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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

4 votes
1 answer
162
test series counting
The number of pairs of set (X, Y) are there that satisfy the condition X, Y ⊆ {1, 2, 3, 4, 5, 6} and X ∩ Y = Φ ________.
The number of pairs of set (X, Y) are there that satisfy the condition X, Y ⊆ {1, 2, 3,4, 5, 6} and X ∩ Y = Φ ________.
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4 votes
2 answers
164
Generating function
Find $\large\color{maroon}{a^n}$ for the following generating function, $\color{green}{\begin{align*} \frac{1}{1-2x^2} \end{align*}}$ $\large\color{maroon}{a^n}$ = closed form of the $nth$ term in the corresponding sequence.
Find $\large\color{maroon}{a^n}$ for the following generating function,$$\color{green}{\begin{align*} \frac{1}{1-2x^2} \end{align*}}$$$\large\color{maroon}{a^n}$ = closed...
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4 votes
3 answers
165
Number of solutions
Number of non negative integer solutions to the equation X1 + X2 + X3 + X4 = 15, where $1 \leqslant X1,X2,X3,X4 \leqslant6$ is ________
Number of non negative integer solutions to the equation X1 + X2 + X3 + X4 = 15, where $1 \leqslant X1,X2,X3,X4 \leqslant6$ is ________
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4 votes
2 answers
167
generalised pigeonhole principle
Show that if seven integers are selected from the first 10 positive integers, there must be at least two pairs of these integers with the sum 11. Attempt-:partition will be {(1,10),(2,9),(3,8)(4,7)(5,6)} now how to apply pigeonhole principle to find the answer?
Show that if seven integers are selected from the first10 positive integers, there must be at least two pairsof these integers with the sum 11.Attempt-:partition will be ...
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4 votes
1 answer
168
UGC NET CSE | June 2016 | Part 3 | Question: 31
The number of different binary trees with 6 nodes is 6 42 132 256
The number of different binary trees with 6 nodes is642132256
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4 votes
2 answers
169
GATE Overflow | Mathematics | Test 1 | Question: 25
A 6 digit number 123ABC is exactly divisible by $5,7$ and $9$. How many such possible numbers are there ? 2 3 4 5
A 6 digit number 123ABC is exactly divisible by $5,7$ and $9$. How many such possible numbers are there ?2 3 4 5
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4 votes
1 answer
170
UGC NET CSE | December 2015 | Part 2 | Question: 1
How many committees of five people can be chosen from 20 men and 12 women such that each committee contains at least three women 75240 52492 41800 9900
How many committees of five people can be chosen from 20 men and 12 women such that each committee contains at least three women7524052492418009900
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4 votes
3 answers
172
Combination
For a game in which 2 partners oppose 2 other partners, six men are available. If every possible pair must play against every other pair, the number of games to be played is 9a) 36 (b) 45 (c) 42 (d) 90
For a game in which 2 partners oppose 2 other partners, six men are available. If every possible pair must play against every other pair, the number of games to be played...
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4 votes
2 answers
173
number of function
How many functions are there from the set {1, 2, . . . , n}, where n is a positive integer, to the set {0, 1} a) that assign 1 to exactly one of the positive integers less than n?
How many functions are there from the set {1, 2, . . . , n}, where n is a positive integer, to the set {0, 1}a) that assign 1 to exactly one of the positive integers les...
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3 votes
2 answers
177
GO Classes 2023 | IIITH Mock Test 1 | Question: 4
How many ways are there to arrange the $12$ letters of $\text{AAABBBBCCCCC}$ without having two $\text{Cs}$ together? $2652$ $1960$ $1826$ $2260$
How many ways are there to arrange the $12$ letters of $\text{AAABBBBCCCCC}$ without having two $\text{Cs}$ together?$2652$$1960$$1826$$2260$
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