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Recent questions tagged permutation-combination

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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 is

soujanyareddy13 asked in Quantitative Aptitude Jan 20, 2022

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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, is

soujanyareddy13 asked in Quantitative Aptitude Jan 20, 2022

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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 is

soujanyareddy13 asked in Quantitative Aptitude Jan 19, 2022

by soujanyareddy13

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4

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 $3.$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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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 $7$?

soujanyareddy13 asked in Quantitative Aptitude Sep 16, 2021

by soujanyareddy13

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NIELIT 2017 DEC Scientific Assistant A - Section A: 31
In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together? $10080$ $4989600$ $120960$ None of the options

Lakshman Bhaiya asked in Quantitative Aptitude Mar 31, 2020

by Lakshman Bhaiya

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NIELIT 2017 July Scientist B - Section A: 1
What is the maximum number of the handshakes that can happen in the room with $5$ people in it? $15$ $10$ $6$ $5$

Lakshman Bhaiya asked in Quantitative Aptitude Mar 30, 2020

by Lakshman Bhaiya

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NIELIT 2017 July Scientist B - Section A: 8
In how many different ways can the letters of the word ‘CORPORATION’ be arranged so that the vowels always come together? $810$ $1440$ $2880$ $50400$

Lakshman Bhaiya asked in Quantitative Aptitude Mar 30, 2020

by Lakshman Bhaiya

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NIELIT 2017 DEC Scientist B - Section A: 57
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. $70$ $120$ $60$ $130$

Lakshman Bhaiya asked in Quantitative Aptitude Mar 30, 2020

by Lakshman Bhaiya

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NIELIT 2017 DEC Scientist B - Section A: 58
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 : $5$ $21$ $33$ $60$

Lakshman Bhaiya asked in Quantitative Aptitude Mar 30, 2020

by Lakshman Bhaiya

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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 ... number of boy versus boy matches in senior level is $276$. The number of matches a boy plays against a girl is _________

go_editor asked in Quantitative Aptitude Mar 20, 2020

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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?

go_editor asked in Quantitative Aptitude Mar 20, 2020

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CAT 2017 Set-2 | Question: 96
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? $49$ $48$ $50$ $52$

go_editor asked in Quantitative Aptitude Mar 16, 2020

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CAT 2017 Set-2 | Question: 95
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? $5$ $6$ $7$ $8$

go_editor asked in Quantitative Aptitude Mar 16, 2020

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CAT 2017 Set-1 | Question: 98
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? $16$ $20$ $14$ $15$

go_editor asked in Quantitative Aptitude Mar 13, 2020

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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 ________

go_editor asked in Quantitative Aptitude Mar 11, 2020

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CAT 2016 | Question: 98
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? $72$ $90$ $96$ $144$

go_editor asked in Quantitative Aptitude Mar 11, 2020

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CAT 2011 | Question: 2
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? $2475$ $4950$ $9900$ $1000$

Krithiga2101 asked in Quantitative Aptitude Mar 9, 2020

by Krithiga2101

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CAT 2012 | Question: 26
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 ... , which look the same when seen in a mirror. How many words is he left with? $40$ $20$ $30$ None of these

Chandanachandu asked in Quantitative Aptitude Mar 5, 2020

by Chandanachandu

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CAT 2010 | Question: 18
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 ... wanted. What is the number of hazardous combinations of uranium in a stack of $5?$ $3$ $7$ $8$ $10$

Arjun asked in Quantitative Aptitude Mar 1, 2020

by Arjun

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CAT 2003 | Question: 2-90
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? $80$ $78$ $71$ $69$

go_editor asked in Quantitative Aptitude May 5, 2016

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CAT 2003 | Question: 2-84
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? $72$ $90$ $96$ $144$

go_editor asked in Quantitative Aptitude May 5, 2016

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CAT 2003 | Question: 2-83
Answer the questions on the basis of the information given below. A string of three English letters is formed as per the following rules The first letter is any vowel. The second letter is $m, n$ or $p$. If the second letter is $m,$ then the third letter is ... can possibly be formed using the above rules such that the third letter of the string is $e?$ $8$ $9$ $10$ $11$

go_editor asked in Quantitative Aptitude May 5, 2016

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CAT 2003 | Question: 2-82
Answer the questions on the basis of the information given below. A string of three English letters is formed as per the following rules The first letter is any vowel. The second letter is $m, n$ or $p$. If the second letter is $m,$ then the third ... same as the first letter. How many strings of letters can possibly be formed using the above rules? $40$ $45$ $30$ $35$

go_editor asked in Quantitative Aptitude May 5, 2016

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CAT 2002 | Question: 92
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. How many three-lettered words can be formed such that at least one symmetrical letter is there? $12870$ $18330$ $16420$ None of these

go_editor asked in Quantitative Aptitude May 2, 2016

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CAT 2002 | Question: 100
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 $12332142314223314113234$ At the end of the sequence, what will be the number of fruits in the basket? $10$ $11$ $13$ $17$

go_editor asked in Quantitative Aptitude May 2, 2016

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CAT 2000 | Question: 93
Answer the following question based on the information given below. 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 ... end of the first stage. The number of teams with exactly one win in the second stage of the tournament is $4$

go_editor asked in Quantitative Aptitude Apr 25, 2016

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CAT 2000 | Question: 92
Answer the following question based on the information given below. 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 ... next stage. What is the number of rounds in the second stage of the tournament? $1$ $2$ $3$ $4$

go_editor asked in Quantitative Aptitude Apr 25, 2016

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CAT 2000 | Question: 91
Answer the following question based on the information given below. 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 ... first stage in spite of which it would be eliminated at the end of first stage? $1$ $2$ $3$ $4$

go_editor asked in Quantitative Aptitude Apr 25, 2016

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CAT 2000 | Question: 90
Answer the following question based on the information given below. 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 ... for a team in the first stage to guarantee its advancement to the next stage is $5$ $6$ $7$ $4$

go_editor asked in Quantitative Aptitude Apr 25, 2016

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CAT 2000 | Question: 89
Answer the following questions based on the information given below. 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 ... to the next stage. What is the total number of matches played in the tournament? $28$ $55$ $63$ $35$

go_editor asked in Quantitative Aptitude Mar 29, 2016

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CAT 2000 | Question: 67
What is the number of distinct triangles with integral valued sides and perimeter $14? $ $6$ $5$ $4$ $3$

go_editor asked in Quantitative Aptitude Mar 28, 2016

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CAT 2000 | Question: 63
One red flag, three white flags and two blue flags are arranged in a line such that, no two adjacent flags are of the same colour. the flags at the two ends of the line are of different colours. In how many different ways can the flags be arranged? $6$ $4$ $10$ $2$

go_editor asked in Quantitative Aptitude Mar 28, 2016

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CAT 2002 | Question: 99
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 $12332142314223314113234$ At the end of the sequence, what will be the number of oranges in the basket? $2$ $3$ $4$ $6$

go_editor asked in Quantitative Aptitude Mar 2, 2016

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CAT 2002 | Question: 91
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. How many four-lettered passwords can be formed by using symmetrical letters only? (repetitions not allowed) $1086$ $255$ $7920$ None of these

go_editor asked in Quantitative Aptitude Mar 2, 2016

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CAT 2002 | Question: 86
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? $32$ $96$ $24$ None of these

go_editor asked in Quantitative Aptitude Mar 2, 2016

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CAT 2002 | Question: 85
How many numbers between $0$ and one million can be formed using $0, 7$ and $8?$ $486$ $1086$ $728$ None of these

go_editor asked in Quantitative Aptitude Mar 2, 2016

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CAT 2003 | Question: 1-144
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 $5$ $21$ $33$ $60$

go_editor asked in Quantitative Aptitude Feb 10, 2016

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CAT 2003 | Question: 1-134
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 $x \neq 0?$ $245$ $285$ $240$ $320$

go_editor asked in Quantitative Aptitude Feb 8, 2016

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CAT 2003 | Question: 1-115
$27$ persons attend a party. Which one of the following statements can never be true? There is a person in the party who is acquainted with all the $26$ members. Each person in the party has a different number of acquaintances. There is a person in the party who has odd number of acquaintances. In the party, there is no set of three mutual acquaintances.

go_editor asked in Quantitative Aptitude Feb 7, 2016

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