Syllabus: Combinatorics: Counting, Recurrence relations, Generating functions.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1&1&0&0&2&1&0&0&1&0&0&0.6&2
\\\hline\textbf{2 Marks Count} & 2 &0&1&1&0&1&0&1&2&1&0&0.9&2
\\\hline\textbf{Total Marks} & 5 &1&2&2&2&3&0&2&5&2&0&2.4&5\\\hline
\end{array}}}$$

Recent questions in Combinatory

0 votes

2 answers

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

Shivank121 asked in Combinatory 3 days ago

by Shivank121

42 views

1 vote

0 answers

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

by Roshakaw

75 views

0 votes

2 answers

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.

Roshakaw asked in Combinatory Mar 2

by Roshakaw

63 views

0 votes

1 answer

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

Hattbc asked in Combinatory Feb 17

by Hattbc

186 views

4 votes

1 answer

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 $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$

admin asked in Combinatory Feb 15

by admin

890 views

4 votes

0 answers

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

929 views

0 votes

2 answers

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

GO Classes asked in Combinatory Feb 6

by GO Classes

446 views

1 vote

1 answer

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

GO Classes asked in Combinatory Feb 6

by GO Classes

420 views

0 votes

1 answer

#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)

lekh asked in Combinatory Jan 21

by lekh

70 views

0 votes

0 answers

#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

45 views

21 votes

1 answer

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 ?

AKASH G asked in Combinatory Dec 31, 2022

by AKASH G

575 views

0 votes

0 answers

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

by TusharKumar

160 views

0 votes

0 answers

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

by Shivam_j

142 views

0 votes

1 answer

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

Souvik33 asked in Combinatory Dec 21, 2022

by Souvik33

311 views

1 vote

0 answers

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

50 views

1 vote

1 answer

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 $F_{0}=F_{1}=1$.

admin asked in Combinatory Dec 15, 2022

by admin

129 views

1 vote

0 answers

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

62 views

2 votes

1 answer

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?

admin asked in Combinatory Dec 15, 2022

by admin

71 views

1 vote

1 answer

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

admin asked in Combinatory Dec 15, 2022

by admin

53 views

0 votes

1 answer

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

chinman12 asked in Combinatory Nov 25, 2022

by chinman12

159 views

Page:

tags	tag:apple
author	user:martin
title	title:apple
content	content:apple
exclude	-tag:apple
force match	+apple
views	views:100
score	score:10
answers	answers:2
is accepted	isaccepted:true
is closed	isclosed:true

Recent questions in Combinatory

Subscribe to GATE CSE 2023 Test Series

Subscribe to GO Classes for GATE CSE 2023

Subjects

Network Sites

Recent questions in Combinatory

Subscribe to GATE CSE 2023 Test Series

Subscribe to GO Classes for GATE CSE 2023

Recent Posts

Subjects

Recent Blog Comments

Network Sites