Permutations & Combinations PYQs Set 1 (PDF)

Set 1 of 11 · Questions 1-30 of 315

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions JEE Main Mathematics · Permutations & Combinations · Set 1 (Q1-30)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
1. $The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is$ (1) $48$ (2) $56$ (3) $24$ (4) $16$ 2. $If C_{j} stands for^{n} C_{j}, then \frac{C _{1}}{C _{0}} + \frac{2 \times C _{2}}{C _{1}} + \frac{3 \times C _{3}}{C _{2}} + \dots + \frac{n \times C _{n}}{C _{n - 1}} =$ (1) $\sum_{k = 1}^{n} k^{2}$ (2) $\sum_{k = 1}^{n} \frac{k}{2}$ (3) $\sum_{k = 1}^{n} 2 k$ (4) $\sum_{k = 1}^{n} k$ 3. $Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to$ (1) $25$ (2) $34$ (3) $42$ (4) $41$ 4. $A question paper has 3 parts and each part contains 4 questions. The number of different ways in which a candidate can answer 8 questions choosing at least two from each part is$ (1) $396$ (2) $204$ (3) $224$ (4) $132$ 5. $In an apartment there are 30 kids. If each kid plays table tennis with other kid, then the total number of matches played by them$ (1) $^{30} C_{2}$ (2) $^{30} P_{2}$ (3) $^{30} C_{2} - 1$ (4) $^{30} P_{2} - 1$ 6. $A student is allowed to choose at most n books from a collection of 2 n + 1 books. If the total number. of ways in which he can select atleast one book is 255, then the value of n is$ (1) $4$ (2) $5$ (3) $6$ (4) $7$ 7. $Number of four digit numbers that can be formed using all the digits except zero such that every number has exactly 2 distinct digits in it is$ (1) $189$ (2) $216$ (3) $288$ (4) $504$ 8. $If number of 5 - digit numbers which can be formed without repeating any digit while tenth place of all of the numbers must be 2 is 336 k find the value of k$ (1) $8$ (2) $7$ (3) $6$ (4) $5$ 9. $The total number of three digit and five digit integers which can be formed by using the digits 0, 1, 2, 3, 4, 5 but using each digit not more than once in each number is$ (1) $100$ (2) $600$ (3) $700$ (4) $800$ 10. $There are 10 intermediate stations on a railway line between two particular stations. The number of ways that a train can be made to stop at 3 of these intermediate stations so that no two of these halting stations are consecutive is$ (1) $56$ (2) $20$ (3) $126$ (4) $120$ 11. $A village has 10 players. A team of 6 players is to be formed. 5 members are chosen out of these 10 players and then the captain is chosen from the remaining players. Then total number of ways of choosing such teams is$ (1) $1260$ (2) $210$ (3) $(^{10} C_{6}) 5!$ (4) $(^{10} C_{5}) 6$ 12. $The number of ways to distribute 30 identical candies among four children C,, C_{2}, C_{3} and C_{4} so that C_{2} receives at least 4 and at most 7 candies, C_{3} receives at least 2 and at most 6 candies, is equal to$ (1) $205$ (2) $615$ (3) $510$ (4) $430$ 13. $In how many ways can the letters of the word MAXIMA be arranged such that all vowels are together and all constants are together?$ (1) $18$ (2) $30$ (3) $36$ (4) $42$ 14. $The sum of all - natural numbers ' n^{’} such that 100 < n < 200 and H . C . F . (91, n) > 1 is:$ (1) $3203$ (2) $3303$ (3) $3221$ (4) $3121$ 15. $If a set A has 5 elements, then the number of ways of selecting two subsets P and Q from A such that P and Q are mutually disjoint, is$ (1) $64$ (2) $128$ (3) $243$ (4) $729$ 16. $The number of natural numbers less than 7, 000 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digitsallowed) is equal to:$ (1) $374$ (2) $372$ (3) $375$ (4) $250$ 17. $Number of numbers of the form xxyy which are perfect squares of a natural number.$ 18. $Let n_{1} < n_{2} < n_{3} < n_{4} < n_{5} be positive integers such that n_{1} + n_{2} + n_{3} + n_{4} + n_{5} = 20. Then the number of such distinct arrangements (n_{1}, n_{2}, n_{3}, n_{4}, n_{5}) is$ 19. $The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is$ 20. $The number of 4 -letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is____.$ 21. $Let S = 1, 2, 3, 5, 7, 10, 11 . the number of non empty subsets of S that have the sum of all elements a multiple of 3, is _______$ 22. $The sum of all the elements of the set { {1, 2,..., 100} : HCF (, 24) = 1} is_____.$ 23. $Number of times is the digit 5 written when listing all numbers from 1 to 1 0^{5} ?$ 24. $Let n be a non-negative integer. Then the number of divisors of the form “4n+1” of the number (10)^{10} . (11)^{11} . (13)^{13} is equal to$ 25. $Find the number of 4-digit numbers (in base 10) having non-zero digits and which are divisible by 4 but not by 8.$ 26. $The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1,2,3,4,5,7and 9 is_____.$ 27. $A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is$ 28. $Suppose Anil’s mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 orange, at least one red apple and at least one white apple must be given, then the number of ways, Anil’s mother can offer 5 fruits to Anil is$ 29. $The number of permutations, of the digits 1, 2, 3, ..., 7 without repetition, which neither contain the string 153 nor the string 2467, is_______.$ 30. $A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is________.$