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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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Recent questions in Combinatory

1 votes
2 answers
1291
Different color combination of identical balls
There are three identical red balls and four identical blue balls in bag.Three balls are drawn.what is the number of different color combinations ?
There are three identical red balls and four identical blue balls in bag.Three balls are drawn.what is the number of different color combinations ?
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3 votes
1 answer
1292
ISRO-2013-53
A CPU scheduling algorithm determines an order for the execution of its scheduled processes. Given 'n' processes to be scheduled on one processor, how many possible different schedules are there? $n$ $n^{2}$ $n!$ $2^{n}$
A CPU scheduling algorithm determines an order for the execution of its scheduled processes. Given 'n' processes to be scheduled on one processor, how many possible diffe...
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0 votes
1 answer
1293
Combinatorics
$T_k = \,^{100}C_k \cdot x^{100-k} \quad \text{for} \quad k = 0, 1, 2, \ldots 100$ Then, what will be the value of $\Bigl (T_0 - T_2 + T_4 - \cdots + T_{100} \Bigr )^2 + \Bigl (T_1 - T_3 + T_5 - \cdots - T_{99} \Bigr )^2$ The answer should be in terms of $x$
$$T_k = \,^{100}C_k \cdot x^{100-k} \quad \text{for} \quad k = 0, 1, 2, \ldots 100$$Then, what will be the value of$$\Bigl (T_0 - T_2 + T_4 - \cdots + T_{100} \Bigr )^2 +...
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1 votes
2 answers
1297
circular arrangement
how many ways are there to arrange 6 girls and 15 boys in a circle such that there are atleast two boys between two adjacent girls?
how many ways are there to arrange 6 girls and 15 boys in a circle such that there are atleast two boys between two adjacent girls?
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1 votes
1 answer
1299
No. of ways in which 2n white and 2n black balls can be arranged such that no consecutive n white balls are together
The number of ways in which $2n$ white and $2n$ black balls can be arranged such that no consecutive $n$ white balls are together, is${}^{2n+1}C_2 + {}^{4n}C_{2n}$${}^{2n...
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2 votes
0 answers
1301
Find the coefficient of x7 in expansion of (1+3x-2x3)10.
Find the coefficient of x7 in expansion of (1+3x-2x3)10. How to apply multinomial theorem to solve this types of problems?
Find the coefficient of x7 in expansion of (1+3x-2x3)10. How to apply multinomial theorem to solve this types of problems?
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1 votes
1 answer
1302
How many bit strings with length not exceeding n, where n is a positive integer, consist entirely of 1's ?
why do we count here empty string also , it has no 1's , so what's the reason for counting this ?
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1 votes
1 answer
1303
In how many ways can 5 chocolates be chosen from an unlimited number of Cadbury,Five-star, and Perk chocolates?
we have to choose five chocolates,say, C1, C2, C3, C4 and C5. Now for C1 we can choose among three kinds of chocolates. Since the supply of chocolates is infinite, for C2...
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0 votes
2 answers
1304
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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0 votes
3 answers
1305
Circular Permutation
A class is composed of 2 brothers and 6 other boys. In how many ways can all the boys be seated at a round table so that the two brothers are not seated together? a. 3000 b.3600 c. 2050 d. 2600
A class is composed of 2 brothers and 6 other boys. In how many ways can all the boys beseated at a round table so that the two brothers are not seated together?a. 3000b....
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67 votes
10 answers
1306
GATE CSE 2016 Set 1 | Question: 27
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
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57 votes
17 answers
1307
GATE CSE 2016 Set 1 | Question: 26
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
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44 votes
11 answers
1309
GATE CSE 2016 Set 2 | Question: 29
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
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1 votes
1 answer
1310
combinations
A, B are two 8-bit numbers such that A+B < 2^8. The number of possible combinations of A and B are
A, B are two 8-bit numbers such that A+B < 2^8. The number of possible combinations of A and B are
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