Recent questions and answers in Engineering Mathematics

22 votes

3 answers

1

GATE CSE 2008 | Question: 3
The following system of equations $x_1 + x_2 + 2x_3 = 1$ $x_1 + 2x_2 + 3x_3 = 2$ $x_1 + 4x_2 + αx_3 = 4$ has a unique solution. The only possible value(s) for $α$ is/are $0$ either $0$ or $1$ one of $0, 1$, or $-1$ any real number

raj26 answered in Linear Algebra 3 days ago

by raj26

5.8k views

1 vote

1 answer

2

Probability
An ISP has a link of 100Mbps which is shared by its subscribers. Considering the fact that all of its subscribers are active 50% of the time and the probabilities of being active are independent, the ISP has promised 25 Mbps to its 6 subscribers. What is the probability that any subscriber gets degraded service (less than promised speed).

manghil007 answered in Probability 4 days ago

495 views

0 votes

1 answer

3

Applied Test Series
A Professor tells 3 Jokes in his maths class each year. How large a set of jokes does the professor need in order never to repeat the exact same triple of jokes over a period of 12 years?_________

Sudhanshu10 answered in Combinatory 5 days ago

28 views

16 votes

4 answers

4

GATE CSE 2002 | Question: 1.6
Which of the following is true? The set of all rational negative numbers forms a group under multiplication. The set of all non-singular matrices forms a group under multiplication. The set of all matrices forms a group under multiplication. Both B and C are true.

imkeshav answered in Set Theory & Algebra Oct 15

6.4k views

32 votes

5 answers

5

GATE CSE 2003 | Question: 5
$n$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is \(^{2n}\mathrm{C}_n\times 2^n\) \(3^n\) \(\frac{(2n)!}{2^n}\) \(^{2n}\mathrm{C}_n\)

Arpit Patel answered in Combinatory Oct 13

5.7k views

2 votes

3 answers

6

NIELIT 2017 July Scientist B (IT) - Section B: 13
Which of the following statements is false? $(P\land Q)\lor(\sim P\land Q)\lor(P \land \sim Q)$ is equal to $\sim Q\land \sim P$ $(P\land Q)\lor(\sim P\land Q)\lor(P \wedge \sim Q)$ is equal to $Q\lor P$ ... $(P\land Q)\lor(\sim P\land Q)\lor (P \land \sim Q)$ is equal to $P\lor (Q\land \sim P)$

Mohitdas answered in Mathematical Logic Oct 11

314 views

51 votes

14 answers

7

GATE CSE 2015 Set 3 | Question: 5
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.

Kanwae Kan answered in Combinatory Oct 11

8.8k views

4 votes

4 answers

8

TIFR2010-Maths-A-8
Let $f(x)= |x|^{3/2}, x \in \mathbb{R}$. Then $f$ is uniformly continuous. $f$ is continuous, but not differentiable at $x=0$. $f$ is differentiable and $f ' $ is continuous. $f$ is differentiable, but $f ' $ is discontinuous at $x=0$.

huny answered in Calculus Oct 9

by huny

650 views

10 votes

6 answers

9

GATE CSE 2021 Set 1 | Question: 36
Let $G=(V, E)$ be an undirected unweighted connected graph. The diameter of $G$ is defined as: $\text{diam}(G)=\displaystyle \max_{u,v\in V} \{\text{the length of shortest path between $u$ and $v$}\}$ Let $M$ be the adjacency matrix of $G$. Define graph $G_2$ ... $\text{diam}(G_2) = \text{diam}(G)$ $\text{diam}(G)< \text{diam}(G_2)\leq 2\; \text{diam}(G)$

Nihal Singh answered in Graph Theory Oct 8

1.8k views

7 votes

4 answers

10

GATE CSE 2021 Set 2 | Question: 15
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$

Mohitdas answered in Mathematical Logic Oct 8

1.5k views

2 votes

5 answers

11

GATE CSE 2021 Set 1 | Question: 16
In an undirected connected planar graph $G$, there are eight vertices and five faces. The number of edges in $G$ is _________.

kalam_11 answered in Graph Theory Oct 6

2k views

0 votes

0 answers

12

Differentiate between Conditional probability and Joint Probability
Hey all, I have a confusion regarding when to use P(A∩B) or P(A/B). Like in following question: A group consists of equal no of men and women .of this grp 20% of men and 50% of women are unemployed .If a ... is here, how to understand that 50% of women unemployed is P(Unemployed/Women) and not P(Women ∩ Unemployed) ? Thanks

Acejoy asked in Probability Oct 3

by Acejoy

23 views

10 votes

5 answers

13

GATE CSE 2021 Set 2 | Question: 24
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________

Umakant_Mukhiya answered in Linear Algebra Oct 1

by Umakant_Mukhiya

2.8k views

0 votes

1 answer

14

Kenneth Rosen Edition 7th Exercise 2.3 Question 35 (Page No. 154)
If $f$ and $fog$ are onto, does it follow that $g$ is onto?Justify your answer.

Vishal_kumar98 answered in Set Theory & Algebra Sep 30

by Vishal_kumar98

92 views

0 votes

1 answer

15

GATE ACADEMY TEST SERIES
What is the minimum number of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee that there are at least 100 who come from the same state?

raja11sep answered in Mathematical Logic Sep 26

89 views

0 votes

0 answers

16

Biconditional Operator in the logical expression for Symmetric Relation.
"The logical expression for the symmetric relation should contain the biconditional operator <-> instead of implication -> . Because, if u keep ->, then for the case when F -> T the ... " Could someone plz help, this seems to be correct. Also https://en.wikipedia.org/wiki/Symmetric_relation.

SHM asked in Mathematical Logic Sep 26

by SHM

28 views

0 votes

0 answers

17

math book
$\int_{0}^{1}\tan^{-1} (1-\frac{1}{x})$ d(x) find

amit166 asked in Calculus Sep 25

46 views

2 votes

2 answers

18

Probability - Gravner-35
Roll a die, then select at random, without replacement, as many cards from the deck as the number shown on the die. What is the probability that you get at least one Ace?

rish1602 answered in Probability Sep 24

190 views

0 votes

1 answer

19

Kenneth Rosen Edition 6th Exercise 2.2 Question 8 (Page No. 120)
Determine whether these statements are true or false. ∅ ∈ {∅} ∅ ∈ {∅, {∅}} {∅} ∈ {∅} {∅} ∈ {{∅}} {∅} ⊂ {∅, {∅}} {{∅}} ⊂ {∅, {∅}} {{∅}} ⊂ {{∅}, {∅}}

its_vaibhav answered in Set Theory & Algebra Sep 23

86 views

7 votes

3 answers

20

GATE CSE 1988 | Question: 13iii
Are the two digraphs shown in the above figure isomorphic? Justify your answer.

Pkaryan123 answered in Graph Theory Sep 21

638 views

23 votes

7 answers

21

GATE CSE 2015 Set 1 | Question: 54
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.

Prarbdh Tiwari answered in Graph Theory Sep 20

by Prarbdh Tiwari

13.6k views

0 votes

1 answer

22

Linear Algebra Eigenvalues
If the eigenvalues of a 3x3 matrix A are 1,2 and 3 then inverse of A is?

atulcse answered in Linear Algebra Sep 18

87 views

20 votes

6 answers

23

GATE CSE 1995 | Question: 1.24
The rank of the following $(n+1) \times (n+1)$ matrix, where $a$ ... $1$ $2$ $n$ Depends on the value of $a$

Rojer Tufani answered in Linear Algebra Sep 18

by Rojer Tufani

3.1k views

33 votes

7 answers

24

GATE CSE 2016 Set 1 | Question: 05
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {-1})$ and $3$. The determinant of $P$ is _______

Rojer Tufani answered in Linear Algebra Sep 18

by Rojer Tufani

8.3k views

0 votes

1 answer

25

Rajat Agrawal007 answered in Set Theory & Algebra Sep 16

by Rajat Agrawal007

141 views

26 votes

4 answers

26

GATE CSE 2011 | Question: 33
Consider a finite sequence of random values $X=[x_1,x_2,\dots x_n]$. Let $\mu_x$ be the mean and $\sigma_x$ be the standard deviation of $X$. Let another finite sequence $Y$ of equal length be derived from this as $y_i=a*x_i+b$, where $a$ and $b$ are positive ... $Y$ in $Y$ $\mu_y=a \mu_x + b$ $\sigma_y=a \sigma_x + b$

jaswanth431 answered in Probability Sep 16

5.4k views

1 vote

1 answer

27

gateacademy test series
There are 12 stations on a rail route. How many ways a special train can stop at 4 of these stations, so that no two stops are consecutive stations? please explain in detail

Nibchee answered in Combinatory Sep 16

61 views

0 votes

1 answer

28

#mathematics
What is the difference between Integration and Summation? Which one produces a greater value in the same range?

Nibchee answered in Calculus Sep 15

52 views

27 votes

5 answers

29

GATE CSE 2014 Set 3 | Question: 48
Let $S$ be a sample space and two mutually exclusive events $A$ and $B$ be such that $A \cup B = S$. If $P(.)$ denotes the probability of the event, the maximum value of $P(A)P(B)$ is_____.

jaswanth431 answered in Probability Sep 12

5.1k views

0 votes

1 answer

30

Marks Distribution for Engineering and Discrete Maths
Hey all, As per brochure there will be 13 marks alloted for engineering maths. My quer is whether discrete maths will too be included in this 13 marks i.e. EM+DM=13, or Discrete maths will have separate marks? Like in Gate 2021 paper , the combined marks for Engineering and Discrete maths was over 13.

Arjun answered in Mathematical Logic Sep 12

by Arjun

66 views

0 votes

1 answer

31

gateacademy testseries
In how many ways can seven different jobs be assigned to four different employees so that each employee is assigned at least one job and the most difficult job is assigned to the best employee?

nishant.singhal.cs answered in Combinatory Sep 8

by nishant.singhal.cs

55 views

0 votes

1 answer

32

Kenneth H Rosen 7th edition
Please see example 6. l am not getting the mathematical insight. Can anyone please tell how they are arriving at the answer.

Sahiltam answered in Combinatory Sep 7

292 views

0 votes

0 answers

33

#calculus #limits
$\lim_{x\rightarrow a} f(x)^{g(x)} = e^{\lim_{x\rightarrow a}g(x)[f(x)-1]}$ Solve the below limit without using the above formula, $\lim_{x \rightarrow 0} ({\frac{sin x}{x}})^{\frac{sin x}{x - sin x}}$

dutta007sourish asked in Calculus Sep 7

by dutta007sourish

61 views

3 votes

3 answers

34

KENETH ROSEN
How many different ways are there to seat four people around a circular table, where two seatings are considered the same when each person has the same left neighbor and the same right neighbor? ANSWER IS 6 OR 3 .????

M_eight answered in Combinatory Sep 7

1.3k views

0 votes

1 answer

35

Kenneth Rosen Edition 7th Exercise 6.4 Question 16 (Page No. 421)
Use question $14$ and Corollary $1$ to show that if $n$ is an integer greater than $1,$ then $\binom{n}{\left \lfloor n/2 \right \rfloor}\geq \frac{2^{n}}{2}.$ Conclude from part $(A)$ that if $n$ is a positive integer, then $\binom{2n}{n}\geq \frac{4^{n}}{2n}.$

harsh_sojitra answered in Combinatory Sep 6

by harsh_sojitra

51 views

0 votes

3 answers

36

Kenneth Rosen Edition 7th Exercise 6.1 Question 2 (Page No. 396)
An office building contains $27$ floors and has $37$ offices on each floor. How many offices are in the building?

harsh_sojitra answered in Combinatory Sep 6

by harsh_sojitra

78 views

19 votes

4 answers

37

CMI2014-A-01
For the inter-hostel six-a-side football tournament, a team of $6$ players is to be chosen from $11$ players consisting of $5$ forwards, $4$ defenders and $2$ goalkeepers. The team must include at least $2$ forwards, at least $2$ defenders and at least $1$ goalkeeper. Find the number of different ways in which the team can be chosen. $260$ $340$ $720$ $440$

Nirmalya Pratap 1 answered in Combinatory Sep 5

by Nirmalya Pratap 1

1.4k views

18 votes

5 answers

38

GATE CSE 1989 | Question: 1-iv
The transitive closure of the relation $\left\{(1, 2), (2, 3), (3, 4), (5, 4)\right\}$ on the set $\left\{1, 2, 3, 4, 5\right\}$ is ___________.

raja11sep answered in Set Theory & Algebra Sep 4

4.1k views

0 votes

1 answer

39

NIELIT 2017 July Scientist B (IT) - Section B: 15
The number of diagonals that can be drawn by joining the vertices of an octagon is $28$ $48$ $20$ None of the option

M_eight answered in Graph Theory Aug 28

228 views

29 votes

4 answers

40

GATE CSE 1996 | Question: 2.2
Let $R$ be a non-empty relation on a collection of sets defined by $_{A}R_ B$ if and only if $A \cap B = \phi$. Then, (pick the true statement) $A$ is reflexive and transitive $R$ is symmetric and not transitive $R$ is an equivalence relation $R$ is not reflexive and not symmetric

Varn Gupta answered in Set Theory & Algebra Aug 28

10.1k views

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