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Highest voted questions in Engineering Mathematics
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121
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...
admin
46.4k
points
134
views
admin
asked
Nov 29, 2022
Calculus
tifrece2017
calculus
functions
+
–
1
votes
0
answers
122
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...
admin
46.4k
points
88
views
admin
asked
Nov 29, 2022
Linear Algebra
tifrece2017
linear-algebra
eigen-values
+
–
1
votes
0
answers
123
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
73
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2017
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
124
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...
admin
46.4k
points
91
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2017
probability-and-statistics
probability
expectation
+
–
1
votes
0
answers
125
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
77
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2017
probability-and-statistics
probability
uniform-distribution
+
–
1
votes
0
answers
126
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...
admin
46.4k
points
82
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2017
probability-and-statistics
probability
probability-density-function
+
–
1
votes
0
answers
127
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}...
admin
46.4k
points
85
views
admin
asked
Nov 29, 2022
Linear Algebra
tifrece2017
linear-algebra
matrices
+
–
1
votes
0
answers
128
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...
admin
46.4k
points
88
views
admin
asked
Nov 29, 2022
Calculus
tifrece2017
calculus
maxima-minima
+
–
1
votes
0
answers
129
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} ...
admin
46.4k
points
87
views
admin
asked
Nov 29, 2022
Calculus
tifrece2016
calculus
definite-integrals
+
–
1
votes
0
answers
130
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
131
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...
admin
46.4k
points
100
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2016
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
132
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 $X+Y?$
admin
46.4k
points
98
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2016
+
–
1
votes
0
answers
133
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
134
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 ...
admin
46.4k
points
81
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2016
probability-and-statistics
probability
uniform-distribution
+
–
1
votes
0
answers
135
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...
admin
46.4k
points
30
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2016
probability-and-statistics
probability
expectation
+
–
1
votes
0
answers
136
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...
admin
46.4k
points
28
views
admin
asked
Nov 29, 2022
Probability and Statistics
tifrece2016
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
137
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 ...
admin
46.4k
points
41
views
admin
asked
Nov 29, 2022
Linear Algebra
tifrece2016
linear-algebra
matrices
+
–
1
votes
0
answers
138
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
41
views
admin
asked
Nov 29, 2022
Linear Algebra
tifrece2016
linear-algebra
rank-of-matrix
+
–
1
votes
0
answers
139
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...
admin
46.4k
points
39
views
admin
asked
Nov 29, 2022
Linear Algebra
tifrece2016
linear-algebra
system-of-equations
+
–
1
votes
0
answers
140
GATE ECE 2009 | Question: 1
The order of the differential equation $\dfrac{d^{2} y}{d t^{2}}+\left(\dfrac{d y}{d t}\right)^{3}+y^{4}=e^{-t} \quad$ is $1$ $2$ $3$ $4$
The order of the differential equation $\dfrac{d^{2} y}{d t^{2}}+\left(\dfrac{d y}{d t}\right)^{3}+y^{4}=e^{-t} \quad$ is$1$$2$$3$$4$
admin
46.4k
points
213
views
admin
asked
Sep 15, 2022
Differential Equations
gate2009-ec
differential-equations
second-order-differential-equation
+
–
1
votes
0
answers
141
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
47
views
admin
asked
Sep 15, 2022
Linear Algebra
gate2010-ec
linear-algebra
eigen-values
+
–
1
votes
0
answers
142
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...
admin
46.4k
points
40
views
admin
asked
Sep 15, 2022
Differential Equations
gate2010-ec
differential-equations
second-order-differential-equation
+
–
1
votes
0
answers
143
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
43
views
admin
asked
Sep 15, 2022
Calculus
gate2010-ec
calculus
maxima-minima
+
–
1
votes
0
answers
144
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
62
views
admin
asked
Sep 15, 2022
Probability and Statistics
gate2010-ec
probability-and-statistics
probability
independent-events
+
–
1
votes
0
answers
145
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
49
views
admin
asked
Sep 15, 2022
Differential Equations
gate2010-ec
differential-equations
first-order-differential-equation
+
–
1
votes
0
answers
146
GATE ECE 2011 | Question: 25
The solution of the differential equation $\frac{d y}{d x}=k y, y(0)=c$ is $x=c e^{-k y}$ $x=k e^{c y}$ $y=c e^{k x}$ $y=c e^{-k x}$
The solution of the differential equation $\frac{d y}{d x}=k y, y(0)=c$ is$x=c e^{-k y}$$x=k e^{c y}$$y=c e^{k x}$$y=c e^{-k x}$
admin
46.4k
points
112
views
admin
asked
Sep 3, 2022
Differential Equations
gate2011-ec
differential-equations
first-order-differential-equation
+
–
1
votes
0
answers
147
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$$1 / 2$
admin
46.4k
points
58
views
admin
asked
Sep 3, 2022
Probability and Statistics
gate2011-ec
probability-and-statistics
probability
+
–
1
votes
0
answers
148
GATE ECE 2021 | Question: 2
Consider the differential equation given below. $\frac{dy}{dx}+\frac{x}{1-x^{2}}y=x\sqrt{y}$ The integrating factor of the differential equation is $\left ( 1-x^{2} \right )^{-3/4}$ $\left ( 1-x^{2} \right )^{-1/4}$ $\left ( 1-x^{2} \right )^{-3/2}$ $\left ( 1-x^{2} \right )^{-1/2}$
Consider the differential equation given below.$$\frac{dy}{dx}+\frac{x}{1-x^{2}}y=x\sqrt{y}$$The integrating factor of the differential equation is$\left ( 1-x^{2} \right...
Arjun
6.6k
points
284
views
Arjun
asked
Feb 19, 2021
Differential Equations
gateec-2021
differential-equations
first-order-differential-equation
+
–
1
votes
0
answers
149
GATE ECE 2020 | Question: 2
For a vector field $\overrightarrow{A}$, which one of the following is $\text{FALSE}$? $\overrightarrow{A}$ is solenoidal if $\triangledown \cdot \overrightarrow{A}=0.$ $\triangledown \times \overrightarrow{A}$ ...
For a vector field $\overrightarrow{A}$, which one of the following is $\text{FALSE}$?$\overrightarrow{A}$ is solenoidal if $\triangledown \cdot \overrightarrow{A}=0.$$\t...
go_editor
1.9k
points
415
views
go_editor
asked
Feb 13, 2020
Vector Analysis
gate2020-ec
vector-analysis
+
–
1
votes
1
answer
150
GATE ECE 2020 | Question: 25
The two sides of a fair coin are labelled as $0$ to $1$. The coin is tossed two times independently. Let $M$ and $N$ denote the labels corresponding to the outcomes of those tosses. For a random variable $X$, defined as $X = \text{min}(M, N)$, the expected value $E(X)$ (rounded off to two decimal places) is ___________.
The two sides of a fair coin are labelled as $0$ to $1$. The coin is tossed two times independently. Let $M$ and $N$ denote the labels corresponding to the outcomes of th...
go_editor
1.9k
points
368
views
go_editor
asked
Feb 13, 2020
Probability and Statistics
gate2020-ec
numerical-answers
probability-and-statistics
probability
independent-events
random-variable
expectation
+
–
1
votes
1
answer
151
GATE ECE 2016 Set 3 | Question: 27
If the vectors $e_1=(1,0,2)$, $e_2=(0,1,0)$ and $e_3=(-2,0,1)$ form an orthogonal basis of the three-dimensional real space $\mathbb{R}^3$, then the vector $\textbf{u}=(4,3,-3)\in \mathbb{R}^3 $ can be expressed as $\textbf{u}=-$ ... \frac{2}{5}$e_1+3e_2+$\large\frac{11}{5}$e_3 \\$ $\textbf{u}=-$\large\frac{2}{5}$e_1+3e_2-$\large\frac{11}{5}$e_3$
If the vectors $e_1=(1,0,2)$, $e_2=(0,1,0)$ and $e_3=(-2,0,1)$ form an orthogonal basis of the three-dimensional real space $\mathbb{R}^3$, then the vector $\textbf{u}=(4...
Milicevic3306
16.0k
points
293
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2016-ec-3
vector-analysis
+
–
1
votes
0
answers
152
GATE ECE 2015 Set 3 | Question: 1
For $A = \begin{bmatrix} 1 &\tan x \\ -\tan x &1 \end{bmatrix},$ the determinant of $A^{T}A^{-1}$ is $\sec^{2}x$ $\cos 4x$ $1$ $0$
For $A = \begin{bmatrix} 1 &\tan x \\ -\tan x &1 \end{bmatrix},$ the determinant of $A^{T}A^{-1}$ is$\sec^{2}x$$\cos 4x$$1$$0$
Milicevic3306
16.0k
points
99
views
Milicevic3306
asked
Mar 27, 2018
Linear Algebra
gate2015-ec-3
linear-algebra
matrices
determinant
+
–
1
votes
1
answer
153
GATE ECE 2014 Set 1 | Question: 2
In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is ________.
In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at r...
Milicevic3306
16.0k
points
749
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-ec-1
numerical-answers
probability-and-statistics
probability
+
–
1
votes
0
answers
154
GATE ECE 2017 Set 2 | Question: 29
Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is $40 \%$ chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is __________
Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is $40 \%$ chance of getting reservation...
admin
46.4k
points
319
views
admin
asked
Nov 23, 2017
Probability and Statistics
gate2017-ec-2
numerical-answers
probability-and-statistics
probability
+
–
1
votes
0
answers
155
GATE ECE 2017 Set 1 | Question: 27
A three dimensional region $R$ of finite volume is described by $x^2 + y^2 \leq z^3; \: \: 0 \leq z \leq 1,$ where $x,y,z$ are real. The volume of $R$ (up to two decimal places) is _________
A three dimensional region $R$ of finite volume is described by $x^2 + y^2 \leq z^3; \: \: 0 \leq z \leq 1,$ where $x,y,z$ are real. The volume of $R$ (up to two decimal...
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46.4k
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Nov 17, 2017
Vector Analysis
gate2017-ec-1
vector-analysis
numerical-answers
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0
votes
0
answers
156
TIFR ECE 2023 | Question: 1
Consider a fair coin with probability of heads and tails equal to $1 / 2$. Moreover consider two dice, first $\mathrm{D}_{1}$ that has three faces numbered $1,3,5$ and second $\mathrm{D}_{2}$ that has three faces numbered $2,4,6$ ... dice in the experiment. What is $\mathbb{E}[X]$ ? $\frac{7}{2}$ $4$ $3$ $\frac{9}{2}$ None of the above
Consider a fair coin with probability of heads and tails equal to $1 / 2$. Moreover consider two dice, first $\mathrm{D}_{1}$ that has three faces numbered $1,3,5$ and se...
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46.4k
points
308
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Mar 14, 2023
Probability and Statistics
tifrece2023
probability
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–
0
votes
0
answers
157
TIFR ECE 2023 | Question: 2
$\begin{array}{rlr}a^*=\max_{x, y} & x^2+y^2-8 x+7 \\ \text { s.t. } & \qquad x^2+y^2 \leq 1 \\ & \qquad \qquad y \geq 0\end{array}$ Then $a^{\star}$ is $16$ $14$ $12$ $10$ None of the above
$\begin{array}{rlr}a^*=\max_{x, y} & x^2+y^2-8 x+7 \\ \text { s.t. } & \qquad x^2+y^2 \leq 1 \\ & \qquad \qquad y \geq 0\end{array}$Then $a^{\star}$ is$16$$14$$12$$10$Non...
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46.4k
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144
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Mar 14, 2023
Linear Algebra
tifrece2023
engineering-mathematics
linear-algebra
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0
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0
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158
TIFR ECE 2023 | Question: 7
Let $f(x)$ be a positive continuous function on the real line that is the density of a random variable $X$. The differential entropy of $X$ is defined to be $-\int_{-\infty}^{\infty} f(x) \ln f(x) d x$. In which case does $X$ have the least differential entropy? You may use these facts: The ... $f(x):=(1 / 4) e^{-|x| / 2}$. $f(x):=e^{-2|x|}$.
Let $f(x)$ be a positive continuous function on the real line that is the density of a random variable $X$. The differential entropy of $X$ is defined to be $-\int_{-\inf...
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46.4k
points
122
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Mar 14, 2023
Probability and Statistics
tifrece2023
engineering-mathematics
probability-and-statistics
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0
votes
0
answers
159
TIFR ECE 2023 | Question: 8
Suppose a bag contains $5$ red balls, $3$ blue balls, and $2$ black balls. Balls are drawn without replacement until the bag is empty. Let $X_{i}$ be a random variable which takes value $1$ if the $i$-th ball drawn is red, value $2$ if that ball is blue, and $3$ if it is ... $\text{(i), (ii),}$ and $\text{(iii)}$ None of $\text{(i), (ii),}$ or $\text{(iii)}$
Suppose a bag contains $5$ red balls, $3$ blue balls, and $2$ black balls. Balls are drawn without replacement until the bag is empty. Let $X_{i}$ be a random variable wh...
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46.4k
points
136
views
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Mar 14, 2023
Probability and Statistics
tifrece2023
engineering-mathematics
probability
+
–
0
votes
0
answers
160
TIFR ECE 2023 | Question: 9
Consider an $n \times n$ matrix $A$ with the property that each element of $A$ is non-negative and the sum of elements of each row is $1$. Consider the following statements. $1$ is an eigenvalue of $A$ The magnitude of any eigenvalue of $A$ is at ... statements $1$ and $3$ are correct Only statements $2$ and $3$ are correct All statements $1,2$ , and $3$ are correct
Consider an $n \times n$ matrix $A$ with the property that each element of $A$ is non-negative and the sum of elements of each row is $1$.Consider the following statement...
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46.4k
points
124
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Mar 14, 2023
Linear Algebra
tifrece2023
engineering-mathematics
linear-algebra
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