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Recent questions and answers in Engineering Mathematics
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votes
1
answer
1
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...
Aditya_
answered
in
Set Theory & Algebra
Aug 4
by
Aditya_
41
views
set-theory
61
votes
12
answers
2
GATE CSE 1994 | Question: 1.6, ISRO2008-29
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
Cs_Gate_22
answered
in
Graph Theory
Aug 4
by
Cs_Gate_22
26.3k
views
gate1994
graph-theory
combinatory
normal
isro2008
counting
0
votes
0
answers
3
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
asked
in
Calculus
Aug 3
by
Hailemariam
24
views
calculus
54
votes
13
answers
4
GATE CSE 2014 Set 1 | Question: 49
A pennant is a sequence of numbers, each number being $1$ or $2$. An $n-$pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a $4-$pennant. The set of all possible $1-$pennants is ${(1)}$, the set of all possible ... $(1,2)$ is not the same as the pennant $(2,1)$. The number of $10-$pennants is________
A pennant is a sequence of numbers, each number being $1$ or $2$. An $n-$pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a $4-$pennant. ...
Argharupa Adhikary
answered
in
Combinatory
Jul 31
by
Argharupa Adhikary
7.0k
views
gatecse-2014-set1
combinatory
numerical-answers
normal
43
votes
7
answers
5
GATE CSE 2007 | Question: 84
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. How many distinct paths are there for the ... $(10,10)$ starting from the initial position $(0,0)$? $^{20}\mathrm{C}_{10}$ $2^{20}$ $2^{10}$ None of the above
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move...
Argharupa Adhikary
answered
in
Combinatory
Jul 31
by
Argharupa Adhikary
8.6k
views
gatecse-2007
combinatory
0
votes
1
answer
6
Mathematics for Natural Science
Prove that $2n < (n + 1)!, $ for all $ n \geq 3.$
Prove that $2n < (n + 1)!, $ for all $ n \geq 3.$
Kabir5454
answered
in
Combinatory
Jul 29
by
Kabir5454
31
views
discrete-mathematics
mathematical-logic
calculus
set-theory
15
votes
5
answers
7
GATE CSE 2002 | Question: 3
Let $A$ be a set of $n(>0)$ elements. Let $N_r$ be the number of binary relations on $A$ and let $N_f$ be the number of functions from $A$ to $A$ Give the expression for $N_r,$ in terms of $n.$ Give the expression for $N_f,$ terms of $n.$ Which is larger for all possible $n,N_r$ or $N_f$
Let $A$ be a set of $n(>0)$ elements. Let $N_r$ be the number of binary relations on $A$ and let $N_f$ be the number of functions from $A$ to $A$ Give the expression for ...
Genius
answered
in
Set Theory & Algebra
Jul 29
by
Genius
2.9k
views
gatecse-2002
set-theory&algebra
normal
descriptive
relations
0
votes
1
answer
8
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 $(A\cap B) = \varnothing .$
Kabir5454
answered
in
Combinatory
Jul 29
by
Kabir5454
32
views
discrete-mathematics
mathematical-logic
calculus
set-theory
0
votes
0
answers
9
Mathematics for Natural Science
Sketch the graph of $f(x) = \frac{x^{3}-1}{x^{2}-1}$
Sketch the graph of $f(x) = \frac{x^{3}-1}{x^{2}-1}$
kidussss
asked
in
Calculus
Jul 29
by
kidussss
56
views
calculus
0
votes
0
answers
10
Mathematics for Natural Science
Let y in the form of $a + bi$, where $a$ and $b$ are real numbers, be the cubic roots of complex number $z^{20},$ where $z=\frac{2}{4 + 3i}.$ Find $a + b.$
Let y in the form of $a + bi$, where $a$ and $b$ are real numbers, be the cubic roots of complex number $z^{20},$ where $z=\frac{2}{4 + 3i}.$ Find $a + b.$
kidussss
asked
in
Combinatory
Jul 29
by
kidussss
36
views
discrete-mathematics
mathematical-logic
calculus
set-theory
0
votes
0
answers
11
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 ...
kidussss
asked
in
Mathematical Logic
Jul 29
by
kidussss
49
views
mathematical-logic
discrete-mathematics
0
votes
1
answer
12
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 someo...
Arjun
answered
in
Probability
Jul 29
by
Arjun
49
views
probability
sheldon-ross
35
votes
8
answers
13
GATE CSE 2009 | Question: 22
For the composition table of a cyclic group shown below: ... $a,b$ are generators $b,c$ are generators $c,d$ are generators $d,a$ are generators
For the composition table of a cyclic group shown below: $$\begin{array}{|c|c|c|c|c|} \hline \textbf{*} & \textbf{a}& \textbf{b} &\textbf{c} & \textbf{d}\\\hline \textbf{...
Argharupa Adhikary
answered
in
Set Theory & Algebra
Jul 26
by
Argharupa Adhikary
6.2k
views
gatecse-2009
set-theory&algebra
normal
group-theory
1
vote
1
answer
14
Made Easy Test Series
How to solve this question?
How to solve this question?
Aditya_
answered
in
Mathematical Logic
Jul 25
by
Aditya_
102
views
made-easy-test-series
combinatory
discrete-mathematics
1
vote
3
answers
15
GO Classes Weekly Quiz 2 | Programming in C | Propositional Logic | Question: 11
Let $P,S,R$ be three statements(propositions). Let $S$ be a sufficient condition for $P$, Let $R$ is a necessary condition for $P$ then which of the following is/are true? $S$ is a sufficient condition ... is neither sufficient, nor a necessary condition for $R.$ $S$ is a sufficient and necessary condition for $R$.
Let $P,S,R$ be three statements(propositions). Let $S$ be a sufficient condition for $P$, Let $R$ is a necessary condition for $P$ then which of the following is/are true...
Argharupa Adhikary
answered
in
Mathematical Logic
Jul 25
by
Argharupa Adhikary
164
views
goclasses_wq2
goclasses
mathematical-logic
propositional-logic
multiple-selects
2-marks
0
votes
1
answer
16
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.
Kabir5454
answered
in
Combinatory
Jul 24
by
Kabir5454
72
views
combinatory
38
votes
6
answers
17
GATE CSE 2006 | Question: 73
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of connected components in $G$ is: $n$ $n + 2$ $2^{\frac{n}{2}}$ $\frac{2^{n}}{n}$
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets ...
Abhrajyoti00
answered
in
Graph Theory
Jul 23
by
Abhrajyoti00
6.0k
views
gatecse-2006
graph-theory
normal
graph-connectivity
52
votes
4
answers
18
GATE CSE 2003 | Question: 8, ISRO2009-53
Let $G$ be an arbitrary graph with $n$ nodes and $k$ components. If a vertex is removed from $G$, the number of components in the resultant graph must necessarily lie down between $k$ and $n$ $k-1$ and $k+1$ $k-1$ and $n-1$ $k+1$ and $n-k$
Let $G$ be an arbitrary graph with $n$ nodes and $k$ components. If a vertex is removed from $G$, the number of components in the resultant graph must necessarily lie dow...
Abhrajyoti00
answered
in
Graph Theory
Jul 23
by
Abhrajyoti00
11.4k
views
gatecse-2003
graph-theory
graph-connectivity
normal
isro2009
54
votes
7
answers
19
GATE IT 2006 | Question: 25
Consider the undirected graph $G$ defined as follows. The vertices of $G$ are bit strings of length $n$. We have an edge between vertex $u$ and vertex $v$ if and only if $u$ and $v$ differ in exactly one bit position (in other words, $v$ can be obtained from $u$ by ... $\left(\frac{1}{n}\right)$ $\left(\frac{2}{n}\right)$ $\left(\frac{3}{n}\right)$
Consider the undirected graph $G$ defined as follows. The vertices of $G$ are bit strings of length $n$. We have an edge between vertex $u$ and vertex $v$ if and only if ...
Abhrajyoti00
answered
in
Graph Theory
Jul 23
by
Abhrajyoti00
9.3k
views
gateit-2006
graph-theory
graph-coloring
normal
43
votes
6
answers
20
GATE CSE 2009 | Question: 3
Which one of the following is TRUE for any simple connected undirected graph with more than $2$ vertices? No two vertices have the same degree. At least two vertices have the same degree. At least three vertices have the same degree. All vertices have the same degree.
Which one of the following is TRUE for any simple connected undirected graph with more than $2$ vertices? No two vertices have the same degree. At least two vertices have...
Abhrajyoti00
answered
in
Graph Theory
Jul 23
by
Abhrajyoti00
8.2k
views
gatecse-2009
graph-theory
normal
degree-of-graph
3
votes
3
answers
21
UGC NET CSE | Junet 2015 | Part 2 | Question: 3
In how many ways can $15$ indistinguishable fish be placed into $5$ different ponds, so that each pond contains at least one fish? $1001$ $3876$ $775$ $200$
In how many ways can $15$ indistinguishable fish be placed into $5$ different ponds, so that each pond contains at least one fish? $1001$ $3876$ $775$ $200$
Vasudevarnab23
answered
in
Combinatory
Jul 21
by
Vasudevarnab23
3.9k
views
ugcnetjune2015ii
combinatory
counting
4
votes
2
answers
22
UGC NET CSE | Junet 2015 | Part 2 | Question: 1
How many strings of $5$ digits have the property that the sum of their digits is $7$? $66$ $330$ $495$ $99$
How many strings of $5$ digits have the property that the sum of their digits is $7$? $66$ $330$ $495$ $99$
Vasudevarnab23
answered
in
Combinatory
Jul 21
by
Vasudevarnab23
1.9k
views
ugcnetjune2015ii
discrete-mathematics
counting
0
votes
1
answer
23
Self Doubt - Planarity of Complete Bipartite Graph
How to determine for which m, n the complete bipartite graph $Km,n$ is planar? I am getting two answers from two sources:- A complete bipartite graph $Kmn$ is planar if and only if m<3 or n>3. Source: https://www.javatpoint.com/ ... m ≤ 2 or n ≤ 2. Source: http://www.matthewkahle.org/download/file/fid/573 Need a proper proof of the solution.
How to determine for which m, n the complete bipartite graph $Km,n$ is planar? I am getting two answers from two sources:- A complete bipartite graph $Kmn$ is planar if a...
Aditya_
answered
in
Graph Theory
Jul 21
by
Aditya_
54
views
graph-theory
bipartite-graph
discrete-mathematics
graph-planarity
2
votes
1
answer
24
Applied Grand Test 2
What is the value of the given determinant ?
What is the value of the given determinant ?
Ratul Chatterjee
answered
in
Linear Algebra
Jul 20
by
Ratul Chatterjee
333
views
linear-algebra
test-series
determinant
33
votes
5
answers
25
GATE CSE 1989 | Question: 4-i
How many substrings (of all lengths inclusive) can be formed from a character string of length $n$? Assume all characters to be distinct, prove your answer.
How many substrings (of all lengths inclusive) can be formed from a character string of length $n$? Assume all characters to be distinct, prove your answer.
neopentane
answered
in
Combinatory
Jul 20
by
neopentane
4.5k
views
gate1989
descriptive
combinatory
normal
proof
17
votes
6
answers
26
GATE CSE 2020 | Question: 52
Graph $G$ is obtained by adding vertex $s$ to $K_{3,4}$ and making $s$ adjacent to every vertex of $K_{3,4}$. The minimum number of colours required to edge-colour $G$ is _______
Graph $G$ is obtained by adding vertex $s$ to $K_{3,4}$ and making $s$ adjacent to every vertex of $K_{3,4}$. The minimum number of colours required to edge-colour $G$ is...
ankitgupta.1729
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Graph Theory
Jul 19
by
ankitgupta.1729
7.6k
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gatecse-2020
numerical-answers
graph-theory
graph-coloring
1
vote
0
answers
27
maths
A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card ?
closed
A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability th...
jugnu1337
asked
in
Probability
Jul 19
by
jugnu1337
39
views
discrete-mathematics
probability
57
votes
7
answers
28
GATE IT 2005 | Question: 32
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is $3$ $4$ $5$ $6$
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is $...
Arkaprava
answered
in
Probability
Jul 18
by
Arkaprava
16.6k
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gateit-2005
probability
binomial-distribution
expectation
normal
3
votes
2
answers
29
Spannig trees
For a complete graph with 10 vertices, The number of spanning trees is at least_____?
For a complete graph with 10 vertices, The number of spanning trees is at least_____?
afroze
answered
in
Graph Theory
Jul 17
by
afroze
1.8k
views
spanning-tree
graph-theory
3
votes
2
answers
30
GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 8
Which of the following associative multiplication tables defined on the set $G = \{a, b, c, d\}$ form a group?
Which of the following associative multiplication tables defined on the set $G = \{a, b, c, d\}$ form a group?
Abhrajyoti00
answered
in
Set Theory & Algebra
Jul 17
by
Abhrajyoti00
89
views
goclasses_wq12
goclasses
set-theory&algebra
group-theory
multiple-selects
2-marks
2
votes
2
answers
31
GO Classes 2023 | Weekly Quiz 3 | Question: 3
Here are some very useful ways of characterizing propositional formulas. Start by constructing a truth table for the formula and look at the column of values obtained. We say that the formula is: satisfiable if there is at least one $T$ ... Necessarily false: $F2$ is tautology $F3$ is tautology $F1$ is a contingency. $F1\wedge F3$ is contradiction.
Here are some very useful ways of characterizing propositional formulas. Start by constructing a truth table for the formula and look at the column of values obtained. We...
Abhrajyoti00
answered
in
Mathematical Logic
Jul 16
by
Abhrajyoti00
167
views
goclasses
goclasses_wq3
mathematical-logic
propositional-logic
multiple-selects
2-marks
4
votes
2
answers
32
GATE CSE 2022 | Question: 40
The following simple undirected graph is referred to as the Peterson graph. Which of the following statements is/are $\text{TRUE}?$ The chromatic number of the graph is $3.$ The graph has a Hamiltonian path. The following graph is isomorphic to the Peterson ... $3.$ (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)
The following simple undirected graph is referred to as the Peterson graph. Which of the following statements is/are $\text{TRUE}?$ The chromatic number of the graph is $...
ankitgupta.1729
answered
in
Graph Theory
Jul 15
by
ankitgupta.1729
1.2k
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gatecse-2022
graph-theory
graph-isomorphism
multiple-selects
0
votes
1
answer
33
Discrete mathematics C.L.Liu Solutions
Can I have solutions of ELEMENTS OF DISCRETE MATHEMATICS by C.L.Liu Solutions. Pls help
Can I have solutions of ELEMENTS OF DISCRETE MATHEMATICS by C.L.Liu Solutions. Pls help
Bikram 1
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Mathematical Logic
Jul 15
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Bikram 1
1.4k
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discrete-mathematics
0
votes
2
answers
34
can any one suggest resources for discrete mathematics for gate
suggest some good resources for discrete mathematics
suggest some good resources for discrete mathematics
Bikram 1
answered
in
Mathematical Logic
Jul 14
by
Bikram 1
215
views
0
votes
2
answers
35
Kenneth Rosen Edition 7 Exercise 6.4 Question 25 (Page No. 422)
Let n be a positive integer. Show that $\binom{2n}{n + 1} + \binom{2n}{n} = \dfrac{\binom{2n + 2}{n + 1}}{2}.$
Let n be a positive integer. Show that $\binom{2n}{n + 1} + \binom{2n}{n} = \dfrac{\binom{2n + 2}{n + 1}}{2}.$
ASNR1010
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in
Combinatory
Jul 14
by
ASNR1010
91
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kenneth-rosen
discrete-mathematics
counting
binomial-theorem
descriptive
40
votes
7
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36
GATE CSE 2015 Set 3 | Question: 41
Let $R$ be a relation on the set of ordered pairs of positive integers such that $((p,q),(r,s)) \in R$ if and only if $p-s=q-r$. Which one of the following is true about $R$? Both reflexive and symmetric Reflexive but not symmetric Not reflexive but symmetric Neither reflexive nor symmetric
Let $R$ be a relation on the set of ordered pairs of positive integers such that $((p,q),(r,s)) \in R$ if and only if $p-s=q-r$. Which one of the following is true about ...
Abhrajyoti00
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Set Theory & Algebra
Jul 13
by
Abhrajyoti00
9.3k
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gatecse-2015-set3
set-theory&algebra
relations
normal
0
votes
3
answers
37
Discrete Mathematics
Any Good resource to understand this topic.
Any Good resource to understand this topic.
Kushal06
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in
Combinatory
Jul 13
by
Kushal06
267
views
combinatory
ace-test-series
0
votes
1
answer
38
Discrete Mathematics
Somebody please clarify the answer
Somebody please clarify the answer
Aditya_
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Combinatory
Jul 11
by
Aditya_
65
views
combinatory
ace-test-series
0
votes
2
answers
39
Applied Mathematics Calculus and Limit Question
Evaluate the question of the following limits. $\lim_{x\rightarrow 1} \frac{x}{(x-1)^{2}}$
Evaluate the question of the following limits. $\lim_{x\rightarrow 1} \frac{x}{(x-1)^{2}}$
ASNR1010
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Calculus
Jul 9
by
ASNR1010
234
views
limits
calculus
0
votes
2
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40
Applied Mathematics Calculus and Limit Question
Evaluate the question of the following limits. $\lim_{x\rightarrow \infty} \frac{2x^{3}+3x-5}{5x^{3}+1}$
Evaluate the question of the following limits. $\lim_{x\rightarrow \infty} \frac{2x^{3}+3x-5}{5x^{3}+1}$
Kabir5454
answered
in
Calculus
Jul 9
by
Kabir5454
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views
calculus
limits
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