Fundamental Principle of Counting

JEE Main Mathematics · Permutations and Combinations · 17 questions, latest first

• The number of 3 × 2 matrices A, which can be formed using the elements of the set {-2,-1,0,1,2} such that the sum of all the…202624 January, Shift 1 · Q21
• The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0, 1, 2, 5, 9, if…202624 January, Shift 1 · Q22
• Let S={(m, n): m, n ∈{1,2,3, ….., 50}}. If the number of elements (m, n) in S such that 6^m+9^n is a multiple of 5 is p and the…202621 January, Shift 1 · Q23
• The number of singular matrices of order 2, whose elements are from the set {2,3,6,9}, is ____.20257 April, Shift 1 · Q22
• If the number of seven-digit numbers, such that the sum of their digits is even, is m · n · 10^n; m, n ∈{1,2,3, …, 9}, then m+n…20253 April, Shift 1 · Q21
• Number of functions f:{1,2, …, 100} →{0,1}, that assign 1 to exactly one of the positive integers less than or equal to 98, is…202524 January, Shift 2 · Q21
• Let A={1,2,3, …., 7} and let P(A) denote the power set of A. If the number of functions f: A → P(A) such that a ∈ f(a), ∀ a ∈ A…202430 January, Shift 1 · Q21
• The total number of three-digit numbers, divisible by 3, which can be formed using the digits 1, 3, 5, 8, if repetition of digits…202315 April, Shift 1 · Q6
• Total numbers of 3 -digit numbers that are divisible by 6 and can be formed by using the digits 1,2,3,4,5 with repetition, is ____202313 April, Shift 2 · Q22
• The number of symmetric matrices of order 3, with all the entries from the set \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}, is202313 April, Shift 1 · Q5
• Let A={1,2,3,4,5} and B={1,2,3,4,5,6}. Then the number of functions f: A → B satisfying f(1)+f(2)=f(4)-1 is equal to ____.202311 April, Shift 2 · Q22
• The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6, is ____.20231 February, Shift 2 · Q81
• The number of ways of selecting two numbers a and b, a ∈{2,4,6, ….., 100} and b ∈{1,3,5, ….., 99} such that 2 is the remainder…202330 January, Shift 2 · Q65
• Let A={1,2,3,5,8,9}. Then the number of possible functions f: A → A such that f(m · n)=f(m) · f(n) for every m, n ∈ A with m · n…202330 January, Shift 2 · Q81
• Let S={1,2,3,4,5,6}. Then the number of one-one functions f: S → P(S), where P(S) denote the power set of S, such that f(n) ⊂ f(…202330 January, Shift 1 · Q83
• Number of 4 -digit numbers (the repeation of digits is allowed) which are made using the digits 1,2, 3 and 5, and are divisible…202330 January, Shift 1 · Q87
• 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…202325 January, Shift 1 · Q87