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Recent questions in Discrete Mathematics
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361
Maths
Can anyone please suggest any single resource which has a comprehensive list of Trigonometric Identities which might be useful to solve sums ?? (Inverses, Half angles, Double Angles, Sum rule, Product Rule etc.).
Sunnidhya Roy
asked
in
Mathematical Logic
Dec 20, 2022
by
Sunnidhya Roy
269
views
trigonometry
engineering-mathematics
discrete-mathematics
1
vote
1
answer
362
Unacademy All India Mock 18 Dec. 2022.Counting
Let S={0,1,2,3,….,9}. The number of subsets of 5 contains at least two even numbers? HELP ANYONE Ans.-832
Rajender gill
asked
in
Set Theory & Algebra
Dec 19, 2022
by
Rajender gill
650
views
set-theory&algebra
counting
functions
1
vote
0
answers
363
DRDO CSE 2022 Paper 1 | Question: 8
Given a powerset $S$ of $\{1,2,3\}$, its partial order $\leq$ is given by set inclusion. That is, for any subsets $T_{1} \neq T_{2}$ of $\{1,2,3\}$ we have $T_{1} \leq T_{2}$ if and only if $T_{1} \subset T_{2}$. Construct the Hasse diagram on $S$ under this partial order definition.
admin
asked
in
Set Theory & Algebra
Dec 15, 2022
by
admin
234
views
drdocse-2022-paper1
set-theory&algebra
partial-order
4-marks
descriptive
3
votes
0
answers
364
DRDO CSE 2022 Paper 1 | Question: 9
Count the number of perfect matchings in the bipartite graph whose adjacency matrix $\text{A}$ is as follows. \[\left[\begin{array}{lll} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right]\]
admin
asked
in
Graph Theory
Dec 15, 2022
by
admin
376
views
drdocse-2022-paper1
graph-theory
bipartite-graph
graph-matching
4-marks
descriptive
1
vote
0
answers
365
DRDO CSE 2022 Paper 1 | Question: 10
Given a tree $\text{T}$ and $\lambda \geq 2$ colours $\left(c_{1}, c_{2}, \ldots, c_{\lambda}\right),$ how many proper colourings of the tree $\text{T}$ are possible?
admin
asked
in
Graph Theory
Dec 15, 2022
by
admin
282
views
drdocse-2022-paper1
graph-theory
graph-coloring
4-marks
descriptive
1
vote
0
answers
366
DRDO CSE 2022 Paper 1 | Question: 11
Consider the following graph. Find closeness centrality of $\text{‘A’}$ node.
admin
asked
in
Graph Theory
Dec 15, 2022
by
admin
266
views
drdocse-2022-paper1
graph-theory
graph-connectivity
5-marks
descriptive
1
vote
1
answer
367
DRDO CSE 2022 Paper 1 | Question: 12
Given two propositions $P$ and $Q$. "if $P$ then $Q$" denoted by $P \rightarrow Q$ is called Implication. Such implication and its ____________ are logically equivalent.
admin
asked
in
Mathematical Logic
Dec 15, 2022
by
admin
254
views
drdocse-2022-paper1
mathematical-logic
propositional-logic
2-marks
fill-in-the-blanks
1
vote
0
answers
368
DRDO CSE 2022 Paper 1 | Question: 13
Consider the following graph. Which nodes form the cliques of size $3?$
admin
asked
in
Graph Theory
Dec 15, 2022
by
admin
273
views
drdocse-2022-paper1
graph-theory
graph-connectivity
5-marks
descriptive
1
vote
0
answers
369
DRDO CSE 2022 Paper 1 | Question: 14
Derangements are permutations $\pi$ of the set $\{1,2, \ldots, n\}$ such that $\pi(i) \neq i.$ Compute the number of derangements on the set $1,2, \ldots, n$.
admin
asked
in
Combinatory
Dec 15, 2022
by
admin
176
views
drdocse-2022-paper1
combinatory
counting
7-marks
descriptive
1
vote
1
answer
370
DRDO CSE 2022 Paper 1 | Question: 15
What is the generating function corresponding to Fibonacci series. \[F_{n}=F_{n-1}+F_{n-2} .\] Note that $F_{0}=F_{1}=1$.
admin
asked
in
Combinatory
Dec 15, 2022
by
admin
482
views
drdocse-2022-paper1
combinatory
generating-functions
6-marks
descriptive
1
vote
0
answers
371
DRDO CSE 2022 Paper 1 | Question: 16
Let us say we have a supply of $1$ rupee and $2$ rupee coins in large quantities. What is the generating function for the number of ways of giving change with $1$ rupee and $2$ rupee coins.
admin
asked
in
Combinatory
Dec 15, 2022
by
admin
380
views
drdocse-2022-paper1
combinatory
generating-functions
5-marks
descriptive
1
vote
0
answers
372
DRDO CSE 2022 Paper 1 | Question: 17
Total number of functions from set $B$ to set $A$ with $n$ and $m$ elements, respectively are ___________.
admin
asked
in
Set Theory & Algebra
Dec 15, 2022
by
admin
233
views
drdocse-2022-paper1
set-theory&algebra
functions
3-marks
fill-in-the-blanks
2
votes
1
answer
373
DRDO CSE 2022 Paper 1 | Question: 18
A gardener wants to buy $3$ neem plants, $5$ rose plants and $1$ banyan plant from a nursery having $7$ neem, $10$ rose and $6$ banyan plants. How many choices does a gardener have?
admin
asked
in
Combinatory
Dec 15, 2022
by
admin
312
views
drdocse-2022-paper1
combinatory
counting
5-marks
descriptive
1
vote
1
answer
374
DRDO CSE 2022 Paper 1 | Question: 19
How many seven digit numbers are possible with exactly four $4 \mathrm{s}?$
admin
asked
in
Combinatory
Dec 15, 2022
by
admin
347
views
drdocse-2022-paper1
combinatory
counting
5-marks
descriptive
1
vote
0
answers
375
DRDO CSE 2022 Paper 1 | Question: 20
A partially ordered set $S=(\{3,4,12,24,48,72\}, /)$ is a _________ with _________ cycle$(s).$
admin
asked
in
Set Theory & Algebra
Dec 15, 2022
by
admin
150
views
drdocse-2022-paper1
set-theory&algebra
partial-order
4-marks
fill-in-the-blanks
0
votes
2
answers
376
Set Theory
We have a set of cardinality 7. Suppose P is the power set of S. We have a subset of Power set, Ps such that every pair of elements (a, b) in subset is such that, either a is a subset of b or b is a subset of a. What could be the max cardinality of Ps?
shub2204
asked
in
Set Theory & Algebra
Dec 14, 2022
by
shub2204
400
views
set-theory
set-theory
2
votes
1
answer
377
GO 2023 Topic Wise Free Test 2 | First Order Logic | Question: 1
In first-order logic, how would you express that "something likes something"? $\exists x \exists y \operatorname{Likes}(x, y)$ $\exists x \forall y \operatorname{Likes}(x, \mathrm{y})$ $\forall x \exists y \text{Likes}(x, y)$ $\forall x \forall y \operatorname{Likes}(x, \mathrm{y})$
GO Classes
asked
in
Mathematical Logic
Dec 13, 2022
by
GO Classes
131
views
goclasses2024-topictest-2
goclasses
mathematical-logic
first-order-logic
1-mark
3
votes
1
answer
378
GO 2023 Topic Wise Free Test 2 | First Order Logic | Question: 2
Which of the following propositional formulas is a tautology? $p \rightarrow(q \rightarrow p).$ $p.$ $p \vee p.$ $(p \rightarrow q) \wedge(q \rightarrow p).$
GO Classes
asked
in
Mathematical Logic
Dec 13, 2022
by
GO Classes
113
views
goclasses2024-topictest-2
goclasses
mathematical-logic
first-order-logic
1-mark
2
votes
1
answer
379
GO 2023 Topic Wise Free Test 2 | First Order Logic | Question: 4
Consider the following predicates: $\operatorname{bird}(x): x$ is a bird. $\text{penguin} (x): x$ is a penguin. $\text{fly} (x) : x$ ... $\neg$ penguin(Tweety) Tweety is a penguin or not, can not be determined. fly(Tweety)
GO Classes
asked
in
Mathematical Logic
Dec 13, 2022
by
GO Classes
164
views
goclasses2024-topictest-2
goclasses
mathematical-logic
first-order-logic
1-mark
3
votes
1
answer
380
GO 2023 Topic Wise Free Test 2 | First Order Logic | Question: 5
Which of the following is a valid inference of $\mathrm{X, Y}$ ... $\forall x .(\mathrm{Q}(x) \rightarrow \mathrm{R}(x))$
GO Classes
asked
in
Mathematical Logic
Dec 13, 2022
by
GO Classes
130
views
goclasses2024-topictest-2
goclasses
mathematical-logic
first-order-logic
multiple-selects
1-mark
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