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Recent questions and answers in Engineering Mathematics
+18
votes
5
answers
1
GATE20001.1
The minimum number of cards to be dealt from an arbitrarily shuffled deck of $52$ cards to guarantee that three cards are from same suit is $3$ $8$ $9$ $12$
answered
21 hours
ago
in
Combinatory
by
Asim Siddiqui 4
Active
(
1.2k
points)

2.9k
views
gate2000
easy
pigeonholeprinciple
permutationandcombination
+1
vote
1
answer
2
Gatebook Test
answered
22 hours
ago
in
Linear Algebra
by
aditi19
Active
(
4.9k
points)

43
views
0
votes
1
answer
3
Gatebook Test
answered
22 hours
ago
in
Linear Algebra
by
aditi19
Active
(
4.9k
points)

44
views
+25
votes
4
answers
4
GATE200673
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of connected components in $G$ is: $n$ $n + 2$ $2^{\frac{n}{2}}$ $\frac{2^{n}}{n}$
answered
1 day
ago
in
Graph Theory
by
shaktisingh
(
241
points)

2.4k
views
gate2006
graphtheory
normal
graphconnectivity
+38
votes
6
answers
5
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
3 days
ago
in
Combinatory
by
techbd123
Active
(
1.4k
points)

4.2k
views
gate2005
settheory&algebra
normal
pigeonholeprinciple
+3
votes
2
answers
6
CMI2015A10
The school athletics coach has to choose 4 students for the relay team. He calculates that there are 3876 ways of choosing the team if the order in which the runners are placed is not considered. How many ways are there of choosing the team if the order of the ... taken into account? Between 12,000 and 25,000 Between 75,000 and 99,999 Between 30,000 and 60,000 More than 100,000
answered
3 days
ago
in
Combinatory
by
chirudeepnamini
Active
(
1.8k
points)

92
views
cmi2015
permutationandcombination
+21
votes
5
answers
7
GATE201827
Let $N$ be the set of natural numbers. Consider the following sets, $P:$ Set of Rational numbers (positive and negative) $Q:$ Set of functions from $\{0,1\}$ to $N$ $R:$ Set of functions from $N$ to $\{0, 1\}$ $S:$ Set of finite subsets of $N$ Which of the above sets are countable? $Q$ and $S$ only $P$ and $S$ only $P$ and $R$ only $P, Q$ and $S$ only
answered
3 days
ago
in
Set Theory & Algebra
by
JashanArora
Junior
(
827
points)

4.6k
views
gate2018
settheory&algebra
countableuncountableset
normal
+1
vote
2
answers
8
set theory
answered
4 days
ago
in
Set Theory & Algebra
by
Spidey_guy
(
111
points)

50
views
settheory&algebra
discretemathematics
engineeringmathematics
sets
+50
votes
7
answers
9
GATE2016228
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. Consider the following statements: Each compound in U \ S reacts with an odd number ... in U \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.
answered
4 days
ago
in
Set Theory & Algebra
by
Spidey_guy
(
111
points)

4.8k
views
gate20162
settheory&algebra
difficult
sets
+32
votes
8
answers
10
GATE19941.6, ISRO200829
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
answered
4 days
ago
in
Graph Theory
by
Saurabh666
(
389
points)

9.3k
views
gate1994
graphtheory
permutationandcombination
normal
isro2008
counting
+11
votes
3
answers
11
GATE19961.6
The formula used to compute an approximation for the second derivative of a function $f$ at a point $X_0$ is $\dfrac{f(x_0 +h) + f(x_0 – h)}{2}$ $\dfrac{f(x_0 +h)  f(x_0 – h)}{2h}$ $\dfrac{f(x_0 +h) + 2f(x_0) + f(x_0 – h)}{h^2}$ $\dfrac{f(x_0 +h)  2f(x_0) + f(x_0 – h)}{h^2}$
answered
5 days
ago
in
Calculus
by
neeraj2681
(
33
points)

1.3k
views
gate1996
calculus
differentiability
normal
0
votes
1
answer
12
Rosen 7e Recurrence Relation Exercise8.1 Question no25 page no511
How many bit sequences of length seven contain an even number of 0s? I'm trying to solve this using recurrence relation Is my approach correct? Let T(n) be the string having even number of 0s T(1)=1 {1} T(2)=2 {00, 11} T(3)=4 {001, ... add 0 to strings of length n1 having odd number of 0s T(n)=T(n1) Hence, we have T(n)=2T(n1)
answered
6 days
ago
in
Combinatory
by
anonymousgamer
(
11
points)

53
views
kennethrosen
discretemathematics
permutationandcombination
#recurrencerelations
recurrence
+2
votes
3
answers
13
Made easy
What is the chromatic number of following graphs? 1) 2)
answered
Oct 16
in
Graph Theory
by
chirudeepnamini
Active
(
1.8k
points)

167
views
graphcoloring
discrete
engineeringmathematics
+10
votes
2
answers
14
ISI2015MMA7
Suppose $X$ is distributed as Poisson with mean $λ.$ Then $E(1/(X + 1))$ is $\frac{e^{\lambda }1}{\lambda }$ $\frac{e^{\lambda }1}{\lambda +1}$ $\frac{1e^{\lambda }}{\lambda}$ $\frac{1e^{\lambda }}{\lambda + 1}$
answered
Oct 14
in
Probability
by
Gaurav Yadav
(
233
points)

809
views
isi2015
engineeringmathematics
poissondistribution
0
votes
1
answer
15
Combinatorics
There are 6n flowers of one type and 3 flowers of second type, total no. Of garlands possible?
answered
Oct 11
in
Combinatory
by
shivamgo
(
11
points)

29
views
permutationandcombination
+1
vote
1
answer
16
Mean Value Theorem
f(x) is a differentiable function that satisfies 5 ≤ f′(x) ≤ 14 for all x. Let a and b be the maximum and minimum values, respectively, that f(11)−f(3) can possibly have, then what is the value of a+b?
answered
Oct 10
in
Calculus
by
Nirmal Gaur
Active
(
2k
points)

35
views
+8
votes
4
answers
17
GATE19893v
Answer the following: Which of the following wellformed formulas are equivalent? $P \rightarrow Q$ $\neg Q \rightarrow \neg P$ $\neg P \vee Q$ $\neg Q \rightarrow P$
answered
Oct 8
in
Mathematical Logic
by
vupadhayayx86
Active
(
1.4k
points)

587
views
gate1989
normal
mathematicallogic
propositionallogic
+3
votes
2
answers
18
TIFR2010MathsA1
A cyclic group of order 60 has 12 Generators 15 Generators 16 Generators 20 Generators
answered
Oct 6
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Veteran
(
51.5k
points)

940
views
tifrmaths2010
groups
+2
votes
3
answers
19
TIFR2014MathsB4
Let $H_{1}$, $H_{2}$ be two distinct subgroups of a finite group $G$, each of order $2$. Let $H$ be the smallest subgroup containing $H_{1}$ and $H_{2}$. Then the order of $H$ is Always 2 Always 4 Always 8 None of the above.
answered
Oct 5
in
Set Theory & Algebra
by
Harry Richie
(
17
points)

328
views
tifrmaths2014
settheory&algebra
groups
+1
vote
1
answer
20
TIFR2014MathsA15
How many proper subgroups does the group $\mathbb{Z} ⊕ \mathbb{Z}$ have? $1$ $2$ $3$ Infinitely many
answered
Oct 5
in
Set Theory & Algebra
by
Harry Richie
(
17
points)

182
views
tifrmaths2014
groups
+8
votes
5
answers
21
GATE2007IT80
Let $P_{1},P_{2},\ldots,P_{n}$ be $n$ points in the $xy$plane such that no three of them are collinear. For every pair of points $P_{i}$ and $P_{j}$, let $L_{ij}$ be the line passing through them. Let $L_{ab}$ be the line with the ... largest or the smallest $y$coordinate among all the points The difference between $x$coordinates $P_{a}$ and $P_{b}$ is minimum None of the above
answered
Oct 4
in
Linear Algebra
by
sujeetkumar
(
11
points)

1k
views
gate2007it
cartesiancoordinates
+13
votes
2
answers
22
GATE201529
The number of divisors of $2100$ is ____.
answered
Oct 3
in
Set Theory & Algebra
by
JashanArora
Junior
(
827
points)

3.2k
views
gate20152
settheory&algebra
numbertheory
easy
numericalanswers
+5
votes
10
answers
23
GATE201921
The value of $3^{51} \text{ mod } 5$ is _____
answered
Oct 3
in
Combinatory
by
techbd123
Active
(
1.4k
points)

3k
views
gate2019
numericalanswers
permutationandcombination
modulararithmetic
0
votes
1
answer
24
ISI2016DCG45
The value of $\underset{x \to 0}{\lim} \dfrac{\tan^{2}\:xx\:\tan\:x}{\sin\:x}$ is $\frac{\sqrt{3}}{2}$ $\frac{1}{2}$ $0$ None of these
answered
Oct 2
in
Calculus
by
`JEET
Loyal
(
8.2k
points)

19
views
isi2016dcg
limits
+1
vote
1
answer
25
graph Theory
Consider an undirected 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 between (a, b) and (c, d) if ac<=1 and bd<=1. The number of edges in this graph is __________.
answered
Oct 1
in
Graph Theory
by
Mac2
(
11
points)

116
views
discretemathematics
graphtheory
+5
votes
2
answers
26
GATE199525b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
answered
Sep 27
in
Set Theory & Algebra
by
techbd123
Active
(
1.4k
points)

237
views
gate1995
settheory&algebra
numericalanswers
sets
+31
votes
3
answers
27
GATE20012.15
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices? $\frac{n(n1)} {2}$ $2^n$ $n!$ $2^\frac{n(n1)} {2} $
answered
Sep 26
in
Graph Theory
by
HeartBleed
Junior
(
691
points)

3.9k
views
gate2001
graphtheory
normal
counting
+1
vote
1
answer
28
ISI2014DCG39
The function $f(x) = x^{1/x}, \: x \neq 0$ has a minimum at $x=e$; a maximum at $x=e$; neither a maximum nor a minimum at $x=e$; None of the above
answered
Sep 24
in
Calculus
by
`JEET
Loyal
(
8.2k
points)

36
views
isi2014dcg
maximaminima
calculus
0
votes
1
answer
29
ISI2014DCG12
The integral $\int _0^{\frac{\pi}{2}} \frac{\sin^{50} x}{\sin^{50}x +\cos^{50}x} dx$ equals $\frac{3 \pi}{4}$ $\frac{\pi}{3}$ $\frac{\pi}{4}$ none of these
answered
Sep 24
in
Calculus
by
Verma Ashish
Boss
(
10.7k
points)

47
views
isi2014dcg
calculus
definiteintegrals
integration
0
votes
1
answer
30
Kenneth Rosen Edition 7th Exercise 2.2 Question 14 (Page No. 136)
Find the sets $A$ and $B$ if $AB=\left \{ 1,5,7,8 \right \}, BA=\left \{ 2,10 \right \},$ and $A \cap B=\left \{ 3,6,9 \right \}.$
answered
Sep 24
in
Set Theory & Algebra
by
anurag_cs
(
41
points)

15
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
2
answers
31
SelfDoubt:Mathematical logic
“Every asymmetric relation is antisymmetric” Is this statement is True or False? I think it is false, because asymmetric relation never allows loops and antisymmetric relation allows loops. Am I not correct?
answered
Sep 24
in
Set Theory & Algebra
by
anurag_cs
(
41
points)

31
views
discretemathematics
+33
votes
9
answers
32
GATE2014351
If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have? $\left\lfloor\frac {n}{k}\right\rfloor$ $\left\lceil \frac{n}{k} \right\rceil$ $nk$ $nk+1$
answered
Sep 24
in
Graph Theory
by
HeartBleed
Junior
(
691
points)

4.4k
views
gate20143
graphtheory
graphconnectivity
normal
+1
vote
3
answers
33
ISI2018MMA12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$
answered
Sep 23
in
Linear Algebra
by
aditi19
Active
(
4.9k
points)

108
views
isi2018mma
engineeringmathematics
linearalgebra
rankofmatrix
0
votes
2
answers
34
ISI2018MMA13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is $2$ $2(1+i)$ $0$ $2^{10}$
answered
Sep 23
in
Linear Algebra
by
aditi19
Active
(
4.9k
points)

73
views
isi2018mma
engineeringmathematics
linearalgebra
determinant
0
votes
2
answers
35
ugc net 2018 july80
answered
Sep 23
in
Probability
by
muthuct8
(
11
points)

185
views
+2
votes
3
answers
36
ISI2017MMA13
An even function $f(x)$ has left derivative $5$ at $x=0$. Then the right derivative of $f(x)$ at $x=0$ need not exist the right derivative of $f(x)$ at $x=0$ exists and is equal to $5$ the right derivative of $f(x)$ at $x=0$ exists and is equal to $5$ none of the above is necessarily true
answered
Sep 22
in
Calculus
by
techbd123
Active
(
1.4k
points)

277
views
isi2017mma
engineeringmathematics
calculus
differentiability
+17
votes
6
answers
37
GATE199810a
Prove by induction that the expression for the number of diagonals in a polygon of $n$ sides is $\frac{n(n3)}{2}$
answered
Sep 20
in
Set Theory & Algebra
by
Gaurav Yadav
(
233
points)

1.2k
views
gate1998
settheory&algebra
descriptive
relations
+24
votes
5
answers
38
GATE2016105
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {1})$ and $3$. The determinant of $P$ is _______
answered
Sep 19
in
Linear Algebra
by
neeraj2681
(
33
points)

3.6k
views
gate20161
linearalgebra
eigenvalue
numericalanswers
normal
+10
votes
3
answers
39
GATE199714
Let $R$ be a reflexive and transitive relation on a set $A$. Define a new relation $E$ on $A$ as $E=\{(a, b) \mid (a, b) \in R \text{ and } (b, a) \in R \}$ Prove that $E$ is an equivalence relation on $A$. Define a relation $\leq$ on the equivalence classes of $E$ ... $\exists a, b$ such that $a \in E_1, b \in E_2 \text{ and } (a, b) \in R$. Prove that $\leq$ is a partial order.
answered
Sep 19
in
Set Theory & Algebra
by
Sambhrant Maurya
Active
(
3.2k
points)

805
views
gate1997
settheory&algebra
relations
normal
proof
descriptive
+15
votes
4
answers
40
GATE19943.8
Give a relational algebra expression using only the minimum number of operators from $(∪, −)$ which is equivalent to $R$ $∩$ $S.$
answered
Sep 18
in
Set Theory & Algebra
by
Anurag007
(
11
points)

830
views
gate1994
settheory&algebra
normal
sets
descriptive
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