The Gateway to Computer Science Excellence
For all GATE CSE Questions
Toggle navigation
Facebook Login
or
Email or Username
Password
Remember
Login
Register

I forgot my password
All Activity
Questions
Unanswered
Tags
Categories
Users
Ask a Question
Prev
Blogs
New Blog
Exams
First time here? Checkout the
FAQ
!
x
×
Close
Use the google search bar on side panel. It searches through all previous GATE/other questions. For hardcopy of previous year questions please see
here
Recent questions and answers in Combinatory
+19
votes
4
answers
1
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
9 hours
ago
in
Combinatory
by
Verma Ashish
Loyal
(
9.1k
points)

1.4k
views
gate2000
permutationandcombination
normal
descriptive
+4
votes
7
answers
2
TIFR2018B1
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
tifr2018
modulararithmetic
permutationandcombination
+2
votes
6
answers
3
GATE201921
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
gate2019
numericalanswers
permutationandcombination
modulararithmetic
+34
votes
5
answers
4
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
JashanArora
(
63
points)

3.9k
views
gate2005
settheory&algebra
normal
pigeonholeprinciple
+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/isimtechcs2019interviewexperience
answered
Aug 8
in
Combinatory
by
Shaik Masthan
Veteran
(
61.9k
points)

74
views
permutationandcombination
+1
vote
2
answers
6
UGCNETJune2019II3
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
ugcnetjune2019ii
permutationandcombination
inclusionexclusion
+13
votes
4
answers
7
GATE2007IT76
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 nonempty, open interval $(a, b)$ such that for all $x_0$ satisfying $a < x_0 < b$, the sequence converges ... sequence converges to the value? $\frac{1+\sqrt{1+8c}}{2c}$ $\frac{1\sqrt{1+8c}}{2c}$ $2$ $\frac{2}{2c1}$
answered
Jul 20
in
Combinatory
by
ankitgupta.1729
Boss
(
14k
points)

1.2k
views
gate2007it
permutationandcombination
normal
recurrence
+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
permutationandcombination
counting
+1
vote
2
answers
9
UGCNETJune2019II2
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
ugcnetjune2019ii
permutationandcombination
+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
counting
+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
permutationandcombination
isi2004
discretemathematics
normal
+10
votes
6
answers
12
TIFR2015A7
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
tifr2015
permutationandcombination
+2
votes
1
answer
13
UGCNETJune2019II63
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
ugcnetjune2019ii
eulerphifunction
+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
iisc
cds
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
probability
permutationandcombination
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
engineeringmathematics
discretemathematics
permutationandcombination
+1
vote
1
answer
17
UGCNETJune2019II7
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
ugcnetjune2019ii
permutationandcombination
pigeonholeprinciple
0
votes
3
answers
18
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
Jul 2
in
Combinatory
by
sahil bhalla
(
11
points)

86
views
discretemathematics
permutationandcombination
+4
votes
6
answers
19
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 26
in
Combinatory
by
Arkaprava
Active
(
2.1k
points)

373
views
tifr2019
engineeringmathematics
discretemathematics
permutationandcombination
medium
+13
votes
6
answers
20
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
Jun 25
in
Combinatory
by
Satbir
Boss
(
17.2k
points)

1.4k
views
gate2005
normal
generatingfunctions
0
votes
1
answer
21
Kenneth Rosen: Counting13
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
counting
discretemathematics
+22
votes
12
answers
22
GATE201846
The number of possible minheaps 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
gate2018
permutationandcombination
numericalanswers
+38
votes
11
answers
23
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 ________.
answered
Jun 19
in
Combinatory
by
Kuldeep Pal
Active
(
1.4k
points)

3.9k
views
gate20153
permutationandcombination
normal
numericalanswers
+23
votes
7
answers
24
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
Jun 19
in
Combinatory
by
Kuldeep Pal
Active
(
1.4k
points)

2.6k
views
gate2004it
permutationandcombination
normal
ballsinbins
+19
votes
3
answers
25
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
in
Combinatory
by
Kuldeep Pal
Active
(
1.4k
points)

862
views
tifr2014
permutationandcombination
discretemathematics
normal
pigeonholeprinciple
+34
votes
7
answers
26
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
in
Combinatory
by
mohan123
Junior
(
663
points)

5.5k
views
gate20172
permutationandcombination
generatingfunctions
numericalanswers
normal
+13
votes
8
answers
27
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
in
Combinatory
by
Kuldeep Pal
Active
(
1.4k
points)

5.8k
views
gate2018
generatingfunctions
normal
permutationandcombination
+18
votes
3
answers
28
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)

3.8k
views
gate1999
permutationandcombination
normal
0
votes
1
answer
29
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
Junior
(
555
points)

30
views
isi2017
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
0
answers
30
#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 ${\Big[\frac{2^{n+1} + (1)^n}{3}\Big]}^2$ $(n+1)^2$ $(n1)^3$ $(n1)^2$
asked
Jun 5
in
Combinatory
by
`JEET
Active
(
3.5k
points)

89
views
discretemathematics
permutationandcombination
recurrence
#recurrencerelations
0
votes
0
answers
31
#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
(
249
points)

29
views
counting
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
probability
sheldonross
0
votes
2
answers
33
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
Active
(
4k
points)

73
views
discretemathematics
kennethrosen
inclusionexclusion
0
votes
2
answers
34
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
Active
(
1.5k
points)

1.6k
views
ugcnetdec2012iii
0
votes
1
answer
35
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
(
333
points)

47
views
relations
recurrence
recurrenceeqation
discretemathematics
combinational
0
votes
2
answers
36
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
(
333
points)

146
views
discretemathematics
recurrence
relations
recurrenceeqation
0
votes
0
answers
37
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
Active
(
4k
points)

39
views
kennethrosen
discretemathematics
#recurrencerelations
recurrence
0
votes
0
answers
38
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 I’m getting $a_n$=$3^{n+1}2^{n+1}$
asked
May 13
in
Combinatory
by
aditi19
Active
(
4k
points)

27
views
kennethrosen
discretemathematics
#recurrencerelations
recurrence
0
votes
1
answer
39
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
(
7k
points)

43
views
isi2018
engineeringmathematics
discretemathematics
permutationandcombination
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
probability
To see more, click for all the
questions in this category
.
Quick search syntax
tags
tag:apple
author
user:martin
title
title:apple
content
content:apple
exclude
tag:apple
force match
+apple
views
views:100
score
score:10
answers
answers:2
is accepted
isaccepted:true
is closed
isclosed:true
Recent Posts
ISI MTECH CS 2019 INTERVIEW EXPERIENCE
IIT HYDERABAD MTECH TA INTERVIEW EXPERIENCE
How to prepare for GATE with a fulltime job??
Interview Experience at IISc
All subject Gate notes from Standard Books!!
All categories
General Aptitude
1.8k
Engineering Mathematics
7.3k
Discrete Mathematics
5.1k
Mathematical Logic
2.1k
Set Theory & Algebra
1.3k
Combinatory
879
Graph Theory
804
Probability
987
Linear Algebra
682
Calculus
489
Digital Logic
2.9k
Programming and DS
4.9k
Algorithms
4.3k
Theory of Computation
6.1k
Compiler Design
2.1k
Operating System
4.2k
Databases
4.1k
CO and Architecture
3.4k
Computer Networks
4.1k
Non GATE
1.4k
Others
1.6k
Admissions
595
Exam Queries
576
Tier 1 Placement Questions
23
Job Queries
72
Projects
17
Follow @csegate
Recent questions and answers in Combinatory
Recent Blog Comments
Can you tell me when the stock will be back in...
received the GO books in good conditions!! thanks
Sir please update your stocks, when it will be...
Yes. Stock is over with Indiapost.
But on Amazon the stock is there and a way too...
49,845
questions
54,771
answers
189,417
comments
80,390
users