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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

13 votes
2 answers
321
TIFR CSE 2011 | Part A | Question: 2
In how many ways can the letters of the word $\text{ABACUS}$ be rearranged such that the vowels always appear together? $\dfrac{(6+3)!}{2!}$ $\dfrac{6!}{2!}$ $\dfrac{3!3!}{2!}$ $\dfrac{4!3!}{2!}$ None of the above
In how many ways can the letters of the word $\text{ABACUS}$ be rearranged such that the vowels always appear together?$\dfrac{(6+3)!}{2!}$ $\dfrac{6!}{2!}$ $\dfrac{3!3!}...
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10 votes
2 answers
324
GATE1991-01,xiii
The number of integer-triples $(i,j,k)$ with $1 \leq i,j,k \leq 300$ such that $i+j+k$ is divisible by 3 is________
The number of integer-triples $(i,j,k)$ with $1 \leq i,j,k \leq 300$ such that $i+j+k$ is divisible by 3 is________
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1 votes
2 answers
325
Kenneth Rosen Edition 7 Exercise 6.1 Question 20 (Page No. 396)
How many positive integers between $5$ and $31$ are divisible by $3?$ Which integers are these? are divisible by $4?$ Which integers are these? are divisible by $3$ and by $4?$ Which integers are these?
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6 votes
1 answer
326
Generating function
What is the coefficient of $\large\color{green}{x^{6}}$ in the following series expansion? $\color{maroon}{\begin{align*} \frac{1}{1-x}.\frac{1}{1-x^2}.\frac{1}{1-x^3}........ \end{align*}}$
What is the coefficient of $\large\color{green}{x^{6}}$ in the following series expansion?$$\color{maroon}{\begin{align*} \frac{1}{1-x}.\frac{1}{1-x^2}.\frac{1}{1-x^3}......
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1 votes
1 answer
327
UGC NET CSE | December 2012 | Part 2 | Question: 10
The number of bit strings of length eight that will either start with a 1 bit and end with two bits 00 shall be 32 64 128 160
The number of bit strings of length eight that will either start with a 1 bit and end with two bits 00 shall be3264128160
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2 votes
2 answers
329
Mathmatics problem
how many 4 digit numbers possible whose sum is equal to 12 ?
how many 4 digit numbers possible whose sum is equal to 12 ?
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0 votes
0 answers
332
in how many ways 4 different balls can be placed in 5 different boxes so that no box contains all 4 balls
in how many ways 4 different balls can be distributed in 5 different boxes so that no box contains all 4 balls
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0 votes
1 answer
334
how to find number of terms in gp
(2n−2+2n−3+⋯+22+2+1) how to find sum?
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2 votes
1 answer
335
numbers
find number of 7 digit number with sum of digits equal to 11 and formed using digits 1 ,2 ,3
find number of 7 digit number with sum of digits equal to 11 and formed using digits 1 ,2 ,3
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0 votes
0 answers
336
NIELITDEC 2017 set -c 115
In boolean algebra 1+1+1+1+..........800 times ones A) 0 B)1 C)11 D)800
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2 votes
3 answers
340
counting
how many number are possible of 4 digits whose sum is 12.
how many number are possible of 4 digits whose sum is 12.
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