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Recent questions and answers in Combinatory
+6
votes
8
answers
1
TIFR2018B1
What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$
answered
2 days
ago
in
Combinatory
by
Lakshman Patel RJIT
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58.7k
points)

557
views
tifr2018
modulararithmetic
permutationandcombination
+1
vote
1
answer
2
Made Easy Test Series 2019: Combinatory  Permutations And Combinations
in how many ways 6 letters can be placed in 6 envelopes such that at least 4 letters go into their corresponding envelopes ?
answered
4 days
ago
in
Combinatory
by
suvradip das
(
149
points)

198
views
discretemathematics
permutationandcombination
madeeasytestseries2019
madeeasytestseries
+37
votes
2
answers
3
GATE199116,a
Find the number of binary strings $w$ of length $2n$ with an equal number of $1's$ and $0's$ and the property that every prefix of $w$ has at least as many $0's$ as $1's.$
answered
4 days
ago
in
Combinatory
by
Rishiryanemo
(
19
points)

1.6k
views
gate1991
permutationandcombination
normal
descriptive
catalannumber
+26
votes
4
answers
4
GATE20012.1
How many $4$digit even numbers have all $4$ digits distinct $2240$ $2296$ $2620$ $4536$
answered
6 days
ago
in
Combinatory
by
Kushagra गुप्ता
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(
4k
points)

3.8k
views
gate2001
permutationandcombination
normal
+39
votes
7
answers
5
GATE200544
What is the minimum number of ordered pairs of nonnegative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$ $4$ $6$ $16$ $24$
answered
6 days
ago
in
Combinatory
by
Kushagra गुप्ता
Active
(
4k
points)

4.7k
views
gate2005
settheory&algebra
normal
pigeonholeprinciple
+15
votes
7
answers
6
GATE200550
Let $G(x) = \frac{1}{(1x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $x < 1$. What is $g(i)$? $i$ $i+1$ $2i$ $2^i$
answered
Jan 9
in
Combinatory
by
arjuno
(
275
points)

1.9k
views
gate2005
normal
generatingfunctions
+28
votes
2
answers
7
GATE20035
$n$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is \(^{2n}\mathrm{C}_n\times 2^n\) \(3^n\) \(\frac{(2n)!}{2^n}\) \(^{2n}\mathrm{C}_n\)
answered
Jan 9
in
Combinatory
by
arjuno
(
275
points)

2.6k
views
gate2003
permutationandcombination
normal
+16
votes
10
answers
8
GATE20181
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1x)^2}$ $\frac{3x}{(1x)^2}$ $\frac{2x}{(1x)^2}$ $\frac{3x}{(1x)^2}$
answered
Jan 6
in
Combinatory
by
Çșȇ ʛấẗẻ
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1.9k
points)

6.9k
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gate2018
generatingfunctions
normal
permutationandcombination
+1
vote
3
answers
9
ISI2019MMA27
A general election is to be scheduled on $5$ days in May such that it is not scheduled on two consecutive days. In how many ways can the $5$ days be chosen to hold the election? $\begin{pmatrix} 26 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 27 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 30 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 31 \\ 5 \end{pmatrix}$
answered
Jan 6
in
Combinatory
by
Navneet Singh Tomar
Junior
(
735
points)

2.8k
views
isi2019mma
engineeringmathematics
discretemathematics
permutationandcombination
+1
vote
1
answer
10
ISI2017DCG11
The coefficient of $x^6y^3$ in the expression $(x+2y)^9$ is $84$ $672$ $8$ none of these
answered
Dec 24, 2019
in
Combinatory
by
swatiraoo45#
(
21
points)

20
views
isi2017dcg
permutationandcombination
binomialtheorem
+1
vote
1
answer
11
Kenneth Rosen Edition 6th Exercise 6.4 Question 39 (Page No. 442)
What is the generating function for the sequence of Fibonacci numbers?
answered
Dec 11, 2019
in
Combinatory
by
Anup dogrial
(
321
points)

79
views
permutationandcombination
propositionallogic
kennethrosen
discretemathematics
generatingfunctions
+25
votes
8
answers
12
GATE2004IT35
In how many ways can we distribute $5$ distinct balls, $B_1, B_2, \ldots, B_5$ in $5$ distinct cells, $C_1, C_2, \ldots, C_5$ such that Ball $B_i$ is not in cell $C_i$, $\forall i= 1,2,\ldots 5$ and each cell contains exactly one ball? $44$ $96$ $120$ $3125$
answered
Dec 8, 2019
in
Combinatory
by
Madhab
Loyal
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5.7k
points)

3.2k
views
gate2004it
permutationandcombination
normal
ballsinbins
+8
votes
5
answers
13
TIFR2018A6
What is the minimum number of students needed in a class to guarantee that there are at least $6$ students whose birthdays fall in the same month ? $6$ $23$ $61$ $72$ $91$
answered
Dec 3, 2019
in
Combinatory
by
`JEET
Boss
(
18.9k
points)

469
views
tifr2018
pigeonholeprinciple
permutationandcombination
+28
votes
13
answers
14
GATE201846
The number of possible minheaps containing each value from $\{1,2,3,4,5,6,7\}$ exactly once is _______
answered
Dec 2, 2019
in
Combinatory
by
Praveenk99
(
83
points)

9.6k
views
gate2018
permutationandcombination
numericalanswers
+38
votes
11
answers
15
GATE2016126
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
answered
Dec 2, 2019
in
Combinatory
by
pritishc
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1.9k
points)

9.7k
views
gate20161
permutationandcombination
generatingfunctions
normal
numericalanswers
+1
vote
2
answers
16
ISI2014DCG71
Five letters $A, B, C, D$ and $E$ are arranged so that $A$ and $C$ are always adjacent to each other and $B$ and $E$ are never adjacent to each other. The total number of such arrangements is $24$ $16$ $12$ $32$
answered
Nov 28, 2019
in
Combinatory
by
noob_coder
Junior
(
785
points)

38
views
isi2014dcg
permutationandcombination
arrangements
circularpermutation
+2
votes
1
answer
17
Kenneth Rosen Edition 6th Exercise 6.4 Question 13 (Page No. 440)
Use Generating function to determine,the number of different ways $10$ identical balloons can be given to four children if each child receives atleast $2$ ballons? Ans given $(x^{2}+x^{3}+.........................)^{4}$ But as there is a upper ... Which one is correct? plz confirm
answered
Nov 26, 2019
in
Combinatory
by
Kushagra गुप्ता
Active
(
4k
points)

213
views
kennethrosen
discretemathematics
generatingfunctions
+1
vote
2
answers
18
ISI2016PCBA3
A bit string is called legitimate if it contains no consecutive zeros $, e.g., 0101110$ is legitimate, where as $10100111$ is not. Let $a_n$ denote the number of legitimate bit strings of length $n$. Define $a_0=1$. Derive a recurrence relation for $a_n ( i.e.,$ express $a_n$ in terms of the preceding $a_i's).$
answered
Nov 22, 2019
in
Combinatory
by
chirudeepnamini
Active
(
4.3k
points)

37
views
isi2016pcba
permutationandcombination
recurrencerelations
nongate
descriptive
+2
votes
3
answers
19
ISI2014DCG18
$^nC_0+2^nC_1+3^nC_2+\cdots+(n+1)^nC_n$ equals $2^n+n2^{n1}$ $2^nn2^{n1}$ $2^n$ none of these
answered
Nov 20, 2019
in
Combinatory
by
chirudeepnamini
Active
(
4.3k
points)

65
views
isi2014dcg
permutationandcombination
binomialtheorem
+1
vote
1
answer
20
ISI2018DCG14
In a room there are $8$ men, numbered $1,2, \dots ,8$. These men have to be divided into $4$ teams in such a way that every team has exactly $2$ ... of such $4$team combinations is $\frac{8!}{2^4}$ $\frac{8!}{2^4(4!)}$ $\frac{8!}{4!}$ $\frac{8!}{(4!)^2}$
answered
Nov 19, 2019
in
Combinatory
by
Yash4444
Junior
(
833
points)

35
views
isi2018dcg
permutationandcombination
+2
votes
1
answer
21
ISI2016DCG21
The value of the term independent of $x$ in the expansion of $(1x)^{2}(x+\frac{1}{x})^{7}$ is $70$ $70$ $35$ None of these
answered
Nov 18, 2019
in
Combinatory
by
Verma Ashish
Boss
(
12.9k
points)

30
views
isi2016dcg
permutationandcombination
binomialtheorem
+9
votes
3
answers
22
GATE20195
Let $U = \{1, 2, \dots , n\}$ Let $A=\{(x, X) \mid x \in X, X \subseteq U \}$. Consider the following two statements on $\mid A \mid$. $\mid A \mid = n2^{n1}$ $\mid A \mid = \Sigma_{k=1}^{n} k \begin{pmatrix} n \\ k \end{pmatrix}$ Which of the above statements is/are TRUE? Only I Only II Both I and II Neither I nor II
answered
Nov 14, 2019
in
Combinatory
by
Optimus Prime
Junior
(
631
points)

3.1k
views
gate2019
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
2
answers
23
MadeEasy Full Length Test 2019: Combinatory  Permutations And Combinations
The number of ways 5 letter be put in 3 letter boxes A,B,C. If letter box A must contain at least 2 letters.
answered
Nov 11, 2019
in
Combinatory
by
SaurabhKatkar
(
231
points)

233
views
discretemathematics
permutationandcombination
madeeasytestseries2019
madeeasytestseries
+2
votes
2
answers
24
Discrete Mathematics Thegatebook
how many positive integers between 50 and 100, (a) divisible by 7 (b) divisible by 11 (c) divisible by 7 and 11?
answered
Nov 10, 2019
in
Combinatory
by
Ram Swaroop
Loyal
(
5.3k
points)

310
views
inclusionexclusion
0
votes
2
answers
25
Rosen 7e Exercise8.1 Question no10 Page no511
Find a recurrence relation for the number of bit strings of length n that contain the string 01.
answered
Nov 9, 2019
in
Combinatory
by
Sandeep shahu
(
73
points)

69
views
kennethrosen
discretemathematics
permutationandcombination
#recurrencerelations
recurrence
+1
vote
1
answer
26
CMI2018A5
How many paths are there in the plane from $(0,0)$ to $(m,n)\in \mathbb{N}\times \mathbb{N},$ if the possible steps from $(i,j)$ are either $(i+1,j)$ or $(i,j+1)?$ $\binom{2m}{n}$ $\binom{m}{n}$ $\binom{m+n}{n}$ $m^{n}$
answered
Nov 9, 2019
in
Combinatory
by
`JEET
Boss
(
18.9k
points)

52
views
cmi2018
permutationandcombination
+1
vote
1
answer
27
#ACE ACADEMY BOOKLET QUESTION
The solution of $\sqrt{a_n} – 2\sqrt{a_{n1}} + \sqrt{a_{n2}} = 0$ where $a_0 = 1$ and $a_1 = 2$ is ${\Big[\frac{2^{n+1} + (1)^n}{3}\Big]}^2$ $(n+1)^2$ $(n1)^3$ $(n1)^2$
[closed]
answered
Nov 5, 2019
in
Combinatory
by
techbd123
Active
(
3.5k
points)

146
views
discretemathematics
permutationandcombination
recurrence
#recurrencerelations
+7
votes
4
answers
28
MadeEasy Test Series: Combinatory  Permutations And Combinations
MY SOLUTION : Fix the root then next level 2 elements ( 2! possibilities) next level 4 elements( 4! possibilities) last level 2 elements ( 2! possibilities) total possibility = 2! * 4! * 2! = 2 * 24 * 2 = 96 what ... that if node of above graph is filled with these elements it satisfies max heap property a)96 b)896 c)2688 d) none
answered
Nov 4, 2019
in
Combinatory
by
kunal goswami
Junior
(
615
points)

1.1k
views
permutationandcombination
madeeasytestseries
+2
votes
0
answers
29
The Interesting combination sum problems
Find the number of possible solutions for $x,y,z$ for each the following cases. $Case\ 1.$ Case of unlimited repetition. $x + y +z = 10$ and $x \geq 0\ , y \geq 0,\ z \geq 0 $ $Case\ 2 $ Case of unlimited repetition with variable lower bounds $x + y +z = 10$ and ... variable. $x + y +z = 10$ and $8 \geq x \geq 1\ , \ 20 \geq y \geq 2 \ , 12 \geq z \geq 3\ $
asked
Nov 1, 2019
in
Combinatory
by
Satbir
Boss
(
23.8k
points)

211
views
permutationandcombination
+39
votes
11
answers
30
GATE2014149
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 $2$pennants is ... $(1,2)$ is not the same as the pennant $(2,1)$. The number of $10$pennants is________
answered
Oct 28, 2019
in
Combinatory
by
paraskk
(
441
points)

3.2k
views
gate20141
permutationandcombination
numericalanswers
normal
+20
votes
5
answers
31
GATE20001.1
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 $3$ $8$ $9$ $12$
answered
Oct 22, 2019
in
Combinatory
by
Asim Siddiqui 4
Active
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1.5k
points)

3.3k
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gate2000
easy
pigeonholeprinciple
permutationandcombination
+2
votes
1
answer
32
ISI2018DCG4
The number of terms with integral coefficients in the expansion of $\left(17^\frac{1}{3}+19^\frac{1}{2}x\right)^{600}$ is $99$ $100$ $101$ $102$
answered
Oct 21, 2019
in
Combinatory
by
`JEET
Boss
(
18.9k
points)

51
views
isi2018dcg
permutationandcombination
binomialtheorem
+4
votes
2
answers
33
CMI2015A10
The school athletics coach has to choose $4$ students for the relay team. He calculates that there are $3876$ ways of choosing the team if the order in which the runners are placed is not considered. How many ways are there of choosing the team if the order of the runners is to be ... $12,000$ and $25,000$ Between $75,000$ and $99,999$ Between $30,000$ and $60,000$ More than $100,000$
answered
Oct 19, 2019
in
Combinatory
by
chirudeepnamini
Active
(
4.3k
points)

107
views
cmi2015
permutationandcombination
+1
vote
2
answers
34
ISI2015MMA8
Let $A$ be a set of $n$ elements. The number of ways, we can choose an ordered pair $(B,C)$, where $B,C$ are disjoint subsets of $A$, equals $n^2$ $n^3$ $2^n$ $3^n$
answered
Oct 19, 2019
in
Combinatory
by
chirudeepnamini
Active
(
4.3k
points)

44
views
isi2015mma
permutationandcombination
sets
0
votes
1
answer
35
ISI2015MMA9
Let $(1+x)^n = C_0+C_1x+C_2x^2+ \ldots +C_nx^n, \: n$ being a positive integer. The value of $\left( 1+\frac{C_0}{C_1} \right) \left( 1+\frac{C_1}{C_2} \right) \cdots \left( 1+\frac{C_{n1}}{C_n} \right)$ is $\left( \frac{n+1}{n+2} \right) ^n$ $ \frac{n^n}{n!} $ $\left( \frac{n}{n+1} \right) ^n$ $\frac{(n+1)^n}{n!}$
answered
Oct 19, 2019
in
Combinatory
by
chirudeepnamini
Active
(
4.3k
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16
views
isi2015mma
permutationandcombination
binomialtheorem
+2
votes
3
answers
36
ISI2015MMA4
Suppose in a competition $11$ matches are to be played, each having one of $3$ distinct outcomes as possibilities. The number of ways one can predict the outcomes of all $11$ matches such that exactly $6$ of the predictions turn out to be correct is $\begin{pmatrix}11 \\ 6 \end{pmatrix} \times 2^5$ $\begin{pmatrix}11 \\ 6 \end{pmatrix} $ $3^6$ none of the above
answered
Oct 19, 2019
in
Combinatory
by
chirudeepnamini
Active
(
4.3k
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46
views
isi2015mma
permutationandcombination
0
votes
1
answer
37
Rosen 7e Recurrence Relation Exercise8.1 Question no25 page no511
How many bit sequences of length seven contain an even number of 0s? I'm trying to solve this using recurrence relation Is my approach correct? Let T(n) be the string having even number of 0s T(1)=1 {1} T(2)=2 {00, 11} T(3)=4 {001, ... add 0 to strings of length n1 having odd number of 0s T(n)=T(n1) Hence, we have T(n)=2T(n1)
answered
Oct 17, 2019
in
Combinatory
by
anonymousgamer
(
11
points)

73
views
kennethrosen
discretemathematics
permutationandcombination
#recurrencerelations
recurrence
0
votes
1
answer
38
Combinatorics
There are 6n flowers of one type and 3 flowers of second type, total no. Of garlands possible?
answered
Oct 11, 2019
in
Combinatory
by
shivamgo
(
11
points)

38
views
permutationandcombination
+1
vote
1
answer
39
ISI2014DCG72
The sum $\sum_{k=1}^n (1)^k \:\: {}^nC_k \sum_{j=0}^k (1)^j \: \: {}^kC_j$ is equal to $1$ $0$ $1$ $2^n$
answered
Oct 10, 2019
in
Combinatory
by
techbd123
Active
(
3.5k
points)

37
views
isi2014dcg
permutationandcombination
summation
+7
votes
10
answers
40
GATE201921
The value of $3^{51} \text{ mod } 5$ is _____
answered
Oct 3, 2019
in
Combinatory
by
techbd123
Active
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3.5k
points)

4.1k
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gate2019
numericalanswers
permutationandcombination
modulararithmetic
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