Recent questions and answers in Combinatory

+19 votes

4 answers

1

GATE2000-5
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 9 hours ago in Combinatory by Verma Ashish Loyal (9.1k points) | 1.4k views

+4 votes

7 answers

2

TIFR2018-B-1
What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$

answered 15 hours ago in Combinatory by Verma Ashish Loyal (9.1k points) | 377 views

+2 votes

6 answers

3

GATE2019-21
The value of $3^{51} \text{ mod } 5$ is _____

answered 15 hours ago in Combinatory by Verma Ashish Loyal (9.1k points) | 2.7k views

+34 votes

5 answers

4

GATE2005-44
What is the minimum number of ordered pairs of non-negative 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 JashanArora (63 points) | 3.9k views

+2 votes

1 answer

5

ISI MTECH CS 2019 INTERVIEW question
As due to rain, the match between the teams in ICC world cup got canceled , So lets the total team be 10, exclude semi finals and finals , consider only league match, What is the total number of matches that played between the teams ... many ways those n matches can be conducted ? Source : https://gateoverflow.in/blog/8548/isi-mtech-cs-2019-interview-experience

answered Aug 8 in Combinatory by Shaik Masthan Veteran (61.9k points) | 74 views

+1 vote

2 answers

6

UGCNET-June-2019-II-3
How many bit strings of length ten either start with a $1$ bit or end with two bits $00$ ? $320$ $480$ $640$ $768$

answered Jul 23 in Combinatory by Lakshman Patel RJIT Boss (45.1k points) | 115 views

+13 votes

4 answers

7

GATE2007-IT-76
Consider the sequence $\langle x_n \rangle , \: n \geq 0$ defined by the recurrence relation $x_{n+1} = c . x^2_n -2$, where $c > 0$. Suppose there exists a non-empty, open interval $(a, b)$ such that for all $x_0$ satisfying $a < x_0 < b$, the sequence converges ... sequence converges to the value? $\frac{1+\sqrt{1+8c}}{2c}$ $\frac{1-\sqrt{1+8c}}{2c}$ $2$ $\frac{2}{2c-1}$

answered Jul 20 in Combinatory by ankitgupta.1729 Boss (14k points) | 1.2k views

+8 votes

8 answers

8

Kenneth Rosen Edition 6 Question 45 (Page No. 346)
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?

answered Jul 14 in Combinatory by srestha Veteran (113k points) | 2.2k views

+1 vote

2 answers

9

UGCNET-June-2019-II-2
How many ways are there to place $8$ indistinguishable balls into four distinguishable bins? $70$ $165$ $^8C_4$ $^8P_4$

answered Jul 13 in Combinatory by Lakshman Patel RJIT Boss (45.1k points) | 180 views

+2 votes

2 answers

10

MADEEASY
Consider a set S={1000,1001,1002........,9999}. The numbers in set S having atleast one digit as 2 and atleast one digit as 5 are?

answered Jul 11 in Combinatory by srestha Veteran (113k points) | 246 views

+9 votes

4 answers

11

ISI 2004 MIII
The number of permutation of $\{1,2,3,4,5\}$ that keep at least one integer fixed is. $81$ $76$ $120$ $60$

answered Jul 9 in Combinatory by Debargha Bhattacharj Junior (515 points) | 629 views

+10 votes

6 answers

12

TIFR2015-A-7
A $1 \times 1$ chessboard has one square, a $2 \times 2$ chessboard has five squares. Continuing along this fashion, what is the number of squares on the regular $8 \times 8$ chessboard? $64$ $65$ $204$ $144$ $256$

answered Jul 7 in Combinatory by Bishal1997 (11 points) | 721 views

+2 votes

1 answer

13

UGCNET-June-2019-II-63
Consider the Euler’s phi function given by $\phi(n) = n \underset{p/n}{\Pi } \bigg( 1 – \frac{1}{p} \bigg)$ where $p$ runs over all the primes dividing $n$. What is the value of $\phi(45)$? $3$ $12$ $6$ $24$

answered Jul 6 in Combinatory by Ram Swaroop Active (3.9k points) | 39 views

+1 vote

3 answers

14

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?

answered Jul 6 in Combinatory by venkatesh pagadala Junior (555 points) | 292 views

0 votes

1 answer

15

Four cups and saucers
A tea set has four cups and saucers with two cups and saucers in each of two different colours. If the cups are placed at random on the saucers, what is the probability that no cup is on a saucer of the same colour?

answered Jul 4 in Combinatory by Yash4444 Junior (565 points) | 36 views

0 votes

2 answers

16

Permutation and combination
9 different books are to be arranged on a bookshelf. 4 of these books were written by Shakespeare, 2 by Dickens, and 3 by Conrad. How many possible permutations are there if the books by Conrad must be separated from one another?

answered Jul 3 in Combinatory by Gurdeep Saini Loyal (9.9k points) | 120 views

+1 vote

1 answer

17

UGCNET-June-2019-II-7
How many cards must be selected from a standard deck of $52$ cards to guarantee that at least three hearts are present among them? $9$ $13$ $17$ $42$

answered Jul 2 in Combinatory by Satbir Boss (17.2k points) | 88 views

0 votes

3 answers

18

Self Doubt-Combinatory
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 Jul 2 in Combinatory by sahil bhalla (11 points) | 86 views

+4 votes

6 answers

19

TIFR2019-B-13
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 26 in Combinatory by Arkaprava Active (2.1k points) | 373 views

+13 votes

6 answers

20

GATE2005-50
Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$? $i$ $i+1$ $2i$ $2^i$

answered Jun 25 in Combinatory by Satbir Boss (17.2k points) | 1.4k views

0 votes

1 answer

21

Kenneth Rosen: Counting-13
How many bit strings with length not exceeding $n$ ,where n is a positive integer ,consist entirely of $1's?$

answered Jun 25 in Combinatory by srestha Veteran (113k points) | 88 views

+22 votes

12 answers

22

GATE2018-46
The number of possible min-heaps containing each value from $\{1,2,3,4,5,6,7\}$ exactly once is _______

answered Jun 19 in Combinatory by Kuldeep Pal Active (1.4k points) | 7.6k views

+38 votes

11 answers

23

GATE2015-3-5
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 ________.

answered Jun 19 in Combinatory by Kuldeep Pal Active (1.4k points) | 3.9k views

+23 votes

7 answers

24

GATE2004-IT-35
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 Jun 19 in Combinatory by Kuldeep Pal Active (1.4k points) | 2.6k views

+19 votes

3 answers

25

TIFR2014-A-5
The rules for the University of Bombay five-a-side 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 in Combinatory by Kuldeep Pal Active (1.4k points) | 862 views

+34 votes

7 answers

26

GATE2017-2-47
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .

answered Jun 17 in Combinatory by mohan123 Junior (663 points) | 5.5k views

+13 votes

8 answers

27

GATE2018-1
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1-x)^2}$ $\frac{3x}{(1-x)^2}$ $\frac{2-x}{(1-x)^2}$ $\frac{3-x}{(1-x)^2}$

answered Jun 17 in Combinatory by Kuldeep Pal Active (1.4k points) | 5.8k views

+18 votes

3 answers

28

GATE1999-2.2
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 bruce-bayne (21 points) | 3.8k views

0 votes

1 answer

29

ISI2017-MMA-26
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 Junior (555 points) | 30 views

0 votes

0 answers

30

#ACE ACADEMY BOOKLET QUESTION
The solution of $\sqrt{a_n} – 2\sqrt{a_{n-1}} + \sqrt{a_{n-2}} = 0$ where $a_0 = 1$ and $a_1 = 2$ is ${\Big[\frac{2^{n+1} + (-1)^n}{3}\Big]}^2$ $(n+1)^2$ $(n-1)^3$ $(n-1)^2$

asked Jun 5 in Combinatory by `JEET Active (3.5k points) | 89 views

0 votes

0 answers

31

#Rosen exercise-1 ,question-71 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 (249 points) | 29 views

0 votes

1 answer

32

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 Active (1k points) | 50 views

0 votes

2 answers

33

Rosen 7e Exercise-8.5 Question-15 page no-558 Inclusion-Exclusion
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 Active (4k points) | 73 views

0 votes

2 answers

34

UGCNET-Dec2012-III-25
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 Active (1.5k points) | 1.6k views

0 votes

1 answer

35

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?

answered May 14 in Combinatory by Raghava45 (333 points) | 47 views

0 votes

2 answers

36

Recurrence Relation
Let $T(n) = T(n-1) + \frac{1}{n} , T(1) = 1 ;$ then $T(n) = ? $ $O(n^{2})$ $O(logn)$ $O(nlogn)$ $O(n^{2}logn)$

answered May 14 in Combinatory by Raghava45 (333 points) | 146 views

0 votes

0 answers

37

Rosen 7e Exercise 8.2 Questionno-26 page no-525 Recurrence Relation
What is the general form of the particular solution guaranteed to exist of the linear nonhomogeneous recurrence relation $a_n$=$6a_{n-1}$-$12a_{n-2}$+$8a_{n-3}$+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 Active (4k points) | 39 views

0 votes

0 answers

38

Rosen 7e Exercise-8.2 Question no-23 page no-525 Recurrence Relation
Consider the nonhomogeneous linear recurrence relation $a_n$=$3a_{n-1}$+$2^n$ in the book solution is given $a_n$=$-2^{n+1}$ but I’m getting $a_n$=$3^{n+1}-2^{n+1}$

asked May 13 in Combinatory by aditi19 Active (4k points) | 27 views

0 votes

1 answer

39

ISI2018-MMA-10
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 (7k points) | 43 views

0 votes

2 answers

40

#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 (113k points) | 40 views

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