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Recent questions and answers in Combinatory

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1

kenneth rosen, counting, exercise: 6.5, question: 50
How many ways are there to distribute five distinguishable objects into three indistinguishable boxes?

Roshakaw asked in Combinatory Mar 24

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0 answers

2

Kenneth Rosen, exercise: 6.2, question: 8
Show that if f is a function from S to T , where S and T are finite sets with |S| > |T |, then there are elements s1 and s2 in S such that f (s1) = f (s2), or in other words, f is not one-to-one. How can I prove it by using “proof by contradiction”? Is it possible to prove the same by using “proof by contraposition”? If yes, how?

Roshakaw asked in Combinatory Mar 23

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2 answers

3

Can any one solve this , 6B and 4G ,at least 2 girls should be together in circular arrangement

saiyam answered in Combinatory Mar 21

by saiyam

55 views

40 votes

5 answers

4

GATE CSE 2015 Set 1 | Question: 26
$\sum\limits_{x=1}^{99}\frac{1}{x(x+1)}$ = ______.

39Gaurav_singh answered in Combinatory Mar 11

by 39Gaurav_singh

6.2k views

1 vote

2 answers

5

Recurrence Relation Self-Doubt
What will be solution of recurrence relation if roots are like this: r1=-2, r2=2, r3=-2, r4=2 is this the case of repetitive roots?

Bharat Bhushan answered in Combinatory Mar 9

by Bharat Bhushan

466 views

21 votes

1 answer

6

Recurrence Relation - Self Doubt
What is the recurrence relation for the ternary strings of length $n$ which can be constructed using 0,1 or 2 only such that the number of 0’s and number of 1's is odd ?

Bharat Bhushan answered in Combinatory Mar 9

by Bharat Bhushan

584 views

0 votes

2 answers

7

Discrete Maths by Kenneth Rosen, exercise 6.1, Qs - 12
How many bit strings are there of length six or less, not counting the empty string? Solution given:- We use the sum rule, adding the number of bit strings of each length up to 6. If we include the empty string, then we get 2^0 ... a binary string such as 000100 of length 3, and so on Please let me know if I am wrong somewhere in my approach.

Bharat Bhushan answered in Combinatory Mar 5

by Bharat Bhushan

73 views

1 vote

0 answers

8

Kenneth Rosen, exercise 6.1, Qs - 42 (d)
How many 4-element DNA sequences contain exactly three of the four bases A, T, C, and G? Solution given: There are four ways to choose which letter is to occur twice and three ways to decide which of the other letters to leave ... wrong. It would be of great help if you can show what combinations my approach is not including but the given solution includes.

Roshakaw asked in Combinatory Mar 3

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1 answer

9

#Combinatorics #Self doubt
How many 3 digits number are there which are divisible by 3 and repetition of digits NOT allowed.?

hdutta answered in Combinatory Feb 21

by hdutta

192 views

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1 answer

10

#Combinatorics and Counting # Permutations and Combinations
If each of ‘a’ points on a straight line is joined to each of ‘b’ points on another straight line, excluding the points on the given two lines,then which of the following represents the number of points of intersection of these lines? Select all that apply. (ab(a-1)(b-1))/4 (ab(a-1)(b-1))/2 ab C(a,2) * C(b,2)

Roshakaw answered in Combinatory Feb 17

72 views

4 votes

1 answer

11

GATE CSE 2023 | Question: 5
The Lucas sequence $L_{n}$ is defined by the recurrence relation: \[ L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3, \] with $L_{1}=1$ and $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$

ankitgupta.1729 answered in Combinatory Feb 15

by ankitgupta.1729

941 views

4 votes

0 answers

12

GATE CSE 2023 | Question: 38
Let $U=\{1,2, \ldots, n\},$ where $n$ is a large positive integer greater than $1000.$ Let $k$ be a positive integer less than $n$. Let $A, B$ be subsets of $U$ with $|A|=|B|=k$ and $A \cap B=\emptyset$. We say that a permutation of $U$ separates $A$ from $B$ if ... $2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k !)^{2}$

admin asked in Combinatory Feb 15

by admin

973 views

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2 answers

13

GATE CSE 2023 | Memory Based Question: 15
The Lucas sequence $L_n$ is defined by the recurrence relation: $L_n=L_{n-1}+L_{n-2}$, for $n \geq 3$ with $L_1=1$ and $L_2=3$. Which one of the options given is TRUE? $L_n=\left(\frac{1+\sqrt{5}}{2}\right)^n+\left(\frac{1-\sqrt{5}}{3}\right)^n$ ... $L_n=\left(\frac{1+\sqrt{5}}{2}\right)^n+\left(\frac{1-\sqrt{5}}{2}\right)^n$ closed

ankitgupta.1729 answered in Combinatory Feb 10

by ankitgupta.1729

468 views

1 vote

1 answer

14

GATE CSE 2023 | Memory Based Question: 16
How many permutations of $U$ separate $A$ from $B?$ $2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k!)^2$ $\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k)!(n!)$ $n!$ $\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k !)^2$ closed

Deepak Poonia answered in Combinatory Feb 6

by Deepak Poonia

427 views

2 votes

1 answer

15

DRDO CSE 2022 Paper 1 | Question: 18
A gardener wants to buy $3$ neem plants, $5$ rose plants and $1$ banyan plant from a nursery having $7$ neem, $10$ rose and $6$ banyan plants. How many choices does a gardener have?

elsar martin answered in Combinatory Feb 2

by elsar martin

75 views

61 votes

15 answers

16

GATE CSE 2015 Set 3 | Question: 5
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.

GNANESWARA SAI answered in Combinatory Jan 28

by GNANESWARA SAI

11.9k views

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0 answers

17

#selfdoubt
Let n players enter a chess tournament. How many tournament trees are possible? RULES: a player is eliminated after one loss and games are played until only one entrant is left(assume no ties) My approach: (please check if it is correct) there are 3 possible binary tree skeletons w.r.t ... )C2 * (n-4)C2 *...*1} * 2^(n-1) similarly we can do the remaining cases. Is the above method right?

robinofautumn asked in Combinatory Jan 11

by robinofautumn

46 views

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0 answers

18

Unacademy AIMT 1
How many integers are there in the set {1,2,3,…..,1000} with no digit being repeated?

TusharKumar asked in Combinatory Dec 25, 2022

163 views

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0 answers

19

kenneth h rosen chapter 6
What is the closed form for the generating function for the sequence : 0,1,-2,4,-8,16,-32,64,... closed

Shivam_j asked in Combinatory Dec 23, 2022

148 views

0 votes

1 answer

20

Number Of Substrings | Made Easy Test Series
The number of subwords for w=’SCALABLE” is equal to: 34 35 37

Souvik33 answered in Combinatory Dec 21, 2022

330 views

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1 answer

21

Kenneth Rosen Edition 7 Exercise 6.2 Question 45 (Page No. 407)
Let $x$ be an irrational number. Show that for some positive integer $j$ not exceeding the positive integer $n,$ the absolute value of the difference between $j x$ and the nearest integer to $j x$ is less than $1/n.$

rsjbits answered in Combinatory Dec 19, 2022

232 views

1 vote

1 answer

22

DRDO CSE 2022 Paper 1 | Question: 15
What is the generating function corresponding to Fibonacci series. \[F_{n}=F_{n-1}+F_{n-2} .\] Note that $F_{0}=F_{1}=1$.

Shubhodeep answered in Combinatory Dec 16, 2022

135 views

1 vote

1 answer

23

DRDO CSE 2022 Paper 1 | Question: 19
How many seven digit numbers are possible with exactly four $4 \mathrm{s}?$

rsansiya111 answered in Combinatory Dec 16, 2022

54 views

1 vote

0 answers

24

DRDO CSE 2022 Paper 1 | Question: 14
Derangements are permutations $\pi$ of the set $\{1,2, \ldots, n\}$ such that $\pi(i) \neq i.$ Compute the number of derangements on the set $1,2, \ldots, n$.

admin asked in Combinatory Dec 15, 2022

by admin

52 views

1 vote

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25

DRDO CSE 2022 Paper 1 | Question: 16
Let us say we have a supply of $1$ rupee and $2$ rupee coins in large quantities. What is the generating function for the number of ways of giving change with $1$ rupee and $2$ rupee coins.

admin asked in Combinatory Dec 15, 2022

by admin

64 views

1 vote

2 answers

26

GATE DIscrete Solve Recurrence Relation
Solve the Recurrence Relation S(r) - 6 S(r-1) +8 S(r-2) = 3r; S(0) =8, S(1)=7

manoj0606 answered in Combinatory Dec 13, 2022

1.4k views

42 votes

8 answers

27

GATE CSE 2016 Set 2 | Question: 29
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.

Jaideep Singh answered in Combinatory Nov 27, 2022

by Jaideep Singh

14.0k views

0 votes

1 answer

28

Solve the simultaneous recurrence relations
an = an−1 + bn−1 bn = an−1 − bn−1 with a0 = 1 and b0 = 2.

Kabir5454 answered in Combinatory Nov 26, 2022

166 views

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0 answers

29

Engineering Mathematics
Can somebody brief description about this topic(means formula or link to study). Actually this question is asked in TOC test, but looking more like mathematics part.

Overflow04 asked in Combinatory Oct 30, 2022

117 views

2 votes

2 answers

30

Ace Test series: Combinatory - Generating Functions
Answer is B as given in solution.

Abhrajyoti00 answered in Combinatory Oct 12, 2022

by Abhrajyoti00

324 views

1 vote

1 answer

31

binomial coefficient

Gate Shark answered in Combinatory Oct 12, 2022

451 views

11 votes

6 answers

32

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 $\text{TRUE}?$ ... $f(2^{n}) = 1$ $f(5 \cdot 2^{n}) = 2^{n+1} + 1$ $f(2^{n} + 1) = 2^{n} + 1$

dutta18 answered in Combinatory Oct 11, 2022

4.0k views

20 votes

5 answers

33

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.$ ... $\frac{2x}{(1-x^{2})^{2}} + \frac{1}{1-x}$ $\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$

Jaideep Singh answered in Combinatory Oct 7, 2022

by Jaideep Singh

4.2k views

0 votes

1 answer

34

[email protected] Test Series 2023
Ans: 211

SKMAKM asked in Combinatory Sep 19, 2022

by SKMAKM

281 views

1 vote

2 answers

35

[email protected] Test Series 2023
Ans: 43333

SKMAKM asked in Combinatory Sep 19, 2022

by SKMAKM

234 views

1 vote

1 answer

36

igate test series
Selection of how many integers from the first ten positive integers (1, 2, ...) guarantees that there must be a pair of these integers with a sum equal to 11 ?

jugnu1337 asked in Combinatory Sep 7, 2022

248 views

2 votes

1 answer

37

TIFR CSE 2022 | Part B | Question: 9
Let $n \geq 2$ be any integer. Which of the following statements is $\text{FALSE}?$ $n!$ divides the product of any $n$ consecutive integers $\displaystyle{}\sum_{i=0}^n\left(\begin{array}{c}n \\ i\end{array}\right)=2^n$ ... an odd prime, then $n$ divides $2^{n-1}-1$ $n$ divides $\left(\begin{array}{c}2 n \\ n\end{array}\right)$

admin asked in Combinatory Sep 1, 2022

by admin

143 views

0 votes

1 answer

38

TIFR CSE 2022 | Part A | Question: 1
A snail crawls up a vertical pole $75$ feet high, starting from the ground. Each day it crawls up $5$ feet, and each night it slides down $4$ feet. When will it first reach the top of the pole? $75^{\text {th}}$ day $74^{\text {th}}$ day $73^{ \text{rd}}$ day $72^{\text {nd }}$ day $71^{\text {st }}$ day

Lakshman Patel RJIT asked in Combinatory Sep 1, 2022

by Lakshman Patel RJIT

267 views

0 votes

1 answer

39

combinatorics problem-2
How many ways are there to distribute 5 distinct toys among 3 children such that every child gets at least 1 toy? answer given is 150. but I'm getting 9. My approach go as follows: step-1 : give 1 toy to all 3 children, now, I am left with (5-3) = ... to either of first or second or third child. thus, toy1 has 3 choices and so do toy2. Therefore, my answer would be 3*3 = 9.

Roshakaw asked in Combinatory Aug 25, 2022

250 views

1 vote

2 answers

40

Combinatorics
How many ways are there to distribute 10 identical candies among 3 children such that the first child receives at least 2 candies, the second child receives atmost 6 candies and the third child receives atmost 3 candies.

Roshakaw asked in Combinatory Aug 25, 2022

277 views

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