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
Activity
Questions
Unanswered
Tags
Subjects
Users
Ask
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
+18
votes
5
answers
1
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
21 hours
ago
in
Combinatory
by
Asim Siddiqui 4
Active
(
1.2k
points)

2.9k
views
gate2000
easy
pigeonholeprinciple
permutationandcombination
+38
votes
6
answers
2
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
3 days
ago
in
Combinatory
by
techbd123
Active
(
1.4k
points)

4.2k
views
gate2005
settheory&algebra
normal
pigeonholeprinciple
+3
votes
2
answers
3
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 ... taken into account? Between 12,000 and 25,000 Between 75,000 and 99,999 Between 30,000 and 60,000 More than 100,000
answered
3 days
ago
in
Combinatory
by
chirudeepnamini
Active
(
1.8k
points)

92
views
cmi2015
permutationandcombination
0
votes
1
answer
4
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
6 days
ago
in
Combinatory
by
anonymousgamer
(
11
points)

53
views
kennethrosen
discretemathematics
permutationandcombination
#recurrencerelations
recurrence
0
votes
1
answer
5
Combinatorics
There are 6n flowers of one type and 3 flowers of second type, total no. Of garlands possible?
answered
Oct 11
in
Combinatory
by
shivamgo
(
11
points)

29
views
permutationandcombination
+5
votes
10
answers
6
GATE201921
The value of $3^{51} \text{ mod } 5$ is _____
answered
Oct 3
in
Combinatory
by
techbd123
Active
(
1.4k
points)

3k
views
gate2019
numericalanswers
permutationandcombination
modulararithmetic
0
votes
3
answers
7
Permutations and combinations
In how any ways can 8 different shirts be distributed among 4 different people so that each recieves 2 shirts?
answered
Sep 13
in
Combinatory
by
gajendercse
(
11
points)

252
views
permutationandcombination
+5
votes
2
answers
8
permutation combo
In how many ways can seven different jobs be assigned to 4 different employees so that each employee is assigned at least one job and the most difficult job is assigned to the best employee?
answered
Sep 3
in
Combinatory
by
aditi19
Active
(
4.9k
points)

374
views
permutationandcombination
+2
votes
2
answers
9
Combinatoric
Find number of zero's at the end of (2018)! ?
answered
Sep 3
in
Combinatory
by
Lakshman Patel RJIT
Veteran
(
51.5k
points)

60
views
permutationandcombination
+1
vote
2
answers
10
Pigeon hole
Show that in a group of $n$ people there are two who have identical number of friends in that group.
answered
Aug 24
in
Combinatory
by
chirudeepnamini
Active
(
1.8k
points)

48
views
pigeonholeprinciple
permutationandcombination
+15
votes
5
answers
11
TIFR2013A9
There are $n$ kingdoms and $2n$ champions. Each kingdom gets $2$ champions. 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
Aug 22
in
Combinatory
by
Verma Ashish
Boss
(
10.7k
points)

826
views
tifr2013
permutationandcombination
discretemathematics
normal
ballsinbins
+20
votes
4
answers
12
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
Aug 21
in
Combinatory
by
Verma Ashish
Boss
(
10.7k
points)

1.5k
views
gate2000
permutationandcombination
normal
descriptive
+5
votes
7
answers
13
TIFR2018B1
What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$
answered
Aug 21
in
Combinatory
by
Verma Ashish
Boss
(
10.7k
points)

399
views
tifr2018
modulararithmetic
permutationandcombination
+3
votes
1
answer
14
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
(
63.6k
points)

121
views
permutationandcombination
+1
vote
2
answers
15
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
Veteran
(
51.5k
points)

207
views
ugcnetjune2019ii
permutationandcombination
inclusionexclusion
+14
votes
4
answers
16
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
(
15.4k
points)

1.3k
views
gate2007it
permutationandcombination
normal
recurrence
+8
votes
8
answers
17
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
(
116k
points)

2.3k
views
permutationandcombination
counting
+1
vote
2
answers
18
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
Veteran
(
51.5k
points)

289
views
ugcnetjune2019ii
permutationandcombination
+2
votes
2
answers
19
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
(
116k
points)

254
views
counting
+9
votes
4
answers
20
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
(
653
points)

660
views
permutationandcombination
isi2004
discretemathematics
normal
+10
votes
6
answers
21
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)

744
views
tifr2015
permutationandcombination
+2
votes
1
answer
22
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
(
4.2k
points)

80
views
ugcnetjune2019ii
eulerphifunction
+1
vote
3
answers
23
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)

303
views
iisc
cds
0
votes
1
answer
24
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
(
609
points)

36
views
probability
permutationandcombination
0
votes
2
answers
25
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
Boss
(
10.1k
points)

124
views
engineeringmathematics
discretemathematics
permutationandcombination
+1
vote
1
answer
26
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
(
19.5k
points)

154
views
ugcnetjune2019ii
permutationandcombination
pigeonholeprinciple
0
votes
3
answers
27
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)

96
views
discretemathematics
permutationandcombination
+6
votes
6
answers
28
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
(
2.2k
points)

429
views
tifr2019
engineeringmathematics
discretemathematics
permutationandcombination
medium
+14
votes
6
answers
29
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
(
19.5k
points)

1.5k
views
gate2005
normal
generatingfunctions
0
votes
1
answer
30
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
(
116k
points)

89
views
counting
discretemathematics
+23
votes
12
answers
31
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)

8k
views
gate2018
permutationandcombination
numericalanswers
+41
votes
11
answers
32
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)

4.1k
views
gate20153
permutationandcombination
normal
numericalanswers
+25
votes
7
answers
33
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)

2.8k
views
gate2004it
permutationandcombination
normal
ballsinbins
+19
votes
3
answers
34
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)

888
views
tifr2014
permutationandcombination
discretemathematics
normal
pigeonholeprinciple
+35
votes
7
answers
35
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
(
967
points)

5.6k
views
gate20172
permutationandcombination
generatingfunctions
numericalanswers
normal
+15
votes
8
answers
36
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)

6k
views
gate2018
generatingfunctions
normal
permutationandcombination
+20
votes
3
answers
37
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
(
51
points)

3.9k
views
gate1999
permutationandcombination
normal
0
votes
0
answers
38
#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
Loyal
(
8.2k
points)

108
views
discretemathematics
permutationandcombination
recurrence
#recurrencerelations
0
votes
0
answers
39
#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
(
259
points)

36
views
counting
0
votes
2
answers
40
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?
asked
May 24
in
Combinatory
by
aditi19
Active
(
4.9k
points)

79
views
discretemathematics
kennethrosen
inclusionexclusion
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
Standard Book Exercise Questions for Computer Science
Resource to Learn Graph Theory Interactively
Recruitment to the post of Scientist/Engineer 'SC' (Electronics, Mechanical and Computer Science)
Standard Videos for Calculus
Standard Videos for Linear Algebra
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
805
Probability
987
Linear Algebra
682
Calculus
493
Digital Logic
2.9k
Programming and DS
4.9k
Algorithms
4.4k
Theory of Computation
6.2k
Compiler Design
2.1k
Operating System
4.2k
Databases
4.1k
CO and Architecture
3.4k
Computer Networks
4.1k
Non GATE
1.6k
Others
1.8k
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
Are the answers also present ?
@Arjun sir , Is there any page or something where...
@arjun sir but u called about providing the pdfs...
But anyhow I appreciate this. The questions of...
All these PYQ blogs and standard videos blogs...
50,407
questions
55,861
answers
192,658
comments
91,649
users