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

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

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Recent questions in Combinatory

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41
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?
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42
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,...
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1 answer
43
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
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1 votes
0 answers
44
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 $1,2, \ldots, n$.
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1 votes
1 answer
45
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 $F_{0}=F_{1}=1$.
What is the generating function corresponding to Fibonacci series.\[F_{n}=F_{n-1}+F_{n-2} .\]Note that $F_{0}=F_{1}=1$.
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1 votes
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46
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...
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2 votes
1 answer
47
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?
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 gar...
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1 votes
1 answer
48
DRDO CSE 2022 Paper 1 | Question: 19
How many seven digit numbers are possible with exactly four $4 \mathrm{s}?$
How many seven digit numbers are possible with exactly four $4 \mathrm{s}?$
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50
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.
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0 votes
1 answer
51
Gate@Zeal Test Series 2023
Ans: 211
Ans: 211
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2 votes
2 answers
52
Gate@Zeal Test Series 2023
Ans: 43333
Ans: 43333
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1 votes
1 answer
53
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 ?
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 ?
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1 votes
2 answers
57
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.
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 cand...
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6 votes
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58
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
How many ways are there to Distribute 7 distinct objects to 3 Distinct boxes andNo box should be EmptyAny box can be Empty
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0 votes
1 answer
59
NPTEL Assignment
In how many ways can the word ‘DOCUMENTATION’ be arranged so that all the consonants come together.
In how many ways can the word ‘DOCUMENTATION’ be arranged so that all the consonants come together.
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