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GATE EE 2025 Set 1

All 65 solved GATE EE 2025 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 22Medium 35Hard 8

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Kavya _______ go to work yesterday as she ________ feeling well.
    Select the most appropriate option to complete the above sentence.
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    Question

    Good : Evil :: Genuine : _______
    Select the most appropriate option to complete the analogy.
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    Question

    The relationship between two variables xx and yy is given by x+py+q=0x + py + q = 0 and is shown in the figure. Find the values of pp and qq.
    Note: The figure shown is representative.
    A linear graph in the x-y plane passing through points (-2, 0) and (0, 4).
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    Question

    Each row of Column-I has three items and each item is represented by a circle in Column-II. The arrangement of circles in Column-II represents the relationship among the items in Column-I.
    Identify the option that has the most appropriate match between Column-I and Column-II.
    Note: The figures shown are representative.

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    Question

    What is the value of (381274)13(\frac{3^{81}}{27^4})^{\frac{1}{3}} ?
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    Question

    Identify the option that has the most appropriate sequence such that a coherent paragraph is formed:
    P. It is because deer, like most of the animals that tigers normally prey on, run much faster! It simply means, another day of empty stomach for the big cats.
    Q. Tigers spend most of their life searching for food.
    R. If they trace the scent of deer, tigers follow the trail, chase the deer for a mile or two in the dark, and yet may not catch them.
    S. For several nights, they relentlessly prowl through the forest, hunting for a trail that may lead to their prey.
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    Question

    In the given figure, EF and HJ are coded as 30 and 80, respectively. Which one among the given options is most appropriate for the entries marked (i) and (ii) ?
    A circular diagram divided into 8 sectors. Clockwise from top-left: EF, HJ, (i), (ii), 30, 80, 35, FG.
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    Question

    Scores obtained by two students P and Q in seven courses are given in the table below. Based on the information given in the table, which one of the following statements is INCORRECT?
    P22895045786039
    Q35656056814550
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    Question

    Spheres of unit diameter are centered at (l,m,n)(l, m, n) where l,ml, m, and nn take every possible integer values.
    The distance between two spheres is computed from the center of one sphere to the center of the other sphere. For a given sphere, xx is the distance to its nearest sphere and yy is the distance to its next nearest sphere. The value of yx\frac{y}{x} is:
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    Question

    In the triangle PQRPQR, the lengths of PTPT and TRTR are in the ratio of 3:23:2. STST is parallel to QRQR. Two semicircles are drawn with PSPS and PQPQ as diameters, as shown in the figure.
    Which one of the following statements is true about the shaded area PQSPQS?
    Note: The figure shown is representative.

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Electrical Engineering (EE)

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    Question

    Consider the set SS of points (x,y)∈R2(x, y) \in \mathbb{R}^2 which minimize the real valued functionf(x,y)=(x+y−1)2+(x+y)2f(x, y) = (x + y - 1)^2 + (x + y)^2Which of the following statements is true about the set SS?
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    Question

    Let v1\mathbf{v_1} and v2\mathbf{v_2} be the two eigenvectors corresponding to distinct eigenvalues of a 3×33 \times 3 real symmetric matrix. Which one of the following statements is true?
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    Question

    Let A=[111−1−1−101−1]A = \begin{bmatrix} 1 & 1 & 1 \\ -1 & -1 & -1 \\ 0 & 1 & -1 \end{bmatrix}, and b=[1/3−1/30]b = \begin{bmatrix} 1/3 \\ -1/3 \\ 0 \end{bmatrix}. Then, the system of linear equations Ax=bAx = b has
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    Question

    Let P=[210−100001]P = \begin{bmatrix} 2 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix} and let II be the identity matrix. Then P2P^2 is equal to
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    Question

    Consider discrete random variables XX and YY with probabilities as follows:P(X=0 and Y=0)=14P(X = 0 \text{ and } Y = 0) = \frac{1}{4}P(X=1 and Y=0)=18P(X = 1 \text{ and } Y = 0) = \frac{1}{8}P(X=0 and Y=1)=12P(X = 0 \text{ and } Y = 1) = \frac{1}{2}P(X=1 and Y=1)=18P(X = 1 \text{ and } Y = 1) = \frac{1}{8}Given X=1X = 1, the expected value of YY is
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    Question

    Which one of the following statements is true about the small signal voltage gain of a MOSFET based single stage amplifier?
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    Question

    Assuming ideal op-amps, the circuit represents a
    Circuit diagram with two op-amps in a composite feedback configuration
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    Question

    The I-V characteristics of the element between the nodes X and Y is best depicted by

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    Question

    A nullator is defined as a circuit element where the voltage across the device and the current through the device are both zero. A series combination of a nullator and a resistor of value, RR, will behave as a
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    Question

    Consider a discrete-time linear time-invariant (LTI) system S\boldsymbol{S}, wherey[n]=S{x[n]}y[n] = \boldsymbol{S}\{x[n]\}LetS{δ[n]}={1,n∈{0,1,2}0,otherwise\boldsymbol{S}\{\delta[n]\} = \begin{cases} 1, & n \in \{0, 1, 2\} \\ 0, & \text{otherwise} \end{cases}where δ[n]\delta[n] is the discrete-time unit impulse function. For an input signal x[n]x[n], the output y[n]y[n] is
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    Question

    Consider a continuous-time signalx(t)=−t2{u(t+4)−u(t−4)}x(t) = -t^2 \{u(t + 4) - u(t - 4)\}where u(t)u(t) is the continuous-time unit step function. Let δ(t)\delta(t) be the continuous-time unit impulse function. The value of∫−∞∞x(t)δ(t+3)dt\int_{-\infty}^{\infty} x(t)\delta(t + 3)dtis
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    Question

    Selected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time-constant, in sec, of the system is
    Time (sec)0.61.62.610∞\infty
    Output0.781.652.182.983
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    Question

    The Nyquist plot of a strictly stable G(s)G(s) having the numerator polynomial as (s−3)(s - 3) encircles the critical point −1-1 once in the anti-clockwise direction. Which one of the following statements on the closed-loop system shown in figure, is correct?

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    Question

    During a power failure, a domestic household uninterruptible power supply (UPS) supplies AC power to a limited number of lights and fans in various rooms. As per a Newton-Raphson load-flow formulation, the UPS would be represented as a
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    Question

    Which one of the following figures represents the radial electric field distribution ERE_R caused by a spherical cloud of electrons with a volume charge density, ρ=−3ρ0\rho = -3\rho_0 for 0≤R≤a0 \leq R \leq a (both ρ0\rho_0, aa are positive and RR is the radial distance) and ρ=0\rho = 0 for R>aR > a ?

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    Question

    The operating region of the developed torque (TemT_{em}) and speed (ω\omega) of an induction motor drive is given by the shaded region OQRE in the figure. The load torque (TLT_L) characteristic is also shown. The motor drive moves from the initial operating point O to the final operating point S. Which one of the following trajectories will take the shortest time?

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    Question

    The input voltage v(t)v(t) and current i(t)i(t) of a converter are given by,
    v(t)=300sin⁡(ωt)Vv(t) = 300 \sin(\omega t) V
    i(t)=10sin⁡(ωt−π6)+2sin⁡(3ωt+π6)+sin⁡(5ωt+π2)Ai(t) = 10 \sin (\omega t - \frac{\pi}{6}) + 2 \sin (3\omega t + \frac{\pi}{6}) + \sin (5\omega t + \frac{\pi}{2}) A
    where, ω=2π×50\omega = 2\pi \times 50 rad/s. The input power factor of the converter is closest to
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    Question

    Instrument(s) required to synchronize an alternator to the grid is/are
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    Question

    The open-loop transfer function of the system shown in the figure, isG(s)=Ks(s+2)(s+5)(s+7)G(s) = \frac{Ks(s + 2)}{(s + 5)(s + 7)}For K≥0K \geq 0, which of the following real axis point(s) is/are on the root locus?

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    Question

    A continuous time periodic signal x(t)x(t) isx(t)=1+2cos⁡2πt+2cos⁡4πt+2cos⁡6πt.x(t) = 1 + 2 \cos 2\pi t + 2 \cos 4\pi t + 2 \cos 6\pi t .If TT is the period of x(t)x(t), then 1T∫0T∣x(t)∣2 dt=\frac{1}{T}\int_{0}^{T} |x(t)|^2\,dt= _____(round off to the nearest integer).
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    Question

    The maximum percentage error in the equivalent resistance of two parallel-connected resistors of 100 Ω100\ \Omega and 900 Ω900\ \Omega with each having a maximum 5%5\% error is ____________ %\% (round off to nearest integer value).
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    Question

    Consider a distribution feeder, with R/XR/X ratio of 55. At the receiving end, a 350 kVA350\ \text{kVA} load is connected. The maximum voltage drop will occur from the sending end to the receiving end, when the power factor of the load is ___________(round off to three decimal places).
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    Question

    The bus impedance matrix of a 3-bus system (in pu) is Zbus=[j0.059j0.061j0.038j0.061j0.093j0.066j0.038j0.066j0.110]Z_{bus} = \begin{bmatrix} j0.059 & j0.061 & j0.038 \\ j0.061 & j0.093 & j0.066 \\ j0.038 & j0.066 & j0.110 \end{bmatrix}A symmetrical fault (through a fault impedance of j0.007j0.007 pu) occurs at bus 2. Neglecting pre-fault loading conditions, the voltage at bus 1, during the fault is ________ pu (round off to three decimal places).
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    Question

    In the circuit with ideal devices, the power MOSFET is operated with a duty cycle of 0.4 in a switching cycle with I=10I = 10 A and V=15V = 15 V. The power delivered by the current source, in W, is ____________ (round off to the nearest integer).

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    Question

    The induced emf in a 3.3 kV3.3 \text{ kV}, 44 pole, 33-phase star connected synchronous motor is considered to be equal and in phase with the terminal voltage under no load condition. On application of a mechanical load, the induced emf phasor is deflected by an angle of 2∘2^\circ mechanical with respect to the terminal voltage phasor. If the synchronous reactance is 2 Ω2 \, \Omega, and stator resistance is negligible, then the motor armature current magnitude, in ampere, during loaded condition is closest to, ____________ (round off to two decimal places).
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    Question

    Let XX and YY be continuous random variables with probability density functions PX(x)P_X(x) and PY(y)P_Y(y), respectively. Further, let Y=X2Y = X^2 andPX(x)={1,x∈(0,1]0,otherwiseP_X(x) = \begin{cases} 1, & x \in (0,1] \\ 0, & \text{otherwise} \end{cases}Which one of the following options is correct?
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    Question

    A Boolean function is given as
    f=(uˉ+v+wˉ+x)⋅(uˉ+v+w+xˉ)⋅(uˉ+v+w+x)⋅(uˉ+v+wˉ+xˉ)f = (\bar{u} + v + \bar{w} + x) \cdot (\bar{u} + v + w + \bar{x}) \cdot (\bar{u} + v + w + x) \cdot (\bar{u} + v + \bar{w} + \bar{x})
    The simplified form of this function is represented by
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    Question

    In the circuit, IDCI_{DC} is an ideal current source. The transistors M1M_1 and M2M_2 are assumed to be biased in saturation, wherein VinV_{in} is the input signal and VDCV_{DC} is fixed DC voltage. Both transistors have a small signal resistance of rdsr_{ds} and trans-conductance of gmg_m. The small signal output impedance of this circuit is

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    In the circuit, shown below, if the values of RR and CC are very large, the form of the output voltage for a very high frequency square wave input, is best represented by

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    Question

    Let continuous-time signals x1(t)x_1(t) and x2(t)x_2(t) bex1(t)={1,t∈[0,1]2−t,t∈[1,2]0,otherwiseandx2(t)={t,t∈[0,1]2−t,t∈[1,2]0,otherwisex_1(t) = \begin{cases} 1, & t \in [0,1] \\ 2 - t, & t \in [1,2] \\ 0, & otherwise \end{cases} \quad \text{and} \quad x_2(t) = \begin{cases} t, & t \in [0,1] \\ 2 - t, & t \in [1,2] \\ 0, & otherwise \end{cases}Consider the convolution y(t)=x1(t)∗x2(t)y(t) = x_1(t) * x_2(t). Then ∫−∞∞y(t)dt\int_{-\infty}^{\infty} y(t) dt is
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    Let G(s)=1(s+1)(s+2)G(s) = \frac{1}{(s+1)(s+2)}. Then the closed-loop system shown in the figure below, is
    A unity negative feedback control system with forward path transfer function $K(s-1)G(s)$
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    Question

    The continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system 𝑺. The output is observed to be the continuous-time unit step signal u(t)u(t). Which one of the following statements is true?
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    Question

    The transformer connection given in the figure is part of a balanced 3-phase circuit where the phase sequence is “abc”. The primary to secondary turns ratio is 2:1. If (Ia+Ib+Ic=0)(I_a + I_b + I_c = 0), then the relationship between IAI_A and IadI_{ad} will be
    A 3-phase transformer connection diagram. The primary side is star-connected with line currents $I_A, I_B, I_C$ entering terminals A, B, C. The secondary side is an interconnected star (zig-zag) connection with line currents $I_{ad}, I_{bd}, I_{cd}$ leaving terminals a, b, c. The secondary windings are labeled with currents $I_a, I_b, I_c$.
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    Question

    A DC series motor with negligible series resistance is running at a certain speed driving a load, where the load torque varies as cube of the speed. The motor is fed from a 400 V400\text{ V} DC source and draws 40 A40\text{ A} armature current. Assume linear magnetic circuit. The external resistance, in Ω\Omega, that must be connected in series with the armature to reduce the speed of the motor by half, is closest to
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    Question

    A 3-phase, 400 V400\text{ V}, 44 pole, 50 Hz50\text{ Hz} star connected induction motor has the following parameters referred to the stator:
    Rr′=1 Ω,Xs=Xr′=2 ΩR_r' = 1\text{ }\Omega, X_s = X_r' = 2\text{ }\Omega
    Stator resistance, magnetizing reactance and core loss of the motor are neglected. The motor is run with constant V/fV/f control from a drive. For maximum starting torque, the voltage and frequency output, respectively, from the drive, is closest to,
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    Question

    The 3-phase modulating waveforms (va(t)v_a(t), vb(t)v_b(t) and vc(t)v_c(t)), used in sinusoidal PWM in a Voltage Source Inverter (VSI) areva(t)=0.8sin⁡(ωt) Vv_a(t) = 0.8 \sin (\omega t) \text{ V}vb(t)=0.8sin⁡(ωt−2π3) Vv_b(t) = 0.8 \sin (\omega t - \frac{2\pi}{3}) \text{ V}vc(t)=0.8sin⁡(ωt+2π3) Vv_c(t) = 0.8 \sin (\omega t + \frac{2\pi}{3}) \text{ V}where ω=2π×40 rad/s\omega = 2\pi \times 40 \text{ rad/s} is the fundamental frequency. The modulating waveforms are compared with a 10 kHz triangular carrier whose magnitude varies between +1 and −1. The VSI has a DC link voltage of 600 V and feeds a star connected motor. The per phase fundamental RMS motor voltage, in volts, is closest to
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    Question

    An ideal sinusoidal voltage source v(t)=2302sin⁡(2π×50t)Vv(t) = 230\sqrt{2} \sin(2\pi \times 50t) V feeds an ideal inductor LL through an ideal SCR with firing angle α=0∘\alpha = 0^\circ. If L=100mHL = 100 mH, then the peak of the inductor current, in ampere, is closest to
    Circuit diagram showing a sinusoidal voltage source v(t) connected in series with an SCR and an inductor L.
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    Question

    In the following circuit, the average voltageVo=400(1+cos⁡α3) V,V_o = 400 \left(1 + \frac{\cos \alpha}{3}\right) \text{ V},where α\alpha is the firing angle. If the power dissipated in the resistor is 64 W, then the closest value of α\alpha in degrees is
    A circuit diagram showing a three-phase AC source connected to a controlled rectifier block, feeding a load consisting of a 1 $\Omega$ resistor, a 100 mH inductor, and a 500 V DC source.
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    Question

    In the system shown below, the generator was initially supplying power to the grid. A temporary LLLG bolted fault occurs at FF very close to circuit breaker 1. The circuit breakers open to isolate the line. The fault self-clears. The circuit breakers reclose and restore the line. Which one of the following diagrams best indicates the rotor accelerating and decelerating areas?

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    Question

    An air filled cylindrical capacitor (capacitance C0C_0) of length LL, with aa and bb as its inner and outer radii, respectively, consists of two coaxial conducting surfaces. Its cross-sectional view is shown in Fig. (i). In order to increase the capacitance, a dielectric material of relative permittivity ϵr\epsilon_r is inserted inside 50% of the annular region as shown in Fig. (ii). The value of ϵr\epsilon_r for which the capacitance of the capacitor in Fig. (ii), becomes 5C05C_0 is

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    Question

    Let aR\mathbf{a}_R be the unit radial vector in the spherical co-ordinate system. For which of the following value(s) of nn, the divergence of the radial vector field f(R)=aR1Rn\mathbf{f}(\mathbf{R}) = \mathbf{a}_R \frac{1}{R^n} is independent of RR?
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    Question

    Consider two coupled circuits, having self-inductances L1L_1 and L2L_2, that carry non-zero currents I1I_1 and I2I_2, respectively. The mutual inductance between the circuits is MM with unity coupling coefficient. The stored magnetic energy of the coupled circuits is minimum at which of the following value(s) of I1I2\frac{I_1}{I_2}?
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    Let (x,y)∈ℜ2(x, y) \in \Re^2. The rate of change of the real valued function,V(x,y)=x2+x+y2+1V(x, y) = x^2 + x + y^2 + 1at the origin in the direction of the point (1,2)(1, 2) is ___________ (round off to the nearest integer).
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    Question

    Consider ordinary differential equations given byx˙1(t)=2x2(t)\dot{x}_1(t) = 2x_2(t)x˙2(t)=r(t)\dot{x}_2(t) = r(t)with initial conditions x1(0)=1x_1(0) = 1 and x2(0)=0x_2(0) = 0.
    If r(t)={1,t≥00,t<0r(t) = \begin{cases} 1, & t \geq 0 \\ 0, & t < 0 \end{cases}, then at t=1t = 1, x1(t)=x_1(t) =__________ (round off to the nearest integer).
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    Question

    Let CC be a clockwise oriented closed curve in the complex plane defined by ∣z∣=1|z| = 1. Further, let f(z)=jzf(z) = jz be a complex function, where j=−1j = \sqrt{-1}. Then, ∮Cf(z)dz=_______\oint_C f(z) dz = \_\_\_\_\_\_\_ (round off to the nearest integer).
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    The op-amps in the following circuit are ideal. The voltage gain of the circuit is ____ (round off to the nearest integer).
    A circuit diagram with two operational amplifiers and four 10 kΩ resistors.
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    Question

    The switch (S) closes at t=0t = 0 sec. The time, in sec, the capacitor takes to charge to 50 V is _____ (round off to one decimal place).

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    Question

    In an experiment to measure the active power drawn by a single-phase RL Load connected to an AC source through a 2 Ω2\ \Omega resistor, three voltmeters are connected as shown in the figure below. The voltmeter readings are as follows: VSource=200 VV_{\text{Source}} = 200\ V, VR=9 VV_R = 9\ V, VLoad=199 VV_{\text{Load}} = 199\ V. Assuming perfect resistors and ideal voltmeters, the Load-active power measured in this experiment, in W, is ________ (round off to one decimal place).

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    In the Wheatstone bridge shown below, the sensitivity of the bridge in terms of change in balancing voltage EE for unit change in the resistance RR, in mV/Ω\Omega, is ______________ (round off to two decimal places).

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    Question

    The steady state capacitor current of a conventional DC-DC buck converter, working in CCM, is shown in one switching cycle. If the input voltage is 30 V30\ V, the value of the inductor used, in mH, is _____________ (round off to one decimal place).
    Capacitor current waveform $i_C(t)$ for a buck converter over one switching cycle
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    An ideal low pass filter has frequency response given by H(jω)={1,∣ω∣≤200π0,otherwiseH(j\omega) = \begin{cases} 1, & |\omega| \leq 200\pi \\ 0, & otherwise \end{cases}Let h(t)h(t) be its time domain representation. Then h(0)=________h(0) = \_\_\_\_\_\_\_\_ (round off to the nearest integer).
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    Consider the state-space modelx˙(t)=Ax(t)+Br(t),\dot{\mathbf{x}}(t) = A\mathbf{x}(t) + Br(t),y(t)=Cx(t)y(t) = C\mathbf{x}(t)where x(t),r(t),y(t)\mathbf{x}(t), r(t), y(t) are the state, input and output, respectively. The matrices A,B,CA, B, C are given belowA=[01−2−3],B=[01],C=[10]A = \begin{bmatrix} 0 & 1 \\ -2 & -3 \end{bmatrix}, B = \begin{bmatrix} 0 \\ 1 \end{bmatrix}, C = \begin{bmatrix} 1 & 0 \end{bmatrix}The sum of the magnitudes of the poles is _______________ (round off to nearest integer).
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    Question

    Using shunt capacitors, the power factor of a 3-phase, 4 kV4 \text{ kV} induction motor (drawing 390 kVA390 \text{ kVA} at 0.77 pf lag0.77 \text{ pf lag}) is to be corrected to 0.85 pf lag0.85 \text{ pf lag}. The line current of the capacitor bank, in A\text{A}, is ____________ (round off to one decimal place).
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    Two units, rated at 100 MW and 150 MW, are enabled for economic load dispatch. When the overall incremental cost is 10,000 Rs./MWh, the units are dispatched to 50 MW and 80 MW respectively. At an overall incremental cost of 10,600 Rs./MWh, the power output of the units are 80 MW and 92 MW, respectively. The total plant MW-output (without overloading any unit) at an overall incremental cost of 11,800 Rs./MWh is ________ (round off to the nearest integer).
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    A controller D(s)D(s) of the form (1+KDs)(1 + K_D s) is to be designed for the plant G(s)=10002s(s+10)2G(s) = \frac{1000\sqrt{2}}{s(s+10)^2} as shown in the figure. The value of KDK_D that yields a phase margin of 45∘45^\circ at the gain cross-over frequency of 10 rad/sec10 \text{ rad/sec} is ________________ (round off to one decimal place).

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