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+1
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1
TIFR2013B1
Let $G= (V, E)$ be a simple undirected graph on $n$ vertices. A colouring of $G$ is an assignment of colours to each vertex such that endpoints of every edge are given different colours. Let $\chi (G)$ denote the chromatic number of $G$, i.e. the minimum numbers of colours ... \chi (G)\leq a(G)$ $a(G)\geq n/\chi (G)$ $a(G)\leq n/\chi (G)$ None of the above.
answered
Oct 21
in
Graph Theory

325
views
tifr2013
graphtheory
graphcoloring
+2
votes
2
GATE200340
A graph $G=(V,E)$ satisfies $E \leq 3 V  6$. The mindegree of $G$ is defined as $\min_{v\in V}\left\{degree (v)\right \}$. Therefore, mindegree of $G$ cannot be 3 4 5 6
answered
Oct 15
in
Graph Theory

1.3k
views
gate2003
graphtheory
normal
degreeofgraph
+3
votes
3
GATE200672
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 maximum degree of a vertex in G is: $\binom{n/2}{2}2^{n/2}$ $2^{n2}$ $2^{n3}\times 3$ $2^{n1}$
answered
Oct 12
in
Graph Theory

1.2k
views
gate2006
graphtheory
normal
degreeofgraph
+5
votes
4
GATE201238
Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to 15 30 90 360
answered
Oct 11
in
Graph Theory

3.7k
views
gate2012
graphtheory
normal
markstoall
counting
0
votes
5
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 $1/p$ $1/(1  p)$ $1/p^2$ $1/(1  p^2)$
answered
Oct 2
in
Probability

810
views
gate2006it
probability
binomialdistribution
expectation
normal
+1
vote
6
Practice
All Conflict serializable schedule are also view serializable but reverse is not true . True or False
answered
Sep 30
in
Databases

53
views
databases
view_serializable
+3
votes
7
GATE2012_33
Suppose a fair sixsided die is rolled once. If the value on the die is 1, 2, or 3, the die is rolled a second time. What is the probability that the sum total of values that turn up is at least 6? $10/21$ $5/12$ $2/3$ $1/6$
answered
Sep 26
in
Probability

2.2k
views
gate2012
probability
conditionalprobability
bayestheorem
normal
0
votes
8
GATE2006IT1
In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to 25°C, the probability that it will rain in the afternoon is 0.4. ... it will rain in the afternoon on a day when the temperature at noon is above 25°C? 0.4 0.6 0.8 0.9
answered
Sep 25
in
Probability

551
views
gate2006it
probability
normal
0
votes
9
GATE2014248
The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2, 3 or 5 is ______ .
answered
Sep 23
in
Probability

931
views
gate20142
probability
numericalanswers
normal
0
votes
10
GATE200827
Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is 0.6. If she studies mathematics on a day, then the probability that she studies ... on Monday, what is the probability that she studies computer science on Wednesday? 0.24 0.36 0.4 0.6
answered
Sep 23
in
Probability

737
views
gate2008
probability
normal
+2
votes
11
query on exams
what are all the PSUs for CS undergrads which conduct their own exams for recruitment.when will be the exam registration dates for them? Does IIT kanpur,IIIT hyderabad conducts a separate exam for M.tech admissions? is there any other exam other than Gate ,that I could get an M.tech admission in IITs or IISc? please let me know.
answered
Sep 22
in
GATE

51
views
psu
gate
+4
votes
12
GATE 2016129
Consider the following experiment. Step 1. Flip a fair coin twice. Step 2. If the outcomes are (TAILS, HEADS) then output $Y$ and stop. Step 3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output $N$ and stop. ... , then go to Step 1. The probability that the output of the experiment is $Y$ is (up to two decimal places) ____________.
answered
Sep 21
in
Probability

1.8k
views
gate20161
probability
normal
numericalanswers
+1
vote
13
TIFR2011A3
The probability of three consecutive heads in four tosses of a fair coin is. $\frac{1}{4}$ $\frac{1}{8}$ $\frac{1}{16}$ $\frac{3}{16}$ None of the above.
answered
Sep 21
in
Probability

178
views
tifr2011
probability
0
votes
14
TIFR2013A14
An unbiased die is thrown $n$ times. The probability that the product of numbers would be even is $1/(2n)$ $1/[(6n)!]$ $1  6^{n}$ $6^{n}$ None of the above.
answered
Sep 21
in
Probability

212
views
tifr2013
probability
0
votes
15
TIFR2013A13
Doctors $A$ and $B$ perform surgery on patients in stages $III$ and $IV$ of a disease. Doctor $A$ has performed a $100$ surgeries (on $80$ stage $III$ and $20$ stage $IV$ patients) and $80$ out of her $100$ patients have survived ( ... successful There is not enough data since the choice depends on the stage of the disease the patient is suffering from.
answered
Sep 21
in
Probability

369
views
tifr2013
probability
0
votes
16
TIFR2013A6
You are lost in the National park of Kabrastan. The park population consists of tourists and Kabrastanis. Tourists comprise twothirds of the population the park, and give a correct answer to requests for directions with probability $3/4$. The air of Kabrastan ... is again East. What is the probability of East being correct? $1/4$ $1/3$ $1/2$ $2/3$ $3/4$
answered
Sep 21
in
Probability

274
views
tifr2013
probability
+1
vote
17
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
Sep 21
in
Probability

300
views
tifr2012
probability
+2
votes
18
TIFR2011A19
Three dice are rolled independently. What is the probability that the highest and the lowest value differ by 4? $\frac{1}{3}$ $\frac{1}{6}$ $\frac{1}{9}$ $\frac{5}{18}$ $\frac{2}{9}$
answered
Sep 16
in
Probability

323
views
tifr2011
probability
+1
vote
19
EC,GATE2007
An examination consists of two papers , paper1 and paper2 . the probability of failing in paper 1 is 0.3 and that in paper 2 is 0.2 . Given that a student has failed in paper2 , the probability of failing in paper1 is 0.6 .The ... creat sample space and then try to find probability, what's wrong here ? Someone verify pls ...M getting different ans ...
answered
Sep 9
in
Probability

112
views
engineeringmathematics
+1
vote
20
TIFR2014A3
The Fibonacci sequence is defined as follows: $F_{0} = 0, F_{1} = 1,$ and for all integers $n \geq 2, F_{n} = F_{n−1} + F_{n−2}$. Then which of the following statements is FALSE? $F_{n+2} = 1 + \sum ^{n}_{i=0} ... . $F_{4n}$ is a multiple of $3$, for every integer $n \geq 0$. $F_{5n}$ is a multiple of $4$, for every integer $n \geq 0$.
answered
Sep 5
in
Combinatory

160
views
tifr2014
recurrence
easy
–1
vote
21
GATE2004IT34
Let H1, H2, H3, ... be harmonic numbers. Then, for n ∊ Z+, $\sum_{j=1}^{n} H_j$ can be expressed as nHn+1  (n + 1) (n + 1)Hn  n nHn  n (n + 1) Hn+1  (n + 1)
answered
Sep 5
in
Combinatory

646
views
gate2004it
recurrence
permutationsandcombinations
normal
+1
vote
22
application form
i missed uploading thumb impression in gate application form its not given in brochure i got the copy of application form should i worry? I am giving gate 2nd time
answered
Sep 4
in
Others

74
views
gateapplication
–2
votes
23
GATE2008IT25
In how many ways can b blue balls and r red balls be distributed in n distinct boxes? $\frac{(n+b1)!\,(n+r1)!}{(n1)!\,b!\,(n1)!\,r!}$ $\frac{(n+(b+r)1)!}{(n1)!\,(n1)!\,(b+r)!}$ $\frac{n!}{b!\,r!}$ $\frac{(n + (b + r)  1)!} {n!\,(b + r  1)}$
answered
Aug 31
in
Combinatory

871
views
gate2008it
permutationsandcombinations
normal
0
votes
24
GATE1994_1.15
The number of substrings (of all lengths inclusive) that can be formed from a character string of length $n$ is $n$ $n^2$ $\frac{n(n1)}{2}$ $\frac{n(n+1)}{2}$
answered
Aug 31
in
Combinatory

897
views
gate1994
permutationsandcombinations
normal
+1
vote
25
GATE1999_1.3
The number of binary strings of $n$ zeros and $k$ ones in which no two ones are adjacent is $^{n1}C_k$ $^nC_k$ $^nC_{k+1}$ None of the above
answered
Aug 31
in
Combinatory

760
views
gate1999
permutationsandcombinations
normal
0
votes
26
GATE20035
$n$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is \(^{2n}\mathrm{C}_n\times 2^n\) \(3^n\) \(\frac{(2n)!}{2^n}\) \(^{2n}\mathrm{C}_n\)
answered
Aug 31
in
Combinatory

825
views
gate2003
permutationsandcombinations
normal
0
votes
27
GATE200213
In how many ways can a given positive integer $n \geq 2$ be expressed as the sum of 2 positive integers (which are not necessarily distinct). For example, for $n=3$ the number of ways is 2, i.e., 1+2, 2+1. Give only ... $n \geq k$ be expressed as the sum of k positive integers (which are not necessarily distinct). Give only the answer without explanation.
answered
Aug 31
in
Combinatory

465
views
gate2002
permutationsandcombinations
normal
descriptive
0
votes
28
GATE1998_1.23
How many sub strings of different lengths (nonzero) can be found formed from a character string of length $n$? $n$ $n^2$ $2^n$ $\frac{n(n+1)}{2}$
answered
Aug 31
in
Combinatory

1.3k
views
gate1998
permutationsandcombinations
normal
+1
vote
29
TIFR2011A2
In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together? $\displaystyle\frac{(6+3)!}{2!}$ $\displaystyle\frac{6!}{2!}$ $\displaystyle\frac{3!3!}{2!}$ $\displaystyle\frac{4!3!}{2!}$ None of the above.
answered
Aug 31
in
Combinatory

206
views
tifr2011
permutationsandcombinations
+1
vote
30
group theory
Which book to follow for Group Theory ?
answered
Aug 31
in
Set Theory & Algebra

54
views
0
votes
31
TIFR2012A7
It is required to divide the $2n$ members of a club into $n$ disjoint teams of 2 members each. The teams are not labelled. 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
Aug 31
in
Combinatory

482
views
tifr2012
permutationsandcombinations
+4
votes
32
ISI 2004 MIII
A subset S of set of numbers {2,3,4,5,6,7,8,9,10} is said to be good if has exactly 4 elements and their gcd=1, Then number of good subset is 126 125 123 121
answered
Aug 30
in
Combinatory

219
views
permutationsandcombinations
isi2004
0
votes
33
ISI 2004 MIII
A club with x members is organized into four committees such that each member is in exactly two comittees, any two committees have exactly one member in common . Then $x$ has exactly two values both between 4 and 8. exactly one value and this lies between 4 and 8. exactly two values both between 8 and 16. exactly one value and this lies between 8 and 16.
answered
Aug 30
in
Combinatory

156
views
permutationsandcombinations
isi2004
+1
vote
34
TIFR2017A6
How many distinct words can be formed by permuting the letters of the word ABRACADABRA? $\frac{11!}{5! \: 2! \: 2!}$ $\frac{11!}{5! \: 4! }$ $11! \: 5! \: 2! \: 2!\:$ $11! \: 5! \: 4!$ $11! $
answered
Aug 30
in
Combinatory

161
views
tifr2017
permutationsandcombinations
+1
vote
35
TIFR2017A5
How many distinct ways are there to split 50 identical coins among three people so that each person gets at least 5 coins? $3^{35}$ $3^{50}2^{50}$ $\begin{pmatrix} 35 \\ 2 \end{pmatrix}$ $\begin{pmatrix} 50 \\ 15 \end{pmatrix}. 3^{35}$ $\begin{pmatrix} 37 \\ 2 \end{pmatrix}$
answered
Aug 28
in
Combinatory

300
views
tifr2017
permutationsandcombinations
+1
vote
36
GATE19894i
Provide short answers to the following questions: How many substrings (of all lengths inclusive) can be formed from a character string of length $n$? Assume all characters to be distinct, prove your answer.
answered
Aug 28
in
Combinatory

340
views
gate1989
descriptive
permutationsandcombinations
+1
vote
37
ISI 2017
For each positive integer $n$ consider the set $S_n$ defined as follows: $S_1 = \{1\},\:S_2 = \{2, 3\},\:S_3 = \{4,5,6\}, \: \dots $ and in general, $S_{n+1}$ consists of $n+1$ consecutive integers the smallest of which is one more than the largest integer in $S_n$. Then the sum of all the integers in $S_{21}$ equals to 1113 53361 5082 4641
answered
Aug 28
in
Combinatory

157
views
engineeringmathematics
isi2017
permutationsandcombinations
0
votes
38
ISI 2016
A palindrome is a sequence of digits which reads the same backward or forward. For example, 7447, 1001 are palindromes, but 7455, 1201 are not palindromes. How many 8 digit prime palindromes are there?
answered
Aug 28
in
Combinatory

256
views
isi2016
permutationsandcombinations
+1
vote
39
TIFR2012A10
In how many different ways can $r$ elements be picked from a set of $n$ elements if Repetition is not allowed and the order of picking matters? Repetition is allowed and the order of picking does not matter? $\frac{n!}{\left(n  r\right)!}$ and $\frac{\left(n ... {n!}{\left(n  r\right)!}$, respectively. $\frac{n!}{r!}$ and $\frac{r!}{n!}$, respectively.
answered
Aug 27
in
Combinatory

255
views
tifr2012
permutationsandcombinations
+1
vote
40
Engineering mathematics
Standard books required for linear algebra and calculus for gate syllabus ?
answered
Aug 23
in
Linear Algebra

67
views
linear
algebra
and
calculus
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