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Recent questions and answers in Combinatory
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NIELIT 2017 July Scientist B (IT)  Section B: 14
There are four bus lines between A and B; and three bus lines between B and C The number of way a person roundtrip by bus from A to C by way of B will be $12$ $7$ $144$ $264$
answered
5 days
ago
in
Combinatory
by
immanujs
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2.9k
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10
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nielit2017julyscientistbit
0
votes
0
answers
2
NIELIT 2016 MAR Scientist B  Section B: 1
The number of ways to cut a six sided convex polygon whose vertices are labeled into four triangles using diagonal lines that do not cross is $13$ $14$ $12$ $11$
asked
Mar 31
in
Combinatory
by
Lakshman Patel RJIT
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61.4k
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6
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nielit2016marscientistb
0
votes
0
answers
3
NIELIT 2016 MAR Scientist B  Section B: 2
The number of ways in which a team of eleven players can be selected from $22$ players including $2$ of them and excluding $4$ of them is $16\large_{C_{11}}$ $16\large_{C_{5}}$ $16\large_{C_{9}}$ $20\large_{C_{9}}$
asked
Mar 31
in
Combinatory
by
Lakshman Patel RJIT
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(
61.4k
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9
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nielit2016marscientistb
0
votes
0
answers
4
NIELIT 2016 DEC Scientist B (IT)  Section B: 34
Mala has a colouring book in which each english letter is drawn two times. She wants to point each of these $52$ prints with one of $k$ colours, such that the colourpairs used to colour ay two letters are different. Both prints of a letter ... with the same colour. What is the minimum value of $k$ that satisfies this requirement? $9$ $8$ $7$ $6$
asked
Mar 31
in
Combinatory
by
Lakshman Patel RJIT
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(
61.4k
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6
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nielit2016decscientistbit
+1
vote
1
answer
5
ISI2016PCBCS8
Consider all possible trees with $n$ nodes. Let $k$ be the number of nodes with degree greater than 1 in a given tree. What is the maximum possible value of $k$? Justify your answer. Consider $2n$ committees, each having at least $2n$ persons, formed from a group of $4n$ persons. Prove that there exists at least one person who belongs to at least $n$ committees.
answered
Mar 18
in
Combinatory
by
Falahamin
(
21
points)

48
views
isi2016pcbcs
permutationandcombination
descriptive
0
votes
1
answer
6
ISI2016MMA25
A integer is said to be a $\textbf{palindrome}$ if it reads the same forward or backward. For example, the integer $14541$ is a $5$digit palindrome and $12345$ is not a palindrome. How many $8$digit palindromes are prime? $0$ $1$ $11$ $19$
answered
Mar 18
in
Combinatory
by
Falahamin
(
21
points)

25
views
isi2016mmamma
permutationandcombination
+4
votes
6
answers
7
GATE2020CS42
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 ______.
answered
Mar 15
in
Combinatory
by
felics moses 1
(
139
points)

1.5k
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gate2020cs
numericalanswers
engineeringmathematics
+1
vote
2
answers
8
ISI2017MMA26
Let $n$ be the number of ways in which $5$ men and $7$ women can stand in a queue such that all the women stand consecutively. Let $m$ be the number of ways in which the same $12$ persons can stand in a queue such that exactly $6$ women stand consecutively. Then the value of $\frac{m}{n}$ is $5$ $7$ $\frac{5}{7}$ $\frac{7}{5}$
answered
Mar 9
in
Combinatory
by
kraken_wizard
(
41
points)

99
views
isi2017mma
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
1
answer
9
website
There is 4 coins 1 paisa, 5 paise, 10 paise, 25 paise using these coins we have to make 50 paisa how many combination can we make ?
answered
Mar 1
in
Combinatory
by
smsubham
Boss
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16.8k
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46
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permutationandcombination
+3
votes
2
answers
10
Rosen 7e Exercise6.5 question 45.b page 433
How many ways can n books be placed on k distinguishable shelves if no two books are the same, and the positions of the books on the shelves matter?
answered
Mar 1
in
Combinatory
by
smsubham
Boss
(
16.8k
points)

216
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kennethrosen
discretemathematics
permutationandcombination
+17
votes
3
answers
11
TIFR2012A7
It is required to divide the $2n$ members of a club into $n$ disjoint teams of $2$ members each. The teams are not labelled. The number of ways in which this can be done is: $\frac{\left ( 2n \right )!}{2^{n}}$ $\frac{\left ( 2n \right )!}{n!}$ $\frac{\left ( 2n \right )!}{2^n . n!}$ $\frac{n!}{2}$ None of the above.
answered
Feb 15
in
Combinatory
by
Pratyush Priyam Kuan
Active
(
1.1k
points)

1.4k
views
tifr2012
permutationandcombination
ballsinbins
+30
votes
9
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
Feb 15
in
Combinatory
by
Pratyush Priyam Kuan
Active
(
1.1k
points)

3.5k
views
gate2004it
permutationandcombination
normal
ballsinbins
+16
votes
6
answers
13
GATE200334
$m$ identical balls are to be placed in $n$ distinct bags. You are given that $m \geq kn$, where $k$ is a natural number $\geq 1$. In how many ways can the balls be placed in the bags if each bag must contain at least $k$ ... $\left( \begin{array}{c} m  kn + n + k  2 \\ n  k \end{array} \right)$
answered
Feb 15
in
Combinatory
by
Pratyush Priyam Kuan
Active
(
1.1k
points)

2.8k
views
gate2003
permutationandcombination
ballsinbins
normal
+22
votes
4
answers
14
GATE200213
In how many ways can a given positive integer $n \geq 2$ be expressed as the sum of $2$ positive integers (which are not necessarily distinct). For example, for $n=3$ the number of ways is $2$, i.e., $1+2, 2+1$. Give only the answer ... integer $n \geq k$ be expressed as the sum of $k$ positive integers (which are not necessarily distinct). Give only the answer without explanation.
answered
Feb 15
in
Combinatory
by
Pratyush Priyam Kuan
Active
(
1.1k
points)

1.6k
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gate2002
permutationandcombination
normal
descriptive
ballsinbins
+9
votes
12
answers
15
GATE201921
The value of $3^{51} \text{ mod } 5$ is _____
answered
Feb 14
in
Combinatory
by
Pratyush Priyam Kuan
Active
(
1.1k
points)

6.1k
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gate2019
numericalanswers
permutationandcombination
modulararithmetic
+44
votes
10
answers
16
GATE2016127
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
answered
Feb 2
in
Combinatory
by
Lakshman Patel RJIT
Veteran
(
61.4k
points)

8.5k
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gate20161
permutationandcombination
recurrence
normal
numericalanswers
0
votes
1
answer
17
sheldon ross
Three balls are to be randomly selected without replacement from an urn containing $20$ balls numbered $1$ through $20$. If we bet that at least one of the balls that are drawn has a number as large as or larger than $17$, what is the probability that we win the bet?
answered
Jan 31
in
Combinatory
by
Ayan Kumar Pahari
Junior
(
553
points)

132
views
probability
randomvariable
+41
votes
12
answers
18
GATE2016126
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
answered
Jan 29
in
Combinatory
by
Srividyaketharaju
(
117
points)

10.4k
views
gate20161
permutationandcombination
generatingfunctions
normal
numericalanswers
+7
votes
10
answers
19
TIFR2018B1
What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$
answered
Jan 29
in
Combinatory
by
shivam001
Active
(
1.2k
points)

702
views
tifr2018
modulararithmetic
permutationandcombination
+37
votes
8
answers
20
GATE2017247
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1z)^3}$, then $a_3a_0$ is equal to ___________ .
answered
Jan 29
in
Combinatory
by
ankitgupta.1729
Boss
(
18.1k
points)

6.8k
views
gate20172
permutationandcombination
generatingfunctions
numericalanswers
normal
+21
votes
5
answers
21
GATE20005
A multiset is an unordered collection of elements where elements may repeat any number of times. The size of a multiset is the number of elements in it, counting repetitions. What is the number of multisets of size $4$ that can be constructed from n distinct elements so that at least one element occurs exactly twice? How many multisets can be constructed from n distinct elements?
answered
Jan 26
in
Combinatory
by
blackcloud
Junior
(
675
points)

1.8k
views
gate2000
permutationandcombination
normal
descriptive
+1
vote
1
answer
22
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
Jan 16
in
Combinatory
by
suvradip das
(
189
points)

245
views
discretemathematics
permutationandcombination
madeeasytestseries2019
madeeasytestseries
+38
votes
2
answers
23
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
Jan 16
in
Combinatory
by
Rishiryanemo
(
29
points)

1.7k
views
gate1991
permutationandcombination
normal
descriptive
catalannumber
+27
votes
4
answers
24
GATE20012.1
How many $4$digit even numbers have all $4$ digits distinct $2240$ $2296$ $2620$ $4536$
answered
Jan 14
in
Combinatory
by
Kushagra गुप्ता
Loyal
(
6k
points)

4k
views
gate2001
permutationandcombination
normal
+42
votes
7
answers
25
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
Jan 13
in
Combinatory
by
Kushagra गुप्ता
Loyal
(
6k
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5k
views
gate2005
settheory&algebra
normal
pigeonholeprinciple
+17
votes
7
answers
26
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
(
323
points)

2k
views
gate2005
normal
generatingfunctions
+30
votes
2
answers
27
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
(
323
points)

2.8k
views
gate2003
permutationandcombination
normal
+23
votes
10
answers
28
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
Active
(
1.9k
points)

7.7k
views
gate2018
generatingfunctions
normal
permutationandcombination
+1
vote
3
answers
29
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
(
927
points)

2.9k
views
isi2019mma
engineeringmathematics
discretemathematics
permutationandcombination
+1
vote
1
answer
30
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)

48
views
isi2017dcg
permutationandcombination
binomialtheorem
+1
vote
1
answer
31
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
(
369
points)

86
views
permutationandcombination
propositionallogic
kennethrosen
discretemathematics
generatingfunctions
+10
votes
5
answers
32
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
(
19.7k
points)

532
views
tifr2018
pigeonholeprinciple
permutationandcombination
+31
votes
13
answers
33
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
(
99
points)

10.8k
views
gate2018
permutationandcombination
numericalanswers
+1
vote
2
answers
34
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
(
825
points)

61
views
isi2014dcg
permutationandcombination
arrangements
circularpermutation
+2
votes
1
answer
35
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
Loyal
(
6k
points)

246
views
kennethrosen
discretemathematics
generatingfunctions
+1
vote
2
answers
36
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
Loyal
(
5.3k
points)

55
views
isi2016pcba
permutationandcombination
recurrencerelations
nongate
descriptive
+3
votes
0
answers
37
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
(
25.5k
points)

248
views
permutationandcombination
+2
votes
2
answers
38
ISI2014DCG1
Let $(1+x)^n = C_0+C_1x+C_2x^2+ \dots + C_nx^n$, $n$ being a positive integer. The value of $\left( 1+\dfrac{C_0}{C_1} \right) \left( 1+\dfrac{C_1}{C_2} \right) \cdots \left( 1+\dfrac{C_{n1}}{C_n} \right)$ 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!} $
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
436k
points)

206
views
isi2014dcg
permutationandcombination
binomialtheorem
+2
votes
3
answers
39
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
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
436k
points)

102
views
isi2014dcg
permutationandcombination
binomialtheorem
+2
votes
0
answers
40
ISI2014DCG32
Consider $30$ multiplechoice questions, each with four options of which exactly one is correct. Then the number of ways one can get only the alternate questions correctly answered is $3^{15}$ $2^{31}$ $2 \times \begin{pmatrix} 30 \\ 15 \end{pmatrix}$ $2 \times 3^{15}$
asked
Sep 23, 2019
in
Combinatory
by
Arjun
Veteran
(
436k
points)

115
views
isi2014dcg
permutationandcombination
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