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Use the google search bar on side panel. It searches through all previous GATE/other questions. For hardcopy of previous year questions please see
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Search results for dm2
+2
votes
1
answer
1
GATEBOOK2019DM211
A decimal number is called “increasing” if each digit is greater than the previous one (e.g. $24589$ is one). How many $5$ digit increasing numbers are there?
asked
Oct 28, 2018
in
Discrete Mathematics
by
GATEBOOK
Boss
(
15.3k
points)

84
views
gb2019dm2
discretemathematics
permutationsandcombinations
numericalanswers
0
votes
1
answer
2
GATEBOOK2019DM215
A landscaper is planting a row of $12$ trees including $4$ birch trees and $8$ pine trees. How many ways can this be done without having two birch trees next to each other? $\frac{16!}{12!4!}$ $\frac{16!}{12!}$ $\frac{16!}{4!}$ $\begin{pmatrix}9 \\ 4 \end{pmatrix}$
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

49
views
gb2019dm2
discretemathematics
permutationsandcombinations
+2
votes
1
answer
3
GATEBOOK2019DM220
How many ways a set of $5$ elements can be divided into two unordered partitions where each partition gets at least one element?
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

135
views
gb2019dm2
discretemathematics
numericalanswers
permutationsandcombinations
+3
votes
1
answer
4
GATEBOOK2019DM210
How many license plates with $3$ decimal digits followed by $3$ letters do not contain both the number $0$ and the letter $\text{O}$? $17047279$ $14074279$ $17074279$ $12436759$
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

128
views
gb2019dm2
discretemathematics
permutationsandcombinations
0
votes
1
answer
5
GATEBOOK2019DM22
In how many ways can $2$ RED and $4$ BLUE ROOKS be placed on an $8by8$ board so that no two ROOKS can attack one another? $8! \times 8!$ $8! \times \frac{8!}{2!4!}$ $8! \times \frac{8!}{2!4!2!2!}$ ${}^8P_4$
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

135
views
gb2019dm2
discretemathematics
permutationsandcombinations
0
votes
1
answer
6
GATEBOOK2019DM212
How many even integers $≥ 4000$ and $< 7000$ have four different digits? $128$ $728$ $328$ $528$
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

88
views
gb2019dm2
discretemathematics
permutationsandcombinations
+1
vote
2
answers
7
GATEBOOK2019DM29
How many bit strings of length $6$ have more zeroes than ones?
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

63
views
gb2019dm2
discretemathematics
numericalanswers
+3
votes
1
answer
8
GATEBOOK2019DM23
How many numbers in $\{1, 2, \ldots,10000\}$ have their digits sum to $7?\:(e.g. 502)$
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

123
views
gb2019dm2
discretemathematics
permutationsandcombinations
numericalanswers
+1
vote
1
answer
9
GATEBOOK2019DM24
The number of permutations of $\{1, 2, 3, 4, 5\}$ in which at least one odd integer is in its natural position is ______
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

129
views
gb2019dm2
discretemathematics
permutationsandcombinations
numericalanswers
+2
votes
1
answer
10
GATEBOOK2019DM25
In how many ways can the letters $\{a, b, c, d, e\}$ be placed into $3$ identical boxes such that no box is empty?
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

152
views
gb2019dm2
discretemathematics
permutationsandcombinations
numericalanswers
+1
vote
1
answer
11
GATEBOOK2019DM216
How many solutions does the equation $a+b+c+d+e+f = 2006$ have where $a, b, c, d, e$ and $f$ are all positive integers? $\begin{pmatrix} 2005 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 2006 \\ 4 \end{pmatrix}$ $\begin{pmatrix} 2011 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 2005 \\ 6 \end{pmatrix}$
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

121
views
gb2019dm2
discretemathematics
permutationsandcombinations
+1
vote
1
answer
12
GATEBOOK2019DM26
In how many ways can $10$ women and $4$ men line up in a straight line so that no two men are consecutive? $10! \begin{pmatrix} 11 \\ 4 \end{pmatrix} 4!$ $10! \begin{pmatrix} 9 \\ 4 \end{pmatrix} 4!$ $\frac{14!}{4!}$ $\begin{pmatrix} 11 \\ 4 \end{pmatrix} $
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

70
views
gb2019dm2
discretemathematics
permutationsandcombinations
+2
votes
0
answers
13
GATEBOOK2019DM213
How many ways are there to seat $10$ people, consisting of $5$ couples, in a row of seats ($10$ seats wide) if all couples are to get adjacent seats?
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

66
views
gb2019dm2
discretemathematics
permutationsandcombinations
numericalanswers
+2
votes
0
answers
14
GATEBOOK2019DM28
A bowl contains $5$ red balls and $7$ silver ones. A woman chooses balls at random without looking at them. How many must she choose, to be sure of having at least $3$ of the same color? $7$ $11$ $10$ $5$
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

50
views
gb2019dm2
discretemathematics
permutationsandcombinations
+1
vote
0
answers
15
GATEBOOK2019DM21
How many paths are there from the lower left corner to the upper right corner, moving only up or to the right ? Path can not go through any of the dotted lines ...
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

95
views
gb2019dm2
discretemathematics
permutationsandcombinations
+1
vote
0
answers
16
GATEBOOK2019DM217
How many bit strings of length $5$ are there, such that every $1$ is followed immediately by a zero?
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

79
views
gb2019dm2
discretemathematics
permutationsandcombinations
numericalanswers
0
votes
0
answers
17
GATEBOOK2019DM27
$50$ people are to be divided (partitioned) into $5$ teams of $10$ players each. In how many ways can this be done if each team has a different name $\frac{50!}{10!^5}$ $\frac{50!}{5!^{10}}$ $\frac{\begin{pmatrix}50 \\ 10 \end{pmatrix}}{10!}$ None
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

72
views
gb2019dm2
discretemathematics
permutationsandcombinations
0
votes
0
answers
18
GATEBOOK2019DM214
An integer is called snakelike if its decimal representation $a_1a_2a_3 \dots a_k$ satisfies $a_i < a_{i+1}$ if $i$ is odd and $a_i > a_{i+1}$ if $i$ is even. How many snakelike integers between $1000$ and $9999$ have four distinct digits?
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

59
views
gb2019dm2
discretemathematics
numericalanswers
0
votes
0
answers
19
GATEBOOK2019DM218
How many numbers (minimum) must you pick to ensure that at least three of them have the same remainder when divided by $11?$
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

54
views
gb2019dm2
discretemathematics
permutationsandcombinations
numericalanswers
0
votes
0
answers
20
GATEBOOK2019DM219
A pool of available computer programmers has $13$ members–six men and seven women In how many ways can you choose a team of five, with at most three men?
asked
Oct 28, 2018
in
Combinatory
by
GATEBOOK
Boss
(
15.3k
points)

45
views
gb2019dm2
discretemathematics
permutationsandcombinations
numericalanswers
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