Recent questions and answers in Combinatory

Recent questions and answers in Combinatory

2 votes

4 answers

1

GATE CSE 2022 | Question: 26
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below? $ a_{n} = \left\{\begin{matrix} n + 1, & \text{n is odd} & \\ 1, & \text{otherwise} & \end{matrix}\right.$ ... $\frac{2x}{(1-x^{2})^{2}} + \frac{1}{1-x}$ $\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$

ankitgupta.1729 answered in Combinatory 2 days ago

by ankitgupta.1729

804 views

0 votes

1 answer

2

No of 5 letter english words that contains atleast one 'a' ?
No of 5 letter english words that contains atleast one 'a' ? i used the approch that

Kabir5454 answered in Combinatory May 15

21 views

1 vote

3 answers

3

ISI2017-MMA-26
Let $n$ be the number of ways in which $5$ men and $7$ women can stand in a queue such that all the women stand consecutively. Let $m$ be the number of ways in which the same $12$ persons can stand in a queue such that exactly $6$ women stand consecutively. Then the value of $\frac{m}{n}$ is $5$ $7$ $\frac{5}{7}$ $\frac{7}{5}$

s_dr_13 answered in Combinatory Apr 26

915 views

1 vote

1 answer

4

NIELIT 2022 Jan Scientist B | Section B | Question: 48
The particular solution of the recurrence relation $a_{r+2} – 4a_{r+1} + 4a_{r} = 2^{r}$ is: $r.2^{r}$ $r(r-1)2^{r-1}$ $r(r-1)2^{r-2}$ $r(r-1)2^{r-3}$

Kabir5454 answered in Combinatory Apr 18

55 views

5 votes

5 answers

5

GATE CSE 2022 | Question: 41
Consider the following recurrence: $\begin{array}{} f(1) & = & 1; \\ f(2n) & = & 2f(n) - 1, & \; \text{for}\; n \geq 1; \\ f(2n+1) & = & 2f(n) + 1, & \; \text{for}\; n \geq 1. \end{array}$ Then, which of the following statements is/are $\text{TRUE}?$ ... $f(2^{n}) = 1$ $f(5 \cdot 2^{n}) = 2^{n+1} + 1$ $f(2^{n} + 1) = 2^{n} + 1$

ankitgupta.1729 answered in Combinatory Apr 14

by ankitgupta.1729

1.2k views

1 vote

1 answer

6

Self Doubt
Give a combinatorial argument to establish the identity below for any nonnegative integer n: $\sum_{k=0}^{n} k\binom{n}{k}=n\ast 2^{n-1}$

dd answered in Combinatory Mar 15

by dd

73 views

1 vote

3 answers

7

ACE Test Series: Generating Function
The generating function of the sequence $\left \{ a_{0},a_{1},a_{2}..........a_{n}………...\infty \right \}$ where $a_{n}=\left ( n+2 \right )\left ( n+1 \right ).3^{n}$ is $a)3\left ( 1+3x \right )^{-2}$ $b)3\left ( 1-3x \right )^{-2}$ $c)2\left ( 1+3x \right )^{-3}$ $d)2\left ( 1-3x \right )^{-3}$

s_dr_13 answered in Combinatory Mar 12

921 views

3 votes

3 answers

8

GATE CSE 2022 | Question: 22
The number of arrangements of six identical balls in three identical bins is _____________ .

Chandrabhan Vishwa 1 answered in Combinatory Feb 16

by Chandrabhan Vishwa 1

1.1k views

0 votes

1 answer

9

combinatorics
How many 5-digit even numbers have all digits distinct?

Isha_99 answered in Combinatory Jan 12

127 views

0 votes

1 answer

10

madeeasy test series
Plz explain this..If possible share some resources.

Zack Fair answered in Combinatory Jan 9

191 views

0 votes

0 answers

11

(Closed) Probability, P&C doubt cleared
Question - If there is a bag that has 2 balls, with the colour of the balls being unknown, what is the probability that both turn out to be blue coloured balls? My doubt - which of the 2 following methods is correct and why : 1) Both balls can either ... : 0 blue balls, 1 blue ball or 2 blue balls as the order of balls doesn't matter here hence $\frac{1}{3}$

o asked in Combinatory Dec 30, 2021

by o

126 views

1 vote

2 answers

12

Kenneth Rosen Edition 7th Exercise 8.1 Question 25 (Page No. 511)
How many bit sequences of length seven contain an even number of $0s?$

Isha_99 answered in Combinatory Dec 28, 2021

149 views

3 votes

3 answers

13

Applied Test Series
The number of possible ways in which 5 identical helicopters can take off given that we are having 5 helipads.____

LRU asked in Combinatory Nov 9, 2021

by LRU

251 views

1 vote

1 answer

14

Applied Test Series
There are 4 parts of an encyclopedia which are available in a library which are arranged on the shelf along with other books on a shelf which add up to a total 25 books, if the books are arranged randomly then the number of ways in which the encyclopedia is in the correct order is (the parts need not be beside each other)____

LRU asked in Combinatory Nov 9, 2021

by LRU

128 views

1 vote

1 answer

15

Combinatorics Question| Discrete Maths
Suppose there are 4 cricket matches to be played in 3 grounds. The number of ways the matches can be assigned to the grounds so that each ground gets at least one match is

Acejoy asked in Combinatory Oct 25, 2021

by Acejoy

185 views

2 votes

1 answer

16

Applied Test Series
A Professor tells 3 Jokes in his maths class each year. How large a set of jokes does the professor need in order never to repeat the exact same triple of jokes over a period of 12 years?_________

LRU asked in Combinatory Oct 15, 2021

by LRU

160 views

0 votes

1 answer

17

gateacademy testseries
In how many ways can seven different jobs be assigned to four different employees so that each employee is assigned at least one job and the most difficult job is assigned to the best employee?

Sanjay chauhan 123 asked in Combinatory Sep 6, 2021

by Sanjay chauhan 123

122 views

1 vote

1 answer

18

gateacademy test series
There are 12 stations on a rail route. How many ways a special train can stop at 4 of these stations, so that no two stops are consecutive stations? please explain in detail

Sanjay chauhan 123 asked in Combinatory Sep 6, 2021

by Sanjay chauhan 123

128 views

15 votes

5 answers

19

GATE CSE 2021 Set 2 | Question: 50
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________

Arjun asked in Combinatory Feb 18, 2021

by Arjun

4.7k views

16 votes

3 answers

20

GATE CSE 2021 Set 1 | Question: 19
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that: The fastest computer gets the toughest job and the slowest computer gets the easiest job. Every computer gets at least one job. The number of ways in which this can be done is ___________.

Arjun asked in Combinatory Feb 18, 2021

by Arjun

4.8k views

1 vote

0 answers

21

JEST2020
For two n-bit strings x, y ∈ {0, 1}n, define z := x ⊕ y to be the bitwise XOR of the two strings (that is, if xi, yi, zi denote the i-th bits of x, y, z respectively, then zi = xi + yi mod 2). A function h : {0, 1}n → {0, 1}n is called linear if h(x ⊕ y) = h(x) ⊕ h(y), for every x, y ∈ {0, 1}n. The number of such linear functions for n ≥ 2: 2^n 2^2n 2^(n+1) n

vivek_mishra asked in Combinatory Feb 15, 2021

by vivek_mishra

312 views

2 votes

2 answers

22

UGCNET-Oct2020-II: 2
How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books? $4$ $6$ $7$ $9$

go_editor asked in Combinatory Nov 20, 2020

1.8k views

2 votes

1 answer

23

K H Rosen Ex
15. a) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces are chosen? b) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces and ... cards must be chosen from a standard deck of 52 cards to guarantee that there are at least two cards of each of two different kinds?

Sanjay Sharma asked in Combinatory Jul 4, 2020

by Sanjay Sharma

504 views

4 votes

1 answer

24

Counting number of pairs whose sum is less than k
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k > 0$. Solve by summation rules. Solve by combinatorial argument.

dd asked in Combinatory Jun 8, 2020

by dd

772 views

0 votes

1 answer

25

Kenneth Rosen Edition 7th Exercise 8.3 Question 16 (Page No. 535)
Solve the recurrence relation for the number of rounds in the tournament described in question $14.$

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

765 views

0 votes

1 answer

26

Kenneth Rosen Edition 7th Exercise 8.3 Question 15 (Page No. 535)
How many rounds are in the elimination tournament described in question $14$ when there are $32$ teams?

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

296 views

0 votes

2 answers

27

Kenneth Rosen Edition 7th Exercise 8.3 Question 14 (Page No. 535)
Suppose that there are $n = 2^{k}$ teams in an elimination tournament, where there are $\frac{n}{2}$ games in the first round, with the $\frac{n}{2} = 2^{k-1}$ winners playing in the second round, and so on. Develop a recurrence relation for the number of rounds in the tournament.

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

740 views

0 votes

1 answer

28

Kenneth Rosen Edition 7th Exercise 8.3 Question 13 (Page No. 535)
Give a big-O estimate for the function $f$ given below if $f$ is an increasing function. $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

330 views

1 vote

2 answers

29

Kenneth Rosen Edition 7th Exercise 8.3 Question 12 (Page No. 535)
Find $f (n)$ when $n = 3k,$ where $f$ satisfies the recurrence relation $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

303 views

0 votes

1 answer

30

Kenneth Rosen Edition 7th Exercise 8.3 Question 11 (Page No. 535)
Give a big-O estimate for the function $f$ in question $10$ if $f$ is an increasing function.

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

209 views

0 votes

1 answer

31

Kenneth Rosen Edition 7th Exercise 8.3 Question 10 (Page No. 535)
Find $f (n)$ when $n = 2^{k},$ where $f$ satisfies the recurrence relation $f (n) = f (n/2) + 1 \:\text{with}\: f (1) = 1.$

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

184 views

0 votes

1 answer

32

Kenneth Rosen Edition 7th Exercise 8.3 Question 9 (Page No. 535)
Suppose that $f (n) = f (n/5) + 3n^{2}$ when $n$ is a positive integer divisible by $5, \:\text{and}\: f (1) = 4.$ Find $f (5)$ $f (125)$ $f (3125)$

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

167 views

0 votes

1 answer

33

Kenneth Rosen Edition 7th Exercise 8.3 Question 8 (Page No. 535)
Suppose that $f (n) = 2f (n/2) + 3$ when $n$ is an even positive integer, and $f (1) = 5.$ Find $f (2)$ $f (8)$ $f (64)$ $(1024)$

Lakshman Patel RJIT asked in Combinatory May 10, 2020

by Lakshman Patel RJIT

231 views

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