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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
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Sep 23
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Calculus
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isi2014dcg
calculus
definiteintegrals
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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
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Sep 23
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Calculus
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Arjun
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isi2014dcg
maximaminima
calculus
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3
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?
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Sep 22
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Calculus
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Nirmal Gaur
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35
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0
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1
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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
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Sep 18
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Calculus
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gatecse
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19
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isi2016dcg
limits
0
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1
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5
CUTSET
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Aug 28
in
Graph Theory
by
Sanjay Sharma
Boss
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48.5k
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64
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+3
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1
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6
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
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Aug 8
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Combinatory
by
Shaik Masthan
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63.6k
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permutationandcombination
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3
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7
UGCNETJune2019II1
Consider the poset $( \{3,5,9,15,24,45 \}, \mid).$ Which of the following is correct for the given poset ? There exist a greatest element and a least element There exist a greatest element but not a least element There exist a least element but not a greatest element There does not exist a greatest element and a least element
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Jul 2
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Set Theory & Algebra
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Arjun
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421k
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453
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ugcnetjune2019ii
poset
settheory&algebra
+1
vote
2
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8
UGCNETJune2019II2
How many ways are there to place $8$ indistinguishable balls into four distinguishable bins? $70$ $165$ $^8C_4$ $^8P_4$
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Jul 2
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Combinatory
by
Arjun
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421k
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286
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ugcnetjune2019ii
permutationandcombination
+1
vote
2
answers
9
UGCNETJune2019II3
How many bit strings of length ten either start with a $1$ bit or end with two bits $00$ ? $320$ $480$ $640$ $768$
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Jul 2
in
Combinatory
by
Arjun
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421k
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204
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ugcnetjune2019ii
permutationandcombination
inclusionexclusion
+2
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1
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10
UGCNETJune2019II4
Suppose that a connected planar graph has six vertices, each of degree four. Into how many regions is the plane divided by a planar representation of this graph? $6$ $8$ $12$ $20$
asked
Jul 2
in
Graph Theory
by
Arjun
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421k
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183
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ugcnetjune2019ii
graphplanarity
handshakingtheorem
+3
votes
2
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11
UGCNETJune2019II5
For which values of $m$ and $n$ does the complete bipartite graph $k_{m,n}$ have a Hamiltonian circuit ? $m\neq n,\ \ m,n \geq 2$ $m\neq n,\ \ m,n \geq 3$ $m=n,\ \ m,n \geq 2$ $m= n,\ \ m,n \geq 3$
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Jul 2
in
Graph Theory
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Arjun
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421k
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166
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ugcnetjune2019ii
graphtheory
+3
votes
2
answers
12
UGCNETJune2019II6
Which of the following is principal conjunctive normal form for $[(p\vee q)\wedge\ \rceil p \rightarrow \rceil q ]$ ? $p\ \vee \rceil q$ $p \vee q $ $\rceil p \vee q$ $\rceil p\ \vee \rceil q$
asked
Jul 2
in
Mathematical Logic
by
Arjun
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421k
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166
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ugcnetjune2019ii
propositionallogic
+1
vote
1
answer
13
UGCNETJune2019II7
How many cards must be selected from a standard deck of $52$ cards to guarantee that at least three hearts are present among them? $9$ $13$ $17$ $42$
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Jul 2
in
Combinatory
by
Arjun
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421k
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151
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ugcnetjune2019ii
permutationandcombination
pigeonholeprinciple
+3
votes
2
answers
14
UGCNETJune2019II8
Match ListI with ListII: ... )  (iv); (b)  (i); (c)  (iii); (d)  (ii) (a)  (iv); (b)  (iii); (c)  (i); (d)  (ii)
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Jul 2
in
Mathematical Logic
by
Arjun
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421k
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119
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ugcnetjune2019ii
propositionallogic
+1
vote
2
answers
15
UGCNETJune2019II9
Find the zeroone matrix of the transitive closure of the relation given by the matrix $A$ : $A =\begin{bmatrix} 1 & 0& 1\\ 0 & 1 & 0\\ 1& 1& 0 \end{bmatrix}$ ... $\begin{bmatrix} 1 & 1& 1\\ 0 & 1 & 0\\ 1& 0& 1 \end{bmatrix}$
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Jul 2
in
Set Theory & Algebra
by
Arjun
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421k
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176
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ugcnetjune2019ii
settheory&algebra
+2
votes
1
answer
16
UGCNETJune2019II13
How many different Boolean functions of degree $n$ are the $2^{2^n}$ $(2^2)^n$ $2^{2^n} 1$ $2^n$
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Jul 2
in
Set Theory & Algebra
by
Arjun
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421k
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107
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ugcnetjune2019ii
boolean
function
+2
votes
1
answer
17
UGCNETJune2019II63
Consider the Euler’s phi function given by $\phi(n) = n \underset{p/n}{\Pi } \bigg( 1 – \frac{1}{p} \bigg)$ where $p$ runs over all the primes dividing $n$. What is the value of $\phi(45)$? $3$ $12$ $6$ $24$
asked
Jul 2
in
Combinatory
by
Arjun
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421k
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80
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ugcnetjune2019ii
eulerphifunction
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1
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18
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 $P_2$
asked
Jul 2
in
Graph Theory
by
Arjun
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421k
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71
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ugcnetjune2019ii
flownetwork
0
votes
1
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19
Sheldon Ross Chapter2 Question15b
If it is assumed that all $\binom{52}{5}$ poker hands are equally likely, what is the probability of being dealt two pairs? (This occurs when the cards have denominations a, a, b, b, c, where a, b, and c are all distinct.) my approach is: selecting a ... I'm getting answer 0.095 but in the book answer is given 0.0475 where am I going wrong?
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Jun 14
in
Probability
by
aditi19
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4.9k
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121
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probability
sheldonross
engineeringmathematics
0
votes
1
answer
20
Sheldon Ross Example5n
Compute the probability that if 10 married couples are seated at random at a round table, then no wife sits next to her husband 1 wife sits next to her husband. pick one of the 10 couples=$\binom{10}{1}$. These couples can interchange their position such that ... sits together=$\frac{N}{19!}$ so probability that no couple sits together=$1\frac{N}{19!}$ is this correct?
asked
Jun 11
in
Probability
by
aditi19
Active
(
4.9k
points)

156
views
permutationandcombination
probability
discretemathematics
sheldonross
+5
votes
2
answers
21
GATE199525b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
asked
Jun 6
in
Set Theory & Algebra
by
Arjun
Veteran
(
421k
points)

236
views
gate1995
settheory&algebra
numericalanswers
sets
0
votes
1
answer
22
Linear Algebra (Self Doubt)
Let $A$ be a $n \times n$ square matrix whose all columns are independent. Is $Ax = b$ always solvable? Actually, I know that $Ax= b$ is solvable if $b$ is in the column space of $A$. However, I am not sure if it is solvable for all values of $b$.
asked
Jun 6
in
Linear Algebra
by
Debargha Bhattacharj
Junior
(
653
points)

96
views
linearalgebra
0
votes
0
answers
23
#ACE ACADEMY BOOKLET QUESTION
The solution of $\sqrt{a_n} – 2\sqrt{a_{n1}} + \sqrt{a_{n2}} = 0$ where $a_0 = 1$ and $a_1 = 2$ is ${\Big[\frac{2^{n+1} + (1)^n}{3}\Big]}^2$ $(n+1)^2$ $(n1)^3$ $(n1)^2$
asked
Jun 5
in
Combinatory
by
`JEET
Loyal
(
8k
points)

107
views
discretemathematics
permutationandcombination
recurrence
#recurrencerelations
+1
vote
1
answer
24
Mathematical Logic Ques:Self doubt
“Not every satisfiable logic is valid” Representation of it will be $1)\sim \left ( \forall S(x)\rightarrow V(x) \right )$ or $2)\sim \left ( \forall S(x)\vee V(x) \right )$ Among $1)$ and $2)$, which one is correct? and why?
asked
Jun 4
in
Mathematical Logic
by
srestha
Veteran
(
116k
points)

146
views
discretemathematics
mathematicallogic
0
votes
0
answers
25
Doubt on a math question
Chk this question https://gateoverflow.in/100202/testseriescounting $1)$Can someone verify this ans?? See if $\left ( _{0}^{6}\textrm{C} \right )$ in one set, other set will contain $\left ( _{6}^{6}\textrm{C} \right )$ elements. right?? Now why do we again need $2^{n}$ ... meaning of it?? $2)$ How $\sum_{I=0}^{n}\left ( _{i}^{n}\textrm{C} \right ).2^{ni}=3^{n}$??
asked
Jun 4
in
Set Theory & Algebra
by
srestha
Veteran
(
116k
points)

42
views
discretemathematics
settheory&algebra
+2
votes
1
answer
26
Mathematics: GATE2017 EC222
Consider the random process: $X\left ( t \right )=U+Vt$ where $U$ is zeromean Gaussian random variable and $V$ is a random variable uniformly distributed between $0$ and $2.$ Assume $U$ and $V$ statistically independent. The mean value of random process at $t=2$ is ___________
asked
Jun 3
in
Probability
by
srestha
Veteran
(
116k
points)

119
views
gate2017ec2
probability
0
votes
1
answer
27
GATE 2019:EC
The value of integral $\int_{0}^{\pi }\int_{y}^{\pi }\frac{\sin x}{x}dxdy$ is equal to_________
asked
Jun 2
in
Linear Algebra
by
srestha
Veteran
(
116k
points)

74
views
discretemathematics
0
votes
2
answers
28
GATE 2017:EC
Consider the $5\times 5$ matrix: $\begin{bmatrix} 1 & 2 &3 & 4 &5 \\ 5 &1 &2 & 3 &4 \\ 4& 5 &1 &2 &3 \\ 3& 4 & 5 & 1 &2 \\ 2&3 & 4 & 5 & 1 \end{bmatrix}$ It is given $A$ has only one real eigen value. Then the real eigen value of $A$ is ________
[closed]
asked
Jun 2
in
Linear Algebra
by
srestha
Veteran
(
116k
points)

152
views
discretemathematics
linearalgebra
matrix
matrices
+2
votes
4
answers
29
GATE2017 EC
The rank of the matrix $\begin{bmatrix} 1 & 1 & 0 &0 & 0\\ 0 & 0 & 1 &1 &0 \\ 0 &1 &1 &0 &0 \\ 1 & 0 &0 & 0 &1 \\ 0&0 & 0 & 1 & 1 \end{bmatrix}$ is ________. Ans 5?
asked
Jun 1
in
Linear Algebra
by
srestha
Veteran
(
116k
points)

198
views
discretemathematics
matrix
+1
vote
1
answer
30
Doubt on GATE Question
Read the statements: All women are entrepreneurs. Some women are doctors. Which of the following conclusions can be logically inferred from the above statements? All women are doctors All doctors are entrepreneurs All entrepreneurs are women Some entrepreneurs are doctors ... Is it because , if we make set of doctor as 0, then All doctors are entrepreneurs is meaningless.
asked
Jun 1
in
Mathematical Logic
by
srestha
Veteran
(
116k
points)

56
views
discretemathematics
mathematicallogic
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