x(t)∗y(t)z(t) = x(t) * y(t) is maximum at t=T1t = T_1. Then T1T_1 in seconds is ___________ (Round off to the nearest integer).

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    Question

    For the circuit shown in the figure, V1=8 V, DCV_1 = 8\text{ V, DC} and I1=8 A, DCI_1 = 8\text{ A, DC}. The voltage VabV_{ab} in Volts is _________ (Round off to 1 decimal place).

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    Question

    A 50 Hz, 275 kV line of length 400 km has the following parameters:
    Resistance, R=0.035 Ω/kmR = 0.035\ \Omega/\text{km};
    Inductance, L=1 mH/kmL = 1\ \text{mH}/\text{km};
    Capacitance, C=0.01 μF/kmC = 0.01\ \mu\text{F}/\text{km};
    The line is represented by the nominal-π\pi model. With the magnitudes of the sending end and the receiving end voltages of the line (denoted by VSV_S and VRV_R, respectively) maintained at 275 kV, the phase angle difference (θ\theta) between VSV_S and VRV_R required for maximum possible active power to be delivered to the receiving end, in degree is _____________ (Round off to 2 decimal places).
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    Question

    In the following differential equation, the numerically obtained value of y(t)y(t), at t=1t = 1, is _______________ (Round off to 2 decimal places).dydt=e−αt2+αt,α=0.01 and y(0)=0\frac{dy}{dt} = \frac{e^{-\alpha t}}{2 + \alpha t}, \alpha = 0.01 \text{ and } y(0) = 0
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    Question

    Three points in the xx-yy plane are (−1,0.8)(-1, 0.8), (0,2.2)(0, 2.2) and (1,2.8)(1, 2.8). The value of the slope of the best fit straight line in the least square sense is ____________ (Round off to 2 decimal places).
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    Question

    The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is
    Magnitude plot constant at 8 dB and phase plot falling linearly to -60 degrees at log10(omega)=0
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    Question

    Consider the OP AMP based circuit shown in the figure. Ignore the conduction drops of diodes D1D_1 and D2D_2. All the components are ideal and the breakdown voltage of the Zener is 5 V. Which of the following statements is true?
    Inverting op-amp circuit: source Vin = 10sin 1000t V, plus terminal up, drives the inverting input through a 1 kilo-ohm resistor; non-inverting input grounded; op-amp supplies +15 V and -15 V; output VO measured to ground. Two parallel feedback branches between the inverting input and the output: top branch is a 1 kilo-ohm resistor in series with diode D1, D1 anode toward the inverting input and cathode toward the output; lower branch is Zener DZ with anode at the inverting input, in series with diode D2 whose anode is at the output, so DZ and D2 are joined cathode to cathode.
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    Question

    Consider a lead compensator of the formK(s)=1+sa1+sβa,β>1,a>0K(s) = \frac{1 + \frac{s}{a}}{1 + \frac{s}{\beta a}}, \beta > 1, a > 0The frequency at which this compensator produces maximum phase lead is 4 rad/s. At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of K(s)K(s), is 6 dB. The values of a,βa, \beta, respectively, are
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    Question

    A 3-phase, star-connected, balanced load is supplied from a 3-phase, 400400 V (rms), balanced voltage source with phase sequence R-Y-B, as shown in the figure. If the wattmeter reading is −400-400 W and the line current is IR=2I_R = 2 A (rms), then the power factor of the load per phase is
    A 3 phase 400 V balanced source feeds a 3 phase star connected balanced load through lines R, Y and B. A wattmeter has its current coil, terminals M and L, in series with line R carrying current IR from source to load. Its pressure coil terminal C, marked plus, is connected to line Y and terminal V, marked minus, is connected to line B.
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    Question

    An 8 bit ADC converts analog voltage in the range of 0 to +5 V+5\text{ V} to the corresponding digital code as per the conversion characteristics shown in figure. For Vin=1.9922 VV_{in} = 1.9922\text{ V}, which of the following digital output, given in hex, is true?

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    Question

    The three-bus power system shown in the figure has one alternator connected to bus 2 which supplies 200 MW200\text{ MW} and 40 MVAr40\text{ MVAr} power. Bus 3 is infinite bus having a voltage of magnitude ∣V3∣=1.0 p.u.|V_3| = 1.0\text{ p.u.} and angle of −15∘-15^\circ. A variable current source, ∣I∣∠ϕ|I|\angle\phi is connected at bus 1 and controlled such that the magnitude of the bus 1 voltage is maintained at 1.05 p.u.1.05\text{ p.u.} and the phase angle of the source current, ϕ=θ1±π2\phi = \theta_1 \pm \frac{\pi}{2}, where θ1\theta_1 is the phase angle of the bus 1 voltage. The three buses can be categorized for load flow analysis as

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    Question

    Consider the following equation in a 2-D real-space.
    ∣x1∣p+∣x2∣p=1|x_1|^p + |x_2|^p = 1 for p>0p > 0
    Which of the following statement(s) is/are true.
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    Question

    In the figure, the electric field E and the magnetic field B point to x and z directions, respectively, and have constant magnitudes. A positive charge ‘q’ is released from rest at the origin. Which of the following statement(s) is/are true.
    3-D axes with charge q at the origin, electric field E along z and magnetic field B along x
    1. A.
      The charge will move in the direction of z with constant velocity.
    2. B.
      The charge will always move on the y-z plane only.
    3. C.
      The trajectory of the charge will be a circle.
    4. D.
      The charge will progress in the direction of y.

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    Question

    All the elements in the circuit shown in the following figure are ideal. Which of the following statements is/are true?

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    Question

    The expected number of trials for first occurrence of a “head” in a biased coin is known to be 4. The probability of first occurrence of a “head” in the second trial is __________ (Round off to 3 decimal places).
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    Question

    Consider the state-space description of an LTI system with matricesA=[01−1−2],B=[01],C=[3−2],D=1A = \begin{bmatrix} 0 & 1 \\ -1 & -2 \end{bmatrix}, B = \begin{bmatrix} 0 \\ 1 \end{bmatrix}, C = \begin{bmatrix} 3 & -2 \end{bmatrix}, D = 1For the input, sin⁡(ωt)\sin(\omega t), ω>0\omega > 0, the value of ω\omega for which the steady-state output of the system will be zero, is ___________ (Round off to the nearest integer).
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    Question

    A three-phase synchronous motor with synchronous impedance of 0.1+j0.30.1+j0.3 per unit per phase has a static stability limit of 2.52.5 per unit. The corresponding excitation voltage in per unit is ___________ (Round off to 2 decimal places).
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    A three phase 415 V415\text{ V}, 50 Hz50\text{ Hz}, 66-pole, 960 RPM960\text{ RPM}, 4 HP4\text{ HP} squirrel cage induction motor drives a constant torque load at rated speed operating from rated supply and delivering rated output. If the supply voltage and frequency are reduced by 20%20\%, the resultant speed of the motor in RPM (neglecting the stator leakage impedance and rotational losses) is __________ (Round off to the nearest integer).
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    Question

    The period of the discrete-time signal x[n]x[n] described by the equation below is N=‾N = \underline{\qquad\quad} (Round off to the nearest integer).
    x[n]=1+3sin⁡(15π8n+3π4)−5sin⁡(π3n−π4)x[n] = 1 + 3\sin(\frac{15\pi}{8}n + \frac{3\pi}{4}) - 5\sin(\frac{\pi}{3}n - \frac{\pi}{4})
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    The discrete-time Fourier transform of a signal x[n]x[n] is X(Ω)=(1+cos⁡Ω)e−jΩX(\Omega) = (1 + \cos\Omega)e^{-j\Omega}. Consider that xp[n]x_p[n] is a periodic signal of period N=5N = 5 such that
    xp[n]=x[n], for n=0,1,2x_p[n] = x[n], \text{ for } n = 0, 1, 2
    =0, for n=3,4= 0, \text{ for } n = 3, 4
    Note that xp[n]=∑k=0N−1akej2πNknx_p[n] = \sum_{k=0}^{N-1} a_k e^{j\frac{2\pi}{N}kn}. The magnitude of the Fourier series coefficient a3a_3 is __________ (Round off to 3 decimal places).
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    Question

    For the circuit shown, if i=sin⁡1000ti = \sin 1000t, the instantaneous value of the Thevenin's equivalent voltage (in Volts) across the terminals a-b at time t=5 mst = 5\text{ ms} is __________ (Round off to 2 decimal places).
    Circuit with terminals a and b. From a, a branch of 10 ohm in series with -j10 ohm capacitor goes down to b, with current i_x flowing downward through it. The top line from a continues through a dependent voltage source 4 i_x, plus on the left toward a and minus on the right, to a right node. From the right node, a branch of 10 ohm in series with j10 ohm inductor goes down to b, and an independent current source i = sin1000t, arrow pointing up, connects b to the right node.
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    Question

    The admittance parameters of the passive resistive two-port network shown in the figure are y11=5 S,y22=1 S,y12=y21=−2.5 Sy_{11} = 5\text{ S}, y_{22} = 1\text{ S}, y_{12} = y_{21} = -2.5\text{ S}. The power delivered to the load resistor RLR_L in Watt is __________ (Round off to 2 decimal places).

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    Question

    When the winding c-d of the single-phase, 50 Hz, two winding transformer is supplied from an AC current source of frequency 50 Hz, the rated voltage of 200 V (rms), 50 Hz is obtained at the open-circuited terminals a-b. The cross sectional area of the core is 5000 mm2^2 and the average core length traversed by the mutual flux is 500 mm. The maximum allowable flux density in the core is Bmax=1 Wb/m2B_{max} = 1\text{ Wb/m}^2 and the relative permeability of the core material is 5000. The leakage impedance of the winding a-b and winding c-d at 50 Hz are (5+j100π×0.16) Ω(5 + j100\pi \times 0.16)\ \Omega and (11.25+j100π×0.36) Ω(11.25 + j100\pi \times 0.36)\ \Omega, respectively. Considering the magnetizing characteristics to be linear and neglecting core loss, the self-inductance of the winding a-b in millihenry is ___________ (Round off to 1 decimal place).
    Diagram of a single-phase transformer core with two windings. Winding a-b is on the left limb and winding c-d is on the right limb. Winding c-d is connected to a 50 Hz AC current source. Winding a-b is open-circuited with a measured voltage $V_{ab} = 200\text{ V}$.
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    Question

    The circuit shown in the figure is initially in the steady state with the switch KK in open condition and Kˉ\bar{K} in closed condition. The switch KK is closed and Kˉ\bar{K} is opened simultaneously at the instant t=t1t = t_1, where t1>0t_1 > 0. The minimum value of t1t_1 in milliseconds, such that there is no transient in the voltage across the 100μF100 \mu F capacitor, is ____________ (Round off to 2 decimal places).

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    Question

    The circuit shown in the figure has reached steady state with thyristor ‘T’ in OFF condition. Assume that the latching and holding currents of the thyristor are zero. The thyristor is turned ON at t=0t = 0 sec. The duration in microseconds for which the thyristor would conduct, before it turns off, is _____ (Round off to 2 decimal places).

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    Neglecting the delays due to the logic gates in the circuit shown in figure, the decimal equivalent of the binary sequence [ABCD] of initial logic states, which will not change with clock, is ____________.
    Logic circuit. Input point A drives both inputs of a NOR gate; the NOR output is point B. An X-OR gate takes inputs B and C, and its output is point D. Two D flip-flops share a common CLK. Point D feeds the D input of the right flip-flop. The Q output of the right flip-flop is point C, and it also feeds the D input of the left flip-flop. The Q bar output of the left flip-flop is connected back to point A.
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    Question

    In a given 8-bit general purpose micro-controller there are following flags.
    C-Carry, A-Auxiliary Carry, O-Overflow flag, P-Parity (0 for even, 1 for odd)
    R0 and R1 are the two general purpose registers of the micro-controller.
    After execution of the following instructions, the decimal equivalent of the binary sequence of the flag pattern [CAOP] will be __________.
    MOV R0, +0x60 
MOV R1, +0x46
ADD R0, R1
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    The single phase rectifier consisting of three thyristors T1T_1, T2T_2, T3T_3 and a diode D1D_1 feed power to a 10 A constant current load. T1T_1 and T3T_3 are fired at α=60∘\alpha = 60^\circ and T2T_2 is fired at α=240∘\alpha = 240^\circ. The reference for α\alpha is the positive zero crossing of VinV_{in}. The average voltage VOV_O across the load in volts is _______ (Round off to 2 decimal places).
    Single-phase bridge with two vertical legs between a top rail and a bottom rail. Left leg: thyristor T1 on top, thyristor T2 below. Right leg: diode D1 on top, thyristor T3 below. All four devices conduct upward, anodes toward the bottom rail and cathodes toward the top rail. AC source Vin = 100 sin of 100 pi t V, + terminal at top, connects to the T1-T2 midpoint; its other terminal connects to the D1-T3 midpoint. A 10 A current source load between the rails, arrow pointing down, output Vo with + at the top rail.
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    The Zener diode in circuit has a breakdown voltage of 5 V. The current gain β\beta of the transistor in the active region in 99. Ignore base-emitter voltage drop VBEV_{BE}. The current through the 20 Ω20\ \Omega resistance in milliamperes is ________(Round off to 2 decimal places).
    Transistor circuit with Zener diode and resistors
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    The two-bus power system shown in figure (i) has one alternator supplying a synchronous motor load through a Y-Δ\Delta transformer. The positive, negative and zero-sequence diagrams of the system are shown in figures (ii), (iii) and (iv), respectively. All reactances in the sequence diagrams are in p.u. For a bolted line-to-line fault (fault impedance = zero) between phases ‘b’ and ‘c’ at bus 1, neglecting all pre-fault currents, the magnitude of the fault current (from phase ‘b’ to ‘c’) in p.u. is _____________ (Round off to 2 decimal places).

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    An infinite surface of linear current density K=5a^x\mathbf{K} = 5\hat{\mathbf{a}}_x A/m exists on the x-y plane, as shown in the figure. The magnitude of the magnetic field intensity (H\mathbf{H}) at a point (1,1,1) due to the surface current in Ampere/meter is _______ (Round off to 2 decimal places).

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    The closed curve shown in the figure is described byr=1+cos⁡θr = 1 + \cos\theta, where r=x2+y2r = \sqrt{x^2 + y^2}; x=rcos⁡θ,y=rsin⁡θx = r\cos\theta, y = r\sin\thetaThe magnitude of the line integral of the vector field F=−yi^+xj^F = -y\hat{i} + x\hat{j} around the closed curve is ____________ (Round off to 2 decimal places).
    A plot of the cardioid curve $r = 1 + \cos\theta$ in the $x$-$y$ plane
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    A signal x(t)=2cos⁡(180πt)cos⁡(60πt)x(t) = 2\cos(180\pi t)\cos(60\pi t) is sampled at 200 Hz and then passed through an ideal low pass filter having cut-off frequency of 100 Hz. The maximum frequency present in the filtered signal in Hz is _____________ (Round off to the nearest integer).
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    A balanced delta connected load consisting of the series connection of one resistor (R=15 ΩR = 15\ \Omega) and a capacitor (C=212.21 μFC = 212.21\ \mu\text{F}) in each phase is connected to three-phase, 50 Hz, 415 V supply terminals through a line having an inductance of L=31.83 mHL = 31.83\ \text{mH} per phase, as shown in the figure. Considering the change in the supply terminal voltage with loading to be negligible, the magnitude of the voltage across the terminals VABV_{AB} in Volts is _____________ (Round off to the nearest integer).
    Three-phase 415 V 50 Hz supply feeding, through line inductors L, a delta connected load of R and C per phase, with terminals A, B, C and the parameter values
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    A quadratic function of two variables is given asf(x1,x2)=x12+2x22+3x1+3x2+x1x2+1f(x_1, x_2) = x_1^2 + 2x_2^2 + 3x_1 + 3x_2 + x_1x_2 + 1The magnitude of the maximum rate of change of the function at the point (1,1) is _________ (Round off to the nearest integer).
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