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GATE EE 2014 Set 1

All 65 solved GATE EE 2014 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 39Hard 4

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Which of the following options is the closest in meaning to the phrase underlined in the sentence below?
    It is fascinating to see life forms cope with varied environmental conditions.
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    Question

    Choose the most appropriate word from the options given below to complete the following sentence.
    He could not understand the judges awarding her the first prize, because he thought that her performance was quite __________.
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    Question

    In a press meet on the recent scam, the minister said, "The buck stops here". What did the minister convey by the statement?
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    Question

    If (z+1/z)2=98(z + 1/z)^2 = 98, compute (z2+1/z2)(z^2 + 1/z^2).
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    Question

    The roots of ax2+bx+c=0ax^2 + bx + c = 0 are real and positive. a,ba, b and cc are real. Then ax2+b∣x∣+c=0ax^2 + b|x| + c = 0 has
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    Question

    The Palghat Gap (or Palakkad Gap), a region about 30 km wide in the southern part of the Western Ghats in India, is lower than the hilly terrain to its north and south. The exact reasons for the formation of this gap are not clear. It results in the neighbouring regions of Tamil Nadu getting more rainfall from the South West monsoon and the neighbouring regions of Kerala having higher summer temperatures.
    What can be inferred from this passage?
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    Question

    Geneticists say that they are very close to confirming the genetic roots of psychiatric illnesses such as depression and schizophrenia, and consequently, that doctors will be able to eradicate these diseases through early identification and gene therapy.
    On which of the following assumptions does the statement above rely?
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    Question

    Round-trip tickets to a tourist destination are eligible for a discount of 10% on the total fare. In addition, groups of 4 or more get a discount of 5% on the total fare. If the one way single person fare is Rs 100, a group of 5 tourists purchasing round-trip tickets will be charged Rs _________.
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    Question

    In a survey, 300 respondents were asked whether they own a vehicle or not. If yes, they were further asked to mention whether they own a car or scooter or both. Their responses are tabulated below. What percent of respondents do not own a scooter?
    MenWomen
    Own vehicle
    Car4034
    Scooter3020
    Both6046
    Do not own vehicle2050
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    Question

    When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines?
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ELECTRICAL – EE

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    Question

    Given a system of equations:x+2y+2z=b15x+y+3z=b2\begin{aligned} x + 2y + 2z &= b_1 \\ 5x + y + 3z &= b_2 \end{aligned}Which of the following is true regarding its solutions
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    Question

    Let f(x)=xe−xf(x) = x e^{-x}. The maximum value of the function in the interval (0,∞)(0, \infty) is
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    Question

    The solution for the differential equation d2xdt2=−9x\frac{d^2x}{dt^2} = -9x, with initial conditions x(0)=1x(0) = 1 and dxdt∣t=0=1\frac{dx}{dt} \big|_{t=0} = 1, is
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    Question

    Let X(s)=3s+5s2+10s+21X(s) = \frac{3s+5}{s^2+10s+21} be the Laplace Transform of a signal x(t)x(t). Then, x(0+)x(0^+) is
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    Question

    Let SS be the set of points in the complex plane corresponding to the unit circle. (That is, S={z:∣z∣=1}S = \{ z : |z| = 1 \}). Consider the function f(z)=zz∗f(z) = z z^* where z∗z^* denotes the complex conjugate of zz. The f(z)f(z) maps SS to which one of the following in the complex plane
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    Question

    The three circuit elements shown in the figure are part of an electric circuit. The total power absorbed by the three circuit elements in watts is __________.
    A circuit diagram showing a central node connected to three branches. The left branch has a 100V source with current 10A entering from the left. The right branch has an 80V source with current 8A leaving to the right. The bottom branch has a 15V source connected to ground.
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    Question

    C0C_0 is the capacitance of a parallel plate capacitor with air as dielectric (as in figure (a)). If, half of the entire gap as shown in figure (b) is filled with a dielectric of permittivity ϵr\epsilon_r, the expression for the modified capacitance is

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    Question

    A combination of µFµF capacitor with an initial voltage vc(0)=−2 Vv_c(0) = -2\text{ V} in series with a 100Ω100 Ω resistor is connected to a 20 mA20\text{ mA} ideal dc current source by operating both switches at t=0 st = 0\text{ s} as shown. Which of the following graphs shown in the options approximates the voltage vsv_s across the current source over the next few seconds?
    Circuit diagram showing a 20 mA current source connected to a series RC circuit with R = 100 Ω and C = 1 μF
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    Question

    x(t)x(t) is nonzero only for Tx<t<Tx′T_x < t < T'_x, and similarly, y(t)y(t) is nonzero only for Ty<t<Ty′T_y < t < T'_y. Let z(t)z(t) be convolution of x(t)x(t) and y(t)y(t). Which one of the following statements is TRUE?
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    Question

    For a periodic square wave, which one of the following statements is TRUE?
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    Question

    An 8-pole, 3-phase, 50 Hz induction motor is operating at a speed of 700 rpm. The frequency of the rotor current of the motor in Hz is ____________.
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    Question

    For a specified input voltage and frequency, if the equivalent radius of the core of a transformer is reduced by half, the factor by which the number of turns in the primary should change to maintain the same no load current is
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    Question

    A star connected 400 V, 50 Hz, 4 pole synchronous machine gave the following open circuit and short circuit test results:
    Open circuit test: Voc=400V_{oc} = 400 V (rms, line-to-line) at field current, If=2.3I_f = 2.3 A
    Short circuit test: Isc=10I_{sc} = 10 A (rms, phase) at field current, If=1.5I_f = 1.5 A
    The value of per phase synchronous impedance in Ω\Omega at rated voltage is __________.
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    Question

    The undesirable property of an electrical insulating material is
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    Question

    Three-phase to ground fault takes place at locations F1F_1 and F2F_2 in the system shown in the figure
    System diagram showing two generators $E_A$ and $E_B$, two buses A and B, and two fault locations $F_1$ and $F_2$
    If the fault takes place at location F1F_1, then the voltage and the current at bus A are VF1V_{F1} and IF1I_{F1} respectively. If the fault takes place at location F2F_2, then the voltage and the current at bus A are VF2V_{F2} and IF2I_{F2} respectively. The correct statement about voltages and currents during faults at F1F_1 and F2F_2 is
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    Question

    A 2-bus system and corresponding zero sequence network are shown in the figure.

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    Question

    In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of
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    Question

    The root locus of a unity feedback system is shown in the figure

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    Question

    Power consumed by a balanced 3-phase, 3-wire load is measured by the two wattmeter method. The first wattmeter reads twice that of the second. Then the load impedance angle in radians is
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    Question

    In an oscilloscope screen, linear sweep is applied at the
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    Question

    A cascade of three identical modulo-5 counters has an overall modulus of
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    Question

    In the Wien Bridge oscillator circuit shown in figure, the bridge is balanced when

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    Question

    The magnitude of the mid-band voltage gain of the circuit shown in figure is (assuming hfeh_{fe} of the transistor to be 100)

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    Question

    The figure shows the circuit of a rectifier fed from a 230-V (rms), 50-Hz sinusoidal voltage source. If we want to replace the current source with a resistor so that the rms value of the current supplied by the voltage source remains unchanged, the value of the resistance (in ohms) is __________ (Assume diodes to be ideal.)

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    Question

    Figure shows four electronic switches (i), (ii), (iii) and (iv). Which of the switches can block voltages of either polarity (applied between terminals ‘a’ and ‘b’) when the active device is in the OFF state?
    Four electronic switch configurations labeled (i) to (iv)
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    Question

    Let g:[0,∞)→[0,∞)g: [0,\infty) \to [0,\infty) be a function defined by g(x)=x−[x]g(x) = x - [x], where [x][x] represents the integer part of xx. (That is, it is the largest integer which is less than or equal to xx).
    The value of the constant term in the Fourier series expansion of g(x)g(x) is __________
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    A fair coin is tossed nn times. The probability that the difference between the number of heads and tails is (n−3)(n-3) is
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    Question

    The line integral of function F=yziF = yzi, in the counterclockwise direction, along the circle x2+y2=1x^2+y^2 = 1 at z=1z = 1 is
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    Question

    An incandescent lamp is marked 40 W,240V40\text{ W}, 240\text{V}. If resistance at room temperature (26∘C26^\circ\text{C}) is 120 Ω120\ \Omega, and temperature coefficient of resistance is 4.5×10−3/∘C4.5 \times 10^{-3}/^\circ\text{C}, then its ‘ON’ state filament temperature in ∘C^\circ\text{C} is approximately _______
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    Question

    In the figure, the value of resistor RR is (25+I/2) Ω(25 + I/2)\ \Omega, where II is the current in amperes. The current II is ______
    Circuit diagram showing a 300V DC source connected to a resistor R
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    Question

    In an unbalanced three phase system, phase current Ia=1∠(−90∘)I_a = 1\angle(-90^\circ) pu, negative sequence current Ib2=4∠(−150∘)I_{b2} = 4\angle(-150^\circ) pu, zero sequence current Ic0=3∠90∘I_{c0} = 3\angle 90^\circ pu. The magnitude of phase current IbI_b in pu is
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    Question

    The following four vector fields are given in Cartesian co-ordinate system. The vector field which does not satisfy the property of magnetic flux density is
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    Question

    The function shown in the figure can be represented as
    Graph of a piecewise function starting at 1 from t=0 to T, then ramping from 0 at t=T to 1 at t=2T, and remaining at 1 for t > 2T
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    Question

    Let X(z)=11−z−3X(z) = \frac{1}{1-z^{-3}} be the Z-transform of a causal signal x[n]x[n]. Then, the values of x[2]x[2] and x[3]x[3] are
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    Question

    Let f(t)f(t) be a continuous time signal and let F(ω)F(\omega) be its Fourier Transform defined byF(ω)=∫−∞∞f(t)e−jωtdtF(\omega) = \int_{-\infty}^{\infty} f(t) e^{-j\omega t} dtDefine g(t)g(t) byg(t)=∫−∞∞F(u)e−jutdug(t) = \int_{-\infty}^{\infty} F(u) e^{-jut} duWhat is the relationship between f(t)f(t) and g(t)g(t)?
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    Question

    The core loss of a single phase, 230/115 V, 50 Hz power transformer is measured from 230 V side by feeding the primary (230 V side) from a variable voltage variable frequency source while keeping the secondary open circuited. The core loss is measured to be 1050 W for 230 V, 50 Hz input. The core loss is again measured to be 500 W for 138 V, 30 Hz input. The hysteresis and eddy current losses of the transformer for 230 V, 50 Hz input are respectively,
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    Question

    A 15 kW, 230 V dc shunt motor has armature circuit resistance of 0.4 Ω0.4\ \Omega and field circuit resistance of 230 Ω230\ \Omega. At no load and rated voltage, the motor runs at 1400 rpm and the line current drawn by the motor is 5 A. At full load, the motor draws a line current of 70 A. Neglect armature reaction. The full load speed of the motor in rpm is _________.
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    Question

    A 3 phase, 50 Hz, six pole induction motor has a rotor resistance of 0.1 Ω\Omega and reactance of 0.92 Ω\Omega. Neglect the voltage drop in stator and assume that the rotor resistance is constant. Given that the full load slip is 3%, the ratio of maximum torque to full load torque is
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    Question

    A three phase synchronous generator is to be connected to the infinite bus. The lamps are connected as shown in the figure for the synchronization. The phase sequence of bus voltage is R-Y-B and that of incoming generator voltage is R'-Y'-B'.
    Circuit diagram showing synchronization of a 3-phase generator to an infinite bus using three lamps La, Lb, Lc connected between phases R-R', Y-B', and B-Y'.
    It was found that the lamps are becoming dark in the sequence La−Lb−LcL_a-L_b-L_c. It means that the phase sequence of incoming generator is
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    Question

    A distribution feeder of 1 km length having resistance, but negligible reactance, is fed from both the ends by 400V, 50 Hz balanced sources. Both voltage sources S1S_1 and S2S_2 are in phase. The feeder supplies concentrated loads of unity power factor as shown in the figure.

    The contributions of S1S_1 and S2S_2 in 100 A current supplied at location P respectively, are
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    Question

    A two bus power system shown in the figure supplies load of 1.0+j0.51.0+j0.5 p.u.
    The values of V1V_1 in p.u. and δ2\delta_2 respectively are

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    Question

    The fuel cost functions of two power plants are
    Plant P1P_1: C1=0.05Pg12+APg1+BC_1 = 0.05 P_{g1}^2 + AP_{g1} + B
    Plant P2P_2: C2=0.10Pg22+3APg2+2BC_2 = 0.10 P_{g2}^2 + 3AP_{g2} + 2B
    where, Pg1P_{g1} and Pg2P_{g2} are the generated powers of two plants, and AA and BB are the constants. If the two plants optimally share 1000 MW load at incremental fuel cost of 100 Rs/MWh, the ratio of load shared by plants P1P_1 and P2P_2 is
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    Question

    The overcurrent relays for the line protection and loads connected at the buses are shown in the figure.
    Relay coordination diagram with buses A, B, C and relays RA, RB
    The relays are IDMT in nature having the characteristictop=0.14×Time Multiplier Setting(Plug Setting Multiplier)0.02−1t_{op} = \frac{0.14 \times \text{Time Multiplier Setting}}{(\text{Plug Setting Multiplier})^{0.02} - 1}The maximum and minimum fault currents at bus B are 2000 A and 500 A respectively. Assuming the time multiplier setting and plug setting for relay RBR_B to be 0.1 and 5A respectively, the operating time of RBR_B (in seconds) is ____________
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    For the given system, it is desired that the system be stable. The minimum value of α\alpha for this condition is _______________.

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    Question

    The Bode magnitude plot of the transfer function G(s)=K(1+0.5s)(1+as)s(1+s8)(1+bs)(1+s36)G(s) = \frac{K(1+0.5s)(1+as)}{s(1+\frac{s}{8})(1+bs)(1+\frac{s}{36})} is shown below:
    Bode magnitude plot showing slopes and corner frequencies
    Note that −6 dB/octave=−20 dB/decade-6 \text{ dB/octave} = -20 \text{ dB/decade}. The value of abK\frac{a}{bK} is _____________.
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    Question

    A system matrix is given as follows.A=[01−1−6−116−6−115]A = \begin{bmatrix} 0 & 1 & -1 \\ -6 & -11 & 6 \\ -6 & -11 & 5 \end{bmatrix}The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is _______
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    Question

    The reading of the voltmeter (rms) in volts, for the circuit shown in the figure is __________
    A bridge circuit connected to a sinusoidal voltage source 100sin(wt) through a series resistor R = 0.5 Ω. The bridge has four arms: top-left (1j Ω), bottom-left (1/j Ω), top-right (1/j Ω), and bottom-right (1j Ω). A voltmeter V is connected between the left and right nodes of the bridge.
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    Question

    The dc current flowing in a circuit is measured by two ammeters, one PMMC and another electrodynamometer type, connected in series. The PMMC meter contains 100 turns in the coil, the flux density in the air gap is 0.2 Wb/m20.2 \text{ Wb/m}^2, and the area of the coil is 80 mm280 \text{ mm}^2. The electrodynamometer ammeter has a change in mutual inductance with respect to deflection of 0.5 mH/deg0.5 \text{ mH/deg}. The spring constants of both the meters are equal. The value of current, at which the deflections of the two meters are same, is ________
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    Question

    Given that the op-amps in the figure are ideal, the output voltage V0V_0 is

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    Question

    Which of the following logic circuits is a realization of the function FF whose Karnaugh map is shown in figure
    C \ AB00011110
    011
    111
    Karnaugh map for function F
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    Question

    In the figure shown, assume the op-amp to be ideal. Which of the alternatives gives the correct Bode plots for the transfer function Vo(ω)Vi(ω)\frac{V_o(\omega)}{V_i(\omega)}?

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    Question

    An output device is interfaced with 8-bit microprocessor 8085A. The interfacing circuit is shown in figure. The interfacing circuit makes use of 3 Line to 8 Line decoder having 3 enable lines E1,Eˉ2,Eˉ3E_1, \bar{E}_2, \bar{E}_3. The address of the device is

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    Question

    The figure shows the circuit diagram of a rectifier. The load consists of a resistance 10 Ω10\ \Omega and an inductance 0.05 H0.05\ H connected in series. Assuming ideal thyristor and ideal diode, the thyristor firing angle (in degree) needed to obtain an average load voltage of 70 V70\ V is ______

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    Question

    Figure (i) shows the circuit diagram of a chopper. The switch SS in the circuit in figure (i) is switched such that the voltage vDv_D across the diode has the wave shape as shown in figure (ii). The capacitance CC is large so that the voltage across it is constant. If switch SS and the diode are ideal, the peak to peak ripple (in A) in the inductor current is ______

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    Question

    The figure shows one period of the output voltage of an inverter. α\alpha should be chosen such that 60∘<α<90∘60^\circ < \alpha < 90^\circ. If rms value of the fundamental component is 5050 V, then α\alpha in degree is______________

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