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Recent questions and answers in Combinatory

8 votes

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

Jaideepyadav910 answered in Combinatory 4 hours ago

by Jaideepyadav910

1.7k views

1 vote

2 answers

2

[email protected] Test Series 2023
Ans: 43333

Pranavpurkar answered in Combinatory Sep 22

by Pranavpurkar

102 views

0 votes

1 answer

3

[email protected] Test Series 2023
Ans: 211

afroze answered in Combinatory Sep 19

by afroze

105 views

1 vote

1 answer

4

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 ?

maverick answered in Combinatory Sep 10

106 views

50 votes

17 answers

5

GATE CSE 2016 Set 1 | Question: 26
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.

[ Jiren ] answered in Combinatory Aug 25

19.4k views

0 votes

1 answer

6

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.

[ Jiren ] answered in Combinatory Aug 25

121 views

1 vote

2 answers

7

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.

Kabir5454 answered in Combinatory Aug 25

130 views

15 votes

8 answers

8

GATE CSE 2020 | Question: 42
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.

[ Jiren ] answered in Combinatory Aug 25

10.5k views

4 votes

2 answers

9

GO Classes Scholarship 2023 | Test | Question: 13
Let $\text{T}_{n}$ be the number of ways to arrange cars in a row with $n$ parking spaces if we can use sedans, SUVs, trucks to park such that a truck requires two spaces, whereas a sedan or SUV requires just one space each, and No two ... i.e. initial conditions are already given, hence no need to compute them)

Udhay_Brahmi answered in Combinatory Aug 24

by Udhay_Brahmi

312 views

44 votes

8 answers

10

GATE CSE 2007 | Question: 84
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. How many distinct paths are there for the ... $(10,10)$ starting from the initial position $(0,0)$? $^{20}\mathrm{C}_{10}$ $2^{20}$ $2^{10}$ None of the above

[ Jiren ] answered in Combinatory Aug 24

8.9k views

34 votes

9 answers

11

GATE CSE 2001 | Question: 2.1
How many $4$-digit even numbers have all $4$ digits distinct? $2240$ $2296$ $2620$ $4536$

TusharRana answered in Combinatory Aug 23

8.8k views

17 votes

15 answers

12

GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____

[ Jiren ] answered in Combinatory Aug 23

13.7k views

5 votes

0 answers

13

Combinatorics : Distinct objects and Distinct boxes
How many ways are there to Distribute 7 distinct objects to 3 Distinct boxes and No box should be Empty Any box can be Empty

[ Jiren ] asked in Combinatory Aug 22

105 views

3 votes

2 answers

14

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 15
In an examination, a question paper consists of $12$ questions divided into two parts i.e, Part I and Part II, containing $5$ and $7$ questions respectively. A student is required to attempt $8$ questions in all, selecting at least $3$ from each part. In how many ways can a student select the questions?

Udhay_Brahmi answered in Combinatory Aug 20

by Udhay_Brahmi

165 views

3 votes

3 answers

15

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 14
The number of ways of selecting at least one Indian and at least one American for a debate from a group comprising $3$ Indians and $4$ Americans and no one else?

Udhay_Brahmi answered in Combinatory Aug 20

by Udhay_Brahmi

168 views

0 votes

1 answer

16

NPTEL Assignment
In how many ways can the word ‘DOCUMENTATION’ be arranged so that all the consonants come together.

Coding skill answered in Combinatory Aug 16

by Coding skill

129 views

0 votes

1 answer

17

Kenneth Rosen Edition 7 Exercise 6.5 Question 59 (Page No. 434)
How many ways are there to distribute five balls into three boxes if each box must have at least one ball in it if both the balls and boxes are labeled? the balls are labeled, but the boxes are unlabeled? the balls are unlabeled, but the boxes are labeled? both the balls and boxes are unlabeled?

ankit-saha answered in Combinatory Aug 15

124 views

1 vote

1 answer

18

Kenneth Rosen Edition 7 Exercise 6.5 Question 58 (Page No. 434)
How many ways are there to distribute five balls into seven boxes if each box must have at most one ball in it if both the balls and boxes are labeled? the balls are labeled, but the boxes are unlabeled? the balls are unlabeled, but the boxes are labeled? both the balls and boxes are unlabeled?

ankit-saha answered in Combinatory Aug 15

181 views

0 votes

1 answer

19

Kenneth Rosen Edition 7 Exercise 6.5 Question 57 (Page No. 434)
How many ways are there to pack nine identical DVDs into three indistinguishable boxes so that each box contains at least two DVDs?

ankit-saha answered in Combinatory Aug 15

115 views

1 vote

1 answer

20

Kenneth Rosen Edition 7 Exercise 6.5 Question 56 (Page No. 434)
How many ways are there to pack eight identical DVDs into five indistinguishable boxes so that each box contains at least one DVD?

ankit-saha answered in Combinatory Aug 15

118 views

1 vote

1 answer

21

Kenneth Rosen Edition 7 Exercise 6.1 Question 41 (Page No. 397)
A palindrome is a string whose reversal is identical to the string. How many bit strings of length $n$ are palindromes?

ankit-saha answered in Combinatory Aug 11

127 views

1 vote

1 answer

22

Kenneth Rosen Edition 7 Exercise 6.1 Question 40 (Page No. 397)
How many subsets of a set with $100$ elements have more than one element?

ankit-saha answered in Combinatory Aug 11

87 views

57 votes

14 answers

23

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 ________.

Himanshu555 answered in Combinatory Aug 11

10.8k views

5 votes

2 answers

24

GO Classes Scholarship 2023 | Test | Question: 4
Consider a $3 \times 11$ rectangular grid as depicted in Figure $1,$ formed by $33$ tiles of area $1\text{m}^2.$ A staircase walk is a path in the grid which moves only right or up. How many staircase walks are there from $\text{A}$ to $\text{B}$ which start by going to the right two times?

[ Jiren ] answered in Combinatory Aug 8

227 views

3 votes

1 answer

25

GO Classes Scholarship 2023 | Test | Question: 5
Consider $5$ cards, each has a distinct value from the set $\{2,3,4,5,6\},$ so there are $5$ different values, and we put them face down on the table. There are $5$ players and each player is given a number from $2$ ... with the value that player has. If no player loses, then the dealer loses. How many ways are there so that the dealer loses?

GO Classes answered in Combinatory Aug 7

168 views

4 votes

1 answer

26

GO Classes Scholarship 2023 | Test | Question: 6
Consider three boxes and $12$ balls of the same size. We have $3$ indistinguishable red balls and $9$ distinguishable blue balls. The first box can fit at most three balls, the second box can fit at most four balls and the third box can fit ... all the red balls go into the same box. What is the total number of ways to put all the balls in the boxes?

GO Classes answered in Combinatory Aug 7

178 views

3 votes

1 answer

27

GO Classes Scholarship 2023 | Test | Question: 7
Define the generating functions $\text{B}(x)=\displaystyle{} \sum_{n=0}^{\infty} 2^{n} x^{n}$ and $F(x)=\displaystyle{} \sum_{n=0}^{\infty} f_{n} x^{n}$ where $f_{n}$ ... $x^{5}$ is $\mathrm{G}(x)?$

GO Classes answered in Combinatory Aug 7

157 views

54 votes

13 answers

28

GATE CSE 2014 Set 1 | Question: 49
A pennant is a sequence of numbers, each number being $1$ or $2$. An $n-$pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a $4-$pennant. The set of all possible $1-$pennants is ${(1)}$, the set of all possible ... $(1,2)$ is not the same as the pennant $(2,1)$. The number of $10-$pennants is________

Argharupa Adhikary answered in Combinatory Jul 31

by Argharupa Adhikary

7.2k views

0 votes

1 answer

29

Mathematics for Natural Science
Prove that $2n < (n + 1)!, $ for all $ n \geq 3.$

Kabir5454 answered in Combinatory Jul 29

56 views

0 votes

1 answer

30

Mathematics for Natural Science
Simplify $(A\cup B)\cap (A\cup B')\cap (A - B)$ for a given non empty sets $A$ and $B$, where $(A\cap B) = \varnothing .$

Kabir5454 answered in Combinatory Jul 29

59 views

0 votes

0 answers

31

Mathematics for Natural Science
Let y in the form of $a + bi$, where $a$ and $b$ are real numbers, be the cubic roots of complex number $z^{20},$ where $z=\frac{2}{4 + 3i}.$ Find $a + b.$

kidussss asked in Combinatory Jul 29

74 views

0 votes

1 answer

32

Cengage algebra jee advanced.
Coefficient of x^8 in ( (1-x^6)/(1-x) )^3.

Kabir5454 answered in Combinatory Jul 24

108 views

3 votes

3 answers

33

UGC NET CSE | Junet 2015 | Part 2 | Question: 3
In how many ways can $15$ indistinguishable fish be placed into $5$ different ponds, so that each pond contains at least one fish? $1001$ $3876$ $775$ $200$

Vasudevarnab23 answered in Combinatory Jul 21

by Vasudevarnab23

4.0k views

5 votes

2 answers

34

UGC NET CSE | Junet 2015 | Part 2 | Question: 1
How many strings of $5$ digits have the property that the sum of their digits is $7$? $66$ $330$ $495$ $99$

Vasudevarnab23 answered in Combinatory Jul 21

by Vasudevarnab23

2.0k views

33 votes

5 answers

35

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.

neopentane answered in Combinatory Jul 20

4.6k views

0 votes

2 answers

36

Kenneth Rosen Edition 7 Exercise 6.4 Question 25 (Page No. 422)
Let n be a positive integer. Show that $\binom{2n}{n + 1} + \binom{2n}{n} = \dfrac{\binom{2n + 2}{n + 1}}{2}.$

ASNR1010 answered in Combinatory Jul 14

109 views

0 votes

3 answers

37

Discrete Mathematics
Any Good resource to understand this topic.

Kushal06 answered in Combinatory Jul 13

514 views

0 votes

1 answer

38

Discrete Mathematics
Somebody please clarify the answer

GateOverflow04 asked in Combinatory Jul 11

by GateOverflow04

116 views

0 votes

0 answers

39

Discrete Mathematics and Combinatorics
Solve the recurrence relation $a^{2}n-5a^{2}_{n-1}+4a^{2} _{n-2}=0$, if $a_{0}=4, a_{1}=13, n>1$

kidussss asked in Combinatory Jul 9

148 views

3 votes

2 answers

40

GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 1
How many words can be formed by re-arranging the letters of the word “PROBLEMS” such that $P$ and $S$ occupy the first and last position respectively? (Note: The words thus formed need not be meaningful)

GO Classes asked in Combinatory Jun 14

288 views

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Recent questions and answers in Combinatory