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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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Recent questions in Combinatory

1 votes
1 answer
99
NIELIT 2022 April Scientist B | Section B | Question: 48
The particular solution of the recurrence relation $a_{r+2} – 4a_{r+1} + 4a_{r} = 2^{r}$ is: $r.2^{r}$ $r(r-1)2^{r-1}$ $r(r-1)2^{r-2}$ $r(r-1)2^{r-3}$
The particular solution of the recurrence relation $a_{r+2} – 4a_{r+1} + 4a_{r} = 2^{r}$ is:$r.2^{r}$$r(r-1)2^{r-1}$$r(r-1)2^{r-2}$$r(r-1)2^{r-3}$
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1 votes
1 answer
100
Self Doubt
Give a combinatorial argument to establish the identity below for any nonnegative integer n: $\sum_{k=0}^{n} k\binom{n}{k}=n\ast 2^{n-1}$
Give a combinatorial argument to establish the identity below for any nonnegative integer n:$\sum_{k=0}^{n} k\binom{n}{k}=n\ast 2^{n-1}$
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17 votes
3 answers
101
GATE CSE 2022 | Question: 22
The number of arrangements of six identical balls in three identical bins is _____________ .
The number of arrangements of six identical balls in three identical bins is _____________ .
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2 votes
1 answer
104
GATE Overflow Test Series | Mock GATE | Test 6 | Question: 12
A decimal number is called “increasing” if each digit is greater than the previous one (e.g., $1267$ is one increasing number). The total number of $5$ digit increasing numbers is _______
A decimal number is called “increasing” if each digit is greater than the previous one (e.g., $1267$ is one increasing number). The total number of $5$ digit increasi...
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0 votes
1 answer
106
combinatorics
How many 5-digit even numbers have all digits distinct?
How many 5-digit even numbers have all digits distinct?
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0 votes
1 answer
107
madeeasy test series
Plz explain this..If possible share some resources.
Plz explain this..If possible share some resources.
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1 votes
1 answer
109
NPTEL Assignment Question
The number of possible subsequences in a string of length n are: $n^{2}$ $2^{n}$ n! n(n-1)
The number of possible subsequences in a string of length n are:$n^{2}$$2^{n}$ n!n(n-1)
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3 votes
3 answers
110
Applied Test Series
The number of possible ways in which 5 identical helicopters can take off given that we are having 5 helipads.____
The number of possible ways in which 5 identical helicopters can take off given that we are having 5 helipads.____
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