Doubts
Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents
Sign in to save progress →
Doubts
Sign in

Permutations and Combinations question

2025 · Shift 1 · Q26
Guest · try one question or challengeGuest · try one question or challenge
  1. PYQ Library
  2. /JEE Advanced
  3. /Mathematics
  4. /Permutations and Combinations
  5. /2025 · Shift 1 · Q26

Permutations and Combinations question

2025 · Shift 1 · Q26

JEE AdvancedMathematicsPermutations and CombinationsNumerical+4 / −1
Let SSS be the set of all seven-digit numbers that can be formed using the digits 0,10, 10,1 and 222. For example, 221022222102222210222 is in SSS, but 021022202102220210222 is NOT in SSS. Then the number of elements xxx in SSS such that at least one of the digits 000 and 111 appears exactly twice in xxx, is equal to ‾\underline{\hspace{2cm}}​.
Numerical answer
PreviousNext

More from Permutations and Combinations

  • 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 · Numerical
  • 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 · Numerical
  • 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 · Numerical
  • 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 · Numerical
  • 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 · MCQ
  • 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 · Multiple correct
  • 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 · Numerical
  • 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 · Numerical