Permutations & Combinations: JEE Main Mathematics Previous Year Questions

315 previous year questions from Permutations & Combinations. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. 1.Number of numbers of the form xxyy which are perfect squares of a natural number.
2. 2.Let $n_1$ < $n_2$ < $n_3$ < $n_4$ < $n_5$ be positive integers such that $n_1$ + $n_2$ + $n_3$ + $n_4$ + $n_5$ = 20. Then the number of such distinct…
3. 3.The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is
4. 4.The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is
5. 5.If $C_j$ stands for ${}^n{C}_j$, then…
6. 6.The number of 4 -letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is $\text{\_}\text{\_}\text{\_}\text{\_}$ .
7. 7.Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to
8. 8.A question paper has 3 parts and each part contains 4 questions. The number of different ways in which a candidate can answer 8 questions choosing at least two from each…
9. 9.In an apartment there are 30 kids. If each kid plays table tennis with other kid, then the total number of matches played by them
10. 10.A student is allowed to choose at most $n$ books from a collection of $2n+1$ books. If the total number. of ways in which he can select atleast one book is 255, then th…
11. 11.Let $S=\text{1,2,3,5,7,10,11}$. the number of non empty subsets of S that have the sum of all elements a multiple of 3…
12. 12.Number of four digit numbers that can be formed using all the digits except zero such that every number has exactly 2 distinct digits in it is
13. 13.The sum of all the elements of the set {$\alpha \text{∈}$ {1, 2,..., 100} : HCF ($\alpha$, 24) = 1} is_____.
14. 14.If number of 5 - digit numbers which can be formed without repeating any digit while tenth place of all of the numbers must be 2 is 336 $k$ find the value of $k$
15. 15.Number of times is the digit 5 written when listing all numbers from 1 to $10^5$?
16. 16.Let n be a non-negative integer. Then the number of divisors of the form “4n+1” of the number $(10{)}^{10}$.$(11{)}^{11}$.$(13{)}^{13}$ is equal to
17. 17.The total number of three digit and five digit integers which can be formed by using the digits $0\text{,}1\text{,}2\text{,}3\text{,}4\text{,}5$ but using each digit not…
18. 18.There are 10 intermediate stations on a railway line between two particular stations. The number of ways that a train can be made to stop at 3 of these intermediate stati…
19. 19.A village has 10 players. A team of 6 players is to be formed. 5 members are chosen out of these 10 players and then the captain is chosen from the remaining players. The…
20. 20.The number of ways to distribute 30 identical candies among four children C,, $C_2$, $C_3$ and $C_4$ so that $C_2$ receives at least 4 and at most 7 candies,…
21. 21.Find the number of 4-digit numbers (in base 10) having non-zero digits and which are divisible by 4 but not by 8.
22. 22.The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1,2,3,4,5,7and 9 is_____.
23. 23.In how many ways can the letters of the word MAXIMA be arranged such that all vowels are together and all constants are together?
24. 24.A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number…
25. 25.Suppose Anil’s mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 orange, at…