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Recent questions and answers in Engineering Mathematics
+14
votes
5
answers
1
TIFR2013A9
There are $n$ kingdoms and $2n$ champions. Each kingdom gets $2$ champions. The number of ways in which this can be done is: $\frac{\left ( 2n \right )!}{2^{n}}$ $\frac{\left ( 2n \right )!}{n!}$ $\frac{\left ( 2n \right )!}{2^{n} . n!}$ $\frac{n!}{2}$ None of the above.
answered
27 minutes
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Combinatory
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Verma Ashish
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798
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tifr2013
permutationandcombination
discretemathematics
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ballsinbins
0
votes
2
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2
UGC NET NOV 2017 PAPER III Q59
59. Consider the following two wellformed formulas in prepositional logic. F1 : P ⇒ ¬ P F2 : (P ⇒ ¬ P) ∨ (¬ P ⇒ P) Which of the following statements is correct ? (1) F1 is Satisfiable, F2 is valid (2) F1 is unsatisfiable, F2 is Satisfiable (3) F1 is unsatisfiable, F2 is valid (4) F1 and F2 both are Satisfiable
answered
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Discrete Mathematics
by
GoalSet1
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581
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ugcnetnov2017iii
discretemathematics
propositionallogic
0
votes
2
answers
3
UGC NET NOV 2017 PAPER III Q58
58. “If X, then Y unless Z” is represented by which of the following formulae in propositional logic ? (1) (X ∧ Y) → ¬ Z (2) (X ∧ ¬ Z) → Y (3) X → (Y ∧ ¬ Z) (4) Y → (X ∧ ¬ Z)
answered
39 minutes
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in
Discrete Mathematics
by
GoalSet1
(
97
points)

428
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ugcnetnov2017iii
discretemathematics
propositionallogic
+19
votes
4
answers
4
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?
answered
16 hours
ago
in
Combinatory
by
Verma Ashish
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9.1k
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1.4k
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gate2000
permutationandcombination
normal
descriptive
+4
votes
7
answers
5
TIFR2018B1
What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$
answered
21 hours
ago
in
Combinatory
by
Verma Ashish
Loyal
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9.1k
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377
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tifr2018
modulararithmetic
permutationandcombination
+2
votes
6
answers
6
GATE201921
The value of $3^{51} \text{ mod } 5$ is _____
answered
22 hours
ago
in
Combinatory
by
Verma Ashish
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9.1k
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2.7k
views
gate2019
numericalanswers
permutationandcombination
modulararithmetic
+22
votes
3
answers
7
GATE20002.5
A relation $R$ is defined on the set of integers as $xRy$ iff $(x + y)$ is even. Which of the following statements is true? $R$ is not an equivalence relation $R$ is an equivalence relation having 1 equivalence class $R$ is an equivalence relation having 2 equivalence classes $R$ is an equivalence relation having 3 equivalence classes
answered
1 day
ago
in
Set Theory & Algebra
by
MRINMOY_HALDER
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1.7k
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2.7k
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gate2000
settheory&algebra
relations
normal
+26
votes
6
answers
8
GATE2014251
A cycle on $n$ vertices is isomorphic to its complement. The value of $n$ is _____.
answered
1 day
ago
in
Graph Theory
by
King Suleiman
Junior
(
629
points)

3.6k
views
gate20142
graphtheory
numericalanswers
normal
graphisomorphism
nongate
+1
vote
2
answers
9
Continuity and Differentiability
If the function f(x) =[(x2)3 /a] sin(x2) + acos(x2), [.] denotes greatest integer function, is continuous & differentiable in (4,6) then find ‘a’ range: (A) a ϵ (∞,∞) (B) a ϵ [64, ∞) (C) a ϵ [128, ∞) (D) Not defined
answered
1 day
ago
in
Calculus
by
moharanaguruprasad
(
11
points)

319
views
+1
vote
1
answer
10
set theory
answered
2 days
ago
in
Set Theory & Algebra
by
Debadrita Talapatra
(
11
points)

48
views
settheory&algebra
discretemathematics
engineeringmathematics
sets
+25
votes
3
answers
11
GATE201431
Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q Which one of the following about L, M, and N is CORRECT? Only L is TRUE. Only M is TRUE. Only N is TRUE. L, M and N are TRUE.
answered
6 days
ago
in
Mathematical Logic
by
sohailkhan
(
47
points)

2.4k
views
gate20143
mathematicallogic
easy
propositionallogic
+9
votes
4
answers
12
TIFR2012A20
There are $1000$ balls in a bag, of which $900$ are black and $100$ are white. I randomly draw $100$ balls from the bag. What is the probability that the $101$st ball will be black? $9/10$ More than $9/10$ but less than $1$. Less than $9/10$ but more than $0$. $0$ $1$
answered
6 days
ago
in
Probability
by
!KARAN
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1.8k
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629
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tifr2012
probability
+34
votes
5
answers
13
GATE200544
What is the minimum number of ordered pairs of nonnegative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$ $4$ $6$ $16$ $24$
answered
Aug 15
in
Combinatory
by
JashanArora
(
93
points)

3.9k
views
gate2005
settheory&algebra
normal
pigeonholeprinciple
+25
votes
4
answers
14
GATE200922
For the composition table of a cyclic group shown below: ... $a,b$ are generators $b,c$ are generators $c,d$ are generators $d,a$ are generators
answered
Aug 9
in
Set Theory & Algebra
by
spike500
(
29
points)

1.8k
views
gate2009
settheory&algebra
normal
groups
0
votes
1
answer
15
recurrence relation
Which recurrence relation satisfy the sequence: 2, 3, 4, . . ., for n ≥ 1. A ) T(N) = 2 T(N1)  T(N2) B)T(N) = T(N1) + T(N2) C)T(N) = N+1 D) None of these
answered
Aug 8
in
Mathematical Logic
by
Rohit Suryanarayan
(
15
points)

439
views
recurrence
+2
votes
1
answer
16
ISI MTECH CS 2019 INTERVIEW question
As due to rain, the match between the teams in ICC world cup got canceled , So lets the total team be 10, exclude semi finals and finals , consider only league match, What is the total number of matches that played between the teams ... many ways those n matches can be conducted ? Source : https://gateoverflow.in/blog/8548/isimtechcs2019interviewexperience
answered
Aug 8
in
Combinatory
by
Shaik Masthan
Veteran
(
61.9k
points)

74
views
permutationandcombination
+52
votes
4
answers
17
GATE200333
Consider the following formula and its two interpretations \(I_1\) and \(I_2\). \(\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]\) \(I_1\) : Domain: the set of ... , \(I_1\) does not Neither \(I_1\) nor \(I_2\) satisfies \(\alpha\) Both \(I_1\) and \(I_2\) satisfies \(\alpha\)
answered
Aug 6
in
Mathematical Logic
by
MRINMOY_HALDER
Active
(
1.7k
points)

4k
views
gate2003
mathematicallogic
difficult
firstorderlogic
+1
vote
2
answers
18
Graph Connectivity
Consider the given statements S1: In a simple graph G with 6 vertices, if degree of each vertex is 2, then Euler circuit exists in G. S2:In a simple graph G, if degree of each vertex is 3 then the graph G is connected. Which of the following is/are true?
answered
Aug 5
in
Graph Theory
by
IamDRD
(
11
points)

162
views
graphtheory
eulergraph
graphconnectivity
+15
votes
5
answers
19
GATE2005IT3
The determinant of the matrix given below is $\begin{bmatrix} 0 &1 &0 &2 \\ 1& 1& 1& 3\\ 0&0 &0 & 1\\ 1& 2& 0& 1 \end{bmatrix}$ $1$ $0$ $1$ $2$
answered
Aug 5
in
Linear Algebra
by
Satbir
Boss
(
17.2k
points)

1.8k
views
gate2005it
linearalgebra
normal
determinant
+1
vote
2
answers
20
#ACE_ACADEMY_DISCRETE_MATHS_BOOKLET.
Which of the following is not true? (a) Number of edgedisjoint Hamiltonian cycles in $K_7$ is $3$ (b) If $G$ is a simple graph with $6$ vertices and the degree of each vertex is at least $3$, then the Hamiltonian cycle exists in ... simple graph with $5$ vertices and $7$ edges, then the Hamiltonian cycle exists in $G$ Please help me understand all the options.
answered
Aug 1
in
Graph Theory
by
Raghava45
(
333
points)

65
views
discretemathematics
graphtheory
+1
vote
3
answers
21
UGCNETJune2015II5
Consider a Hamiltonian Graph(G) with no loops and parallel edges. Which of the following is true with respect to this graph (G)? deg (v) $\geq$ n/2 for each vertex of G $\mid E(G) \mid \geq $1/2 (n1)(n2)+2 edges deg(v) + deg(w) $\geq$ n fr every v and $\omega$ not connected by an edge a and b b and c a and c a, b, and c
answered
Aug 1
in
Graph Theory
by
tripu
(
11
points)

1.9k
views
ugcnetjune2015ii
discretemathematics
graphtheory
+9
votes
3
answers
22
GATE20021.1
The rank of the matrix $\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$ is $4$ $2$ $1$ $0$
answered
Jul 31
in
Linear Algebra
by
thambu
(
11
points)

831
views
gate2002
linearalgebra
easy
matrices
0
votes
1
answer
23
Probability  Gravner49.c
You have $16$ balls, $4$ green, and $9$ red. You also have $3$ urns. For each of the $16$ balls. you select an urn at random and put the ball into it.(Urns are large enough to accommodate any number of balls.) (c) What is the probability that each urn contains all three colors?
answered
Jul 31
in
Probability
by
blackcloud
(
79
points)

20
views
gravner
probability
engineeringmathematics
0
votes
1
answer
24
MADE EASY
The Necessary condition to diagonalize a matrix is that A) ITS all eigen values should be distdist B) its eigen vectors should be indeindepent C) its eigen values should be real D) matrix is non singular
answered
Jul 30
in
Linear Algebra
by
Jyotish Ranjan
(
11
points)

51
views
+1
vote
1
answer
25
UGCNETJune2019II69
Consider the following properties with respect to a flow network $G=(V,E)$ in which a flow is a realvalued function $f:V \times V \rightarrow R$: $P_1$: For all $u, v, \in V, \: f(u,v)=f(v,u)$ $P_2$: $\underset{v \in V}{\Sigma} f(u,v)=0$ for all $u \in V$ Which one of the following is/are correct? Only $P_1$ Only $P_2$ Both $P_1$ and $P_2$ Neither $P_1$ nor $P_2$
answered
Jul 29
in
Graph Theory
by
abhinav kumar
(
17
points)

31
views
ugcnetjune2019ii
flownetwork
+2
votes
3
answers
26
ACE ACADEMY BOOKLET QUESTION
Let $G$ $=$ $(V, E)$ be a simple nonempty connected undirected graph, in which every vertex has degree 4. For any partition $V$ into two nonempty and nonoverlapping subsets $S$ and $T$. Which of the following is true? There are at least two edges that ... $S$ and one end point in $T$ There are exactly one edge that have one end point in $S$ and one end point in $T$
answered
Jul 26
in
Graph Theory
by
gvjha3
(
11
points)

95
views
+11
votes
13
answers
27
TIFR2012A1
Amar and Akbar both tell the truth with probability $\dfrac{3 } {4}$ and lie with probability $\dfrac{1}{4}$. Amar watches a test match and talks to Akbar about the outcome. Akbar, in turn, tells Anthony, "Amar told me that India won". What probability should Anthony ... $\left(\dfrac{7}{16}\right)$ $\left(\dfrac{10}{16}\right)$ None of the above
answered
Jul 25
in
Probability
by
Arghya Mukherjee
(
17
points)

1.5k
views
tifr2012
probability
conditionalprobability
0
votes
1
answer
28
Gate 2002  ME
Which of the following functions is not differentiable in the domain $[1,1]$ ? (a) $f(x) = x^2$ (b) $f(x) = x1$ (c) $f(x) = 2$ (d) $f(x) = Maximum (x,x)$
answered
Jul 24
in
Calculus
by
Arif_Faizan
(
35
points)

64
views
engineeringmathematics
usergate2002
usermod
calculus
differentiability
0
votes
1
answer
29
ISI2018MMA28
Consider the following functions $f(x)=\left\{\begin{matrix} 1 &, if\ x \leq 1 \\ 0 & ,if\ x>1 \end{matrix}\right.$ ... at $ 1$ $h_2$ is continuous everywhere and $h_1$ has discontinuity at $ 2$ $h_1$ has discontinuity at $ 2$ and $h_2$ has discontinuity at $ 1$.
answered
Jul 24
in
Calculus
by
Arif_Faizan
(
35
points)

41
views
isi2018
engineeringmathematics
calculus
continuity
+1
vote
1
answer
30
graph theory(basic doubt)
Q.1)How many nonisomorphic simple graph are there with 6 vertices and 4 edges??
answered
Jul 24
in
Graph Theory
by
gorya506
(
163
points)

56
views
+41
votes
7
answers
31
GATE2014247
The product of the nonzero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$
answered
Jul 24
in
Linear Algebra
by
srestha
Veteran
(
113k
points)

9.4k
views
gate20142
linearalgebra
eigenvalue
normal
numericalanswers
+1
vote
2
answers
32
UGCNETJune2019II3
How many bit strings of length ten either start with a $1$ bit or end with two bits $00$ ? $320$ $480$ $640$ $768$
answered
Jul 23
in
Combinatory
by
Lakshman Patel RJIT
Boss
(
45.1k
points)

115
views
ugcnetjune2019ii
permutationandcombination
inclusionexclusion
+1
vote
3
answers
33
Suppose that 100 people enter a contest and that different winners are selected at random for first, second, and third prizes. What is the probability that Michelle wins one of these prizes if she is one of the contestants?
answered
Jul 21
in
Probability
by
mohan123
Junior
(
663
points)

926
views
+13
votes
4
answers
34
GATE2007IT76
Consider the sequence $\langle x_n \rangle , \: n \geq 0$ defined by the recurrence relation $x_{n+1} = c . x^2_n 2$, where $c > 0$. Suppose there exists a nonempty, open interval $(a, b)$ such that for all $x_0$ satisfying $a < x_0 < b$, the sequence converges ... sequence converges to the value? $\frac{1+\sqrt{1+8c}}{2c}$ $\frac{1\sqrt{1+8c}}{2c}$ $2$ $\frac{2}{2c1}$
answered
Jul 20
in
Combinatory
by
ankitgupta.1729
Boss
(
14k
points)

1.2k
views
gate2007it
permutationandcombination
normal
recurrence
0
votes
1
answer
35
Probability
Suppose that a bag contains 8 blue cubes and 4 green cubes. We draw 2 cubes from the bag without replacement. It is given that blue balls are of weight 1Kg and green balls are of weight 0.5 Kg. Suppose that the probability that a given cube in the bag ... is its weight divided by the sum of the weights of all cubes currently in the bag. What is the probability that both cubes are blue.
answered
Jul 20
in
Probability
by
bankeshk
(
27
points)

43
views
probability
engineeringmathematics
0
votes
1
answer
36
Probability
Prabha is working in a software company. Her manager is running a dinner for those employees having atleast one son. If Prabha is invited to the dinner and everyone knows she has two children. What is the probability that they are both boys?
answered
Jul 20
in
Mathematical Logic
by
bankeshk
(
27
points)

36
views
probability
engineeringmathematics
conditionalprobability
0
votes
1
answer
37
Kenneth Rosen Edition 7th Exercise 2.3 Question 27 (Page No. 153)
Prove that a strictly decreasing function from $R$ to itself is onetoone. Give an example of an decreasing function from $R$ to itself that is not onetoone
answered
Jul 17
in
Set Theory & Algebra
by
chirudeepnamini
(
219
points)

11
views
kennethrosen
discretemathematics
settheory&algebra
+1
vote
2
answers
38
ProbabilityGFG
In a bunch of $13$ Tshirts only $1$ is of Medium size, which is correct fit for the searching person. Each time wrong size is picked, the person throws it away and pick the next Tshirt. What is the probability that the correct size Tshirt can be searched in $8^{th}$ attempt ? My attempt : $\frac{1}{13}$ where i went wrong ?
answered
Jul 16
in
Probability
by
arjun0001
(
21
points)

330
views
probability
+8
votes
8
answers
39
Kenneth Rosen Edition 6 Question 45 (Page No. 346)
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?
answered
Jul 14
in
Combinatory
by
srestha
Veteran
(
113k
points)

2.2k
views
permutationandcombination
counting
+36
votes
7
answers
40
GATE200340
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid  6$. The mindegree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, mindegree of $G$ cannot be $3$ $4$ $5$ $6$
answered
Jul 14
in
Graph Theory
by
PRANAV M
(
143
points)

3.5k
views
gate2003
graphtheory
normal
degreeofgraph
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