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Recent questions and answers in Engineering Mathematics
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Linear AlgebraMETest
If the determinant of the below matrix is 245, what is the value of X? $\begin{bmatrix} 0 & 4& 2 &1 \\ 3& 1 & 0 & 2\\ 5&2 & x& 4\\ 6& 1 & 1 & 0 \end{bmatrix}$ ... , because by keeping 6 in place of x I am getting determinant as 245(Result verified by computer program). Please let me know where I am going wrong?
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Linear Algebra
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linearalgebra
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4
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GATE20005
A multiset is an unordered collection of elements where elements may repeat any number of times. The size of a multiset is the number of elements in it, counting repetitions. What is the number of multisets of size $4$ that can be constructed from n distinct elements so that at least one element occurs exactly twice? How many multisets can be constructed from n distinct elements?
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Combinatory
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Central limit theorem
(Central Limit Theorem) Let X1, X2, . . . , X81 be i.i.d., each with expected value µ = E(Xi) = 5, and variance σ2 = Var(Xi) = 4. Approximate P(X1 + X2 +· · · X81 > 369), using the central limit theorem.
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Probability
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Na462
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probability
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Grewal
Suppose avg waiting time of a process to get chance in a queue is 5 min. What will the probability that process get chance at first minute is ________________
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Probability
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probability
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Probability mass function
Suppose that the cdf of X is given by: F(a) ={ 0 for a < 0 1/5 for 0 ≤ a < 2 2/5 for 2 ≤ a < 4 1 for a ≥ 4. } Determine the pmf of X.
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Probability
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Probability density function
Let R be the rate at which customers are served in a queue. Suppose that R is exponential with pdf f(r) = 2e^(−2r) on [0, ∞). Find the pdf of the waiting time per customer T = 1/R.
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Probability
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Expectation
Suppose 100 people all toss a hat into a box and then proceed to randomly pick out a hat. What is the expected number of people to get their own hat back. Hint: express the number of people who get their own hat as a sum of random variables whose expected value is easy to compute.
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Probability
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#probability#expectation
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8
Kenneth rosen Q.36 Ex.2.3
Let f be a function from the set A to the set B.Let S and T be subsets of A.Show that $f(S\cup T)=f(S)\cup f(T)$ $f(S\cap T)\subseteq f(S)\cap f(T)$ Show that inclusion in part b can be proper
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1
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9
GATE  2014  1 51 modified
Consider an directed graph G where selfloops are not allowed. The vertex set of G is {(i,j)∣1≤i≤12,1≤j≤12}There is an edge from(a,b) to (c,d) if a−c≤1 and b−d≤1. The number of edges in this graph is______
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Graph Theory
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kenneth rosen Ex 2.3 Q.29,30
Justify the statements. 1. if f and f o g are one to one,does it follows that g is one to one. 2 if f and f o g are onto,does it follow that g is onto
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Set Theory & Algebra
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1
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11
JEST 2019
Three dice are rolled independently. Probability of obtaining the difference from largest and smallest number as exactly 4 :
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Probability
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Satbir
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jest
probability
+20
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4
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12
GATE2015227
Perform the following operations on the matrix $\begin{bmatrix} 3 & 4 & 45 \\ 7 & 9 & 105 \\ 13 & 2 & 195 \end{bmatrix}$ Add the third row to the second row Subtract the third column from the first column. The determinant of the resultant matrix is _____.
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Linear Algebra
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Conditional Probability
A multiple choice exam has 4 choices for each question. A student has studied enough so that the probability they will know the answer to a question is 0.5, the probability that they will be able to eliminate one choice is 0.25, otherwise ... the test to measure what the student knows. If the student answers a question correctly what's the probability they knew the answer?
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Probability
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prashant jha 1
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Kenneth Rosen Ex.2.3 Q.3(c)
https://prnt.sc/cncgcv plz explain the c part!
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Set Theory & Algebra
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3
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15
GATE19982.1
The rank of the matrix given below is: $\begin{bmatrix} 1 &4 &8 &7\\ 0 &0& 3 &0\\ 4 &2& 3 &1\\ 3 &12 &24 &2 \end{bmatrix}$ $3$ $1$ $2$ $4$
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Linear Algebra
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gate1998
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16
JEST 2019
A directed graph with n vertices, in which each vertex has exactly 3 outgoing edges. Which one is true? A) All the vertices have indegree = 3 . B) Some vertices will have indegree exactly 3. C)Some vertices have indegree atleast 3. D) Some of the vertices have indegree atmost 3
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Graph Theory
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Sayan Bose
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jest
graphtheory
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0
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17
JEST 2019
Let ${(0,1)}^n$ set of all binary string of length n. Hamming sphere of radius around a string C in ${(0,1)}^n$ is the set of all strings d$\epsilon$ ${(0,1)}^n$ that differ from C in at most r of n position, S(C,r) for n=2k+1 For C,C’ $\epsilon$ ${(0,1)}^n$ S(C,k) and S(C’,k) are disjoint couldn't remember rest of the options.
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Set Theory & Algebra
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vivek_mishra
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399
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jest
2019
discretemathematics
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0
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18
JEST 2019 Descriptive Q3 (8 Marks)
Determine the number of functions f:{1,2,3…,n}→{1995,1996} satisfying the condition that f(1)+f(2)+…f(n) is odd.
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Set Theory & Algebra
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dan31
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657
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60
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jest2019
discretemathematics
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19
JEST 2019 Descriptive Q2 (8 Marks)
Given a sequence $a_1$, $a_2$ , $a_3$ ... $a_n$ of any different positive integers, exhibit an arrangement of integers between 1 and $n^2$ which has no increasing or decreasing subsequence of length n+1.
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Graph Theory
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dan31
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24
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jest
2019
discretemathematics
0
votes
0
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20
JEST 2019 Descriptive Q1 (8 Marks)
Suppose that G contains a cycle C, and a path of length at least k between some two vertices of C. Show that G contains a cycle of length at least √k.
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Graph Theory
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dan31
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jest
2019
discretemathematics
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2
answers
21
TIFR2011MathsA16
The polynomial $x^{4}+7x^{3}13x^{2}+11x$ has exactly one real root.
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Set Theory & Algebra
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Sreyasree Mandal
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tifrmaths2011
polynomials
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22
Conditional probability
Oscar has lost his dog in either forest A (with a priori probability 0.4) or in forest B (with a priori probability 0.6). On any given day, if the dog is in A and Oscar spends a day searching for it in A, the conditional probability that he will ﬁnd the dog that day is 0.25. ... +(1/2)*0.15; but the answer given is=(0.5*0.4*0.25)+(0.5*0.6*0.15); what is wrong with my logic?
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Probability
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DIYA BASU
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241
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20
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conditionalprobability
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vote
3
answers
23
TIFR2011MathsB10
Suppose a box contains three cards, one with both sides white, one with both sides black, and one with one side white and the other side black. If you pick a card at random, and the side facing you is white, then the probability that the other side is white is $1/2$.
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Probability
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Sreyasree Mandal
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117
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183
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tifrmaths2011
probability
conditionalprobability
0
votes
1
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24
Kenneth Rosen chapter 5 20 discrete mathematics
A playoff between two teams consists of at most five games . The first team that wins three games wins the playoff. In how many different way playoff occur?
[closed]
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Combinatory
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subhrob
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363
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kennethrosen
discretemathematics
permutationsandcombinations
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votes
1
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25
Linear algebra
The number of different n×n symmetric matrices with each element being 0 or 1 is
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Mathematical Logic
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26
Discrete Maths and Its Applications, 7th Edition, Kenneth Rosen
1. Which of these sentences are propositions? What are the truth values of those that are propositions? a) Boston is the capital of Massachusetts. b) Miami is the capital of Florida. c) 2+3 = 5. d) 5+7 = 10. e) x +2 ... is answer for f) as I am thinking I can answer this question or I will not answer this question is it a proposition?
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Mathematical Logic
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prashant jha 1
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3
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27
CMI2013A06
A simple graph is one in which there are no selfloops and each pair of distinct vertices is connected by at most one edge.Let $G$ be a simple graph on $8$ vertices such that there is a vertex of degree $1$, a vertex of degree $2$, a vertex of degree $3$, a vertex of ... degree $6$ and a vertex of degree $7$. Which of the following can be the degree of the last vertex? $3$ $0$ $5$ $4$
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Graph Theory
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cmi2013
graphtheory
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1
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28
JEST Sample Question 1b
When is the following statement true? (A ∪ B) ∩ C = A ∩ C (A) If Ā ∩ B ∩ C = φ (B) If A ∩ B ∩ C = φ (C) always (D) never
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jest
gate
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0
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29
JEST Sample Question 1a
Let a and b be positive integers such that a > b and a^ 2 − b^ 2 is a prime number. Then a^2 − b^ 2 is equal to (A) a − b (B) a + b (C) a × b (D) none of the above
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30
JEST Sample Question 1c
If a fair die (with 6 faces) is cast twice, what is the probability that the two numbers obtained differ by 2? (A) 1/12 (B) 1/6 (C) 2/9 (D) 1/2
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Probability
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jest
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probability
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31
Jest Exam sample question3
How many subsets of even cardinality does an nelement set have ? Justify answer. Please give a proof if possible.This is part of subjective JEST paper.
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Set Theory & Algebra
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32
JEST Sample Question6
Two gamblers have an argument. The first one claims that if a fair coin is tossed repeatedly, getting two consecutive heads is very unlikely. The second, naturally, is denying this. They decide to settle this by an actual trial; if, within n coin tosses, ... demonstrated. What happens for larger values of n? Is it true that P (n) only increases with n? Justify your answer.
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For All & There Exist property
is For All V is distributive on AND operator? 1 is ‘’there exist’’ is distributive over OR operator? 2 I have example in which this is true , but is true in general? so logically checking without using any property above four statements are correct. But is 1 and 2 always correct?
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Mathematical Logic
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votes
4
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34
GATE201912
Let $G$ be an undirected complete graph on $n$ vertices, where $n > 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to $n!$ $(n1)!$ $1$ $\frac{(n1)!}{2}$
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Graph Theory
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gate2019
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Sheldon ross example 5f
A poker hand consists of 5 cards.If the cards have distinct consecutive values and are not all of the same suit,we say that hand is straight.For instance a hand consisting of the five of spades,six of spades,seven of spades,eight of spades and nine of hearts is a straight.What is the probability that one is dealt is a straight?
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Probability
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Probability
Bob has a peculiar pair of foursided dice. When he rolls the dice, the probability of any particular outcome is proportional to the sum of the results of each die. All outcomes that result in a particular sum are equally likely. (a) What is the probability of the ... Here what do we mean by the line  any particular outcome is proportional to the sum of the results of each die.
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Probability
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Permutation and Combination
The total number of ways in which 5 balls of different color can be distributed among 3 persons so that each person gets at least one ball is:
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A family has two children. Given that one of the children is a boy, what is the probability that both children are boys?
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Probability
Let 3 cards are drawn from a pack of 52 cards one by one without replacement then find the prob that 3 cards are drawn out of which 2 are ace Ace and one is King?
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ISRODEC201717
If $C$ is a skewsymmetric matrix of order $n$ and $X$ is $n\times 1$ column matrix, then $X{^T} CX$ is a scalar matrix null matrix unit matrix matrix will all elements $1$
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