Permutations and Combinations PYQs - Last 10 Years

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Practice 37 COMEDK 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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Mathematics / Algebra

2020-2026

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37

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2017-2026

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Last 10 Years Permutations and Combinations Questions

Showing 37 of 37 filtered questions.

1Permutations And Combinations

A batch of $\mathbf{1 0}$ cupcakes consists of $\mathbf{5}$ chocolate, $\mathbf{3}$ vanilla, and $\mathbf{2}$ strawberry. If 4 cupcakes are selected to be put into a gift box, find the number of different ways they can be chosen if the sele...

2Permutations And Combinations

The range of the function $f(x)={ }^{(7-x)} P_{(x-3)}$ is

3Permutations And Combinations

In how many ways can the squares of a $\mathbf{4} \times \mathbf{2}$ grid ( 4 rows and 2 columns) be filled with the letters of the word 'SPHERE' such that each row contains at least one letter?

4Permutations And Combinations

\(\text { If }{ }^{\mathrm{n}} C_{13},{ }^{\mathrm{n}} C_{14} \text { and }{ }^{\mathrm{n}} C_{15} \text { are in arithmetic progression, then the positive integer value of ' } \mathbf{n} \text { ' can be }\)

5Permutations And Combinations

A coach needs to select a $\mathbf{4}$-player starting lineup from a pool of $\mathbf{1 0}$ players:

5 guards
3 forwards
2 centres

Find the number of different selections if the 4-player starting lineup must include:

At least 1 guard
At ...

6Permutations And Combinations

Codes used for vehicle identification consists of two distinct English alphabets followed by two distinct digits from 1 to 9 . How many of them end with an even number.

7Permutations And Combinations

A shopkeeper sells three varieties of fruit juice. He has a large number of bottles of same size of each variety. The number of different ways of displaying all the three varieties on the shelf with 5 places in a row and each display must h...

8Permutations And Combinations

The number of words that can be formed with the letters of the word 'DEFINITE' if two vowels are together and the other two are also together but separated from the first two is

9Permutations And Combinations

How many natural numbers are there between 100 and 1000 such that at least one of their digits is $6 ?$

10Permutations And Combinations

On each working day of a school there are six periods. The number of ways in which five subjects are arranged if each subject is allotted at least one period and no period remains vacant is

11Permutations And Combinations

If ${ }^{n+2} C_8:{ }^{n-2} P_4=57: 16$, then ' $n$ ' is

12Permutations And Combinations

In how many ways can the word "CHRISTMAS" be arranged so that the letters '\(\mathrm{C}\)' and '\(\mathrm{M}\)' are never adjacent?

13Permutations And Combinations

If \(\left[{ }^{n+1} C_{r+1}\right]:\left[{ }^n C_r\right]:\left[{ }^{n-1} C_{r-1}\right]=11: 6: 3\) then \(n r=\)

14Permutations And Combinations

The letters of the word "COCHIN" are permuted and all the permutations are arranged in alphabetical order as in an English dictionary. The number of words that appear before the word "COCHIN" is

15Permutations And Combinations

For an examination a candidate has to select 7 questions from three different groups \(\mathrm{A}, \mathrm{B}\) and C. The three groups contain 4, 5 and 6 questions respectively. In how many different ways can a candidate make his selection...

16Permutations And Combinations

A student has 3 library cards and 8 books of his interest in the library. Out of these 8 books he does not want to borrow Chemistry part 2 unless he can borrow Chemistry part 1 also. In how many ways can he choose the three books to be borr...

17Permutations And Combinations

The number of four digit numbers strictly greater than 4321 formed using the digits \(0,1,2,3,4,5\) with repetition of digit is

18Permutations And Combinations

In a 12 storey house, 10 people enter a lift cabin. It is known that they will leave the lift in pre-decided groups of 2, 3 & 5 people at different storeys. The number of ways they can do so if the lift does not stop up to the second storey...

19Permutations And Combinations

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. The number of ways in which he can choo...

20Permutations And Combinations

How many factors of \(2^5 \times 3^6 \times 5^2\) are perfect squares?

21Permutations And Combinations

A polygon of n sides has 105 diagonals, then n is equal to

22Permutations And Combinations

The total number of numbers greater than 1000 but less than 4000 that can be formed using 0, 2, 3, 4 (using repetition allowed) are

23Permutations And Combinations

There are 10 points in a plane out of which 4 points are collinear. How many straight lines can be drawn by joining any two of them?

24Permutations And Combinations

\(\text { Find }{ }^n C_{21} \text {, if }{ }^n C_{10}={ }^n C_{12}\)

25Permutations And Combinations

How many 5-digit numbers greater than 50,000 can be formed using the digits 1, 2, 3, 4, 5 without repetition?

26Permutations And Combinations

A regular polygon of n sides has 170 diagonals, then n is equal to

27Permutations And Combinations

There are 12 points in a plane out of which 3 points are collinear. How many straight lines can be drawn by joining any two of them?

28Permutations And Combinations

If nC3 = 220, then n = ?

29Permutations And Combinations

\(\sum\limits_{n = 1}^m {n\,.\,n!}\) is equal to

30Permutations And Combinations

\((2^{3n}-1)\) is divisible by

31Permutations And Combinations

If a polygon of n sides has 275 diagonals, then n is equal to

32Permutations And Combinations

How many numbers greater than 40000 can be formed from the digits 2, 4, 5, 5, 7?

33Permutations And Combinations

Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from those 8 points?

34Permutations And Combinations

The number of triangles which can be formed by using the vertices of a regular polygon of \((n+3)\) sides is 220. Then, \(n\) is equal to

35Permutations And Combinations

The value of \(1\,.\,1! + 2\,.\,2! + 3\,.\,3! + \,...\, + \,n\,.\,n!\) is

36Permutations And Combinations

The remainder obtained when 5124 is divided by 124 is

37Permutations And Combinations

The number of positive divisors of 252 is