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Recent questions in Engineering Mathematics

1 vote
2 answers
1
The number of positive integers not exceeding $100$ that are either odd or the square of an integer is _______ $63$ $59$ $55$ $50$
asked Nov 20, 2020 in Set Theory & Algebra jothee 221 views
2 votes
2 answers
2
How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books? $4$ $6$ $7$ $9$
asked Nov 20, 2020 in Combinatory jothee 134 views
0 votes
1 answer
3
Which of the following pairs of propositions are not logically equivalent? $((p \rightarrow r) \wedge (q \rightarrow r))$ and $((p \vee q) \rightarrow r)$ $p \leftrightarrow q$ and $(\neg p \leftrightarrow \neg q)$ $((p \wedge q) \vee (\neg p \wedge \neg q))$ and $p \leftrightarrow q$ $((p \wedge q) \rightarrow r)$ and $((p \rightarrow r) \wedge (q \rightarrow r))$
asked Nov 20, 2020 in Discrete Mathematics jothee 129 views
0 votes
1 answer
4
Let $G$ be a directed graph whose vertex set is the set of numbers from $1$ to $100$. There is an edge from a vertex $i$ to a vertex $j$ if and only if either $j=i+1$ or $j=3i$. The minimum number of edges in a path in $G$ from vertex $1$ to vertex $100$ is ______ $23$ $99$ $4$ $7$
asked Nov 20, 2020 in Discrete Mathematics jothee 77 views
0 votes
1 answer
5
If $f(x)=x$ is my friend, and $p(x) =x$ is perfect, then correct logical translation of the statement “some of my friends are not perfect” is ______ $\forall _x (f(x) \wedge \neg p(x))$ $\exists _x (f(x) \wedge \neg p(x))$ $\neg (f(x) \wedge \neg p(x))$ $\exists _x (\neg f(x) \wedge \neg p(x))$
asked Nov 20, 2020 in Discrete Mathematics jothee 48 views
0 votes
1 answer
6
What kind of clauses are available in conjunctive normal form? Disjunction of literals Disjunction of variables Conjunction of literals Conjunction of variables
asked Nov 20, 2020 in Discrete Mathematics jothee 32 views
0 votes
1 answer
7
Consider the following properties: Reflexive Antisymmetric Symmetric Let $A=\{a,b,c,d,e,f,g\}$ and $R=\{(a,a), (b,b), (c,d), (c,g), (d,g), (e,e), (f,f), (g,g)\}$ be a relation on $A$. Which of the following property (properties) is (are) satisfied by the relation $R$? Only $a$ Only $c$ Both $a$ and $b$ $b$ and not $a$
asked Nov 20, 2020 in Discrete Mathematics jothee 66 views
0 votes
1 answer
8
Consider the following argument with premise $\forall _x (P(x) \vee Q(x))$ and conclusion $(\forall _x P(x)) \wedge (\forall _x Q(x))$ ... valid argument Steps $(C)$ and $(E)$ are not correct inferences Steps $(D)$ and $(F)$ are not correct inferences Step $(G)$ is not a correct inference
asked Nov 20, 2020 in Discrete Mathematics jothee 30 views
0 votes
1 answer
9
Consider the following statements: Any tree is $2$-colorable A graph $G$ has no cycles of even length if it is bipartite A graph $G$ is $2$-colorable if is bipartite A graph $G$ can be colored with $d+1$ colors if $d$ is the maximum degree of any vertex in the graph $G$ ... and $(e)$ are incorrect $(b)$ and $(c)$ are incorrect $(b)$ and $(e)$ are incorrect $(a)$ and $(d)$ are incorrect
asked Nov 20, 2020 in Discrete Mathematics jothee 35 views
0 votes
1 answer
10
Consider the statement below. A person who is radical $(R)$ is electable $(E)$ if he/she is conservative $(C)$, but otherwise not electable. Few probable logical assertions of the above sentence are given below. $(R \wedge E) \Leftrightarrow C$ $R \rightarrow (E \leftrightarrow C)$ ... answer from the options given below: $(B)$ only $(C)$ only $(A)$ and $(C)$ only $(B)$ and $(D)$ only
asked Nov 20, 2020 in Discrete Mathematics jothee 27 views
0 votes
0 answers
11
Let $G$ be a simple undirected graph, $T_D$ be a DFS tree on $G$, and $T_B$ be the BFS tree on $G$. Consider the following statements. Statement $I$: No edge of $G$ is a cross with respect to $T_D$ Statement $II$: For every edge $(u,v)$ of $G$ ... Statement $I$ and Statement $II$ are false Statement $I$ is correct but Statement $II$ is false Statement $I$ is incorrect but Statement $II$ is true
asked Nov 20, 2020 in Discrete Mathematics jothee 33 views
0 votes
0 answers
12
The limit $\underset{n\rightarrow \infty }{\lim}\:n^{2}\int_{0}^{1}\:\frac{1}{\left ( 1+x^{2} \right )^{n}}\:dx$ is equal to $1$ $0$ $+\infty$ $1/2$
asked Aug 30, 2020 in Calculus soujanyareddy13 179 views
0 votes
0 answers
13
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$ $e^{-2t}u(t)$ $e^{2t}u(t)$ $e^{-t}u(t)$ $e^{t}u(t)$
asked Aug 28, 2020 in Calculus Lakshman Patel RJIT 68 views
2 votes
1 answer
14
15. a) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces are chosen? b) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces and at least ... many cards must be chosen from a standard deck of 52 cards to guarantee that there are at least two cards of each of two different kinds?
asked Jul 4, 2020 in Combinatory Sanjay Sharma 313 views
4 votes
1 answer
15
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k > 0$. Solve by summation rules. Solve by combinatorial argument.
asked Jun 8, 2020 in Combinatory dd 412 views
0 votes
2 answers
18
Suppose that there are $n = 2^{k}$ teams in an elimination tournament, where there are $\frac{n}{2}$ games in the first round, with the $\frac{n}{2} = 2^{k-1}$ winners playing in the second round, and so on. Develop a recurrence relation for the number of rounds in the tournament.
asked May 10, 2020 in Combinatory Lakshman Patel RJIT 196 views
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