Aptitude Overflow - Recent questions tagged permutation-combination
https://aptitude.gateoverflow.in/tag/permutation-combination
Powered by Question2AnswerCAT 2021 Set-3 | Quantitative Aptitude | Question: 13
https://aptitude.gateoverflow.in/8506/cat-2021-set-3-quantitative-aptitude-question-13
A four-digit number is formed by using only the digits $1, 2$ and $3$ such that both $2$ and $3$ appear at least once. The number of all such four-digit numbers isQuantitative Aptitudehttps://aptitude.gateoverflow.in/8506/cat-2021-set-3-quantitative-aptitude-question-13Thu, 20 Jan 2022 09:29:56 +0000CAT 2021 Set-2 | Quantitative Aptitude | Question: 4
https://aptitude.gateoverflow.in/8449/cat-2021-set-2-quantitative-aptitude-question-4
The number of ways of distributing $15$ identical balloons, $6$ identical pencils and $3$ identical erasers among $3$ children, such that each child gets at least four balloons and one pencil, isQuantitative Aptitudehttps://aptitude.gateoverflow.in/8449/cat-2021-set-2-quantitative-aptitude-question-4Thu, 20 Jan 2022 09:24:36 +0000CAT 2021 Set-1 | Quantitative Aptitude | Question: 10
https://aptitude.gateoverflow.in/8371/cat-2021-set-1-quantitative-aptitude-question-10
The number of groups of three or more distinct numbers that can be chosen from $1, 2, 3, 4, 5, 6, 7,$ and $8$ so that the groups always include $3$ and $5,$ while $7$ and $8$ are never included together isQuantitative Aptitudehttps://aptitude.gateoverflow.in/8371/cat-2021-set-1-quantitative-aptitude-question-10Wed, 19 Jan 2022 05:24:04 +0000CAT 2020 Set-2 | Question: 65
https://aptitude.gateoverflow.in/8035/cat-2020-set-2-question-65
How many $4$-digit numbers, each greater than $1000$ and each having all four digits distinct, are there with $7$ coming before $3.$Quantitative Aptitudehttps://aptitude.gateoverflow.in/8035/cat-2020-set-2-question-65Fri, 17 Sep 2021 04:49:07 +0000CAT 2020 Set-1 | Question: 51
https://aptitude.gateoverflow.in/7970/cat-2020-set-1-question-51
How many $3-$digit numbers are there, for which the product of their digits is more than $2$ but less than $7$?Quantitative Aptitudehttps://aptitude.gateoverflow.in/7970/cat-2020-set-1-question-51Thu, 16 Sep 2021 02:16:33 +0000NIELIT 2017 DEC Scientific Assistant A - Section A: 31
https://aptitude.gateoverflow.in/6474/nielit-2017-dec-scientific-assistant-a-section-a-31
<p>In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$10080$</li>
<li>$4989600$</li>
<li>$120960$</li>
<li>None of the options</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6474/nielit-2017-dec-scientific-assistant-a-section-a-31Tue, 31 Mar 2020 16:51:47 +0000NIELIT 2017 July Scientist B - Section A: 1
https://aptitude.gateoverflow.in/6371/nielit-2017-july-scientist-b-section-a-1
<p>What is the maximum number of the handshakes that can happen in the room with $5$ people in it?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$15$</li>
<li>$10$</li>
<li>$6$</li>
<li>$5$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6371/nielit-2017-july-scientist-b-section-a-1Mon, 30 Mar 2020 11:18:40 +0000NIELIT 2017 July Scientist B - Section A: 8
https://aptitude.gateoverflow.in/6364/nielit-2017-july-scientist-b-section-a-8
<p>In how many different ways can the letters of the word ‘CORPORATION’ be arranged so that the vowels always come together?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$810$</li>
<li>$1440$</li>
<li>$2880$</li>
<li>$50400$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6364/nielit-2017-july-scientist-b-section-a-8Mon, 30 Mar 2020 11:18:39 +0000NIELIT 2017 DEC Scientist B - Section A: 57
https://aptitude.gateoverflow.in/6255/nielit-2017-dec-scientist-b-section-a-57
<p>In a big farm in Wisconsin, there are only hens and cows. When the owner counted the heads of the stock in the farm, the number summed up to $200$, while counting the number of legs, the number summed up to $540$. How many more hens were there in the farm ? Assume each cow had $4$ legs and each hen had $2$ legs.</p>
<ol style="list-style-type:upper-alpha" type="A">
<li>$70$</li>
<li>$120$</li>
<li>$60$</li>
<li>$130$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6255/nielit-2017-dec-scientist-b-section-a-57Mon, 30 Mar 2020 11:10:46 +0000NIELIT 2017 DEC Scientist B - Section A: 58
https://aptitude.gateoverflow.in/6254/nielit-2017-dec-scientist-b-section-a-58
<p>There are $6$ boxes numbered $1,2$,$\dots$,$6$. Each box is to be filled up either with a red or a green ball in such a way that at least $1$ box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is :</p>
<ol style="list-style-type:upper-alpha" type="A">
<li>$5$</li>
<li>$21$</li>
<li>$33$</li>
<li>$60$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/6254/nielit-2017-dec-scientist-b-section-a-58Mon, 30 Mar 2020 11:10:46 +0000CAT 2018 Set-2 | Question: 84
https://aptitude.gateoverflow.in/6133/cat-2018-set-2-question-84
In a tournament, there are $43$ junior level and $51$ senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior level is $153$, while the number of boy versus boy matches in senior level is $276$. The number of matches a boy plays against a girl is _________Quantitative Aptitudehttps://aptitude.gateoverflow.in/6133/cat-2018-set-2-question-84Fri, 20 Mar 2020 05:48:50 +0000CAT 2018 Set-1 | Question: 91
https://aptitude.gateoverflow.in/6020/cat-2018-set-1-question-91
How many numbers with two or more digits can be formed with the digits $1,2,3,4,5,6,7,8,9$, so that in every such number, each digit is used at most once and the digits appear in the ascending order?Quantitative Aptitudehttps://aptitude.gateoverflow.in/6020/cat-2018-set-1-question-91Thu, 19 Mar 2020 22:39:05 +0000CAT 2017 Set-2 | Question: 96
https://aptitude.gateoverflow.in/5845/cat-2017-set-2-question-96
<p>How many four digits number, which are divisible by $6$ , can be formed using the digits $0,2,3,4,6$ such that no digit is used more than once and $0$ does not occur in the left-most positions?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$49$</li>
<li>$48$</li>
<li>$50$</li>
<li>$52$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/5845/cat-2017-set-2-question-96Mon, 16 Mar 2020 05:43:43 +0000CAT 2017 Set-2 | Question: 95
https://aptitude.gateoverflow.in/5846/cat-2017-set-2-question-95
<p>In how many ways can $8$ identical pens be distributed among Amal, Bimal, Kamal so that Amal gets at least $1$ pen, Bimal gets a least $2$ pens, and Kamal gets a least $3$ pens?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$5$</li>
<li>$6$</li>
<li>$7$</li>
<li>$8$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/5846/cat-2017-set-2-question-95Mon, 16 Mar 2020 05:43:43 +0000CAT 2017 Set-1 | Question: 98
https://aptitude.gateoverflow.in/5756/cat-2017-set-1-question-98
<p>In how many ways can $7$ identical erasers be distributed among $4$ kids in such a way that each kid gets at least one eraser but nobody gets more than $3$ erasers? </p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$16$</li>
<li>$20$</li>
<li>$14$</li>
<li>$15$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/5756/cat-2017-set-1-question-98Fri, 13 Mar 2020 07:23:46 +0000CAT 2016 | Question: 91
https://aptitude.gateoverflow.in/5677/cat-2016-question-91
A man has $9$ friends: $4$ boys and $5$ girls. In how many ways can he invite them, if there have to be exactly $3$ girls in the invitees ________Quantitative Aptitudehttps://aptitude.gateoverflow.in/5677/cat-2016-question-91Wed, 11 Mar 2020 11:50:30 +0000CAT 2016 | Question: 98
https://aptitude.gateoverflow.in/5670/cat-2016-question-98
<p>There are $12$ towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$72$</li>
<li>$90$</li>
<li>$96$</li>
<li>$144$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/5670/cat-2016-question-98Wed, 11 Mar 2020 11:50:29 +0000CAT 2011 | Question: 2
https://aptitude.gateoverflow.in/5549/cat-2011-question-2
<p>Rajat draws a $10\times10$ grid on the ground such that there are $100$ identical squares numbered $1\:\text{to}\:100$. If he has to place two identical stones on any two separate squares in the grid, how many distinct ways are possible?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$2475$</li>
<li>$4950$</li>
<li>$9900$</li>
<li>$1000$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/5549/cat-2011-question-2Mon, 09 Mar 2020 06:28:09 +0000CAT 2012 | Question: 26
https://aptitude.gateoverflow.in/5079/cat-2012-question-26
<p>Letters of the word “ATTRACT” are written on cards and are kept on a table. Manish is asked to lift three cards at a time, write all possible combinations of the three letters on a piece of paper and then replace the three cards. The exercise ends when all possible combinations of letters are exhausted. Then, he is asked to strike out all words in his list, which look the same when seen in a mirror. How many words is he left with?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$40$</li>
<li>$20$</li>
<li>$30$</li>
<li>None of these</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/5079/cat-2012-question-26Thu, 05 Mar 2020 11:35:07 +0000CAT 2010 | Question: 18
https://aptitude.gateoverflow.in/5016/cat-2010-question-18
<p>In a factory making radioactive substances, it was considered that the three cubes of uranium together are hazardous. So the company authorities decided to have the stack of uranium interspersed with lead cubes. But there is a new worker in a company who does not know the rule. So he arranges the uranium stack the way he wanted. What is the number of hazardous combinations of uranium in a stack of $5?$</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$3$</li>
<li>$7$</li>
<li>$8$</li>
<li>$10$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/5016/cat-2010-question-18Sun, 01 Mar 2020 08:18:27 +0000CAT 2003 | Question: 2-90
https://aptitude.gateoverflow.in/2035/cat-2003-question-2-90
<p>An intelligence agency forms a code of two distinct digits selected from $0, 1, 2, \dots 9$ such that the first digit of the code is nonzero. The code, handwritten on a slip, can however potentially create confusion, when read upside down – for example, the code $91$ may appear as $16.$ How many codes are there for which no such confusion can arise?</p>
<ol style="list-style-type:upper-alpha">
<li>$80$</li>
<li>$78$</li>
<li>$71$</li>
<li>$69$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/2035/cat-2003-question-2-90Thu, 05 May 2016 07:38:36 +0000CAT 2003 | Question: 2-84
https://aptitude.gateoverflow.in/2029/cat-2003-question-2-84
<p>There are $12$ towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required?</p>
<ol style="list-style-type:upper-alpha">
<li>$72$</li>
<li>$90$</li>
<li>$96$</li>
<li>$144$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/2029/cat-2003-question-2-84Thu, 05 May 2016 07:21:44 +0000CAT 2003 | Question: 2-83
https://aptitude.gateoverflow.in/2028/cat-2003-question-2-83
<p><strong>Answer the questions on the basis of the information given below.</strong></p>
<ol start="1" style="list-style-type:lower-alpha">
<li>A string of three English letters is formed as per the following rules</li>
<li>The first letter is any vowel.</li>
<li>The second letter is $m, n$ or $p$.</li>
<li>If the second letter is $m,$ then the third letter is any vowel which is different from the first letter.</li>
<li>If the second letter is $n,$ then the third letter is $e$ or $u.$</li>
<li>If the second letter is $p,$ then the third letter is the same as the first letter.</li>
</ol>
<p>How many strings of letters can possibly be formed using the above rules such that the third letter of the string is $e?$</p>
<ol style="list-style-type:upper-alpha">
<li>$8$</li>
<li>$9$</li>
<li>$10$</li>
<li>$11$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/2028/cat-2003-question-2-83Thu, 05 May 2016 07:20:37 +0000CAT 2003 | Question: 2-82
https://aptitude.gateoverflow.in/2027/cat-2003-question-2-82
<p><strong>Answer the questions on the basis of the information given below.</strong></p>
<ol style="list-style-type:lower-alpha">
<li>A string of three English letters is formed as per the following rules</li>
<li>The first letter is any vowel.</li>
<li>The second letter is $m, n$ or $p$.</li>
<li>If the second letter is $m,$ then the third letter is any vowel which is different from the first letter.</li>
<li>If the second letter is $n,$ then the third letter is $e$ or $u.$</li>
<li>If the second letter is $p,$ then the third letter is the same as the first letter.</li>
</ol>
<p>How many strings of letters can possibly be formed using the above rules?</p>
<ol style="list-style-type:upper-alpha">
<li>$40$</li>
<li>$45$</li>
<li>$30$</li>
<li>$35$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/2027/cat-2003-question-2-82Thu, 05 May 2016 07:19:36 +0000CAT 2002 | Question: 92
https://aptitude.gateoverflow.in/1816/cat-2002-question-92
<p><strong>There are 11 alphabets A, H, I, M, O, T, U, V, W, X, Y, Z. They are called symmetrical alphabets. The remaining alphabets are known as asymmetrical alphabets.</strong></p>
<p>How many three-lettered words can be formed such that at least one symmetrical letter is there?</p>
<ol style="list-style-type:upper-alpha">
<li>$12870$</li>
<li>$18330$</li>
<li>$16420$</li>
<li>None of these</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1816/cat-2002-question-92Mon, 02 May 2016 03:52:48 +0000CAT 2002 | Question: 100
https://aptitude.gateoverflow.in/1815/cat-2002-question-100
<p>A boy is supposed to put a mango into a basket if ordered $1,$ an orange if ordered $2$ and an apple if ordered $3.$ He took out $1$ mango and $1$ orange if ordered $4.$ he was given the following sequence of orders</p>
<p>$12332142314223314113234$</p>
<p>At the end of the sequence, what will be the number of fruits in the basket?</p>
<ol style="list-style-type:upper-alpha">
<li>$10$</li>
<li>$11$</li>
<li>$13$</li>
<li>$17$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1815/cat-2002-question-100Mon, 02 May 2016 03:50:35 +0000CAT 2000 | Question: 93
https://aptitude.gateoverflow.in/1479/cat-2000-question-93
<p><strong>Answer the following question based on the information given below.</strong><br>
Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top four teams from each group advance to the second stage while the rest are eliminated. The second stage comprises of several rounds. A round involves one match for each team. The winner of a match in a round advances to the next round, while the loser is eliminated. The team that remains undefeated in the second stage is declared the winner and claims the Gold Cup.<br>
The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage, a team earns one point for each win and no points for a loss. At the end of the first stage teams in each group are ranked on the basis of total points to determine the qualifiers advancing to the next stage. Ties are resolved by a series of complex tie-breaking rules so that exactly four teams from each group advance to the next stage.</p>
<p>Which of the following statements is true?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>The winner will have more wins than any other team in the tournament.</li>
<li>At the end of the first stage, no team eliminated from the tournament will have more wins than any of the teams qualifying for the second stage.</li>
<li>It is the possible that the winner will have the same number of wins in the entire tournament as a team eliminated at the end of the first stage.</li>
<li>The number of teams with exactly one win in the second stage of the tournament is $4$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1479/cat-2000-question-93Mon, 25 Apr 2016 02:56:34 +0000CAT 2000 | Question: 92
https://aptitude.gateoverflow.in/1478/cat-2000-question-92
<p><strong>Answer the following question based on the information given below.</strong><br>
Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top four teams from each group advance to the second stage while the rest are eliminated. The second stage comprises of several rounds. A round involves one match for each team. The winner of a match in a round advances to the next round, while the loser is eliminated. The team that remains undefeated in the second stage is declared the winner and claims the Gold Cup.<br>
The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage, a team earns one point for each win and no points for a loss. At the end of the first stage teams in each group are ranked on the basis of total points to determine the qualifiers advancing to the next stage. Ties are resolved by a series of complex tie-breaking rules so that exactly four teams from each group advance to the next stage.</p>
<p>What is the number of rounds in the second stage of the tournament?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$1$</li>
<li>$2$</li>
<li>$3$</li>
<li>$4$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1478/cat-2000-question-92Mon, 25 Apr 2016 02:55:46 +0000CAT 2000 | Question: 91
https://aptitude.gateoverflow.in/1477/cat-2000-question-91
<p><strong>Answer the following question based on the information given below.</strong><br>
Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top four teams from each group advance to the second stage while the rest are eliminated. The second stage comprises of several rounds. A round involves one match for each team. The winner of a match in a round advances to the next round, while the loser is eliminated. The team that remains undefeated in the second stage is declared the winner and claims the Gold Cup.<br>
The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage, a team earns one point for each win and no points for a loss. At the end of the first stage teams in each group are ranked on the basis of total points to determine the qualifiers advancing to the next stage. Ties are resolved by a series of complex tie-breaking rules so that exactly four teams from each group advance to the next stage.</p>
<p>What is the highest number of wins for a team in the first stage in spite of which it would be eliminated at the end of first stage?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$1$</li>
<li>$2$</li>
<li>$3$</li>
<li>$4$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1477/cat-2000-question-91Mon, 25 Apr 2016 02:55:11 +0000CAT 2000 | Question: 90
https://aptitude.gateoverflow.in/1476/cat-2000-question-90
<p><strong>Answer the following question based on the information given below.</strong><br>
Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top four teams from each group advance to the second stage while the rest are eliminated. The second stage comprises of several rounds. A round involves one match for each team. The winner of a match in a round advances to the next round, while the loser is eliminated. The team that remains undefeated in the second stage is declared the winner and claims the Gold Cup.<br>
The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage, a team earns one point for each win and no points for a loss. At the end of the first stage teams in each group are ranked on the basis of total points to determine the qualifiers advancing to the next stage. Ties are resolved by a series of complex tie-breaking rules so that exactly four teams from each group advance to the next stage.</p>
<p>The minimum number of wins needed for a team in the first stage to guarantee its advancement to the next stage is</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$5$ </li>
<li>$6$</li>
<li>$7$</li>
<li>$4$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1476/cat-2000-question-90Mon, 25 Apr 2016 02:54:28 +0000CAT 2000 | Question: 89
https://aptitude.gateoverflow.in/1217/cat-2000-question-89
<p><strong>Answer the following questions based on the information given below.</strong><br>
Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top four teams from each group advance to the second stage while the rest are eliminated. The second stage comprises of several rounds. A round involves one match for each team. The winner of a match in a round advances to the next round, while the loser is eliminated. The team that remains undefeated in the second stage is declared the winner and claims the Gold Cup.<br>
The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage, a team earns one point for each win and no points for a loss. At the end of the first stage teams in each group are ranked on the basis of total points to determine the qualifiers advancing to the next stage. Ties are resolved by a series of complex tie-breaking rules so that exactly four teams from each group advance to the next stage.</p>
<p>What is the total number of matches played in the tournament?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$28$ </li>
<li>$55$</li>
<li>$63$</li>
<li>$35$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1217/cat-2000-question-89Tue, 29 Mar 2016 04:56:50 +0000CAT 2000 | Question: 67
https://aptitude.gateoverflow.in/1204/cat-2000-question-67
<p>What is the number of distinct triangles with integral valued sides and perimeter $14? $</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$6$</li>
<li>$5$</li>
<li>$4$</li>
<li>$3$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1204/cat-2000-question-67Mon, 28 Mar 2016 05:11:41 +0000CAT 2000 | Question: 63
https://aptitude.gateoverflow.in/1200/cat-2000-question-63
<p>One red flag, three white flags and two blue flags are arranged in a line such that,</p>
<ol style="list-style-type:upper-alpha">
<li>no two adjacent flags are of the same colour.</li>
<li>the flags at the two ends of the line are of different colours.</li>
</ol>
<p>In how many different ways can the flags be arranged?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$6$</li>
<li>$4$</li>
<li>$10$</li>
<li>$2$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1200/cat-2000-question-63Mon, 28 Mar 2016 01:20:14 +0000CAT 2002 | Question: 99
https://aptitude.gateoverflow.in/1111/cat-2002-question-99
<p>A boy is supposed to put a mango into a basket if ordered $1,$ an orange if ordered $2$ and an apple if ordered $3.$ He took out $1$ mango and $1$ orange if ordered $4.$ he was given the following sequence of orders</p>
<p>$12332142314223314113234$</p>
<p>At the end of the sequence, what will be the number of oranges in the basket?</p>
<ol style="list-style-type:upper-alpha">
<li>$2$</li>
<li>$3$</li>
<li>$4$</li>
<li>$6$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1111/cat-2002-question-99Wed, 02 Mar 2016 11:18:42 +0000CAT 2002 | Question: 91
https://aptitude.gateoverflow.in/1104/cat-2002-question-91
<p><strong>There are 11 alphabets A, H, I, M, O, T, U, V, W, X, Y, Z. They are called symmetrical alphabets. The remaining alphabets are known as asymmetrical alphabets.</strong></p>
<p>How many four-lettered passwords can be formed by using symmetrical letters only? (repetitions not allowed)</p>
<ol style="list-style-type:upper-alpha">
<li>$1086$</li>
<li>$255$</li>
<li>$7920$</li>
<li>None of these</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1104/cat-2002-question-91Wed, 02 Mar 2016 05:36:20 +0000CAT 2002 | Question: 86
https://aptitude.gateoverflow.in/1101/cat-2002-question-86
<p>In how many ways, we can choose a black and a white square on a chess board such that the two are not in the same row or column?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$32$</li>
<li>$96$</li>
<li>$24$</li>
<li>None of these</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1101/cat-2002-question-86Wed, 02 Mar 2016 05:09:38 +0000CAT 2002 | Question: 85
https://aptitude.gateoverflow.in/1100/cat-2002-question-85
<p>How many numbers between $0$ and one million can be formed using $0, 7$ and $8?$</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$486$</li>
<li>$1086$</li>
<li>$728$</li>
<li>None of these</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1100/cat-2002-question-85Wed, 02 Mar 2016 05:08:13 +0000CAT 2003 | Question: 1-144
https://aptitude.gateoverflow.in/1037/cat-2003-question-1-144
<p>There are $6$ boxes numbered $1, 2, \dots,6.$ Each box is to be filled up with a red or green ball in such a way that at least one box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is</p>
<ol style="list-style-type:upper-alpha">
<li>$5$</li>
<li>$21$</li>
<li>$33$</li>
<li>$60$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1037/cat-2003-question-1-144Wed, 10 Feb 2016 04:33:04 +0000CAT 2003 | Question: 1-134
https://aptitude.gateoverflow.in/1027/cat-2003-question-1-134
<p>How many three digit positive integers, with digits $x, y$ and $z$ in the hundred's, ten's and unit's place respectively, exist such that $x < y, z < y$ and $x \neq 0?$</p>
<ol style="list-style-type:upper-alpha">
<li>$245$</li>
<li>$285$</li>
<li>$240$</li>
<li>$320$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1027/cat-2003-question-1-134Mon, 08 Feb 2016 07:12:57 +0000CAT 2003 | Question: 1-115
https://aptitude.gateoverflow.in/1011/cat-2003-question-1-115
<p>$27$ persons attend a party. Which one of the following statements can never be true?</p>
<ol style="list-style-type:upper-alpha">
<li>There is a person in the party who is acquainted with all the $26$ members.</li>
<li>Each person in the party has a different number of acquaintances.</li>
<li>There is a person in the party who has odd number of acquaintances.</li>
<li>In the party, there is no set of three mutual acquaintances. </li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/1011/cat-2003-question-1-115Sun, 07 Feb 2016 10:57:15 +0000CAT 2014 | Question: 34
https://aptitude.gateoverflow.in/921/cat-2014-question-34
<p>A five digit number is formed using digits $1, 3, 5, 7$ and $9$ without repeating any one of them. What is the sum of all such possible numbers? </p>
<ol style="list-style-type:lower-alpha">
<li>$6666600$ </li>
<li>$6666660$ </li>
<li>$6666666$ </li>
<li>None </li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/921/cat-2014-question-34Sat, 16 Jan 2016 14:26:34 +0000CAT 2004 | Question: 71
https://aptitude.gateoverflow.in/881/cat-2004-question-71
<p>A new flag is to be designed with six vertical stripes using some or all of the colors yellow, green, blue and red. Then the number of ways this can be done such that no two adjacent stripes have the same color is</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$12 \times 81$</li>
<li>$16 \times 192$</li>
<li>$20 \times 125$</li>
<li>$24 \times 216$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/881/cat-2004-question-71Thu, 14 Jan 2016 04:18:41 +0000CAT 2004 | Question: 68
https://aptitude.gateoverflow.in/873/cat-2004-question-68
<p>In the adjoining figure, the lines represent one-way roads allowing travel only northwards or only westwards. Along how many distinct routes can a car reach point B from point A?</p>
<p><img alt="" src="http://aptitude.gateoverflow.in/?qa=blob&qa_blobid=6271350590401871428"></p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$15$</li>
<li>$56$</li>
<li>$120$</li>
<li>$336$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/873/cat-2004-question-68Wed, 13 Jan 2016 06:02:48 +0000CAT 2005 | Question: 15
https://aptitude.gateoverflow.in/761/cat-2005-question-15
<p>Let $\text{S}$ be the set of five digit numbers formed by the digits $1,2, 3, 4$ and $5$ using each digit exactly once such that exactly two odd positions are occupied by odd digits. What is the sum of the digits in the rightmost position of the numbers in $\text{S}?$</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$228$</li>
<li>$216$</li>
<li>$294$</li>
<li>$192$</li>
</ol>
<p> </p>Quantitative Aptitudehttps://aptitude.gateoverflow.in/761/cat-2005-question-15Tue, 29 Dec 2015 07:41:25 +0000CAT 2005 | Question: 05
https://aptitude.gateoverflow.in/751/cat-2005-question-05
<p>In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in $45$ games both the players were girls, and in $190$ games both were boys. The number of games in which one player was a boy and other was a girl is </p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$200$</li>
<li>$216$</li>
<li>$235$</li>
<li>$256$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/751/cat-2005-question-05Tue, 29 Dec 2015 07:07:56 +0000CAT 2006 | Question: 56
https://aptitude.gateoverflow.in/728/cat-2006-question-56
<p>A group of $630$ children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What numbers of rows is not possible?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$3$</li>
<li>$4$</li>
<li>$5$</li>
<li>$6$</li>
<li>$7$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/728/cat-2006-question-56Mon, 28 Dec 2015 07:37:59 +0000CAT 2007 | Question: 11
https://aptitude.gateoverflow.in/581/cat-2007-question-11
<p>In a tournament, there are $n$ teams $T_1, T_2 ......., T$ with $n > 5$. Each team consists of $k$ players, $k>3$. The following pairs of teams have one player in common:</p>
<p>$T_1 \text{ and } T_2 , T_2 \text{ and } T_3, ...... , T_{n-1} \text{ and } T_n, \text{ and } T_n \text{ and } T_1 $</p>
<p>No other pair of teams has any player in common. How many players are participating in the tournament, considering all the $n$ teams together?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$n(k-1)$</li>
<li>$k(n-1)$</li>
<li>$n(k-2)$</li>
<li>$k(k-2)$</li>
<li>$(n-1) (k-1)$</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/581/cat-2007-question-11Sun, 06 Dec 2015 06:05:53 +0000CAT 2008 | Question: 02
https://aptitude.gateoverflow.in/501/cat-2008-question-02
<p>What is the number of distinct terms in the expansion of $(a + b + c)^{20}?$</p>
<ol style="list-style-type:upper-alpha">
<li>
<p>$231$</p>
</li>
<li>
<p>$253$</p>
</li>
<li>
<p>$242$</p>
</li>
<li>
<p>$210$</p>
</li>
<li>
<p>$228$</p>
</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/501/cat-2008-question-02Thu, 26 Nov 2015 06:41:30 +0000CAT 2008 | Question: 01
https://aptitude.gateoverflow.in/500/cat-2008-question-01
<p>How many integers, greater than $999$ but not greater than $4000,$ can be formed with the digits $0, 1, 2, 3$ and $4,$ if repetition of digits is allowed?</p>
<ol style="list-style-type:upper-alpha">
<li>
<p>$499$</p>
</li>
<li>
<p>$500$</p>
</li>
<li>
<p>$375$</p>
</li>
<li>
<p>$376$</p>
</li>
<li>
<p>$501$</p>
</li>
</ol>Quantitative Aptitudehttps://aptitude.gateoverflow.in/500/cat-2008-question-01Thu, 26 Nov 2015 06:40:06 +0000