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
Recent questions and answers in Combinatory
+8
votes
5
answers
1
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
3 days
ago
in
Combinatory
by
`JEET
Boss
(
13.1k
points)

419
views
tifr2018
pigeonholeprinciple
permutationandcombination
+24
votes
13
answers
2
GATE201846
The number of possible minheaps containing each value from $\{1,2,3,4,5,6,7\}$ exactly once is _______
answered
4 days
ago
in
Combinatory
by
Praveenk99
(
49
points)

8.4k
views
gate2018
permutationandcombination
numericalanswers
+37
votes
11
answers
3
GATE2016126
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
answered
4 days
ago
in
Combinatory
by
pritishc
Junior
(
669
points)

9k
views
gate20161
permutationandcombination
generatingfunctions
normal
numericalanswers
+1
vote
2
answers
4
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
in
Combinatory
by
noob_coder
Junior
(
657
points)

26
views
isi2014dcg
permutationandcombination
arrangements
circularpermutation
+2
votes
1
answer
5
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
in
Combinatory
by
Kushagra गुप्ता
Active
(
1.9k
points)

198
views
kennethrosen
discretemathematics
generatingfunctions
+1
vote
2
answers
6
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
in
Combinatory
by
chirudeepnamini
Active
(
3.1k
points)

29
views
isi2016pcba
permutationandcombination
recurrencerelations
nongate
descriptive
+2
votes
3
answers
7
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
answered
Nov 20
in
Combinatory
by
chirudeepnamini
Active
(
3.1k
points)

43
views
isi2014dcg
permutationandcombination
binomialtheorem
+1
vote
1
answer
8
ISI2018DCG14
In a room there are $8$ men, numbered $1,2, \dots ,8$. These men have to be divided into $4$ teams in such a way that every team has exactly $2$ ... of such $4$team combinations is $\frac{8!}{2^4}$ $\frac{8!}{2^4(4!)}$ $\frac{8!}{4!}$ $\frac{8!}{(4!)^2}$
answered
Nov 19
in
Combinatory
by
Yash4444
Junior
(
731
points)

17
views
isi2018dcg
permutationandcombination
+1
vote
1
answer
9
ISI2016DCG21
The value of the term independent of $x$ in the expansion of $(1x)^{2}(x+\frac{1}{x})^{7}$ is $70$ $70$ $35$ None of these
answered
Nov 18
in
Combinatory
by
Verma Ashish
Boss
(
11.8k
points)

18
views
isi2016dcg
permutationandcombination
binomialtheorem
+6
votes
3
answers
10
GATE20195
Let $U = \{1, 2, \dots , n\}$ Let $A=\{(x, X) \mid x \in X, X \subseteq U \}$. Consider the following two statements on $\mid A \mid$. $\mid A \mid = n2^{n1}$ $\mid A \mid = \Sigma_{k=1}^{n} k \begin{pmatrix} n \\ k \end{pmatrix}$ Which of the above statements is/are TRUE? Only I Only II Both I and II Neither I nor II
answered
Nov 14
in
Combinatory
by
Optimus Prime
Junior
(
543
points)

2.7k
views
gate2019
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
2
answers
11
MadeEasy Full Length Test 2019: Combinatory  Permutations And Combinations
The number of ways 5 letter be put in 3 letter boxes A,B,C. If letter box A must contain at least 2 letters.
answered
Nov 11
in
Combinatory
by
SaurabhKatkar
(
151
points)

207
views
discretemathematics
permutationandcombination
madeeasytestseries2019
madeeasytestseries
+2
votes
2
answers
12
Discrete Mathematics Thegatebook
how many positive integers between 50 and 100, (a) divisible by 7 (b) divisible by 11 (c) divisible by 7 and 11?
answered
Nov 10
in
Combinatory
by
Ram Swaroop
Active
(
4.6k
points)

303
views
inclusionexclusion
0
votes
2
answers
13
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
Nov 9
in
Combinatory
by
Sandeep shahu
(
71
points)

59
views
kennethrosen
discretemathematics
permutationandcombination
#recurrencerelations
recurrence
+1
vote
1
answer
14
CMI2018A5
How many paths are there in the plane from $(0,0)$ to $(m,n)\in \mathbb{N}\times \mathbb{N},$ if the possible steps from $(i,j)$ are either $(i+1,j)$ or $(i,j+1)?$ $\binom{2m}{n}$ $\binom{m}{n}$ $\binom{m+n}{n}$ $m^{n}$
answered
Nov 9
in
Combinatory
by
`JEET
Boss
(
13.1k
points)

37
views
cmi2018
permutationandcombination
paths
+1
vote
1
answer
15
#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 ${\Big[\frac{2^{n+1} + (1)^n}{3}\Big]}^2$ $(n+1)^2$ $(n1)^3$ $(n1)^2$
answered
Nov 5
in
Combinatory
by
techbd123
Active
(
3.1k
points)

129
views
discretemathematics
permutationandcombination
recurrence
#recurrencerelations
+6
votes
4
answers
16
MadeEasy Test Series: Combinatory  Permutations And Combinations
MY SOLUTION : Fix the root then next level 2 elements ( 2! possibilities) next level 4 elements( 4! possibilities) last level 2 elements ( 2! possibilities) total possibility = 2! * 4! * 2! = 2 * 24 * 2 = 96 what ... that if node of above graph is filled with these elements it satisfies max heap property a)96 b)896 c)2688 d) none
answered
Nov 4
in
Combinatory
by
kunal goswami
Junior
(
533
points)

961
views
permutationandcombination
madeeasytestseries
+1
vote
0
answers
17
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
in
Combinatory
by
Satbir
Boss
(
21.5k
points)

161
views
permutationandcombination
+36
votes
11
answers
18
GATE2014149
A pennant is a sequence of numbers, each number being $1$ or $2$. An $n$pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a $4$pennant. The set of all possible $1$pennants is ${(1)}$, the set of all possible $2$pennants is ... $(1,2)$ is not the same as the pennant $(2,1)$. The number of $10$pennants is________
answered
Oct 28
in
Combinatory
by
paraskk
(
335
points)

3k
views
gate20141
permutationandcombination
numericalanswers
normal
+19
votes
5
answers
19
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
Oct 22
in
Combinatory
by
Asim Siddiqui 4
Active
(
1.3k
points)

3.1k
views
gate2000
easy
pigeonholeprinciple
permutationandcombination
+1
vote
1
answer
20
ISI2018DCG4
The number of terms with integral coefficients in the expansion of $(17^\frac{1}{3}+19^\frac{1}{2}x)^{600}$ is $99$ $100$ $101$ $102$
answered
Oct 21
in
Combinatory
by
`JEET
Boss
(
13.1k
points)

18
views
isi2018dcg
permutationandcombination
binomialtheorem
coefficients
+39
votes
6
answers
21
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
Oct 20
in
Combinatory
by
techbd123
Active
(
3.1k
points)

4.4k
views
gate2005
settheory&algebra
normal
pigeonholeprinciple
+3
votes
2
answers
22
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 runners is to be ... $12,000$ and $25,000$ Between $75,000$ and $99,999$ Between $30,000$ and $60,000$ More than $100,000$
answered
Oct 19
in
Combinatory
by
chirudeepnamini
Active
(
3.1k
points)

98
views
cmi2015
permutationandcombination
+1
vote
2
answers
23
ISI2015MMA8
Let $A$ be a set of $n$ elements. The number of ways, we can choose an ordered pair $(B,C)$, where $B,C$ are disjoint subsets of $A$, equals $n^2$ $n^3$ $2^n$ $3^n$
answered
Oct 19
in
Combinatory
by
chirudeepnamini
Active
(
3.1k
points)

33
views
isi2015mma
permutationandcombination
disjointsubsets
0
votes
1
answer
24
ISI2015MMA9
Let $(1+x)^n = C_0+C_1x+C_2x^2+ \cdots +C_nx^n, \: n$ being a positive integer. The value of $\bigg( 1+\frac{C_0}{C_1} \bigg) \bigg( 1+\frac{C_1}{C_2} \bigg) \cdots \bigg( 1+\frac{C_{n1}}{C_n} \bigg)$ is $\bigg( \frac{n+1}{n+2} \bigg) ^n$ $ \frac{n^n}{n!} $ $\bigg( \frac{n}{n+1} \bigg) ^n$ $\frac{(n+1)^n}{n!}$
answered
Oct 19
in
Combinatory
by
chirudeepnamini
Active
(
3.1k
points)

9
views
isi2015mma
permutationandcombination
binomialtheorem
+2
votes
3
answers
25
ISI2015MMA4
Suppose in a competition $11$ matches are to be played, each having one of $3$ distinct outcomes as possibilities. The number of ways one can predict the outcomes of all $11$ matches such that exactly $6$ of the predictions turn out to be correct is $\begin{pmatrix}11 \\ 6 \end{pmatrix} \times 2^5$ $\begin{pmatrix}11 \\ 6 \end{pmatrix} $ $3^6$ none of the above
answered
Oct 19
in
Combinatory
by
chirudeepnamini
Active
(
3.1k
points)

36
views
isi2015mma
permutationandcombination
0
votes
1
answer
26
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
Oct 17
in
Combinatory
by
anonymousgamer
(
11
points)

64
views
kennethrosen
discretemathematics
permutationandcombination
#recurrencerelations
recurrence
0
votes
1
answer
27
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)

35
views
permutationandcombination
0
votes
1
answer
28
ISI2014DCG72
The sum $\sum_{k=1}^n (1)^k \:\: {}^nC_k \sum_{j=0}^k (1)^j \: \: {}^kC_j$ is equal to $1$ $0$ $1$ $2^n$
answered
Oct 10
in
Combinatory
by
techbd123
Active
(
3.1k
points)

28
views
isi2014dcg
permutationandcombination
summation
+5
votes
10
answers
29
GATE201921
The value of $3^{51} \text{ mod } 5$ is _____
answered
Oct 3
in
Combinatory
by
techbd123
Active
(
3.1k
points)

3.2k
views
gate2019
numericalanswers
permutationandcombination
modulararithmetic
+1
vote
1
answer
30
ISI2014DCG34
The following sum of $n+1$ terms $2 + 3 \times \begin{pmatrix} n \\ 1 \end{pmatrix} + 5 \times \begin{pmatrix} n \\ 2 \end{pmatrix} + 9 \times \begin{pmatrix} n \\ 3 \end{pmatrix} + 17 \times \begin{pmatrix} n \\ 4 \end{pmatrix} + \cdots$ up to $n+1$ terms is equal to $3^{n+1}+2^{n+1}$ $3^n \times 2^n$ $3^n + 2^n$ $2 \times 3^n$
answered
Sep 30
in
Combinatory
by
techbd123
Active
(
3.1k
points)

33
views
isi2014dcg
permutationandcombination
binomialtheorem
summation
+1
vote
2
answers
31
ISI2014DCG1
Let $(1+x)^n = C_0+C_1x+C_2x^2+ \dots + C_nx^n$, $n$ being a positive integer. The value of $\bigg( 1+\dfrac{C_0}{C_1} \bigg) \bigg( 1+\dfrac{C_1}{C_2} \bigg) \cdots \bigg( 1+\dfrac{C_{n1}}{C_n} \bigg)$ is $\bigg( \frac{n+1}{n+2} \bigg) ^n$ $ \frac{n^n}{n!} $ $\bigg( \frac{n}{n+1} \bigg) ^n$ $ \frac{(n+1)^n}{n!} $
answered
Sep 27
in
Combinatory
by
STUDYGATE2019
(
91
points)

128
views
isi2014dcg
permutationandcombination
binomialtheorem
+1
vote
1
answer
32
ISI2015MMA1
Let $\{f_n(x)\}$ be a sequence of polynomials defined inductively as $ f_1(x)=(x2)^2$ $f_{n+1}(x) = (f_n(x)2)^2, \: \: \: n \geq 1$ Let $a_n$ and $b_n$ respectively denote the constant term and the coefficient of $x$ in $f_n(x)$. Then $a_n=4, \: b_n=4^n$ $a_n=4, \: b_n=4n^2$ $a_n=4^{(n1)!}, \: b_n=4^n$ $a_n=4^{(n1)!}, \: b_n=4n^2$
answered
Sep 26
in
Combinatory
by
`JEET
Boss
(
13.1k
points)

29
views
isi2015mma
recurrencerelations
nongate
0
votes
1
answer
33
ISI2015MMA6
A club with $x$ members is organized into four committees such that each member is in exactly two committees, any two committees have exactly one member in common. Then $x$ has exactly two values both between $4$ and $8$ exactly one value and this lies between $4$ and $8$ exactly two values both between $8$ and $16$ exactly one value and this lies between $8$ and $16$
answered
Sep 25
in
Combinatory
by
`JEET
Boss
(
13.1k
points)

20
views
isi2015mma
permutationandcombination
+1
vote
1
answer
34
ISI2014DCG63
If $^nC_{r1}=36$, $^nC_r=84$ an $^nC_{r+1}=126$ then $r$ is equal to $1$ $2$ $3$ none of these
answered
Sep 25
in
Combinatory
by
`JEET
Boss
(
13.1k
points)

15
views
isi2014dcg
permutationandcombination
0
votes
1
answer
35
ISI2014DCG66
Consider all possible words obtained by arranging all the letters of the word $\textbf{AGAIN}$. These words are now arranged in the alphabetical order, as in a dictionary. The fiftieth word in this arrangement is $\text{IAANG}$ $\text{NAAGI}$ $\text{NAAIG}$ $\text{IAAGN}$
answered
Sep 25
in
Combinatory
by
`JEET
Boss
(
13.1k
points)

15
views
isi2014dcg
permutationandcombination
arrangingletters
+1
vote
1
answer
36
ISI2014DCG41
The number of permutations of the letters $a, b, c$ and $d$ such that $b$ does not follow $a,c$ does not follow $b$, and $c$ does not follow $d$, is $11$ $12$ $13$ $14$
answered
Sep 24
in
Combinatory
by
`JEET
Boss
(
13.1k
points)

30
views
isi2014dcg
permutationandcombination
+2
votes
0
answers
37
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
in
Combinatory
by
Arjun
Veteran
(
424k
points)

50
views
isi2014dcg
permutationandcombination
0
votes
0
answers
38
ISI2015MMA60
Let $\sigma$ be the permutation: $\begin{array} {}1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ 3 & 5 & 6 & 2 & 4 & 9 & 8 & 7 & 1, \end{array}$ $I$ be the identity permutation and $m$ be the order of $\sigma$ i.e. $m=\text{min}\{\text{positive integers }n: \sigma ^n=I \}$. Then $m$ is $8$ $12$ $360$ $2520$
asked
Sep 23
in
Combinatory
by
Arjun
Veteran
(
424k
points)

6
views
isi2015mma
permutationandcombination
+2
votes
1
answer
39
ISI2016DCG24
If the letters of the word $\text{COMPUTER}$ be arranged in random order, the number of arrangements in which the three vowels $O, U$ and $E$ occur together is $8!$ $6!$ $3!6!$ None of these
answered
Sep 22
in
Combinatory
by
`JEET
Boss
(
13.1k
points)

10
views
isi2016dcg
permutationandcombination
arrangements
+1
vote
1
answer
40
ISI2018DCG17
The value of $^{13}C_{3} + ^{13}C_{5} + ^{13}C_{7} +\dots + ^{13}C_{13}$ is $4096$ $4083$ $2^{13}1$ $2^{12}1$
answered
Sep 21
in
Combinatory
by
kp1
(
115
points)

13
views
isi2018dcg
permutationandcombination
binomialtheorem
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
Linear Algebra Important Points
GATE 2020
OFFICIAL GATE MOCK TEST RELEASED
IIITH: Winter Research Admissions 2019 (For Spring 2020)
TIFR and JEST exam
All categories
General Aptitude
1.9k
Engineering Mathematics
7.5k
Discrete Mathematics
5.2k
Mathematical Logic
2.1k
Set Theory & Algebra
1.4k
Combinatory
914
Graph Theory
816
Probability
1k
Linear Algebra
722
Calculus
592
Digital Logic
2.9k
Programming and DS
4.9k
Algorithms
4.3k
Theory of Computation
6.2k
Compiler Design
2.1k
Operating System
4.5k
Databases
4.1k
CO and Architecture
3.4k
Computer Networks
4.1k
Non GATE
1.5k
Others
1.5k
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
i also don't have any pdf, actually, I added the...
i don't have , if you have upload it
@mohan123 Do you have all standard book...
bro can be upload all standard book questions in...
it'll take 34 days but for most purpose you can...
50,648
questions
56,441
answers
195,294
comments
100,083
users