GATE 2019 Electronics & Communication

It would take one machine 4 hours to complete a production order and another machine 2 hours to complete the same order. If both machine work simultaneously at their respective con...

Four people are standing in a line facing you. They are Rahul, Mathew, Seema and Lohit. One is engineer, one is a doctor, one a teacher and another a dancer. You are told that : 1....

"Indian history was written by British historians – extremely well documented and researched, but not always impartial. History had to serve its purpose : Everything was made subse...

Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when hour hand moved by 210...

The strategies that the company _______ to sell its products ________ house-to-house marketing.

When he did not come home, she ___ him lying dead on the roadside somewhere.

Five people P, Q, R, S and T work in a bank. P and Q don’t like each other but have to share an office till T gets a promotion and moves to the big office next to the garden. R, wh...

Five different books (P, Q, R, S, T) are to be arranged on a shelf. The books R and S are to be arranged first and second respectively from right side of the shelf. The number of d...

The boat arrived _______ dawn.

The families of curves represented by the solution of the equation $${{dy} \over {dx}} = - {\left( {{x \over y}} \right)^n}$$ for n = –1 and n = 1 respectively, are

The strategies that the company ________ to sell its products ________ house-to-house marketing.

Which one of the following functions is analytic over the entire complex plane?

The boat arrived ________ dawn.

The families of curves represented by the solution of the equation dy/dx = -(x/y)^n for n = -1 and n = +1, respectively, are

Let H(z) be the z-transform of a real-valued discrete-time signal h[n]. If P(z) = H(z)H(1/z) has a zero at z = 1/2 + 1/2j, and P(z) has a total of four zeros, which one of the foll...

It would take one machine 4 hours to complete a production order and another machine 2 hours to complete the same order. If both machines work simultaneously at their respective co...

Consider the two-port resistive network shown in the figure. When an excitation of 5 V is applied across Port 1, and Port 2 is shorted, the current through the short circuit at Por...

Five different books (P, Q, R, S, T) are to be arranged on a shelf. The books R and S are to be arranged first and second, respectively from the right side of the shelf. The number...

When he did not come home, she ________ him lying dead on the roadside somewhere.

Let Y(s) be the unit-step response of a causal system having a transfer function $G(s) = \frac{3-s}{(s+1)(s+3)}$. That is, $Y(s) = \frac{G(s)}{s}$. The forced response of the syste...

Four people are standing in a line facing you. They are Rahul, Mathew, Seema and Lohit. One is an engineer, one is a doctor, one a teacher and another a dancer. You are told that:...

For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles Np and the number of system zeros Nz in the frequency range 1 Hz ≤ f...

A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is linear. If the message 0001 is mapped to the codeword 0000111, and the message 0011 i...

The bar graph in Panel (a) shows the proportion of male and female illiterates in 2001 and 2011. The proportions of males and females in 2001 and 2011 are given in Panel (b) and (c...

"Indian history was written by British historians – extremely well documented and researched, but not always impartial. History had to serve its purpose: Everything was made subser...

Which one of the following options describes correctly the equilibrium band diagram at T=300 K of a Silicon pnn+p++ configuration shown in the figure?

Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when the hour hand moved by...

The correct circuit representation of the structure shown in the figure is

Five people P, Q, R, S and T work in a bank. P and Q don't like each other but have to share an office till T gets a promotion and moves to the big office next to the garden. R, wh...

The figure shows the high-frequency C-V curve of a MOS capacitor (at T = 300 K) with Φms = 0 V and no oxide charges. The flat-band, inversion, and accumulation conditions are repre...

What is the electric flux (∫ E ⋅ da) through a quarter-cylinder of height H (as shown in the figure) due to an infinitely long line charge along the axis of the cylinder with a cha...

In the table shown, List I and List II, respectively, contain terms appearing on the left-hand side and the right-hand side of Maxwell's equations (in their standard form). Match t...

A standard CMOS inverter is designed with equal rise and fall times ($\beta_n = \beta_p$). If the width of the pMOS transistor in the inverter is increased, what would be the effec...

In the circuit shown, what are the values of F for EN = 0 and EN = 1, respectively?

In the circuit shown, A and B are the inputs and F is the output. What is the functionality of the circuit?

The value of the contour integral $\frac{1}{2\pi j} \oint (z + \frac{1}{z})^2 dz$ evaluated over the unit circle $|z| = 1$ is ________.

The number of distinct eigenvalues of the matrix $A = \begin{bmatrix} 2 & 2 & 3 & 3 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 3 & 3 \\ 0 & 0 & 0 & 2 \end{bmatrix}$ is equal to ________.

If X and Y are random variables such that E[2X + Y] = 0 and E[X + 2Y] = 33, then E[X] + E[Y] = _________.

The value of the integral $\int_0^\pi \int_y^\pi \frac{\sin x}{x} dx dy$, is equal to _________.

Let Z be an exponential random variable with mean 1. That is, the cumulative distribution function of Z is given by $F_Z(x) = \begin{cases} 1 - e^{-x} & \text{if } x \ge 0 \\ 0 & \...

Consider the signal $f(t) = 1 + 2 \cos(\pi t) + 3 \sin(\frac{2\pi}{3} t) + 4 \cos(\frac{\pi}{2} t + \frac{\pi}{4})$, where t is in seconds. Its fundamental time period, in seconds,...

The baseband signal m(t) shown in the figure is phase-modulated to generate the PM signal $\varphi(t) = \cos(2\pi f_c t + k m(t))$. The time t on the x-axis in the figure is in mil...

Radiation resistance of a small dipole current element of length l at a frequency of 3 GHz is 3 ohms. If the length is changed by 1%, then the percentage change in the radiation re...

In the circuit shown, V_S is a square wave of period T with maximum and minimum values of 8 V and -10 V, respectively. Assume that the diode is ideal and R_1 = R_2 = 50 Ω. The aver...

In the circuit shown, the clock frequency, i.e., the frequency of the Clk signal, is 12 kHz. The frequency of the signal at Q_2 is _________ kHz.

Consider a differentiable function f (x) on the set of real numbers such that f(-1) = 0 and |f'(x)| ≤ 2. Given these conditions, which one of the following inequalities is necessar...

Consider the line integral ∫_C (xdy - ydx) the integral being taken in a counterclockwise direction over the closed curve C that forms the boundary of the region R shown in the fig...

Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal-flow graph corresponding to X[1] is shown in the figure. Let $W_6 = \exp\left(-...

It is desired to find a three-tap causal filter which gives zero signal as an output to an input of the form $x[n] = c_1 \exp\left(-\frac{j\pi n}{2}\right) + c_2 \exp\left(\frac{j\...

In the circuit shown, if v(t) = 2 sin(1000 t) volts, R = 1 kΩ and C = 1 µF, then the steady-state current i(t), in milliamperes (mA), is

Consider a causal second-order system with the transfer function G(s) = \frac{1}{1 + 2s + s^2} with a unit-step R(s) = \frac{1}{s} as an input. Let C(s) be the corresponding output...

The block diagram of a system is illustrated in the figure shown, where X(s) is the input and Y(s) is the output. The transfer function H(s) = \frac{Y(s)}{X(s)} is

Let the state-space representation of an LTI system be $\dot{x}(t) = A x(t) + B u(t)$, $y(t) = C x(t) + d u(t)$ where A, B, C are matrices, d is a scalar, u(t) is the input to the...

A single bit, equally likely to be 0 and 1, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density $N_0/2$. Binary signaling, with $0 \map...

The quantum efficiency ($\eta$) and responsivity (R) at a wavelength $\lambda$ (in $\mu$m) in a p-i-n photodetector are related by

Two identical copper wires W1 and W2, placed in parallel as shown in the figure, carry currents I and 2I, respectively, in opposite directions. If the two wires are separated by a...

The dispersion equation of a waveguide, which relates the wavenumber k to the frequency $\omega$, is $k(\omega) = (1/c)\sqrt{\omega^2 - \omega_0^2}$ where the speed of light $c = 3...

In the circuit shown, the breakdown voltage and the maximum current of the Zener diode are 20 V and 60 mA, respectively. The values of R1 and RL are 200 Ω and 1 kΩ, respectively. W...

The state transition diagram for the circuit shown is

In the circuits shown, the threshold voltage of each nMOS transistor is 0.6 V. Ignoring the effect of channel length modulation and body bias, the values of Vout1 and Vout2, respec...

The RC circuit shown below has a variable resistance R(t) given by the following expression: R(t) = R₀ (1 - t/T) for 0 ≤ t < T where R₀ = 1 Ω, and C = 1 F. We are also given that T...

Consider a unity feedback system, as in the figure shown, with an integral compensator $\frac{K}{s}$ and open-loop transfer function $G(s) = \frac{1}{s^2 + 3s + 2}$ where K > 0. Th...

Consider the homogeneous ordinary differential equation $x^2 \frac{d^2y}{dx^2} - 3x \frac{dy}{dx} + 3y = 0$, $x > 0$ with $y(x)$ as a general solution. Given that $y(1) = 1$ and $y...

Let $h[n]$ be a length-7 discrete-time finite impulse response filter, given by $h[0] = 4$, $h[1] = 3$, $h[2] = 2$, $h[3] = 1$, $h[-1] = -3$, $h[-2] = -2$, $h[-3] = -1$, and $h[n]$...

Let a random process Y(t) be described as Y(t) = h(t) * X(t) + Z(t), where X(t) is a white noise process with power spectral density Sx (f) = 5 W/Hz. The filter h(t) has a magnitud...

A voice signal m(t) is in the frequency range 5 kHz to 15 kHz. The signal is amplitude-modulated to generate an AM signal f(t) = A(1 + m(t)) cos 2πfct, where fc = 600 kHz. The AM s...

A random variable X takes values -1 and +1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise N, so that the random variable at the c...

A Germanium sample of dimensions 1 cm × 1 cm is illuminated with a 20 mW, 600 nm laser light source as shown in the figure. The illuminated sample surface has a 100 nm of loss-less...

In an ideal pn junction with an ideality factor of 1 at T=300 K, the magnitude of the reverse-bias voltage required to reach 75% of its reverse saturation current, rounded off to 2...

Consider a long-channel MOSFET with a channel length 1 µm and width 10 µm. The device parameters are acceptor concentration N_A= 5 × 10¹⁶ cm⁻³, electron mobility µ_n=800 cm²/V-s, o...

A rectangular waveguide of width w and height h has cut-off frequencies for TE₁₀ and TE₁₁ modes in the ratio 1: 2. The aspect ratio w/h, rounded off to two decimal places, is _____...

In the circuit shown, Vs is a 10 V square wave of period, T = 4 ms with R = 500 Ω and C = 10 µF. The capacitor is initially uncharged at t=0, and the diode is assumed to be ideal....

A CMOS inverter, designed to have a mid-point voltage V_I equal to half of Vdd, as shown in the figure, has the following parameters: Vdd = 3 V μn Cox = 100 μA/V^2 ; Vtn = 0.7 V fo...

In the circuit shown, the threshold voltages of the pMOS (|Vtp|) and nMOS (Vtn) transistors are both equal to 1 V. All the transistors have the same output resistance rds of 6 MΩ....

In the circuit shown, V₁ = 0 and V₂ = Vdd. The other relevant parameters are mentioned in the figure. Ignoring the effect of channel length modulation and the body effect, the valu...