Recent questions in Combinatory

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

$$\small{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&2&1&0&0&1&0&0&0.7&1
\\\hline\textbf{2 Marks Count}&0&1&0&1&2&1&0&0.8&2
\\\hline\textbf{Total Marks}&2&3&0&2&5&2&0&2.3&5\\\hline
\end{array}}}$$