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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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Highest voted questions in Combinatory

23 votes
3 answers
45
GATE CSE 1998 | Question: 1.23
How many sub strings of different lengths (non-zero) can be formed from a character string of length $n$? $n$ $n^2$ $2^n$ $\frac{n(n+1)}{2}$
How many sub strings of different lengths (non-zero) can be formed from a character string of length $n$?$n$$n^2$$2^n$$\frac{n(n+1)}{2}$
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22 votes
1 answer
47
Recurrence Relation - Self Doubt
What is the recurrence relation for the ternary strings of length $n$ which can be constructed using 0,1 or 2 only such that the number of 0’s and number of 1's is odd ?
What is the recurrence relation for the ternary strings of length $n$ which can be constructed using 0,1 or 2 only such that the number of 0’s and number of 1's is od...
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20 votes
8 answers
52
TIFR CSE 2015 | Part A | Question: 7
A $1 \times 1$ chessboard has one square, a $2 \times 2$ chessboard has five squares. Continuing along this fashion, what is the number of squares on the regular $8 \times 8$ chessboard? $64$ $65$ $204$ $144$ $256$
A $1 \times 1$ chessboard has one square, a $2 \times 2$ chessboard has five squares. Continuing along this fashion, what is the number of squares on the regular $8 \time...
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19 votes
18 answers
53
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
The value of $3^{51} \text{ mod } 5$ is _____
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19 votes
5 answers
54
ISI 2004 MIII
In how many ways can three person, each throwing a single die once, make a score of $11$ $22$ $27$ $24$ $38$
In how many ways can three person, each throwing a single die once, make a score of $11$$22$$27$$24$$38$
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19 votes
4 answers
55
ISI 2004 MIII
A subset $S$ of set of numbers $\{2,3,4,5,6,7,8,9,10\}$ is said to be good if has exactly $4$ elements and their $gcd=1$, Then number of good subset is $126$ $125$ $123$ $121$
A subset $S$ of set of numbers $\{2,3,4,5,6,7,8,9,10\}$ is said to be good if has exactly $4$ elements and their $gcd=1$, Then number of good subset is$126$$125$$123$$121...
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19 votes
4 answers
56
TIFR CSE 2017 | Part A | Question: 5
How many distinct ways are there to split $50$ identical coins among three people so that each person gets at least $5$ coins? $3^{35}$ $3^{50}-2^{50}$ $\binom{35}{2}$ $\binom{50}{15} \cdot 3^{35}$ $\binom{37}{2}$
How many distinct ways are there to split $50$ identical coins among three people so that each person gets at least $5$ coins?$3^{35}$$3^{50}-2^{50}$$\binom{35}{2}$$\bino...
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19 votes
4 answers
58
ISI2016
A palindrome is a sequence of digits which reads the same backward or forward. For example, $7447$, $1001$ are palindromes, but $7455$, $1201$ are not palindromes. How many $8$ digit prime palindromes are there?
A palindrome is a sequence of digits which reads the same backward or forward. For example, $7447$, $1001$ are palindromes, but $7455$, $1201$ are not palindromes. How ma...
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18 votes
3 answers
59
GATE CSE 2022 | Question: 22
The number of arrangements of six identical balls in three identical bins is _____________ .
The number of arrangements of six identical balls in three identical bins is _____________ .
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18 votes
2 answers
60
GATE CSE 1994 | Question: 15
Use the patterns given to prove that $\sum\limits_{i=0}^{n-1} (2i+1) = n^2$ (You are not permitted to employ induction) Use the result obtained in (A) to prove that $\sum\limits_{i=1}^{n} i = \frac{n(n+1)}{2}$
Use the patterns given to prove that$\sum\limits_{i=0}^{n-1} (2i+1) = n^2$(You are not permitted to employ induction)Use the result obtained in (A) to prove that $\sum\li...
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