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Recent questions and answers in Combinatory
0
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1
kenneth rosen, counting, exercise: 6.5, question: 50
How many ways are there to distribute five distinguishable objects into three indistinguishable boxes?
Roshakaw
asked
in
Combinatory
Mar 24
by
Roshakaw
26
views
discrete-mathematics
kenneth-rosen
0
votes
0
answers
2
Kenneth Rosen, exercise: 6.2, question: 8
Show that if f is a function from S to T , where S and T are finite sets with |S| > |T |, then there are elements s1 and s2 in S such that f (s1) = f (s2), or in other words, f is not one-to-one. How can I prove it by using “proof by contradiction”? Is it possible to prove the same by using “proof by contraposition”? If yes, how?
Roshakaw
asked
in
Combinatory
Mar 23
by
Roshakaw
17
views
discrete-mathematics
kenneth-rosen
pigeonhole-principle
0
votes
2
answers
3
Can any one solve this , 6B and 4G ,at least 2 girls should be together in circular arrangement
saiyam
answered
in
Combinatory
Mar 21
by
saiyam
55
views
discrete-mathematics
combinatory
40
votes
5
answers
4
GATE CSE 2015 Set 1 | Question: 26
$\sum\limits_{x=1}^{99}\frac{1}{x(x+1)}$ = ______.
39Gaurav_singh
answered
in
Combinatory
Mar 11
by
39Gaurav_singh
6.2k
views
gatecse-2015-set1
combinatory
normal
numerical-answers
summation
1
vote
2
answers
5
Recurrence Relation Self-Doubt
What will be solution of recurrence relation if roots are like this: r1=-2, r2=2, r3=-2, r4=2 is this the case of repetitive roots?
Bharat Bhushan
answered
in
Combinatory
Mar 9
by
Bharat Bhushan
466
views
relations
recurrence-relation
discrete-mathematics
combinational-circuit
21
votes
1
answer
6
Recurrence Relation - Self Doubt
What is the recurrence relation for the ternary strings of length $n$ which can be constructed using 0,1 or 2 only such that the number of 0’s and number of 1's is odd ?
Bharat Bhushan
answered
in
Combinatory
Mar 9
by
Bharat Bhushan
584
views
recurrence-relation
discrete-mathematics
0
votes
2
answers
7
Discrete Maths by Kenneth Rosen, exercise 6.1, Qs - 12
How many bit strings are there of length six or less, not counting the empty string? Solution given:- We use the sum rule, adding the number of bit strings of each length up to 6. If we include the empty string, then we get 2^0 ... a binary string such as 000100 of length 3, and so on Please let me know if I am wrong somewhere in my approach.
Bharat Bhushan
answered
in
Combinatory
Mar 5
by
Bharat Bhushan
73
views
discrete-mathematics
kenneth-rosen
counting
1
vote
0
answers
8
Kenneth Rosen, exercise 6.1, Qs - 42 (d)
How many 4-element DNA sequences contain exactly three of the four bases A, T, C, and G? Solution given: There are four ways to choose which letter is to occur twice and three ways to decide which of the other letters to leave ... wrong. It would be of great help if you can show what combinations my approach is not including but the given solution includes.
Roshakaw
asked
in
Combinatory
Mar 3
by
Roshakaw
86
views
kenneth-rosen
discrete-mathematics
counting
combinatory
0
votes
1
answer
9
#Combinatorics #Self doubt
How many 3 digits number are there which are divisible by 3 and repetition of digits NOT allowed.?
hdutta
answered
in
Combinatory
Feb 21
by
hdutta
192
views
counting
combinatory
0
votes
1
answer
10
#Combinatorics and Counting # Permutations and Combinations
If each of ‘a’ points on a straight line is joined to each of ‘b’ points on another straight line, excluding the points on the given two lines,then which of the following represents the number of points of intersection of these lines? Select all that apply. (ab(a-1)(b-1))/4 (ab(a-1)(b-1))/2 ab C(a,2) * C(b,2)
Roshakaw
answered
in
Combinatory
Feb 17
by
Roshakaw
72
views
combinatory
counting
4
votes
1
answer
11
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 $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$
ankitgupta.1729
answered
in
Combinatory
Feb 15
by
ankitgupta.1729
941
views
gatecse-2023
combinatory
recurrence-relation
1-mark
4
votes
0
answers
12
GATE CSE 2023 | Question: 38
Let $U=\{1,2, \ldots, n\},$ where $n$ is a large positive integer greater than $1000.$ Let $k$ be a positive integer less than $n$. Let $A, B$ be subsets of $U$ with $|A|=|B|=k$ and $A \cap B=\emptyset$. We say that a permutation of $U$ separates $A$ from $B$ if ... $2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k !)^{2}$
admin
asked
in
Combinatory
Feb 15
by
admin
973
views
gatecse-2023
combinatory
counting
2-marks
0
votes
2
answers
13
GATE CSE 2023 | Memory Based Question: 15
The Lucas sequence $L_n$ is defined by the recurrence relation: $L_n=L_{n-1}+L_{n-2}$, for $n \geq 3$ with $L_1=1$ and $L_2=3$. Which one of the options given is TRUE? $L_n=\left(\frac{1+\sqrt{5}}{2}\right)^n+\left(\frac{1-\sqrt{5}}{3}\right)^n$ ... $L_n=\left(\frac{1+\sqrt{5}}{2}\right)^n+\left(\frac{1-\sqrt{5}}{2}\right)^n$
closed
ankitgupta.1729
answered
in
Combinatory
Feb 10
by
ankitgupta.1729
468
views
memorybased-gatecse2023
goclasses
combinatory
recurrence-relation
1
vote
1
answer
14
GATE CSE 2023 | Memory Based Question: 16
How many permutations of $U$ separate $A$ from $B?$ $2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k!)^2$ $\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k)!(n!)$ $n!$ $\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k !)^2$
closed
Deepak Poonia
answered
in
Combinatory
Feb 6
by
Deepak Poonia
427
views
memorybased-gatecse2023
goclasses
combinatory
counting
2
votes
1
answer
15
DRDO CSE 2022 Paper 1 | Question: 18
A gardener wants to buy $3$ neem plants, $5$ rose plants and $1$ banyan plant from a nursery having $7$ neem, $10$ rose and $6$ banyan plants. How many choices does a gardener have?
elsar martin
answered
in
Combinatory
Feb 2
by
elsar martin
75
views
drdocse-2022-paper1
combinatory
counting
5-marks
descriptive
61
votes
15
answers
16
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 ________.
GNANESWARA SAI
answered
in
Combinatory
Jan 28
by
GNANESWARA SAI
11.9k
views
gatecse-2015-set3
combinatory
normal
numerical-answers
0
votes
0
answers
17
#selfdoubt
Let n players enter a chess tournament. How many tournament trees are possible? RULES: a player is eliminated after one loss and games are played until only one entrant is left(assume no ties) My approach: (please check if it is correct) there are 3 possible binary tree skeletons w.r.t ... )C2 * (n-4)C2 *...*1} * 2^(n-1) similarly we can do the remaining cases. Is the above method right?
robinofautumn
asked
in
Combinatory
Jan 11
by
robinofautumn
46
views
discrete-mathematics
graph-theory
combinatory
binary-tree
0
votes
0
answers
18
Unacademy AIMT 1
How many integers are there in the set {1,2,3,…..,1000} with no digit being repeated?
TusharKumar
asked
in
Combinatory
Dec 25, 2022
by
TusharKumar
163
views
combinatory
number-system
0
votes
0
answers
19
kenneth h rosen chapter 6
What is the closed form for the generating function for the sequence : 0,1,-2,4,-8,16,-32,64,...
closed
Shivam_j
asked
in
Combinatory
Dec 23, 2022
by
Shivam_j
148
views
generating-functions
0
votes
1
answer
20
Number Of Substrings | Made Easy Test Series
The number of subwords for w=’SCALABLE” is equal to: 34 35 37
Souvik33
answered
in
Combinatory
Dec 21, 2022
by
Souvik33
330
views
combinatory
counting
made-easy-test-series
0
votes
1
answer
21
Kenneth Rosen Edition 7 Exercise 6.2 Question 45 (Page No. 407)
Let $x$ be an irrational number. Show that for some positive integer $j$ not exceeding the positive integer $n,$ the absolute value of the difference between $j x$ and the nearest integer to $j x$ is less than $1/n.$
rsjbits
answered
in
Combinatory
Dec 19, 2022
by
rsjbits
232
views
kenneth-rosen
discrete-mathematics
counting
pigeonhole-principle
descriptive
1
vote
1
answer
22
DRDO CSE 2022 Paper 1 | Question: 15
What is the generating function corresponding to Fibonacci series. \[F_{n}=F_{n-1}+F_{n-2} .\] Note that $F_{0}=F_{1}=1$.
Shubhodeep
answered
in
Combinatory
Dec 16, 2022
by
Shubhodeep
135
views
drdocse-2022-paper1
combinatory
generating-functions
6-marks
descriptive
1
vote
1
answer
23
DRDO CSE 2022 Paper 1 | Question: 19
How many seven digit numbers are possible with exactly four $4 \mathrm{s}?$
rsansiya111
answered
in
Combinatory
Dec 16, 2022
by
rsansiya111
54
views
drdocse-2022-paper1
combinatory
counting
5-marks
descriptive
1
vote
0
answers
24
DRDO CSE 2022 Paper 1 | Question: 14
Derangements are permutations $\pi$ of the set $\{1,2, \ldots, n\}$ such that $\pi(i) \neq i.$ Compute the number of derangements on the set $1,2, \ldots, n$.
admin
asked
in
Combinatory
Dec 15, 2022
by
admin
52
views
drdocse-2022-paper1
combinatory
counting
7-marks
descriptive
1
vote
0
answers
25
DRDO CSE 2022 Paper 1 | Question: 16
Let us say we have a supply of $1$ rupee and $2$ rupee coins in large quantities. What is the generating function for the number of ways of giving change with $1$ rupee and $2$ rupee coins.
admin
asked
in
Combinatory
Dec 15, 2022
by
admin
64
views
drdocse-2022-paper1
combinatory
generating-functions
5-marks
descriptive
1
vote
2
answers
26
GATE DIscrete Solve Recurrence Relation
Solve the Recurrence Relation S(r) - 6 S(r-1) +8 S(r-2) = 3r; S(0) =8, S(1)=7
manoj0606
answered
in
Combinatory
Dec 13, 2022
by
manoj0606
1.4k
views
discrete-mathematics
combinatory
42
votes
8
answers
27
GATE CSE 2016 Set 2 | Question: 29
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
Jaideep Singh
answered
in
Combinatory
Nov 27, 2022
by
Jaideep Singh
14.0k
views
gatecse-2016-set2
modular-arithmetic
normal
numerical-answers
0
votes
1
answer
28
Solve the simultaneous recurrence relations
an = an−1 + bn−1 bn = an−1 − bn−1 with a0 = 1 and b0 = 2.
Kabir5454
answered
in
Combinatory
Nov 26, 2022
by
Kabir5454
166
views
discrete-mathematics
counting
recurrence-relation
descriptive
0
votes
0
answers
29
Engineering Mathematics
Can somebody brief description about this topic(means formula or link to study). Actually this question is asked in TOC test, but looking more like mathematics part.
Overflow04
asked
in
Combinatory
Oct 30, 2022
by
Overflow04
117
views
test-series
engineering-mathematics
2
votes
2
answers
30
Ace Test series: Combinatory - Generating Functions
Answer is B as given in solution.
Abhrajyoti00
answered
in
Combinatory
Oct 12, 2022
by
Abhrajyoti00
324
views
ace-test-series
discrete-mathematics
generating-functions
1
vote
1
answer
31
binomial coefficient
Gate Shark
answered
in
Combinatory
Oct 12, 2022
by
Gate Shark
451
views
generating-functions
11
votes
6
answers
32
GATE CSE 2022 | Question: 41
Consider the following recurrence: $\begin{array}{} f(1) & = & 1; \\ f(2n) & = & 2f(n) - 1, & \; \text{for}\; n \geq 1; \\ f(2n+1) & = & 2f(n) + 1, & \; \text{for}\; n \geq 1. \end{array}$ Then, which of the following statements is/are $\text{TRUE}?$ ... $f(2^{n}) = 1$ $f(5 \cdot 2^{n}) = 2^{n+1} + 1$ $f(2^{n} + 1) = 2^{n} + 1$
dutta18
answered
in
Combinatory
Oct 11, 2022
by
dutta18
4.0k
views
gatecse-2022
combinatory
recurrence-relation
multiple-selects
2-marks
20
votes
5
answers
33
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.$ ... $\frac{2x}{(1-x^{2})^{2}} + \frac{1}{1-x}$ $\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$
Jaideep Singh
answered
in
Combinatory
Oct 7, 2022
by
Jaideep Singh
4.2k
views
gatecse-2022
combinatory
generating-functions
2-marks
0
votes
1
answer
34
[email protected]
Test Series 2023
Ans: 211
SKMAKM
asked
in
Combinatory
Sep 19, 2022
by
SKMAKM
281
views
combinatory
1
vote
2
answers
35
[email protected]
Test Series 2023
Ans: 43333
SKMAKM
asked
in
Combinatory
Sep 19, 2022
by
SKMAKM
234
views
combinatory
1
vote
1
answer
36
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 ?
jugnu1337
asked
in
Combinatory
Sep 7, 2022
by
jugnu1337
248
views
discrete-mathematics
counting
test-series
2
votes
1
answer
37
TIFR CSE 2022 | Part B | Question: 9
Let $n \geq 2$ be any integer. Which of the following statements is $\text{FALSE}?$ $n!$ divides the product of any $n$ consecutive integers $\displaystyle{}\sum_{i=0}^n\left(\begin{array}{c}n \\ i\end{array}\right)=2^n$ ... an odd prime, then $n$ divides $2^{n-1}-1$ $n$ divides $\left(\begin{array}{c}2 n \\ n\end{array}\right)$
admin
asked
in
Combinatory
Sep 1, 2022
by
admin
143
views
tifr2022
combinatory
binomial-theorem
0
votes
1
answer
38
TIFR CSE 2022 | Part A | Question: 1
A snail crawls up a vertical pole $75$ feet high, starting from the ground. Each day it crawls up $5$ feet, and each night it slides down $4$ feet. When will it first reach the top of the pole? $75^{\text {th}}$ day $74^{\text {th}}$ day $73^{ \text{rd}}$ day $72^{\text {nd }}$ day $71^{\text {st }}$ day
Lakshman Patel RJIT
asked
in
Combinatory
Sep 1, 2022
by
Lakshman Patel RJIT
267
views
tifr2022
combinatory
counting
0
votes
1
answer
39
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.
Roshakaw
asked
in
Combinatory
Aug 25, 2022
by
Roshakaw
250
views
combinatory
counting
numerical-answers
1
vote
2
answers
40
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.
Roshakaw
asked
in
Combinatory
Aug 25, 2022
by
Roshakaw
277
views
combinatory
counting
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Please upload updated previous year question...
The last hardcopy that was made was for GATE 2022...
overall only 3 post .no post for gen male
for gen GS in the range of 720-750 approx.
can we get 2023 hark copy from amazon?