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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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Most viewed questions in Combinatory

0 votes
2 answers
152
Kenneth Rosen Edition 7 Exercise 6.5 Question 7 (Page No. 432)
How many ways are there to select three unordered elements from a set with five elements when repetition is allowed?
How many ways are there to select three unordered elements from a set with five elements when repetition is allowed?
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0 votes
1 answer
153
ISI2019-MMA-2
The number of $6$ digit positive integers whose sum of the digits is at least $52$ is $21$ $22$ $27$ $28$
The number of $6$ digit positive integers whose sum of the digits is at least $52$ is$21$$22$$27$$28$
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0 votes
1 answer
154
NPTEL Question
Find the particular solution of the given Recurrence relation or Difference equation. ar - 5ar-1 + 6ar-2 = 2r + r
Find the particular solution of the given Recurrence relation or Difference equation.ar - 5ar-1 + 6ar-2 = 2r + r
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16 votes
6 answers
155
TIFR CSE 2018 | Part A | Question: 6
What is the minimum number of students needed in a class to guarantee that there are at least $6$ students whose birthdays fall in the same month ? $6$ $23$ $61$ $72$ $91$
What is the minimum number of students needed in a class to guarantee that there are at least $6$ students whose birthdays fall in the same month ?$6$$23$$61$$72$$91$
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2 votes
3 answers
157
Self Doubt: Permutations & Combinations
How many solutions are there to the equation $x+y+z=17$ in positive integers? $120$ $171$ $180$ $121$
How many solutions are there to the equation $x+y+z=17$ in positive integers?$120$$171$$180$$121$
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1 votes
1 answer
159
Kenneth Rosen Edition 6th Exercise 6.4 Question 33 (Page No. 442)
Use generating function to solve the recurrence relation $a_k=3{a_{k-1}} + 2$ with initial conditions $a_0=1 $.
Use generating function to solve the recurrence relation $a_k=3{a_{k-1}} + 2$ with initial conditions $a_0=1 $.
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2 votes
2 answers
162
UGC NET CSE | October 2020 | Part 2 | Question: 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$$9$
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0 votes
2 answers
163
Rosen 7e Exercise-8.1 Question no-10 Page no-511
Find a recurrence relation for the number of bit strings of length n that contain the string 01.
Find a recurrence relation for the number of bit strings of length n that contain the string 01.
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0 votes
1 answer
164
Kenneth Rosen Edition 7 Exercise 6.5 Question 1 (Page No. 432)
In how many different ways can five elements be selected in order from a set with three elements when repetition is allowed?
In how many different ways can five elements be selected in order from a set with three elements when repetition is allowed?
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14 votes
5 answers
165
ISI 2004 MIII
The number of permutation of $\{1,2,3,4,5\}$ that keep at least one integer fixed is. $81$ $76$ $120$ $60$
The number of permutation of $\{1,2,3,4,5\}$ that keep at least one integer fixed is.$81$$76$$120$$60$
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3 votes
3 answers
166
KENETH ROSEN
How many different ways are there to seat four people around a circular table, where two seatings are considered the same when each person has the same left neighbor and the same right neighbor? ANSWER IS 6 OR 3 .????
How many different ways are there to seat four people around a circular table, where two seatings are considered the same when each person has the same left neighbor and ...
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1 votes
2 answers
167
Use generating function to solve question
Use generating function to determine the number of different ways 10 identical balloons can be given to 4 children if each children receives at least 2 balloons.
Use generating function to determine the number of different ways 10 identical balloons can be given to 4 children if each children receives at least 2 balloons.
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0 votes
3 answers
168
Kenneth Rosen Edition 7 Exercise 6.1 Question 12 (Page No. 396)
How many bit strings are there of length six or less, not counting the empty string?
How many bit strings are there of length six or less, not counting the empty string?
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0 votes
2 answers
169
UGC NET CSE | December 2012 | Part 3 | Question: 25
The number of distinct bracelets of five beads made up of red, blue and green beads (two bracelets are indistinguishable if the rotation of one yield another) is, 243 81 51 47
The number of distinct bracelets of five beads made up of red, blue and green beads (two bracelets are indistinguishable if the rotation of one yield another) is,24381514...
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20 votes
8 answers
170
TIFR CSE 2015 | Part A | Question: 7
A $1 \times 1$ chessboard has one square, a $2 \times 2$ chessboard has five squares. Continuing along this fashion, what is the number of squares on the regular $8 \times 8$ chessboard? $64$ $65$ $204$ $144$ $256$
A $1 \times 1$ chessboard has one square, a $2 \times 2$ chessboard has five squares. Continuing along this fashion, what is the number of squares on the regular $8 \time...
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