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Recent questions and answers in Combinatory
8
votes
5
answers
1
GATE CSE 2022 | Question: 26
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below? $ a_{n} = \left\{\begin{matrix} n + 1, & \text{n is odd} & \\ 1, & \text{otherwise} & \end{matrix}\right.$ ... $\frac{2x}{(1-x^{2})^{2}} + \frac{1}{1-x}$ $\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$
Jaideepyadav910
answered
in
Combinatory
4 hours
ago
by
Jaideepyadav910
1.7k
views
gatecse-2022
combinatory
generating-functions
1
vote
2
answers
2
[email protected]
Test Series 2023
Ans: 43333
Pranavpurkar
answered
in
Combinatory
Sep 22
by
Pranavpurkar
102
views
combinatory
0
votes
1
answer
3
[email protected]
Test Series 2023
Ans: 211
afroze
answered
in
Combinatory
Sep 19
by
afroze
105
views
combinatory
1
vote
1
answer
4
igate test series
Selection of how many integers from the first ten positive integers (1, 2, ...) guarantees that there must be a pair of these integers with a sum equal to 11 ?
maverick
answered
in
Combinatory
Sep 10
by
maverick
106
views
discrete-mathematics
counting
test-series
50
votes
17
answers
5
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 ___________.
[ Jiren ]
answered
in
Combinatory
Aug 25
by
[ Jiren ]
19.4k
views
gatecse-2016-set1
combinatory
generating-functions
normal
numerical-answers
0
votes
1
answer
6
combinatorics problem-2
How many ways are there to distribute 5 distinct toys among 3 children such that every child gets at least 1 toy? answer given is 150. but I'm getting 9. My approach go as follows: step-1 : give 1 toy to all 3 children, now, I am left with (5-3) = ... to either of first or second or third child. thus, toy1 has 3 choices and so do toy2. Therefore, my answer would be 3*3 = 9.
[ Jiren ]
answered
in
Combinatory
Aug 25
by
[ Jiren ]
121
views
combinatory
counting
numerical-answers
1
vote
2
answers
7
Combinatorics
How many ways are there to distribute 10 identical candies among 3 children such that the first child receives at least 2 candies, the second child receives atmost 6 candies and the third child receives atmost 3 candies.
Kabir5454
answered
in
Combinatory
Aug 25
by
Kabir5454
130
views
combinatory
counting
15
votes
8
answers
8
GATE CSE 2020 | Question: 42
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.
[ Jiren ]
answered
in
Combinatory
Aug 25
by
[ Jiren ]
10.5k
views
gatecse-2020
numerical-answers
combinatory
4
votes
2
answers
9
GO Classes Scholarship 2023 | Test | Question: 13
Let $\text{T}_{n}$ be the number of ways to arrange cars in a row with $n$ parking spaces if we can use sedans, SUVs, trucks to park such that a truck requires two spaces, whereas a sedan or SUV requires just one space each, and No two ... i.e. initial conditions are already given, hence no need to compute them)
Udhay_Brahmi
answered
in
Combinatory
Aug 24
by
Udhay_Brahmi
312
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
counting
recurrence-relation
2-marks
44
votes
8
answers
10
GATE CSE 2007 | Question: 84
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. How many distinct paths are there for the ... $(10,10)$ starting from the initial position $(0,0)$? $^{20}\mathrm{C}_{10}$ $2^{20}$ $2^{10}$ None of the above
[ Jiren ]
answered
in
Combinatory
Aug 24
by
[ Jiren ]
8.9k
views
gatecse-2007
combinatory
34
votes
9
answers
11
GATE CSE 2001 | Question: 2.1
How many $4$-digit even numbers have all $4$ digits distinct? $2240$ $2296$ $2620$ $4536$
TusharRana
answered
in
Combinatory
Aug 23
by
TusharRana
8.8k
views
gatecse-2001
combinatory
normal
17
votes
15
answers
12
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
[ Jiren ]
answered
in
Combinatory
Aug 23
by
[ Jiren ]
13.7k
views
gatecse-2019
numerical-answers
combinatory
modular-arithmetic
5
votes
0
answers
13
Combinatorics : Distinct objects and Distinct boxes
How many ways are there to Distribute 7 distinct objects to 3 Distinct boxes and No box should be Empty Any box can be Empty
[ Jiren ]
asked
in
Combinatory
Aug 22
by
[ Jiren ]
105
views
combinatory
counting
3
votes
2
answers
14
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 15
In an examination, a question paper consists of $12$ questions divided into two parts i.e, Part I and Part II, containing $5$ and $7$ questions respectively. A student is required to attempt $8$ questions in all, selecting at least $3$ from each part. In how many ways can a student select the questions?
Udhay_Brahmi
answered
in
Combinatory
Aug 20
by
Udhay_Brahmi
165
views
goclasses_wq13
numerical-answers
goclasses
combinatory
counting
2-marks
3
votes
3
answers
15
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 14
The number of ways of selecting at least one Indian and at least one American for a debate from a group comprising $3$ Indians and $4$ Americans and no one else?
Udhay_Brahmi
answered
in
Combinatory
Aug 20
by
Udhay_Brahmi
168
views
goclasses_wq13
numerical-answers
goclasses
combinatory
counting
2-marks
0
votes
1
answer
16
NPTEL Assignment
In how many ways can the word ‘DOCUMENTATION’ be arranged so that all the consonants come together.
Coding skill
answered
in
Combinatory
Aug 16
by
Coding skill
129
views
0
votes
1
answer
17
Kenneth Rosen Edition 7 Exercise 6.5 Question 59 (Page No. 434)
How many ways are there to distribute five balls into three boxes if each box must have at least one ball in it if both the balls and boxes are labeled? the balls are labeled, but the boxes are unlabeled? the balls are unlabeled, but the boxes are labeled? both the balls and boxes are unlabeled?
ankit-saha
answered
in
Combinatory
Aug 15
by
ankit-saha
124
views
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
1
vote
1
answer
18
Kenneth Rosen Edition 7 Exercise 6.5 Question 58 (Page No. 434)
How many ways are there to distribute five balls into seven boxes if each box must have at most one ball in it if both the balls and boxes are labeled? the balls are labeled, but the boxes are unlabeled? the balls are unlabeled, but the boxes are labeled? both the balls and boxes are unlabeled?
ankit-saha
answered
in
Combinatory
Aug 15
by
ankit-saha
181
views
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
0
votes
1
answer
19
Kenneth Rosen Edition 7 Exercise 6.5 Question 57 (Page No. 434)
How many ways are there to pack nine identical DVDs into three indistinguishable boxes so that each box contains at least two DVDs?
ankit-saha
answered
in
Combinatory
Aug 15
by
ankit-saha
115
views
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
1
vote
1
answer
20
Kenneth Rosen Edition 7 Exercise 6.5 Question 56 (Page No. 434)
How many ways are there to pack eight identical DVDs into five indistinguishable boxes so that each box contains at least one DVD?
ankit-saha
answered
in
Combinatory
Aug 15
by
ankit-saha
118
views
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
1
vote
1
answer
21
Kenneth Rosen Edition 7 Exercise 6.1 Question 41 (Page No. 397)
A palindrome is a string whose reversal is identical to the string. How many bit strings of length $n$ are palindromes?
ankit-saha
answered
in
Combinatory
Aug 11
by
ankit-saha
127
views
kenneth-rosen
discrete-mathematics
counting
descriptive
1
vote
1
answer
22
Kenneth Rosen Edition 7 Exercise 6.1 Question 40 (Page No. 397)
How many subsets of a set with $100$ elements have more than one element?
ankit-saha
answered
in
Combinatory
Aug 11
by
ankit-saha
87
views
kenneth-rosen
discrete-mathematics
counting
descriptive
57
votes
14
answers
23
GATE CSE 2015 Set 3 | Question: 5
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.
Himanshu555
answered
in
Combinatory
Aug 11
by
Himanshu555
10.8k
views
gatecse-2015-set3
combinatory
normal
numerical-answers
5
votes
2
answers
24
GO Classes Scholarship 2023 | Test | Question: 4
Consider a $3 \times 11$ rectangular grid as depicted in Figure $1,$ formed by $33$ tiles of area $1\text{m}^2.$ A staircase walk is a path in the grid which moves only right or up. How many staircase walks are there from $\text{A}$ to $\text{B}$ which start by going to the right two times?
[ Jiren ]
answered
in
Combinatory
Aug 8
by
[ Jiren ]
227
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
counting
1-mark
3
votes
1
answer
25
GO Classes Scholarship 2023 | Test | Question: 5
Consider $5$ cards, each has a distinct value from the set $\{2,3,4,5,6\},$ so there are $5$ different values, and we put them face down on the table. There are $5$ players and each player is given a number from $2$ ... with the value that player has. If no player loses, then the dealer loses. How many ways are there so that the dealer loses?
GO Classes
answered
in
Combinatory
Aug 7
by
GO Classes
168
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
counting
2-marks
4
votes
1
answer
26
GO Classes Scholarship 2023 | Test | Question: 6
Consider three boxes and $12$ balls of the same size. We have $3$ indistinguishable red balls and $9$ distinguishable blue balls. The first box can fit at most three balls, the second box can fit at most four balls and the third box can fit ... all the red balls go into the same box. What is the total number of ways to put all the balls in the boxes?
GO Classes
answered
in
Combinatory
Aug 7
by
GO Classes
178
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
counting
2-marks
3
votes
1
answer
27
GO Classes Scholarship 2023 | Test | Question: 7
Define the generating functions $\text{B}(x)=\displaystyle{} \sum_{n=0}^{\infty} 2^{n} x^{n}$ and $F(x)=\displaystyle{} \sum_{n=0}^{\infty} f_{n} x^{n}$ where $f_{n}$ ... $x^{5}$ is $\mathrm{G}(x)?$
GO Classes
answered
in
Combinatory
Aug 7
by
GO Classes
157
views
goclasses-scholarship-test1
numerical-answers
goclasses
combinatory
generating-functions
2-marks
54
votes
13
answers
28
GATE CSE 2014 Set 1 | Question: 49
A pennant is a sequence of numbers, each number being $1$ or $2$. An $n-$pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a $4-$pennant. The set of all possible $1-$pennants is ${(1)}$, the set of all possible ... $(1,2)$ is not the same as the pennant $(2,1)$. The number of $10-$pennants is________
Argharupa Adhikary
answered
in
Combinatory
Jul 31
by
Argharupa Adhikary
7.2k
views
gatecse-2014-set1
combinatory
numerical-answers
normal
0
votes
1
answer
29
Mathematics for Natural Science
Prove that $2n < (n + 1)!, $ for all $ n \geq 3.$
Kabir5454
answered
in
Combinatory
Jul 29
by
Kabir5454
56
views
discrete-mathematics
mathematical-logic
calculus
set-theory
0
votes
1
answer
30
Mathematics for Natural Science
Simplify $(A\cup B)\cap (A\cup B')\cap (A - B)$ for a given non empty sets $A$ and $B$, where $(A\cap B) = \varnothing .$
Kabir5454
answered
in
Combinatory
Jul 29
by
Kabir5454
59
views
discrete-mathematics
mathematical-logic
calculus
set-theory
0
votes
0
answers
31
Mathematics for Natural Science
Let y in the form of $a + bi$, where $a$ and $b$ are real numbers, be the cubic roots of complex number $z^{20},$ where $z=\frac{2}{4 + 3i}.$ Find $a + b.$
kidussss
asked
in
Combinatory
Jul 29
by
kidussss
74
views
discrete-mathematics
mathematical-logic
calculus
set-theory
0
votes
1
answer
32
Cengage algebra jee advanced.
Coefficient of x^8 in ( (1-x^6)/(1-x) )^3.
Kabir5454
answered
in
Combinatory
Jul 24
by
Kabir5454
108
views
combinatory
3
votes
3
answers
33
UGC NET CSE | Junet 2015 | Part 2 | Question: 3
In how many ways can $15$ indistinguishable fish be placed into $5$ different ponds, so that each pond contains at least one fish? $1001$ $3876$ $775$ $200$
Vasudevarnab23
answered
in
Combinatory
Jul 21
by
Vasudevarnab23
4.0k
views
ugcnetcse-june2015-paper2
combinatory
counting
5
votes
2
answers
34
UGC NET CSE | Junet 2015 | Part 2 | Question: 1
How many strings of $5$ digits have the property that the sum of their digits is $7$? $66$ $330$ $495$ $99$
Vasudevarnab23
answered
in
Combinatory
Jul 21
by
Vasudevarnab23
2.0k
views
ugcnetcse-june2015-paper2
discrete-mathematics
counting
33
votes
5
answers
35
GATE CSE 1989 | Question: 4-i
How many substrings (of all lengths inclusive) can be formed from a character string of length $n$? Assume all characters to be distinct, prove your answer.
neopentane
answered
in
Combinatory
Jul 20
by
neopentane
4.6k
views
gate1989
descriptive
combinatory
normal
proof
0
votes
2
answers
36
Kenneth Rosen Edition 7 Exercise 6.4 Question 25 (Page No. 422)
Let n be a positive integer. Show that $\binom{2n}{n + 1} + \binom{2n}{n} = \dfrac{\binom{2n + 2}{n + 1}}{2}.$
ASNR1010
answered
in
Combinatory
Jul 14
by
ASNR1010
109
views
kenneth-rosen
discrete-mathematics
counting
binomial-theorem
descriptive
0
votes
3
answers
37
Discrete Mathematics
Any Good resource to understand this topic.
Kushal06
answered
in
Combinatory
Jul 13
by
Kushal06
514
views
combinatory
ace-test-series
0
votes
1
answer
38
Discrete Mathematics
Somebody please clarify the answer
GateOverflow04
asked
in
Combinatory
Jul 11
by
GateOverflow04
116
views
combinatory
ace-test-series
0
votes
0
answers
39
Discrete Mathematics and Combinatorics
Solve the recurrence relation $a^{2}n-5a^{2}_{n-1}+4a^{2} _{n-2}=0$, if $a_{0}=4, a_{1}=13, n>1$
kidussss
asked
in
Combinatory
Jul 9
by
kidussss
148
views
discrete-mathematics
combinatory
recurrence-relation
3
votes
2
answers
40
GO Classes Weekly Quiz 13 | Discrete Mathematics | Combinatorics | Question: 1
How many words can be formed by re-arranging the letters of the word “PROBLEMS” such that $P$ and $S$ occupy the first and last position respectively? (Note: The words thus formed need not be meaningful)
GO Classes
asked
in
Combinatory
Jun 14
by
GO Classes
288
views
goclasses_wq13
numerical-answers
goclasses
combinatory
counting
1-mark
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