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TIFR ECE 2017 | Question: 3
What is the maximum average power that can be dissipated by a load connected to the output terminals of the following circuit with an alternating current source? $23 \mathrm{~W}$ $11.5 \mathrm{~W}$ $8.1317 \mathrm{~W}$ $2.875 \mathrm{~W}$ None of the above
What is the maximum average power that can be dissipated by a load connected to the output terminals of the following circuit with an alternating current source?$23 \math...
admin
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81
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admin
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Nov 29, 2022
Others
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1
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0
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362
TIFR ECE 2020 | Question: 12
Consider a unit disc $D$. Let a point $x$ be chosen uniformly on $D$ and let the random distance to $x$ from the center of $D$ be $R$. Which of the following is $\text{TRUE?}$ $R^{2}$ is uniformly distributed in $[0,1]$ $\pi R^{2}$ is uniformly ... $[0,1]$ $2 \pi R^{2}$ is uniformly distributed in $[0,1]$ None of the above
Consider a unit disc $D$. Let a point $x$ be chosen uniformly on $D$ and let the random distance to $x$ from the center of $D$ be $R$. Which of the following is $\text{TR...
admin
46.4k
points
37
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admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2020
probability-and-statistics
probability
uniform-distribution
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1
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0
answers
363
TIFR ECE 2020 | Question: 5
Let $f(t)$ be a periodic signal of period $1$, i.e. $f(t+1)=f(t) \forall t$. Define the averaging operator depending on a fixed parameter $h>0$ as below: \[g(x)=\frac{1}{2 h} \int_{x-h}^{x+h} f(t) d t .\] Which of the following is ... $\frac{1}{2}$ $g(x)$ is periodic with period $1$ The value of $h$ determines whether or not $g(x)$ is periodic None of the above
Let $f(t)$ be a periodic signal of period $1$, i.e. $f(t+1)=f(t) \forall t$. Define the averaging operator depending on a fixed parameter $h>0$ as below:\[g(x)=\frac{1}{2...
admin
46.4k
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37
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admin
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Nov 30, 2022
Others
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1
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364
TIFR ECE 2019 | Question: 11
Let $X$ and $Y$ be independent Gaussian random variables with means $1$ and $2$ and variances $3$ and $4$ respectively. What is the minimum possible value of $\mathbf{E}\left[(X+Y-t)^{2}\right]$, when $t$ varies over all real numbers? $7$ $5$ $1.5$ $3.5$ $2.5$
Let $X$ and $Y$ be independent Gaussian random variables with means $1$ and $2$ and variances $3$ and $4$ respectively. What is the minimum possible value of $\mathbf{E}\...
admin
46.4k
points
37
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admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2019
probability-and-statistics
probability
expectation
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1
votes
0
answers
365
TIFR ECE 2017 | Question: 11
Consider a unit length interval $[0,1]$ and choose a point $X$ on it with uniform distribution. Let $L_{1}=X$ and $L_{2}=1-X$ be the length of the two sub-intervals created by this point on the unit interval. Let $L=\max \left\{L_{1}, L_{2}\right\}$. Consider ... $\text{(ii)}$ Only $\text{(i)}$ and $\text{(iii)}$ Only $\text{(ii)}$ and $\text{(iv)}$ None of the above
Consider a unit length interval $[0,1]$ and choose a point $X$ on it with uniform distribution. Let $L_{1}=X$ and $L_{2}=1-X$ be the length of the two sub-intervals creat...
admin
46.4k
points
79
views
admin
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Nov 29, 2022
Probability and Statistics
tifrece2017
probability-and-statistics
probability
uniform-distribution
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1
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0
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366
TIFR ECE 2019 | Question: 8
Let $K$ be a cube of side $1$ in $\mathbb{R}^{3}$, with its centre at the origin, and its sides parallel to the co-ordinate axes. For $t \geq 0$, let $K_{t}$ be the set of all points in $\mathbb{R}^{3}$ whose Euclidean distance to $K$ is less than or equal to $t$ ... $V \leq \frac{4}{3} \pi\left(\frac{\sqrt{3}}{2}+t\right)^{3}$ $V \geq(1+2 t)^{3}$
Let $K$ be a cube of side $1$ in $\mathbb{R}^{3}$, with its centre at the origin, and its sides parallel to the co-ordinate axes. For $t \geq 0$, let $K_{t}$ be the set o...
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46.4k
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35
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admin
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Nov 30, 2022
Others
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367
TIFR ECE 2016 | Question: 9
Suppose $Y=X+Z$, where $X$ and $Z$ are independent zero-mean random variables each with variance $1.$ Let $\hat{X}(Y)=a Y$ be the optimal linear least-squares estimate of $X$ from $Y$, i.e., $a$ is chosen such that $E\left[(X-a Y)^{2}\right]$ is minimized. What is the resulting ... $1$ $\frac{2}{3}$ $\frac{1}{2}$ $\frac{1}{3}$ $\frac{1}{4}$
Suppose $Y=X+Z$, where $X$ and $Z$ are independent zero-mean random variables each with variance $1.$ Let $\hat{X}(Y)=a Y$ be the optimal linear least-squares estimate of...
admin
46.4k
points
78
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admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2016
probability-and-statistics
probability
random-variable
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1
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0
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368
TIFR ECE 2020 | Question: 11
Suppose that $X$ is a real valued random variable and $E[\exp X]=2$. Then, which of the following must be $\text{TRUE? Hint:}$ $(\exp (x)+\exp (y)) / 2 \geq \exp ((x+y) / 2)$. $E[X]<\ln 2$ $E[X]>\ln 2$ $E[X] \geq \ln 2$ $E[X] \leq \ln 2$ None of the above
Suppose that $X$ is a real valued random variable and $E[\exp X]=2$. Then, which of the following must be $\text{TRUE? Hint:}$ $(\exp (x)+\exp (y)) / 2 \geq \exp ((x+y) /...
admin
46.4k
points
34
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2020
probability-and-statistics
probability
random-variable
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1
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0
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369
TIFR ECE 2019 | Question: 15
Anu reached a bus stop at $\text{9:00 AM.}$ She knows that the number of minutes after $\text{9:00 AM}$ when the bus will arrive is distributed with probability density function (p.d.f.) $f$ where \[f(x)=\frac{1}{10} \exp (-x / 10)\] for $x \geq 0$, ... time, measured in minutes after $\text{9:00 AM,}$ would Anu expect the bus to arrive? $12.5$ $15$ $7.5$ $10$ $12.5$
Anu reached a bus stop at $\text{9:00 AM.}$ She knows that the number of minutes after $\text{9:00 AM}$ when the bus will arrive is distributed with probability density f...
admin
46.4k
points
34
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2019
probability-and-statistics
probability
probability-density-function
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1
votes
0
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370
TIFR ECE 2019 | Question: 13
For $t>0$, let $S_{t}$ denote the ball of radius $t$ centered at the origin in $\mathbb{R}^{n}$. That is, \[S_{t}=\left\{\mathbf{x} \in \mathbb{R}^{n} \mid \sum_{i=1}^{n} x_{i}^{2} \leq t^{2}\right\} .\] Let $N_{t}$ be the number of ... $\lim _{t \rightarrow \infty} \frac{N_{t}}{V_{t}}=1$ $N_{t}$ is a monotonically decreasing function of $t$
For $t>0$, let $S_{t}$ denote the ball of radius $t$ centered at the origin in $\mathbb{R}^{n}$. That is,\[S_{t}=\left\{\mathbf{x} \in \mathbb{R}^{n} \mid \sum_{i=1}^{n} ...
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46.4k
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34
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admin
asked
Nov 30, 2022
Others
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371
TIFR ECE 2019 | Question: 9
Consider a coin which comes up heads with probability $p$ and tails with probability $1-p$, where $0 < p < 1.$ Suppose we keep tossing the coin until we have seen both sides of the coin. What is the expected number of times we would have seen tails? (Hint: the expected number of ... $(1/p.)$ $\frac{1}{p}$ $1+\frac{1}{1-p}$ $p+\frac{1}{p}-1$ $2$ None of the above
Consider a coin which comes up heads with probability $p$ and tails with probability $1-p$, where $0 < p < 1.$ Suppose we keep tossing the coin until we have seen both si...
admin
46.4k
points
34
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2019
probability-and-statistics
probability
expectation
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372
TIFR ECE 2019 | Question: 3
Consider a function $f: \mathbf{R} \rightarrow \mathbf{R}$ such that $f(x)=1$ if $x$ is rational, and $f(x)=1-\epsilon,$ where $0<\epsilon<1$, if $x$ is irrational. Which of the following is $\text{TRUE}?$ $\lim _{x \rightarrow \infty} f(x)=1$ ... $1-\epsilon$ $\max _{x \geq 1} f(x)=1$ None of the above
Consider a function $f: \mathbf{R} \rightarrow \mathbf{R}$ such that $f(x)=1$ if $x$ is rational, and $f(x)=1-\epsilon,$ where $0<\epsilon<1$, if $x$ is irrational. Which...
admin
46.4k
points
33
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admin
asked
Nov 30, 2022
Calculus
tifrece2019
calculus
limits
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373
TIFR ECE 2019 | Question: 10
Let $X, Z_{1}$, and $Z_{2}$ be independent random variables taking values in the set $\{0,1\}$. $X$ is uniformly distributed in $\{0,1\}$, while the distributions of $Z_{1}$ and $Z_{2}$ are such that if we define $Y_{1}=X+Z_{1}$ and $Y_{2}=X+Z_{2}$, where addition ... $\left(1 / p_{1}+1 / p_{2}\right)^{-1}$ $\left(1+1 / p_{1}+1 / p_{2}\right)^{-1}$ None of the above
Let $X, Z_{1}$, and $Z_{2}$ be independent random variables taking values in the set $\{0,1\}$. $X$ is uniformly distributed in $\{0,1\}$, while the distributions of $Z_{...
admin
46.4k
points
33
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admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2019
probability-and-statistics
probability
random-variable
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374
TIFR ECE 2017 | Question: 8
Consider the two positive integer sequences, defined for a fixed positive integer $c \geq 2$ \[f(n)=\frac{1}{n}\left\lfloor\frac{n}{c}\right\rfloor, \quad g(n)=n\left\lfloor\frac{c}{n}\right\rfloor\] where $\lfloor t\rfloor$ denotes the ... $0$ The first sequence converges to $1 / c$, while the second sequence converges to $c$
Consider the two positive integer sequences, defined for a fixed positive integer $c \geq 2$\[f(n)=\frac{1}{n}\left\lfloor\frac{n}{c}\right\rfloor, \quad g(n)=n\left\lflo...
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46.4k
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75
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Others
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375
TIFR ECE 2020 | Question: 14
Two matrices $A$ and $B$ are called similar if there exists an invertible matrix $X$ such that $A=X^{-1} B X$. Let $A$ and $B$ be two similar matrices. Consider the following statements: $\operatorname{det}(x I-A)=\operatorname{det}(x I-B)$ ... statement $2$ is correct Only statements $1$ and $2$ are correct All Statements $1, 2$ and $3$ are correct None of the above
Two matrices $A$ and $B$ are called similar if there exists an invertible matrix $X$ such that $A=X^{-1} B X$. Let $A$ and $B$ be two similar matrices. Consider the follo...
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46.4k
points
32
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admin
asked
Nov 30, 2022
Linear Algebra
tifrece2020
linear-algebra
matrices
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376
TIFR ECE 2019 | Question: 6
Suppose that $X_{1}$ and $X_{2}$ denote the random outcomes of independent rolls of two dice. Each of the dice takes each of the six values $1,2,3,4,5$, and $6$ with equal probability. What is the value of the conditional expectation \[\mathbf{E}\left[\max \left(X_{1}, X_{2}\right) \mid \min \left(X_{1}, X_{2}\right)=3\right] ?\] $33 / 7$ $4$ $5$ $9 / 2$ $19 / 4$
Suppose that $X_{1}$ and $X_{2}$ denote the random outcomes of independent rolls of two dice. Each of the dice takes each of the six values $1,2,3,4,5$, and $6$ with equa...
admin
46.4k
points
32
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2019
probability-and-statistics
probability
expectation
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377
TIFR ECE 2019 | Question: 5
Consider the function $f(x)=e^{x^{2}}-8 x^{2}$ for all $x$ on the real line. For how many distinct values of $x$ do we have $f(x)=0?$ $1$ $4$ $2$ $3$ $5$
Consider the function $f(x)=e^{x^{2}}-8 x^{2}$ for all $x$ on the real line. For how many distinct values of $x$ do we have $f(x)=0?$ $1$$4$$2$$3$$5$
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46.4k
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32
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admin
asked
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Calculus
tifrece2019
calculus
functions
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378
TIFR ECE 2019 | Question: 12
Consider an urn with $a$ red and $b$ blue balls. Balls are drawn out one-by-one, without replacement and uniformly at random, until the first red ball is drawn. What is the expected total number of balls drawn by this process? (Hint: Consider deriving an appropriate recurrence.) $\frac{a+b}{a+1}$ $\frac{a+b+1}{a}$ $\frac{a+b}{a}$ $\frac{a+b+1}{a+1}$ $a$
Consider an urn with $a$ red and $b$ blue balls. Balls are drawn out one-by-one, without replacement and uniformly at random, until the first red ball is drawn. What is t...
admin
46.4k
points
32
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2019
probability-and-statistics
probability
expectation
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379
TIFR ECE 2017 | Question: 9
Recall that for a random variable $X$ which takes values in $\mathbb{N}$, the set of natural numbers, its entropy in bits is defined as \[H(X)=\sum_{n=1}^{\infty} p_{n} \log _{2} \frac{1}{p_{n}},\] where, for $n \in \mathbb{N}, p_{n}$ denotes the ... entropy of $X$ in bits? $1$ $1.5$ $\frac{1+\sqrt{5}}{2} \approx 1.618$ (the golden ratio) $2$ None of the above
Recall that for a random variable $X$ which takes values in $\mathbb{N}$, the set of natural numbers, its entropy in bits is defined as\[H(X)=\sum_{n=1}^{\infty} p_{n} \l...
admin
46.4k
points
74
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admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2017
probability-and-statistics
probability
random-variable
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0
answers
380
TIFR ECE 2019 | Question: 2
Let $A$ and $B$ be two square matrices that have full rank. Let $\lambda_{A}$ be an eignevalue of $A$ and $\lambda_{B}$ an eigenvalue of $B$. Which of the following is always $\text{TRUE}?$ $A B$ has full rank $A-B$ ... an eigenvalue of $A B$ $A+B$ has full rank At least one of $\lambda_{A}$ or $\lambda_{B}$ is an eigenvalue of $A B$
Let $A$ and $B$ be two square matrices that have full rank. Let $\lambda_{A}$ be an eignevalue of $A$ and $\lambda_{B}$ an eigenvalue of $B$. Which of the following is al...
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46.4k
points
31
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admin
asked
Nov 30, 2022
Linear Algebra
tifrece2019
linear-algebra
matrices
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1
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0
answers
381
TIFR ECE 2019 | Question: 7
Consider two random variables $X$ and $Y$ which take values in a finite set $S$. Let $p_{X, Y}$ represent their joint probability mass function (p.m.f.) and let $p_{X}$ and $p_{Y}$, respectively, be the marginal p.m.f.'s of $X$ and $Y$, respectively. Which of ... None of the above
Consider two random variables $X$ and $Y$ which take values in a finite set $S$. Let $p_{X, Y}$ represent their joint probability mass function (p.m.f.) and let $p_{X}$ a...
admin
46.4k
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29
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admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2019
probability-and-statistics
probability
random-variable
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1
votes
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answers
382
TIFR ECE 2019 | Question: 4
Let $f(x)=\sqrt{x^{2}-4 x+4},$ for $x \in(-\infty, \infty)$. Here, $\sqrt{y}$ denotes the non-negative square root of $y$ when $y$ is non-negative. Then, which of the following is $\text{TRUE}?$ $f(x)$ is ... differentiable $f(x)$ is continuous and differentiable $f(x)$ is continuous but not differentiable $f(x)$ is neither continuous nor differentiable None of the above
Let $f(x)=\sqrt{x^{2}-4 x+4},$ for $x \in(-\infty, \infty)$. Here, $\sqrt{y}$ denotes the non-negative square root of $y$ when $y$ is non-negative. Then, which of the fol...
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46.4k
points
29
views
admin
asked
Nov 30, 2022
Calculus
tifrece2019
calculus
continuity-and-differentiability
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0
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383
TIFR ECE 2019 | Question: 14
Consider the circle of radius $1$ centred at the origin in two dimensions. Choose two points $x$ and $y$ independently at random so that both are uniformly distributed on the circle. Let the vectors joining the origin to $x$ and $y$ be $X$ and $Y$, respectively. Let $\theta$ be ... $\mathbf{E}\left[|x-y|^{2}\right]=\sqrt{3}$ $\mathbf{E}\left[|x-y|^{2}\right]=1$
Consider the circle of radius $1$ centred at the origin in two dimensions. Choose two points $x$ and $y$ independently at random so that both are uniformly distributed on...
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46.4k
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27
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admin
asked
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Probability and Statistics
tifrece2019
probability-and-statistics
probability
uniform-distribution
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–
1
votes
0
answers
384
TIFR ECE 2017 | Question: 1
Consider a system which in response to input $x(t)$ outputs \[ y(t)=2 x(t-2)+x(2 t-1)+1 . \] Which of the following describes the system? linear, time-invariant, causal linear, time-invariant, non-causal non-linear, time-invariant, causal non-linear, time-invariant, non-causal non-linear, time-variant
Consider a system which in response to input $x(t)$ outputs\[y(t)=2 x(t-2)+x(2 t-1)+1 .\]Which of the following describes the system?linear, time-invariant, causallinear,...
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46.4k
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Others
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385
TIFR ECE 2016 | Question: 14
Consider matrices $A \in \mathbb{R}^{n \times m}, B \in \mathbb{R}^{m \times m}$, and $C \in \mathbb{R}^{m \times n}$. Let $r=\operatorname{rank}(A B C)$. Which of the following must be true? $\min (m, n) \leq r \leq \max (m, n)$ ... $\min (m, n) \leq r \leq \max (\operatorname{rank}(A), \operatorname{rank}(B), \operatorname{rank}(C))$ None of the above
Consider matrices $A \in \mathbb{R}^{n \times m}, B \in \mathbb{R}^{m \times m}$, and $C \in \mathbb{R}^{m \times n}$. Let $r=\operatorname{rank}(A B C)$. Which of the fo...
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46.4k
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42
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admin
asked
Nov 29, 2022
Linear Algebra
tifrece2016
linear-algebra
rank-of-matrix
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1
votes
0
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386
TIFR ECE 2016 | Question: 13
Suppose $m$ and $n$ are positive integers, $m \neq n$, and $A$ is an $m \times n$ matrix with real entires. Consider the following statements. $\operatorname{rank}\left(A A^{T}\right)=\operatorname{rank}\left(A^{T} A\right)$ ... Which of the above statements is true for all such $A?$ Only (i) Only (ii) Only (iii) (i) and (iii) None of them
Suppose $m$ and $n$ are positive integers, $m \neq n$, and $A$ is an $m \times n$ matrix with real entires. Consider the following statements.$\operatorname{rank}\left(A ...
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46.4k
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41
views
admin
asked
Nov 29, 2022
Linear Algebra
tifrece2016
linear-algebra
matrices
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1
votes
0
answers
387
TIFR ECE 2016 | Question: 15
What is \[ \max _{x, y}\left[\begin{array}{ll} x & y \end{array}\right]\left[\begin{array}{cc} 3 & \sqrt{2} \\ \sqrt{2} & 2 \end{array}\right]\left[\begin{array}{l} x \\ y \end{array}\right] \] subject to \[ x^{2}+y^{2}=1 ? \] $1$ $\sqrt{2}$ $2$ $3$ $4$
What is\[\max _{x, y}\left[\begin{array}{ll}x & y\end{array}\right]\left[\begin{array}{cc}3 & \sqrt{2} \\\sqrt{2} & 2\end{array}\right]\left[\begin{array}{l}x \\y\end{arr...
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46.4k
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40
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admin
asked
Nov 29, 2022
Linear Algebra
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linear-algebra
system-of-equations
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1
votes
0
answers
388
TIFR ECE 2016 | Question: 11
Suppose that a random variable $X$ has a probability density function (pdf) given by \[f(x)=c \exp (-2 x)\] for $x \geq 1$, and $f(x)=0$, for $x<1$, where $c$ is an appropriate constant so that $f(x)$ is a valid pdf. What is the expected value of $X$ given that $X \geq 5?$ $5 \frac{1}{2}$ $7$ $10$ $8 \frac{1}{2}$ $6$
Suppose that a random variable $X$ has a probability density function (pdf) given by\[f(x)=c \exp (-2 x)\]for $x \geq 1$, and $f(x)=0$, for $x<1$, where $c$ is an appropr...
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46.4k
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32
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admin
asked
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Probability and Statistics
tifrece2016
probability-and-statistics
probability
expectation
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–
1
votes
0
answers
389
TIFR ECE 2016 | Question: 12
Recall that the Shannon entropy of a random variables $X$ taking values in a finite set $S$ is given by \[H[X]=-\sum_{x \in S} \operatorname{Pr}[X=x] \log _{2} \operatorname{Pr}[X=x] .\] (We set $0 \log _{2} 0=0$.) For a pair of random variables $(X, Y)$ taking ... $H\left[R_{513}, C_{513} \mid R_{1}, R_{2}, \ldots, R_{512}\right]?$ $\log _{2} 513$ $9$ $10$ $19$ $81$
Recall that the Shannon entropy of a random variables $X$ taking values in a finite set $S$ is given by\[H[X]=-\sum_{x \in S} \operatorname{Pr}[X=x] \log _{2} \operatorna...
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46.4k
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28
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asked
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Probability and Statistics
tifrece2016
probability-and-statistics
probability
random-variable
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0
votes
0
answers
390
GATE ECE 2005 | Question: 83b
Statement for Linked Answer Questions 83a and 83b Asymmetric three-level midtread quantizer is to be designed assuming equiprobable occurence of all quantization levels. The quantization noise power for the quantization region between $-a$ and $+a$ in the figure is $\frac{4}{81}$ $\frac{1}{9}$ $\frac{5}{81}$ $\frac{2}{81}$
Statement for Linked Answer Questions 83a and 83bAsymmetric three-level midtread quantizer is to be designed assuming equiprobable occurence of all quantization levels.Th...
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46.4k
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150
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Oct 17, 2022
Others
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391
GATE ECE 2005 | Question: 85b
Statement of Linked Answer Questions $85 a$ and $85b$ A sequence $x(n)$ has non-zero values as shown in the figure The Fourier transform of $y(2 n)$ will be $e^{-j2w} [\cos 4 w+2 \cos 2 w+2]$ $[\cos 2 w+2 \cos w+2]$ $e^{-jw} [\cos 2 w+2 \cos w+2]$ $e^{-j2w} [\cos 2 w+2 \cos w+2]$
Statement of Linked Answer Questions $85 a$ and $85b$A sequence $x(n)$ has non-zero values as shown in the figureThe Fourier transform of $y(2 n)$ will be$e^{-j2w} [\cos ...
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392
GATE ECE 2005 | Question: 84b
Statement of Linked Answer Questions $84a$ and $84b$ Voltage standing wave pattern in a lossless transmission line with characteristic impedance $50 \mathrm{W}$ and a resistive load is shown in the figure. The reflection coefficient is given by $-0.6$ $-1$ $0.6$ $0$
Statement of Linked Answer Questions $84a$ and $84b$Voltage standing wave pattern in a lossless transmission line with characteristic impedance $50 \mathrm{W}$ and a resi...
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393
GATE ECE 2005 | Question: 81b
Statement for Linked Answer Questions $81 a$ and $81 b$: Consider an $8085$ microprocessor system If in addition following code exists from $019 \mathrm{H}$ onwards, $\text{ORI 40 H}$ $\text{ADD M}$ What will be the result in the accumulator after the last instruction is executed? $40 \; \mathrm{H}$ $20 \; \mathrm{H}$ $60 \; \mathrm{H}$ $42 \; \mathrm{H}$
Statement for Linked Answer Questions $81 a$ and $81 b$:Consider an $8085$ microprocessor systemIf in addition following code exists from $019 \mathrm{H}$ onwards,$\text{...
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GATE ECE 2005 | Question: 82b
Statement for Linked Answer Questions $82a$ and $82b:$ The dopen loop transfer function of a unity feedback system is given by \[\mathrm{G}(s)=\frac{3 e^{-2}}{s(s+2)}\] Based on the above results, the gain and phase margins of the system will be $-7.09$ ... $87.5^{\circ}$ $7.09 \mathrm{~dB}$ and $-87.5^{\circ}$ $-7.09 \mathrm{~dB}$ and $-87.5^{\circ}$
Statement for Linked Answer Questions $82a$ and $82b:$The dopen loop transfer function of a unity feedback system is given by\[\mathrm{G}(s)=\frac{3 e^{-2}}{s(s+2)}\]Base...
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395
GATE ECE 1997 | Question 4.2
The decoding circuit shown in the figure is has been used to generate the active low chip select signal for a microprocessor peripheral. (The address lines are designated as $\mathrm{AO}$ to $\mathrm{A} 7$ for $\mathrm{l} / \mathrm{O}$ ... $30 \; \mathrm{H}$ to $33 \; \mathrm{H}$ $70 \; \mathrm{H}$ to $73 \; \mathrm{H}$
The decoding circuit shown in the figure is has been used to generate the active low chip select signal for a microprocessor peripheral. (The address lines are designated...
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GATE ECE 1997 | Question 1.10
A deterministic signal has the power spectrum given in the figure is, The minimum sampling rate needed to completely represent this signal is $1 \; \mathrm{kHz}$ $2 \; \mathrm{kHz}$ $3 \; \mathrm{kHz}$ None of the above
A deterministic signal has the power spectrum given in the figure is, The minimum sampling rate needed to completely represent this signal is$1 \; \mathrm{kHz}$$2 \; \mat...
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GATE ECE 2000 | Question 2.12
One period $(0, T)$ each of two periodic waveforms $W_{1}$ and $W_{2}$ are shown in figure. The magnitudes of the $n$th Fourier series coefficients of $W_{1}$ and $W_{2}$. for $n \geq 1, n$ odd, are respectively proportional to $n^{-3} \mid$ and $n^{-2} \mid$ $n^{-2} \mid$ and $n^{-3} \mid$ $n^{-1}$ and $n^{-2} \mid$ $n^{-4} \mid$ and $n^{-2} \mid$
One period $(0, T)$ each of two periodic waveforms $W_{1}$ and $W_{2}$ are shown in figure. The magnitudes of the $n$th Fourier series coefficients of $W_{1}$ and $W_{2}$...
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GATE ECE 1997 | Question 3.11
The skin depth at $10\; \mathrm{MHz}$ for a conductor is $1 \; \mathrm{cm}$. The phase velocity of an electromagnetic wave in the conductor at $1,000 \; \mathrm{MHz}$ is about $6 \times 10^{6} \mathrm{~m} / \mathrm{sec}$ $6 \times 10^{7} \mathrm{~m} / \mathrm{sec}$ $3 \times 10^{8} \mathrm{~m} / \mathrm{sec}$ $6 \times 10^{8} \mathrm{~m} / \mathrm{sec}$
The skin depth at $10\; \mathrm{MHz}$ for a conductor is $1 \; \mathrm{cm}$. The phase velocity of an electromagnetic wave in the conductor at $1,000 \; \mathrm{MHz}$ is ...
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399
GATE ECE 1997 | Question 1.1
The current $i_4$ in the circuit of the figure is equal to $12 \mathrm{~A}$ $-12 \mathrm{~A}$ $4 \mathrm{~A}$ None of these
The current $i_4$ in the circuit of the figure is equal to$12 \mathrm{~A}$$-12 \mathrm{~A}$$4 \mathrm{~A}$None of these
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GATE ECE 1997 | Question 3.1
In the circuit of the figure is the energy absorbed by the $4 \; \Omega$ resistor in the time interval $(0, \infty)$ is $36$ Joules $16$ Joules $256$ Joules None of the above
In the circuit of the figure is the energy absorbed by the $4 \; \Omega$ resistor in the time interval $(0, \infty)$ is$36$ Joules$16$ Joules$256$ JoulesNone of the above...
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