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Recent questions tagged permutationandcombination
+18
votes
3
answers
1
GATE19941.15
The number of substrings (of all lengths inclusive) that can be formed from a character string of length $n$ is $n$ $n^2$ $\frac{n(n1)}{2}$ $\frac{n(n+1)}{2}$
asked
Oct 4, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

2k
views
gate1994
permutationandcombination
normal
+34
votes
9
answers
2
GATE19941.6, ISRO200829
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
asked
Oct 4, 2014
in
Graph Theory
by
Kathleen
Veteran
(
52.2k
points)

9.7k
views
gate1994
graphtheory
permutationandcombination
normal
isro2008
counting
+29
votes
6
answers
3
GATE201065
Given digits$ 2, 2, 3, 3, 3, 4, 4, 4, 4$ how many distinct $4$ digit numbers greater than $3000$ can be formed? $50$ $51$ $52$ $54$
asked
Sep 30, 2014
in
Numerical Ability
by
jothee
Veteran
(
105k
points)

7.5k
views
gate2010
numericalability
permutationandcombination
normal
+37
votes
5
answers
4
GATE2014150
Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $ \log_2 \log_2N $ is _______.
asked
Sep 28, 2014
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

4k
views
gate20141
settheory&algebra
functions
permutationandcombination
numericalanswers
+36
votes
11
answers
5
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________
asked
Sep 28, 2014
in
Combinatory
by
jothee
Veteran
(
105k
points)

3k
views
gate20141
permutationandcombination
numericalanswers
normal
+16
votes
2
answers
6
GATE19981.23
How many sub strings of different lengths (nonzero) can be formed from a character string of length $n$? $n$ $n^2$ $2^n$ $\frac{n(n+1)}{2}$
asked
Sep 26, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

3.5k
views
gate1998
permutationandcombination
normal
+14
votes
3
answers
7
GATE19981.8
The number of functions from an $m$ element set to an $n$ element set is $m + n$ $m^n$ $n^m$ $m*n$
asked
Sep 26, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

1.6k
views
gate1998
settheory&algebra
permutationandcombination
functions
easy
+20
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
asked
Sep 23, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

4k
views
gate1999
permutationandcombination
normal
+20
votes
3
answers
9
GATE19991.3
The number of binary strings of $n$ zeros and $k$ ones in which no two ones are adjacent is $^{n1}C_k$ $^nC_k$ $^nC_{k+1}$ None of the above
asked
Sep 23, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

2.3k
views
gate1999
permutationandcombination
normal
+15
votes
1
answer
10
GATE19991.2
The number of binary relations on a set with $n$ elements is: $n^2$ $2^n$ $2^{n^2}$ None of the above
asked
Sep 23, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

2k
views
gate1999
settheory&algebra
relations
permutationandcombination
easy
+28
votes
5
answers
11
GATE200784
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. How many distinct paths are there for the robot to reach the point $(10,10)$ starting from the initial position $(0,0)$? $^{20}\mathrm{C}_{10}$ $2^{20}$ $2^{10}$ None of the above
asked
Sep 22, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

3.6k
views
gate2007
permutationandcombination
+22
votes
4
answers
12
GATE20073
What is the maximum number of different Boolean functions involving $n$ Boolean variables? $n^2$ $2^n$ $2^{2^n}$ $2^{n^2}$
asked
Sep 22, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
52.2k
points)

2.1k
views
gate2007
permutationandcombination
functions
normal
+44
votes
3
answers
13
GATE200479
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2  3n)}{ 2}$ edges ? $^{\left(\frac{n^2n}{2}\right)}C_{\left(\frac{n^23n} {2}\right)}$ $^{{\large\sum\limits_{k=0}^{\left (\frac{n^23n}{2} \right )}}.\left(n^2n\right)}C_k\\$ $^{\left(\frac{n^2n}{2}\right)}C_n\\$ $^{{\large\sum\limits_{k=0}^n}.\left(\frac{n^2n}{2}\right)}C_k$
asked
Sep 19, 2014
in
Graph Theory
by
Kathleen
Veteran
(
52.2k
points)

4.4k
views
gate2004
graphtheory
permutationandcombination
normal
counting
+34
votes
5
answers
14
GATE200475
Mala has the colouring book in which each English letter is drawn two times. She wants to paint each of these $52$ prints with one of $k$ colours, such that the colour pairs used to colour any two letters are different. Both prints of a letter can also be coloured with the same colour. What is the minimum value of $k$ that satisfies this requirement? $9$ $8$ $7$ $6$
asked
Sep 19, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

3.9k
views
gate2004
permutationandcombination
+14
votes
5
answers
15
GATE200334
$m$ identical balls are to be placed in $n$ distinct bags. You are given that $m \geq kn$, where $k$ is a natural number $\geq 1$. In how many ways can the balls be placed in the bags if each bag must contain at least $k$ ... $\left( \begin{array}{c} m  kn + n + k  2 \\ n  k \end{array} \right)$
asked
Sep 16, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

2.3k
views
gate2003
permutationandcombination
ballsinbins
normal
+28
votes
1
answer
16
GATE20035
$n$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is \(^{2n}\mathrm{C}_n\times 2^n\) \(3^n\) \(\frac{(2n)!}{2^n}\) \(^{2n}\mathrm{C}_n\)
asked
Sep 16, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

2.4k
views
gate2003
permutationandcombination
normal
+28
votes
3
answers
17
GATE20034
Let $A$ be a sequence of $8$ distinct integers sorted in ascending order. How many distinct pairs of sequences, $B$ and $C$ are there such that each is sorted in ascending order, $B$ has $5$ and $C$ has $3$ elements, and the result of merging $B$ and $C$ gives $A$ $2$ $30$ $56$ $256$
asked
Sep 16, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

3.7k
views
gate2003
permutationandcombination
normal
+19
votes
3
answers
18
GATE200213
In how many ways can a given positive integer $n \geq 2$ be expressed as the sum of $2$ positive integers (which are not necessarily distinct). For example, for $n=3$ the number of ways is $2$, i.e., $1+2, 2+1$. Give only the answer ... integer $n \geq k$ be expressed as the sum of $k$ positive integers (which are not necessarily distinct). Give only the answer without explanation.
asked
Sep 16, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

1.3k
views
gate2002
permutationandcombination
normal
descriptive
ballsinbins
+14
votes
5
answers
19
GATE20141GA10
When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines?
asked
Sep 15, 2014
in
Numerical Ability
by
gatecse
Boss
(
16.8k
points)

2.7k
views
gate20141
numericalability
geometry
permutationandcombination
normal
numericalanswers
+26
votes
3
answers
20
GATE20012.1
How many $4$digit even numbers have all $4$ digits distinct $2240$ $2296$ $2620$ $4536$
asked
Sep 14, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

3.6k
views
gate2001
permutationandcombination
normal
+20
votes
4
answers
21
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?
asked
Sep 14, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

1.5k
views
gate2000
permutationandcombination
normal
descriptive
+19
votes
5
answers
22
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 $3$ $8$ $9$ $12$
asked
Sep 14, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

3.1k
views
gate2000
easy
pigeonholeprinciple
permutationandcombination
+34
votes
1
answer
23
GATE199116,a
Find the number of binary strings $w$ of length $2n$ with an equal number of $1's$ and $0's$ and the property that every prefix of $w$ has at least as many $0's$ as $1's.$
asked
Sep 13, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

1.5k
views
gate1991
permutationandcombination
normal
descriptive
catalannumber
+24
votes
4
answers
24
GATE199102iv
Match the pairs in the following questions by writing the corresponding letters only. ...
asked
Sep 12, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

1.3k
views
gate1991
permutationandcombination
normal
matchthefollowing
+12
votes
3
answers
25
GATE200824
Let $P =\sum_{\substack{1\le i \le 2k \\ i\;odd}} i$ and $Q = \sum_{\substack{1 \le i \le 2k \\ i\;even}} i$, where $k$ is a positive integer. Then $P = Q  k$ $P = Q + k$ $P = Q$ $P = Q + 2k$
asked
Sep 12, 2014
in
Combinatory
by
Kathleen
Veteran
(
52.2k
points)

1.1k
views
gate2008
permutationandcombination
easy
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