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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
3 answers
401
Discrete Mathematics
Any Good resource to understand this topic.
Any Good resource to understand this topic.
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0 votes
1 answer
403
Kenneth Rosen Edition 7 Exercise 6.1 Question 45 (Page No. 397)
How many ways are there to seat six people around a circular table where two seating are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors?
How many ways are there to seat six people around a circular table where two seating are considered the same when everyone has the same two neighbors without regard to wh...
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0 votes
1 answer
404
Kenneth Rosen Edition 7 Exercise 6.5 Question 42 (Page No. 433)
In bridge, the $52$ cards of a standard deck are dealt to four players. How many different ways are there to deal bridge hands to four players?
In bridge, the $52$ cards of a standard deck are dealt to four players. How many different ways are there to deal bridge hands to four players?
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0 votes
3 answers
405
NET nov-17 paper-2 Q8
Let P and Q be two propositions , ~(P<->Q) is equivalent to : a)P<->~Q b)~P<->Q c)~P<->~Q d)Q->P
Let P and Q be two propositions , ~(P<->Q) is equivalent to :a)P<->~Q b)~P<->Q c)~P<->~Q d)Q->P
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5 votes
1 answer
406
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.
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0 votes
1 answer
407
Find Sum of four digit Number
Find the sum of all four digit numbers that can be formed by the digits {0,1,2,3,4}? a)183450 b)259980 c)266640 d)6600
Find the sum of all four digit numbers that can be formed by the digits {0,1,2,3,4}?a)183450b)259980c)266640d)6600
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0 votes
1 answer
408
Kenneth Rosen Edition 7 Exercise 6.2 Question 6 (Page No. 405)
Let $d$ be a positive integer. Show that among any group of $d + 1$ (not necessarily consecutive) integers there are two with exactly the same remainder when they are divided by $d.$
Let $d$ be a positive integer. Show that among any group of $d + 1$ (not necessarily consecutive) integers there are two with exactly the same remainder when they are div...
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0 votes
0 answers
410
MadeEasy Full Length Test: Combinatory - Recurrence
What’s the trick to do it under 2 min here?
What’s the trick to do it under 2 min here?
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0 votes
1 answer
411
rosen excercise
How many solutions are there to the equation x1 + x2 + x3 + x4 + x5 + x6 = 29, where xi , i = 1, 2, 3, 4, 5, 6, is a nonnegative integer such that a) x1 ≤ 5? b) x1 < 8 and x2 > 8?
How many solutions are there to the equationx1 + x2 + x3 + x4 + x5 + x6 = 29,where xi , i = 1, 2, 3, 4, 5, 6, is a nonnegative integer suchthata) x1 ≤ 5?b) x1 < 8 and x...
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0 votes
1 answer
412
In how many ways can 2n+1 seats in a congress be divided among 3 parties ?
In how many ways can $2n+1$ seats in a congress be divided among 3 parties so that coalition of any 2 parties will ensure them majority?
In how many ways can $2n+1$ seats in a congress be divided among 3 parties so that coalition of any 2 parties will ensure them majority?
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0 votes
1 answer
413
Kenneth Rosen Edition 7 Exercise 6.1 Question 34 (Page No. 397)
How many different functions are there from a set with $10$ elements to sets with the following numbers of elements? $2$ $3$ $4$ $5$
How many different functions are there from a set with $10$ elements to sets with the following numbers of elements?$2$$3$$4$$5$
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0 votes
2 answers
414
permutations
The number of ways in which 6 rings can be worn on the four fingers of one hand is: a. 360 b. 4^6 c. 6C4 d. 6^4
The number of ways in which 6 rings can be worn on the four fingers of one hand is:a. 360b. 4^6c. 6C4d. 6^4
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1 votes
1 answer
416
NIELIT 2022 April Scientist B | Section B | Question: 48
The particular solution of the recurrence relation $a_{r+2} – 4a_{r+1} + 4a_{r} = 2^{r}$ is: $r.2^{r}$ $r(r-1)2^{r-1}$ $r(r-1)2^{r-2}$ $r(r-1)2^{r-3}$
The particular solution of the recurrence relation $a_{r+2} – 4a_{r+1} + 4a_{r} = 2^{r}$ is:$r.2^{r}$$r(r-1)2^{r-1}$$r(r-1)2^{r-2}$$r(r-1)2^{r-3}$
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0 votes
0 answers
417
Pigeonhole Principle
During a month with 30 days, a baseball team plays at least one game a day, but no more than 45 games. Show that there must be a period of some number of consecutive days during which the team must play exactly 14 games.
During a month with 30 days, a baseball team plays at least one game a day, but no morethan 45 games. Show that there must be a period of some number of consecutive days ...
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3 votes
0 answers
418
combinatrics
How many 7 length bit strings have atleast 3 consecutive ones?
How many 7 length bit strings have atleast 3 consecutive ones?
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0 votes
3 answers
420
Permutations and combinations
In how any ways can 8 different shirts be distributed among 4 different people so that each recieves 2 shirts?
In how any ways can 8 different shirts be distributed among 4 different people so that each recieves 2 shirts?
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