GATE 2025 Electronics & Communication

Consider an additive white Gaussian noise (AWGN) channel with bandwidth $W$ and noise power spectral density $\frac{N_o}{2}$. Let $P_{a v}$ denote the average transmit power constr...

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 of $X$ is ___________ (roun...

Had I learnt acting as a child, I__________a famous film star. Select the most appropriate option to complete the above sentence.

An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is 20\% of the consulting fee, if the...

Which of the following statements is/are TRUE with respect to an ideal opamp?

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 medals won by them. Based only o...

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. Group-I: Abuse $\rightarrow$ Ins...

Identify the option that has the most appropriate sequence such that a coherent paragraph is formed: P. Over time, such adaptations lead to significant evolutionary changes with th...

Consider the matrix $A$ below: $$ A=\left[\begin{array}{llll} 2 & 3 & 4 & 5 \\ 0 & 6 & 7 & 8 \\ 0 & 0 & \alpha & \beta \\ 0 & 0 & 0 & \gamma \end{array}\right] $$ For which of the...

Which of the following statements is/are TRUE with respect to ideal MOSFET-based DCcoupled single-stage amplifiers having finite load resistors?

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 frequency 500 kHz , the maximum...

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 the system are given by...

The 12 musical notes are given as $C, C^{\#}, D, D^{\#}, E, F, F^{\#}, G, G^{\#}, A, A^{\#}$. Frequency of each note is $\sqrt[12]{2}$ times the frequency of the previous note. If...

Consider the vectors $$ a=\left[\begin{array}{l} 1 \\ 1 \end{array}\right], b=\left[\begin{array}{c} 0 \\ 3 \sqrt{2} \end{array}\right] $$ For real-valued scalar variable $x$, the...

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 minimum values of $f(x)...

The function $y(t)$ satisfies $$ t^2 y^{\prime \prime}(t)-2 t y^{\prime}(t)+2 y(t)=0 $$ where $y^{\prime}(t)$ and $y^{\prime \prime}(t)$ denote the first and second derivatives of...

Which of the following statements involving contour integrals (evaluated counter-clockwise) on the unit circle $C$ in the complex plane is/are TRUE?

Consider the polynomial $p(s)=s^5+7 s^4+3 s^3-33 s^2+2 s-40$. Let $(L, I, R)$ be defined as follows. $L$ is the number of roots of $p(s)$ with negative real parts. $I$ is the numbe...

Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined as $$ f(x)=2 x^3-3 x^2-12 x+1 $$ Which of the following statements is/are correct? (Here, $\mathbb{R}$ is the s...

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 $F$ is logic ' 0 ' if tw...

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 balls drawn have different col...

Which one of the following plots represents $f(x)=-\frac{|x|}{x}$, where $x$ is a non-zero real number? Note: The figures shown are representative.

Consider a continuous-time finite-energy signal $f(t)$ whose Fourier transform vanishes outside the frequency interval $\left[-\omega_c, \omega_c\right]$, where $\omega_c$ is in ra...

Consider a continuous-time, real-valued signal $f(t)$ whose Fourier transform $F(\omega)=$$\mathop f\limits_{ - \infty }^\infty $$ f(t) \exp (-j \omega t) d t$ exists. Which one of...

The electron mobility $\mu_n$ in a non-degenerate germanium semiconductor at 300 K is $0.38 \mathrm{~m}^2 / \mathrm{Vs}$. The electron diffusivity $D_n$ at 300 K (in $\mathrm{cm}^2...

The intrinsic carrier concentration of a semiconductor is $2.5 \times 10^{16} / \mathrm{m}^3$ at 300 K . If the electron and hole mobilities are $0.15 \mathrm{~m}^2 / \mathrm{Vs}$...

An ideal p-n junction germanium diode has a reverse saturation current of $10 \mu \mathrm{~A}$ at 300 K . The voltage (in Volts, rounded off to two decimal places) to be applied ac...

Let $x[n]$ be a discrete-time signal whose $z$-transform is $X(z)$. Which of the following statements is/are TRUE?

Let $f(t)$ be a periodic signal with fundamental period $T_0>0$. Consider the signal $y(t)=f(\alpha t)$, where $\alpha>1$. The Fourier series expansions of $f(t)$ and $y(t)$ are gi...

Which of the following can be used as an n-type dopant for silicon? Select the correct option(s).

Consider a real-valued random process $$ f(t)=\sum\limits_{n=1}^N a_n p(t-n T), $$ where $T>0$ and $N$ is a positive integer. Here, $p(t)=1$ for $t \in[0,0.5 T]$ and 0 otherwise. T...

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 random variable indep...

$X$ and $Y$ are Bernoulli random variables taking values in $\{0,1\}$. The joint probability mass function of the random variables is given by: $$ \begin{aligned} & P(X=0, Y=0)=0.0...

A $50 \Omega$ lossless transmission line is terminated with a load $Z_L$ of $(50-j 75) \Omega$. If the average incident power on the line is 10 mW , then the average power delivere...

The random variable $X$ takes values in $\{-1,0,1\}$ with probabilities $P(X=-1)=P(X=1)$ and $\alpha$ and $P(X=0)=1-2 \alpha$, where $0 Let $g(\alpha)$ denote the entropy of $X$ (i...

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: Double sideband-suppr...

The generator matrix of a $(6,3)$ binary linear block code is given by $$ G=\left[\begin{array}{llllll} 1 & 0 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 1 & 1 & 0 \end...

Consider a frequency-modulated (FM) signal $$ f(t)=A_c \cos \left(2 \pi f_c t+3 \sin \left(2 \pi f_1 t\right)+4 \sin \left(6 \pi f_1 t\right)\right) $$ where $A_c$ and $f_c$ are, r...

Consider the following series: (i) $\sum\limits_{n=1}^{\infty} \frac{1}{\sqrt{n}}$ (ii) $ \sum\limits_{n=1}^{\infty} \frac{1}{n(n+1)}$ (iii) $\sum\limits_{n=1}^{\infty} \frac{1}{n!...

An electric field of $0.01 \mathrm{~V} / \mathrm{m}$ is applied along the length of a copper wire of circular crosssection with diameter 1 mm . Copper has a conductivity of $5.8 \t...

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. Group-I: Abuse → Insult → Ridicu...

Had I learnt acting as a child, I ________ a famous film star. Select the most appropriate option to complete the above sentence.

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 $\sqrt[12]{2}$ times the frequency of the previous note. If the frequency o...

The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after 'Iteration n' is: Note: The figures shown are represen...

Which one of the following plots represents $f(x) = -\frac{|x|}{x}$, where x is a non-zero real number? Note: The figures shown are representative.

Identify the option that has the most appropriate sequence such that a coherent paragraph is formed: P. Over time, such adaptations lead to significant evolutionary changes with th...

A stick of length one meter is broken at two locations at distances of b₁ and b₂ from the origin (0), as shown in the figure. Note that 0 < b₁ < b₂ < 1. Which one of the following...

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 play the game by moving forward...

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 medals won by them. Based only o...

An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is 20% of the consulting fee, if the...

Consider the matrix A below: A = $\begin{bmatrix} 2 & 3 & 4 & 5 \\ 0 & 6 & 7 & 8 \\ 0 & 0 & \alpha & \beta \\ 0 & 0 & 0 & \gamma \end{bmatrix}$ For which of the following combinati...

Consider the following series: (i) $\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}}$ (ii) $\sum_{n=1}^{\infty} \frac{1}{n(n+1)}$ (iii) $\sum_{n=1}^{\infty} \frac{1}{n!}$ Choose the correct...

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 balls drawn have different col...

Consider a frequency-modulated (FM) signal $f(t) = A_c \cos(2\pi f_c t + 3 \sin(2\pi f_1 t) + 4 \sin(6\pi f_1 t))$, where $A_c$ and $f_c$ are, respectively, the amplitude and frequ...

Consider an additive white Gaussian noise (AWGN) channel with bandwidth W and noise power spectral density $\frac{N_0}{2}$. Let $P_{av}$ denote the average transmit power constrain...

The Nyquist plot of a system is given in the figure below. Let $\omega_P, \omega_Q, \omega_R$, and $\omega_S$ be the positive frequencies at the points P, Q, R, and S, respectively...

Consider the discrete-time system below with input x[n] and output y[n]. In the figure, h₁[n] and h₂[n] denote the impulse responses of LTI Subsystems 1 and 2, respectively. Also,...

Consider a continuous-time, real-valued signal f(t) whose Fourier transform F(ω) = ∫_(-∞)^∞ f(t) exp(-j ωt) dt exists. Which one of the following statements is always TRUE?

Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the 3Ω resistor are as indicated. The voltage (in Volts) at node X is _...

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 admittances are given in Siemens...

A simplified small-signal equivalent circuit of a BJT-based amplifier is given below. The small-signal voltage gain Vo/Vs (in V/V) is _________.

The ideal BJT in the circuit given below is biased in the active region with a β of 100. If I_B is 10 µA, then V_CE (in Volts, rounded off to two decimal places) is ________.

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 is logic '0' if two or more of...

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 the carry-in input of the full...

Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$, defined as $f(x) = 2x^3 - 3x^2 - 12x + 1$. Which of the following statements is/are correct? (Here, $\mathbb{R}$ is th...

Consider the unity-negative-feedback system shown in Figure (i) below, where gain K ≥ 0. The root locus of this system is shown in Figure (ii) below. For what value(s) of K will th...

Let x[n] be a discrete-time signal whose Z-transform is X(z). Which of the following statements is/are TRUE?

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: * Double sideband-supp...

Which of the following statements is/are TRUE with respect to an ideal opamp?

Which of the following statements is/are TRUE with respect to ideal MOSFET-based DC-coupled single-stage amplifiers having finite load resistors?

Which of the following can be used as an n-type dopant for silicon? Select the correct option(s).

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 y'(0) = 1 and y'(1) = −1, th...

The generator matrix of a (6,3) binary linear block code is given by G = [1 0 0 1 0 1; 0 1 0 0 1 1; 0 0 1 1 1 0]. The minimum Hamming distance d_min between codewords equals ______...

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, rounded off to the nearest int...

A 4-bit weighted-resistor DAC with inputs b3, b2, b1, and b0 (MSB to LSB) is designed using an ideal opamp, as shown below. The switches are closed when the corresponding input bit...

Let $G(s) = \frac{1}{10s^2}$ 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. Consider the...

Consider the polynomial p(s) = s^5 + 7s^4 + 3s^3 - 33s^2 + 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 the number...

Consider a continuous-time finite-energy signal $f(t)$ whose Fourier transform vanishes outside the frequency interval $[-\omega_c, \omega_c]$, where $\omega_c$ is in rad/sec. The...

In the circuit below, M₁ is an ideal AC voltmeter and M₂ is an ideal AC ammeter. The source voltage (in Volts) is v_s(t) = 100 cos(200t). What should be the value of the variable c...

The Z-parameter matrix of a two port network relates the port voltages and port currents as follows: $\begin{bmatrix} V_1 \\ V_2 \end{bmatrix} = Z \begin{bmatrix} I_1 \\ I_2 \end{b...

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 random variable independent...

Consider a real-valued random process $f(t) = \sum_{n=1}^{N} a_n p(t - nT)$, where $T > 0$ and $N$ is a positive integer. Here, $p(t) = 1$ for $t \in [0, 0.5T]$ and $0$ otherwise....

The identical MOSFETS M₁ and M₂ in the circuit given below are ideal and biased in the saturation region. M₁ and M₂ have a transconductance gₘ of 5 mS. The input signals (in Volts)...

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 frequency 500 kHz, the maximum S...

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 to logic '1' at all times. Th...

The intrinsic carrier concentration of a semiconductor is 2.5 x 10^16 /m³ at 300 K. If the electron and hole mobilities are 0.15 m²/Vs and 0.05 m²/Vs, respectively, then the intrin...

In the circuit shown, the identical transistors Q1 and Q2 are biased in the active region with β = 120. The Zener diode is in the breakdown region with Vz = 5 V and Iz = 25 mA. If...

The electron mobility μn in a non-degenerate germanium semiconductor at 300 K is 0.38 m²/Vs. The electron diffusivity Dn at 300 K (in cm²/s, rounded off to the nearest integer) is...

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 ρs(x, y) = 4|y|, then the total...

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 5.8 × 10^7 S/m. The current (i...

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 minimum values of $f(x)$...

Which of the following statements involving contour integrals (evaluated counter-clockwise) on the unit circle C in the complex plane is/are TRUE?

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 the system are given...

The random variable X takes values in {-1,0,1} with probabilities P(X = -1) = P(X = 1) = α and P(X = 0) = 1 − 2α, where 0 < α < 1/2. Let g(α) denote the entropy of X (in bits), par...

Let f (t) be a periodic signal with fundamental period T₀ > 0. Consider the signal y(t) = f(αt), where α > 1. The Fourier series expansions of f(t) and y(t) are given by f(t) = $\s...

Consider a system represented by the block diagram shown below. Which of the following signal flow graphs represent(s) this system? Choose the correct option(s).

All the diodes in the circuit given below are ideal. Which of the following plots is/are correct when Vᵢ (in Volts) is swept from -M to M?

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 of X is ________ (rounded off...

Consider the vectors $a = \begin{bmatrix} 1 \\ 1 \end{bmatrix}$, $b = \begin{bmatrix} 0 \\ 3\sqrt{2} \end{bmatrix}$. For real-valued scalar variable X, the value of $\min_{x} ||ax...

X and Y are Bernoulli random variables taking values in {0,1}. The joint probability mass function of the random variables is given by: $P(X = 0, Y = 0) = 0.06$ $P(X = 0, Y = 1) =...

The diode in the circuit shown below is ideal. The input voltage (in Volts) is given by V₁ = 10 sin 100πt, where time t is in seconds. The time duration (in ms, rounded off to two...

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 ns, and a clock-to-Q delay of 2...

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 be applied across the junctio...

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 power delivered to the load (i...

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 time-varying magnetic flux, with flux-...