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Most viewed questions in Engineering Mathematics
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321
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...
admin
46.4k
points
83
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2016
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
322
TIFR ECE 2010 | Question: 10
$\text{H}$ is a circulant matrix (row $n$ is obtained by circularly shifting row $1$ to the right by $n$ positions) and $\text{F}$ is the $\text{DFT}$ matrix. Which of the following is true? $F H F^{H}$ is circulant, where $F^{H}$ is the inverse $\text{DFT}$ matrix. $F H F^{H}$ is tridiagonal $F H F^{H}$ is diagonal $F H F^{H}$ has real entries None of the above
$\text{H}$ is a circulant matrix (row $n$ is obtained by circularly shifting row $1$ to the right by $n$ positions) and $\text{F}$ is the $\text{DFT}$ matrix. Which of th...
admin
46.4k
points
82
views
admin
asked
Nov 30, 2022
Linear Algebra
tifr2010
linear-algebra
matrices
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–
0
votes
0
answers
323
GATE ECE 2014 Set 4 | Question: 29
For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the triangle, the angle between the hypotenuse and the side is $12^{\circ}$ $36^{\circ}$ $60^{\circ}$ $45^{\circ}$
For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the triangle, the ang...
Milicevic3306
16.0k
points
82
views
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2014-ec-4
calculus
maxima-minima
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–
1
votes
0
answers
324
TIFR ECE 2010 | Question: 15
Let $\imath=\sqrt{-1}$. Then $\imath^{\imath}$ could be $\exp (\pi / 2)$ $\exp (\pi / 4)$ Can't determine Takes infinite values Is a complex number
Let $\imath=\sqrt{-1}$. Then $\imath^{\imath}$ could be$\exp (\pi / 2)$$\exp (\pi / 4)$Can't determineTakes infinite valuesIs a complex number
admin
46.4k
points
81
views
admin
asked
Nov 30, 2022
Complex Analysis
tifr2010
complex-analysis
complex-number
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–
1
votes
0
answers
325
TIFR ECE 2022 | Question: 6
Consider a degree-$5$ polynomial function $f:(-\infty, \infty) \rightarrow(-\infty, \infty)$. If $f$ exhibits at least four local maxima, which of the following is necessarily true? (Note: A local maximum is a point where the function value is the maximum in a ... derivative of $f(x)$ is negative for some $x \in[0,100]$ $f$ has exactly $4$ local maxima None of the above
Consider a degree-$5$ polynomial function $f:(-\infty, \infty) \rightarrow(-\infty, \infty)$. If $f$ exhibits at least four local maxima, which of the following is necess...
admin
46.4k
points
81
views
admin
asked
Nov 30, 2022
Calculus
tifrece2022
calculus
maxima-minima
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–
0
votes
0
answers
326
GATE ECE 2015 Set 1 | Question: 25
The solution of the differential equation $\frac{d^2y}{dt^2} + 2 \frac{dy}{dt}+y=0$ with $y(0)=y’(0)=1$ is $(2-t)e^t$ $(1+2t)e^{-t}$ $(2+t)e^{-t}$ $(1-2t)e^t$
The solution of the differential equation $\frac{d^2y}{dt^2} + 2 \frac{dy}{dt}+y=0$ with $y(0)=y’(0)=1$ is$(2-t)e^t$$(1+2t)e^{-t}$$(2+t)e^{-t}$$(1-2t)e^t$
Milicevic3306
16.0k
points
80
views
Milicevic3306
asked
Mar 27, 2018
Differential Equations
gate2015-ec-1
differential-equations
+
–
1
votes
0
answers
327
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
asked
Nov 29, 2022
Probability and Statistics
tifrece2017
probability-and-statistics
probability
uniform-distribution
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–
0
votes
0
answers
328
GATE ECE 2015 Set 2 | Question: 26
Consider the differential equation $\dfrac{\mathrm{d} x }{\mathrm{d} t} = 10 – 0.2x$ with initial condition $x(0) = 1$. The response $x(t)$ for $t>0$ is $2-e^{-0.2t}$ $2-e^{0.2t}$ $50-49e^{-0.2t}$ $50-49e^{0.2t}$
Consider the differential equation $\dfrac{\mathrm{d} x }{\mathrm{d} t} = 10 – 0.2x$ with initial condition $x(0) = 1$. The response $x(t)$ for $t>0$ is$2-e^{-0.2t}$$2-...
Milicevic3306
16.0k
points
79
views
Milicevic3306
asked
Mar 27, 2018
Differential Equations
gate2015-ec-2
differential-equations
+
–
0
votes
0
answers
329
GATE ECE 2014 Set 4 | Question: 4
If $a$ and $b$ are constants, the most general solution of the differential equation $\frac{d^2x}{dt^2}+2 \frac{dx}{dt}+x=0$ is $ae^{-t}$ $ae^{-t} + bte^{-t}$ $ae^t+bte^{-t}$ $ae^{-2t}$
If $a$ and $b$ are constants, the most general solution of the differential equation $$\frac{d^2x}{dt^2}+2 \frac{dx}{dt}+x=0$$ is$ae^{-t}$$ae^{-t} + bte^{-t}$$ae^t+bte^{-...
Milicevic3306
16.0k
points
79
views
Milicevic3306
asked
Mar 26, 2018
Differential Equations
gate2014-ec-4
differential-equations
+
–
1
votes
0
answers
330
TIFR ECE 2016 | Question: 9
Suppose $Y=X+Z$, where $X$ and $Z$ are independent zero-mean random variables each with variance $1.$ Let $\hat{X}(Y)=a Y$ be the optimal linear least-squares estimate of $X$ from $Y$, i.e., $a$ is chosen such that $E\left[(X-a Y)^{2}\right]$ is minimized. What is the resulting ... $1$ $\frac{2}{3}$ $\frac{1}{2}$ $\frac{1}{3}$ $\frac{1}{4}$
Suppose $Y=X+Z$, where $X$ and $Z$ are independent zero-mean random variables each with variance $1.$ Let $\hat{X}(Y)=a Y$ be the optimal linear least-squares estimate of...
admin
46.4k
points
78
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2016
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
331
TIFR ECE 2021 | Question: 15
We have the sequence, $a_{n}=\frac{1}{n \log ^{2} n}, n \geq 2$, where log is the logarithm to the base $2$ and let $A=\sum_{n=2}^{\infty} a_{n}$ ... $H(X)?$ $H(X) \leq 3$ $H(X) \in(3,5]$ $H(X) \in(5,10]$ $H(X)>10$ but finite $H(X)$ is unbounded
We have the sequence, $a_{n}=\frac{1}{n \log ^{2} n}, n \geq 2$, where log is the logarithm to the base $2$ and let $A=\sum_{n=2}^{\infty} a_{n}$ be the sum of the sequen...
admin
46.4k
points
77
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2021
probability-and-statistics
probability
random-variable
+
–
0
votes
0
answers
332
GATE ECE 2016 Set 2 | Question: 26
The ordinary differential equation $\frac{dx}{dt}=-3x+2, \text{ with }x(0) = 1$ is to be solved using the forward Euler method. The largest time step that can be used to solve the equation without making the numerical solution unstable is _________
The ordinary differential equation $$\frac{dx}{dt}=-3x+2, \text{ with }x(0) = 1$$ is to be solved using the forward Euler method. The largest time step that can be used t...
Milicevic3306
16.0k
points
77
views
Milicevic3306
asked
Mar 27, 2018
Differential Equations
gate2016-ec-2
numerical-answers
differential-equations
+
–
1
votes
0
answers
333
TIFR ECE 2012 | Question: 11
A Poisson random variable $X$ is given by $\operatorname{Pr}\{X=k\}=\mathrm{e}^{-\lambda} \lambda^{k} / k !, k=0,1,2, \ldots$ for $\lambda>0$. The variance of $X$ scales as $\lambda$ $\lambda^{2}$ $\lambda^{3}$ $\sqrt{\lambda}$ None of the above
A Poisson random variable $X$ is given by $\operatorname{Pr}\{X=k\}=\mathrm{e}^{-\lambda} \lambda^{k} / k !, k=0,1,2, \ldots$ for $\lambda>0$. The variance of $X$ scales ...
admin
46.4k
points
76
views
admin
asked
Dec 8, 2022
Probability and Statistics
tifr2012
probability-and-statistics
probability
poisson-distribution
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–
1
votes
0
answers
334
TIFR ECE 2011 | Question: 4
Let $\lim _{n \rightarrow \infty} x_{n}=x$. Then which of the following is $\text{TRUE.}$ There exists an $n_{0}$, such that for all $n>n_{0},\left|x_{n}-x\right|=0$. There exists an $n_{0}$ ... $n>n_{0},\left|\frac{x_{n}}{x}\right| \leq \epsilon$ for any $\epsilon>0$. None of the above.
Let $\lim _{n \rightarrow \infty} x_{n}=x$. Then which of the following is $\text{TRUE.}$There exists an $n_{0}$, such that for all $n>n_{0},\left|x_{n}-x\right|=0$.There...
admin
46.4k
points
76
views
admin
asked
Dec 5, 2022
Calculus
tifr2011
calculus
limits
+
–
1
votes
0
answers
335
TIFR ECE 2021 | Question: 14
A tourist starts by taking one of the $n$ available paths, denoted by $1,2, \cdots, n$. An hour into the journey, the path $i$ subdivides into further $1+i$ subpaths, only one of which leads to the destination. The tourist has no map and makes random choices of the path and the ... $\frac{10}{36}$ $\frac{11}{36}$ $\frac{12}{36}$ $\frac{13}{36}$ $\frac{14}{36}$
A tourist starts by taking one of the $n$ available paths, denoted by $1,2, \cdots, n$. An hour into the journey, the path $i$ subdivides into further $1+i$ subpaths, onl...
admin
46.4k
points
76
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2021
probability-and-statistics
probability
random-variable
+
–
0
votes
0
answers
336
GATE ECE 2015 Set 2 | Question: 4
The general solution of the differential equation $\dfrac{\mathrm{d} y}{\mathrm{d} x} = \dfrac{1+\cos 2y}{1-\cos 2x}$ is $ \tan y – \cot x = c\:\text{(c is a constant)}$ $\tan x – \cot y = c\:\text{(c is a constant)}$ $\tan y + \cot x = c\:\text{(c is a constant)}$ $\tan x + \cot y = c\:\text{(c is a constant)}$
The general solution of the differential equation $\dfrac{\mathrm{d} y}{\mathrm{d} x} = \dfrac{1+\cos 2y}{1-\cos 2x}$ is$ \tan y – \cot x = c\:\text{(c is a constant)}...
Milicevic3306
16.0k
points
75
views
Milicevic3306
asked
Mar 27, 2018
Differential Equations
gate2015-ec-2
differential-equations
+
–
1
votes
0
answers
337
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
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2017
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
338
TIFR ECE 2013 | Question: 16
A surprise quiz contains three multiple choice questions; question $1$ has $3$ suggested answers, question $2$ has four, and question $3$ has two. A completely unprepared student decides to choose the answers at random. If $X$ is the number of questions the student answers ... expected number of correct answers is $15 / 12$ $7 / 12$ $13 / 12$ $18 / 12$ None of the above
A surprise quiz contains three multiple choice questions; question $1$ has $3$ suggested answers, question $2$ has four, and question $3$ has two. A completely unprepared...
admin
46.4k
points
73
views
admin
asked
Dec 12, 2022
Probability and Statistics
tifr2013
probability-and-statistics
probability
random-variable
+
–
0
votes
0
answers
339
GATE ECE 2014 Set 4 | Question: 46
The state transition matrix $\phi(t)$ of a system $\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}$ is $\begin{bmatrix} t & 1 \\ 1 & 0 \end{bmatrix} \\$ ... $\begin{bmatrix} 0 & 1 \\ 1 & t \end{bmatrix} \\$ $\begin{bmatrix} 1 & t \\ 0 & 1 \end{bmatrix}$
The state transition matrix $\phi(t)$ of a system $\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \...
Milicevic3306
16.0k
points
70
views
Milicevic3306
asked
Mar 26, 2018
Linear Algebra
gate2014-ec-4
linear-algebra
matrices
+
–
1
votes
0
answers
340
GATE ECE 2010 | Question: 27
A fair coin is tossed independently four times. The probability of the event "the number of times heads show up is more than the number of times tails show up" is $\frac{1}{16}$ $\frac{1}{8}$ $\frac{1}{4}$ $\frac{5}{16}$
A fair coin is tossed independently four times. The probability of the event "the number of times heads show up is more than the number of times tails show up" is$\frac{1...
admin
46.4k
points
65
views
admin
asked
Sep 15, 2022
Probability and Statistics
gate2010-ec
probability-and-statistics
probability
independent-events
+
–
1
votes
0
answers
341
TIFR ECE 2020 | Question: 13
Alice and Bob have one coin each with probability of Heads $p$ and $q$, respectively. In each round, both Alice and Bob independently toss their coin once, and the game stops if one of them gets a Heads and the other gets a Tails. If they both get either Heads or both get Tails in ... $R$ is independent of $p$ and $q$ $R=\frac{1}{1+2 p q-p-q}$ None of the above
Alice and Bob have one coin each with probability of Heads $p$ and $q$, respectively. In each round, both Alice and Bob independently toss their coin once, and the game s...
admin
46.4k
points
64
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2020
probability-and-statistics
probability
conditional-probability
+
–
1
votes
0
answers
342
GATE ECE 2011 | Question: 36
A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is $2 / 36$ $2 / 6$ $5 / 12$ $1 / 2$
A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is$2 / 36$$2 / 6$$5 / 12$$1 / 2$
admin
46.4k
points
63
views
admin
asked
Sep 3, 2022
Probability and Statistics
gate2011-ec
probability-and-statistics
probability
+
–
1
votes
0
answers
343
GATE ECE 2010 | Question: 30
Consider a differential equation $\dfrac{d y(x)}{d x}-y(x)=x$ with the initial condition $y(0)=0$. Using Euler's first order method with a step size of $0.1$, the value of $y(0.3)$ is $0.01$ $0.031$ $0.0631$ $0.1$
Consider a differential equation $\dfrac{d y(x)}{d x}-y(x)=x$ with the initial condition $y(0)=0$. Using Euler's first order method with a step size of $0.1$, the value o...
admin
46.4k
points
56
views
admin
asked
Sep 15, 2022
Differential Equations
gate2010-ec
differential-equations
first-order-differential-equation
+
–
1
votes
0
answers
344
TIFR ECE 2020 | Question: 4
Let $f, g: \mathbb{R} \rightarrow \mathbb{R}$ be two functions that are continuous and differentiable. Consider the following statements: $\min \{f, g\}$ is continuous $\max \{f, g\}$ is continuous $\max \{f, g\}$ is differentiable Which ... is correct Only statement $2$ is correct Only statement $3$ is correct Only statements $1$ and $2$ are correct None of the above
Let $f, g: \mathbb{R} \rightarrow \mathbb{R}$ be two functions that are continuous and differentiable. Consider the following statements:$\min \{f, g\}$ is continuous$\ma...
admin
46.4k
points
52
views
admin
asked
Nov 30, 2022
Calculus
tifrece2020
calculus
continuity-and-differentiability
+
–
1
votes
0
answers
345
TIFR ECE 2013 | Question: 18
Consider a coin tossing game between Santa and Banta. Both of them toss two coins sequentially, first Santa tosses a coin then Banta and so on. Santa tosses a fair coin: Probability of heads is $1 / 2$ and probability of tails is $1 / 2$. Banta's coin probabilities depend on ... the two trials conducted by each of them? $1 / 2$ $5 / 16$ $3 / 16$ $1 / 4$ $1 / 3$
Consider a coin tossing game between Santa and Banta. Both of them toss two coins sequentially, first Santa tosses a coin then Banta and so on. Santa tosses a fair coin: ...
admin
46.4k
points
51
views
admin
asked
Dec 12, 2022
Probability and Statistics
tifr2013
probability-and-statistics
probability
conditional-probability
+
–
1
votes
0
answers
346
GATE ECE 2010 | Question: 1
The eigenvalues of a skew-symmetric matrix are always zero always pure imaginary either zero or pure imaginary always real
The eigenvalues of a skew-symmetric matrix arealways zeroalways pure imaginaryeither zero or pure imaginaryalways real
admin
46.4k
points
50
views
admin
asked
Sep 15, 2022
Linear Algebra
gate2010-ec
linear-algebra
eigen-values
+
–
1
votes
0
answers
347
TIFR ECE 2020 | Question: 15
Suppose $\vec{u}, \vec{v}_{1}, \vec{v}_{2} \in \mathbb{R}^{n}$ are linearly independent vectors such that $\vec{v}_{1}^{T} \vec{v}_{2}=0$. Let the pair of real numbers $\left(a_{1}^{*}, a_{2}^{*}\right)$ be such that they solve the following optimization problem \[ ... $\left\|\vec{v}_{*}\right\|^{2}-\|\vec{u}\|^{2}$ $0$ None of the above
Suppose $\vec{u}, \vec{v}_{1}, \vec{v}_{2} \in \mathbb{R}^{n}$ are linearly independent vectors such that $\vec{v}_{1}^{T} \vec{v}_{2}=0$. Let the pair of real numbers $\...
admin
46.4k
points
45
views
admin
asked
Nov 30, 2022
Vector Analysis
tifrece2020
vector-analysis
vector-in-planes
+
–
1
votes
0
answers
348
GATE ECE 2010 | Question: 26
If $e^{y}=x^{\frac{1}{x}}$, then $y$ has a maximum at $x=e$ minimum at $x=e$ maximum at $x=e^{-1}$ minimum at $x=e^{-1}$
If $e^{y}=x^{\frac{1}{x}}$, then $y$ has amaximum at $x=e$minimum at $x=e$maximum at $x=e^{-1}$minimum at $x=e^{-1}$
admin
46.4k
points
45
views
admin
asked
Sep 15, 2022
Calculus
gate2010-ec
calculus
maxima-minima
+
–
1
votes
0
answers
349
TIFR ECE 2013 | Question: 10
Consider the following series of square matrices: \[ \begin{array}{l} H_{1}=[1], \\ H_{2}=\left[\begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array}\right], \end{array} \] and for $k=2,3, \ldots$, the $2^{k} \times 2^{k}$ matrix $H_{2^{k}}$ is recursively defined as \[ H_{2^{k}}=\ ... is $H_{2^{k}} H_{2^{k}}^{T}?)$ $0$ $2^{k}$ $2^{k / 2}$ $2^{k 2^{k-1}}$ $2^{k 2^{k}}$
Consider the following series of square matrices:\[\begin{array}{l}H_{1}= , \\H_{2}=\left[\begin{array}{cc}1 & 1 \\1 & -1\end{array}\right],\end{array}\]and for $k=2,3, \...
admin
46.4k
points
44
views
admin
asked
Dec 12, 2022
Linear Algebra
tifr2013
linear-algebra
determinant
+
–
1
votes
0
answers
350
TIFR ECE 2013 | Question: 13
Let $A$ be a square matrix and $x$ be a vector whose dimensions match $A$. Let $B^{\dagger}$ be the conjugate transpose of $B$. Then which of the following is not true: $x^{\dagger} A^{2} x$ is always non-negative $x^{\dagger} A x$ ... $A=A^{\dagger}$ then $x^{\dagger} A y$ is complex for some vector $y$ with same dimensions as $x$
Let $A$ be a square matrix and $x$ be a vector whose dimensions match $A$. Let $B^{\dagger}$ be the conjugate transpose of $B$. Then which of the following is not true:$x...
admin
46.4k
points
44
views
admin
asked
Dec 12, 2022
Linear Algebra
tifr2013
linear-algebra
matrices
+
–
1
votes
0
answers
351
TIFR ECE 2013 | Question: 19
Which of the following is true for polynomials defined over real numbers $\mathbb{R}$. Every odd degree polynomial has a real root. Every odd degree polynomial has at least one complex root. Every even degree polynomial has at least one complex root. Every even degree polynomial has a real root. None of the above
Which of the following is true for polynomials defined over real numbers $\mathbb{R}$.Every odd degree polynomial has a real root.Every odd degree polynomial has at least...
admin
46.4k
points
44
views
admin
asked
Dec 12, 2022
Calculus
tifr2013
calculus
polynomials
+
–
1
votes
0
answers
352
TIFR ECE 2021 | Question: 9
A stick of length $1$ is broken at a point chosen uniformly at random. Which of the following is false? Twice the length of the smaller piece is greater than the length of the larger piece with positive probability. One half of the length of the ... . The product of the length of the smaller piece and the larger piece is greater than $1 / 4$ with positive probability.
A stick of length $1$ is broken at a point chosen uniformly at random. Which of the following is false?Twice the length of the smaller piece is greater than the length of...
admin
46.4k
points
44
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2021
probability-and-statistics
probability
uniform-distribution
+
–
1
votes
0
answers
353
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...
admin
46.4k
points
44
views
admin
asked
Nov 29, 2022
Linear Algebra
tifrece2016
linear-algebra
rank-of-matrix
+
–
1
votes
0
answers
354
TIFR ECE 2013 | Question: 12
Let $A$ be a Hermitian matrix and let $I$ be the Identity matrix with same dimensions as $A$. Then for a scalar $\alpha>0, A+\alpha I$ has the same eigenvalues as of $A$ but different eigenvectors the same eigenvalues and eigenvectors as of ... those of $A$ and same eigenvectors as of $A$ eigenvalues and eigenvectors with no relation to those of $A$ None of the above
Let $A$ be a Hermitian matrix and let $I$ be the Identity matrix with same dimensions as $A$. Then for a scalar $\alpha>0, A+\alpha I$ hasthe same eigenvalues as of $A$ b...
admin
46.4k
points
43
views
admin
asked
Dec 12, 2022
Linear Algebra
tifr2013
linear-algebra
eigen-values
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1
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0
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355
TIFR ECE 2013 | Question: 14
$X, Y, Z$ are integer valued random variables with the following two properties: $X$ and $Y$ are independent. For all integer $x$, conditioned on the event $\{X=x\}$, we have that $Y$ and $Z$ are independent (in other words, conditioned on ... and $Z$ are independent Conditioned on $Z$, the random variables $X$ and $Y$ are independent All of the above None of the above
$X, Y, Z$ are integer valued random variables with the following two properties:$X$ and $Y$ are independent.For all integer $x$, conditioned on the event $\{X=x\}$, we ha...
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Probability and Statistics
tifr2013
probability-and-statistics
probability
random-variable
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1
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0
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356
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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Linear Algebra
tifrece2016
linear-algebra
matrices
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1
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357
TIFR ECE 2013 | Question: 17
Consider four coins, three of which are fair, that is they have heads on one side and tails on the other and both are equally likely to occur in a toss. The fourth coin has heads on both sides. Given that one coin amongst the four is picked at random and is tossed, and the ... is the probability that its other side is tails? $1 / 2$ $3 / 8$ $3 / 5$ $3 / 4$ $5 / 7$
Consider four coins, three of which are fair, that is they have heads on one side and tails on the other and both are equally likely to occur in a toss. The fourth coin h...
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46.4k
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Dec 12, 2022
Probability and Statistics
tifr2013
probability-and-statistics
probability
random-variable
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358
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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Nov 29, 2022
Linear Algebra
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linear-algebra
system-of-equations
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359
GATE ECE 2010 | Question: 3
A function $n(x)$ satisfies the differential equation $\frac{d^{2} n(x)}{d x^{2}}-\frac{n(x)}{L^{2}}=0$ where $L$ is a constant. The boundary conditions are: $n(0)=K$ and $n(\infty)=0$. The solution to this equation is $n(x)=K \exp (x / L)$ $n(x)=K \exp (-x / \sqrt{L})$ $n(x)=K^{2} \exp (-x / L)$ $n(x)=K \exp (-x / L)$
A function $n(x)$ satisfies the differential equation $\frac{d^{2} n(x)}{d x^{2}}-\frac{n(x)}{L^{2}}=0$ where $L$ is a constant. The boundary conditions are: $n(0)=K$ and...
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46.4k
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Sep 15, 2022
Differential Equations
gate2010-ec
differential-equations
second-order-differential-equation
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1
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0
answers
360
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}\...
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Nov 30, 2022
Probability and Statistics
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probability-and-statistics
probability
expectation
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