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

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

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Highest voted questions in Combinatory

7 votes
3 answers
93
combinatory
How many ways are there for a horse race with 4 horses to finish if ties are possible?(any number of horses may tie)
How many ways are there for a horse race with 4 horses to finish if ties are possible?(any number of horses may tie)
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7 votes
1 answer
95
ISRO2014-19
The number of bit strings of length $8$ that will either start with $1$ or end with $00$ is? $32$ $128$ $160$ $192$
The number of bit strings of length $8$ that will either start with $1$ or end with $00$ is?$32$ $128$ $160$ $192$
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6 votes
0 answers
98
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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6 votes
1 answer
103
Generating function
What is the coefficient of $\large\color{green}{x^{6}}$ in the following series expansion? $\color{maroon}{\begin{align*} \frac{1}{1-x}.\frac{1}{1-x^2}.\frac{1}{1-x^3}........ \end{align*}}$
What is the coefficient of $\large\color{green}{x^{6}}$ in the following series expansion?$$\color{maroon}{\begin{align*} \frac{1}{1-x}.\frac{1}{1-x^2}.\frac{1}{1-x^3}......
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6 votes
1 answer
104
The English alphabet contains 21 consonants and five vowels. How many strings of six lowercase letters of the English alphabet contain a) exactly one vowel? b) exactly two vowels? c) at least one vowel? d) at least two vowels?
Hi Answer to each option is given as:a) 122,523,030b) 72,930,375c) 223,149,655d) 100,626,625And I used the following approach to each option but answers don't match.a) C(...
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6 votes
1 answer
105
GATE CSE 1996 | Question: 9
The Fibonacci sequence $\{f_1, f_2, f_3 \ldots f_n\}$ is defined by the following recurrence:$f_{n+2} = f_{n+1} + f_n, n \geq 1; f_2 =1:f_1=1$Prove by induction that every third element of the sequence is even.
The Fibonacci sequence $\{f_1, f_2, f_3 \ldots f_n\}$ is defined by the following recurrence:$$f_{n+2} = f_{n+1} + f_n, n \geq 1; f_2 =1:f_1=1$$Prove by induction that ev...
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