GATE 2021 Electronics & Communication

A digital transmission system uses a $(7,4)$ systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-code word pairs in this code ( $m_i...

Consider the integral $$\oint {{{\sin (x)} \over {{x^2}({x^2} + 4)}}dx} $$ where C is counter-clockwise oriented circle defined as |x $$-$$ i| = 2. The value of the integral is

A box contains the following three coins. I. A fair coin head on one face and tail on the other face. II. A coin with heads to both the faces. III. A coin with tails on both the fa...

Two continuous random variables X and Y are related as Y = 2X + 3. Let $$\sigma _x^2$$ and $$\sigma _y^2$$ denote the variances of X and Y, respectively. The variances are related...

For an $n$-channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity ( $\partial V_T / \partial\left|V_{B S}\right|$ ) is found to be $50 \mathrm{mV} / \mat...

Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its...

Given below are two statements and two conclusions. Statement 1 : All purple are green Statement 2 : All black are green Conclusion I : Some black are purple. Conclusion II : No bl...

Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic AI e...

Nostalgia is to anticipation as _____ is to _____. Which one of the following options maintains a similar logical relation in the above sentence?

Consider the differential equation given below. $${{dy} \over {dx}} + {x \over {1 - {x^2}}}y = x\sqrt y $$ The integrating factor of the differential equation is

A real 2 $$\times$$ 2 non-singular matrix A with repeated eigen value is given as $$A = \left[ {\matrix{ x & { - 3.0} \cr {3.0} & {4.0} \cr } } \right]$$ where x is a real positive...

In a high school having equal number of boy students and girl students, 75% of the students study Science and the remaining 25% students study Commerce. Commerce students are two t...

p and q are positive integers and $${p \over q} + {q \over p} = 3$$, then $${{{p^2}} \over {{q^2}}} + {{{q^2}} \over {{p^2}}}$$ =

Consider the following sentences : (i) I woke up from sleep. (ii) I woked up from sleep (iii) I was woken up from sleep (iv) I was wokened up from sleep. Which of the above sentenc...

For a vector field $\overrightarrow{\mathbf{D}}=\rho \cos ^2 \phi \hat{\mathbf{a}}_{\boldsymbol{\rho}}+z^2 \sin ^2 \phi \hat{\mathbf{a}}_\phi$ in a cylindrical coordinate system $(...

Consider a super heterodyne receiver tuned to 600 kHz . If the local oscillator feeds a 1000 kHz signal to the mixer. The image frequency (in integer) is $\_\_\_\_$ kHz .

Consider a polar non-return to Zero (NRZ) waveform, using +2 V and -2 V for representing binary ' 1 ' and ' 0 ' respectively, is transmitted in the presence of additive zero-mean w...

A sinusoidal message signal having root mean square value of 4 V and frequency of 1 kHz is fed to a phase modulator with phase deviation constant $2 \mathrm{rad} /$ volt. If the ca...

The content of the registers are $R_1=25 \mathrm{H}, R_2=30 \mathrm{H}$ and $R_3 =40 \mathrm{H}$. The following machine instructions are executed. $$ \begin{aligned} & \operatornam...

Consider the vector field $\overline{\mathbf{F}}=\hat{\mathbf{a}}_{\mathbf{x}}\left(4 y-c_1 z\right)+\hat{\mathbf{a}}_{\mathbf{y}}(4 x+2 z)+\hat{\mathbf{a}}_{\mathbf{z}}(2 y+z)$ in...

Addressing of a $32 K \times 16$ memory is realized using a single decoder. The minimum number of AND gates required for the decoder is :

An 8-bit unipolar (all analog output values are positive) digital-to-analog converter (DAC) has a full-scale voltage range from 0 V to 7.68 V . If the digital input code is 1001011...

The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 yeas ago?

If the vectors (1.0, $$-$$1.0, 2.0), (7.0, 3.0, x) and (2.0, 3.0, 1.0) in R 3 are linearly dependent, the value of x is _______.

Consider two 16-point sequences x[n] and h[n]. Let the linear convolution of x[n] and h[n] be denoted by y[n], while z[n] denotes the 16-point inverse discrete Fourier transform (I...

Consider the signals $x[n]=2^{n-1} u[-n+2]$ and $y[n]=2^{-n+2} u[n+1]$, where $u[n]$ is the unit step sequence. Let $X\left(e^{j \omega}\right)$ and $Y\left(e^{j \omega}\right)$ be...

For a unit step input $u[n]$, a discreate-time $L T I$ system produces an output signal $(2 \delta[n+1]+\delta[n]+\delta[n-1])$. Let $y[n]$ be the output of the system for an input...

The exponential Fourier series representation of a continu-ous-time periodic signal $X(t)$ is defined as $$ x(t)=\sum\limits_{k=-\infty}^{\infty} a_k e^{j k w_0 t} $$ Where $\omega...

A bar of silicon is doped with boron concentration of $10^{16} \mathrm{cm}^{-3}$ and assumed to be fully ionized. It is exposed to light such that electron-hole pairs are generated...

Consider a real-valued base-band signal $x(t)$. band limited to 10 kHz . The Nyquist rate for the signal $y(t)=x(t) \times \left(1+\frac{t}{2}\right)$ is

A message signal having peak-to-peak value of 2 V , root mean square value of 0.1 V and bandwidth of 5 kHz is sampled and fed to a pulse code modulation (PCM) system that uses a un...

A 4 kHz sinusoidal message signal having amplitude 4 V is fed to a delta modulator (DM) operating at a sampling rate of 32 kHz . The minimum step size required to avoid slope overl...

Consider a rectangular coordinate system $(x, y, z)$ with unit vectors $a_x, a_y$ and $a_z$. A plane wave traveling in the region $z \geq 0$ with electric field vector $E=10 \cos \...

The refractive indices of the core and cladding of an optical fiber are 1.50 and 1.48 respectively. The critical propagation angle. Which is defined as the maximum angle that the l...

Consider a carrier signal which is amplitude modulated by a single - tone sinusoidal message signal with a modulation index of $50 \%$. If the carrier and one of the side bands are...

An antenna with a directive gain of 6 dB is radiating a total power of 16 kw . The amplitude of the electric field in free space at a distance of 8 km from the antenna in the direc...

A standard air-filled rectangular waveguide with dimensions $a=8 \mathrm{~cm}, b=4 \mathrm{~cm}$, operates at 3.4 GHz . For the dominant mode of wave propagation, the phase velocit...