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Recent questions in Combinatory

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

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

Recent questions in Combinatory

4 votes
5 answers
1
GATE CSE 2021 Set 2 | Question: 50
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 ___________
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 ___________
asked Feb 18 in Combinatory Arjun 974 views
5 votes
2 answers
2
GATE CSE 2021 Set 1 | Question: 19
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that: The fastest computer gets the toughest job and the slowest computer gets the easiest job. Every computer gets at least one job. The number of ways in which this can be done is ___________.
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that: The fastest computer gets the toughest job and the slowest computer gets the easiest job. Every computer gets at least one job. The number of ways in which this can be done is ___________.
asked Feb 18 in Combinatory Arjun 1k views
1 vote
0 answers
3
JEST2020
For two n-bit strings x, y ∈ {0, 1}n, define z := x ⊕ y to be the bitwise XOR of the two strings (that is, if xi, yi, zi denote the i-th bits of x, y, z respectively, then zi = xi + yi mod 2). A function h : {0, 1}n → {0, 1}n is called linear if h(x ⊕ y) = h(x) ⊕ h(y), for every x, y ∈ {0, 1}n. The number of such linear functions for n ≥ 2: 2^n 2^2n 2^(n+1) n
For two n-bit strings x, y ∈ {0, 1}n, define z := x ⊕ y to be the bitwise XOR of the two strings (that is, if xi, yi, zi denote the i-th bits of x, y, z respectively, then zi = xi + yi mod 2). A function h : {0, 1}n → {0, 1}n is called linear if h(x ⊕ y) = h(x) ⊕ h(y), for every x, y ∈ {0, 1}n. The number of such linear functions for n ≥ 2: 2^n 2^2n 2^(n+1) n
asked Feb 15 in Combinatory vivek_mishra 162 views
2 votes
2 answers
4
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 Nov 20, 2020 in Combinatory jothee 598 views
2 votes
1 answer
5
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, 2020 in Combinatory Sanjay Sharma 338 views
4 votes
1 answer
6
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, 2020 in Combinatory dd 470 views
0 votes
2 answers
9
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, 2020 in Combinatory Lakshman Patel RJIT 279 views
0 votes
1 answer
10
Kenneth Rosen Edition 7th Exercise 8.3 Question 13 (Page No. 535)
Give a big-O estimate for the function $f$ given below if $f$ is an increasing function. $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$
Give a big-O estimate for the function $f$ given below if $f$ is an increasing function. $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$
asked May 10, 2020 in Combinatory Lakshman Patel RJIT 215 views
0 votes
1 answer
14
Kenneth Rosen Edition 7th Exercise 8.3 Question 9 (Page No. 535)
Suppose that $f (n) = f (n/5) + 3n^{2}$ when $n$ is a positive integer divisible by $5, \:\text{and}\: f (1) = 4.$ Find $f (5)$ $f (125)$ $f (3125)$
Suppose that $f (n) = f (n/5) + 3n^{2}$ when $n$ is a positive integer divisible by $5, \:\text{and}\: f (1) = 4.$ Find $f (5)$ $f (125)$ $f (3125)$
asked May 10, 2020 in Combinatory Lakshman Patel RJIT 76 views
0 votes
1 answer
15
Kenneth Rosen Edition 7th Exercise 8.3 Question 8 (Page No. 535)
Suppose that $f (n) = 2f (n/2) + 3$ when $n$ is an even positive integer, and $f (1) = 5.$ Find $f (2)$ $f (8)$ $f (64)$ $(1024)$
Suppose that $f (n) = 2f (n/2) + 3$ when $n$ is an even positive integer, and $f (1) = 5.$ Find $f (2)$ $f (8)$ $f (64)$ $(1024)$
asked May 10, 2020 in Combinatory Lakshman Patel RJIT 72 views
0 votes
1 answer
16
Kenneth Rosen Edition 7th Exercise 8.3 Question 7 (Page No. 535)
Suppose that $f (n) = f (n/3) + 1$ when $n$ is a positive integer divisible by $3,$ and $f (1) = 1.$ Find $f (3)$ $f (27)$ $f (729)$
Suppose that $f (n) = f (n/3) + 1$ when $n$ is a positive integer divisible by $3,$ and $f (1) = 1.$ Find $f (3)$ $f (27)$ $f (729)$
asked May 10, 2020 in Combinatory Lakshman Patel RJIT 64 views
0 votes
0 answers
18
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, 2020 in Combinatory Lakshman Patel RJIT 68 views
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