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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 answered questions in Combinatory

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391
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 5
How many integer solutions does the equation $ x_{1}+x_{2}+x_{3}+x_{4}=15 $ have, if we require that $x_{1} \geq 2, x_{2} \geq 3, x_{3} \geq 10$ and $x_{4} \geq-3 ?$
How many integer solutions does the equation$$x_{1}+x_{2}+x_{3}+x_{4}=15$$have, if we require that $x_{1} \geq 2, x_{2} \geq 3, x_{3} \geq 10$ and $x_{4} \geq-3 ?$
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399
A question paper is divided into two parts A and B and each part contains 5 questions. In how many ways a student can answer the question paper, if he has to solve total 6 questions including atleast 2 from each section.
I solved the question using the logic first select two questions from each sections. ($\binom{5}{2} * \binom{5}{2}$). Then from remaining 6 questions choose any 2. theref...
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400
No of 5 letter english words that contains atleast one 'a' ?
No of 5 letter english words that contains atleast one 'a' ? i used the approch that
No of 5 letter english words that contains atleast one 'a' ?i used the approch that
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1 votes
1 answer
407
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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1 votes
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408
Self Doubt
Give a combinatorial argument to establish the identity below for any nonnegative integer n: $\sum_{k=0}^{n} k\binom{n}{k}=n\ast 2^{n-1}$
Give a combinatorial argument to establish the identity below for any nonnegative integer n:$\sum_{k=0}^{n} k\binom{n}{k}=n\ast 2^{n-1}$
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409
GATE Overflow Test Series | Mock GATE | Test 6 | Question: 12
A decimal number is called “increasing” if each digit is greater than the previous one (e.g., $1267$ is one increasing number). The total number of $5$ digit increasing numbers is _______
A decimal number is called “increasing” if each digit is greater than the previous one (e.g., $1267$ is one increasing number). The total number of $5$ digit increasi...
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