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1

TIFR CSE 2013 | Part B | Question: 1
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 ... $a\left(G\right)\leq \frac{n}{\chi \left(G\right)}$ None of the above

answered in Graph Theory Oct 21, 2017

3.6k views

29 votes

2

GATE CSE 2003 | Question: 40
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-degree of $G$ cannot be $3$ $4$ $5$ $6$

answered in Graph Theory Oct 15, 2017

12.8k views

15 votes

3

GATE CSE 2006 | Question: 72
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: $\binom{\frac{n}{2}}{2}.2^{\frac{n}{2}}$ $2^{n-2}$ $2^{n-3}\times 3$ $2^{n-1}$

answered in Graph Theory Oct 12, 2017

15.2k views

96 votes

4

GATE CSE 2012 | Question: 38
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 in Graph Theory Oct 11, 2017

29.7k views

7 votes

5

GATE IT 2006 | Question: 22
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 in Probability Oct 2, 2017

7.3k views

2 votes

6

Practice
All Conflict serializable schedule are also view serializable but reverse is not true . True or False

answered in Databases Sep 30, 2017

441 views

23 votes

7

GATE CSE 2012 | Question: 33
Suppose a fair six-sided 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 $6$ ? $\dfrac{10}{21}$ $\dfrac{5}{12}$ $\dfrac{2}{3}$ $\dfrac{1}{6}$

answered in Probability Sep 26, 2017

18.3k views

5 votes

8

GATE IT 2006 | Question: 1
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 $0.4$. The temperature ... in the afternoon on a day when the temperature at noon is above $25°C$? $0.4$ $0.6$ $0.8$ $0.9$

answered in Probability Sep 25, 2017

5.6k views

7 votes

9

GATE CSE 2014 Set 2 | Question: 48
The probability that a given positive integer lying between $1$ and $100$ (both inclusive) is NOT divisible by $2$, $3$ or $5$ is ______ .

answered in Probability Sep 23, 2017

10.9k views

6 votes

10

GATE CSE 2008 | Question: 27
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 computer ... what is the probability that she studies computer science on Wednesday? $0.24$ $0.36$ $0.4$ $0.6$

answered in Probability Sep 23, 2017

6.1k views

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 in GATE Sep 22, 2017

407 views

29 votes

12

GATE CSE 2016 Set 1 | Question: 29
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. Step 4. If ... , TAILS), then go to Step $1.$ The probability that the output of the experiment is $Y$ is (up to two decimal places)

answered in Probability Sep 21, 2017

9.0k views

3 votes

13

TIFR CSE 2011 | Part A | Question: 3
The probability of three consecutive heads in four tosses of a fair coin is $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{8}\right)$ $\left(\dfrac{1}{16}\right)$ $\left(\dfrac{3}{16}\right)$ None of the above

answered in Probability Sep 21, 2017

2.4k views

4 votes

14

TIFR CSE 2013 | Part A | Question: 14
An unbiased die is thrown $n$ times. The probability that the product of numbers would be even is $\dfrac{1}{(2n)}$ $\dfrac{1}{[(6n)!]}$ $1 - 6^{-n}$ $6^{-n}$ None of the above

answered in Probability Sep 21, 2017

1.3k views

2 votes

15

TIFR CSE 2013 | Part A | Question: 13
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 ... she appears to be more successful There is not enough data since the choice depends on the stage of the disease the patient is suffering from.

answered in Probability Sep 21, 2017

1.1k views

0 votes

16

TIFR CSE 2013 | Part A | Question: 6
You are lost in the National park of Kabrastan. The park population consists of tourists and Kabrastanis. Tourists comprise two-thirds of the population the park and give a correct answer to requests for directions with probability $\dfrac{3}{4}$. The air of Kabrastan has an ... $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{2}{3}\right)$ $\left(\dfrac{3}{4}\right)$

answered in Probability Sep 21, 2017

2.6k views

8 votes

17

TIFR CSE 2012 | Part A | Question: 20
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 in Probability Sep 21, 2017

2.2k views

14 votes

18

TIFR CSE 2011 | Part A | Question: 19
Three dice are rolled independently. What is the probability that the highest and the lowest value differ by $4$? $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{9}\right)$ $\left(\dfrac{5}{18}\right)$ $\left(\dfrac{2}{9}\right)$

answered in Probability Sep 16, 2017

2.4k views

5 votes

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 probability of student ... i just creat sample space and then try to find probability, what's wrong here ? Someone verify pls ...M getting different ans ...

answered in Probability Sep 9, 2017

3.1k views

4 votes

20

TIFR CSE 2014 | Part A | Question: 3
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? $F_{n+2} = 1 + \sum ^{n}_{i=0} F_{i}$ ... $3$, for every integer $n \geq 0$. $F_{5n}$ is a multiple of $4$, for every integer $n \geq 0$.

answered in Combinatory Sep 5, 2017

1.3k views

1 vote

21

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 in Others Sep 4, 2017

343 views

0 votes

22

GATE CSE 1999 | Question: 1.3
The number of binary strings of $n$ zeros and $k$ ones in which no two ones are adjacent is $^{n-1}C_k$ $^nC_k$ $^nC_{k+1}$ None of the above

answered in Combinatory Aug 31, 2017

7.4k views

1 vote

23

GATE CSE 2002 | Question: 13
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 in Combinatory Aug 31, 2017

5.7k views

–3 votes

24

GATE CSE 1998 | Question: 1.23
How many sub strings of different lengths (non-zero) can be formed from a character string of length $n$? $n$ $n^2$ $2^n$ $\frac{n(n+1)}{2}$

answered in Combinatory Aug 31, 2017

12.1k views

0 votes

25

TIFR CSE 2011 | Part A | Question: 2
In how many ways can the letters of the word $\text{ABACUS}$ be rearranged such that the vowels always appear together? $\dfrac{(6+3)!}{2!}$ $\dfrac{6!}{2!}$ $\dfrac{3!3!}{2!}$ $\dfrac{4!3!}{2!}$ None of the above

answered in Combinatory Aug 31, 2017

1.3k views

1 vote

26

group theory
Which book to follow for Group Theory ?

answered in Set Theory & Algebra Aug 31, 2017

703 views

26 votes

27

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 in Combinatory Aug 30, 2017

2.4k views

–1 vote

28

ISI 2004 MIII
A club with $x$ members is organized into four committees such that each member is in exactly two committees, 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 in Combinatory Aug 30, 2017

1.3k views

3 votes

29

TIFR CSE 2017 | Part A | Question: 5
How many distinct ways are there to split $50$ identical coins among three people so that each person gets at least $5$ coins? $3^{35}$ $3^{50}-2^{50}$ $\binom{35}{2}$ $\binom{50}{15} \cdot 3^{35}$ $\binom{37}{2}$

answered in Combinatory Aug 28, 2017

3.4k views

0 votes

30

GATE CSE 1989 | Question: 4-i
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 in Combinatory Aug 28, 2017

5.4k views

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