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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2024-1} & \textbf{2024-2} & \textbf{2023} & \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &0&0&1& 1&1&0&0&0.5&1
\\\hline\textbf{2 Marks Count} &0&0&1& 2 &0&1&0&0.67&2
\\\hline\textbf{Total Marks} & 0&0&3&5 &1&2&0&1.83&5\\\hline
\end{array}}}$$

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Most viewed questions in Combinatory

1 votes
3 answers
201
ISI2018-MMA-5
One needs to choose six real numbers $x_1,x_2,....,x_6$ such that the product of any five of them is equal to other number. The number of such choices is $3$ $33$ $63$ $93$
One needs to choose six real numbers $x_1,x_2,....,x_6$ such that the product of any five of them is equal to other number. The number of such choices is$3$$33$$63$$93$
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2 votes
1 answer
203
Kenneth Rosen Edition 7 Exercise 6.5 Question 13 (Page No. 432)
A book publisher has $3000$ copies of a discrete mathematics book. How many ways are there to store these books in their three warehouses if the copies of the book are indistinguishable?
A book publisher has $3000$ copies of a discrete mathematics book. How many ways are there to store these books in their three warehouses if the copies of the book are in...
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0 votes
1 answer
204
Kenneth Rosen Edition 7 Exercise 6.2 Question 1 (Page No. 405)
Show that in any set of six classes, each meeting regularly once a week on a particular day of the week, there must be two that meet on the same day, assuming that no classes are held on weekends.
Show that in any set of six classes, each meeting regularly once a week on a particular day of the week, there must be two that meet on the same day, assuming that no cla...
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0 votes
1 answer
205
NIELIT 2017 DEC Scientist B - Section B: 15
In how many ways $8$ girls and $8$ boys can sit around a circular table so that no two boys sit together? $(7!)^2$ $(8!)^2$ $7!8!$ $15!$
In how many ways $8$ girls and $8$ boys can sit around a circular table so that no two boys sit together?$(7!)^2$$(8!)^2$$7!8!$$15!$
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2 votes
2 answers
207
[Discrete Maths] Counting ,Number of solutions to the equation
How many solutions are there to the equation x1 + x2 + x3 + x4 + x5 = 21, where xi , i = 1, 2, 3, 4, 5, is a nonnegative integer such that: 0 ≤ x1 ≤ 3 , 1 ≤ x2 < 4 and 15≤x3 ?
How many solutions are there to the equationx1 + x2 + x3 + x4 + x5 = 21,where xi , i = 1, 2, 3, 4, 5, is a nonnegative integer such that:0 ≤ x1 ≤ 3 , 1 ≤ x2 < 4 an...
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1 votes
2 answers
209
log question
if (x lg x)=4608 , then how to calculate value of x ? Base is 2
if (x lg x)=4608 , then how to calculate value of x ?Base is 2
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0 votes
1 answer
210
Pigeon hole principle
A teacher gives a multiple choice quiz that has 5 questions, each with 4 possible answers: a, b, c,d What is the minimum number of students that must be in the class in order to guarantee that at least 4 answer sheets will be identical? how to do this problem
A teacher gives a multiple choice quiz that has 5 questions, each with4 possible answers: a, b, c,d What is the minimum number of students thatmust be in the class in ord...
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5 votes
1 answer
212
Kenneth Rosen Edition 6th Exercise 5.5 Question 46 (Page No. 381)
46) A shelf holds 12 books in a row. How many ways are there to choose five books so that no two adjacent books are chosen?
46) A shelf holds 12 books in a row. How many ways are there to choose five books so that no two adjacent books are chosen?
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2 votes
1 answer
213
Combination
The Solution of the recurrence relation An-2An-1=2n where A0=1 ?
The Solution of the recurrence relation An-2An-1=2n where A0=1 ?
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0 votes
1 answer
214
Kenneth Rosen: Counting-13
How many bit strings with length not exceeding $n$ ,where n is a positive integer ,consist entirely of $1's?$
How many bit strings with length not exceeding $n$ ,where n is a positive integer ,consist entirely of $1's?$
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1 votes
2 answers
216
Permutation and Combination
A mint prepares metallic calendars specifying months , dates and days in the form of monthly sheets (one plate for each month ) . how many type of feburary calendars should be prepare to serve all the possibilities in the future year ?
A mint prepares metallic calendars specifying months , dates and days in the form of monthly sheets (one plate for each month ) . how many type of feburary calendars shou...
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0 votes
1 answer
217
Kenneth Rosen Edition 7 Exercise 8.2 Question 22 (Page No. 525)
What is the general form of the solutions of a linear homogeneous recurrence relation if its characteristic equation has the roots $-1, -1, -1, 2, 2, 5, 5, 7?$
What is the general form of the solutions of a linear homogeneous recurrence relation if its characteristic equation has the roots $-1, -1, -1, 2, 2, 5, 5, 7?$
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1 votes
1 answer
218
Combination of 4 Letter in MATHEMATICS?
The given word is MATHEMATICS which can be arranged in different ways by taking some or all the letters used in the word. the number of words that can be formed by taking 4 letters at a time out of the letters of the given word.
The given word is MATHEMATICS which can be arranged in different ways by taking some or all the letters used in the word.the number of words that can be formed by taking ...
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4 votes
3 answers
219
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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