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Recent questions in Engineering Mathematics
0
votes
3
answers
41
Predicate Translation
S(x): x is a Student P(x): x is a Professor A(x, y): x has asked a question to y Domain not given, so we have to think about default domain Q1) Translate There is a student who has asked every professor a question Q2) Translate ... a professor who has been asked a question by every student Q4) Translate There is a student who has been asked a question by every professor
prithatiti
asked
in
Mathematical Logic
Sep 6
by
prithatiti
164
views
propositional-logic
mathematical-logic
discrete-mathematics
0
votes
0
answers
42
Eigen Value Of A Matrix
For given Matrix: [ 1 2 3 1 5 1 3 1 1 ] Why does the sum of the eigen values of above matrix is the sum of diagonal elements of that matrix?
ryandany07
asked
in
Linear Algebra
Sep 4
by
ryandany07
119
views
eigen-value
matrix
engineering-mathematics
3
votes
1
answer
43
TIFR CSE 2022 | Part B | Question: 2
Let $G=(V, E)$ be an undirected simple graph. A subset $M \subseteq E$ is a matching in $G$ if distinct edges in $M$ do not share a vertex. A matching is maximal if no strict superset of $M$ is a matching. How many maximal matchings does the following graph have? $1$ $2$ $3$ $4$ $5$
admin
asked
in
Graph Theory
Sep 1
by
admin
137
views
tifr2022
graph-theory
graph-matching
2
votes
1
answer
44
TIFR CSE 2022 | Part B | Question: 6
We are given a graph $G$ along with a matching $M$ and a vertex cover $C$ in it such that $|M|=|C|$. Consider the following statements: $M$ is a maximum matching in $G$. $C$ is a minimum vertex cover in $G$. $G$ is a bipartite graph. Which of ... $(1)$ and $(2)$ are correct All the three statements $(1), (2),$ and $(3)$ are correct
admin
asked
in
Graph Theory
Sep 1
by
admin
131
views
tifr2022
graph-theory
graph-matching
2
votes
1
answer
45
TIFR CSE 2022 | Part B | Question: 9
Let $n \geq 2$ be any integer. Which of the following statements is $\text{FALSE}?$ $n!$ divides the product of any $n$ consecutive integers $\displaystyle{}\sum_{i=0}^n\left(\begin{array}{c}n \\ i\end{array}\right)=2^n$ ... an odd prime, then $n$ divides $2^{n-1}-1$ $n$ divides $\left(\begin{array}{c}2 n \\ n\end{array}\right)$
admin
asked
in
Combinatory
Sep 1
by
admin
78
views
tifr2022
combinatory
binomial-theorem
1
vote
0
answers
46
TIFR CSE 2022 | Part B | Question: 12
Given an undirected graph $G$, an ordering $\sigma$ of its vertices is called a perfect ordering if for every vertex $v$, the neighbours of $v$ which precede $v$ in $\sigma$ form a clique in $G$. Recall that given an undirected ... SPECIAL-COLOURING are in $\mathrm{P}$ Neither of SPECIAL-CLiQUE and SPECIAL-COLOURING is in $\mathrm{P},$ but both are decidable
admin
asked
in
Graph Theory
Sep 1
by
admin
67
views
tifr2022
graph-theory
graph-coloring
p-np-npc-nph
1
vote
1
answer
47
TIFR CSE 2022 | Part B | Question: 14
Let $G$ be a directed graph (with no self-loops or parallel edges) with $n \geq 2$ vertices and $m$ edges. Consider the $n \times m$ incidence matrix $M$ of $G$, whose rows are indexed by the vertices of $G$ and the columns by the edges of $G$ ... . Then, what is the rank of $M?$ $m-1$ $m-n+1$ $\lceil m / 2\rceil$ $n-1$ $\lceil n / 2\rceil$
admin
asked
in
Graph Theory
Sep 1
by
admin
69
views
tifr2022
graph-theory
graph-connectivity
rank-of-matrix
1
vote
0
answers
48
TIFR CSE 2022 | Part B | Question: 15
Let $\mathbb{R}$ denote the set of real numbers. Let $d \geq 4$ and $\alpha \in \mathbb{R}$ ... $\left(a_0, a_1, \ldots, a_d\right) \in S$, the function $ x \mapsto \sum_{i=0}^d a_i x^i $ has a local optimum at $\alpha$
admin
asked
in
Linear Algebra
Sep 1
by
admin
78
views
tifr2022
linear-algebra
vector-space
0
votes
1
answer
49
TIFR CSE 2022 | Part A | Question: 1
A snail crawls up a vertical pole $75$ feet high, starting from the ground. Each day it crawls up $5$ feet, and each night it slides down $4$ feet. When will it first reach the top of the pole? $75^{\text {th}}$ day $74^{\text {th}}$ day $73^{ \text{rd}}$ day $72^{\text {nd }}$ day $71^{\text {st }}$ day
Lakshman Patel RJIT
asked
in
Combinatory
Sep 1
by
Lakshman Patel RJIT
160
views
tifr2022
combinatory
counting
0
votes
2
answers
50
TIFR CSE 2022 | Part A | Question: 2
We would like to invite a minimum number $n$ of people (their birthdays are independent of each other) to a party such that the expected number of pairs of people that share the same birthday is at least $1.$ What should $n$ be? (Ignore leap years, so ... birthdays fall with equal probability on each of the $365$ days of the year.) $23$ $28$ $92$ $183$ $366$
Lakshman Patel RJIT
asked
in
Probability
Sep 1
by
Lakshman Patel RJIT
178
views
tifr2022
probability
expectation
1
vote
1
answer
51
TIFR CSE 2022 | Part A | Question: 4
Consider the polynomial $p(x)=x^3-x^2+x-1$. How many symmetric matrices with integer entries are there whose characteristic polynomial is $p$? (Recall that the characteristic polynomial of a square matrix $A$ in the variable $x$ is defined to be the determinant of the matrix $(A-x I)$ where $I$ is the identity matrix.) $0$ $1$ $2$ $4$ Infinitely many
Lakshman Patel RJIT
asked
in
Linear Algebra
Sep 1
by
Lakshman Patel RJIT
102
views
tifr2022
linear-algebra
matrix
determinant
2
votes
1
answer
52
TIFR CSE 2022 | Part A | Question: 5
Let $\mathcal{F}$ be the set of all functions mapping $\{1, \ldots, n\}$ to $\{1, \ldots, m\}$. Let $f$ be a function that is chosen uniformly at random from $\mathcal{F}$. Let $x, y$ be distinct elements from the set $\{1, \ldots, n\}$. Let $p$ denote the probability ... Then, $p=0$ $p=\frac{1}{n^m}$ $0<p \leq \frac{1}{m^n}$ $p=\frac{1}{m}$ $p=\frac{1}{n}$
Lakshman Patel RJIT
asked
in
Probability
Sep 1
by
Lakshman Patel RJIT
83
views
tifr2022
probability
uniform-distribution
functions
0
votes
0
answers
53
TIFR CSE 2022 | Part A | Question: 6
Let $f$ be a polynomial of degree $n \geq 3$ all of whose roots are non-positive real numbers. Suppose that $f(1)=1$. What is the maximum possible value of $f^{\prime}(1)?$ $1$ $n$ $n+1$ $\frac{n(n+1)}{2}$ $f^{\prime}(1)$ can be arbitrarily large given only the constraints in the question
Lakshman Patel RJIT
asked
in
Calculus
Sep 1
by
Lakshman Patel RJIT
64
views
tifr2022
calculus
maxima-minima
1
vote
1
answer
54
TIFR CSE 2022 | Part A | Question: 7
Initially, $N$ white beads are arranged in a circle. A number $k$ is chosen uniformly at random from $\{1, \ldots, N-1\}$. Then a set of $k$ beads is chosen uniformly from the white beads, and these $k$ beads are coloured black. The position of the beads remains ... None of the above
Lakshman Patel RJIT
asked
in
Probability
Sep 1
by
Lakshman Patel RJIT
106
views
tifr2022
probability
uniform-distribution
13
votes
1
answer
55
TIFR CSE 2022 | Part A | Question: 8
Let $A$ be the $(n+1) \times(n+1)$ matrix given below, where $n \geq 1$. For $i \leq n$, the $i$-th row of $A$ has every entry equal to $2i-1$ and the last row, i.e., the $(n+1)$-th row of $A$ has every entry equal to $-n^2$ ... $A$ has rank $n$ $A^2$ has rank $1$ All the eigenvalues of $A$ are distinct All the eigenvalues of $A$ are $0$ None of the above
Lakshman Patel RJIT
asked
in
Linear Algebra
Sep 1
by
Lakshman Patel RJIT
239
views
tifr2022
linear-algebra
rank-of-matrix
eigen-value
0
votes
1
answer
56
TIFR CSE 2022 | Part A | Question: 9
You are given the following properties of sets $A, B, X$, and $Y$. For notation, $|A|$ denotes the cardinality of set $A$ (i.e., the number of elements in $A$ ), and $A \backslash B$ denotes the set of elements that are in $A$ but not in $B$. $A \cup B=X \cup Y$ ... $|X|=5$ $|Y|=5$ $|A \cup X|=|B \cup Y|$ $|A \cap X|=|B \cap Y|$ $|A|=|B|$
Lakshman Patel RJIT
asked
in
Set Theory & Algebra
Sep 1
by
Lakshman Patel RJIT
87
views
tifr2022
set-theory&algebra
set-theory
0
votes
1
answer
57
TIFR CSE 2022 | Part A | Question: 10
Consider a bag containing colored marbles. There are $n$ marbles in the bag such that there is exactly one pair of marbles of color $i$ for each $i \in\{1, \ldots, m\}$ and the rest of the marbles are of distinct colors (different from colors $\{1, \ldots, m\}$ ). You draw ... $\frac{2m}{n}$ $\frac{2m}{n(n-1)}$ $\frac{2m}{n^2}$ $\frac{m}{n(n-1)}$
Lakshman Patel RJIT
asked
in
Probability
Sep 1
by
Lakshman Patel RJIT
66
views
tifr2022
probability
conditional-probability
0
votes
0
answers
58
TIFR CSE 2022 | Part A | Question: 11
Let $X$ be a finite set. A family $\mathcal{F}$ of subsets of $X$ is said to be upward closed if the following holds for all sets $A, B \subseteq X$ ... $\mathcal{F} \sqcup \mathcal{G}=\mathcal{G} \backslash \mathcal{F}$ None of the above
Lakshman Patel RJIT
asked
in
Set Theory & Algebra
Sep 1
by
Lakshman Patel RJIT
59
views
tifr2022
set-theory&algebra
set-theory
0
votes
1
answer
59
TIFR CSE 2022 | Part A | Question: 12
Alice plays the following game on a math show. There are $7$ boxes and identical prizes are hidden inside $3$ of the boxes. Alice is asked to choose a box where a prize might be. She chooses a box uniformly at random. From the unchosen boxes which do not have a prize, ... ). Her probability of winning the prize is $3 / 7$ $1 / 2$ $17 / 30$ $18 / 35$ $9 / 19$
Lakshman Patel RJIT
asked
in
Probability
Sep 1
by
Lakshman Patel RJIT
89
views
tifr2022
probability
conditional-probability
0
votes
0
answers
60
TIFR CSE 2022 | Part A | Question: 14
Suppose $w(t)=4 e^{i t}, x(t)=3 e^{i(t+\pi / 3)}, y(t)=3 e^{i(t-\pi / 3)}$ and $z(t)=3 e^{i(t+\pi)}$ are points that move in the complex plane as the time $t$ varies in $(-\infty, \infty)$. Let $c(t)$ ... $\frac{1}{2 \pi}$ $2 \pi$ $\sqrt{3} \pi$ $\frac{1}{\sqrt{3} \pi}$ $1$
Lakshman Patel RJIT
asked
in
Calculus
Sep 1
by
Lakshman Patel RJIT
47
views
tifr2022
calculus
differentiation
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