Recent questions and answers in Engineering Mathematics - GATE Overflow

+11 votes

5 answers

1

TIFR2015-A-6
Ram has a fair coin, i.e., a toss of the coin results in either head or tail and each event happens with probability exactly half $(1/2)$. He repeatedly tosses the coin until he gets heads in two consecutive tosses. The expected number of coin tosses that Ram does is. $2$ $4$ $6$ $8$ None of the above.

answered 22 hours ago in Probability by tanishk1999 (11 points) | 1.4k views

+1 vote

1 answer

2

UGCNET-Dec2007-II: 1
A box contains six red balls and four green balls. Four balls are selected at random from the box. What is the probability that two of the selected balls are red and two are green ? $\large\frac{3}{7}$ $\large\frac{4}{7}$ $\large\frac{5}{7}$ $\large\frac{6}{7}$

answered 3 days ago in Probability by haralk10 Active (1.2k points) | 31 views

0 votes

1 answer

3

UGCNET-Dec2007-II: 2
The number of edges in a complete graph with ‘n’ vertices is equal to : $n(n-1)$ $\large\frac{n(n-1)}{2}$ $n^2$ $2n-1$

answered 3 days ago in Graph Theory by chirudeepnamini Loyal (5.3k points) | 19 views

0 votes

1 answer

4

UGCNET-Dec2006-II: 3
The number of edges in a complete graph with N vertices is equal to: $N (N−1)$ $2N−1$ $N−1$ $N(N−1)/2$

answered 5 days ago in Graph Theory by Sanjay Sharma Boss (49.6k points) | 13 views

0 votes

1 answer

5

UGCNET-Dec2004-II: 4
The following lists are the degrees of all the vertices of a graph : $1,2,3,4,5$ $3,4,5,6,7$ $1, 4, 5, 8, 6$ $3,4,5,6$ (i) and (ii) (iii) and (iv) (iii) and (ii) (ii) and (iv)

answered 5 days ago in Graph Theory by Divya Devi (23 points) | 16 views

+10 votes

5 answers

6

GATE1987-1-xxii
The equation $7x^{7}+14x^{6}+12x^{5}+3x^{4}+12x^{3}+10x^{2}+5x+7=0$ has All complex roots At least one real root Four pairs of imaginary roots None of the above

answered 5 days ago in Set Theory & Algebra by SatyamK (229 points) | 561 views

0 votes

0 answers

7

UGCNET-Dec2006-II: 2
The proposition ~ q ∨ p is equivalent to :

asked 5 days ago in Mathematical Logic by jothee Veteran (107k points) | 21 views

0 votes

1 answer

8

UGCNET-Dec2004-II: 2
If $f (x)=x+1\:\text{and}\:g(x)=x+3$ then $f 0 f 0 f 0 f$ is : $g$ $g+1$ $g^4$ None of these

answered 6 days ago in Set Theory & Algebra by Shobhit Joshi Loyal (5.5k points) | 11 views

+1 vote

0 answers

9

UGCNET-Dec2004-II: 1
AVA=A is called : Identity law De Morgan s law Idempotent law Complement law

asked 6 days ago in Linear Algebra by jothee Veteran (107k points) | 25 views

0 votes

0 answers

10

UGCNET-Dec2004-II: 23
Weighted graph : Is a bi-directional graph. Is directed graph. Is graph in which number associated with arc. Eliminates table method.

asked 6 days ago in Graph Theory by jothee Veteran (107k points) | 5 views

0 votes

1 answer

11

ISI2016-MMA-10
If $A_1, A_2, \dots , A_n$ are independent events with probabilities $p_1, p_2, \dots , p_n$ respectively, then $P( \cup_{i=1}^n A_i)$ equals $\Sigma_{i=1}^n \: \: p_i$ $\Pi_{i=1}^n \: \: p_i$ $\Pi_{i=1}^n \: \: (1-p_i)$ $1-\Pi_{i=1}^n \: \: (1-p_i)$

answered Mar 19 in Probability by SatyamK (229 points) | 43 views

0 votes

3 answers

12

NIELIT Scientist-B Dec 2017_14
The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is _____. (A) 269 (B) 270 (C) 271 (D) 272

answered Mar 19 in Linear Algebra by topper98 Junior (589 points) | 228 views

0 votes

2 answers

13

NIELIT Scientist-B Dec 2017_44
On a set A = {a, b, c, d} a binary operation * is defined as given in the following table. * a b c d a b c d a c b d c b d a b d a c d a c b The relation is : (A) Commutative but not associative (B) Neither commutative nor associative (C) Both commutative and associative (D) Associative but not commutative

answered Mar 19 in Set Theory & Algebra by topper98 Junior (589 points) | 152 views

0 votes

1 answer

14

NIELIT Scientist-B Dec 2017_51
Let $u$ and $v$ be two vectors in R2 whose Euclidean norms satisfy $|u|=2|v|$. What is the value of $\alpha$ such that $w=u+\alpha v$ bisects the angle between $u$ and $v$ ? (A) 2 (B) 1 (C) 1/2 (D) -2

answered Mar 19 in Set Theory & Algebra by topper98 Junior (589 points) | 107 views

0 votes

2 answers

15

NIELIT Scientist-B Dec 2017_24
Using bisection method, one root of X4-X-1 lies between 1 and 2. After second iteration the root may lie in interval : (A) (1.25, 1.5) (B) (1, 1.25) (C) (1, 1.5) (D) None of the options

answered Mar 19 in Set Theory & Algebra by topper98 Junior (589 points) | 205 views

+1 vote

2 answers

16

NIELIT DEC 2017 SET-C 62
If a random coin is tossed 11 times then what is the probability that for 7th toss head appears exactly 4 times? A) 5/32 B) 15/128 C) 35/128 D) None of the options

answered Mar 19 in Probability by topper98 Junior (589 points) | 247 views

0 votes

2 answers

17

NIELIT July 2017_75
Choose the most appropriate definition of plane graph A) A simple graph which is isomorphic to Hamiltonian graph B) A graph drawn in a plane such away that if the vertex set of graph can be partitioned into two non - empty disjoint subset X and Y in such a way ... A graph drawn in a plane in such a way that any pair of edges meet only at their end vertices D) None of the option

answered Mar 19 in Graph Theory by topper98 Junior (589 points) | 340 views

+3 votes

5 answers

18

NIELIT July 2017_73
For the graph shown, which of the following paths is a Hamilton circuit ? A) ABCDCFDEFAEA B) AEDCBAF C) AEFDCBA D) AFCDEBA

answered Mar 19 in Graph Theory by topper98 Junior (589 points) | 628 views

0 votes

2 answers

19

NIELIT July 2017_72
The following graph has no Euler circuit because A) It has 7 vertices B) It is even-valent (all vertices have even valence) C) It is not connected D) It does not have an Euler circuit

answered Mar 19 in Graph Theory by topper98 Junior (589 points) | 361 views

0 votes

2 answers

20

NIELIT July 2017_71
Consider the following graph L and find the bridges, if any A) No bridge B) {d, e} C) {c, d} D) {c, d} and {c, f}

answered Mar 19 in Graph Theory by topper98 Junior (589 points) | 395 views

+1 vote

1 answer

21

ISI2016-PCB-CS-8
Consider all possible trees with $n$ nodes. Let $k$ be the number of nodes with degree greater than 1 in a given tree. What is the maximum possible value of $k$? Justify your answer. Consider $2n$ committees, each having at least $2n$ persons, formed from a group of $4n$ persons. Prove that there exists at least one person who belongs to at least $n$ committees.

answered Mar 18 in Combinatory by Falahamin (21 points) | 46 views

0 votes

1 answer

22

ISI2016-MMA-25
A integer is said to be a $\textbf{palindrome}$ if it reads the same forward or backward. For example, the integer $14541$ is a $5$-digit palindrome and $12345$ is not a palindrome. How many $8$-digit palindromes are prime? $0$ $1$ $11$ $19$

answered Mar 18 in Combinatory by Falahamin (21 points) | 24 views

+3 votes

3 answers

23

GATE2020-CS-45
For $n>2$, let $a \in \{0,1\}^n$ be a non-zero vector. Suppose that $x$ is chosen uniformly at random from $\{0,1\}^n$. Then, the probability that $\displaystyle{} \Sigma_{i=1}^n a_i x_i$ is an odd number is______________

answered Mar 17 in Mathematical Logic by felics moses 1 (119 points) | 1k views

+13 votes

6 answers

24

GATE2019-38
Let $G$ be any connected, weighted, undirected graph. $G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight. $G$ has a unique minimum spanning tree, if, for every cut of $G$, there is a unique minimum-weight edge crossing the cut. Which of the following statements is/are TRUE? I only II only Both I and II Neither I nor II

answered Mar 17 in Graph Theory by immanujs Active (3.3k points) | 4.7k views

+4 votes

6 answers

25

GATE2020-CS-42
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.

answered Mar 15 in Combinatory by felics moses 1 (119 points) | 1.5k views

0 votes

1 answer

26

ISI2016-DCG-69
Consider the differential equation $(x^{2}-y^{2})\frac{\mathrm{d} y}{\mathrm{d} x}=2xy.$ Assuming $y=10$ for $x=0,$ its solution is $x^{2}+(y-5)^{2}=25$ $x^{2}+y^{2}=100$ $(x-5)^{2}+y^{2}=125$ $(x-5)^{2}+(y-5)^{2}=50$

answered Mar 14 in Calculus by haralk10 Active (1.2k points) | 26 views

0 votes

1 answer

27

ISI2016-DCG-68
The general solution of the differential equation $x+y-x{y}'=0$ is (assuming $C$ as an arbitrary constant of integration) $y=x(\log x+C)$ $x=y(\log y+C)$ $y=x(\log y+C)$ $y=y(\log x+C)$

answered Mar 14 in Calculus by haralk10 Active (1.2k points) | 25 views

0 votes

1 answer

28

ISI2016-DCG-67
The general solution of the differential equation $2y{y}'-x=0$ is (assuming $C$ as an arbitrary constant of integration) $x^{2}-y^{2}=C$ $2x^{2}-y^{2}=C$ $2y^{2}-x^{2}=C$ $x^{2}+y^{2}=C$

answered Mar 14 in Calculus by haralk10 Active (1.2k points) | 27 views

0 votes

1 answer

29

ISI2015-DCG-50
The piecewise linear function for the following graph is $f(x) = \begin{cases} = x, \: x \leq -2 \\ =4, \: -2<x<3 \\ =x+1, \: x \geq 3 \end{cases}$ $f(x) = \begin{cases} = x-2, \: x \leq -2 \\ =4, \: -2<x<3 \\ =x-1, \: x \geq 3 \end{cases}$ ... $f(x) = \begin{cases} = 2-x, \: x \leq -2 \\ =4, \: -2<x<3 \\ =x+1, \: x \geq 3 \end{cases}$

answered Mar 14 in Calculus by haralk10 Active (1.2k points) | 28 views

0 votes

1 answer

30

ISI2015-MMA-42
Let $\lambda_1, \lambda_2, \lambda_3$ denote the eigenvalues of the matrix $A \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & - \sin t & \cos t \end{pmatrix}.$ If $\lambda_1+\lambda_2+\lambda_3 = \sqrt{2}+1$ ... $\{ - \frac{\pi}{4}, \frac{\pi}{4} \}$ $\{ - \frac{\pi}{3}, \frac{\pi}{3} \}$

answered Mar 14 in Linear Algebra by haralk10 Active (1.2k points) | 76 views

0 votes

1 answer

31

ISI2014-DCG-48
If $x$ is real, the set of real values of $a$ for which the function $y=x^2-ax+1-2a^2$ is always greater than zero is $- \frac{2}{3} < a \leq \frac{2}{3}$ $- \frac{2}{3} \leq a < \frac{2}{3}$ $- \frac{2}{3} < a < \frac{2}{3}$ None of these

answered Mar 12 in Calculus by haralk10 Active (1.2k points) | 22 views

0 votes

1 answer

32

JEST 2020
X AND Y is an arbitrary sets, F: $X\rightarrow Y$ show that a and b are equivalent F is one-one For all set Z and function g1: $Z\rightarrow X$ and g2: $Z\rightarrow X$, if $g1 \neq g2$ implies $f \bigcirc g1 \neq f \bigcirc g2$ Where $\bigcirc$ is a fucntion composition.

answered Mar 12 in Set Theory & Algebra by commenter commenter Active (1.6k points) | 150 views

+20 votes

4 answers

33

GATE1996-1.4
Which of the following statements is FALSE? The set of rational numbers is an abelian group under addition The set of integers in an abelian group under addition The set of rational numbers form an abelian group under multiplication The set of real numbers excluding zero is an abelian group under multiplication

answered Mar 11 in Set Theory & Algebra by vivekgatecs2020 (137 points) | 2.2k views

+1 vote

2 answers

34

ISI2017-MMA-26
Let $n$ be the number of ways in which $5$ men and $7$ women can stand in a queue such that all the women stand consecutively. Let $m$ be the number of ways in which the same $12$ persons can stand in a queue such that exactly $6$ women stand consecutively. Then the value of $\frac{m}{n}$ is $5$ $7$ $\frac{5}{7}$ $\frac{7}{5}$

answered Mar 9 in Combinatory by kraken_wizard (41 points) | 93 views

0 votes

1 answer

35

TIFR2020-A-2
Let $M$ be a real $n\times n$ matrix such that for every non-zero vector $x\in \mathbb{R}^{n},$ we have $x^{T}M x> 0.$ Then Such an $M$ cannot exist Such $Ms$ exist and their rank is always $n$ Such $Ms$ exist, but their eigenvalues are always real No eigenvalue of any such $M$ can be real None of the above

answered Mar 8 in Linear Algebra by ankitgupta.1729 Boss (18.1k points) | 46 views

0 votes

3 answers

36

NIELIT Scientist-B Dec 2017_56
Let G be a simple undirected graph on $n=3x$ vertices ($x>=1$) with chromatic number 3, then maximum number of edges in G is : (A) $n(n-1)/2$ (B) $n^{n-2}$ (C) $nx$ (D) $n$

answered Mar 8 in Graph Theory by vivekgatecs2020 (137 points) | 460 views

+28 votes

3 answers

37

GATE2002-1.4
The minimum number of colours required to colour the vertices of a cycle with $n$ nodes in such a way that no two adjacent nodes have the same colour is $2$ $3$ $4$ $n-2 \left \lfloor \frac{n}{2} \right \rfloor+2$

answered Mar 7 in Graph Theory by vivekgatecs2020 (137 points) | 3.1k views

+33 votes

4 answers

38

GATE2009-3
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.

answered Mar 7 in Graph Theory by vivekgatecs2020 (137 points) | 2.7k views

+1 vote

1 answer

39

GF MT 4
Is the answer and explaination given correct ?

answered Mar 4 in Linear Algebra by smsubham Boss (16k points) | 161 views

+2 votes

2 answers

40

Let a relation R be defined on the set of all real numbers by a R b <=> 1 + ab > 0 thus R is ?

answered Mar 3 in Set Theory & Algebra by MKraza (11 points) | 7.4k views

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