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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

18 votes
3 answers
31
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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26 votes
5 answers
32
GATE CSE 1994 | Question: 1.15
The number of substrings (of all lengths inclusive) that can be formed from a character string of length $n$ is $n$ $n^2$ $\frac{n(n-1)}{2}$ $\frac{n(n+1)}{2}$
The number of substrings (of all lengths inclusive) that can be formed from a character string of length $n$ is$n$$n^2$$\frac{n(n-1)}{2}$$\frac{n(n+1)}{2}$
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39 votes
6 answers
33
GATE CSE 2000 | Question: 1.1
The minimum number of cards to be dealt from an arbitrarily shuffled deck of $52$ cards to guarantee that three cards are from same suit is $3$ $8$ $9$ $12$
The minimum number of cards to be dealt from an arbitrarily shuffled deck of $52$ cards to guarantee that three cards are from same suit is$3$$8$$9$$12$
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5 votes
5 answers
34
Kenneth Rosen Edition 6th Exercise 5.5 Question 15 (Page No. 380)
How many solutions are there to the equation x1 + x2 + x3 + x4 + x5 = 21, where xi , i = 1, 2, 3, 4, 5, is a nonnegative integer such that: 0$\leq$ x1$\leq$10 ?
How many solutions are there to the equationx1 + x2 + x3 + x4 + x5 = 21,where xi , i = 1, 2, 3, 4, 5, is a nonnegative integer such that: 0$\leq$ x1$\leq$10 ?
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36 votes
8 answers
35
GATE CSE 1987 | Question: 10b
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
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9 votes
9 answers
39
Kenneth Rosen Edition 6 Question 45 (Page No. 346)
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?
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2 votes
1 answer
40
From the word ASSASSINATION ,now in how many ways can we form 4 letter word from it ?
My confusion is how to deal with the case when I have 2 same and 2 different ,now since I have 3A's ,4 S so why can't I chose 2A's like 3C2 , what 's the problem in this ?
My confusion is how to deal with the case when I have 2 same and 2 different ,now since I have 3A's ,4 S so why can't I chose 2A's like 3C2 , what 's the problem in this ...
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30 votes
5 answers
42
GATE CSE 1999 | Question: 1.3
The number of binary strings of $n$ zeros and $k$ ones in which no two ones are adjacent is $^{n-1}C_k$ $^nC_k$ $^nC_{k+1}$ None of the above
The number of binary strings of $n$ zeros and $k$ ones in which no two ones are adjacent is$^{n-1}C_k$$^nC_k$$^nC_{k+1}$None of the above
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38 votes
3 answers
43
GATE IT 2008 | Question: 25
In how many ways can $b$ blue balls and $r$ red balls be distributed in $n$ distinct boxes? $\frac{(n+b-1)!\,(n+r-1)!}{(n-1)!\,b!\,(n-1)!\,r!}$ $\frac{(n+(b+r)-1)!}{(n-1)!\,(n-1)!\,(b+r)!}$ $\frac{n!}{b!\,r!}$ $\frac{(n + (b + r) - 1)!} {n!\,(b + r - 1)}$
In how many ways can $b$ blue balls and $r$ red balls be distributed in $n$ distinct boxes?$\frac{(n+b-1)!\,(n+r-1)!}{(n-1)!\,b!\,(n-1)!\,r!}$$\frac{(n+(b+r)-1)!}{(n-1)!\...
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3 votes
4 answers
44
How many solutions are there to the equation x+y+z=17 ?They are non-negative integers
How many solutions are there to the equation x+y+z=17 ?They are non-negative integers A) 120 B)171 C)180 D)121
How many solutions are there to the equation x+y+z=17 ?They are non-negative integers A) 120 B)171 C)180 D)121
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28 votes
8 answers
45
GATE CSE 2005 | Question: 50
Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$? $i$ $i+1$ $2i$ $2^i$
Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$?$i$$i+1$$2i$$2^i$
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0 votes
2 answers
47
Kenneth Rosen Edition 7 Exercise 6.1 Question 4 (Page No. 396)
A particular brand of shirt comes in $12$ colors, has a male version and a female version, and comes in three sizes for each sex. How many different types of this shirt are made?
A particular brand of shirt comes in $12$ colors, has a male version and a female version, and comes in three sizes for each sex. How many different types of this shirt a...
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7 votes
4 answers
49
GATE CSE 2023 | Question: 5
The Lucas sequence $L_{n}$ is defined by the recurrence relation: \[ L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3, \] with $L_{1}=1$ and $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$
The Lucas sequence $L_{n}$ is defined by the recurrence relation:\[L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3,\]with $L_{1}=1$ and $L_{2}=3$.Which one of t...
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0 votes
2 answers
50
Kenneth Rosen Edition 7 Exercise 6.1 Question 8 (Page No. 396)
How many different three-letter initials with none of the letters repeated can people have?
How many different three-letter initials with none of the letters repeated can people have?
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