Permutations and Combinations PYQs - Last 5 Years

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Practice 55 MHT CET Mathematics questions from Permutations and Combinations. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 5 Years Permutations and Combinations Questions

Showing 50 of 55 filtered questions.

1Permutations And Combinations

The number of permutations of the letters of the word INSTITUTION are .......

2Permutations And Combinations

Four men and three women are to be arranged at a round table. The number of arrangements in which no two women are together is ....

3Permutations And Combinations

If ${}^{n}C_4, {}^{n}C_5$ and ${}^{n}C_6$ are in arithmetic progression (A.P.), then the value of n is...

4Permutations And Combinations

11 players of the Indian cricket team are sitting at a circular table. The number of ways they can sit so that two players, the wicket keeper and the captain never sit together is ___

5Permutations And Combinations

In a test, there are 7 questions of the type 'True or False'. No student got all the answers correct. If the sequence of answers for every student is unique, then the maximum number of students who appeared for the test is $\ldots$

6Permutations And Combinations

The number of arrangements of the letters in the word SOLAPUR, so that consonants and vowels are placed alternately is

7Permutations And Combinations

In a test, there are 5 questions of the 'true or false' type. No student has got all the answers correct and the sequence of answers for every student is unique. The maximum number of students who could have appeared for the test is....

8Permutations And Combinations

The number of arrangements of the numbers strictly between 10 and 1000 formed with the digits 0, 1, 2, 3, 4, 5, 6 without repetition is

9Permutations And Combinations

The number of 4-letter words formed from the English alphabet such that there are exactly 2 vowels and 2 consonants and no vowel is repeated, but consonants may be repeated is:

10Permutations And Combinations

The number of five-digit numbers formed using the digits $2, 3, 5, 7, 9$ without repetition and which are greater than $24000$ are

11Permutations And Combinations

A bag contains 23 balls, of which 7 are identical. The number of ways of selecting 12 balls from the bag is....

12Permutations And Combinations

The number of cubic equations that can be formed with the coefficients 0, 3, 2, 4, 5, 6 when repetition of coefficients is allowed, is....

13Permutations And Combinations

There are $5$ boys and $3$ girls seated in a row for a photograph. The number of ways in which a photograph can be taken if the girls occupy only odd places is...

14Permutations And Combinations

The number of ways that 8 beads of different colours can be strung to form a necklace is

15Permutations And Combinations

The value of ${ }^{47} \mathrm{C}_4+\sum\limits_{\mathrm{j}=1}^5{ }^{(52-\mathrm{j})} \mathrm{C}_3$ is

16Permutations And Combinations

The number of ways in which a team of 11 players can be formed out of 25 players, if 6 out of them are always to be included and 5 of them are always to be excluded, is

17Permutations And Combinations

The number of ways in which 6 boys and 4 girls can be seated around a round table such that 2 special boys and a special girl never sit together is

18Permutations And Combinations

There are 11 points in a plane of which 5 points are collinear. Then the total number of distinct quadrilaterals with vertices at these points is

19Permutations And Combinations

A family consisting of a mother, father and their 8 children ( 4 boys and 4 girls) are to be seated at a round table in a party. How many ways can this be done if the mother and father sit together and the males and females alternate?

20Permutations And Combinations

If ${ }^{15} \mathrm{C}_4+{ }^{15} \mathrm{C}_5+{ }^{16} \mathrm{C}_6+{ }^{17} \mathrm{C}_7+{ }^{18} \mathrm{C}_8={ }^{19} \mathrm{C}_{\mathrm{r}}$, then the value of $r$ is equal to

21Permutations And Combinations

21 friends were invited for a party. Two round tables can accommodate 12 and 9 friends each, The number of ways of the seating arrangements of friends is …..

22Permutations And Combinations

If four digit numbers are formed by using the digits $1,2,3,4,5,6,7$ without repetition, then out of these numbers, the numbers exactly divisible by 25 are

23Permutations And Combinations

The greatest possible number of points of intersection of 8 distinct straight lines and 4 distinct circles is

24Permutations And Combinations

If ${ }^{n+4} C_{n+1}-{ }^{n+3} C_n=15(n+2)$, then $n=$

25Permutations And Combinations

A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides are

26Permutations And Combinations

4 red balls and 5 green balls are selected from $n$ balls. If the sum of both the selections is greater than ${ }^{n+1} C_4$ then the value of $n$ is equal to

27Permutations And Combinations

The number of ways, in which 6 boys and 5 girls can sit at a round table, if no two girls are to sit together, is

28Permutations And Combinations

Total number of 3-digit numbers, whose g.c.d with 36 is 2 , is

29Permutations And Combinations

The domain of the function $\mathrm{f}(x)={ }^{7-x} \mathrm{P}_{x-1}$ is

30Permutations And Combinations

In a class of 300 students, every student reads 5 news papers and every news paper is read by 60 students. Then the number of newspapers is

31Permutations And Combinations

Consider a group of 5 boys and 7 girls. The number of different teams, consisting of 2 boys and 3 girls that can be formed from this group if there are two specific girls A and B , who refuse to be the members of the same team, is

32Permutations And Combinations

The number of ways in which 5 boys and 3 girls can be seated on a round table, if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other, is

33Permutations And Combinations

Five persons $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ and E are seated in a circular arangement, if each of them is given a hat of one of the three colours red, blue and green, then the number of ways, of distributing the hats such ...

34Permutations And Combinations

The number of four letter words that can be formed using letters of the word BARRACK

35Permutations And Combinations

A committee of 11 members is to be formed from 8 males and 5 females. If $m$ is the number of ways the committee is formed with at least 6 males and $n$ is the number of ways the committee is formed with at least 3 females, then

36Permutations And Combinations

If 3 books on Physics, 2 books on Chemistry and 4 books on Mathematics are to be arranged on a shelf so that all the Physics books are together and all the Mathematics books are together, then the number of such arrangements is

37Permutations And Combinations

Number of different nine digit numbers, that can be formed from the digits in the number 223355888 by rearranging its digits, so that the odd digits occupy even positions, is

38Permutations And Combinations

Eight chairs are numbered 1 to 8 . Two women and three men wish to occupy one chair each. First the women choose chairs from amongst the chairs marked 1 to 4 , and then the men select the chairs from amongst the remaining. The number of pos...

39Permutations And Combinations

A five digit number divisible by 3 is to be formed using the digits $0,1,2,3,4,5$ without repetition, then the total number of ways this can be done is

40Permutations And Combinations

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose t...

41Permutations And Combinations

_________ numbers greater than a million can be formed with the digits 2, 3, 0, 3, 4, 2, 3.

42Permutations And Combinations

The number of arrangements, of the letters of the word MANAMA in which two M's do not appear adjacent, is

43Permutations And Combinations

Words of length 10 are formed by using the letters A, B, C, D, E, F, G, H, I, J. Let $x$ be number of such words where no letter is repeated and $y$ be number of such words where exactly two letters are repeated twice and no other letter is...

44Permutations And Combinations

If at the end of certain meeting, everyone had shaken hands with everyone else, it was found that 45 handshakes were exchanged, then the number of members present at the meeting, are

45Permutations And Combinations

A linguistic club of a certain Institute consists of 6 girls and 4 boys. A team of 4 members to be selected from this group including the selection of a Captain (from among these 4 members) for the team. If the team has to include atmost on...

46Permutations And Combinations

A linguistic club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this group including the selection of a leader (from among these 4 members) for the team. If the team has to include at most one boy, the number of...

47Permutations And Combinations

If in a regular polygon, the number of diagonals are 54, then the number of sides of the polygon are

48Permutations And Combinations

Five persons \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}\) and \(\mathrm{E}\) are seated in a circular arrangement. If each of them is given a cap of one of the three colours red, blue and green, then the number of ways of distributing...

49Permutations And Combinations

Five students are selected from \(n\) students such that the ratio of number of ways in which 2 particular students are selected to the number of ways 2 particular students not selected is \(2: 3\). Then, the value of \(n\) is

50Permutations And Combinations

If \(\mathrm{T}_{\mathrm{n}}\) denotes the number of triangles which can be formed using the vertices of regular polygon of \(\mathrm{n}\) sides and \(T_{n+1}-T_n=21\), then \(\mathrm{n}=\)