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Recent questions and answers in Engineering Mathematics
+11
votes
5
answers
1
TIFR2015A6
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
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tifr2015
expectation
+1
vote
1
answer
2
UGCNETDec2007II: 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
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1.2k
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31
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ugcnetdec2007ii
0
votes
1
answer
3
UGCNETDec2007II: 2
The number of edges in a complete graph with ‘n’ vertices is equal to : $n(n1)$ $\large\frac{n(n1)}{2}$ $n^2$ $2n1$
answered
3 days
ago
in
Graph Theory
by
chirudeepnamini
Loyal
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5.3k
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19
views
ugcnetdec2007ii
0
votes
1
answer
4
UGCNETDec2006II: 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
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49.6k
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13
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ugcnetdec2006ii
0
votes
1
answer
5
UGCNETDec2004II: 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
ugcnetdec2004ii
+10
votes
5
answers
6
GATE19871xxii
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
gate1987
polynomials
0
votes
0
answers
7
UGCNETDec2006II: 2
The proposition ~ q ∨ p is equivalent to :
asked
5 days
ago
in
Mathematical Logic
by
jothee
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107k
points)

21
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ugcnetdec2006ii
0
votes
1
answer
8
UGCNETDec2004II: 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
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5.5k
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11
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ugcnetdec2004ii
+1
vote
0
answers
9
UGCNETDec2004II: 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
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107k
points)

25
views
ugcnetdec2004ii
0
votes
0
answers
10
UGCNETDec2004II: 23
Weighted graph : Is a bidirectional 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
ugcnetdec2004ii
0
votes
1
answer
11
ISI2016MMA10
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 $\Sigma_{i=1}^n \: \: p_i$ $\Pi_{i=1}^n \: \: p_i$ $\Pi_{i=1}^n \: \: (1p_i)$ $1\Pi_{i=1}^n \: \: (1p_i)$
answered
Mar 19
in
Probability
by
SatyamK
(
229
points)

43
views
isi2016mmamma
probability
independentevents
0
votes
3
answers
12
NIELIT ScientistB 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 ScientistB 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 ScientistB Dec 2017_51
Let $u$ and $v$ be two vectors in R2 whose Euclidean norms satisfy $u=2v$. 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 ScientistB Dec 2017_24
Using bisection method, one root of X4X1 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 SETC 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 evenvalent (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
ISI2016PCBCS8
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
isi2016pcbcs
permutationandcombination
descriptive
0
votes
1
answer
22
ISI2016MMA25
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
isi2016mmamma
permutationandcombination
+3
votes
3
answers
23
GATE2020CS45
For $n>2$, let $a \in \{0,1\}^n$ be a nonzero 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
gate2020cs
numericalanswers
+13
votes
6
answers
24
GATE201938
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 minimumweight 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
gate2019
engineeringmathematics
discretemathematics
graphtheory
graphconnectivity
+4
votes
6
answers
25
GATE2020CS42
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
gate2020cs
numericalanswers
engineeringmathematics
0
votes
1
answer
26
ISI2016DCG69
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 $x^{2}+(y5)^{2}=25$ $x^{2}+y^{2}=100$ $(x5)^{2}+y^{2}=125$ $(x5)^{2}+(y5)^{2}=50$
answered
Mar 14
in
Calculus
by
haralk10
Active
(
1.2k
points)

26
views
isi2016dcg
calculus
differentialequation
nongate
0
votes
1
answer
27
ISI2016DCG68
The general solution of the differential equation $x+yx{y}'=0$ 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
isi2016dcg
calculus
differentialequation
nongate
0
votes
1
answer
28
ISI2016DCG67
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
isi2016dcg
calculus
differentialequation
nongate
0
votes
1
answer
29
ISI2015DCG50
The piecewise linear function for the following graph is $f(x) = \begin{cases} = x, \: x \leq 2 \\ =4, \: 2<x<3 \\ =x+1, \: x \geq 3 \end{cases}$ $f(x) = \begin{cases} = x2, \: x \leq 2 \\ =4, \: 2<x<3 \\ =x1, \: x \geq 3 \end{cases}$ ... $f(x) = \begin{cases} = 2x, \: x \leq 2 \\ =4, \: 2<x<3 \\ =x+1, \: x \geq 3 \end{cases}$
answered
Mar 14
in
Calculus
by
haralk10
Active
(
1.2k
points)

28
views
isi2015dcg
calculus
functions
0
votes
1
answer
30
ISI2015MMA42
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
isi2015mma
linearalgebra
matrices
eigenvalue
0
votes
1
answer
31
ISI2014DCG48
If $x$ is real, the set of real values of $a$ for which the function $y=x^2ax+12a^2$ 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
isi2014dcg
calculus
functions
quadraticequations
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 oneone 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
jest
functions
sets
+20
votes
4
answers
33
GATE19961.4
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
gate1996
settheory&algebra
grouptheory
normal
+1
vote
2
answers
34
ISI2017MMA26
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
isi2017mma
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
1
answer
35
TIFR2020A2
Let $M$ be a real $n\times n$ matrix such that for every nonzero 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
tifr2020
engineeringmathematics
linearalgebra
rankofmatrix
eigenvalue
0
votes
3
answers
36
NIELIT ScientistB 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) $n(n1)/2$ (B) $n^{n2}$ (C) $nx$ (D) $n$
answered
Mar 8
in
Graph Theory
by
vivekgatecs2020
(
137
points)

460
views
+28
votes
3
answers
37
GATE20021.4
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 $2$ $3$ $4$ $n2 \left \lfloor \frac{n}{2} \right \rfloor+2$
answered
Mar 7
in
Graph Theory
by
vivekgatecs2020
(
137
points)

3.1k
views
gate2002
graphtheory
graphcoloring
normal
+33
votes
4
answers
38
GATE20093
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
gate2009
graphtheory
normal
degreeofgraph
+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
gateforumtestseries
linearalgebra
rankofmatrix
+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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