GATE 2025 EC – Previous Year Questions with Solutions
All 65 questions of GATE 2025 EC with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Here are two analogous groups, Group-I and Group-II, that list words in their decreasing order of intensity. Identify the missing word in Group-II.…
- Question 2 – Had I learnt acting as a child, I a famous film star. Select the most appropriate option to complete the above sentence.
- Question 3 – The 12 musical notes are given as C, C\#, D, D\#, E, F, F\#, G, G\#, A, A\#, and B. Frequency of each note is [12]2 times the frequency of the…
- Question 4 – The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after ‘Iteration n’ is: Note:…
- Question 5 – Which one of the following plots represents f(x)=- x x, where x is a non-zero real number? Note: The figures shown are representative.
- Question 6 – Identify the option that has the most appropriate sequence such that a coherent paragraph is formed: P. Over time, such adaptations lead to…
- Question 7 – A stick of length one meter is broken at two locations at distances of b 1 and b 2 from the origin (0), as shown in the figure. Note that 0<b 1<b 2<1.…
- Question 8 – Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They…
- Question 9 – The table lists the top 5 nations according to the number of gold medals won in a tournament; also included are the number of silver and the bronze…
- Question 10 – An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is 20%…
- Question 11 – Consider the matrix A below: A=bmatrix2&3&4&5\\0&6&7&8\\0&0&&\\0&0&0&bmatrix For which of the following combinations of , , and , is the rank of A at…
- Question 12 – Consider the following series: (i) n=11 n (ii) n=11n(n+1) (iii) n=11n! Choose the correct option.
- Question 13 – A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement. What is the probability that the two…
- Question 14 – Consider a frequency-modulated (FM) signal f(t)=A c(2 f ct+3(2 f 1t)+4(6 f 1t)), where A c and f c are, respectively, the amplitude and frequency (in…
- Question 15 – Consider an additive white Gaussian noise (AWGN) channel with bandwidth W and noise power spectral density N 02. Let P av denote the average transmit…
- Question 16 – The Nyquist plot of a system is given in the figure below. Let P, Q, R, and S be the positive frequencies at the points P, Q, R, and S, respectively.…
- Question 17 – Consider the discrete-time system below with input x[n] and output y[n]. In the figure, h 1[n] and h 2[n] denote the impulse responses of LTI…
- Question 18 – Consider a continuous-time, real-valued signal f(t) whose Fourier transform F()= -f(t)(-j t)\,dt exists. Which one of the following statements is…
- Question 19 – Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the 3 Ω resistor are indicated. The…
- Question 20 – Let i C, i L, and i R be the currents flowing through the capacitor, inductor, and resistor, respectively, in the circuit given below. The AC…
- Question 21 – A simplified small-signal equivalent circuit of a BJT-based amplifier is given below. The small-signal voltage gain v o/v s (in V/V) is .
- Question 22 – The ideal BJT in the circuit given below is biased in the active region with a of 100. If I B is 10 μA, then V CE (in Volts, rounded off to two…
- Question 23 – A 3-input majority logic gate has inputs X, Y, and Z. The output F of the gate is logic ‘1’ if two or more of the inputs are logic ‘1’. The output F…
- Question 24 – A full adder and an XOR gate are used to design a digital circuit with inputs X, Y, and Z, and output F, as shown below. The input Z is connected to…
- Question 25 – Consider the function f:RR, defined as f(x)=2x3-3x2-12x+1. Which of the following statements is/are correct? (Here, R is the set of real numbers.)
- Question 26 – Consider the unity-negative-feedback system shown in Figure (i) below, where gain K0. The root locus of this system is shown in Figure (ii) below. For…
- Question 27 – Let x[n] be a discrete-time signal whose z-transform is X(z). Which of the following statements is/are TRUE?
- Question 28 – Consider a message signal m(t) which is bandlimited to [-W,W], where W is in Hz. Consider the following two modulation schemes for the message signal:…
- Question 29 – Which of the following statements is/are TRUE with respect to an ideal opamp?
- Question 30 – Which of the following statements is/are TRUE with respect to ideal MOSFET-based DC-coupled single-stage amplifiers having finite load resistors?
- Question 31 – Which of the following can be used as an n-type dopant for silicon? Select the correct option(s).
- Question 32 – The function y(t) satisfies t2y''(t)-2ty'(t)+2y(t)=0, where y'(t) and y''(t) denote the first and second derivatives of y(t), respectively. Given…
- Question 33 – The generator matrix of a (6,3) binary linear block code is given by G=bmatrix1&0&0&1&0&1\\0&1&0&0&1&1\\0&0&1&1&1&0bmatrix. The minimum Hamming…
- Question 34 – All the components in the bandpass filter given below are ideal. The lower -3 dB frequency of the filter is 1 MHz. The upper -3 dB frequency (in MHz,…
- Question 35 – A 4-bit weighted-resistor DAC with inputs b 3, b 2, b 1, and b 0 (MSB to LSB) is designed using an ideal opamp, as shown below. The switches are…
- Question 36 – Let G(s)=110s2 be the transfer function of a second-order system. A controller M(s) is connected to the system G(s) in the configuration shown below.…
- Question 37 – Consider the polynomial p(s)=s5+7s4+3s3-33s2+2s-40. Let (L,I,R) be defined as follows: L is the number of roots of p(s) with negative real parts. I is…
- Question 38 – Consider a continuous-time finite-energy signal f(t) whose Fourier transform vanishes outside the frequency interval [- c, c], where c is in rad/sec.…
- Question 39 – In the circuit below, M 1 is an ideal AC voltmeter and M 2 is an ideal AC ammeter. The source voltage (in Volts) is v s(t)=100(200t). What should be…
- Question 40 – The Z-parameter matrix of a two port network relates the port voltages and port currents as follows: bmatrixV 1\ 2bmatrix=ZbmatrixI 1\ 2bmatrix The…
- Question 41 – A source transmits symbol S that takes values uniformly at random from the set \-2,0,2\. The receiver obtains Y=S+N, where N is a zero-mean Gaussian…
- Question 42 – Consider a real-valued random process f(t)= n=1Na n\,p(t-nT), where T>0 and N is a positive integer. Here, p(t)=1 for t[0,0.5T] and 0 otherwise. The…
- Question 43 – The identical MOSFETs M 1 and M 2 in the circuit given below are ideal and biased in the saturation region. M 1 and M 2 have a transconductance g m of…
- Question 44 – A 10-bit analog-to-digital converter (ADC) has a sampling frequency of 1 MHz and a full scale voltage of 3.3 V. For an input sinusoidal signal with…
- Question 45 – A positive-edge-triggered sequential circuit is shown below. There are no timing violations in the circuit. Input P0 is set to logic ‘0’ and P1 is set…
- Question 46 – The intrinsic carrier concentration of a semiconductor is 2.51016 /m3 at 300 K. If the electron and hole mobilities are 0.15 m2/Vs and 0.05 m2/Vs,…
- Question 47 – In the circuit shown, the identical transistors Q1 and Q2 are biased in the active region with =120. The Zener diode is in the breakdown region with V…
- Question 48 – The electron mobility n in a non-degenerate germanium semiconductor at 300 K is 0.38 m2/Vs. The electron diffusivity D n at 300 K (in cm2/s, rounded…
- Question 49 – A square metal sheet of 4 m × 4 m is placed on the x-y plane as shown in the figure below. If the surface charge density (in μC/m2) on the sheet is…
- Question 50 – An electric field of 0.01 V/m is applied along the length of a copper wire of circular cross-section with diameter 1 mm. Copper has a conductivity of…
- Question 51 – Consider a non-negative function f(x) which is continuous and bounded over the interval [2,8]. Let M and m denote, respectively, the maximum and the…
- Question 52 – Which of the following statements involving contour integrals (evaluated counter-clockwise) on the unit circle C in the complex plane is/are TRUE?
- Question 53 – Consider a system where x 1(t), x 2(t), and x 3(t) are three internal state signals and u(t) is the input signal. The differential equations governing…
- Question 54 – The random variable X takes values in \-1,0,1\ with probabilities P(X=-1)=P(X=1)= and P(X=0)=1-2, where 0<<12. Let g() denote the entropy of X (in…
- Question 55 – Let f(t) be a periodic signal with fundamental period T 0>0. Consider the signal y(t)=f( t), where >1. The Fourier series expansions of f(t) and y(t)…
- Question 56 – Consider a system represented by the block diagram shown below. Which of the following signal flow graphs represent(s) this system? Choose the correct…
- Question 57 – All the diodes in the circuit given below are ideal. Which of the following plots is/are correct when V I (in Volts) is swept from -M to M?
- Question 58 – Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled. Let the random variable X denote the sum of the outcomes obtained. The expectation…
- Question 59 – Consider the vectors a=bmatrix1\\1bmatrix, b=bmatrix0\\32bmatrix. For real-valued scalar variable x, the value of x\ ax- b\ 2 is (rounded off to two…
- Question 60 – X and Y are Bernoulli random variables taking values in \0,1\. The joint probability mass function of the random variables is given by:…
- Question 61 – The diode in the circuit shown below is ideal. The input voltage (in Volts) is given by V I=10100 t, where time t is in seconds. The time duration (in…
- Question 62 – In the circuit shown below, the AND gate has a propagation delay of 1 ns. The edge-triggered flip-flops have a set-up time of 2 ns, a hold-time of 0…
- Question 63 – An ideal p-n junction germanium diode has a reverse saturation current of 10 μA at 300 K. The voltage (in Volts, rounded off to two decimal places) to…
- Question 64 – A 50 Ω lossless transmission line is terminated with a load Z L of (50-j75) Ω. If the average incident power on the line is 10 mW, then the average…
- Question 65 – Two resistors are connected in a circuit loop of area 5 m2, as shown in the figure below. The circuit loop is placed on the x-y plane. When a…