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Permutations and Combinations

27 questions · Mathematics · JEE Advanced
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Permutations and Combinations

27 questions · Mathematics · JEE Advanced

  1. Let the set of all relations R on the set {a,b,c,d,e,f}, such that R is reflexive and symmetric, and R contains exactly 10 elements, be denoted by S. Then the number of elements in S is ​…2025 · Shift 1 · Q24 · Numerical
  2. Let S be the set of all seven-digit numbers that can be formed using the digits 0,1 and 2. For example, 2210222 is in S, but 0210222 is NOT in S. Then the number of elements x in S such that at least one of the digits…2025 · Shift 1 · Q26 · Numerical
  3. A group of 9 students, s1​,s2​,…,s9​, is to be divided to form three teams X,Y, and Z of sizes 2,3 , and 4 , respectively. Suppose that s1​ cannot be selected for the team X, and s2​ cannot be selected for the team…2024 · Shift 1 · Q28 · Numerical
  4. Let S={1,2,3,4,5,6} and X be the set of all relations R from S to S that satisfy both the following properties: i. R has exactly 6 elements. ii. For each (a,b)∈R, we have ∣a−b∣≥2. Let Y={R∈X: The range of…2024 · Shift 2 · Q31 · Numerical
  5. Let S={1,2,3,4,5,6} and X be the set of all relations R from S to S that satisfy both the following properties: i. R has exactly 6 elements. ii. For each (a,b)∈R, we have ∣a−b∣≥2. Let Y={R∈X: The range of…2024 · Shift 2 · Q32 · Numerical
  6. The number of 4-digit integers in the closed interval [2022, 4482] formed by using the digits 0,2,3,4,6,7 is ​.2022 · Shift 1 · Q25 · Numerical
  7. Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue…2022 · Shift 2 · Q33 · MCQ
  8. Let S1​={(i,j,k):i,j,k∈{1,2,....,10}}, S2​={(i,j):1≤i<j+2≤10,i,j∈{1,2,...,10}}, S3​={(i,j,k,l):1≤i<j<k<l,i,j,k,l∈{1,2,...,10}}…2021 · Shift 2 · Q20 · Multiple correct
  9. An engineer is required to visit a factory for exactly four days during the first 15 days of every month and it is mandatory that no two visits take place on consecutive days. Then the number of all possible ways in which such visits to…2020 · Shift 2 · Q31 · Numerical
  10. In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this…2020 · Shift 2 · Q32 · Numerical
  11. Let |X| denote the number of elements in a set X. Let S = {1, 2, 3, 4, 5, 6} be a sample space, where each element is equally likely to occur. If A and B are independent events associated with S, then the number of ordered pairs (A, B)…2019 · Shift 2 · Q28 · Numerical
  12. Five persons A, B, C, D and E are seated in a circular arrangement. 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 that the persons seated in adjacent…2019 · Shift 2 · Q30 · Numerical
  13. The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is .................2018 · Shift 1 · Q26 · Numerical
  14. In a high school, a committee has to be formed from a group of 6 boys M1, M2, M3, M4, M5, M6 and 5 girls G1, G2, G3, G4, G5. (i) Let α1 be the total number of ways in which the committee can be formed such that the committee has 5… Includes table2018 · Shift 2 · Q34 · MCQ
  15. Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let x be the number of such words where no letter is repeated; and let y be the number of such words where exactly one letter is repeated twice and no other…2017 · Shift 1 · Q30 · Numerical
  16. A debate club consists of 6 girls and 4 boys. A team of 4 members is to be select from this club including the selection of a captain (from among these 4 members ) for the team. If the team has to include at most one boy, then the number…2016 · Shift 1 · Q30 · MCQ
  17. Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that…2015 · Shift 1 · Q21 · Numerical
  18. Let n1​<n2​<n3​<n4​<n5​ be positive integers such that n1​+n2​+n3​+n4​+n5​= 20. Then the number of such destinct arrangements (n1​,n2​,n3​,n4​,n5​)…2014 · Shift 1 · Q21 · Numerical
  19. Let n≥2 be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line…2014 · Shift 1 · Q23 · Numerical
  20. Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered…2014 · Shift 2 · Q30 · MCQ
  21. Consider the set of eight vectors V={ai^+bj^​+ck^:a,b,c∈{−1,1}}. Three non-coplanar vectors can be chosen from v in 2p ways. Then p is2013 · Shift 1 · Q26 · Numerical
  22. The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is2012 · Shift 1 · Q25 · MCQ
  23. Let an​ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0.Let bn​= the number of such n-digit integers ending with digit 1 and cn​=the…2012 · Shift 2 · Q21 · MCQ
  24. Let an​ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0.Let bn​= the number of such n-digit integers ending with digit 1 and cn​ =the…2012 · Shift 2 · Q35 · MCQ
  25. The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is2009 · Shift 1 · Q34 · MCQ
  26. Let (x,y,z) be points with integer coordinates satisfying the system of homogeneous equation: 3x−y−z=0−3x+z=0−3x+2y+z=0​ Then the number of such…2009 · Shift 2 · Q31 · Numerical
  27. Consider all possible permutations of the letters of the word ENDEANOEL. Match the Statements/Expressions in Column I with the Statements/Expressions in Column II. Includes table2008 · Shift 2 · Q39 · MCQ