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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2024-1} & \textbf{2024-2} & \textbf{2023} & \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &0&0&1& 1&1&0&0&0.5&1
\\\hline\textbf{2 Marks Count} &0&0&1& 2 &0&1&0&0.67&2
\\\hline\textbf{Total Marks} & 0&0&3&5 &1&2&0&1.83&5\\\hline
\end{array}}}$$

Hot questions in Combinatory

0 votes

1 answer

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

The number of subwords for w=’SCALABLE” is equal to:343537

Souvik33

865 views

Souvik33 asked Dec 21, 2022

0 votes

0 answers

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

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

TusharKumar

326 views

TusharKumar asked Dec 24, 2022

1 votes

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.

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 a...

admin

403 views

admin asked Dec 15, 2022

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,...

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

Shivam_j

577 views

Shivam_j asked Dec 22, 2022

1 votes

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 $1,2, \ldots, n$.

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

187 views

admin asked Dec 15, 2022

44 votes

4 answers

GATE CSE 2003 | Question: 4
Let $A$ be a sequence of $8$ distinct integers sorted in ascending order. How many distinct pairs of sequences, $B$ and $C$ are there such that each is sorted in ascending order, $B$ has $5$ and $C$ has $3$ elements, and the result of merging $B$ and $C$ gives $A$ $2$ $30$ $56$ $256$

Let $A$ be a sequence of $8$ distinct integers sorted in ascending order. How many distinct pairs of sequences, $B$ and $C$ are there such thateach is sorted in ascending...

Kathleen

13.6k views

Kathleen asked Sep 16, 2014

0 votes

1 answer

Kenneth Rosen Edition 7 Exercise 6.3 Question 39 (Page No. 415)
How many license plates consisting of three letters followed by three digits contain no letter or digit twice?

How many license plates consisting of three letters followed by three digits contain no letter or digit twice?

admin

327 views

admin asked Apr 29, 2020

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.

an = an−1 + bn−1bn = an−1 − bn−1with a0 = 1 and b0 = 2.

chinman12

385 views

chinman12 asked Nov 25, 2022

1 votes

1 answer

Kenneth Rosen Edition 7 Exercise 8.1 Question 13 (Page No. 511)
A string that contains only $0s, 1s,$ and $2s$ is called a ternary string. Find a recurrence relation for the number of ternary strings of length $n$ that do not contain two consecutive $0s.$ What are the initial conditions? How many ternary strings of length six do not contain two consecutive $0s?$

A string that contains only $0s, 1s,$ and $2s$ is called a ternary string.Find a recurrence relation for the number of ternary strings of length $n$ that do not contain t...

admin

368 views

admin asked May 2, 2020

2 votes

2 answers

Gate@Zeal Test Series 2023
Ans: 43333

Ans: 43333

SKMAKM

458 views

SKMAKM asked Sep 19, 2022

0 votes

0 answers

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.

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

356 views

Overflow04 asked Oct 30, 2022

43 votes

11 answers

GATE IT 2004 | Question: 35
In how many ways can we distribute $5$ distinct balls, $B_1, B_2, \ldots, B_5$ in $5$ distinct cells, $C_1, C_2, \ldots, C_5$ such that Ball $B_i$ is not in cell $C_i$, $\forall i= 1,2,\ldots 5$ and each cell contains exactly one ball? $44$ $96$ $120$ $3125$

In how many ways can we distribute $5$ distinct balls, $B_1, B_2, \ldots, B_5$ in $5$ distinct cells, $C_1, C_2, \ldots, C_5$ such that Ball $B_i$ is not in cell $C_i$, $...

Ishrat Jahan

11.7k views

Ishrat Jahan asked Nov 2, 2014

6 votes

2 answers

GO Classes Test Series 2024 | Discrete Mathematics | Test 4 | Question: 13
In a certain land on a planet in a galaxy far away, the alphabet contains only $5$ letters which are $\text{A, I, L, S}$ and $\text{T}.$ All names are $6$ letters long, begin and end ... contain exactly two vowels which are not adjacent to each other. Adjacent consonants must be different. How many possible names are there?

In a certain land on a planet in a galaxy far away, the alphabet contains only $5$ letters which are $\text{A, I, L, S}$ and $\text{T}.$ All names are $6$ letters long, b...

GO Classes

564 views

GO Classes asked May 3, 2022

5 votes

2 answers

GO Classes Test Series 2024 | Discrete Mathematics | Test 4 | Question: 25
The score of a bit string is defined to be the number of $1$'s in that string. For example, the score of $1011$ is $3,$ the score of $01010$ is $2,$ the score of $00$ is $0.$ We want bit strings which ... string must start and end with the symbol $1.$ No two $0$'s are consecutive. How many such bit strings do we have?

The score of a bit string is defined to be the number of $1$’s in that string. For example, the score of $1011$ is $3,$ the score of $01010$ is $2,$ the score of $00$ i...

GO Classes

332 views

GO Classes asked May 3, 2022

23 votes

9 answers

GATE CSE 2003 | Question: 34
$m$ identical balls are to be placed in $n$ distinct bags. You are given that $m \geq kn$, where $k$ is a natural number $\geq 1$. In how many ways can the balls be placed in the bags if each bag must contain at least $k$ ... $\left( \begin{array}{c} m - kn + n + k - 2 \\ n - k \end{array} \right)$

$m$ identical balls are to be placed in $n$ distinct bags. You are given that $m \geq kn$, where $k$ is a natural number $\geq 1$. In how many ways can the balls be place...

Kathleen

11.6k views

Kathleen asked Sep 16, 2014

7 votes

2 answers

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?

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 r...

GO Classes

574 views

GO Classes asked Aug 6, 2022

7 votes

2 answers

GO Classes Test Series 2024 | Discrete Mathematics | Test 4 | Question: 5
By definition, a poker hand is a set of $5$ cards from a standard French deck of $52$ cards. We shall consider a standard French playing deck, which includes thirteen ranks in each of the four French suits. Thus, each ... instance, three sevens and two Queens, or three Aces and two fives. How many full house we can have ?

By definition, a poker hand is a set of $5$ cards from a standard French deck of $52$ cards. We shall consider a standard French playing deck, which includes thirteen ran...

GO Classes

490 views

GO Classes asked May 3, 2022

0 votes

1 answer

Kenneth Rosen Edition 7 Exercise 6.4 Question 33 (Page No. 422)
In this exercise we will count the number of paths in the $xy$ plane between the origin $(0, 0)$ and point $(m, n),$ where $m$ and $n$ are nonnegative integers, such that each path is made up of a series of steps, where each ... move one unit upward. Conclude from part $(A)$ that there are $\binom{m + n}{n}$ paths of the desired type.

In this exercise we will count the number of paths in the $xy$ plane between the origin $(0, 0)$ and point $(m, n),$ where $m$ and $n$ are nonnegative integers, such that...

admin

859 views

admin asked Apr 30, 2020

2 votes

1 answer

Kenneth Rosen Edition 7 Exercise 8.1 Question 11 (Page No. 511)
Find a recurrence relation for the number of ways to climb n stairs if the person climbing the stairs can take one stair or two stairs at a time. What are the initial conditions? In how many ways can this person climb a flight of eight stairs?

Find a recurrence relation for the number of ways to climb n stairs if the person climbing the stairs can take one stair or two stairs at a time.What are the initial cond...

admin

376 views

admin asked May 2, 2020

5 votes

3 answers

100

GO Classes Test Series 2024 | Discrete Mathematics | Test 4 | Question: 12
Consider the set of $4$-digit positive integers. How many of them are odd and don’t have the property that the sum of their digits is even?

Consider the set of $4$-digit positive integers. How many of them are odd and don’t have the property that the sum of their digits is even?

GO Classes

511 views

GO Classes asked May 3, 2022

Page:

« prev
1
2
3
4
5
6
7
8
9
10
...
82
next »

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