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Most answered questions in Engineering Mathematics
3
votes
1
answer
2701
GO Classes Test Series 2023 | Linear Algebra | Test | Question: 15
Let $A$ be an $n \times n$ real skew-symmetric matrix The trace of a real skew-symmetric matrix is always equal to $0.$ If $A$ is skew symmetric matrix, then $A^{2}$ is a symmetric matrix. If $n$ is odd, $A$ is not invertible If $n$ is even, $A$ is invertible
Let $A$ be an $n \times n$ real skew-symmetric matrixThe trace of a real skew-symmetric matrix is always equal to $0.$If $A$ is skew symmetric matrix, then $A^{2}$ is a s...
GO Classes
467
views
GO Classes
asked
Aug 14, 2022
Linear Algebra
goclasses2024-la-weekly_quiz
goclasses
linear-algebra
matrix
multiple-selects
2-marks
+
–
0
votes
1
answer
2702
NPTEL Assignment
In how many ways can the word ‘DOCUMENTATION’ be arranged so that all the consonants come together.
In how many ways can the word ‘DOCUMENTATION’ be arranged so that all the consonants come together.
simi2426
816
views
simi2426
asked
Aug 9, 2022
0
votes
1
answer
2703
ISI 2020 | PCB Mathematics | Question: 3
Suppose $A$ is an $(n \times n)$ matrix over $\mathbb{R}$ such that $A^{p}=0$ for some positive integer $p$. Prove that $I+A$ is an invertible matrix, where $I$ is the $(n \times n)$ identity matrix. Find the characteristic polynomial of $A$.
Suppose $A$ is an $(n \times n)$ matrix over $\mathbb{R}$ such that $A^{p}=0$ for some positive integer $p$.Prove that $I+A$ is an invertible matrix, where $I$ is the $(n...
admin
448
views
admin
asked
Aug 8, 2022
Linear Algebra
isi2020-pcb-mathematics
descriptive
linear-algebra
matrix
+
–
4
votes
1
answer
2704
GO Classes Scholarship 2023 | Test | Question: 1
A relation $\text{R}$ on a set $\text{A}$ is said to be Total Relation iff $a\text{R}b$ Or $b\text{R}a$ Or both, for all $a,b \in \mathrm{A}$. Which of the following options is/are false? Every Total relation is ... total and transitive, then $\mathrm{S}$ is an equivalence relation. The number of total relations on a set of $5$ elements is $1024.$
A relation $\text{R}$ on a set $\text{A}$ is said to be Total Relation iff $a\text{R}b$ Or $b\text{R}a$ Or both, for all $a,b \in \mathrm{A}$.Which of the following optio...
GO Classes
946
views
GO Classes
asked
Aug 6, 2022
Set Theory & Algebra
goclasses-scholarship-test1
goclasses
set-theory&algebra
relations
multiple-selects
2-marks
+
–
4
votes
1
answer
2705
GO Classes Scholarship 2023 | Test | Question: 3
Let $\text{A, B}$ be two disjoint non-empty sets. Let $\text{M}$ be the universal set and $\text{A} \cup \text{B}$ is a proper subset of $\mathrm{M}$. For any set $\mathrm{S}$, let $\mathrm{S}^{\prime}$ be the set of those elements ...
Let $\text{A, B}$ be two disjoint non-empty sets. Let $\text{M}$ be the universal set and $\text{A} \cup \text{B}$ is a proper subset of $\mathrm{M}$. For any set $\mathr...
GO Classes
504
views
GO Classes
asked
Aug 6, 2022
Set Theory & Algebra
goclasses-scholarship-test1
goclasses
set-theory&algebra
set-theory
multiple-selects
2-marks
+
–
4
votes
1
answer
2706
GO Classes Scholarship 2023 | Test | Question: 5
Consider $5$ cards, each has a distinct value from the set $\{2,3,4,5,6\},$ so there are $5$ different values, and we put them face down on the table. There are $5$ players and each player is given a number from $2$ ... with the value that player has. If no player loses, then the dealer loses. How many ways are there so that the dealer loses?
Consider $5$ cards, each has a distinct value from the set $\{2,3,4,5,6\},$ so there are $5$ different values, and we put them face down on the table. There are $5$ playe...
GO Classes
484
views
GO Classes
asked
Aug 6, 2022
Combinatory
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
counting
2-marks
+
–
4
votes
1
answer
2707
GO Classes Scholarship 2023 | Test | Question: 6
Consider three boxes and $12$ balls of the same size. We have $3$ indistinguishable red balls and $9$ distinguishable blue balls. The first box can fit at most three balls, the second box can fit at most four balls and the third box can fit ... all the red balls go into the same box. What is the total number of ways to put all the balls in the boxes?
Consider three boxes and $12$ balls of the same size. We have $3$ indistinguishable red balls and $9$ distinguishable blue balls. The first box can fit at most three ball...
GO Classes
761
views
GO Classes
asked
Aug 6, 2022
Combinatory
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
counting
2-marks
+
–
3
votes
1
answer
2708
GO Classes Scholarship 2023 | Test | Question: 7
Define the generating functions $\text{B}(x)=\displaystyle{} \sum_{n=0}^{\infty} 2^{n} x^{n}$ and $F(x)=\displaystyle{} \sum_{n=0}^{\infty} f_{n} x^{n}$ where $f_{n}$ ... $x^{5}$ is $\mathrm{G}(x)?$
Define the generating functions $\text{B}(x)=\displaystyle{} \sum_{n=0}^{\infty} 2^{n} x^{n}$ and $F(x)=\displaystyle{} \sum_{n=0}^{\infty} f_{n} x^{n}$ where $f_{n}$ is ...
GO Classes
631
views
GO Classes
asked
Aug 6, 2022
Combinatory
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
generating-functions
2-marks
+
–
4
votes
1
answer
2709
GO Classes Scholarship 2023 | Test | Question: 8
In a directed graph $\mathrm{G}=(\mathrm{V}, \mathrm{E})$, two nodes $u$ and $v$ are strongly connected if and only if they are mutually reachable i.e. there is a path from u to $v$ and a path from $v$ to $u$. ... connected components $\dots?$ can not increase can not decrease by more than $1$ can not decrease by more than $2$ may remain unchanged
In a directed graph $\mathrm{G}=(\mathrm{V}, \mathrm{E})$, two nodes $u$ and $v$ are strongly connected if and only if they are mutually reachable i.e. there is a path fr...
GO Classes
973
views
GO Classes
asked
Aug 6, 2022
Graph Theory
goclasses-scholarship-test1
goclasses
graph-theory
graph-connectivity
multiple-selects
1-mark
+
–
3
votes
1
answer
2710
GO Classes Scholarship 2023 | Test | Question: 10
For which of the following does there exist a graph satisfying the specified conditions? A tree with six vertices and six edges. A tree with three or more vertices, two vertices of degree one, and all the other vertices with degree three or ... with $10$ vertices and $8$ edges. A disconnected graph with $12$ vertices and $11$ edges and no cycle.
For which of the following does there exist a graph satisfying the specified conditions?A tree with six vertices and six edges.A tree with three or more vertices, two ver...
GO Classes
505
views
GO Classes
asked
Aug 6, 2022
Graph Theory
goclasses-scholarship-test1
goclasses
graph-theory
graph-connectivity
multiple-selects
2-marks
+
–
4
votes
1
answer
2711
GO Classes Scholarship 2023 | Test | Question: 12
How many non-isomorphic simple undirected graphs are there, each with four vertices and without a cycle?
How many non-isomorphic simple undirected graphs are there, each with four vertices and without a cycle?
GO Classes
730
views
GO Classes
asked
Aug 6, 2022
Graph Theory
goclasses-scholarship-test1
numerical-answers
goclasses
graph-theory
graph-isomorphism
2-marks
+
–
0
votes
1
answer
2712
Maths for natural science
Determine the domain of the function $f(x)=\left | x \right |+1$
Determine the domain of the function $f(x)=\left | x \right |+1$
Hailemariam
302
views
Hailemariam
asked
Aug 5, 2022
Calculus
calculus
functions
+
–
0
votes
1
answer
2713
Self doubt : Set Theory
At a family group meeting of 30 women, 17 are descended from George, 16 are descended from John, and 5 are not descended from George or John. How many of the 30 women are descended from both George and John?
At a family group meeting of 30 women, 17 are descended from George, 16 are descended from John, and 5 are not descended from George or John. How many of the 30 women are...
clendaya
305
views
clendaya
asked
Aug 4, 2022
Set Theory & Algebra
set-theory
+
–
0
votes
1
answer
2714
Mathematics for Natural Science
Determine the domain of the function $f(x) = |x – 2|$
Determine the domain of the function $f(x) = |x – 2|$
Hailemariam
236
views
Hailemariam
asked
Aug 3, 2022
Calculus
calculus
+
–
0
votes
1
answer
2715
Mathematics for Natural Science
Prove that $2n < (n + 1)!, $ for all $ n \geq 3.$
Prove that $2n < (n + 1)!, $ for all $ n \geq 3.$
kidussss
234
views
kidussss
asked
Jul 29, 2022
Combinatory
discrete-mathematics
mathematical-logic
calculus
set-theory
+
–
0
votes
1
answer
2716
Mathematics for Natural Science
Simplify $(A\cup B)\cap (A\cup B')\cap (A - B)$ for a given non empty sets $A$ and $B$, where $(A\cap B) = \varnothing .$
Simplify $(A\cup B)\cap (A\cup B')\cap (A - B)$ for a given non empty sets $A$ and $B$, where $(A\cap B) = \varnothing .$
kidussss
234
views
kidussss
asked
Jul 29, 2022
Combinatory
discrete-mathematics
mathematical-logic
calculus
set-theory
+
–
0
votes
1
answer
2717
Mathematics for Natural Science
Suppose $x, y, z > 1$ are integers, let: $p(x,y)$ : $x$ is a factor of $y$ $q(x,y,z)$ : $z$ = $\text{GCD}(x,y)$ $r(x)$ : $x$ is prime. Check if the following argument is valid or not. $(\forall x \exists y)p(x,y) \implies r(x)$ ... $(\exists x)(\forall y)(p(x,y) \lor r(x))$ $\therefore (\forall y)(\exists z)(\exists x)q(x,y,z)$
Suppose $x, y, z 1$ are integers, let:$p(x,y)$ : $x$ is a factor of $y$$q(x,y,z)$ : $z$ = $\text{GCD}(x,y)$$r(x)$ : $x$ is prime.Check if the following argument is valid...
kidussss
352
views
kidussss
asked
Jul 29, 2022
Mathematical Logic
mathematical-logic
discrete-mathematics
+
–
0
votes
1
answer
2718
A First Course In Probability, 9th Edition, Indian Version, Sheldon Ross, Chapter 2, Problems, 18.
A deck consists of 52 playing cards which is well shuffled. Draw 6 cards. Find the probability that among the cards there will be a representative of all suits? can someone get to this answer –-→ 6283420/20358520
A deck consists of 52 playing cards which is well shuffled. Draw 6 cards. Find the probability that among the cards there will be a representative of all suits?can someon...
lolalo
451
views
lolalo
asked
Jul 28, 2022
Probability
probability
sheldon-ross
+
–
1
votes
1
answer
2719
Made Easy Test Series
How to solve this question?
How to solve this question?
Abhrajyoti00
416
views
Abhrajyoti00
asked
Jul 24, 2022
Mathematical Logic
made-easy-test-series
combinatory
discrete-mathematics
+
–
0
votes
1
answer
2720
Cengage algebra jee advanced.
Coefficient of x^8 in ( (1-x^6)/(1-x) )^3.
Coefficient of x^8 in ( (1-x^6)/(1-x) )^3.
yuyutsu
416
views
yuyutsu
asked
Jul 24, 2022
Combinatory
combinatory
+
–
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