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321
TIFR ECE 2018 | Question: 11
Assume the following well known result: If a coin is flipped independently many times and its probability of heads $(H)$ is $p \in(0,1)$ and probability of tails $(T)$ is $(1-p)$, then the expected number of coin flips till the first time a heads is observed is $1 / p$. What is the ... $\frac{1}{1-(1-p)^{2}}(4+1 / p)$ $\frac{1}{p}+\frac{1}{1-p}$
Assume the following well known result: If a coin is flipped independently many times and its probability of heads $(H)$ is $p \in(0,1)$ and probability of tails $(T)$ is...
94
views
asked
Nov 29, 2022
Probability and Statistics
tifrece2018
probability-and-statistics
probability
expectation
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1
votes
0
answers
322
TIFR ECE 2018 | Question: 12
Suppose that Amitabh Bachchan has ten coins in his pocket. $3$ coins have tails on both sides. $4$ coins have heads on both sides. $3$ coins have heads on one side and tails on the other and both the outcomes are equally likely when that coin is flipped. In a bet with Dharmendra ... that the other side of this coin is heads? $1 / 2$ $3 / 10$ $1 / 4$ $0.3$ $1 / 3$
Suppose that Amitabh Bachchan has ten coins in his pocket. $3$ coins have tails on both sides. $4$ coins have heads on both sides. $3$ coins have heads on one side and ta...
111
views
asked
Nov 29, 2022
Probability and Statistics
tifrece2018
probability-and-statistics
probability
conditional-probability
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1
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0
answers
323
TIFR ECE 2018 | Question: 13
Consider five distinct binary vectors $X_{1}, \ldots, X_{5}$ each of length $10$. Let \[d_{i j}=\sum_{k=1}^{10}\left(X_{i k} \text { XOR } X_{j k}\right),\] (i.e., $d_{i j}$ is the number of coordinates where $X_{i}$ ... to $X_{5}$, and argue about the result noting that there are five binary vectors.] $d=10$ $d=9$ $d=8$ $d<8$ Information is not sufficient
Consider five distinct binary vectors $X_{1}, \ldots, X_{5}$ each of length $10$. Let\[d_{i j}=\sum_{k=1}^{10}\left(X_{i k} \text { XOR } X_{j k}\right),\](i.e., $d_{i j}...
87
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Nov 29, 2022
Others
tifrece2018
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1
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324
TIFR ECE 2018 | Question: 14
Define the $\ell_{p}$ ball in two dimensions as the set of points $(x, y)$ such that $|x|^{p}+|y|^{p} \leq 1$. Which of the following is $\text{FALSE:}$ The $\ell_{2}$ ball is contained in the $\ell_{3}$ ball The $\ell_{2}$ ball is contained in ... $\ell_{2}$ ball is contained in the $\ell_{5}$ ball The $\ell_{1}$ ball is contained in the $\ell_{3}$ ball
Define the $\ell_{p}$ ball in two dimensions as the set of points $(x, y)$ such that $|x|^{p}+|y|^{p} \leq 1$. Which of the following is $\text{FALSE:}$The $\ell_{2}$ bal...
81
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Nov 29, 2022
Others
tifrece2018
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1
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325
TIFR ECE 2018 | Question: 15
Consider real-valued continuous functions $f:[0,2] \rightarrow(-\infty, \infty)$ and let \[A=\int_{0}^{1}|f(x)| d x \quad \text { and } B=\int_{1}^{2}|f(x)| d x .\] Which of the following is $\text{TRUE}?$ There exists an $f$ so that \[A+B<\int_{0}^{2} f(x) ... such that $\int_{0}^{1} f(x) d x=3$ There does not exist an $f$ so that \[A+B \leq-\int_{0}^{2} f(x) d x\]
Consider real-valued continuous functions $f:[0,2] \rightarrow(-\infty, \infty)$ and let\[A=\int_{0}^{1}|f(x)| d x \quad \text { and } B=\int_{1}^{2}|f(x)| d x .\]Which o...
101
views
asked
Nov 29, 2022
Calculus
tifrece2018
calculus
definite-integrals
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1
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0
answers
326
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,...
68
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Nov 29, 2022
Others
tifrece2017
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1
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327
TIFR ECE 2017 | Question: 2
Suppose a $1 \mu \mathrm{H}$ inductor and a $1 \Omega$ resistor are connected in series to a $1 \mathrm{ V}$ battery. What happens to the current in the circuit? The current starts at $0 \mathrm{ A}$, and gradually rises to $1 \mathrm{ A}$ The current ... $1 \mathrm{ A}$ The current oscillates over time between $1 \mathrm{ A}$ and $-1 \mathrm{ A}$
Suppose a $1 \mu \mathrm{H}$ inductor and a $1 \Omega$ resistor are connected in series to a $1 \mathrm{ V}$ battery. What happens to the current in the circuit?The curre...
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Nov 29, 2022
Others
tifrece2017
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328
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...
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Nov 29, 2022
Others
tifrece2017
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329
TIFR ECE 2017 | Question: 4
A Schmitt trigger circuit is a comparator circuit with a hysteresis. Consider the Schmitt trigger circuit in the figure implemented using an opamp. What are the trigger levels for this circuit? $\pm \frac{R_{1}}{R_{2}} V_{s}$ $\pm \frac{R_{2}}{R_{1}} V_{s}$ $\pm \frac{R_{1}}{R_{1}+R_{2}} V_{s}$ $\pm \frac{R_{2}}{R_{1}+R_{2}} V_{s}$ None of the above
A Schmitt trigger circuit is a comparator circuit with a hysteresis. Consider the Schmitt trigger circuit in the figure implemented using an opamp. What are the trigger l...
102
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Nov 29, 2022
Others
tifrece2017
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330
TIFR ECE 2017 | Question: 5
Consider the inequality \[ n-\frac{1}{n} \geq \sqrt{n^{2}-1}, \] where $n$ is an integer $\geq 1$. Which of the following statements is $\text{TRUE?}$ This inequality holds for all integers $n \geq 1$ ... not hold for any integer $n \geq 1$ $n-\frac{1}{n}=\sqrt{n^{2}-1}$ for infinitely many integers $n \geq 1$
Consider the inequality\[n-\frac{1}{n} \geq \sqrt{n^{2}-1},\]where $n$ is an integer $\geq 1$. Which of the following statements is $\text{TRUE?}$This inequality holds fo...
89
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asked
Nov 29, 2022
Quantitative Aptitude
tifrece2017
quantitative-aptitude
inequality
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1
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0
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331
TIFR ECE 2017 | Question: 6
Let $a, b \in\{0,1\}$. Consider the following statements where $*$ is the $\text{AND}$ operator, $\oplus$ is $\text{EXCLUSIVE-OR,}$ and ${ }^{c}$ denotes the complement function. $\max \left\{a * b, b \oplus a^{\mathrm{c}}\right\}=1$ ... $\text{(iii)}$ only $\text{(iii)}$ and $\text{(iv)}$ only $\text{(iv)}$ and $\text{(i)}$ only None of the above
Let $a, b \in\{0,1\}$. Consider the following statements where $*$ is the $\text{AND}$ operator, $\oplus$ is $\text{EXCLUSIVE-OR,}$ and ${ }^{c}$ denotes the complement f...
134
views
asked
Nov 29, 2022
Calculus
tifrece2017
calculus
functions
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1
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0
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332
TIFR ECE 2017 | Question: 7
A circulant matrix is a square matrix whose each row is the preceding row rotated to the right by one element, e.g., the following is a $3 \times 3$ circulant matrix. \[\left(\begin{array}{lll} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \ ... $j=\sqrt{-1}$ A vector whose $k$-th element is $\sinh \left(\frac{2 \pi k}{n}\right)$ None of the above
A circulant matrix is a square matrix whose each row is the preceding row rotated to the right by one element, e.g., the following is a $3 \times 3$ circulant matrix.\[\l...
88
views
asked
Nov 29, 2022
Linear Algebra
tifrece2017
linear-algebra
eigen-values
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1
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0
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333
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...
75
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Nov 29, 2022
Others
tifrece2017
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334
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...
74
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asked
Nov 29, 2022
Probability and Statistics
tifrece2017
probability-and-statistics
probability
random-variable
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1
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0
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335
TIFR ECE 2017 | Question: 10
Consider a single coin where the probability of heads is $p \in(0,1)$ and probability of tails is $1-p$. Suppose that this coin is flipped an infinite number of times. Let $N_{1}$ denote the number of flips till we see heads for the first time. Let $N_{2}$ denote the number of flips after ... $\frac{2}{p}$ $\frac{1}{p^{2}+(1-p)^{2}}$ $\frac{2}{p(1-p)}$
Consider a single coin where the probability of heads is $p \in(0,1)$ and probability of tails is $1-p$. Suppose that this coin is flipped an infinite number of times. Le...
91
views
asked
Nov 29, 2022
Probability and Statistics
tifrece2017
probability-and-statistics
probability
expectation
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1
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0
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336
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...
79
views
asked
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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337
TIFR ECE 2017 | Question: 12
Consider a signal $X$ that can take two values, $-1$ with probability $p$ and $+1$ with probability $1-p$. Let $Y=X+N$, where $N$ is mean zero random noise that has probability density function symmetric about $0.$ Given $p$ and on observing $Y$, the detection problem is ... $\text{(iii)}$ Only $\text{(i)}$ and $\text{(ii)}$ Only $\text{(i)}$ and $\text{(iii)}$
Consider a signal $X$ that can take two values, $-1$ with probability $p$ and $+1$ with probability $1-p$. Let $Y=X+N$, where $N$ is mean zero random noise that has proba...
82
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asked
Nov 29, 2022
Probability and Statistics
tifrece2017
probability-and-statistics
probability
probability-density-function
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1
votes
0
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338
TIFR ECE 2017 | Question: 13
Let $A$ be an $n \times n$ matrix. Consider the following statements. $A$ can have full-rank even if there exists two vectors $v_{1} \neq v_{2}$ such that $A v_{1}=A v_{2}$. $A$ can be similar to the identity matrix, when $A$ is not the identity matrix. Recall that ... $\text{(ii)}$ Only $\text{(iii)}$ $\text{(i), (ii),}$ and $\text{(iii)}$ None of the above
Let $A$ be an $n \times n$ matrix. Consider the following statements.$A$ can have full-rank even if there exists two vectors $v_{1} \neq v_{2}$ such that $A v_{1}=A v_{2}...
85
views
asked
Nov 29, 2022
Linear Algebra
tifrece2017
linear-algebra
matrices
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1
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0
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339
TIFR ECE 2017 | Question: 14
Consider the positive integer sequence \[x_{n}=n^{50} e^{-(\log (n))^{3 / 2}}, \quad n=1,2,3, \ldots\] Which of the following statements is $\text{TRUE?}$ For every $M>0$, there exists an $n$ such that $x_{n}>M$ ... and then increases with $n \geq 1$ Sequence $\left\{x_{n}\right\}$ eventually converges to zero as $n \rightarrow \infty$ None of the above
Consider the positive integer sequence\[x_{n}=n^{50} e^{-(\log (n))^{3 / 2}}, \quad n=1,2,3, \ldots\]Which of the following statements is $\text{TRUE?}$For every $M>0$, t...
88
views
asked
Nov 29, 2022
Calculus
tifrece2017
calculus
maxima-minima
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1
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0
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340
TIFR ECE 2017 | Question: 15
Suppose that $f(x)$ is a real valued continuous function such that $f(x) \rightarrow \infty$ as $x \rightarrow \infty$. Further, let \[a_{n}=\sum_{j=1}^{n} 1 / j\] and \[b_{n}=\sum_{j=1}^{n} 1 / j^{2} .\] Which of the following statements is true ... any number $M$ so that $f\left(b_{n}\right)$ and $f\left(a_{n}\right)$ are greater than $M$ for all $n$ None of the above
Suppose that $f(x)$ is a real valued continuous function such that $f(x) \rightarrow \infty$ as $x \rightarrow \infty$. Further, let\[a_{n}=\sum_{j=1}^{n} 1 / j\]and\[b_{...
87
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Nov 29, 2022
Others
tifrece2017
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341
TIFR ECE 2016 | Question: 1
Suppose $f(x)=c x^{-\alpha}$ for some $c>0$ and $\alpha>0$ such that $\int_{1}^{\infty} f(x) \mathrm{d} x=1$. Then, which of the following is possible? $\int_{1}^{\infty} x f(x) \mathrm{d} x=\infty$ ... $\int_{1}^{\infty} \frac{f(x)}{1+\ln x} \mathrm{~d} x=\infty$ None of the above
Suppose $f(x)=c x^{-\alpha}$ for some $c>0$ and $\alpha>0$ such that $\int_{1}^{\infty} f(x) \mathrm{d} x=1$. Then, which of the following is possible?$\int_{1}^{\infty} ...
87
views
asked
Nov 29, 2022
Calculus
tifrece2016
calculus
definite-integrals
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1
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0
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342
TIFR ECE 2016 | Question: 2
Let $X_{1}$ and $X_{2}$ be two independent continuous real-valued random variables taking values in the unit interval $[0,1]$. Let $Y=\max \left\{X_{1}, X_{2}\right\}$ ... $\operatorname{Pr}[Z=1]>\operatorname{Pr}[Z=2]=\frac{1}{2}$ $\operatorname{Pr}[Z=1]<\operatorname{Pr}[Z=2]$
Let $X_{1}$ and $X_{2}$ be two independent continuous real-valued random variables taking values in the unit interval $[0,1]$. Let $Y=\max \left\{X_{1}, X_{2}\right\}$ an...
83
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asked
Nov 29, 2022
Probability and Statistics
tifrece2016
probability-and-statistics
probability
random-variable
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343
TIFR ECE 2016 | Question: 3
Let $(X, Y)$ be a pair of independent random variables. Suppose $X$ takes values in $\{1, \ldots, 6\}$ with equal probability, and $Y$ takes values in $\{2,3\}$ with $\operatorname{Pr}[Y=2]=p$. Let $Z=(X \bmod Y)+1$ ... $\operatorname{Pr}[Z=1]=\frac{1}{2}$ for $p=\frac{1}{2}$ $\operatorname{Pr}[Z=1]=p(1-p)$ None of the above
Let $(X, Y)$ be a pair of independent random variables. Suppose $X$ takes values in $\{1, \ldots, 6\}$ with equal probability, and $Y$ takes values in $\{2,3\}$ with $\op...
100
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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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344
TIFR ECE 2016 | Question: 4
Consider a system which in response to input $x(t)$ outputs \[y(t)=x\left(t^{2}\right) .\] Which of the following describes the system? linear, time-invariant, causal linear, time-invariant, non-causal linear, time-variant non-linear, time-invariant non-linear, time-variant
Consider a system which in response to input $x(t)$ outputs\[y(t)=x\left(t^{2}\right) .\]Which of the following describes the system?linear, time-invariant, causallinear,...
93
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asked
Nov 29, 2022
Others
tifrece2016
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345
TIFR ECE 2016 | Question: 5
Consider the opamp circuit in the figure. Approximately what is $V_{0}$? $-\left(\frac{V_{1}}{2}+V_{2}\right)$ $-\left(\frac{V_{1}}{4}+\frac{V_{2}}{2}\right)$ $-\left(V_{1}+2 V_{2}\right)$ $-\left(4 V_{1}+2 V_{2}\right)$ None of the above
Consider the opamp circuit in the figure. Approximately what is $V_{0}$?$-\left(\frac{V_{1}}{2}+V_{2}\right)$$-\left(\frac{V_{1}}{4}+\frac{V_{2}}{2}\right)$$-\left(V_{1}+...
83
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Nov 29, 2022
Others
tifrece2016
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346
TIFR ECE 2016 | Question: 6
What is the Laplace transform $F(s)$ of the signal $f(t), t \geq 0$ defined below? In $t \in[0,1),$ ... $\frac{1}{s\left(1-e^{-s / 2}\right)}$ $\frac{1}{s\left(1+e^{-s / 2}\right)}$
What is the Laplace transform $F(s)$ of the signal $f(t), t \geq 0$ defined below? In $t \in[0,1),$\[f(t)=\left\{\begin{array}{ll}1, & t \in\left[0, \frac{1}{2}\right) \\...
92
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Nov 29, 2022
Others
tifrece2016
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347
TIFR ECE 2016 | Question: 7
Suppose $X$ and $Y$ are independent Gaussian random variables, whose pdfs are represented below. Which of the following describes the pdf of the $X+Y?$
Suppose $X$ and $Y$ are independent Gaussian random variables, whose pdfs are represented below. Which of the following describes the pdf of the $X+Y?$
99
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Nov 29, 2022
Probability and Statistics
tifrece2016
+
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1
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348
TIFR ECE 2016 | Question: 8
In terms of their frequency responses, which of the following is the odd one out? All four circuits are equivalent
In terms of their frequency responses, which of the following is the odd one out? All four circuits are equivalent
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Nov 29, 2022
Others
tifrece2016
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349
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...
78
views
asked
Nov 29, 2022
Probability and Statistics
tifrece2016
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
350
TIFR ECE 2016 | Question: 10
Let $U_{1}, U_{2}, U_{3}$ be independent random variables that are each uniformly distributed between zero and one. What is the probability that the second highest value amongst the three lies between $1 / 3$ and $2 / 3?$ $\frac{2}{9}$ $\frac{1}{27}$ $\frac{13}{27}$ $\frac{1}{3}$ $\frac{7}{18}$
Let $U_{1}, U_{2}, U_{3}$ be independent random variables that are each uniformly distributed between zero and one. What is the probability that the second highest value ...
82
views
asked
Nov 29, 2022
Probability and Statistics
tifrece2016
probability-and-statistics
probability
uniform-distribution
+
–
1
votes
0
answers
351
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...
30
views
asked
Nov 29, 2022
Probability and Statistics
tifrece2016
probability-and-statistics
probability
expectation
+
–
1
votes
0
answers
352
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...
28
views
asked
Nov 29, 2022
Probability and Statistics
tifrece2016
probability-and-statistics
probability
random-variable
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–
1
votes
0
answers
353
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 ...
41
views
asked
Nov 29, 2022
Linear Algebra
tifrece2016
linear-algebra
matrices
+
–
1
votes
0
answers
354
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...
42
views
asked
Nov 29, 2022
Linear Algebra
tifrece2016
linear-algebra
rank-of-matrix
+
–
1
votes
0
answers
355
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...
40
views
asked
Nov 29, 2022
Linear Algebra
tifrece2016
linear-algebra
system-of-equations
+
–
0
votes
0
answers
356
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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358
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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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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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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