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Recent questions tagged engineering-mathematics
1
votes
1
answer
121
NIELIT 2017 DEC Scientist B - Section B: 60
Consider two matrices $M_1$ and $M_2$ with $M_1^*M_2=0$ and $M_1$ is non singular. Then which of the following is true? $M_2$ is non singular $M_2$ is null matrix $M_2$ is the identity matrix $M_2$ is transpose of $M_1$
Consider two matrices $M_1$ and $M_2$ with $M_1^*M_2=0$ and $M_1$ is non singular. Then which of the following is true?$M_2$ is non singular$M_2$ is null matrix$M_2$ is t...
admin
581
views
admin
asked
Mar 30, 2020
Linear Algebra
nielit2017dec-scientistb
engineering-mathematics
linear-algebra
matrix
+
–
0
votes
1
answer
122
UGC NET CSE | January 2017 | Part 3 | Question: 71
Let $R$ and $S$ be two fuzzy relations defined as: $\begin{matrix} & & & &y_1& &y_2\end{matrix}\\R=\begin{matrix}x_1\\x_2\end{matrix}\begin{bmatrix} 0.6 &0.4 \\ 0.7&0.3 \end{bmatrix} \text{ and}$ ...
Let $R$ and $S$ be two fuzzy relations defined as:$\begin{matrix} & & & &y_1& &y_2\end{matrix}\\R=\begin{matrix}x_1\\x_2\end{matrix}\begin{bmatrix} 0.6 &0.4 \\ 0.7&0.3 \e...
go_editor
716
views
go_editor
asked
Mar 24, 2020
Others
ugcnetcse-jan2017-paper3
engineering-mathematics
relations
+
–
23
votes
3
answers
123
GATE CSE 2020 | Question: 1
Consider the functions $e^{-x}$ $x^{2}-\sin x$ $\sqrt{x^{3}+1}$ Which of the above functions is/are increasing everywhere in $[ 0,1]$? Ⅲ only Ⅱ only Ⅱ and Ⅲ only Ⅰ and Ⅲ only
Consider the functions $e^{-x}$$x^{2}-\sin x$$\sqrt{x^{3}+1}$Which of the above functions is/are increasing everywhere in $[ 0,1]$?Ⅲ onlyⅡ onlyⅡ and Ⅲ onlyⅠ a...
Arjun
12.1k
views
Arjun
asked
Feb 12, 2020
Calculus
gatecse-2020
engineering-mathematics
calculus
maxima-minima
1-mark
+
–
1
votes
3
answers
124
TIFR CSE 2020 | Part B | Question: 11
Which of the following graphs are bipartite? Only $(1)$ Only $(2)$ Only $(2)$ and $(3)$ None of $(1),(2),(3)$ All of $(1),(2),(3)$
Which of the following graphs are bipartite?Only $(1)$Only $(2)$Only $(2)$ and $(3)$None of $(1),(2),(3)$All of $(1),(2),(3)$
admin
3.4k
views
admin
asked
Feb 10, 2020
Graph Theory
tifr2020
engineering-mathematics
graph-theory
graph-coloring
bipartite-graph
+
–
1
votes
2
answers
125
TIFR CSE 2020 | Part A | Question: 10
In a certain year, there were exactly four Fridays and exactly four Mondays in January. On what day of the week did the $20^{th}$ of the January fall that year (recall that January has $31$ days)? Sunday Monday Wednesday Friday None of the others
In a certain year, there were exactly four Fridays and exactly four Mondays in January. On what day of the week did the $20^{th}$ of the January fall that year (recall th...
admin
2.1k
views
admin
asked
Feb 10, 2020
Probability
tifr2020
engineering-mathematics
probability
+
–
0
votes
2
answers
126
TIFR CSE 2020 | Part A | Question: 8
Consider a function $f:[0,1]\rightarrow [0,1]$ which is twice differentiable in $(0,1).$ Suppose it has exactly one global maximum and exactly one global minimum inside $(0,1)$. What can you say about the behaviour of the first derivative $f'$ and and second ... at at least one point $f'$ is zero at at least two points, $f''$ is zero at at least two points
Consider a function $f:[0,1]\rightarrow [0,1]$ which is twice differentiable in $(0,1).$ Suppose it has exactly one global maximum and exactly one global minimum inside $...
admin
1.2k
views
admin
asked
Feb 10, 2020
Calculus
tifr2020
engineering-mathematics
calculus
maxima-minima
+
–
5
votes
2
answers
127
TIFR CSE 2020 | Part A | Question: 7
A lottery chooses four random winners. What is the probability that at least three of them are born on the same day of the week? Assume that the pool of candidates is so large that each winner is equally likely to be born on any of the seven days of the week independent ... $\dfrac{48}{2401} \\$ $\dfrac{105}{2401} \\$ $\dfrac{175}{2401} \\$ $\dfrac{294}{2401}$
A lottery chooses four random winners. What is the probability that at least three of them are born on the same day of the week? Assume that the pool of candidates is so ...
admin
1.2k
views
admin
asked
Feb 10, 2020
Probability
tifr2020
engineering-mathematics
probability
independent-events
+
–
0
votes
0
answers
128
TIFR CSE 2020 | Part A | Question: 4
Fix $n\geq 4.$ Suppose there is a particle that moves randomly on the number line, but never leaves the set $\{1,2,\dots,n\}.$ Let the initial probability distribution of the particle be denoted by $\overrightarrow{\pi}.$ In the first step, if the particle is at ... $i\neq 1$ $\overrightarrow{\pi}(n) = 1$ and $\overrightarrow{\pi}(i) = 0$ for $i\neq n$
Fix $n\geq 4.$ Suppose there is a particle that moves randomly on the number line, but never leaves the set $\{1,2,\dots,n\}.$ Let the initial probability distribution of...
admin
744
views
admin
asked
Feb 10, 2020
Probability
tifr2020
engineering-mathematics
probability
uniform-distribution
+
–
1
votes
1
answer
129
TIFR CSE 2020 | Part A | Question: 5
Let $A$ be am $n\times n$ invertible matrix with real entries whose column sums are all equal to $1$. Consider the following statements: Every column in the matrix $A^{2}$ sums to $2$ Every column in the matrix $A^{3}$ sums to $3$ Every column in the matrix ... $(1)$ or $(2)$ all the $3$ statements $(1),(2),$ and $(3)$ are correct
Let $A$ be am $n\times n$ invertible matrix with real entries whose column sums are all equal to $1$. Consider the following statements:Every column in the matrix $A^{2}$...
admin
1.1k
views
admin
asked
Feb 10, 2020
Linear Algebra
tifr2020
engineering-mathematics
linear-algebra
matrix
+
–
0
votes
0
answers
130
TIFR CSE 2020 | Part A | Question: 3
Let $d\geq 4$ and fix $w\in \mathbb{R}.$ Let $S = \{a = (a_{0},a_{1},\dots ,a_{d})\in \mathbb{R}^{d+1}\mid f_{a}(w) = 0\: \text{and}\: f'_{a}(w) = 0\},$ where the polynomial function $f_{a}(x)$ ... $d$-dimensional vector subspace of $\mathbb{R}^{d+1}$ $S$ is a $(d-1)$-dimensional vector subspace of $\mathbb{R}^{d+1}$ None of the other options
Let $d\geq 4$ and fix $w\in \mathbb{R}.$ Let $$S = \{a = (a_{0},a_{1},\dots ,a_{d})\in \mathbb{R}^{d+1}\mid f_{a}(w) = 0\: \text{and}\: f’_{a}(w) = 0\},$$ where the pol...
admin
687
views
admin
asked
Feb 10, 2020
Linear Algebra
tifr2020
engineering-mathematics
linear-algebra
vector-space
+
–
2
votes
1
answer
131
TIFR CSE 2020 | Part A | Question: 2
Let $M$ be a real $n\times n$ matrix such that for$ every$ non-zero vector $x\in \mathbb{R}^{n},$ we have $x^{T}M x> 0.$ Then Such an $M$ cannot exist Such $Ms$ exist and their rank is always $n$ Such $Ms$ exist, but their eigenvalues are always real No eigenvalue of any such $M$ can be real None of the above
Let $M$ be a real $n\times n$ matrix such that for$ every$ non-zero vector $x\in \mathbb{R}^{n},$ we have $x^{T}M x 0.$ ThenSuch an $M$ cannot existSuch $Ms$ exist and th...
admin
1.4k
views
admin
asked
Feb 10, 2020
Linear Algebra
tifr2020
engineering-mathematics
linear-algebra
rank-of-matrix
eigen-value
+
–
6
votes
2
answers
132
TIFR CSE 2020 | Part A | Question: 1
Two balls are drawn uniformly at random without replacement from a set of five balls numbered $1,2,3,4,5.$ What is the expected value of the larger number on the balls drawn? $2.5$ $3$ $3.5$ $4$ None of the above
Two balls are drawn uniformly at random without replacement from a set of five balls numbered $1,2,3,4,5.$ What is the expected value of the larger number on the balls dr...
admin
2.3k
views
admin
asked
Feb 10, 2020
Probability
tifr2020
engineering-mathematics
probability
expectation
+
–
1
votes
0
answers
133
Gravner- probability
Each day, you independently decide, with probability p, to flip a fair coin. Otherwise, you do nothing. (a) What is the probability of getting exactly 10 Heads in the first 20 days? (b) What is the probability of getting 10 Heads before 5 Tails?
Each day, you independently decide, with probability p, to flip a fair coin.Otherwise, you do nothing. (a) What is the probability of getting exactly 10 Heads in the firs...
ajaysoni1924
750
views
ajaysoni1924
asked
Oct 23, 2019
Probability
gravner
probability
engineering-mathematics
+
–
0
votes
0
answers
134
ISI2017-DCG-24
The differential equation $x \frac{dy}{dx} -y=x^3$ with $y(0)=2$ has unique solution no solution infinite number of solutions none of these
The differential equation $x \frac{dy}{dx} -y=x^3$ with $y(0)=2$ hasunique solutionno solutioninfinite number of solutionsnone of these
gatecse
310
views
gatecse
asked
Sep 18, 2019
Others
isi2017-dcg
engineering-mathematics
calculus
non-gate
differential-equation
+
–
0
votes
0
answers
135
KPGCET-CSE-2019-16
The matrices represented for transformations in homogeneous co-ordinate system are used to transform Multiplication into addition Addition into multiplication Division into subtraction Subtraction into division
The matrices represented for transformations in homogeneous co-ordinate system are used to transformMultiplication into additionAddition into multiplicationDivision into ...
gatecse
173
views
gatecse
asked
Aug 4, 2019
Linear Algebra
kpgcet-cse-2019
engineering-mathematics
linear-algebra
+
–
0
votes
0
answers
136
KPGCET-CSE-2019-25
The concatenation of three or more matrices is Associative and also commutative Associative but not commutative Commutative but not associative Neither associative nor commutative
The concatenation of three or more matrices isAssociative and also commutativeAssociative but not commutative Commutative but not associativeNeither associative nor commu...
gatecse
217
views
gatecse
asked
Aug 4, 2019
Linear Algebra
kpgcet-cse-2019
engineering-mathematics
linear-algebra
+
–
0
votes
1
answer
137
Sheldon Ross Chapter-2 Question-15b
If it is assumed that all $\binom{52}{5}$ poker hands are equally likely, what is the probability of being dealt two pairs? (This occurs when the cards have denominations a, a, b, b, c, where a, b, and c are all distinct.) my approach is: selecting a ... I'm getting answer 0.095 but in the book answer is given 0.0475 where am I going wrong?
If it is assumed that all $\binom{52}{5}$ poker hands are equally likely, what is the probability of being dealt two pairs? (This occurs when the cards have denominations...
aditi19
1.1k
views
aditi19
asked
Jun 14, 2019
Probability
probability
sheldon-ross
engineering-mathematics
+
–
0
votes
1
answer
138
Self-Doubt: Diagonalizable Matrix
$1)$ How to find a matrix is diagonalizable or not? Suppose a matrix is $A=\begin{bmatrix} \cos \Theta &\sin \Theta \\ \sin\Theta & -\cos\Theta \end{bmatrix}$ Is it diagonalizable? $2)$ What is it’s eigen spaces?
$1)$ How to find a matrix is diagonalizable or not?Suppose a matrix is $A=\begin{bmatrix} \cos \Theta &\sin \Theta \\ \sin\Theta & -\cos\Theta \end{bmatrix}$Is it diagona...
srestha
1.2k
views
srestha
asked
May 27, 2019
Linear Algebra
engineering-mathematics
linear-algebra
matrix
+
–
0
votes
1
answer
139
Maths: Limits
$\LARGE \lim_{n \rightarrow \infty} \frac{n^{\frac{3}{4}}}{log^9 n}$
$\LARGE \lim_{n \rightarrow \infty} \frac{n^{\frac{3}{4}}}{log^9 n}$
Mk Utkarsh
573
views
Mk Utkarsh
asked
May 26, 2019
Calculus
engineering-mathematics
calculus
limits
+
–
1
votes
1
answer
140
ISI2018-PCB-CS3
An $n-$variable Boolean function $f:\{0,1\}^n \rightarrow \{0,1\} $ is called symmetric if its value depends only on the number of $1’s$ in the input. Let $\sigma_n $ denote the number of such functions. Calculate the value of $\sigma_4$. Derive an expression for $\sigma_n$ in terms of $n$.
An $n-$variable Boolean function $f:\{0,1\}^n \rightarrow \{0,1\} $ is called symmetric if its value depends only on the number of $1’s$ in the input. Let $\sigma_n $ d...
akash.dinkar12
480
views
akash.dinkar12
asked
May 12, 2019
Set Theory & Algebra
isi2018-pcb-cs
engineering-mathematics
discrete-mathematics
set-theory&algebra
functions
descriptive
+
–
1
votes
1
answer
141
ISI2018-PCB-A1
Consider a $n \times n$ matrix $A=I_n-\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alpha=1$.Show that $A^2=A$.
Consider a $n \times n$ matrix $A=I_n-\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alp...
akash.dinkar12
510
views
akash.dinkar12
asked
May 12, 2019
Linear Algebra
isi2018-pcb-a
engineering-mathematics
linear-algebra
matrix
descriptive
+
–
1
votes
4
answers
142
ISI2018-MMA-28
Consider the following functions $f(x)=\begin{cases} 1, & \text{if } \mid x \mid \leq 1 \\ 0, & \text{if } \mid x \mid >1 \end{cases}.$ ... at $\pm1$ $h_2$ is continuous everywhere and $h_1$ has discontinuity at $\pm2$ $h_1$ has discontinuity at $\pm 2$ and $h_2$ has discontinuity at $\pm1$.
Consider the following functions$f(x)=\begin{cases} 1, & \text{if } \mid x \mid \leq 1 \\ 0, & \text{if } \mid x \mid >1 \end{cases}.$ and $g(x)=\begin{cases} 1, & \te...
akash.dinkar12
1.2k
views
akash.dinkar12
asked
May 11, 2019
Calculus
isi2018-mma
engineering-mathematics
calculus
continuity
+
–
0
votes
1
answer
143
ISI2018-MMA-30
Consider the function $f(x)=\bigg(1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\dots+\frac{x^n}{n!}\bigg)e^{-x}$, where $n\geq4$ is a positive integer. Which of the following statements is correct? $f$ has no local maximum For every $n$, $f$ has a local maximum at $x = 0$ ... at $x = 0$ when $n$ is even $f$ has no local extremum if $n$ is even and has a local maximum at $x = 0$ when $n$ is odd.
Consider the function$f(x)=\bigg(1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\dots+\frac{x^n}{n!}\bigg)e^{-x}$,where $n\geq4$ is a positive integer. Which of the following statemen...
akash.dinkar12
1.0k
views
akash.dinkar12
asked
May 11, 2019
Calculus
isi2018-mma
engineering-mathematics
calculus
maxima-minima
+
–
2
votes
1
answer
144
ISI2018-MMA-29
Let $f$ be a continuous function with $f(1) = 1$. Define $F(t)=\int_{t}^{t^2}f(x)dx$. The value of $F’(1)$ is $-2$ $-1$ $1$ $2$
Let $f$ be a continuous function with $f(1) = 1$. Define $$F(t)=\int_{t}^{t^2}f(x)dx$$.The value of $F’(1)$ is$-2$$-1$$1$$2$
akash.dinkar12
1.0k
views
akash.dinkar12
asked
May 11, 2019
Calculus
isi2018-mma
engineering-mathematics
calculus
integration
+
–
6
votes
1
answer
145
ISI2018-MMA-26
Let $C_i(i=0,1,2...n)$ be the coefficient of $x^i$ in $(1+x)^n$.Then $\frac{C_0}{2} – \frac{C_1}{3}+\frac{C_2}{4}-\dots +(-1)^n \frac{C_n}{n+2}$ is equal to $\frac{1}{n+1}\\$ $\frac{1}{n+2}\\$ $\frac{1}{n(n+1)}\\$ $\frac{1}{(n+1)(n+2)}$
Let $C_i(i=0,1,2...n)$ be the coefficient of $x^i$ in $(1+x)^n$.Then $\frac{C_0}{2} – \frac{C_1}{3}+\frac{C_2}{4}-\dots +(-1)^n \frac{C_n}{n+2}$ is equal to$\frac{1}{n+...
akash.dinkar12
1.8k
views
akash.dinkar12
asked
May 11, 2019
Combinatory
isi2018-mma
engineering-mathematics
discrete-mathematics
generating-functions
+
–
1
votes
2
answers
146
ISI2018-MMA-20
Consider the set of all functions from $\{1, 2, . . . ,m\}$ to $\{1, 2, . . . , n\}$,where $n > m$. If a function is chosen from this set at random, the probability that it will be strictly increasing is $\binom{n}{m}/n^m\\$ $\binom{n}{m}/m^n\\$ $\binom{m+n-1}{m-1}/n^m\\$ $\binom{m+n-1}{m}/m^n$
Consider the set of all functions from $\{1, 2, . . . ,m\}$ to $\{1, 2, . . . , n\}$,where $n m$. If a function is chosen from this set at random, the probability that i...
akash.dinkar12
2.1k
views
akash.dinkar12
asked
May 11, 2019
Probability
isi2018-mma
engineering-mathematics
probability
+
–
0
votes
1
answer
147
ISI2018-MMA-19
Let $X_1,X_2, . . . ,X_n$ be independent and identically distributed with $P(X_i = 1) = P(X_i = −1) = p\ $and$ P(X_i = 0) = 1 − 2p$ for all $i = 1, 2, . . . , n.$ ... $a_n \rightarrow p, b_n \rightarrow p,c_n \rightarrow 1-2p$ $a_n \rightarrow1/2, b_n \rightarrow1/2,c_n \rightarrow0$ $a_n \rightarrow0, b_n \rightarrow0,c_n \rightarrow1$
Let $X_1,X_2, . . . ,X_n$ be independent and identically distributed with $P(X_i = 1) = P(X_i = −1) = p\ $and$ P(X_i = 0) = 1 − 2p$ for all $i = 1, 2, . . . , n.$ Def...
akash.dinkar12
697
views
akash.dinkar12
asked
May 11, 2019
Calculus
isi2018-mma
engineering-mathematics
calculus
limits
+
–
0
votes
2
answers
148
ISI2018-MMA-18
Let $A_1 = (0, 0), A_2 = (1, 0), A_3 = (1, 1)\ $and$\ A_4 = (0, 1)$ be the four vertices of a square. A particle starts from the point $A_1$ at time $0$ and moves either to $A_2$ or to $A_4$ with equal probability. Similarly, in each of the subsequent ... $T$ be the minimum number of steps required to cover all four vertices. The probability $P(T = 4)$ is $0$ $1/16$ $1/8$ $1/4$
Let $A_1 = (0, 0), A_2 = (1, 0), A_3 = (1, 1)\ $and$\ A_4 = (0, 1)$ be the four vertices of a square. A particle starts from the point $A_1$ at time $0$ and moves either ...
akash.dinkar12
1.0k
views
akash.dinkar12
asked
May 11, 2019
Probability
isi2018-mma
engineering-mathematics
probability
+
–
0
votes
2
answers
149
ISI2018-MMA-17
There are eight coins, seven of which have the same weight and the other one weighs more. In order to find the coin having more weight, a person randomly chooses two coins and puts one coin on each side of a common balance. If these two coins are found to have the same ... as before. The probability that the coin will be identified at the second draw is $1/2$ $1/3$ $1/4$ $1/6$
There are eight coins, seven of which have the same weight and the other one weighs more. In order to find the coin having more weight, a person randomly chooses two coin...
akash.dinkar12
1.2k
views
akash.dinkar12
asked
May 11, 2019
Probability
isi2018-mma
engineering-mathematics
probability
+
–
0
votes
2
answers
150
ISI2018-MMA-16
Consider a large village, where only two newspapers $P_1$ and $P_2$ are available to the families. It is known that the proportion of families not taking $P_1$ is $0.48$, not taking $P_2$ is $0.58$, taking only $P_2$ is $0.30$. The probability that a randomly chosen family from the village takes only $P_1$ is $0.24$ $0.28$ $0.40$ can not be determined
Consider a large village, where only two newspapers $P_1$ and $P_2$ are available to the families. It is known that the proportion of familiesnot taking $P_1$ is $0.48$,n...
akash.dinkar12
1.3k
views
akash.dinkar12
asked
May 11, 2019
Probability
isi2018-mma
engineering-mathematics
probability
+
–
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