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Estudos Gerais • 12/13/2024

17. Number of 4-digit numbers that are less than or equal to...

  1. Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11, is equal to
  2. The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7 is
  3. The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is
  4. The largest natural number n such that 3^n divides 66! is
  5. Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?
  6. The sum of all those terms, of the arithmetic progression 3,8,13,...,373 which are not divisible by 3, is equal to
  7. Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple in a match, is 840, then the total numbers of persons, who participated in the tournament, is
  8. The number of permutations of the digits 1,2,3,...,7 without repetition, which neither contain the string 153 nor the string 2467, is
  9. The number of elements in the set {n ∈ N: 10 ≤ n ≤ 100 and 3^n is a multiple of 7} is:
  10. The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that even digits occupy only even places, is
  11. A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. He can choose at most two language courses, then the number of ways he can choose five courses is
  12. The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is -
  13. The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is
  14. The sum of all the four-digit numbers that can be formed using all the digits 2,1,2,3 is equal to
  15. Let A = {100,101,102,...,700}. Find number of numbers in set A which are neither divisible by 3 nor by 4.
  16. The number of ways to distribute the 21 identical apples to three children so that each child gets at least 2 apples.
  17. Let x and y be distinct integers where 1 ≤ x ≤ 25 and 1 ≤ y ≤ 25. Then, the number of ways of choosing x and y, such that x + y is divisible by 5 is
  18. Let S = {1,2,3,5,7,10,11}. The number of nonempty subsets of S that have the sum of all elements a multiple of 3, is.

Question image: 17. Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11, is equal to 18. The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7 is 19. The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is 20. The largest natural number n such that 3^n divides 66! is 21. Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits such that three consecutive digits are in A.P. at least once. How many such numbers can be formed? 22. The sum of all those terms, of the arithmetic progression 3,8,13,...,373 which are not divisible by 3, is equal to 23. Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple in a match, is 840, then the total numbers of persons, who participated in the tournament, is 24. The number of permutations of the digits 1,2,3,...,7 without repetition, which neither contain the string 153 nor the string 2467, is 25. The number of elements in the set {n ∈ N: 10 ≤ n ≤ 100 and 3^n is a multiple of 7} is: 26. The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that even digits occupy only even places, is 27. A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. He can choose at most two language courses, then the number of ways he can choose five courses is 28. The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is - 29. The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is 30. The sum of all the four-digit numbers that can be formed using all the digits 2,1,2,3 is equal to 31. Let A = {100,101,102,...,700}. Find number of numbers in set A which are neither divisible by 3 nor by 4. 32. The number of ways to distribute the 21 identical apples to three children so that each child gets at least 2 apples. 33. Let x and y be distinct integers where 1 ≤ x ≤ 25 and 1 ≤ y ≤ 25. Then, the number of ways of choosing x and y, such that x + y is divisible by 5 is 34. Let S = {1,2,3,5,7,10,11}. The number of nonempty subsets of S that have the sum of all elements a multiple of 3, is.
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