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Recent questions in Combinatory

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

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

Recent questions in Combinatory

0 votes
1 answer
1
UGCNET-Oct2020-II: 2
How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books? $4$ $6$ $7$ $9$
How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books? $4$ $6$ $7$ $9$
asked 5 days ago in Combinatory jothee 38 views
2 votes
1 answer
2
K H Rosen Ex
15. a) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces are chosen? b) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces and ... cards must be chosen from a standard deck of 52 cards to guarantee that there are at least two cards of each of two different kinds?
15. a) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces are chosen? b) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces and at least ... many cards must be chosen from a standard deck of 52 cards to guarantee that there are at least two cards of each of two different kinds?
asked Jul 4 in Combinatory Sanjay Sharma 300 views
4 votes
1 answer
3
Counting number of pairs whose sum is less than k
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k > 0$. Solve by summation rules. Solve by combinatorial argument.
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k > 0$. Solve by summation rules. Solve by combinatorial argument.
asked Jun 8 in Combinatory dd 379 views
0 votes
2 answers
6
Kenneth Rosen Edition 7th Exercise 8.3 Question 14 (Page No. 535)
Suppose that there are $n = 2^{k}$ teams in an elimination tournament, where there are $\frac{n}{2}$ games in the first round, with the $\frac{n}{2} = 2^{k-1}$ winners playing in the second round, and so on. Develop a recurrence relation for the number of rounds in the tournament.
Suppose that there are $n = 2^{k}$ teams in an elimination tournament, where there are $\frac{n}{2}$ games in the first round, with the $\frac{n}{2} = 2^{k-1}$ winners playing in the second round, and so on. Develop a recurrence relation for the number of rounds in the tournament.
asked May 10 in Combinatory Lakshman Patel RJIT 165 views
0 votes
0 answers
15
Kenneth Rosen Edition 7th Exercise 8.3 Question 5 (Page No. 535)
Determine a value for the constant C in Example $4$ and use it to estimate the number of bit operations needed to multiply two $64$-bit integers using the fast multiplication algorithm.
Determine a value for the constant C in Example $4$ and use it to estimate the number of bit operations needed to multiply two $64$-bit integers using the fast multiplication algorithm.
asked May 10 in Combinatory Lakshman Patel RJIT 50 views
1 vote
0 answers
20
Kenneth Rosen Edition 7th Exercise 8.2 Question 52 (Page No. 527)
Prove Theorem $6:$Suppose that $\{a_{n}\}$ satisfies the liner nonhomogeneous recurrence relation $a_{n} = c_{1}a_{n-1} + c_{2}a_{n-2} + \dots + c_{k}a_{n-k} + F(n),$ where $c_{1}.c_{2},\dots,c_{k}$ ... solution of the form $n^{m}(p_{t}n^{t} + p_{t-1}n^{t-1} + \dots + p_{1}n + p_{0})s^{n}.$
Prove Theorem $6:$Suppose that $\{a_{n}\}$ satisfies the liner nonhomogeneous recurrence relation $a_{n} = c_{1}a_{n-1} + c_{2}a_{n-2} + \dots + c_{k}a_{n-k} + F(n),$ where $c_{1}.c_{2},\dots,c_{k}$ ... is $m,$ there is a particular solution of the form $n^{m}(p_{t}n^{t} + p_{t-1}n^{t-1} + \dots + p_{1}n + p_{0})s^{n}.$
asked May 6 in Combinatory Lakshman Patel RJIT 53 views
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