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Recent questions and answers in Engineering Mathematics
+54
votes
9
answers
1
GATE2015139
Consider the operations $\textit{f (X, Y, Z) = X'YZ + XY' + Y'Z'}$ and $\textit{g (X, Y, Z) = X'YZ + X'YZ' + XY}$ Which one of the following is correct? Both $\left\{\textit{f} \right\}$ and $\left\{ \textit{g}\right\}$ are ... Only $\left\{ \textit{g}\right\}$ is functionally complete Neither $\left\{ \textit{f}\right\}$ nor $\left\{\textit{g}\right\}$ is functionally complete
answered
13 hours
ago
in
Set Theory & Algebra
by
Kuldeep Pal
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1.5k
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7.6k
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gate20151
settheory&algebra
functions
difficult
+23
votes
7
answers
2
GATE200628
A logical binary relation $\odot$ ... $(\sim A\odot B)$ $\sim(A \odot \sim B)$ $\sim(\sim A\odot\sim B)$ $\sim(\sim A\odot B)$
answered
14 hours
ago
in
Set Theory & Algebra
by
haralk10
(
11
points)

1.5k
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gate2006
settheory&algebra
binaryoperation
+2
votes
5
answers
3
TIFR2019A15
Consider the matrix $A = \begin{bmatrix} \frac{1}{2} &\frac{1}{2} & 0\\ 0& \frac{3}{4} & \frac{1}{4}\\ 0& \frac{1}{4} & \frac{3}{4} \end{bmatrix}$ What is $\lim_{n→\infty}$A^n$ ? $\begin{bmatrix} \ 0 & 0 & 0\\ 0& 0 ... $\text{The limit exists, but it is none of the above}$
answered
18 hours
ago
in
Calculus
by
severustux
(
121
points)

383
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tifr2019
engineeringmathematics
calculus
limits
+6
votes
3
answers
4
ISRO200729
The set of all Equivalence Classes of a set A of Cardinality C is of cardinality $2^c$ have the same cardinality as A forms a partition of A is of cardinality $C^2$
answered
1 day
ago
in
Set Theory & Algebra
by
JashanArora
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1.7k
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2.4k
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isro2007
settheory&algebra
equivalenceclasses
+8
votes
5
answers
5
TIFR2018A6
What is the minimum number of students needed in a class to guarantee that there are at least $6$ students whose birthdays fall in the same month ? $6$ $23$ $61$ $72$ $91$
answered
2 days
ago
in
Combinatory
by
`JEET
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(
12.9k
points)

417
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tifr2018
pigeonholeprinciple
permutationandcombination
+4
votes
5
answers
6
TIFR2012A17
A spider is at the bottom of a cliff, and is $n$ inches from the top. Every step it takes brings it one inch closer to the top with probability $1/3$, and one inch away from the top with probability $2/3$, unless it is at the bottom in which case, it ... function of $n$? It will never reach the top. Linear in $n$. Polynomial in $n$. Exponential in $n$. Double exponential in $n$.
answered
2 days
ago
in
Probability
by
pritishc
Junior
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657
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594
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tifr2012
probability
+1
vote
2
answers
7
#set theory #groups
Consider the set H of all 3 × 3 matrices of the type: $\begin{bmatrix} a&f&e\\ 0&b&d\\ 0&0&c\\ \end{bmatrix}$ where a, b, c, d, e and f are real numbers and $abc ≠ 0$. Under the matrix multiplication operation, the set H is: (a) a group (b) a monoid but not a group (c) a semigroup but not a monoid (d) neither a group nor a semigroup
answered
2 days
ago
in
Set Theory & Algebra
by
smsubham
Loyal
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9.6k
points)

75
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settheory&algebra
groups
matrices
+3
votes
4
answers
8
ISRO200834
If a square matrix A satisfies $A^TA=I$, then the matrix $A$ is Idempotent Symmetric Orthogonal Hermitian
answered
2 days
ago
in
Linear Algebra
by
JashanArora
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1.7k
points)

1.4k
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isro2008
linearalgebra
matrices
+34
votes
9
answers
9
GATE19941.6, ISRO200829
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
answered
2 days
ago
in
Graph Theory
by
JashanArora
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1.7k
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9.7k
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gate1994
graphtheory
permutationandcombination
normal
isro2008
counting
+24
votes
13
answers
10
GATE201846
The number of possible minheaps containing each value from $\{1,2,3,4,5,6,7\}$ exactly once is _______
answered
3 days
ago
in
Combinatory
by
Praveenk99
(
49
points)

8.4k
views
gate2018
permutationandcombination
numericalanswers
+37
votes
11
answers
11
GATE2016126
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
answered
3 days
ago
in
Combinatory
by
pritishc
Junior
(
657
points)

9k
views
gate20161
permutationandcombination
generatingfunctions
normal
numericalanswers
+28
votes
5
answers
12
GATE20006
Let $S$ be a set of $n$ elements $\left\{1, 2,....., n\right\}$ and $G$ a graph with 2$^{n}$ vertices, each vertex corresponding to a distinct subset of $S$. Two vertices are adjacent iff the symmetric difference of the corresponding sets has exactly $2$ ... $G$ has the same degree. What is the degree of a vertex in $G$? How many connected components does $G$ have?
answered
3 days
ago
in
Set Theory & Algebra
by
Vimal Patel
(
137
points)

1.8k
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gate2000
settheory&algebra
normal
descriptive
sets
+1
vote
3
answers
13
GATE20014
Consider the function $h: N \times N \rightarrow N$ so that $h(a,b) = (2a +1)2^b  1$, where $N=\{0,1,2,3,\dots\}$ is the set of natural numbers. Prove that the function $h$ is an injection (oneone). Prove that it is also a Surjection (onto)
answered
3 days
ago
in
Set Theory & Algebra
by
Verma Ashish
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11.8k
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453
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gate2001
functions
settheory&algebra
normal
descriptive
+1
vote
1
answer
14
TIFR2019A6
A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is said to be $\textit{convex}$ if for all $x,y \in \mathbb{R}$ and $\lambda$ such that $0 \leq \lambda \leq1,$ $f(\lambda x+ (1\lambda)y) \leq \lambda f (x) + (1\lambda) f(y)$. Let $f:$\mathbb{R}$ $→$ $\mathbb ... $p,q$ and $r$ must be convex? Only $p$ Only $q$ Only $r$ Only $p$ and $r$ Only $q$ and $r$
answered
4 days
ago
in
Set Theory & Algebra
by
Satbir
Boss
(
21.5k
points)

339
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tifr2019
engineeringmathematics
discretemathematics
settheory&algebra
functions
convexsetsfunctions
nongate
+4
votes
3
answers
15
GATE201944
Consider the following matrix: $R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$ The absolute value of the product of Eigen values of $R$ is _______
answered
4 days
ago
in
Linear Algebra
by
JashanArora
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1.7k
points)

2.7k
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gate2019
numericalanswers
engineeringmathematics
linearalgebra
eigenvalue
+7
votes
7
answers
16
GATE201935
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z \mid x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z \mid w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ ... Set of all positive integers $S3:$ Set of all integers Which of the above sets satisfy $\varphi$? S1 and S2 S1 and S3 S2 and S3 S1, S2 and S3
answered
5 days
ago
in
Mathematical Logic
by
JashanArora
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1.7k
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5.1k
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gate2019
engineeringmathematics
discretemathematics
mathematicallogic
firstorderlogic
+5
votes
4
answers
17
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
5 days
ago
in
Graph Theory
by
JashanArora
Active
(
1.7k
points)

3k
views
gate2019
engineeringmathematics
discretemathematics
graphtheory
graphconnectivity
+5
votes
9
answers
18
GATE201912
Let $G$ be an undirected complete graph on $n$ vertices, where $n > 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to $n!$ $(n1)!$ $1$ $\frac{(n1)!}{2}$
answered
5 days
ago
in
Graph Theory
by
JashanArora
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1.7k
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3.3k
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gate2019
engineeringmathematics
discretemathematics
graphtheory
graphconnectivity
+3
votes
5
answers
19
GATE20199
Let $X$ be a square matrix. Consider the following two statements on $X$. $X$ is invertible Determinant of $X$ is nonzero Which one of the following is TRUE? I implies II; II does not imply I II implies I; I does not imply II I does not imply II; II does not imply I I and II are equivalent statements
answered
5 days
ago
in
Linear Algebra
by
JashanArora
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1.7k
points)

2k
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gate2019
engineeringmathematics
linearalgebra
determinant
+19
votes
5
answers
20
GATE201436
If $\int \limits_0^{2 \pi} x \: \sin x dx=k\pi$, then the value of $k$ is equal to ______.
answered
5 days
ago
in
Calculus
by
Lakshman Patel RJIT
Veteran
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54.8k
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2.8k
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gate20143
calculus
integration
limits
numericalanswers
easy
+17
votes
4
answers
21
GATE2014347
The value of the integral given below is $\int \limits_0^{\pi} \: x^2 \: \cos x\:dx$ $2\pi$ $\pi$ $\pi$ $2\pi$
answered
5 days
ago
in
Calculus
by
Lakshman Patel RJIT
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54.8k
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1.9k
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gate20143
calculus
limits
integration
normal
0
votes
2
answers
22
self doubt
What is the general formula for number of simple graph having n unlabelled vertices ??
answered
6 days
ago
in
Graph Theory
by
Muneendra1337
(
11
points)

60
views
simplegraph
0
votes
1
answer
23
group
if (G,*) is a cyclic group of order 97 , then number of generator of G is equal to ___
answered
6 days
ago
in
Set Theory & Algebra
by
GoalSet1
(
203
points)

122
views
groups
discretemathematics
settheory&algebra
+7
votes
2
answers
24
GATE19952.13
A unit vector perpendicular to both the vectors $a=2i3j+k$ and $b=i+j2k$ is: $\frac{1}{\sqrt{3}} (i+j+k)$ $\frac{1}{3} (i+jk)$ $\frac{1}{3} (ijk)$ $\frac{1}{\sqrt{3}} (i+jk)$
answered
Nov 28
in
Linear Algebra
by
Satbir
Boss
(
21.5k
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1.1k
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gate1995
linearalgebra
normal
vectorspace
0
votes
1
answer
25
Probability Gravner 79.c
A random variable $X$ has the density function $f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$ (c) Determine the probability density function of $Y$ $=$ $X^2$
answered
Nov 28
in
Probability
by
Mk Utkarsh
Boss
(
35.7k
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37
views
probability
gravner
engineeringmathematics
randomvariable
+4
votes
3
answers
26
ISRO201349
What is the least value of the function $f(x) = 2x^{2}8x3$ in the interval $[0, 5]$? $15$ $7$ $11$ $3$
answered
Nov 28
in
Calculus
by
Lakshman Patel RJIT
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54.8k
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1.9k
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isro2013
maximaminima
+1
vote
2
answers
27
ISI2014DCG71
Five letters $A, B, C, D$ and $E$ are arranged so that $A$ and $C$ are always adjacent to each other and $B$ and $E$ are never adjacent to each other. The total number of such arrangements is $24$ $16$ $12$ $32$
answered
Nov 28
in
Combinatory
by
noob_coder
Junior
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657
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26
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isi2014dcg
permutationandcombination
arrangements
circularpermutation
0
votes
1
answer
28
Probability  Gravner69.b
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (c) Determine EX and Var(X).
answered
Nov 27
in
Probability
by
Mk Utkarsh
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35.7k
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22
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probability
gravner
engineeringmathematics
randomvariable
0
votes
1
answer
29
Probability  Gravner69.b
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (b) Compute $P(1\leqslant X\leqslant 2)$
answered
Nov 27
in
Probability
by
Mk Utkarsh
Boss
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35.7k
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22
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probability
gravner
engineeringmathematics
randomvariable
0
votes
1
answer
30
Probability  Gravner69.a
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (a) Determine $c$.
answered
Nov 27
in
Probability
by
Mk Utkarsh
Boss
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35.7k
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16
views
gravner
probability
engineeringmathematics
randomvariable
+20
votes
4
answers
31
GATE2006IT22
When a coin is tossed, the probability of getting a Head is $p, 0 < p < 1$. Let $N$ be the random variable denoting the number of tosses till the first Head appears, including the toss where the Head appears. Assuming that successive tosses are independent, the expected value of $N$ is $\dfrac{1}{p}$ $\dfrac{1}{(1  p)}$ $\dfrac{1}{p^{2}}$ $\dfrac{1}{(1  p^{2})}$
answered
Nov 26
in
Probability
by
Mk Utkarsh
Boss
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35.7k
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2.2k
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gate2006it
probability
binomialdistribution
expectation
normal
+2
votes
1
answer
32
Kenneth Rosen Edition 6th Exercise 6.4 Question 13 (Page No. 440)
Use Generating function to determine,the number of different ways $10$ identical balloons can be given to four children if each child receives atleast $2$ ballons? Ans given $(x^{2}+x^{3}+.........................)^{4}$ But as there is a upper ... Which one is correct? plz confirm
answered
Nov 26
in
Combinatory
by
Kushagra गुप्ता
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1.8k
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198
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kennethrosen
discretemathematics
generatingfunctions
+36
votes
7
answers
33
GATE2008IT21
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ ... $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$
answered
Nov 26
in
Mathematical Logic
by
JashanArora
Active
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1.7k
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4.2k
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gate2008it
firstorderlogic
normal
+1
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1
answer
34
TIFR2011MathsA19
The derivative of the function $\int_{0}^{\sqrt{x}} e^{t^{2}}dt$ at $x = 1$ is $e^{1}$ .
answered
Nov 25
in
Calculus
by
seetal samal
(
37
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151
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tifrmaths2011
calculus
differentiability
+1
vote
1
answer
35
TIFR2011MathsA21
Any continuous function from the open unit interval $(0, 1)$ to itself has a fixed point.
answered
Nov 25
in
Calculus
by
seetal samal
(
37
points)

105
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tifrmaths2011
continuity
0
votes
1
answer
36
ISI2015MMA44
Let $P_1$, $P_2$ and $P_3$ denote, respectively, the planes defined by $\begin{array} {} a_1x +b_1y+c_1z=\alpha _1 \\ a_2x +b_2y+c_2z=\alpha _2 \\ a_3x +b_3y+c_3z=\alpha _3 \end{array}$ It is given that $P_1$, $P_2$ and $P_3$ ... then the planes do not have any common point of intersection intersect at a unique point intersect along a straight line intersect along a plane
answered
Nov 25
in
Linear Algebra
by
Lakshman Patel RJIT
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(
54.8k
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14
views
isi2015mma
linearalgebra
systemofequations
+2
votes
2
answers
37
ISI2015MMA39
The eigenvalues of the matrix $X = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{pmatrix}$ are $1,1,4$ $1,4,4$ $0,1,4$ $0,4,4$
answered
Nov 25
in
Linear Algebra
by
Lakshman Patel RJIT
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54.8k
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31
views
isi2015mma
linearalgebra
matrices
eigenvalue
0
votes
1
answer
38
ISI2014DCG64
The value of $\lambda$ such that the system of equation $\begin{array}{} 2x & – & y & + & 2z & = & 2 \\ x & – & 2y & + & z & = & 4 \\ x & + & y & + & \lambda z & = & 4 \end{array}$ has no solution is $3$ $1$ $0$ $3$
answered
Nov 24
in
Linear Algebra
by
Lakshman Patel RJIT
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(
54.8k
points)

31
views
isi2014dcg
linearalgebra
matrices
systemofequations
+28
votes
3
answers
39
GATE20021.25, ISRO200830, ISRO20166
The maximum number of edges in a nnode undirected graph without self loops is $n^2$ $\frac{n(n1)}{2}$ $n1$ $\frac{(n+1)(n)}{2}$
answered
Nov 23
in
Graph Theory
by
Shailendra_
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555
points)

5.5k
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gate2002
graphtheory
easy
isro2008
isro2016
graphconnectivity
+2
votes
2
answers
40
Integration
Solve the following $\int_{0}^{\infty}e^{x^2}x^4dx$
answered
Nov 22
in
Calculus
by
Lakshman Patel RJIT
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54.8k
points)

185
views
engineeringmathematics
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calculus
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