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Recent questions and answers in Combinatory
+20
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12
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1
GATE201846
The number of possible minheaps containing each value from $\{1,2,3,4,5,6,7\}$ exactly once is _______
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Combinatory
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gate2018
permutationandcombination
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+37
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11
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2
GATE201535
The number of $4$ digit numbers having their digits in nondecreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.
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Combinatory
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gate20153
permutationandcombination
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+23
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7
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3
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? $44$ $96$ $120$ $3125$
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gate2004it
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4
Model Question IISc CDS CS Written Test Sample question
Anand is preparing a pizza with 8 slices, and he has 10 toppings to put on the pizza. He can put only one topping on each slice but can use the same topping on zero or more slices. In how many unique ways can he prepare the slices so that the same topping is not used in adjacent slices?
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Combinatory
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Satbir
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205
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iisc
cds
+19
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3
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5
TIFR2014A5
The rules for the University of Bombay fiveaside cricket competition specify that the members of each team must have birthdays in the same month. What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students? $23$ $91$ $60$ $49$ None of the above.
answered
Jun 17
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Combinatory
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Kuldeep Pal
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tifr2014
permutationandcombination
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pigeonholeprinciple
+34
votes
7
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6
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
Jun 17
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Combinatory
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mohan123
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135
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5.4k
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gate20172
permutationandcombination
generatingfunctions
numericalanswers
normal
+13
votes
8
answers
7
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
Jun 17
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Combinatory
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Kuldeep Pal
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1.3k
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5.7k
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gate2018
generatingfunctions
normal
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+17
votes
3
answers
8
GATE19992.2
Two girls have picked $10$ roses, $15$ sunflowers and $15$ daffodils. What is the number of ways they can divide the flowers among themselves? $1638$ $2100$ $2640$ None of the above
answered
Jun 14
in
Combinatory
by
brucebayne
(
21
points)

3.6k
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gate1999
permutationandcombination
normal
0
votes
2
answers
9
Self DoubtCombinatory
In how many ways we can put $n$ distinct balls in $k$ dintinct bins?? Will it be $n^{k}$ or $k^{n}$?? Taking example will be easy way to remove this doubt or some other ways possible??
answered
Jun 9
in
Combinatory
by
Koushik Sinha 2
(
253
points)

61
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discretemathematics
permutationandcombination
+3
votes
5
answers
10
TIFR2019B13
A row of $10$ houses has to be painted using the colours red, blue, and green so that each house is a single colour, and any house that is immediately to the right of a red or a blue house must be green. How many ways are there to paint the houses? $199$ $683$ $1365$ $3^{10}2^{10}$ $3^{10}$
answered
Jun 8
in
Combinatory
by
shaktisingh
(
91
points)

280
views
tifr2019
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
1
answer
11
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 $5$ $7$ $5/7$ $7/5$
answered
Jun 7
in
Combinatory
by
venkatesh pagadala
(
495
points)

27
views
isi2017
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
0
answers
12
#ACE ACADEMY BOOKLET QUESTION
The solution of $\sqrt{a_n} ā 2\sqrt{a_{n1}} + \sqrt{a_{n2}} = 0$ where $a_0 = 1$ and $a_1 = 2$ is ${\Big[\frac{2^{n+1} + (1)^n}{3}\Big]}^2$ $(n+1)^2$ $(n1)^3$ $(n1)^2$
asked
Jun 5
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Combinatory
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`JEET
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67
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discretemathematics
permutationandcombination
recurrence
#recurrencerelations
0
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0
answers
13
#Rosen exercise1 ,question71 counting
use mathematical induction to prove the sum rule for m tasks from the sum rule for two tasks.
asked
May 31
in
Combinatory
by
sandeep singh gaur
(
243
points)

22
views
counting
0
votes
1
answer
14
A first course in probability by Sheldon Ross
What are the relevant chapter of probability by sheldon ross to study for gate? I think whole syllabus is within chapter 5,Should i study everything upto chapter 5 or there are some topics that can be skipped.
answered
May 27
in
Combinatory
by
Asim Siddiqui 4
Junior
(
843
points)

46
views
probability
sheldonross
0
votes
2
answers
15
Rosen 7e Exercise8.5 Question15 page no558 InclusionExclusion
How many permutations of the 10 digits either begin with the 3 digits 987, contain the digits 45 in the fifth and sixth positions, or end with the 3 digits 123?
answered
May 26
in
Combinatory
by
aditi19
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3.7k
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64
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discretemathematics
kennethrosen
inclusionexclusion
0
votes
2
answers
16
UGCNETDec2012III25
The number of distinct bracelets of five beads made up of red, blue and green beads (two bracelets are indistinguishable if the rotation of one yield another) is, 243 81 51 47
answered
May 15
in
Combinatory
by
Kuljeet Shan
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1.5k
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1.6k
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ugcnetdec2012iii
0
votes
1
answer
17
Recurrence Relation SelfDoubt
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?
answered
May 14
in
Combinatory
by
Raghava45
(
331
points)

37
views
relations
recurrence
recurrenceeqation
discretemathematics
combinational
0
votes
2
answers
18
Recurrence Relation
Let $T(n) = T(n1) + \frac{1}{n} , T(1) = 1 ;$ then $T(n) = ? $ $O(n^{2})$ $O(logn)$ $O(nlogn)$ $O(n^{2}logn)$
answered
May 14
in
Combinatory
by
Raghava45
(
331
points)

135
views
discretemathematics
recurrence
relations
recurrenceeqation
0
votes
0
answers
19
Rosen 7e Exercise 8.2 Questionno26 page no525 Recurrence Relation
What is the general form of the particular solution guaranteed to exist of the linear nonhomogeneous recurrence relation $a_n$=$6a_{n1}$$12a_{n2}$+$8a_{n3}$+F(n) if F(n)=$n^2$ F(n)=$2^n$ F(n)=$n2^n$ F(n)=$(2)^n$ F(n)=$n^22^n$ F(n)=$n^3(2)^n$ F(n)=3
asked
May 14
in
Combinatory
by
aditi19
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3.7k
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34
views
kennethrosen
discretemathematics
#recurrencerelations
recurrence
0
votes
0
answers
20
Rosen 7e Exercise8.2 Question no23 page no525 Recurrence Relation
Consider the nonhomogeneous linear recurrence relation $a_n$=$3a_{n1}$+$2^n$ in the book solution is given $a_n$=$2^{n+1}$ but Iām getting $a_n$=$3^{n+1}2^{n+1}$
asked
May 13
in
Combinatory
by
aditi19
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3.7k
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23
views
kennethrosen
discretemathematics
#recurrencerelations
recurrence
0
votes
1
answer
21
ISI2018MMA10
A new flag of ISI club is to be designed with $5$ vertical strips using some or all of the four colors: green, maroon, red and yellow. In how many ways this can be done so that no two adjacent strips have the same color? $120$ $324$ $424$ $576$
answered
May 13
in
Combinatory
by
Sayan Bose
Loyal
(
6.9k
points)

31
views
isi2018
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
2
answers
22
#probability(self doubt)
An automobile showroom has 10 cars, 2 of which are defective. If you are going to buy the 6th car sold that day at random, then the probability of selecting a defective car is??
answered
May 13
in
Combinatory
by
srestha
Veteran
(
111k
points)

34
views
#probability
self
doubt
+1
vote
1
answer
23
ISI2018MMA26
Let $C_i(i=0,1,2...n)$ be the coefficient of $x^i$ in $(1+x)^n$.Then $\frac{C_0}{2} ā \frac{C_1}{3}+\frac{C_2}{4}\dots +(1)^n \frac{C_n}{n+2}$ is equal to $\frac{1}{n+1}\\$ $\frac{1}{n+2}\\$ $\frac{1}{n(n+1)}\\$ $\frac{1}{(n+1)(n+2)}$
answered
May 11
in
Combinatory
by
srestha
Veteran
(
111k
points)

107
views
isi2018
engineeringmathematics
discretemathematics
generatingfunctions
0
votes
2
answers
24
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
May 11
in
Combinatory
by
amolcharpe
(
27
points)

2.8k
views
isi2019
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
2
answers
25
ISI2019MMA20
Suppose that the number plate of a vehicle contains two vowels followed by four digits. However, to avoid confusion, the letter āOā and the digit ā0ā are not used in the same number plate. How many such number plates can be formed? $164025$ $190951$ $194976$ $219049$
answered
May 9
in
Combinatory
by
Utkarsh Joshi
Loyal
(
7.6k
points)

320
views
isi2019
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
1
answer
26
ISI2019MMA2
The number of $6$ digit positive integers whose sum of the digits is at least $52$ is $21$ $22$ $27$ $28$
answered
May 6
in
Combinatory
by
pratekag
Active
(
2k
points)

231
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isi2019
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
1
answer
27
ISI2019MMA4
Suppose that $6$digit numbers are formed using each of the digits $1, 2, 3, 7, 8, 9$ exactly once. The number of such $6$digit numbers that are divisible by $6$ but not divisible by $9$ is equal to $120$ $180$ $240$ $360$
answered
May 6
in
Combinatory
by
pratekag
Active
(
2k
points)

193
views
isi2019
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
1
answer
28
UPPCL AE 2018:66
answered
May 3
in
Combinatory
by
Abhisek Tiwari 4
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4.5k
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26
views
uppcl2018
0
votes
2
answers
29
Suppose a 6 digit number N is formed by rearranging the digits of the number 123456
answered
May 1
in
Combinatory
by
kratos
(
11
points)

535
views
permutationandcombination
0
votes
0
answers
30
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)
asked
Apr 29
in
Combinatory
by
aditi19
Active
(
3.7k
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40
views
kennethrosen
discretemathematics
permutationandcombination
#recurrencerelations
recurrence
0
votes
1
answer
31
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
Apr 28
in
Combinatory
by
srestha
Veteran
(
111k
points)

38
views
kennethrosen
discretemathematics
permutationandcombination
#recurrencerelations
recurrence
+1
vote
1
answer
32
Pgee 2013
You have a box containing 10 black and 10 blue socks.What is the minimum number of times you need to pull out so that you have a pair of the same color?
answered
Apr 22
in
Combinatory
by
Manas Mishra
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(
2.8k
points)

89
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iiithpgee
0
votes
0
answers
33
Kenneth H Rosen 7th edition
Please see example 6. l am not getting the mathematical insight. Can anyone please tell how they are arriving at the answer.
asked
Apr 21
in
Combinatory
by
Psnjit
(
191
points)

45
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kennethrosen
discretemathematics
permutationandcombination
+2
votes
1
answer
34
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
Apr 20
in
Combinatory
by
ma1999
(
11
points)

170
views
kennethrosen
discretemathematics
permutationandcombination
0
votes
1
answer
35
Madeeasy Discrete Maths notes
How many 5 letter word possible having atleast 2 a's ?
answered
Apr 9
in
Combinatory
by
tusharp
Loyal
(
6.5k
points)

65
views
madeeasynotes
discretemathematics
permutationandcombination
0
votes
1
answer
36
Self doubt
How is the problem.. Distribute 5 toys such that each of 3 child get atleast 1 Different from sum of 3 no. X+y+z=5 such that each digit >= 1. Plz explain ?
answered
Apr 4
in
Combinatory
by
hitendra singh
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(
1.7k
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57
views
permutationandcombination
0
votes
0
answers
37
Combinatorics
There are 6n flowers of one type and 3 flowers of second type, total no. Of garlands possible?
asked
Apr 2
in
Combinatory
by
Manoj Kumar Pandey
(
141
points)

18
views
permutationandcombination
0
votes
0
answers
38
General Query: Self doubt(Math+Automata)
Can somebody explain What is identity permutation?
asked
Apr 1
in
Combinatory
by
srestha
Veteran
(
111k
points)

23
views
discretemathematics
finiteautomata
0
votes
0
answers
39
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 ?
asked
Mar 31
in
Combinatory
by
Cristine
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1.8k
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26
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permutationandcombination
+1
vote
3
answers
40
MadeEasy Subject Test 2019: Combinatory  Permutations And Combinations
Q.The number of ways, we can arrange 5 books in 3 shelves ________.
answered
Mar 26
in
Combinatory
by
Arkaprava
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1.8k
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369
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discretemathematics
permutationandcombination
madeeasytestseries2019
madeeasytestseries
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