GATE 2024 EC – Previous Year Questions with Solutions
All 65 questions of GATE 2024 EC with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – If ‘’ denotes increasing order of intensity, then the meaning of the words [charm enamor bewitch] is analogous to [bored weary]. Which one of the…
- Question 2 – P, Q, R, S, and T have launched a new startup. Two of them are siblings. The office of the startup has just three rooms. All of them agree that the…
- Question 3 – Five years ago, the ratio of Aman’s age to his father’s age was 1:4, and five years from now, the ratio will be 2:5. What was his father’s age when…
- Question 4 – For a real number x>1, 1 2x+1 3x+1 4x=1 The value of x is
- Question 5 – The greatest prime factor of (3199-3196) is
- Question 6 – Sequence the following sentences (P, Q, R, S) in a coherent passage: P: Shifu’s student exclaimed, “Why do you run since the bull is an illusion?” Q:…
- Question 7 – Four identical cylindrical chalk-sticks, each of radius r=0.5 cm and length l=10 cm, are bound tightly together using a duct tape as shown in the…
- Question 8 – The bar chart shows the data for the percentage of population falling into different categories based on Body Mass Index (BMI) in 2003 and 2023. Based…
- Question 9 – Examples of mirror and water reflections are shown in the figures below: An object appears as the following image after first reflecting in a mirror…
- Question 10 – Two identical sheets A and B, of dimensions 24 cm × 16 cm, can be folded into half using two distinct operations, FO1 or FO2. In FO1, the axis of…
- Question 11 – The general form of the complementary function of a differential equation is given by y(t)=(At+B)e-2t, where A and B are real constants determined by…
- Question 12 – In the context of Bode magnitude plots, 40 dB/decade is the same as .
- Question 13 – In the feedback control system shown in the figure below, G(s)=6s(s+1)(s+2). R(s), Y(s), and E(s) are the Laplace transforms of r(t), y(t), and e(t),…
- Question 14 – A digital communication system transmits through a noiseless bandlimited channel [-W,W]. The received signal z(t) at the output of the receiving…
- Question 15 – Consider a lossless transmission line terminated with a short circuit as shown in the figure below. As one moves towards the generator from the load,…
- Question 16 – Let i and j be the unit vectors along x and y axes, respectively and let A be a positive constant. Which one of the following statements is true for…
- Question 17 – In the circuit below, assume that the long channel NMOS transistor is biased in saturation. The small signal trans-conductance of the transistor is g…
- Question 18 – For the closed loop amplifier circuit shown below, the magnitude of open loop low frequency small signal voltage gain is 40. All the transistors are…
- Question 19 – For the Boolean function F(A,B,C,D)= m(0,2,5,7,8,10,12,13,14,15), the essential prime implicants are .
- Question 20 – A white Gaussian noise w(t) with zero mean and power spectral density N 02, when applied to a first-order RC low pass filter produces an output n(t).…
- Question 21 – A causal and stable LTI system with impulse response h(t) produces an output y(t) for an input signal x(t). A signal x(0.5t) is applied to another…
- Question 22 – For non-degenerately doped n-type silicon, which one of the following plots represents the temperature (T) dependence of free electron concentration…
- Question 23 – In the circuit shown, the n:1 step-down transformer and the diodes are ideal. The diodes have no voltage drop in forward biased condition. If the…
- Question 24 – For a causal discrete-time LTI system with transfer function H(z)=2z2+3(z+13)(z-13), which of the following statements is/are true?
- Question 25 – Let (x,y,z,t) and u(x,y,z,t) represent density and velocity, respectively, at a point (x,y,z) and time t. Assume t is continuous. Let V be an…
- Question 26 – The free electron concentration profile n(x) in a doped semiconductor at equilibrium is shown in the figure, where the points A, B, and C mark three…
- Question 27 – A machine has a 32-bit architecture with 1-word long instructions. It has 24 registers and supports an instruction set of size 40. Each instruction…
- Question 28 – An amplitude modulator has output (in Volts) s(t)=A(400 t)+B(360 t)+B(440 t). The carrier power normalized to 1\ resistance is 50 Watts. The ratio of…
- Question 29 – In a number system of base r, the equation x2-12x+37=0 has x=8 as one of its solutions. The value of r is .
- Question 30 – Let R and R3 denote the set of real numbers and the three dimensional vector space over it, respectively. The value of for which the set of vectors…
- Question 31 – In the given circuit, the current I x (in mA) is .
- Question 32 – In the circuit given below, the switch S was kept open for a sufficiently long time and is closed at time t=0. The time constant (in seconds) of the…
- Question 33 – Suppose X and Y are independent and identically distributed random variables that are distributed uniformly in the interval [0,1]. The probability…
- Question 34 – A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is .
- Question 35 – As shown in the circuit, the initial voltage across the capacitor is 10 V, with the switch being open. The switch is then closed at t=0. The total…
- Question 36 – Consider the Earth to be a perfect sphere of radius R. Then the surface area of the region, enclosed by the 60N latitude circle, that contains the…
- Question 37 – Consider a unity negative feedback control system with forward path gain G(s)=K(s+1)(s+2)(s+3) as shown. The impulse response of the closed-loop…
- Question 38 – A satellite attitude control system, as shown below, has a plant with transfer function G(s)=1s2 cascaded with a compensator C(s)=K(s+)s+4, where K…
- Question 39 – A uniform plane wave with electric field E(x)=A y a ye-j2 x3 V/m is travelling in the air (relative permittivity, r=1 and relative permeability, r=1)…
- Question 40 – A 4-bit priority encoder has inputs D 3, D 2, D 1, and D 0 in descending order of priority. The two-bit output AB is generated as 00, 01, 10, and 11…
- Question 41 – The propagation delay of the 21 MUX shown in the circuit is 10 ns. Consider the propagation delay of the inverter as 0 ns. If S is set to 1 then the…
- Question 42 – The sequence of states (Q 1Q 0) of the given synchronous sequential circuit is .
- Question 43 – Let z be a complex variable. If f(z)=( z)z2(z-2) and C is the circle in the complex plane with z =3 then Cf(z)\,dz is .
- Question 44 – Consider two continuous time signals x(t) and y(t) as shown below. If X(f) denotes the Fourier transform of x(t), then the Fourier transform of y(t)…
- Question 45 – A source transmits a symbol s, taken from \-4,0,4\ with equal probability, over an additive white Gaussian noise channel. The received noisy symbol r…
- Question 46 – A full scale sinusoidal signal is applied to a 10-bit ADC. The fundamental signal component in the ADC output has a normalized power of 1 W, and the…
- Question 47 – The information bit sequence \1\ 1\ 1\ 0\ 1\ 0\ 1\ 0\ 1\ is to be transmitted by encoding with Cyclic Redundancy Check 4 (CRC-4) code, for which the…
- Question 48 – A continuous time signal x(t)=2(8 t+/3) is sampled at a rate of 15 Hz. The sampled signal x s(t) when passed through an LTI system with impulse…
- Question 49 – The opamps in the circuit shown are ideal, but have saturation voltages of 10 V. Assume that the initial inductor current is 0 A. The input voltage (V…
- Question 50 – In the circuit below, the opamp is ideal. If the circuit is to show sustained oscillations, the respective values of R 1 and the corresponding…
- Question 51 – In the circuit shown below, the transistors M 1 and M 2 are biased in saturation. Their small signal transconductances are g m1 and g m2,…
- Question 52 – Which of the following statements is/are true for a BJT with respect to its DC current gain ?
- Question 53 – Consider a system S represented in state space as dxdt=bmatrix0&-2\\1&-3bmatrixx+bmatrix1\\0bmatrixr, y=bmatrix2&-5bmatrixx. Which of the state space…
- Question 54 – Let F 1, F 2, and F 3 be functions of (x,y,z). Suppose that for every given pair of points A and B in space, the line integral C(F 1dx+F 2dy+F 3dz)…
- Question 55 – Consider the matrix bmatrix1&k\\2&1bmatrix, where k is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix?
- Question 56 – The radian frequency value(s) for which the discrete time sinusoidal signal x[n]=A( n+/3) has a period of 40 is/are .
- Question 57 – Let X(t)=A(2 f 0t+) be a random process, where amplitude A and phase are independent of each other, and are uniformly distributed in the intervals…
- Question 58 – A lossless transmission line with characteristic impedance Z 0=50\ is terminated with an unknown load. The magnitude of the reflection co-efficient is…
- Question 59 – The relationship between any N-length sequence x[n] and its corresponding N-point discrete Fourier transform X[k] is defined as X[k]= F\x[n]\. Another…
- Question 60 – For the two port network shown below, the value of the Y 21 parameter (in Siemens) is .
- Question 61 – A MOS capacitor made with p-type silicon. It has an oxide thickness of 100 nm, a fixed positive oxide charge of 10-8 C/cm2 at the oxide-silicon…
- Question 62 – In the network shown below, maximum power is to be transferred to the load R L. The value of R L (in Ω) is .
- Question 63 – A non-degenerate n-type semiconductor has 5% neutral dopant atoms. Its Fermi level is located at 0.25 eV below the conduction band (E C) and the donor…
- Question 64 – An NMOS transistor operating in the linear region has I DS of 5 μA at V DS of 0.1 V. Keeping V GS constant, the V DS is increased to 1.5 V. Given that…
- Question 65 – The photocurrent of a PN junction diode solar cell is 1 mA. The voltage corresponding to its maximum power point is 0.3 V. If the thermal voltage is…