GATE 2020 Electronics & Communication
66 questions across 2 sessions
Gate Ece 2020
Consider the recombination process via bulk traps in a forward biased $p n$ homojunction diode. The maximum recombination rate is $U_{\max }$. If the electron and the hole capture...
A finite duration discrete-time signal $x[n]$ is obtained by sampling a continuous - time signal $x(t)=\cos (200 \pi t)$ at sampling instants $t=\frac{n}{400}, n=0,1, \ldots ., 7$....
The output $y[n]$ of a discrete - time system for an input $x[n]$ is $$ y[n]=\max\limits_{-\infty \leq k \leq n}|x[k]| $$ The unit impulse response of the system is
A single crystal intrinsic semiconductor is at a temperature of 300 K with effective density of states for holes twice that of electrons. The thermal voltage is 26 mV . The intrins...
The transfer function of a stable discrete - time LTI system is $H(z)=\frac{K(z-\alpha)}{(z+0.5)}$ where $K$ and $\alpha$ are real numbers. The value of $\alpha$ (rounded off to on...
A $p n$ junction solar cell of area $1.0 \mathrm{~cm}^2$, illuminated uniformly with $100 \mathrm{mWcm}^{-2}$; has the following parameter : Efficiency $=15 \%$, open circuit volta...
Which one of the following pole-zero plots corresponds to the transfer function of an LTI system characterized by the input-output difference equation given below? $$ y[n]=\sum_{k=...
The impedances $Z=j X$, for all $X$ in the range ( $-\infty, \infty$ ), map to the Smith chart as
In an 8085 microprocessor, the number of address lines required to access a 16 K bytes memory bank is $\_\_\_\_$ .
A binary random variable $X$ takes the value +2 or -2 . The probability $P(X=+2)=\alpha$. The value of $\alpha$ (rounded off to one decimal place), for which the entropy of $X$ is...
The magnetic field of a uniform plane wave in vacuum is given by $$ \vec{H}(x, y, z, t)=\left(\hat{a}_x+2 \hat{a}_y+b \hat{a}_z\right) \cos (\omega t+3 x-y-z) . $$ The value of $b$...
A transmission line of length $3 \lambda / 4$ and having a characteristic impedance of $50 \Omega$ is terminated with a load of $400 \Omega$. The impedance (rounded off to two deci...
A digital communication system transmits a block of $N$ bits. The probability of error in decoding a bit is $\alpha$. The error event of each bit is independent of the error events...
The random variable $$ Y=\int_{-\infty}^{\infty} W(t) \phi(t) d t, \quad \text { where } \phi(t)=\left\{\begin{array}{cc} 1, & 5 \leq t \leq 7 \\ 0, & \text { otherwise } \end{arra...
In a digital communication system, a symbol $S$ randomly chosen from the set $\left\{s_1, s_2, s_3, s_4\right\}$ is transmitted. It is given that $s_1=-3, s_2=-1, s_3=+1$ and $s_4=...
He was not only accused of theft $\_\_\_\_$ of conspiracy.
The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit and had to pay a six-figure fine to a French speaking...
Select the word that fits the analogy : Explicit : Implicit : : Express : $\_\_\_\_$ .
The untimely loss of life is a cause of serious global concern as thousands of people get killed $\_\_\_\_$ accidents every year while many other die $\_\_\_\_$ diseases like cardi...
A superadditive function $f(\cdot)$ satisfies the following property $$ f\left(x_1+x_2\right) \geq f\left(x_1\right)+f\left(x_2\right) $$ Which of the following functions is a supe...
$a, b, c$ are real numbers. The quadratic equation $a x^2-b x+c=0$ has equal roots, which is $\beta$, then
The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in USA in 2007. The sub-prime...
If $\mathbf{v}_{\mathbf{1}}, \mathbf{v}_{\mathbf{2}} \ldots \mathbf{v}_{\mathbf{6}}$ are six vectors in $\mathbb{R}^4$, which one of the statements is FALSE?
The two sides of a fair coin are labelled as 0 and 1 . The coin is tossed two times independently. Let $M$ and $N$ denote the labels corresponding to the outcomes of those tosses....
The loop transfer function of a negative feedback system is $$ G(s) H(s)=\frac{K(s+11)}{s(s+2)(s+8)} $$ The value of $K$, for which system is marginally stable, is $\_\_\_\_$ .
The general solution of $\frac{d^2 y}{d x^2}-6 \frac{d y}{d x}+9 y=0$ is
A 10 bit D/A converter is calibrated over the full range 0 to 10 V . If the input to the D/A converter is 13 A (in hex), the output (rounded off to three decimal places) is $\_\_\_...
The partial derivative of the function $$ f(x, y, z)=e^{1-x \cos y}+x z e^{\frac{-1}{\left(1+y^2\right)}} $$ with respect to $x$ at the point $(1,0, e)$ is
For a vector field $\vec{A}$, which one of the following is FALSE?
Consider the following system of linear equations. $$ x_1+2 x_2=b_1 ; 2 x_1+4 x_2=b_2 ; 3 x_1+7 x_2=b_3 ; 3 x_1+9 x_2=b_4 $$ Which one of the following conditions ensures that a so...
$P, Q$ and $R$ are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1 's complement and 2 's complement representation, respective...
Which one of the following options contains two solutions of the differential equation $\frac{d y}{d x}=(y-1) x$ ?
A system with transfer function $G(s)=\frac{1}{(s+1)(s+a)}, a>0$ is subjected to input $5 \cos 3 t$. The steady state output of the system is $\frac{1}{\sqrt{10}} \cos (3 t-1.892)$...
$X$ is a random variable with uniform probability density function in the interval $[-2,10]$. For $Y=2 X-6$, the conditional probability $P(Y \leq 7 \mid X \geq 5)$ (rounded off to...
It is quarter past three in your watch. The angle between the hour hand and the minute hand is $\_\_\_\_$ .
The characteristic equation of a system is $$ s^3+3 s^2+(K+2) s+3 K=0 $$ In the root locus plot for the given system, as $K$ varies from 0 to $\infty$, the break-away or break-in p...
Set Master
The number of 4-digit numbers formed by using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 such that the product of the digits is 0 is ______.
The number of ways to arrange the letters of the word 'EQUATION' such that all vowels come together is ______.
The number of ways to choose 4 cards from a pack of 52 playing cards such that all four cards are of the same suit is ______.
The number of ways to choose 3 men and 2 women from a group of 7 men and 5 women is ______.
The number of terms in the expansion of $(x+y+z)^n$ is ______.
The coefficient of $x^3$ in the expansion of $(1+x)^5$ is ______.
The value of $\sum_{r=0}^{n} \binom{n}{r}$ is ______.
The value of $\binom{n}{r} + \binom{n}{r-1}$ is ______.
The number of diagonals in a polygon of $n$ sides is ______.
The number of ways to distribute 10 identical items among 3 distinct persons such that each person gets at least one item is ______.
The number of ways to choose 5 balls from a bag containing 6 red balls and 4 blue balls such that at least 3 red balls are chosen is ______.
The number of ways to seat 5 men and 5 women in a row such that no two women sit together is ______.
The number of ways to arrange 7 books on a shelf such that two particular books are always together is ______.
The number of ways to form a committee of 3 members from 6 men and 4 women such that the committee has at least one woman is ______.
The number of distinct permutations of the letters of the word 'MISSISSIPPI' is ______.
The number of ways to choose 2 distinct numbers from the set {1, 2, 3, ..., 10} such that their sum is even is ______.
The number of ways to arrange 3 boys and 3 girls in a row such that no two boys sit together is ______.
The number of ways to choose 4 items from a set of 10 distinct items is ______.
The number of ways to form a 3-digit number using the digits 1, 2, 3, 4, 5 without repetition is ______.
The number of ways to arrange 4 distinct objects in a circle is ______.
The number of ways to choose 3 students from a class of 10 students for a competition is ______.
The number of ways to arrange the letters of the word 'APPLE' is ______.
The number of ways to choose 2 boys and 2 girls from a group of 4 boys and 3 girls is ______.
The number of ways to distribute 5 identical balls into 3 distinct boxes is ______.
The number of ways to choose a committee of 5 members from 10 people such that a particular person is always included is ______.
The number of ways to choose a committee of 5 members from 10 people such that a particular person is always excluded is ______.
The number of ways to arrange 6 distinct books on a shelf is ______.
The number of ways to choose 3 items from a set of 7 distinct items is ______.
The number of ways to form a 4-letter word using the letters of the word 'ROSE' without repetition is ______.
The number of ways to arrange 5 distinct objects in a row is ______.