GATE 2016 Electronics & Communication

The open-loop transfer function of a unity-feedback control system is $$$G\left(s\right)=\frac K{s^2+5s+5}$$$ The value of K at the breakaway point of the feedback control system's...

Consider a two-port network with the transmission matrix: T = $$\begin{bmatrix}A&B\\C&D\end{bmatrix}$$. If the network is reciprocal, then

The open-loop transfer function of a unity-feedback control system is $$$G\left(S\right)\;=\frac K{s(s\;+\;2)}$$$ For the peak overshoot of the closed-loop system to a unit step in...

Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh's Table of the system characteristic equation. X: The sys...

In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits. Of the unripe fruits, 45% are apples. Of the ripe ones, 66% are oranges. If the pi...

Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I li...

The transfer function of a linear time invariant system is given by $$H\left(s\right)\;=\;2s^4\;-\;5s^3\;+\;5s\;-\;2$$. The number of zeros in the right half of the s-plane is ____...

Two random variables $$X$$ and $$Y$$ are distributed according to $$${f_{X,Y}}\left( {x,y} \right) = \left\{ {\matrix{ {\left( {x + y} \right),} & {0 \le x \le 1,} & {0 \le y \le 1...

The integral $$\,\,{1 \over {2\pi }}\int {\int_D {\left( {x + y + 10} \right)dxdy\,\,} } $$ where $$D$$ denotes the disc: $${x^2} + {y^2} \le 4,$$ evaluates to _________.

Given the following statements about a function $$f:R \to R,$$ select the right option: $$P:$$ If $$f(x)$$ is continuous at $$x = {x_0},$$ then it is also differentiable at $$x = {...

In the following integral, the contour $$C$$ encloses the points $${2\pi j}$$ and $$-{2\pi j}$$. The value of the integral $$ - {1 \over {2\pi }}\oint\limits_c {{{\sin z} \over {{{...

A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C) elements, connected all in series or all in parallel, is excited with a source of th...

Let $${M^4} = {\rm I}$$ (where $${\rm I}$$ denotes the identity matrix) and $$M \ne {\rm I},\,\,{M^2} \ne {\rm I}$$ and $${M^3} \ne {\rm I}$$. Then, for any natural number $$k, $$...

An antenna pointing in a certain direction has a noise temperature of $$50K$$. The ambient temperature is $$290K$$. The antenna is connected to a pre-amplifier that has a noise fig...

The propagation constant of a lossy transmission line is (2 + j5) $${m^{ - 1}}$$ and its characteristic impedance is (50 + j0) $$\Omega $$ at $$\omega = \,{10^6}\,rad\,{S^{ - 1}}$$...

In an 8085 system, a PUSH operation requires more clock cycles than a POP operation. Which one of the following options is the correct reason for this?

Two lossless X-band horn antennas are separated by a distance of $$200\lambda $$. The amplitude reflection coefficients at the terminals of the transmitting and receiving antennas...

The electric field of a uniform plane wave travelling along the negative $$z$$ direction is given by the following equation: $$$\overrightarrow E {}_w^i = \left( {{{\widehat a}_{_x...

The second moment of a Poisson-distributed random variables is $$2.$$ The mean of the random variable is _______.

Consider binary data transmission at a rate of 56 kbps using baseband binary pulse amplitude modulation (PAM) that is designed to have a raised-cosine spectrum. The transmission ba...

An antenna pointing in a certain direction has a noise temperature of 50K. The ambient temperature is 290K. The antenna is connected to a pre-amplifier that has a noise figure of 2...

An analog pulse s(t) is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is r(t) = s(t) + n(t), where n(t) is additive white Gaussian noise wit...

Consider a discreet memoryless source with alphabet $$S = \left\{ {{s_0},\,{s_1},\,{s_2},\,{s_3},\,{s_{4......}}} \right\}$$ and respective probabilities of occurrence $$P = \left\...

A digital communication system uses a repetition code for channel encoding/decoding. During transmission, each bit is repeated three times (0 is transmitted as 000, and 1 is transm...

A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer function

A sequence $$x\left[ n \right]$$ is specified as $$$\left[ {\matrix{ {x\left[ n \right]} \cr {x\left[ {n - 1} \right]} \cr } } \right] = {\left[ {\matrix{ 1 & 1 \cr 1 & 0 \cr } } \...

The region specified by $$\left\{ {\left( {\rho ,\varphi ,{\rm Z}} \right):3 \le \rho \le 5,\,\,{\pi \over 8} \le \phi \le {\pi \over 4},\,\,3 \le z \le 4.5} \right\}$$ in cylindri...

Which one of the following is an eight function of the class of all continuous-time, linear, time- invariant systems u(t) denotes the unit-step function?

Consider the following statements for a metal oxide semiconductor field effect transistor (MOSFET): P: As channel length reduces, OFF-state current increases. Q:As channel length r...

Consider the signal $$x\left[ n \right] = 6\delta \left[ {n + 2} \right] + 3\delta \left[ {n + 1} \right] + 8\delta \left[ n \right] + 7\delta \left[ {n - 1} \right] + 4\delta \lef...

Consider an n-channel metal oxide semiconductor field effect transistor (MOSFET) with a gate-to-source voltage of 1.8 V. Assume that $${W \over L} = 4,{\mu _{\rm N}}{C_{ox}} = 70 \...

A continuous-time sinusoid of frequency 33 Hz is multiplied with a periodic Dirac impulse train of frequency 46 Hz. The resulting signal is passed through an ideal analog low-pass...

Consider the sequence $$x\left[ n \right]$$= $${a^n}u\left[ n \right] + {b^{\partial n}}u\left[ n \right]$$ , where u[n] denotes the unit step sequence and 0<$$\left| a \right| < \...

A first-order low-pass filter of time constant T is excited with different input signals (with zero initial conditions up to t = 0). Match the excitation signals X, Y, Z with the c...

A sequence x$$\left[ n \right]$$ is specified as $$\left[ {\matrix{ {x\left[ n \right]} \cr {x\left[ {n - 1} \right]} \cr } } \right] = {\left[ {\matrix{ 1 \cr 1 \cr } \,\matrix{ 1...

A super heterodyne receiver operates in the frequency range of 58 MHz – 68 MHz. The intermediate frequency f 1F and local oscillator frequency f L0 are chosen such that f 1F $$\leq...

Concentric spherical shells of radii 2 m, 4 m, and 8 m carry uniform surface charge densities of 20 nC/m 2 , −4 nC/m 2 and ρ s ,respectively. The value of ρ s (nC/m 2 ) required to...

The far-zone power density radiated by a helical antenna is approximated as: $$$\overrightarrow W {\,_{rad}} = \overrightarrow W \,average\, \approx \,\widehat a{}_rC{}_0\,{1 \over...

Consider the time-varying vector $$I = \,\hat x\,\,15\,\cos \,(\omega \,t) + \,\hat y\,5\,sin(\omega \,t)$$ in Cartesian coordinates, where $$\omega $$ > 0 is a constant. When the...

The response of the system $$G\left(s\right)\;=\;\frac{s\;-\;2}{\left(s\;+\;1\right)\left(s\;+\;3\right)}$$ to the unit step input u(t) is y(t). The value of $$\frac{\mathrm{dy}}{\...

Given (9 inches) 1/2 = (0.25 yards) 1/2 , which one of the following statements is TRUE?

S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency of others but for half as many days as E worked. S and M have 6 hour shifts in...

Consider the complex valued function $$f\left( z \right) = 2{z^3} + b{\left| z \right|^3}$$ where $$z$$ is a complex variable. The value of $$b$$ for which the function $$f(z)$$ is...

The number and direction of encirclements around the point −1 + j0 in the complex plane by the Nyquist plot of G(s) =$${{1 - s} \over {4 + 2s}}$$ is

The ordinary differential equation $$\,\,{{dx} \over {dt}} = - 3x + 2,\,\,$$ with $$x(0)=1$$ is to be solved using the forward Euler method. The largest time step that can be used...

Which one of the following statements is correct about an ac-coupled common- emitter amplifier operating in the mid-band region?

How many distinct values of $$x$$ satisfy the equation $$sin(x)=x/2,$$ where $$x$$ is in radians ?

Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium be expressed as $$E = \widehat x{E_x}\,{e^{ - j\left( {wt - \beta z} \right)}},$$ ,...

An 8 Kbyte ROM with an active low Chip Select input CS is to be used in an 8085 microprocessor based system. The ROM should occupy the address range 1000H to 2FFFH. Theaddress line...

A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (...

A discrete memoryless source has an alphabet $$({a_1},\,{a_2},\,{a_3},\,{a_4})\,$$ with corresponding probabilities$$\left( {{1 \over 2}\,\,,{1 \over 4},\,{1 \over 8},\,\,{1 \over...

Consider random process $$X(t) = 3V(t) - 8$$, where $$V$$ $$(t)$$ is a zero mean stationary random process with autocorrelation $${R_v}\left( \tau \right) = 4{e^{ - 5\left| \tau \r...

An ideal band-pass channel 500Hz-2000 Hz is deployed for communication. A modem is designed to transmit bits at the rate of 4800 bits/s using 16-QAM. The roll-off factor of a pulse...

A binary communication system makes use of the symbols “zero” and “one”. There are channel errors. Consider the following events: $${x_0}$$ : a " zero " is transmitted $${x_1}$$ :...

An information source generates a binary sequence $$\left\{ {{\alpha _n}} \right\}.{\alpha _n}$$ can take one of the two possible values −1 and +1 with equal probability and are st...

The value of $$x$$ for which the matrix $$A = \left[ {\matrix{ 3 & 2 & 4 \cr 9 & 7 & {13} \cr { - 6} & { - 4} & { - 9 + x} \cr } } \right]$$ has zero as an eigen value is _________...

The matrix $$A = \left[ {\matrix{ a & 0 & 3 & 7 \cr 2 & 5 & 1 & 3 \cr 0 & 0 & 2 & 4 \cr 0 & 0 & 0 & b \cr } } \right]$$ has det $$(A)=100$$ and trace $$(A)=14.$$ The value of $$\le...

Suppose $$C$$ is the closed curve defined as the circle $$\,\,{x^2} + {y^2} = 1\,\,$$ with $$C$$ oriented anti-clockwise. The value of $$\,\,\oint {\left( {x{y^2}dx + {x^2}ydx} \ri...

As $$x$$ varies from $$- 1$$ to $$3,$$ which of the following describes the behavior of the function $$f\left( x \right) = {x^3} - 3{x^2} + 1?$$

The Discrete Fourier Transform (DFT) of the 4-point sequence $$x\left[ n \right]$$= {x[0], x[1], x[2], x[3]} = {3, 2, 3, 4 } is x[k] = {X[0], X[1], X[2], X[3]} = {12, 2j, 0, -2j }...

The Ebers-Moll model of a BJT is valid

A long-channel NMOS transistor is biased in the linear region with V DS = 50 mV and is used as a resistance. Which one of the following statements is NOT correct?

The energy of the signal x(t) =$${{\sin (4\pi t)} \over {4\pi t}}$$ is ___________.

A voltage V G is applied across a MOS capacitor with metal gate and p-type silicon substrate at T=300 K. The inversion carrier density (in number of carriers per unit area) for V G...

A continuous-time filter with transfer function $$\,H(S) = {{2s + 6} \over {{s^2} + 6s + 8}}$$ is converted to a discrete time filter with transfer function $$G(Z) = {{2{z^2} - 0.5...

Consider a long-channel NMOS transistor with source and body connected together. Assume that the electron mobility is independent of V GS and V DS . Given, g m = 0.5$$\mu {\rm A}/V...

A uniform and constant magnetic field $$B=\widehat zB$$ exists in the $$\widehat z$$ direction in vacuum. A particle of mass m with a small charge q is introduced into this region...

Faraday's law of electromagnetic induction is mathematically described by which one of the following equations?

The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as $$G\left(s\right)=\frac{K\left(s+2\right)}...

The number that least fits this set: (324, 441, 97 and 64) is ________.

It takes 10 s and 15 s, respectively, for two trains traveling at different constant speeds to completely pass a telegraph post. The length of the first train is 120 m and that of...

A triangle in the $$xy-$$plane is bounded by the straight lines $$2x=3y, y=0$$ and $$x=3.$$ The volume above the triangle and under the plane $$x+y+z=6Z$$ is ________.

A second-order linear time-invariant system is described by the following state equations $$$\eqalign{& {d \over {dt}}{x_1}\left( t \right) + 2{x_1}\left( t \right) = 3u\left( t \r...

The integral $$\int\limits_0^1 {{{dx} \over {\sqrt {\left( {1 - x} \right)} }}} $$ is equal ________.

If the vectors $${e_1} = \left( {1,0,2} \right),\,{e_2} = \left( {0,1,0} \right)$$ and $${e_3} = \left( { - 2,0,1} \right)$$ form an orthogonal basis of the three dimensional real...

For $$f\left( z \right) = {{\sin \left( z \right)} \over {{z^2}}},$$ the residue of the pole at $$z=0$$ ________.

A binary baseband digital communication system employs the signal $$$p\left( t \right) = \left\{ {\matrix{ {{1 \over {\sqrt {{T_s}} }},} & {0 \le t \le {T_s}} \cr {0,} & {otherwise...

In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0, respectively. If the instruction RLC is executed, then the contents of the accu...

A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of 4.0 kHz and two-sided noise power spectral density $${\eta \over 2} = 2.5\, \times \,{10^{ -...

Consider an air-filled rectangular waveguide with dimensions a = 2.286 cm and b = 1.016 cm. The increasing order of the cut-off frequencies for different modes is

The bit error probability of a memoryless binary symmetric channel is $${10^{ - 5}}$$. If $${10^{ - 5}}$$ bits are sent over this channel, then the probability that not more than o...

If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be

A radar operating at 5 GHz uses a common antenna for transmission and reception. The antenna has a gain of 150 and is aligned for maximum directional radiation and reception to a t...

Consider an air-filled rectangular waveguide with dimensions a = 2.286cm and b = 1.016cm. At 10GHz operating frequency, the value of the propagation constant (per meter) of the cor...

An analog baseband signal, band limited to 100 Hz, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities $...

The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is

Consider the first order initial value problem $$\,y' = y + 2x - {x^2},\,\,y\left( 0 \right) = 1,\,\left( {0 \le x < \infty } \right)$$ With exact solution $$y\left( x \right)\,\,...

The probability of getting a ''head'' in a single toss of a biased coin is $$0.3.$$ The coin is tossed repeatedly till a ''head'' is obtained. If the tosses are independent, then t...

The value of the integral $${1 \over {2\pi j}}\oint\limits_C {{{{e^z}} \over {z - 2}}dz} $$ along a closed contour $$c$$ in anti-clockwise direction for (i) the point $${z_0} = 2$$...

Consider a $$2 \times 2$$ square matrix $$A = \left[ {\matrix{ \sigma & x \cr \omega & \sigma \cr } } \right]$$ Where $$x$$ is unknown. If the eigenvalues of the matrix $$A$$ are $...

The particular solution of the initial value problem given below is $$\,\,{{{d^2}y} \over {d{x^2}}} + 12{{dy} \over {dx}} + 36y = 0\,\,$$ with $$\,y\left( 0 \right) = 3\,\,$$ and $...

A discrete-time signal$$x\left[ n \right]\, = \delta \left[ {n - 3} \right]\, + 2\delta \left[ {n - 5} \right]$$ has z-transform x(z). If Y (z)=X (-z) is the z-transform of another...

If the signal x(t) = $${{\sin (t)} \over {\pi t}}*{{\sin (t)} \over {\pi t}}$$ with * denoting the convolution operation, then x(t) is equal to

A continuous-time speech signal $${x_a}(t)$$ is sampled at a rate of 8 kHz and the samples are subsequently grouped in blocks, each of size N. The DFT of each block is to be comput...

The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded region in the z-plane. If the signal $$x\left[ n \right] = \,{\left( {2.0}...

For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator frequency is 3.5 GHz. If the frequency of the received signal is greater than the loca...