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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&1&0&0&2&1&0&0&1&0&0&0.55&2
\\\hline\textbf{2 Marks Count}&0&1&1&0&1&0&1&2&1&0&0.77&2
\\\hline\textbf{Total Marks}&1&2&2&2&3&0&2&5&2&0&2.11&5\\\hline
\end{array}}}$$

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Previous GATE Questions in Combinatory

3 votes
3 answers
1
The number of arrangements of six identical balls in three identical bins is _____________ .
Arjun asked in Combinatory Feb 15
by Arjun
1.5k views
15 votes
5 answers
4
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
Arjun asked in Combinatory Feb 18, 2021
by Arjun
5.1k views
15 votes
7 answers
6
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.
Arjun asked in Combinatory Feb 12, 2020
by Arjun
10.2k views
16 votes
14 answers
8
30 votes
11 answers
9
49 votes
9 answers
10
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .
Arjun asked in Combinatory Feb 14, 2017
by Arjun
13.1k views
33 votes
5 answers
11
How many substrings (of all lengths inclusive) can be formed from a character string of length $n$? Assume all characters to be distinct, prove your answer.
makhdoom ghaya asked in Combinatory Nov 30, 2016
4.5k views
11 votes
2 answers
12
The number of ways in which $5\; A's, 5\; B's$ and $5\; C's$ can be arranged in a row is: $15!/(5!)^{3}$ $15!$ $\left(\frac{15}{5}\right)$ $15!(5!3!)$.
makhdoom ghaya asked in Combinatory Nov 22, 2016
2.1k views
32 votes
8 answers
14
54 votes
10 answers
16
49 votes
17 answers
17
39 votes
7 answers
19
55 votes
13 answers
20
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ___...
go_editor asked in Combinatory Feb 14, 2015
10.5k views
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