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GATE EE 2024 Set 1

All 65 solved GATE EE 2024 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 15Medium 37Hard 13

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    If ‘→’ denotes increasing order of intensity, then the meaning of the words
    [talk → shout → scream] is analogous to [please → ________ → pander].
    Which one of the given options is appropriate to fill the blank?
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    Question

    PP and QQ have been allotted a hostel room with two beds, a study table, and an almirah. PP is an avid bird-watcher and wants to sit at the table and watch birds outside the window. QQ does not mind that as long as his bed is close to the ceiling fan.
    Which one of the following arrangements suits them the most?
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    Question

    The decimal number system uses the characters 0, 1, 2, …, 8, 9, and the octal number system uses the characters 0, 1, 2, …, 6, 7.
    For example, the decimal number 12(=1×101+2×100)12 (= 1 \times 10^1 + 2 \times 10^0) is expressed as 14(=1×81+4×80)14 (= 1 \times 8^1 + 4 \times 8^0) in the octal number system.
    The decimal number 108 in the octal number system is
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    Question

    A shopkeeper buys shirts from a producer and sells them at 20% profit. A customer has to pay ₹3,186.00 including 18% taxes, per shirt. At what price did the shopkeeper buy each shirt from the producer?
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    Question

    If, for non-zero real variables xx, yy, and real parameter a>1a > 1,x:y=(a+1):(a−1),x: y = (a + 1) : (a - 1),then, the ratio (x2−y2):(x2+y2)(x^2 - y^2) : (x^2 + y^2) is
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    Question

    In the given text, the blanks are numbered (i)−(iv). Select the best match for all the blanks.
    Following a row (i) the shopkeeper (ii) the price of a frying pan, the cook stood (iii) a row to withdraw cash (iv) the ATM booth.
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    Question

    In the following figure,
    CD=5 cmCD = 5\text{ cm}, BE=10 cmBE = 10\text{ cm}, AE=12 cmAE = 12\text{ cm},
    ∠DAB=∠DCB\angle DAB = \angle DCB, and ∠DAE=∠DBC=90∘\angle DAE = \angle DBC = 90^\circ
    Points AFCDAFCD create a rhombus.
    The length of BFBF (in cm) is
    geometry figure with points A, B, C, D, E, F
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    Question

    The chart below shows the data of the number of cars bought by Millennials and Gen X people in a country from the year 2010 to 2020 as well as the yearly fuel consumption of the country (in Million liters).
    Combined bar and line chart versus Year 2010, 2015, 2020. Bars, right axis Number of people buying cars, 0 to 100000: Gen X 40000, 30000, 25000; Millenials 20000, 45000, 60000. Line, left axis Fuel Consumption in Million liters, 0 to 100: 50, 60, 90.

    Considering the data presented in the chart, which one of the following options is true?
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    Question

    The assembly shown below has three teethed circular objects (Pinions) and two teethed flat objects (Racks), which are perfectly mating with each other. Pinions can only rotate clockwise or anti-clockwise staying at its own center. Racks can translate towards the left (←\leftarrow) or the right (→\rightarrow) direction.
    Gear train: upper rack Object A, with an arrow pointing right, meshes with pinion Object P below it. P meshes with pinion Object Q to its lower left, Q meshes with pinion Object R below it, and R meshes with the lower rack Object B.

    If the object A (Rack) is translating towards the right (→\rightarrow) direction, the correct statement among the following is
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    Question

    A surveyor has to measure the horizontal distance from her position to a distant reference point CC. Using her position as the center, a 200 m200\text{ m} horizontal line segment is drawn with the two endpoints AA and BB. Points AA, BB, and CC are not collinear. Each of the angles ∠CAB\angle CAB and ∠CBA\angle CBA are measured as 87.8∘87.8^\circ. The distance (in m) of the reference point CC from her position is nearest to
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Electrical Engineering (EE)

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    Question

    Which one of the following matrices has an inverse?
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    Question

    The number of junctions in the circuit is
    A circuit diagram consisting of resistors, capacitors, and inductors arranged in a grid-like network with an additional parallel capacitor branch on the far right.
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    Question

    All the elements in the circuit are ideal. The power delivered by the 10 V source in watts is
    Circuit with a 10 V source feeding an $\alpha\ \Omega$ resistor, a $1\ \Omega$ resistor to the reference node, and a $2\ \Omega$ resistor in series with a 10 A current source
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    Question

    The circuit shown in the figure with the switch SS open, is in steady state. After the switch SS is closed, the time constant of the circuit in seconds is

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    Question

    Suppose signal y(t)y(t) is obtained by the time-reversal of signal x(t)x(t), i.e., y(t)=x(−t),−∞<t<∞y(t) = x(-t), -\infty < t < \infty. Which one of the following options is always true for the convolution of x(t)x(t) and y(t)y(t)?
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    Question

    If u(t)u(t) is the unit step function, then the region of convergence (ROC) of the Laplace transform of the signal x(t)=et2[u(t−1)−u(t−10)]x(t) = e^{t^2} [u(t - 1) - u(t - 10)]is
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    Question

    A three phase, 50 Hz, 6 pole induction motor runs at 960 rpm. The stator copper loss, core loss, and the rotational loss of the motor can be neglected. The percentage efficiency of the motor is
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    Question

    Which one of the following options represents possible voltage polarities in a single phase two winding transformer? Here, VpV_p is the applied primary voltage, EpE_p is the induced primary voltage, VsV_s is the open circuit secondary voltage, and EsE_s is the induced secondary voltage.
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    Question

    The figure shows the single line diagram of a 4-bus power network. Branches b1,b2,b3,b_1, b_2, b_3, and b4b_4 have impedances 4z,z,2z,4z, z, 2z, and 4z4z per-unit (pu), respectively, where z=r+jxz = r + jx, with r>0r > 0 and x>0x > 0. The current drawn from each load bus (marked as arrows) is equal to II pu, where I≠0I \neq 0. If the network is to operate with minimum loss, the branch that should be opened is
    Single-line diagram: a generator feeds a top bus. Branch b1 runs from the top bus to a left bus and b2 from the top bus to a right bus. Branch b3 runs from the left bus to a bottom bus and b4 from the right bus to the bottom bus, forming a diamond-shaped loop. Each of the left, right and bottom buses has a load arrow labelled I.
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    Question

    For the block-diagram shown in the figure, the transfer function C(s)R(s)\frac{C(s)}{R(s)} is
    Block diagram. R of s enters summing junction 1 with plus sign; C of s is fed back from the output to summing junction 1 with minus sign. The output of junction 1 enters summing junction 2 with a minus sign. C of s is also fed back to summing junction 2 from below with a plus sign. The output of junction 2 drives block G of s, whose output is C of s.
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    Question

    Consider the standard second-order system of the form ωn2s2+2ζωns+ωn2\frac{\omega_n^2}{s^2+2\zeta\omega_ns+\omega_n^2} with the poles pp and p∗p^* having negative real parts. The pole locations are also shown in the figure. Now consider two such second-order systems as defined below:
    System 1: ωn=3\omega_n = 3 rad/sec and θ=60∘\theta = 60^\circ
    System 2: ωn=1\omega_n = 1 rad/sec and θ=70∘\theta = 70^\circWhich one of the following statements is correct?
    s-plane pole plot with sigma and j omega axes. Two poles p, upper, and p conjugate, lower, are marked with crosses in the left half-plane on a dotted semicircle of radius omega_n centred at the origin, which meets the negative real axis at -omega_n. A dotted line joins the origin to p, and the angle theta is marked between this line and the negative real axis.
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    Question

    Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a first-order pole-only approximation such that the steady-state values of the unit step responses of the original and the approximated systems are same?
    Block diagram of a cascaded system with two blocks: 1/(s+1) and (s+40)/(s+20)
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    Question

    The table lists two instrument transformers and their features:
    Instrument TransformersFeatures
    P) Primary is connected in parallel to the grid
    X) Current Transformer (CT)Q) Open circuited secondary is not desirable
    Y) Potential Transformer (PT)R) Primary current is the line current
    S) Secondary burden affects the primary current
    The correct matching of the two columns is
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    Question

    Simplified form of the Boolean function F(P,Q,R,S)=PˉQˉ+PˉQS+PQˉRˉSˉ+PQˉRSˉF(P, Q, R, S) = \bar{P}\bar{Q} + \bar{P}QS + P\bar{Q}\bar{R}\bar{S} + P\bar{Q}R\bar{S}is
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    Question

    In the circuit, the present value of ZZ is 1. Neglecting the delay in the combinatorial circuit, the values of SS and ZZ, respectively, after the application of the clock will be
    Combinatorial circuit realising $S = X \oplus Y \oplus Z$ with inputs $X = 1$, $Y = 0$ and the fed-back signal $Z$; its output $S$ drives the $D$ input of a clocked D flip-flop whose output $Q$ is $Z$
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    Question

    To obtain the Boolean function F(X,Y)=XYˉ+XˉF(X, Y) = X\bar{Y} + \bar{X}, the inputs PQRSPQRS in the figure should be

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    Question

    If the following switching devices have similar power ratings, which one of them is the fastest?
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    Question

    A single-phase triac based AC voltage controller feeds a series RL load. The input AC supply is 230 V, 50 Hz. The values of R and L are 10 Ω\Omega and 18.37 mH, respectively. The minimum triggering angle of the triac to obtain controllable output voltage is
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    Question

    Let XX be a discrete random variable that is uniformly distributed over the set {−10,−9,…,0,…,9,10}\{-10, -9, \dots, 0, \dots, 9, 10\}. Which of the following random variables is/are uniformly distributed?
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    Question

    Which of the following complex functions is/are analytic on the complex plane?
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    Question

    Consider the complex function f(z)=cos⁡z+ez2f(z) = \cos z + e^{z^2}. The coefficient of z5z^5 in the Taylor series expansion of f(z)f(z) about the origin is ______ (rounded off to 1 decimal place).
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    Question

    The sum of the eigenvalues of the matrix A=[1234]2A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}^2 is ______ (rounded off to the nearest integer).
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    Question

    Let X(ω)X(\omega) be the Fourier transform of the signal x(t)=e−t4cos⁡t,−∞<t<∞x(t) = e^{-t^4} \cos t, -\infty < t < \infty. The value of the derivative of X(ω)X(\omega) at ω=0\omega = 0 is _______ (rounded off to 1 decimal place).
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    Question

    The incremental cost curves of two generators (Gen A and Gen B) in a plant supplying a common load are shown in the figure. If the incremental cost of supplying the common load is Rs. 7400 per MWh, then the common load in MW is _______ (rounded off to the nearest integer).
    Incremental cost in Rs per MWh versus Generation in MW, 0 to 160, drawn twice at two sizes. Gen A, solid line, rises linearly from 8000 at 0 MW to 11200 at 160 MW. Gen B, dashed line, rises linearly from 6000 at 0 MW to 12400 at 160 MW. The lines cross.
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    Question

    A forced commutated thyristorized step-down chopper is shown in the figure. Neglect the ON-state drop across the power devices. Assume that the capacitor is initially charged to 50 V with the polarity shown in the figure. The load current (ILI_L) can be assumed to be constant at 10 A. Initially, ThMTh_M is ON and ThATh_A is OFF. The turn-off time available to ThMTh_M in microseconds, when ThATh_A is triggered, is_________ (rounded off to the nearest integer).
    Forced commutated thyristorized step-down chopper circuit
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    Question

    Consider a vector uˉ=2x^+y^+2z^\bar{u} = 2\hat{x} + \hat{y} + 2\hat{z}, where x^,y^,z^\hat{x}, \hat{y}, \hat{z} represent unit vectors along the coordinate axes x,y,zx, y, z respectively. The directional derivative of the function f(x,y,z)=2ln⁡(xy)+ln⁡(yz)+3ln⁡(xz)f(x, y, z) = 2 \ln(xy) + \ln(yz) + 3 \ln(xz) at the point (x,y,z)=(1,1,1)(x, y, z) = (1, 1, 1) in the direction of uˉ\bar{u} is
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    Question

    The input x(t)x(t) and the output y(t)y(t) of a system are related as y(t)=e−t∫−∞teτx(τ)dτ,−∞<t<∞.y(t) = e^{-t} \int_{-\infty}^{t} e^{\tau} x(\tau) d\tau, \quad -\infty < t < \infty.The system is
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    Question

    Consider the discrete-time systems T1T_1 and T2T_2 defined as follows:{T1x}[n]=x[0]+x[1]+⋯+x[n]\{T_1 x\}[n] = x[0] + x[1] + \dots + x[n]{T2x}[n]=x[0]+12x[1]+⋯+12nx[n]\{T_2 x\}[n] = x[0] + \frac{1}{2} x[1] + \dots + \frac{1}{2^n} x[n]Which one of the following statements is true?
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    Question

    If the Z-transform of a finite-duration discrete-time signal x[n]x[n] is X(z)X(z), then the Z-transform of the signal y[n]=x[2n]y[n] = x[2n] is
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    Question

    A 3-phase, 11 kV, 10 MVA synchronous generator is connected to an inductive load of power factor (3/2)(\sqrt{3}/2) via a lossless line with a per-phase inductive reactance of 5 Ω\Omega. The per-phase synchronous reactance of the generator is 30 Ω\Omega with negligible armature resistance. If the generator is producing the rated current at the rated voltage, then the power factor at the terminal of the generator is
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    Question

    For the three-bus lossless power network shown in the figure, the voltage magnitudes at all the buses are equal to 1 per unit (pu), and the differences of the voltage phase angles are very small. The line reactances are marked in the figure, where α\alpha, β\beta, γ\gamma, and xx are strictly positive. The bus injections P1P_1 and P2P_2 are in pu. If P1=mP2P_1 = mP_2, where m>0m > 0, and the real power flow from bus 1 to bus 2 is 0 pu, then which one of the following options is correct?
    Three-bus network drawn as a triangle. Bus 1 at top left and bus 2 at top right are joined by a line of impedance j alpha x ohm. Bus 1 connects to bus 3 at the bottom through j beta x ohm, and bus 2 connects to bus 3 through j gamma x ohm. Arrow P1 points into bus 1, arrow P2 points into bus 2, and a load arrow points downward out of bus 3.
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    Question

    A BJT biasing circuit is shown in the figure, where VBE=0.7V_{BE} = 0.7 V and β=100\beta = 100. The Quiescent Point values of VCEV_{CE} and ICI_C are respectively

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    Question

    Let f(t)f(t) be a real-valued function whose second derivative is positive for −∞<t<∞-\infty < t < \infty. Which of the following statements is/are always true?
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    Question

    Consider the function f(t)=(max⁡(0,t))2f(t) = (\max(0,t))^2 for −∞<t<∞-\infty < t < \infty, where max⁡(a,b)\max(a,b) denotes the maximum of aa and bb. Which of the following statements is/are true?
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    Which of the following differential equations is/are nonlinear?
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    Question

    For a two-phase network, the phase voltages VpV_p and VqV_q are to be expressed in terms of sequence voltages VαV_\alpha and VβV_\beta as [VpVq]=S[VαVβ]\begin{bmatrix} V_p \\ V_q \end{bmatrix} = \mathbf{S} \begin{bmatrix} V_\alpha \\ V_\beta \end{bmatrix}. The possible option(s) for matrix S\mathbf{S} is/are
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    Question

    Which of the following options is/are correct for the Automatic Generation Control (AGC) and Automatic Voltage Regulator (AVR) installed with synchronous generators?
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    Question

    Two passive two-port networks P and Q are connected as shown in the figure. The impedance matrix of network P is ZP=[40 Ω60 Ω80 Ω100 Ω]\mathbf{Z_P} = \begin{bmatrix} 40\ \Omega & 60\ \Omega \\ 80\ \Omega & 100\ \Omega \end{bmatrix}. The admittance matrix of network Q is YQ=[5 S−2.5 S−2.5 S1 S]\mathbf{Y_Q} = \begin{bmatrix} 5\ \text{S} & -2.5\ \text{S} \\ -2.5\ \text{S} & 1\ \text{S} \end{bmatrix}. Let the ABCD matrix of the two-port network R in the figure be [αβγδ]\begin{bmatrix} \alpha & \beta \\ \gamma & \delta \end{bmatrix}. The value of β\beta in Ω\Omega is _____________ (rounded off to 2 decimal places).
    Block diagram showing two-port networks P and Q connected in cascade to form network R
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    Question

    For the circuit shown in the figure, the source frequency is 5000 rad/sec5000 \text{ rad/sec}. The mutual inductance between the magnetically coupled inductors is 5 mH5 \text{ mH} with their self inductances being 125 mH125 \text{ mH} and 1 mH1 \text{ mH}. The Thevenin’s impedance, ZthZ_{th}, between the terminals PP and QQ in Ω\Omega is _________ (rounded off to 2 decimal places).

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    Question

    In the circuit shown, Z1=50∠−90∘ΩZ_1 = 50\angle - 90^\circ \Omega and Z2=200∠−30∘ΩZ_2 = 200\angle - 30^\circ \Omega. It is supplied by a three phase 400 V400 \text{ V} source with the phase sequence being R-Y-B. Assume the watt meters W1W_1 and W2W_2 to be ideal. The magnitude of the difference between the readings of W1W_1 and W2W_2 in watts is ___________ (rounded off to 2 decimal places).

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    In the (x,y,z)(x, y, z) coordinate system, three point-charges QQ, QQ, and αQ\alpha Q are located in free space at (−1,0,0)(-1, 0, 0), (1,0,0)(1, 0, 0), and (0,−1,0)(0, -1, 0), respectively. The value of α\alpha for the electric field to be zero at (0,0.5,0)(0, 0.5, 0) is ______________ (rounded off to 1 decimal place).
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    The given equation represents a magnetic field strength H⃗(r,θ,ϕ)\vec{H}(r, \theta, \phi) in the spherical coordinate system, in free space. Here, r^\hat{r} and θ^\hat{\theta} represent the unit vectors along rr and θ\theta, respectively. The value of PP in the equation should be ____________ (rounded off to the nearest integer).H⃗(r,θ,ϕ)=1r3(r^Pcos⁡θ+θ^sin⁡θ)\vec{H}(r, \theta, \phi) = \frac{1}{r^3} (\hat{r} P \cos \theta + \hat{\theta} \sin \theta)
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    If the energy of a continuous-time signal x(t)x(t) is EE and the energy of the signal 2x(2t−1)2x(2t - 1) is cEcE, then cc is _____ (rounded off to 1 decimal place).
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    A 3-phase star connected slip ring induction motor has the following parameters referred to the stator:Rs=3 Ω,Xs=2 Ω,Xr′=2 Ω,Rr′=2.5 ΩR_s = 3\ \Omega, X_s = 2\ \Omega, X_r' = 2\ \Omega, R_r' = 2.5\ \OmegaThe per phase stator to rotor effective turns ratio is 3:1. The rotor winding is also star connected. The magnetizing reactance and core loss of the motor can be neglected. To have maximum torque at starting, the value of the extra resistance in ohms (referred to the rotor side) to be connected in series with each phase of the rotor winding is _________ (rounded off to 2 decimal places).
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    A 5 kW, 220 V DC shunt motor has 0.5 Ω\Omega armature resistance including brushes. The motor draws a no-load current of 3 A. The field current is constant at 1 A. Assuming that the core and rotational losses are constant and independent of the load, the current (in amperes) drawn by the motor while delivering the rated load, for the best possible efficiency, is ________ (rounded off to 2 decimal places).
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    The single line diagram of a lossless system is shown in the figure. The system is operating in steady-state at a stable equilibrium point with the power output of the generator being Pmaxsin⁡δP_{max} \sin \delta, where δ\delta is the load angle and the mechanical power input is 0.5Pmax0.5 P_{max}. A fault occurs on line 2 such that the power output of the generator is less than 0.5Pmax0.5 P_{max} during the fault. After the fault is cleared by opening line 2, the power output of the generator is {Pmax/2}sin⁡δ\{P_{max}/\sqrt{2}\} \sin \delta. If the critical fault clearing angle is π/2\pi/2 radians, the accelerating area on the power angle curve is ______ times PmaxP_{max} (rounded off to 2 decimal places).

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    Consider the closed-loop system shown in the figure with G(s)=K(s2−2s+2)(s2+2s+5).G(s) = \frac{K(s^2 - 2s + 2)}{(s^2 + 2s + 5)}. The root locus for the closed-loop system is to be drawn for 0≤K<∞0 \leq K < \infty. The angle of departure (between 0∘0^\circ and 360∘360^\circ) of the root locus branch drawn from the pole (−1+j2)(-1 + j2), in degrees, is _________________ (rounded off to the nearest integer).

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    Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of G(s)G(s) has a constant slope of −20-20 dB/decade at least till 100100 rad/sec with the gain crossover frequency being 1010 rad/sec. The asymptotic Bode phase plot remains constant at −90∘-90^\circ at least till ω=10\omega = 10 rad/sec. The steady-state error of the closed-loop system for a unit ramp input is ______________ (rounded off to 2 decimal places).
    Block diagram of a unity feedback system with forward path transfer function G(s)
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    Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of G(s)G(s) are given in the table. The value of the gain KI(>0)K_I (> 0) for a 50∘50^\circ phase margin is _______ (rounded off to 2 decimal places).
    ω\omega in rad/secMagnitude in dBPhase in degrees
    0.5-7-40
    1.0-10-80
    2.0-18-130
    10.0-40-200

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    In the given circuit, the diodes are ideal. The current II through the diode D1D1 in milliamperes is ___________ (rounded off to two decimal places).

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    A difference amplifier is shown in the figure. Assume the op-amp to be ideal. The CMRR (in dB) of the difference amplifier is _________ (rounded off to 2 decimal places).

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    A single-phase half-controlled bridge converter supplies an inductive load with ripple free load current. The triggering angle of the converter is 60∘60^\circ. The ratio of the rms value of the fundamental component of the input current to the rms value of the total input current of the bridge is _________ (rounded off to 3 decimal places).
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    A single-phase full bridge voltage source inverter (VSI) feeds a purely inductive load. The inverter output voltage is a square wave in 180∘180^\circ conduction mode. The fundamental frequency of the output voltage is 50 Hz50\text{ Hz}. If the DC input voltage of the inverter is 100 V100\text{ V} and the value of the load inductance is 20 mH20\text{ mH}, the peak-to-peak load current in amperes is _________ (rounded off to the nearest integer).
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    In the DC-DC converter shown in the figure, the current through the inductor is continuous. The switching frequency is 500500 Hz. The voltage (VoV_o) across the load is assumed to be constant and ripple free. The peak inductor current in amperes is _________ (rounded off to the nearest integer).
    DC-DC Boost converter circuit diagram
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    A single-phase full-controlled thyristor converter bridge is used for regenerative braking of a separately excited DC motor with the following specifications:
    ParameterValue
    Rated armature voltage210 V
    Rated armature current10 A
    Rated speed1200 rpm
    Armature resistance1 Ω\Omega
    Input to the converter bridge240 V at 50 Hz
    The armature of the DC motor is fed from the full-controlled bridge and the field current is kept constant.
    Assume that the motor is running at 600 rpm and the armature terminals of the motor are suitably reversed for regenerative braking. If the armature current of the motor is to be maintained at the rated value, the triggering angle of the converter bridge in degrees should be ____________ (rounded off to 2 decimal places).
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